Brazilian Ethanol: A Gift or Threat to the Environment? (Preliminary and Incomplete -

Please Do Not Cite) ∗

Sriniketh Nagavarapu

Department of Economics and Center for Environmental Studies

Brown University

ssn@brown.edu

August 28, 2009

Abstract

The Brazilian government has been pushing for changes to the United States’ extensive barri-ers to ethanol imports. However, removing these barriers would present a crucial environmentaltradeoff. On the one hand, replacing US consumers’ use of petroleum and corn-based ethanolwith Brazilian sugarcane-based ethanol could have a large positive impact on carbon emissions.On the other hand, this additional ethanol would require an expansion in sugarcane produc-tion that could lead to greater deforestation and other environmentally harmful land clearingin Brazil. This paper addresses this tradeoff by answering the question: Would freely importingBrazilian ethanol into the US lead to enough land clearing to offset the environmental benefitsof greater ethanol use? To answer this question, I develop and estimate an empirical generalequilibrium model of Brazil’s regional agricultural markets. I estimate the model using richhousehold survey data, region-level data on production and land use, and data on the prices ofkey goods. I then use the estimates to simulate the effects of a change in US import barriers,where I examine the sensitivity of the results to alternative assumptions about the level of in-ternational ethanol prices after the policy change. Reassuringly, I predict that if the US couldfreely absorb Brazilian ethanol at a price 12% above the baseline, Brazil would supply 12.4billion gallons of ethanol to the US with a decline of only 37 million acres of non-agriculturalland. However, if the price rose 15%, Brazil would supply approximately 21 billion gallons tothe US, and the additional 8.7 billion gallons of exports would require a large additional declineof 86 million acres, with a large share coming in the regions containing the Amazon Rainforest.Whether or not the US importing Brazilian ethanol is ultimately good or bad for the environ-ment will turn on the exact nature of US and international demand in the future, as well ason the Brazilian government’s ability to direct the above acreage declines away from the mostenvironmentally important land.

∗I owe a large debt to Thomas MaCurdy, John Pencavel, and Jayanta Bhattacharya for their advice, support, and

encouragement. I am also grateful to Luigi Pistaferri and Aprajit Mahajan for their guidance. I benefited greatly

from conversations with Orazio Attanasio, Nick Bloom, Marcus Edvall, Andrew Foster, Zephyr Frank, Giacomo De

Giorgi, Gopi Shah Goda, Caroline Hoxby, Lovell Jarvis, Seema Jayachandran, Colleen Manchester, Naercio Menezes-

Filho, Pedro Miranda, Jonathan Meer, Marc Muendler, Kevin Mumford, Gerald Nelson, Frank Wolak, attendees of

Stanford’s Applications Seminar, and members of Stanford’s Labor Reading Group. Suggestions received in seminars

at Brown University, RAND, the USDA, Mathetmatica Policy Research, and the AEA annual meetings are greatly

appreciated. For their immense help with acquiring data used here, I thank Steven Helfand, Frank McIntyre, Marcia

Moraes, and the staff at Fundacao Getulio Vargas. I appreciate the financial support provided by SIEPR for data

acquisition and by the Taube/SIEPR dissertation fellowship. Remaining errors are, of course, my own.

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1 Introduction

Amid growing economic, security, and environmental concerns related to oil usage, the UnitedStates has shown interest in greater use of ethanol. The 2007 energy bill passed by the UnitedStates Congress requires that the total amount of transportation fuels used in the US contain atleast a minimum level of renewable fuels in each of the next 14 years. For instance, renewables mustconstitute 11.1 billion gallons of total transportation fuel in 2009, 15.2 billion gallons by 2012, and36 billion gallons by 2022.1 While bio-diesel may play a role in the coming years, this renewablefuel mandate will be fulfilled primarily through the use of ethanol.

No country is in a better position to take advantage of this surging interest in ethanol thanBrazil. Brazil’s sugarcane-based ethanol has three important advantages over US corn-basedethanol. First, beginning in the 1970s, Brazil spent a substantial amount of government resourcesto develop infrastructure for ethanol production and distribution. Second, Brazil’s natural en-dowments are conducive to growing sugarcane at low cost. Third, sugarcane can be convertedinto ethanol with a smaller energy input than that needed for corn. Brazil is the most cost- andenergy-efficient producer of ethanol in the world, and the country has vast potential for expandingsugarcane cultivation further.

Brazil would be a natural source of ethanol for the United States, except for one fact: The USprotects its own, less efficient ethanol producers with a 2.5% ad valorem tariff and a 54 cent pergallon duty on imports. These recently extended measures have come under increasing criticismby the Brazilian government. In fact, the government has aggressively pitched freer markets forits ethanol as a potential “win-win.” Increased opportunities for ethanol export could help spurfurther economic development in Brazil. Meanwhile, the rest of the world would gain a significantenvironmental benefit as fossil fuels are displaced with a cost-competitive renewable alternative.2

Nevertheless, more open markets for Brazilian ethanol generate uncertain implications for theenvironment in Brazil and elsewhere. There is a crucial tradeoff. On the one hand, Brazil’ssugarcane-based ethanol is a renewable, lower-carbon alternative to petroleum and US corn-basedethanol. Replacing US consumers’ use of petroleum and corn-based ethanol with Brazilian ethanolcould therefore have a large positive impact on carbon emissions. On the other hand, this additionalsugarcane-based ethanol has to be produced somewhere in Brazil. In particular, the expansion insugarcane production required to produce more ethanol could lead to greater deforestation andother environmentally harmful land clearing.

This paper addresses this tradeoff by answering the research question: Would freely importingBrazilian ethanol into the US lead to enough land clearing to offset the environmental benefits ofgreater ethanol use?

To answer this question, it is necessary to determine how responsive Brazilian ethanol pro-duction is to the opening of the market, and how much land will be brought into agriculture assugarcane cultivation increases to support the greater ethanol production. Crucially, it is not suffi-

1The “Energy Independence and Security Act of 2007” became Public Law 110-140 on December 19, 2007. The

relevant portion of the law is Title II, Subtitle A, Section 202.2For instance, see “Our Biofuels Partnership”, by President Luiz Inacio Lula da Silva, in the March 30, 2007

edition of the Washington Post (page A17).

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cient to simply examine ethanol and sugarcane production in isolation. As the US ethanol marketopens, sugarcane prices will increase in each region of Brazil. Sugarcane supply in each region willrespond to this change in prices. But precisely how much it will respond depends on a large numberof factors. For instance, the appropriateness for sugarcane production of land not currently usedfor sugarcane will help determine the response on the extensive margin. On the other hand, thesubstitutability between labor and land will determine how feasible it is to cultivate existing landmore intensively. This substitutability, along with the elasticity of labor supply to the sugarcanesectors, will have consequences for wages and the amount of labor used in sugarcane and othersectors, which will in turn impact sugarcane supply. Preferences for other goods and the ability toimport these goods to satisfy domestic demand will also play a role. In summary, answering thequestion above involves the consideration of the intimate but complicated links between land usedecisions, labor markets, and product markets.

In view of this, in this paper I develop and estimate a general equilibrium model of regionalagricultural markets in Brazil. The model consists of the intermediate good of sugarcane and fivefinal goods – ethanol, sugar, a non-sugarcane agricultural good, a non-agricultural good, and capi-tal. Producers of these goods compete over the inputs of land, labor, capital, and sugarcane, withtheir input choices dependent on input prices and the relevant production functions. Heterogeneityenters the picture in two important ways. First, in each region, parcels of land have heterogeneousquality in the three possible uses of sugarcane, other agriculture, and non-agriculture. I derive theaggregate supply of sugarcane and other agriculture in each region by aggregating over the produc-tion of these heterogeneous parcels of land, which are individually being allocated to their highestprofit use. Second, consumers have heterogeneous non-labor income and heterogeneous preferencesfor working in the various region/sector combinations, where the possible sectors in each regionare sugarcane, other agriculture, and non-agriculture. I derive the aggregate supply of labor hoursto each region/sector – and the aggregate demand for each product – by aggregating over theseheterogeneous individuals. The resulting upward-sloping supply curves to sugarcane for land andlabor are the most fundamental parts of the model; they capture the linkages between sugarcaneproduction and the rest of the economy.

Using data from the 1995-2005 period, I estimate all parameters of the model using maximumlikelihood methods. For the structural estimation, I bring together rich cross-sectional survey data,state-level information on production and land use, national income accounts data, and informationon the prices of sugarcane and other goods. As described below, the use of the individual-levelsurvey data aids in securing identification of the labor supply parameters. Despite the simultaneoususe of individual-level and aggregate data, my methodology imposes constraints that ensure thelogical consistency and coherence of the overall empirical model.

I then use these parameters to perform simulation exercises in which I assess the consequencesof changes in US policies regarding ethanol imports. I represent the change in US policy in a verysimple way, as making international demand for Brazilian ethanol perfectly elastic at a price higherthan the initial equilibrium price.3 I include results from simulations of three alternative policy

3The exact nature of the simulations will be discussed further below, but the form of the model requires the

simulations to make assumptions about the movement of world sugar prices as well.

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regimes, which set world ethanol prices at 10%, 12%, and 15% above the 2005 equilibrium price.I choose these numbers to keep the price of ethanol competitive with gasoline, while providing arange of possible consequences.

When simulating the effect of opening up the international market for ethanol, I find that in allthree regimes, a significant amount of ethanol could be produced for export. The increase in exportsof ethanol is supported by a shift of sugarcane from sugar to ethanol production, as well as a growthin the total amount of land used for sugarcane in each region. Depending on the regime considered,exports are predicted to increase to 5.5, 12.4, or 21.2 billion gallons (in the 10%,12%, and 15%regimes, respectively). To provide an idea of how large these numbers are, consider that totalethanol production in the US in 2007 was 6.5 billion gallons. With 13 billion gallons of ethanol,the US could have used ten percent ethanol blends in all of its gasoline consumption in 2007.4

The 21.2 billion gallons from the 15% regime would satisfy almost the entire 2016 requirement forrenewable fuels in the 2007 energy bill. Consequently, Brazil could provide enough ethanol to havea significant impact on the use of renewables in the US.

However, we are equally interested in the impact of this increased supply on deforestation andother harmful land clearing. Here, the results are mixed. In interpreting them, it is important tokeep in mind that all the regions in the model contain environmentally sensitive land of one sort oranother. But from a carbon capture point of view, the Mato Grosso region is the most significant,since it is the region in the model that contains the largest amount of the Amazon Rainforest.5

The increase in total agricultural land in the 10% and 12% regimes is moderate enough to thinkthat significant environmental damage could be averted. For instance, moving from the baselineto the 12% regime increases exports by about 12 billion gallons, and leads to a predicted declinein non-agricultural land of only 37 million acres. Moving from there to the 15% regime inducesan additional 8.7 billion gallons of exports, but requires a further predicted decline of a large 86million acres. A large share of this decline comes in the Mato Grosso region.

The regions are very broadly defined in the model, so it could be the case that even in thislatter situation, the decreases in non-agricultural land do not come from deforestation, but ratherfrom relatively unimportant areas. To understand the extent to which the carbon sink of forestedland is lost would require more detailed, disaggregated analysis in the future. Nevertheless, fromthe results presented here, we can still make two conclusions: First, Brazil can supply up to 13billion gallons of ethanol to the US without a large risk of significant deforestation or environmentaldamage; and second, supplying a much larger magnitude – on the order of the complete renewablefuel mandates for 2016 and beyond – could pose extreme risks in particular parts of Brazil.

This paper complements recent work by Elobeid and Tokgoz (2008) and Nelson and Robertson(2008).6 The former paper addresses the response of ethanol production in the US and Brazil topotential changes in U.S. trade policies by using a detailed model of ethanol demand and supplyin the US, Brazil, and the rest of the world. Their model is then paired with an existing partial

4Most vehicles in the US cannot run entirely on ethanol. For the source of these numbers, see the Department of

Energy ar-ticle at http : //apps1.eere.energy.gov/news/news detail.cfm/news id = 11633.5The exact regional classifications are described more completely in Chapter 2.6For other studies of the sugar and sugarcane industries, see Barros, de V. Cavalcanti, Dias, and Magalhaes (2005)

and Moraes (2007), which focus on consequences for worker wages.

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equilibrium model of agriculture in world markets. Nelson and Robertson (2008) examine theenvironmental impact in Brazil of greater incentives for bio-fuel production. These authors’ goalsare broader than mine, in that they aim to simulate the effect of increasing maize and sugarcaneprices on the expansion of total agricultural land, and then quantify the potential effects of thisexpansion on bio-diversity and carbon sequestration. They use detailed data on land-use for arecent year, as well as linked agro-climatic and socio-economic data, to estimate a non-linear modelof the probability that parcels of land are used for particular purposes.7 Using this model, theypredict massive expansions in total agricultural land.

I have a different focus and approach from these useful studies. In contrast to Elobeid andTokgoz (2008), I instead focus on the details of agricultural production and land changes withinBrazil. In doing so, as opposed to Nelson and Robertson (2008), I explicitly model linkages betweenland use decisions and labor markets. More generally, I use an estimable general equilibrium model.8

This necessitates major simplifications in the modeling of trade policy and depiction of land qualityrelative to the previous studies. In exchange, the empirical general equilibrium model allows for abetter understanding of the role of the labor market and results in parameters that emerge fromthe use of multiple years of data, rather than calibration.

In this way, this paper is in the spirit of Foster and Rosenzweig (2003), who use a generalequilibrium framework to examine empirically the relationship between agricultural productionand deforestation in India.9 They find evidence consistent with increased income leading to greaterdemand for wood, and hence more land devoted to forests. Here, I allow for migration (relativelyunimportant in the Indian context) and estimate the general equilibrium model directly. I donot distinguish between the demand for forest products versus the demand for non-sugarcaneagricultural goods, or the use of land for forest versus non-sugarcane agriculture. In Brazil, itis most important to know how much land is left out of production entirely. The most recentAgricultural Census suggests that the large majority of privately owned natural forest land inBrazil is used for uses other than sustainable wood products, including the grazing of animalsand growing of particular crops. Meanwhile, planted forests may have a very different biologicalcomposition than virgin land, and therefore be less acceptable from an environmental point of view.To the extent that privately managed production on forest land is environmentally sustainable andnon-invasive, my results over-state the threat to environmentally sensitive areas.

The remainder of the paper proceeds as follows. Section 2 provides an overview of sugarcane andethanol production in Brazil. It begins by briefly describing the sugarcane and ethanol industries,and then illustrates differences across regions in production levels, land usage, and wages. Section3 develops the general equilibrium model. The sub-sections describe the various components of

7For details on methods, see Nelson and Geoghegan (2002). For studies using broadly similar methods, see Pfaff

(1999) and Pfaff and et al. (2007).8There are also studies of agricultural trade liberalization in Brazil that have used computational general equilib-

rium models. See de Souza Ferreira Filho and Horridge (2005) and Bussolo, Lay, and van der Mensbrugghe (2004).

For an interesting blend of the CGE approach with use of household survey data in a different country, see Ravallion

(2004).9Some empirical work on deforestation looks at another sort of detail, namely the management of forests by

communities in developing countries (see, for example, Edmonds (2002), Alix-Garcia (2008), and Alix-Garcia (2007)).

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the model and how these components come together. A final sub-section discusses limitations ofthe model. Section 4 describes the the sources of data, as well as how the raw data is used toconstruct empirical analogues to quantities in the model. Section 5 takes the model to the data. Itbegins by testing a few of the implications of the model and describing the structural estimationapproach in detail. It goes on to cover the estimation results. Section 6 describes the policysimulations. The first section details the assumptions and methods behind the simulations, andthe second section shows results from the simulations. These results answer the research questionsposed above. Section 7 concludes.

2 The Sugarcane and Ethanol Industries in Brazil

This section describes aspects of the sugarcane and ethanol industries that are essential to un-derstanding the debate behind the research question and formulating the model. Specifically, inthe first section, I briefly examine regional differences in production to illustrate the arguments ofthose in favor of greater production of Brazilian ethanol, as well as the arguments of those who areconcerned about this prospect. In the second section, I discuss key features of the industries thatthe model should be able to capture. I refer to tables and figures that rely on a wide variety ofdata sources, and I leave the description of these data sources to Chapter 4.

2.1 Regional Patterns of Production and the Ethanol Debate

Figure 3 is a map of Brazil, where I have divided states into eight regions. This is the regionalclassification that I will use in the remainder of the paper. I choose to group states together intoregions based primarily on geographical proximity, but also consider anecdotal evidence about theintegration of labor markets. The states composing these regions are: Parana, Santa Catarina, andRio Grande do Sul (region 1); Sao Paulo (region 2); Minas Gerais, Rio de Janeiro, and Espirito Santo(region 3); Bahia and Sergipe (region 4); Mato Grosso, Mato Grosso do Sul, Goias, Tocantins, andthe Federal District (region 5); Pernambuco, Alagoas, Paraiba, and Rio Grande do Norte (region6); and Maranhao, Piaui, and Ceara (region 7).10 In the analysis, I do not include the remainingstates of Brazil, which all come from the sparsely populated North Census region of Brazil. This isunfortunate, given that the majority of the Amazon Rainforest is located in this region. However,household survey data do not contain representative information on the rural parts of these statesfor years before 2004.11

10In determining the number of regions, I strike a balance between, on the one hand, using so few regions that

important heterogeneity within regions is neglected and, on the other hand, using so many regions that the PNAD

does not contain a reasonably large number of sugarcane workers in some regions. I sometimes refer to region 5 as

the “Center-West”, even though Tocantins is technically a part of the North census region, and not the Center-West.

I do so because Tocantins was once connected to Goias.11The North Census region is a small, though non-trivial, part of the economy. In a recent year, about 5% of GDP

was produced in the North. Using the PNAD data described below, I find that in 2005, approximately 6.3% of the

over-15 population lives in the North, and approximately 6.6% of over-15 workers are located in the North. To assess

the importance of omitting the North for this analysis, it would be more helpful to look at migration rates into the

North over the 1995-2005 period. However, doing this in a complete fashion is again only possible after 2003.

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For later reference, Table 1 displays the states composing each region. The second columnprovides the “shorthand reference” that I use to refer to each region in future tables. The tablealso shows how each of my regions come together to form the government-defined “Census regions”.To avoid confusion, whenever I use the term “region” in the paper, I am referring to my definitionof the seven regions and not the Census definition.

Table 1: Composition of Regions

Region Number Shorthand Reference States Census Region

1 Parana Parana South

Santa Catarina

Rio Grande do Sul

2 Sao Paulo Sao Paulo Southeast

3 Minas Minas Gerais Southeast

Rio de Janeiro

Espirito Santo

4 Bahia Bahia Northeast

Sergipe

5 Mato Grosso Mato Grosso Center-West

Mato Grosso do Sul

Goias

Tocantins

Federal District

6 Pernambuco Pernambuco Northeast

Alagoas

Paraiba

Rio Grande do Norte

7 Maranhao Maranhao Northeast

Piaui

Ceara

Note: The Federal District and Tocantins are not officially part of the Center-West Census region.

2.1.1 Regional Environmental Concerns

Before discussing the regional pattern of sugarcane cultivation in Brazil, it is useful to describe thelocation of the most environmentally sensitive areas. The areas of primary environmental concern

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are the Amazon Rainforest, the Atlantic Rainforest, and the Cerrado.12 While many observersidentify the carbon storage potential of the forested areas as the reason to protect them, it is alsothe case that all three areas contain a substantial amount of bio-diversity.

Figure 4 shows the location of the Amazon and Atlantic Rainforests, outlined in black. TheBrazilian portion of the Amazon covers the North Census region almost entirely. While the LegalAmazon includes the entirety of the states of Mato Grosso, Tocantins, and Maranhao (as depicted inthe figure), the actual rainforest exists in only a portion of these states. Of these states, Mato Grossois the most important, containing a substantial amount of rainforest still. The Atlantic Rainforestexists today only as a thin strip along Brazil’s eastern coast, running from Rio Grande do Norte,down through Sao Paulo, and into the southernmost parts of Brazil. Anecdotally, governmentregulations concerning the Atlantic Rainforest are more effective than those concerning the Amazon.

The original area of the savannas known as the Cerrado lie primarily in Mato Grosso, MatoGrosso do Sul, Tocantins, and Goias, though the area also covers the edges of neighboring states.Large swathes of this area are already under agricultural use (to a large extent, pasture), and thereis concern about further expansion. This is especially true given that such small portions of theCerrado are legally protected by the government.

2.1.2 Regional Pattern of Production

With this context in mind, we can examine the regional pattern of production and better understandthe debate over ethanol production in Brazil. One line of argument points to the current distributionof sugarcane across Brazil as evidence suggesting that a sugarcane expansion would have limitedeffects on the Amazon or the Cerrado. The current distribution reflects differing soil qualities,weather patterns, and other characteristics across regions, which together provide an advantage tocurrent sugarcane-growing regions in any future expansion.

The current pattern of production is illustrated in Figures 1 and 2 and Table 2. The firstfigure divides the hectares of cultivated land in sub-state administrative areas into eight quantiles,and depicts areas in higher quantiles with darker colors. The second figure instead classifies theadministrative areas into eight bins of equal size. Both figures depict data from 2007. While the firstfigure shows the areas with the highest relative amounts of sugarcane production, the second figuremakes clear that the majority of sugarcane in Brazil still comes from Sao Paulo in the Southeast.Table 2 puts numbers on these patterns. The table shows land allocations and production quantitiesin 2005 for all seven regions used in the analysis. Except for the sugarcane-growing states ofPernambuco and Alagoas (in the Pernambuco region), the South-Southeast portion of the countrydominates sugarcane production.13 This distribution of sugarcane production across Brazil suggeststhat any future sugarcane expansion might take place primarily in Sao Paulo, Pernambuco, andpossibly other states in the South-Southeast.

12The Pantanal, in Mato Grosso and Mato Grosso do Sul, is another ecologically rich area, but the threats to these

wetlands do not come from agricultural expansion.13The differences in sugarcane production across regions translate naturally into differences in ethanol and sugar

production. Table 3 displays differences across regions in ethanol and sugar production, as well as the value of that

production.

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The counter-argument to this point is that technological changes and other pressures can quicklylead to changing patterns of cultivation. This view gains support in an examination of the regionaltrends over time. First, to put the regional trends into context, it is helpful to first look at trendsin the prices of sugarcane, sugar, and ethanol. Figures 5 and 6 illustrate the changes over time inthese prices. Movement in the absolute level of prices appears in Figure 5, while the latter figuredepicts the price of each good relative to its level in 1995. The petroleum price is provided for thesake of comparison. In order to think about the economic incentives for allocation of land acrossuses, one should also consider movements in prices of non-sugarcane agriculture. Figure 7 compareschanges in the relative price of sugarcane to the relative price of “other agriculture”, using 1990 asthe base year in both cases.

How did sugarcane land allocations and production levels change in each region over this time?Consider Figures 8 and 9, which show the relative sugarcane land share over time for each region,taking the base year for each region as 1990.14 Since the total land area of each region is fairlyconstant over time, these figures could also be interpreted as depicting movements in the relativesugarcane land acreage over time. The top panel shows the trends for the four regions in theCenter-South, and the bottom panel refers to the regions in the Northeast. In all the regions,sugarcane land grows over the 1981-1990 period, though data for the Mato Grosso region are notavailable in this period. Since 1990, the picture is very different. In the Center-South, all regionsexcept Minas Gerais show growth since 1990, while no regions in the Northeast show growth since1990. The strongest relative growth is in Mato Grosso, where new seed varieties made sugarcaneproduction possible in the Center-West soils. The introduction of new distilleries will also haveplayed an important role.15 In summary, these figures tell a very different story from the cross-sectional distributions for 2005 and 2007, and suggest that growth in sugarcane cultivation maynot be confined to Sao Paulo and Pernambuco.

The movements over time and the cross-sectional distributions of regional sugarcane productionare each consistent with one line of argument in the ethanol debate in Brazil. In reality, the patternsin all the tables and figures above are the result of a complicated set of interactions. The modelin this paper is a vehicle to disentangle the various forces at work and predict the response to anopening of the international market to Brazilian ethanol.

2.2 Important Features of the Sugarcane and Ethanol Industries

The most important features of the industries, and ones that are reflected in the model below, are:

• Demand for sugarcane comes almost completely from ethanol and sugar mills. Sugarcaneis essentially an intermediate good, in that the vast majority is used for ethanol and sugar

14Note that this is the share of land cultivated with sugarcane. It is not the share of land planted with sugarcane.

Examination of the data suggests that there is a very close correspondence between the amount cultivated and the

amount planted in almost all regions and periods, though this could be the result of poor data rather than actual

fact.15The patterns in these figures resemble the patterns in Figures 10 and 11, which illustrate the movement in relative

production over time for each region, again taking 1990 as the base year.

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production.16 In some cases, sugar and ethanol are produced in distinct facilities by distinctproducers; in others, a single producer can produce both goods.17 In total, there are morethan 300 distilleries capable of producing ethanol in Brazil, with new projects appearing ata rapid pace.

• Land is very heterogeneous in effectiveness for sugarcane production. Two different parcelsof land may be the same size, but have very different appropriateness for sugarcane pro-duction. Four factors in particular help to determine the appropriateness of a given parcel:precipitation; soil make-up; gradient; and distance to the nearest mill. The first two are self-explanatory. The gradient of the land is important because flatter land is easier to harvest,either with manual harvesting or – if the capital is available – mechanical harvesting.18

• Labor productivity varies markedly across regions. The household survey data, in combina-tion with the data on sugarcane production, reveal substantial regional differences in laborproductivity. Table 4 shows median hours of work and estimated total number of workersin 2005 in each sector/region combination. By comparing this with the production totals inTable 2, one sees that the Center-South regions have a strikingly higher level of productionper hour of labor. Sao Paulo and Mato Grosso generally show the highest labor productivi-ties. To the extent that wages are competitively determined, differences in sugarcane wagesacross regions will reflect differences in the marginal product of labor. Table 5 shows medianwages in sugarcane, and indicates that the marginal product of labor is also higher in theCenter-South.19

• Sugarcane work generally comes with a wage premium. Table 5 illustrates that sugarcanewages in 2005 were generally higher than wages in other agriculture. This is not confinedto 2005. Figures 12 and 13 depict the evolution of median hourly wages in sugarcane, otheragriculture and non-agriculture in each of the seven regions. For many of the regions, thereis a persistent gap between sugarcane wages and other agricultural wages; in fact, sugarcanewages sometimes approach the level of non-agricultural wages.20

16In a recent year, for example, approximately 10% of harvested sugarcane went to a use other than ethanol and

sugar. Such uses include chemical-based products, plastics, etc.17There is a limit to this flexibility, however. Anecdotally, most of these dual activity mills can move their ethanol

production share between a range such as 45% to 55%.18The majority of production shifted from the Northeast to the Center-South of Brazil by the 1950s, partly because

of the advantage of flatter lands. Productivity differences must have also played a role. Nunberg (1986) provides a

detailed description of this shift over time, as well as an analysis of Brazilian sugarcane policies before the 1980s.19All wages are in 2000 Reais, and the Real/US Dollar exchange rate was approximately 1.84 Reais per US Dollar

at the time.20In Mincer regressions not shown here, I examine the role of crop-specific wage premia for agricultural workers.

I regress the logarithm of wages on controls for year, age, education, literacy, and gender, as well as on dummy

variables for major agricultural activities (e.g., sugarcane, coffee, cocoa, livestock, etc.). I find large wage premia in

sugarcane. This finding is not driven by the fact that the household survey takes place during the sugarcane harvest.

Using data from the 2000 Census, which takes place at a different time period, I find the same feature.

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3 Model

I cover the key aspects of the model here, and then describe the model in more detail in the sectionsbelow. To begin with, the model is static. The economy contains seven regions, detailed in Table 1and depicted visually in Figure 3. These constitute the seven regional markets. Wages differ acrossthese markets, but I assume that all other prices are national. In each region, firms produce oneof five goods: sugarcane, another agricultural good (which I will call “other agriculture”), ethanol,sugar, and a composite consumption good. Sugarcane is an intermediate good that is purchasedonly by ethanol producers or sugar producers. Ethanol, sugar, the other agricultural good, and thecomposite consumption good are all final goods, either consumed by individuals in the Brazilianeconomy or exported.

In the following sections, I discuss each of the model’s components separately in order to clearlydelineate the assumptions behind each one. In the first section, I derive expressions for aggregatelabor supply and product demand from an aggregation over individual utility-maximizing decisionsabout work and consumption. In the second section, I set out expressions for government demandfor the final goods. In the third section, I derive expressions for aggregate supply and labor demandin the sugarcane and other agriculture sectors from an aggregation over individual parcels’ profit-maximizing decisions. In the fourth and fifth sections, I describe ethanol and sugar production, aswell as production of the composite good. The sixth section provides the assumptions about theinternational market before and after a change in US ethanol policy. The seventh section definesequilibrium in this economy, and briefly discusses existence and uniqueness of equilibrium. Thefinal section presents a number of features of the ethanol and sugar industries that the model isnot able to capture; future research could investigate the implications of these omissions.

3.1 Aggregate Labor Supply and Product Demand

In this section, I begin by setting out the individual utility maximization problem that underliesall individual choices in the model. The set-up is mostly conventional. Individuals have preferencesdefined over leisure, the composite consumption good, ethanol, sugar, the other agricultural good,and capital. They consume out of their non-labor income and labor income. Their non-laborincome is the value of their capital endowment, plus profits received from land used in agriculturalproduction, plus net transfers from the government.

Nevertheless, two elements of this set-up deserve further note here. The first point regards thetreatment of capital. Having individuals value holding capital is unconventional. However, in astatic setting it is important to make an assumption of this sort. Otherwise, individuals wouldconsume all their income and the national income accounts would be grossly violated. I treatcapital analogously to labor; each individual has a capital endowment and chooses to rent some ofit out and hold the remainder.21 For convenience, we can think of this as individuals holding goodsfor future consumption. The capital rental rate determines how much of the capital endowmentthe individual rents out and how much the individual holds for future consumption. The second

21This is the approach taken in a recent paper by Bovenberg, Goulder, and Jacobsen (2006), which uses a one-period

general equilibrium model to assess the consequences of particular environmental policies.

11

point involves agricultural profits. The quality of the individual’s land in different uses determinesthe specific use of an individual’s land, and the return that she obtains on this activity. Land usedecisions are described more completely in the third section of this chapter, and are assumed to becompletely separable from work decisions.

The second sub-section makes distributional assumptions about individual heterogeneity, andthen uses these to aggregate over individuals. This yields expressions for aggregate labor supply toeach region and sector, as well as aggregate product demand. These aggregate quantities are itemsI will ultimately use in estimation.

3.1.1 Individual-Level Utility Maximization

In period t, individual i chooses consumption levels, whether or not to work and – if she works – aregion-sector combination s, and hours of work.22 The individual’s choices happen simultaneously,in a static setting with no uncertainty. I use a Stone-Geary utility function because it simplifiesaggregation (see, e.g., Deaton and Muellbauer (1983) and Blundell and MaCurdy (2007)). Theindividual’s maximization problem is given by:

max`it,~yit,jit∑s

1(jit = s)[βln(`it − ψhs) + ln(cit) + κst + ηist]

subject tocit = (yeit)γet(ysit)γst(yait)γat(yoit)γot(ykit)γkt

and

wjit`it + potyoit + p2tyat + petyeit + pstysit + rtykit = wjitT + rtK̄it + πit − τit`it ≤ T

`it ≥ 0

yzit ≥ 0 ∀z

There are several choices here. The region-sector choice is denoted by jit and leisure is `it. Mean-while, yo,ya,ye,ys, and yk are the amount of the composite good, the other agricultural good,ethanol, sugar, and capital that the individual consumes.

These choices are made subject to a constraint involving the following quantities. The priceof good x is given by pxt, with rt denoting the capital price and p2t denoting the price for theother agricultural good. The wage that the individual faces in the chosen market-sector is given bywjit , and this wage is common across all individuals.23 The time endowment is T , and the capital

22The vast majority of workers in Brazil report working in only one occupation. In calculations from the PNAD

data described later, I find that in 2005, the reported share of all workers with hours in a second job is less than 5%,

and less than 9% for self-described employers. These numbers are higher – and have an increasing trend over time

– for agricultural workers. However, even for employers in agriculture, the percentage does not increase past about

15%. In principle, unemployment in region 1 could be treated separately from unemployment in region 2, and so on;

however, I do not make this distinction here.23In practice, I use the median wage in a sector/region as the wage for that sector/region.

12

endowment is K̄it; the time endowment is common across individuals but the capital endowmentis not. Land profits appear as πit and net taxes are τit. For convenience, denote total non-laborincome as Mit, with Mit = rtK̄it + πit − τit.

The remaining facet of the maximization problem is the set of items describing preferences.To begin with, the additive term κst gives preferences for a particular region-sector combinations that are common across individuals. I parameterize κst as κst = κs + ϕst. The ϕst termsare region-sector-year specific shocks to preferences. Heterogeneous preferences for a region-sectorcombination arise in ηist. Unemployment is also a sector, denoted with s = 0, and I treat itanalogously to region-sector combinations for work (subject to the additional assumptions below).

The other important part of preferences consists of the items governing the marginal utilitiesof consumption and leisure. I allow the threshold parameters ψhs to differ by sector, with thevalue for the unemployed state being identical to the sugarcane value. This allows the marginalutility of leisure to vary by sector of work. I further assume that the share parameters β, γot, γet,γst, γat, and γkt are common across individuals, with β +

∑i γit = 1. I allow the γ parameters

to vary by year, subject to year-specific shocks. In particular, I use the parameterization γit =(1 − β) exp(ai+δit)

1+∑j exp(aj+δjt)

, where the δ are year-specific shocks to preferences and ao = δo = 0 is anormalization. Together with the condition that 0 < β < 1, this parameterization ensures that theγ parameters remain in the unit interval.

In order to make the aggregation of the next sub-section as transparent as possible, I set outexpressions for the optimal hours choice, optimal consumption choices, and associated indirectutility function Vist for each sector-market combination s. Given a choice of s, for workers theseare:

hist = (1− β)(T − ψhs)−β

wstMit

yiot =γot

pot(1− β)(wsthist +Mit)

yiat =γat

p2t(1− β)(wsthist +Mit)

yiet =γet

pet(1− β)(wsthist +Mit)

yist =γst

pst(1− β)(wsthist +Mit)

yikt =γkt

rt(1− β)(wsthist +Mit)

Vist = log[w1−βst (T − ψh) + w−βst Mit] + ln[ββ] +Wt + κst + ηist

13

and for non-workers these are:

hi0t = 0

yiot =γot

pot(1− β)Mit

yiat =γat

p2t(1− β)Mit

yiet =γet

pet(1− β)Mit

yist =γst

pst(1− β)Mit

yikt =γkt

rt(1− β)Mit

Vi0t = log[(T − ψh)β(Mit

1− β)1−β] +Wt + κ0t + ηi0t

where Wt is a function of the share parameters and national-level prices, as follows:

Wt =∑b

γbtlog(γbtpbt

) + γktlog(γktrt

)

As a final note, a potential complication in this model concerns those who declare themselves as

employers, self-employed, or non-remunerated family workers. I treat these individuals analogously

to wage laborers. Employers and the self-employed work in their chosen sector for the same wage

as other hired laborers in that sector, and profits from their enterprises accrue to them as non-labor

income. A producer (employer or self-employed) is indifferent as to whether a unit of labor comes

from a household member or someone outside of the household, and can hire as much as she wishes.

At the same time, a member of a farm household is indifferent between – and entirely capable of –

working inside the household or outside the household. These assumptions ensure that producers

maximize profits independently of their work decisions.24

3.1.2 Aggregation Over Individuals

Ultimately, I need to obtain expressions for aggregate labor supply to each region-sector and ag-

gregate product demand for each final good. While the aggregate product demands do not require

it, I must make assumptions about individual heterogeneity to derive the aggregate labor supply

expressions from the individual-level optimal choices above. After noting these assumptions, I write

expressions for the aggregate product demands and labor supplies.24On this point, the model is related to a traditional household maximization problem in which “separation”

between the household-operated firm and consumption decisions allows for a two-stage maximization process in

which firm profits are maximized independently of other household characteristics (See Bardhan and Udry (1999)).

Fixed costs to working outside the household, or other labor market frictions, could call this assumption into question.

Calculations based on the PNAD data for households with someone working in agriculture suggest that a fair number

of agricultural households overcome whatever cost there is. After 1992, between 20 and 25% of households contain

both a self-employed person/employer, as well as a hired laborer.

14

The first set of assumptions involves heterogeneity in non-labor income. I assume non-labor

income is given by Mit = eθit+µit , where both θit and µit represent individual heterogeneity. I

now make distributional assumptions on the θ parameters. I assume that the distribution of θ

is a discrete distribution over two points. Denote these points in year t as (θ1t, θ2t), and define

πm = Pr(θ = θm) for m = 1, 2. Note that πm is not time-varying. Finally, assume µit ∼ N(0, σ2),

and is independent of the θi.25 Before continuing, I add here that it is imperative that total non-

labor income equal the integral over individual non-labor income in each year to ensure coherence of

the model. This necessitates a method of shifting the θ parameters in each year to match the non-

labor income for that year. For this purpose, define θit = θi + log(M̄t/M̄2005), with log(M̄t/M̄2005)

as a shifting factor for period t and the constant parameters θ1 and θ2 reflecting 2005 non-labor

income. This ensures that the aggregation is consistent with economy-wide non-labor income.

The second set of assumptions involves heterogeneity in preferences. I assume ηist ∼ Type I Extreme V alue,and is distributed independently of µ,θ1, and θ2. I normalize the unemployment preference shocks

ϕ0t to be zero for all t. However, I make distributional assumptions on the time-constant por-

tion of unemployment preferences, κ0. Specifically, I assume that κ0t can actually take one of

two values, either κ01 = 0 or κ02 = κ0 > 0. This discrete random variable – which indicates

some preference to be unemployed separate from that captured by the direct value of leisure –

is distributed independently of all other individual-level random variables, except θ1 and θ2. Let

d1|h = Pr(κ0i = 0|θi = θ1) and d1|l = Pr(κ0i = 0|θi = θ2), with d2|. = 1− d1|..26

I am now in a position to set out the expression for aggregate labor supply to a particular

region/sector. (For a more complete derivation of this expression, see the Appendix.) In order to

be compatible with the notation for other parts of the economy described below, instead of using s

to denote a particular region-sector combination, use the pair (r, j), where r represents the region

and j represents the sector. Let f(x) be the probability density function of the random vector x.

Let Nt be the total number of individuals in period t. Based on the expressions above, we can

write period t aggregate labor supply in region-sector combination r, j as:

LSjrt = Nt

[∑m

πm

∫ ∞−∞

[(1− β)(T − ψhj)−β

wjrteθmt+µ]Pr(j, r|θmt, µ)f(µ)dµ

]

Therefore, an increase in labor supply to r, j can come from an increase in the exogenous numberof individuals, an increase in the share of individuals in r, j conditional on non-labor income, oran increase in hours among workers. Let S1 be the set of region-sector combinations (exceptingunemployment) for which optimal hours of work are positive. Then the terms in the final expressions

25This follows the approach of Heckman and Singer (1984). This method has been widely used in the labor

literature, with just two notable examples being Mroz (1999) and Eckstein and Wolpin (1999).26These choices regarding the flexible distribution of preferences for unemployment were made after preliminary

estimation showed that a simpler model fit the data very poorly.

15

above are (with the time subscripts implicit):

f(µ) =1

σ√

2πe−12 (µ

σ)2

Pr(j, r|θm, µ) =∑z

dz|θmeκjrββ [w1−β

jr (T − ψhj) + w−βjr eθm+µ]

eκ0z (T − ψh0)β( eθm+µ

1−β )1−β +∑k,p∈S1 eκkpββ [w1−β

kp (T − ψhp) + w−βkp eθm+µ]

if r, j ∈ S1

= 0 if r, j /∈ S1

The (much simpler) expressions for aggregate product demands are:

Y Dot =

γo

pot(1− β)

∑r,j

wjrtLSjrt +Mt

Y D

at =γa

pat(1− β)

∑r,j

wjrtLSjrt +Mt

Y D

et =γe

pet(1− β)

∑r,j

wjrtLSjrt +Mt

Y D

st =γs

pst(1− β)

∑r,j

wjrtLSjrt +Mt

Y D

kt =γk

rt(1− β)

∑r,j

wjrtLSjrt +Mt

3.1.3 Government Demand

I assume that the government takes in net tax revenue of τt, and then spends this intake on

the composite good, the other agriculture good, ethanol, and sugar in the same proportions that

individuals do. Importantly, the government does not consume capital in the model. Therefore,

the consumption shares from above have to be normalized, and the summations below are over all

non-capital final goods only:

Y Got =

γopot∑

j γjτt

Y Gat =

γapat∑

j γjτt

Y Get =

γepet∑

j γjτt

Y Gst =

γspst∑

j γjτt

Y Gkt = 0

The scaling of the consumption shares ensures that the government’s budget balances.27

27This is a simplification for the sake of the model, but in reality the government’s budget does not actually balance.

I briefly return to this in Chapter 4.

16

3.2 Aggregate Agricultural Supply and Land Use

This section describes the portion of the model covering agricultural production and land use. Land

owners use their land for sugarcane production, agricultural production, or non-agriculture.28 Land

is used for sugarcane or other agriculture only if the profit from that use exceeds a threshold. This

threshold indexes two characteristics that are monotonically and positively related to the “quality”

of untouched forest land: one, the expected penalty imposed by the government for developing

the land; and two, the cost of preparing the land for use in agricultural production. That is, the

government will be more likely to penalize the development of the most environmentally important

forest areas. These areas are also likely to have the largest cost of development.29

This set of assumptions poses three potential obstacles, which can be overcome with additional

assumptions. First, if the government actually fines an agricultural producer, I assume that this fine

is simply returned to individuals in lump-sum fashion, so that net transfers from the government

are unaffected. Second, any fixed costs paid to prepare land for production are assumed to be a

transfer from agricultural producers to other individuals in the economy. This leaves total non-

labor income unchanged. Third, if the land under question is public land or lacks any ownership,

I assume that the same considerations apply. Potential “owners” of the land weigh agricultural

profits against the threshold to determine whether or not to infringe on the public land or unowned

land.

At the outset, it is important to note that the production functions on each parcel of land will

take a very particular form. Specifically, the only inputs to agricultural production in the model

are labor and effective land units. The term “effective land units” refers to the quality of a parcel of

land in a particular use.30 In sugarcane production, for example, quality differences arise through

differences in distance from the closest mill or distillery, availability of irrigation, weather, and land

gradient. At the same time, capital does not enter agricultural production, nor do inputs such

as fertilizer. This choice relates to data constraints, since information on capital usage and other28Only a small percentage of land operators rent their land, so focusing on use by owners is superficially an

advantage (See Valdes and Mistiaen (2003)). In actuality, though, the model here is isomorphic to a model in which

parcels of land are rented out to constant returns to scale producers in each agricultural sector.29It is important to note two ways in which this approach to non-agricultural land use is not fully satisfactory.

First, a (relatively small) portion of land is used for industrial development or residential housing in urban areas. The

current framework does not represent this adequately. Second, landowners sometimes hold land purely for speculative

or savings purposes, and do not use it in agriculture for this reason. Assuncao argues convincingly that savings during

times of uncertainty can be a significant motive for a large number of landowners in Brazil. See, e.g., Assuncao (2006).

de Rezende (2002) and Helfand and de Rezende (2004) also point to the role of the macro economy in determining

the evolution of land prices over time, as investors responded to changing risk structures. Such motives cannot be

taken into account in the necessarily simplified model here.30My approach is closely related to the approach used in Timmins (2006). There, land owners in Brazil allocate

land to various uses depending on heterogeneous value of each parcel in each use. The notion of “effective land units”

is exactly analogous to a Roy model framework for labor supply decisions, in which a single person can provide a

different number of effective labor units in different sectors. For a classic discussion, see for instance Heckman and

Sedlacek (1985).

17

inputs in agriculture is only available during agricultural census years. For this reason, differences

in land quality or labor productivity parameters across regions will in part reflect differences in

usage of other inputs.

In the first sub-section below, I describe the profit maximization problem on any individual

parcel of land, and in the second sub-section I use distributional assumptions on the parcel-specific

heterogeneity to aggregate over the parcels in any region. This yields expressions for aggregate

product supply and aggregate labor demand. Since I do not have data on the allocation of individual

parcels of land, I rely entirely on these aggregate expressions in the estimation.

3.2.1 Parcel-Level Profit Maximization

To determine the use to which a parcel of land is allocated, the profits from the two agricultural

endeavors - sugarcane (j = 1) and other agriculture (j = 2) - are compared to the threshold

discussed above. Let j = 3 denote the non-agricultural use. The parcel is used for j if and only if:

π∗jrt > π∗krt for k 6= j

where

π∗jrt = maxLsrt eκjrt [pjtyjrt(Ljrt;ujrt)− wjrtLjrt] forj = 1, 2

π∗3rt = eλ3rt+u3rt

In the above expressions, Ljrt indicates the amount of annual labor hours used on the parcel of

land, ujrt describes parcel-specific heterogeneous effectiveness in use j (described more completely

below) and yjrt gives the amount of annual output on the parcel. The exact form of the production

function appears below. The output price and wage in the region are given by pjt and wjrt. The

vector (κ1rt, κ2rt) can be viewed as frictions in the agricultural output market; those who farm land

lose a portion of the profits due to frictions.31 This does not pose a problem for the framework here

as long as agricultural profits resulting from land allocation decisions accrue to some individual in

the economy.

For the profit-maximizing decision, I assume the production function for sugarcane and other

agriculture on a parcel of land takes a CES form with effective land units of the parcel and labor as

inputs. The effective units of the parcel in use j are eλjrt+ujrt , where λjrt is a region-time-specific

indicator of land quality that is common across all parcels in region r and ujrt is the portion of

land quality that is heterogeneous across parcels. I assume that the production function takes the

following CES form:

yjrt(Ljrt;ujrt) = zjrt((1− αjrt)(eλjrt+ujrt)ρj + αjrtLρjjrt)

1/ρj for j = 1, 2

31Another way to interpret these parameters is as optimization error. That is, people allocating land incorrectly

perceive the return they can get for it. Regardless, from a practical point of view, without the vector of κ’s, the

model imposes too tight a relationship between shares of land and production. The production parameters govern

both the share of land and production in each of the two activities, sugarcane and other agriculture. This imposes a

situation of over-identification that can lead to a very poor fit.

18

where zjrt = eφjrt is a scale or TFP term and ρj < 1.

We now have enough information to write down the profit-maximizing choices on each parcel

of land.32 Dropping the time subscripts for convenience, the optimal product supply and labor

demand for the parcel, as well as the optimal profits, are given for j = 1, 2 by:

yjr(ujr) = zjr(1− αjr)1ρj (wjr)

11−ρj

[(wjr)

ρj1−ρj − (αjr)

11−ρj (pjzjr)

ρj1−ρj

]−1ρj

eλjr+ujr

Ljr(ujr) = (αjrpjzjr)1

1−ρj (1− αjr)1ρj

[(wjr)

ρj1−ρj − (αjr)

11−ρj (pjzjr)

ρj1−ρj

]−1ρj

eλjr+ujr

π∗jr(ujr) = eκjrpjwjrzjr(1− αjr)1ρj

[(wjr)

ρj1−ρj − (αjr)

11−ρj (pjzjr)

ρj1−ρj

] ρj−1

ρj

eλjr+ujr

Finally, there are two identification issues that require normalizations in the model. First, it

is not possible to separately identify zjrt(= eφjrt), αjrt, and λjrt.33 Since the levels of the αjrt are

arbitrary, I set them to the region-specific means of the share of labor costs in total revenue over

the ten year period 1995-2005 (2000 excluded). This facilitates the interpretation of ρ1 and ρ2,

in that values close to zero correspond with Cobb-Douglas production, with share αjrt.34 Second,

observing agricultural production levels will help to identify λ1rt and λ2rt. However, there is no

way to disentangle λ3rt, κ1rt, and κ2rt. Consequently, I simply set κ1rt = 0. Thus, κ2rt = κrt

captures the relative tendency to put land into non-sugarcane agricultural use, regardless of the

level of profits received directly by producers.

3.2.2 Aggregation Over Parcels

By using assumptions for the distribution of land quality in each region, I now derive expressions

for aggregate product supply and aggregate labor demand in each agricultural sector, in each

region. Assume that ujrt for j=1,2,3, are mutually independent and take the Type I extreme

value distribution with parameter γr. That is, the probability density function of ujrt is given by1γre−ujrtγr e−e

−ujrtγr .35

Using these assumptions, I integrate over the parcels of land allocated to each use in order to

derive the share of land devoted to producing each good (Sjrt), total effective units of land in each32There is an important implicit assumption behind the expressions: wages and prices are assumed to take values

such that it is profitable to have non-zero land area devoted to sugarcane or other agriculture. This is true in the

data, but the approach ignores the possibility of zero land area in the simulations of equilibria under alternative

policy environments33To see this, consider a vector (ρ1, z1, α1, λ1) that satisfies the product supply and labor demand equations for

sugarcane in a particular region and year. If z̃1 = (α1α̃1

)1/ρ1z1 and eλ̃1 = ( α̃1α1

1−α11−α̃1

)1/ρ1eλ1 for some α̃1 in (0, 1), then

the vector (ρ1, z̃1, α̃1, λ̃1) also satisfies the system.34Here, the elasticity of substitution is given by 1

1−ρj, with values of 0, 1, and infinite representing, respectively,

Leontief, Cobb-Douglas, and perfectly substitutable production.35Timmins (2006) assumes use-specific land values are linear in heterogeneous errors that take the extreme value

distribution. One might think that land values could be negative in some uses if there are fixed costs to production

in those uses. However, in the setup here, heterogeneous errors across parcels enter through an exponential function,

and it is important for interpretation that effective land units always remain positive.

19

good (Ajrt), total labor demand in each sector (LDjrt), and total supply of each good (Y Sjrt). For

convenience, define πcjrt such that π∗jrt(ujrt) = πcjrteujrt . Let cjrt = ln(πcjrt) and let A∗rt be the

total amount of land in region r at time t. Let Γ(.) denote the gamma function, as opposed to the

gamma density.36 Also, we have κ3rt = 0. Then for k, p 6= j, the allocated land share and the total

effective land units are:

Sjrt =ecjrtγr∑3

i=1 ecirtγr

Ajrt = A∗rteλjrt(Sjrt)1−γrΓ(1− γr)

A more complete derivation of these expressions appears in the Appendix. Note the implicitrestriction that γr ∈ (0, 1).37 This expression corroborates the intuition that the marginal impacton effective land units of increasing the land share slightly is diminishing in the land share. Finally,from the expression for Ajrt and the parcel-level labor demands and product supplies above, it iseasy to see that aggregate labor demand and aggregate product supply in each sector for all regionsr are:

LD1rt = (α1rp1tz1rt)1

1−ρ1 (1− α1r)1ρ1

[(w1rt)

ρ11−ρ1 − (α1r)

11−ρ1 (p1tz1rt)

ρ11−ρ1

]−1ρ1

× A∗eλ1rt(S1rt)1−γrΓ(1− γr)

LD2rt = (α2rpatz2rt)1

1−ρ2 (1− α2r)1ρ2

[(w2rt)

ρ21−ρ2 − (α2r)

11−ρ2 (patz2rt)

ρ21−ρ2

]−1ρ2

× A∗eλ2rt(S2rt)1−γrΓ(1− γr)

and

Y S1rt = z1rt(1− α1r)1ρ1 (w1rt)

11−ρ1

[(w1rt)

ρ11−ρ1 − (α1r)

11−ρ1 (p1tz1rt)

ρ11−ρ1

]−1ρ1

× A∗eλ1rt(S1rt)1−γrΓ(1− γr)

Y S2rt = z2rt(1− α2r)1ρ2 (w2rt)

11−ρ2

[(w2rt)

ρ21−ρ2 − (α2r)

11−ρ2 (patz2rt)

ρ21−ρ2

]−1ρ2

× A∗eλ2rt(S2rt)1−γrΓ(1− γr)

Finally, for use in estimation, I need to parameterize λjrt for j = 1, 2, 3, φ1rt, φ2rt, and κ2rt. Assume

that for each j, λjrt takes the following form:

λjrt = λ0jr + νjrt for j = 1, 2, 3

where νjrt is a shock to land quality that is common to all parcels of land in the given region.

Set φjrt = φ0jr + εjrt for j = 1, 2, where ε1rt and ε2rt are shocks to production. Finally, let

κ2rt = κ2r + νkrt, with νkrt a shock to the tendency to allocate land to other agriculture.36That is, Γ(x) =

∫∞0tx−1e−tdt, and the function is defined for x ∈ (0,∞).

37In the structural estimation below, I impose γr = γ for all r. Preliminary estimation results suggested that the

region-specific values are close to each other.

20

3.3 Ethanol and Sugar Production and Input Demand

I assume production of ethanol and sugar is constant returns to scale, taking capital and sugarcane

as inputs.38 In the production of sugar and ethanol, substitution possibilities between sugarcane

and other inputs are extremely limited; a producer cannot easily economize on sugarcane by using

more of other inputs. Therefore, I use Leontief production functions:

Ysrt = min {αstY1srt, βsKsrt}

Yert = min {αetY1ert, βetKert}

where Y1jrt and Kjrt are the amounts of sugarcane and capital demanded by producers of good

j, where j = s for sugar and j = e for ethanol. Note that the production functions are common

across all regions. The αst, αet, and βet are allowed to vary over time. Specifically, assume that

αst = eαs+εst , αet = eαe+εet , and βet = eβe+εebt where εst, εet, and εebt are shocks to production.

Because of the constant returns to scale assumption, the supply of ethanol and sugar at any

given set of prices is indeterminate. However, cost minimization implies that the input demands

are related to the product supplies as follows, for all regions r:

KDert =

Y Sert

βet

KDsrt =

Y Ssrt

βs

Y D1ert =

Y Sert

αet

Y D1srt =

Y Ssrt

αst

3.4 Composite Good Production and Input Demand

I assume that production of the composite good is Cobb-Douglas, taking capital and labor as

inputs. The share parameters potentially differ across regions. Formally, the production function

for each region r is:

Yort = zortLβortort K

1−βortort

Here, I assume zort and βort are both stochastic. In particular, zort = eφort with φort = φor + εport,

and βort = 1

1+eβor+εbort

. The terms εport and εbort are region-year-specific shocks.

The constant returns to scale assumption implies that composite good supply in any region

is indeterminate. However, cost minimization implies that the input demands are related to the38Due to the industry definitions in the PNAD, it is not possible to clearly identify those who work in the ethanol

and sugar industries prior to 2004. Owing in part to this limitation, I omit labor from the ethanol and sugar

production functions.

21

product supplies as follows, for all regions r:

KDort =

((1− βort)w3rt

βortrt

)βort Y Sort

zort

LDort = βortpotY

Sort

w3rt

3.5 International Market

Since the focus of the paper is not the international market for ethanol or other products, I model

the interaction between Brazil and the rest of the world in a very simple way. All final goods

can be exported and imported. Net exports of the other agriculture good, ethanol, sugar, and the

composite good are denoted by Y Xat , Y X

et , Y Xst , and Y X

ot , respectively.

I assume that the prices of the other agricultural good, the composite good, and sugar are all

determined outside of Brazil. This assumption is least controversial for the case of agriculture.

Brazil’s trade barriers in agriculture fell markedly in the early 1990s. Helfand (2003) illustrates

how domestic agricultural prices move more closely with international prices after the reforms.

However, the assumptions are much more controversial for the composite good and sugar. In

the model, capital can move easily out of composite good production since this good can be freely

imported. But the composite good in part represents services, which in reality are not tradeable.

If the model were to take into account these non-tradeables – and non-tradeables production were

to use capital – then capital could not move as much into ethanol production in response to greater

opportunities for ethanol exports.

The assumption is also controversial in the case of sugar. Brazil is a major player on the world

sugar market, in terms of share of world exports. However, Brazil’s share of world production

is smaller. In the 2005/06 marketing year, data from the Foreign Agricultural Service (FAS) of

the USDA show that of the 144,860 thousand metric tons of sugar produced in the world, 26,850

thousand metric tons were produced in Brazil, approximately 18.5%.39 This will at least reduce

Brazil’s influence on the world sugar price somewhat.

Finally, I need to specify the form of trade barriers for ethanol. For ethanol, the US is by far the

largest potential market for Brazilian output. Currently, the US protects its own ethanol producers

with a $0.54 per gallon duty on imports and a 2.5% ad valorem tariff. To avoid modeling US

ethanol demand, I take a stylized approach: I represent the current policy situation as one in which

Brazil faces downward-sloping domestic demand for ethanol, but also faces L-shaped international

demand. That is, international demand for ethanol is perfectly inelastic at low quantities, and

perfectly elastic once the price gets low enough to overcome the effect of barriers to trade. This price

level at which international demand becomes elastic is assumed to be lower than the equilibrium39See FAS data for the November 2007 World Production, Supply, and Distribution Report, available at

http://www.fas.usda.gov/htp/sugar/2007/November 2007 tables.pdf

22

price level before policy changes are made. In the baseline, then, ethanol prices in Brazil are

determined entirely by Brazilian demand.

For the purposes of answering the research question with policy simulations, I need to decide

how to represent a change in US policy. Removing US import barriers to ethanol is assumed to

increase the price at which Brazilian ethanol becomes competitive with US ethanol. The perfectly

elastic portion of international demand moves upwards, to a point higher than the price in the

baseline equilibrium. That is, in the alternative simulation of no barriers, the ethanol price is

set internationally and ethanol quantities are determined by total (Brazilian plus international)

demand. In the simulations, I consider three cases: in the first, ethanol demand becomes elastic

at a price 10% greater than the price in 2005; in the second and third, ethanol demand becomes

elastic at a price 12% and 15% greater than the baseline. The choice of these numbers is designed

to give a range of possible policy consequences, while at the same time keeping ethanol reasonably

competitive with petroleum.

This discussion of the international market covers the last component of the model. As a final

note, as will be stated formally in the definition of equilibrium in the next section, I close the model

by assuming that the value of total net exports is zero.

3.6 Equilibrium

In this section, I begin by defining the market equilibrium in the model. All quantities appearing

below in the definition of the equilibrium have been defined previously in the relevant section above.

The second sub-section comments briefly on the existence and uniqueness of equilibrium in this

model.

3.6.1 Definition

The only “exogenous” variables in the baseline case are: prices of sugar, the other agricultural good,

and the composite good; net exports of ethanol; total population; total capital stock; and the total

amount of land in each region. All other variables are determined endogenously within the model,

based on the exogenous variables, the parameters, and the values of the shocks. In the alternative

case of lowered trade barriers, I assume the price of ethanol is exogenous and net exports of ethanol

become endogenous. Keeping this in mind, an equilibrium in this economy involves the following

conditions:

Agricultural Goods ∑r

[Y D1ert + Y D

1srt] =∑r

Y S1rt

Y Dat + Y G

at =∑r

Y S2rt − Y X

at

23

Non-agricultural Goods

Y Dot + Y G

ot =∑r

Y Sort − Y X

ot

Y Dst + Y G

st =∑r

Y Ssrt − Y X

st

Y Det + Y G

et =∑r

Y Sert − Y X

et

Capital and Labor

Y Dkt +

∑r

(KDort +KD

ert +KDsrt) = K̄t

LDjrt = LSjrt forj = 1, 2, 3 ∀r

Zero-profit Conditions

potzort =(w3rt

βort

)βort ( rt1− βort

)1−βort∀r

pet =p1t

αet+

rtβet

pst =p1t

αst+

rtβst

Trade Balance and Budget Constraints

potYXot + petY

Xet + pstY

Xst + p2tY

Xat = 0

potYDot + petY

Det + pstY

Dst + p2tY

D2t + rtY

Dkt =

∑r,j

wjrtLSjrt +Mt

potYGot + petY

Get + pstY

Gst + p2tY

G2t = τt

where total non-labor income is given by Mt = rtK̄t+∑

r[p2tYS2rt−w2rtL

D2rt+p1tY

S1rt−w1rtL

D1rt]−τt.

3.6.2 Existence and Uniqueness

There are two natural questions at this stage: Must an equilibrium exist in this economy for any

draw of the production shocks and any set of exogenous variables? And if an equilibrium exists, is

it unique?

First, consider the existence question. The production side of the economy is quite conventional.

The production of the non-agricultural goods is constant returns to scale, and poses no special

difficulties. Examination of the model also reveals that it is isomorphic to a model in which

aggregate agricultural production is constant returns to scale in aggregate effective land units and

aggregate labor, and the representative firms rent effective land units from landowners. Therefore,

the production side of the economy may not by itself pose problems for existence.

24

The “unconventional” aspects of the economy arise in three ways: non-convex individual pref-

erences, land supply, and the trade environment (in combination with the restrictive production

functions – and hence zero profit conditions – for ethanol and sugar). Any one individual’s pref-

erences are non-convex because of the choice of region and sector. This creates obstacles to con-

ventional proofs of existence, though the presence of individual heterogeneity may actually impose

sufficient discipline on the aggregate net labor demand expressions (see Mas-Colell, Whinston, and

Green (1995) for an example of how heterogeneity can be exploited to sidestep obstacles posed by

non-convex preferences).

But such arguments are not sufficient to preserve existence here. To informally see why, consider

the baseline case where net exports of ethanol are exogenous. Suppose net exports take a very large

value while the production shocks in sugarcane production are negative and very large in magnitude.

The need to produce ethanol would then require a high sugarcane price. If this price is high enough,

the zero-profit condition in sugar would be violated by any positive value for the capital rental rate.

In the simulations below, existence is further hampered by the fact that I search for equilibria with

strictly positive land shares, production quantities, and wages in all regions.40

The second issue is whether an equilibrium is unique if it exists. Again, the lack of convex

preferences may be a significant obstacle to applying the common conditions for uniqueness in

a closed economy (see Mas-Colell, Whinston, and Green (1995)). The implicit function theorem

allows us to say something about local uniqueness, however. The method of estimation ensures

that, given the parameter estimates and in the vicinity of the production and preference shocks

for a given year of data, the endogenous variables are a one-to-one function of the shocks. This

guarantees existence and uniqueness in an open set around the realized shocks. I say more about

this point in the section on estimation below. While this is comforting, it does not guarantee

uniqueness at points farther away from the realized production shocks of a given year. Moreover, it

does not guarantee uniqueness for all possible values of the parameters, or all possible combinations

of the exogenous variables and shocks.

3.6.3 Features Not Captured in the Model

There are aspects of the sugarcane industry that are much more difficult to capture in a general

equilibrium model of this nature. These aspects are the following:

• Ethanol distilleries and sugar mills often produce sugarcane in addition to purchasing it from

others. The sugarcane industry consists of two basic types of producers: the independent

cane growers and the millers. The largest growers of sugarcane are often the millers them-

selves, which is a natural arrangement owing to the fact that harvested sugarcane must be40I impose these restrictions not only because these are the most plausible equilibria. It also simplifies the process

of simulation, since the equations from maximum likelihood estimation can be used directly to form the non-linear

system, and these equations rely on positive quantities in certain variables.

25

transported to factories very quickly.41

• Until 1997, the Brazilian government intervened strongly in the market. The Instituto do

Acucar e do Alcool (IAA) operated a system of quotas and price controls for sugarcane,

sugar, and ethanol over a period of 60 years. For sugarcane, IAA production quotas specified

the amount of sugarcane that mills had to purchase from independent growers. Over the

1980s, quotas for sugar production also worked to limit the production of sugarcane by larger

enterprises. 42 In addition to quotas, the IAA set prices. Over the 1980s, the agency reduced

sugarcane prices dramatically, which is reflected in the price data discussed above. As time

went on, the system of quotas and administered prices came under increasing pressure.43

In 1990, the IAA was abolished and sugar exports were privatized. In 1995, sugar quotas

were ended, and from 1997-1999, prices for sugar, ethanol, and sugarcane were liberalized.

Since 1999, sugarcane prices have been determined in essentially a free market. The large

number of independent growers, as many as 60,000 by some measures, assures a fair degree

of competition.

• There is regional heterogeneity in sugarcane, ethanol, and sugar prices. Price differences

across regions persist because of different growing seasons for sugarcane, government policy,

and transportation costs. In some months of the year, ethanol comes primarily from the

Center-South, while in others it comes from the Northeast, in accordance with the differing

harvesting periods. Regarding government action, special allocation of sugar export quota to

the Northeast and subsidies to sugarcane producers in the Northeast also lead to differences.44

Finally, sugarcane is a locally marketed good, since transportation over long distances is

infeasible for biological reasons. Despite all this, examination of the region-level data reveals

that the price of sugarcane moves in similar ways over time in all states.

The model does not deal with any of the three complications noted here. For the sake of

simplicity, ethanol and sugar producers are assumed to procure sugarcane in a competitive market,

and the prices of all three goods involved – ethanol, sugar, and sugarcane – are assumed to be

identical across regions. The results in this paper should be interpreted cautiously in light of these

limitations.41For basic details on the preparation and milling of harvested cane, the website of the Sao Paulo cooperative

COPERSUCAR is a useful source (www.copersucar.com.br).42However, the increasing emphasis on alcohol production, which was not constrained by quotas in the same

way, provided a growing outlet for “excess” sugarcane. Ethanol quotas instead took the form of levels of domestic

production that a mill/distillery had to meet before exporting. Sugar exports also fell under government control.43For a brief listing of major events in government policy, see notes by I.C. Macedo of Unicamp on the website for

Cane Resources Network of South Africa, www.carensa.net/Brazil.htm. For greater detail, see Barros and Moraes

(2002), Lopes and Lopes (1998), and Borrell, Bianco, and Bale (1994).44Unfortunately, I do not have time series data on the size of the government subsidies. While there are some

data on region-specific prices for ethanol and sugar (see http://cepea.esalq.usp.br/), these data do not use consistent

definitions across regions and are available for the Northeast only for 2001 onwards.

26

4 Data

I utilize data from a large array of government and non-government sources. Here, I describe the

primary data sources briefly. For further details on the data and on construction of variables used

in the analysis, please see the Appendix. I rely primarily on five sets of data: first, labor force

data from the Pesquisa Nacional por Amostra de Domicilios (PNAD); second, data for agricultural

production amounts and land allocations from the Producao Agricola Municipal (PAM), the Prod-

ucao Pecuaria Municipal (PPM), the Agricultural Censuses, and regional income accounts; third,

data on output and input prices from Fundacao Getulio Vargas (FGV); fourth, data on ethanol

and sugar production; and fifth, data on other non-agricultural production, capital investment, net

exports, and government spending from the regional and national income accounts. I describe these

sources of data in separate sub-sections.

4.1 Labor Force Data (PNAD)

The PNAD is a cross-sectional representative household survey collected by the Brazilian govern-

ment’s statistical group IBGE. I will use PNAD data from 1981 through 2005 for all but three

years.45 On average, the PNAD surveys roughly 100,000 households each year, which corresponds

to more than 300,000 people. The only region of the country not represented fully in the PNAD

sample is the North Census region.46 This will prevent me from addressing the sugarcane markets

in the Northern portion of the country.

The PNAD has information on several aspects of employment. I use the following information

for each member of a household: whether or not the member is employed (with September being

the reference month); if she is employed, then her monthly income and usual weekly work hours

from her primary job; the sector of her primary job, with sector being narrowly defined enough

to allow for the identification of specific crops; and whether the individual is hired labor, a non-

remunerated family worker, self-employed, or an employer. The advantage of such large samples

is that there are a considerable number of survey respondents working in any particular crop. In

order to construct aggregate hours worked in a particular region/sector, I multiply weekly hours by

52 and take the weighted sum over all individuals in that region/sector, using the PNAD-provided

survey weights.47

45In 1991 and 2000, the PNAD was not conducted because those were national demographic census years. In 1994,

the PNAD was not conducted due to other constraints. Although I have the national census data for 1991 and 2000,

these were conducted at different times of year from the PNAD, making comparisons difficult in the agricultural

sector.46The rural parts of the six states in the North region are not represented through 2003. In the 2004 and 2005

data, this deficiency has been remedied, and the PNAD is now nationally representative.47If “52” is the incorrect factor to multiply weekly hours by, then in general all the estimates shown here will be

affected. I do not analyze the sensitivity of the estimates to this choice in this paper. For region of work, there are

a limited number of cases in which the survey respondent was not present in the current state as of the last week of

September (the reference month). In these cases, I simply drop the respondent.

27

4.2 Agricultural Production and Land Use (PAM, PPM, Forest Values, Agri-

cultural Censuses, Regional Income Accounts)

The analysis below requires an estimate of the total value of production in, and total amount of

land devoted to, the two agricultural sectors in every region and year. I use four sources of data to

construct information on production and land allocations: the PAM, the PPM, the IBGE data on

forest production values, the Agricultural Censuses, and the regional income accounts. The PAM

is a valuable resource that has certain deficiencies, and I use the latter four sources to supplement

the information from the PAM.

To be specific, the PAM provides annual information on total production and total area har-

vested for major crops in each state. Data are available for all permanent and temporary crops in

the 1990-2005 time period, and for the most important crops in the 1981-1989 period.48 Sugarcane

is covered in all years. Moreover, there are data on the acreage planted and the acreage harvested

for sugarcane. These numbers are quite close together, and I use the acreage harvested.

The PAM does not capture four types of land uses: pasture land; land temporarily at rest;

forest land; and land used for minor crops (a problem in the 1981-1989 period). To address this

problem, I use data from the 1980, 1985, 1995, and 2005-06 Agricultural Censuses, which contain

information on pasture, forests, and all other agricultural land (at rest or otherwise). I also use

annual data on cattle herd sizes from Producao Pecuaria Municipal (PPM), and IBGE data on

the total value of forest production. Using these data sources and the PAM data, I use simple

regression equations and extrapolation procedures to project total agricultural area in the years of

my analysis period. These projections are important, and I provide more detail on them in the

Appendix.

Finally, the PAM data I have do not provide the total value of agricultural production for all

years. For this purpose, I use regional income accounts information for the 1985-2005 period. The

value of agricultural production from the income accounts includes the value of forest production,

though this is a small percentage of the total. To construct the value of “other agricultural”

production, I use the sugarcane price data described below and sugarcane production information

to calculate total value of sugarcane production, and then subtract that from the value of total

agricultural production.

4.3 Output and Input Prices (FGV)

The price data come from FGV, a foundation that compiles a large number of price indexes for

Brazil. I use the FGV data sources to construct prices for sugarcane, other agriculture, ethanol,

sugar, petroleum, capital, and the composite non-agricultural good. Sugarcane and petroleum

information appears as absolute prices in the raw data, whereas the prices for the other goods must48The quality of the data varies over time, generally being better near agricultural census years. I obtained the

1990-2005 data from SIDRA, an online database operated by the Brazilian government. The earlier PAM data come

from IPEA, an institute affiliated with the government, with a website at www.ipeadata.com.br.

28

be constructed using FGV price indexes. In the case of the composite non-agricultural good, I

construct a price index by using changes in relative prices of all other goods, the overall consumer

price index, and the shares of all other goods in the “consumption basket”.

The simpler set of data involve absolute prices. The FGV has monthly time series on prices

received for detailed agricultural product categories, by state.49 I obtain the sugarcane prices this

way. I convert petroleum prices from their US dollar values to Reais using exchange rate data from

the Banco Central do Brasil.

In the case of price indexes, I use different procedures depending on the good. Whenever

possible, I construct a series on absolute price levels by benchmarking the index to outside data for

a particular year. I use this procedure for ethanol and sugar prices. For the remaining goods, there

are no natural units. Accordingly, I create an artificial unit by benchmarking a particular year to

a value of 100.

4.4 Ethanol and Sugar Production

I use data on the amount of sugar and ethanol produced in each state and year from the Brazilian

government. These data span the 1995-2005 time period. Unfortunately, these data are for local

harvesting years, rather than calendar years. I impute a measure of the ethanol and sugar quantities

for calendar year t by taking a weighted average of the surrounding harvest years, where the weights

differ between the Northeast regions and the Center-South regions.50

The data on sugar and ethanol production also contain the amount of sugarcane crushed by

mills and distilleries in each harvest year. In this paper, I use data on harvested sugarcane, rather

than crushed sugarcane. There are discrepancies between the total amount of sugarcane crushed

in a region and the total amount harvested, with the total amount produced being larger in every

case besides one region-year observation. This should be expected: Sugarcane will be lost during

transportation and initial processing, and a small amount of sugarcane is used for purposes other

than ethanol and sugar. Here, as noted in Chapter 2, I assume that all sugarcane goes into the

production of either ethanol or sugar.

4.5 Other Data

Finally, I require data on total regional production, national capital investment, government spend-

ing, and net exports (overall, agricultural goods, ethanol, and sugar). For this purpose, I use

national and regional income accounts data from IBGE, and data on imports and exports from

Brazil’s Secretaria de Comercio Exterior (SECEX). In the following section, I discuss the use of

these data to construct empirical analogues to quantities in the model.49These data are collected using farm surveys in the relevant geographical regions.50The harvest year definition runs from May to April in the Center-South, and from September to August in the

Northeast. The heaviest periods of the harvest are located in a few months within those periods.

29

5 Empirical Analysis

In this section, I start by examining some assumptions in the model with a preliminary look at

the data. In the second sub-section I describe my structural estimation approach. Details on an

alternative estimation approach – one that has certain advantages to the one used here – appear

in the Appendix. The third sub-section provides estimates of the model’s parameters.

5.1 Examination of the Model’s Assumptions

The model contains a wide variety of assumptions. In the case of the agricultural component of

the model, these assumptions yield a few testable implications. Here, I examine three of the most

significant:

• CES production functions for sugarcane and other agriculture

• Parcel-specific heterogeneity takes a Type I Extreme Value distribution

• History-independent level of land quality in both agricultural uses

I examine testable implications of each of these assumptions one-by-one. For each of these assump-

tions, rejection of the null hypotheses tested below is not definitive. Rejection could mean that the

assumption is incorrect, or could mean that another, linked part of the model is incorrect. Still,

the tests indicate aspects of the model that should be re-visited in the future.

5.1.1 CES Production Functions

From the assumptions of the model, and using the innocuous normalization that the α parameters

equal 12 , one can derive the following equation for labor productivity for each sector i:

log

(Y Sir

LDir

)=

11− ρi

log(2)− ρi1− ρi

φir +1

1− ρilog(wir)−

11− ρi

log(pi) + ε1r

Therefore, the model implies that the wage and price effects should be of equal magnitude

and opposite sign. Tables 6 and 7 present results from regression estimates of this equation for

sugarcane and other agriculture, respectively. The tables are structured analogously. The first

three columns present estimates of the equations without imposing the equality of the wage and

price effects. I can use these results to conduct a simple Wald test of the constraint on the wage and

price coefficients. The next three columns use the ratio of wages to prices as a regressor, implicitly

imposing the constraint.

Turning to the sugarcane regressions first, the first column shows OLS estimates of the equation.

However, both the wage and the price are endogenous according to the model. This suggests

estimating the equations with instrumental variables. The second and third columns instrument

for the wage and price using the instruments indicated in the table. Both columns suffer from

potential issues with weak instruments, though the excluded instruments enter significantly in

30

most cases. The third column contains a negative coefficient on wages, which is inconsistent with

the model. Still, this is statistically insignificantly different from zero. I test the null that the sum

of the wage and price coefficients is zero. I fail to reject this is the case in the second and third

columns, and in results not shown here, I also fail to reject when using petroleum and sugar prices

as instruments. The size of the coefficients in the second column are consistent with an elasticity

of substitution smaller than 1.51 For the sake of comparison, the next set of three columns show

the results when the constraint is imposed.

Next, I turn to the labor productivity regressions for other agriculture, in Table 7. The Brazilian

government altered the definition of work between the pre- and post-1992 PNAD surveys. Before

1992, subsistence workers or non-remunerated workers who worked fewer than 15 hours per week

were not counted as working in the survey. After 1992, all these individuals were counted as

working. This is not likely to affect the measurement of labor hours in sugarcane because sugarcane

workers are predominantly hired laborers. However, this has a substantial effect in the case of other

agricultural labor prior to 1992. Comparing total labor hours in other agriculture before 1992 and

after 1992 is therefore not possible. Because of the problem with the pre-1992 PNAD definitions,

I use only the post-1992 observations for other agriculture.

Again, the first and fourth columns show the OLS results, while the remaining columns in-

strument for the endogenous regressors. In this case, the price is not endogenous by assumption.

The instruments for the second and third columns both enter significantly, though there is a weak

instrument concern again. The wage variable has the expected positive sign in both cases, and the

magnitudes suggest an elasticity of substitution greater than one. One can reject the null that the

sum of the price and wage effects is zero for both sets of IV estimates. While I show the results

that impose the constraint for the sake of completeness, it appears that there is more reason to

question the form of the production function in the case of other agriculture.

Therefore, the estimates of the sugarcane equation are not inconsistent with the CES production

function assumption, though the fact that some coefficients take an unexpected sign may still cause

some concern. On the other hand, I reject the null hypothesis of wage and price effects of equal

magnitude for the the other agriculture equation. This suggests considering more complicated

production functions in the future.

5.1.2 Distribution of Parcel-Specific Heterogeneity

The next assumption I consider is the assumption of Type I errors in land quality. This assump-

tion implies that the ratio of the sugarcane land share to the non-agricultural land share is not

affected directly by the price or wage in other agriculture. To test this, I use a first-order Taylor

approximation to the model’s expression of this ratio. This gives an equation for the log of the51The magnitude of the wage and price coefficients are both above 1 in the (omitted) regression with petroleum and

sugar prices as instruments, though with large standard errors. More will be said about the elasticity of substitution

for sugarcane and other agriculture in the structural estimation below.

31

ratio between the sugarcane and non-agricultural land shares as follows:

log

(S1r

S3r

)≈ β0r + β1rlog(w1r) + β2rlog(p1) + ε∗s

where the asterisk in the error term indicates that this error does not have a strict interpretation

as a structural error from the model, but instead incorporates approximation error as well.

To test the Type I error assumption, I test whether or not the characteristics of other agriculture

enter the equation above. The first four columns of Table 8 address this issue by including the price

and wage in other agriculture in the regressions. The first two columns do not include interactions

with the Northeast dummy, while the second two columns do include these interactions.52 OLS

should produce inconsistent estimates of these equations because wages and prices are correlated

with the shocks to total factor productivity and land quality that appear in the error terms.

Therefore, I show IV estimates using the logs of the total number of individuals, the petroleum

price, and the sugar price as instruments. Where necessary, I interact the instruments with a

dummy for the Northeast.

In all four columns, the price of other agriculture enters positively and significantly. It is

difficult to know whether this is because of the linear approximation I am using or because the

Type I assumption is incorrect. In the structural estimation, I proceed with the Type I error

assumption. But it is important to investigate this issue and consider a more complicated class of

models in the future.

5.1.3 History-independent Land Quality

Finally, I turn to the issue of land quality being independent of the history of land allocations.

This implies there is no inertia in land allocations, which is an especially strong assumption for

sugarcane. I test this by allowing the land quality term to include a lagged sugarcane land share in

the model for land shares above. The fifth and sixth columns of Table 8 show the relevant results.

Under the assumption of no serial correlation in error terms, there is no need to instrument for

the lagged log sugarcane share. Both the OLS and IV estimates yield positive coefficients that are

statistically different from both zero and one. This is worrying, in that it suggests a non-stationary

process.

In results not shown here, I further explore this issue. The result is sensitive to the instruments

and sample used. An IV regression using petroleum price and total population as instruments

yielded a small and insignificant effect of the lagged share. However, the estimates in this regression

are in general very imprecise. In regards to the sensitivity to the sample, OLS regressions on

samples restricting the years to 1990 and beyond, as well as 1995 and beyond, show much smaller52Small sample sizes prevent me from having the coefficients be fully region-specific, so I instead allow them to

differ between the Center-South regions and the Northeast regions. The constant terms in this equations reflect, in

part, the total factor productivity and land quality parameters. These may potentially change over time, so I include

a time trend in the analysis.

32

coefficients. Below, for simplicity, I estimate the structural model without allowing for any lagged

terms or dynamics. This issues is worth exploring further in the future, however.

5.2 Maximum Likelihood Estimation

In this section, I describe the details of the estimation procedure. A large body of work by Dale

Jorgenson, as well as studies such as Fair and Parke (1980), also pursue estimation of large-scale

macroeconomic models. The work here differs in its derivation of aggregates from underlying

heterogeneity of individual preferences and land quality, as well as its use of individual-level data

to aid in identification. In this way, this paper is closely related to the relatively recent work on

dynamic general equilibrium models with individual labor supply and human capital decisions (see

seminal papers such as Heckman, Lochner, and Taber (1998) and Lee and Wolpin (2006)). This

paper restricts itself to a static setting in order to allow for a more detailed exploration of cross-

region patterns and deal with data limitations. In exchange for having a much simpler setting, I

am able to incorporate an intensive margin of hours of work, give an economic role to all shocks,

and use an estimation approach that guarantees all equilibrium relationships hold. In contrast to

most work on empirical general equilibrium models, I use maximum likelihood instead of SMM or

GMM methods. The first sub-section provides a rationale for using the MLE approach, along with a

description of advantages and disadvantages. The second sub-section goes on to make distributional

assumptions and list the parameters to be estimated. The third and final sub-section describes my

MLE approach in detail.

5.2.1 Rationale for Using MLE

In the past, authors have noted problems with estimating GE models with maximum likelihood, and

have therefore turned to alternative estimation methods (See, e.g., Heckman, Lochner, and Taber

(1998),Lee and Wolpin (2006)). However, I pursue the MLE approach instead for four reasons.

First, maximum likelihood ensures that all the constraints implied by the equilibrium system are

accounted for. It would be possible to implement all these constraints in a more agnostic method

of moments approach, but it would require a great deal of caution. Second, using GMM and SMM

does not address the more fundamental economic problem of existence and uniqueness of equilibria.

Consider the SMM approach, for example. This approach guarantees that at all the error draws

used in the calculation of the moments, one has an equilibrium. However, this does not guarantee

existence and uniqueness in the neighborhood of the actually realized error draws. Third, for the

simulations I need to know what distribution to draw the errors from. At this point, even with

GMM and SMM, I would be forced to make stringent distributional assumptions. Fourth, and

finally, MLE dictates exactly what moments to use, while GMM and SMM would force me to

choose moments somewhat arbitrarily. To be sure, in small samples – and with the concern noted

above – it is difficult to know if the MLE moments are any “better” than the GMM/SMM moments

I could choose; however, MLE does provide a clear guide to the choice of moments.

33

To be sure, MLE has its own obstacles.53 For instance, the small number of observations force

me to make stringent assumptions about the independence of unobservables to secure identification.

In a linear FIML model without constraints on the contemporaneous correlation of the error terms,

identification is impossible if the number of observations is smaller than the sum of the number of

endogenous and exogenous variables in the model (see Sargan (1975)). Independence assumptions

help substantially. Another problem is that there is no guarantee that a solution to the equilibrium

system exists (i.e., that every possible combination of the error terms allowed by the normality

assumptions below has an equilibrium for the endogenous variables associated with it). Third, even

if a solution exists, there is no guarantee that it must be unique for every possible combination of

the error terms allowed by the distributional assumptions. (For a brief discussion of these issues, see

for instance Amemiya (1985)). Therefore, the normality assumptions do not capture restrictions on

the possible distribution of the error terms that are implicit in the model. Keeping these limitations

in mind, I describe my MLE approach below.

5.2.2 Distributional Assumptions and Parameters to be Estimated

Here, I lay out distributional assumptions and clearly state the parameters to be estimated. I

assume that all stochastic errors in the economy are normally distributed, independent of one

another. Each group of agricultural land quality and TFP shocks shares a common variance;

for instance, all regional shocks to land quality in sugarcane have the same variance, etc.54 In

particular,

νirt ∼ N(0, σ2νi) for i = 1, 2, 3

νkrt ∼ N(0, σ2νkr)

εirt ∼ N(0, σ2εi) for i = 1, 2

εeit ∼ N(0, σ2εei) for i = 1, 2

εst ∼ N(0, σ2εs)

εiort ∼ N(0, σ2εoir) for i = p, b

δit ∼ N(0, σ2δi

) for i = e, s, 2, k

ϕjrt ∼ N(zjr, σ2ϕjr)

53One of the earliest applications of non-linear FIML to a large equilibrium system was in Fair and Parke (1980),

where the authors compared this approach to estimates from non-linear 3SLS and 2SLS. See also Fair and Taylor

(1983).54I allow the variance of shocks to vary by region for those shocks that are associated with the most cleanly identified

parameters. The shocks to labor shares in composite good production, for instance, are allowed to be region-specific.

This is because, as will be clear below, the maximum likelihood estimate of the associated parameter will simply be

the mean of a certain transformation of the relevant quantities. The estimate of the variance of the associated shock

is simply the average of the squared deviations from the mean.

34

This leaves us with 174 parameters to estimate: (1) Four parameters governing marginal utilities

of consumption, ae, as, a2, and ak; (2) 21 land quality parameters λ0jr, for j = 1, 2, 3 and all regions;

(3) Seven land allocation friction parameters, κ2r; (4) One land quality distribution parameter γ,

where I assume γr = γ for all r; (5) Seven TFP parameters in sugarcane, φ01r; (6) Two CES

parameters ρ in sugarcane and other agriculture; (7) Seven TFP parameters in other agriculture,

φ02r; (8) Seven labor share parameters in composite good production, βor; (9) Seven TFP parameters

in composite good production, φor; (10) Four parameters governing ethanol and sugar production,

αj and βj , for j = e, s; (11) 21 means of the shocks to labor supply, zjr;55 (12) 21 parameters

governing the consumer preference for region-sector, κjr; (13) Three parameters indicating the

propensity to be unemployed, p0, d1|h, and d1|l; (14) Four parameters giving the properties of the

non-labor income distribution, π1, θ1, θ2, and σ; (15) Four parameters controlling the preference for

leisure, β, ψh1, ψh2, and ψh3; (16) 33 parameters governing the variance of shocks on the production

side of the economy; and (17) 21 parameters governing the variance of shocks to preferences.

Crucially, it is the independence assumptions that give us the leverage necessary to identify

such a large number of parameters from so few observations. Without stringent independence

assumptions on the errors, identification would not be possible.

5.2.3 Implementation of MLE

Finally, I describe the implementation of my maximum likelihood approach. Estimation of the

model will actually require maximizing two likelihood functions. One likelihood function deals

with the individual-level data, while the other deals with the aggregate data. This is necessary

because I would not be able to identify the labor supply parameters using the aggregate data alone.

Theoretical identification of the labor supply parameters using only the aggregate data, if even

possible, would rely heavily on the non-linearities of the labor supply functions. Given the small

sample size (only 10 observations on the entire economy), identification using only the aggregate

data would be practically impossible regardless.

Therefore, I proceed with a two-step estimation procedure. First, I estimate the labor supply

parameters using the individual-based likelihood function. Second, I maximize the likelihood func-

tion that comes from writing down the density of (~V1, ~V2). In doing so, I replace the labor supply

parameters in this likelihood function with estimates from the first step. Below, I describe various

approximations used as I ensure coherence between the individual-level estimates and the aggregate

estimates.

While I do not pursue it here, there is an alternative approach to estimation that can avoid the

separation of the individual estimation from the aggregate estimation. The procedure turns on the

fact that we can write an analytical expression for the conditional density f(~V1t|~ψ2t). One could

then use the following procedure: 1) Choose a trial parameter vector of the non-preference shifter55Note that in the complete model, these are not separately identified from the κjr. These items will play a role

in the linearized version of the model pursued below, however.

35

parameters; 2) Use the non-linear constraints to solve for the preference shifters κjrt; 3) Use GMM

and the κjrt to estimate the κjr; 4) Substitute the values of κjrt into the two likelihood functions

(one individual-level likelihood function and one aggregate likelihood function composed of the

conditional densities); 5) Find the values of all non-preference shifter parameters that maximizes

a weighted sum of these two likelihood functions. This procedure is related to the Micro-BLP

approach, presented in Berry, Levinsohn, and Pakes (2004) (for the original BLP approach, see

Berry (1994) and Berry, Levinsohn, and Pakes (1995)). Unlike in the Micro-BLP case, there is no

clear guarantee that one can find a parameter vector such that all the non-linear constraints are

satisified;56 even if one had this guarantee, there are significant computational difficulties. I instead

pursue the two-step estimation method.

Likelihood of Individual Labor Supply Decisions

For each individual, we potentially observe four choices: whether or not they work, the region

of work, the sector of work, and hours. The last three are observed only for those individuals

who work. To assure coherence of the individual and aggregate models, the likelihood function

conditions on the vector of region-sector wages ~wjr and national-level non-labor income Mt. Let

dit = 1 if individual i works, and equal zero otherwise. The likelihood function is:

L =∏t

Nt∏i=1

[Lit(dit = 1, hijrt, sit = (r, j)|~wjr,Mt)]dit [Pr(dit = 0|~wjr,Mt)]1−dit

where hijrt is the hours choice and sit is the region-sector choice, with sit taking a value (r, j),for r = 1, ..., 7 and j = 1, 2, 3. Given the functional form and distributional assumptions from themodel section above, for workers we have

Lit(dit = 1, hijrt, sit = (r, j)|~wjr,Mt) = P (dit = 1, sit = (r, j)|hijrt, ~wjr,Mt)f(hijrt|~wjr,Mt)

where, leaving the conditioning implicit and dropping some subscripts, we have:

P (d = 1, s = (r, j)|h) =∑z

Pr(κ4z|h)eκjrββ−1[w1−β

jr (T − ψh − h)]

D(z)

D(z) = eκ4z (T − ψh)β[

wjrβ(1− β)

[(1− β)(T − ψh)− h]

]1−β+

∑p,k∈S1

eκpkββ[w−βpk (T − ψh)(wpk − wjr) +

wjrw−βpk

β(T − ψh − h)

]

f(h) =1

σ√

2π

∑m

πm

exp

(− 1

2σ2

[ln(wjrβ

[(1− β)(T − ψh)− h])− θm

]2)(1− β)(T − ψh)− h

56One can show that under certain conditions on the non-preference shifter parameters, the non-linear system will

have a unique solution. But it is not clear that these conditions will always hold.

36

For non-workers, the likelihood contribution is given instead by:

Pr(d = 0) =∑z

∑m

d(z|m)πm

∫ ∞−∞

eκ4(T − ψh)β( eθm+µ

1−β )1−β

Kf(µ)dµ

K = eκ4z (T − ψh)β(eθm+µ

1− β )1−β +∑

p,k∈S1

eκpkββ [w1−βpk (T − ψh) + w−βpk e

θm+µ]

I take two steps to ensure the coherence of the individual-level estimates with the aggregate econ-

omy. First, constraints on the non-labor income parameters in the likelihood function ensure that

in any given year, the expected value of non-labor income will equal per-capita non-labor income

in the aggregate data. Second, I constrain the ϕ preference shifters to approximately ensure that,

for any given region-sector-year, the analytical expression for aggregate labor supply to any region-

sector combination is equal to aggregate labor hours in that region-sector in the data. In practice,

I use a linearized version of the constraints. I solve for the ϕjrt as a linear function of labor hours,

wages, and non-labor income using the linear approximation to labor supply, and substitute these

expressions for ϕjrt into the likelihood function.

I maximize the resulting likelihood function using two other approximations for computational

purposes. The probability of being unemployed is an integral over non-labor income. I numerically

approximate this integral using Gauss-Hermite quadrature with 20 nodes (See, e.g., Judd (1998)).

The other issue is that, in dealing with labor supply, it is important to take into account the fact

that for certain values of non-labor income, the probability of being in particular region/sector com-

binations is zero (due to the zero hours constraint). This leads to a discontinuity in the likelihood

function. To smooth the likelihood function, I multiply the value of being in each region-sector by

Φ(h/sd), where h gives desired hours of work and sd is a small, fixed constant. I use sd = 0.1, and

this causes Φ(h/sd) to be close to 1 when h > 0, and close to zero when h < 0.

Likelihood Function for Aggregate Quantities

Denote the entire vector of endogenous variables in the economy in period t as ~Vt = (~V1, ~V2)

and the entire vector of errors as ~ψ = (~ψ1, ~ψ2). Let the notation ~Zr = (Z1, Z2, ...) represent the

vector of variables Z for all seven regions, and leave the subscripts “t” implicit. Let

~V1 = (~Y1r, ~Y2r, ~S1r, ~S2r, ~Yor, Ye,M, p1, pe, YXs , Y X

2 ,KD, ~w1r, ~w2r, ~w3r)

~V2 = (~L1r, ~L2r, ~L3r)

ψ1 = (~ε1r, ~ν1r,~ε2r, ~ν2r, ~ν3r, ~νkr,~εbor,~ε

por, εs, εe1, εe2, δ2, δe, δs, δk)

ψ2 = (~ϕ1r, ~ϕ2r, ~ϕ3r)

Note that the length of ~V1 and ~ψ1 are both 63, while the length of both ~V2 and ~ψ2 are 21.

37

The joint density of ~Vt is:

f(~V1t, ~V2t) = g(~ψ1t(~V1t, ~V2t), ~ψ2t(~V1t, ~V2t))det

(∂ψ1

∂V1

∂ψ1

∂V2

∂ψ2

∂V1

∂ψ2

∂V2

)

= g(~ψ1t(~V1t, ~V2t))g(~ψ2t(~V1t, ~V2t))det

(∂ψ1

∂V1

∂ψ1

∂V2

∂ψ2

∂V1

∂ψ2

∂V2

)

since ~ψ1 and ~ψ2 are independent. In fact, the errors within the vectors ~ψ1 and ~ψ2 are independent

as well, which breaks apart this density even further.The next step in constructing the likelihood function involves finding expressions for the error

vectors ~ψ1 and ~ψ2 in terms of the endogenous variables. These expressions can then be substitutedinto the densities above in the change of variables formula. There are convenient expressions for~ψ1:

ε1rt =ρ1 − 1

ρ1ln(

Y1rt

L1rt) +

1

ρ1ln(

2w1rt

p1t)− φ1r

ν1rt = ln(Y1rt

A∗rt(S1rt)1−γrΓ(1− γr))− ρ1 − 1

ρ1ln(

Y1rt

L1rt) +

1

ρ1ln(

p1tY1rt − w1rtL1rt

w1rtY1rt)− λ1r

ε2rt =ρ2 − 1

ρ2ln(

Y2rt

L2rt) +

1

ρ2ln(

2w2rt

p2t)− φ2r

ν2rt = ln(Y2rt

A∗rt(S2rt)1−γrΓ(1− γr))− ρ2 − 1

ρ2ln(

Y2rt

L2rt) +

1

ρ2ln(

p2tY2rt − w2rtL2rt

w2rtY2rt)− λ2r

ν3rt = γrln(1− S1rt − S2rt)− ln(S1rt) + ln

(p1tY1rt − w1rtL1rt

A∗rtΓ(1− γr)

)− λ3r

νkrt = ln(S2rt

S1rt) + ln(

p1tY1rt − w1rtL1rt

p2tY2rt − w2rtL2rt)− κr

εst = ln

(p1tβs

pstβs − rt

)− ln(αs)

εe1t = ln

(p1tβsYet

βs(p1t

∑r Y1rt − pstYst) + rtYst

)− ln(αe)

εe2t = ln

(rtβsYet

βs(petYet + pstYst − p1t

∑r Y1rt)− rtYst

)− ln(βe)

εbort = ln (potYort − w3rtL3rt)− ln(w3rtL3rt)− βor

εport = log(rtpot

) + log

[potYort

potYort − w3rtL3rt

]+

w3rtL3rt

potYort

[log(

potYort − w3rtL3rt

rtL3rt)

]− φor

δat = ln

(p2t(

∑r Y2rt − Y X2t )

pot∑r Yort + p2tY X2t + petY Xet + pstY Xst

)− a2

δet = ln

(pet(Yet − Y Xet )

pot∑r Yort + p2tY X2t + petY Xet + pstY Xst

)− ae

δst = ln

(pst(Yst − Y Xst )

pot∑r Yort + p2tY X2t + petY Xet + pstY Xst

)− as

δkt = ln

(rtK

Dt

pot∑r Yort + p2tY X2t + petY Xet + pstY Xst

)− ln

(pot∑r Yort + p2t

∑r Y2rt + petYet + pstYst − τt

pot∑r Yort + p2t

∑r Y2rt + petYet + pstYst

)− ak

38

where

rt =1K̄t

[Mt + τt −

∑(p1tY1rt − w1rtL1rt + p2tY2rt − w2rtL2rt)

]pstYst =

∑j

∑r

wjrtLjrt +Mt + τt − petYet −∑r

potYort −∑r

p2tY2rt − rtKDt

Unfortunately, there are not analogous, simple analytical expressions for ~ψ2. Instead, recallingthat the elements of ~ψ1 will appear in the preference shifters κ, we have:

LSjrt = Nt

[∑m

πm

∫ ∞−∞

[(1− β)(T − ψhj)−β

wjrteθmt+µ]Pr(j, r|θmt, µ)f(µ)dµ

]

where

f(µ) =1

σ√

2πe−12 (µ

σ)2

Pr(j, r|θm, µ) =∑z

dz|θmeκjrββ [w1−β

jr (T − ψhj) + w−βjr eθm+µ]

eκ0z (T − ψh0)β( eθm+µ

1−β )1−β +∑k,p∈S1 eκkpββ [w1−β

kp (T − ψhp) + w−βkp eθm+µ]

if r, j ∈ S1

= 0 if r, j /∈ S1

Analogously to the case of individual-level estimation, I linearize the labor supply functions to

write linear expressions for aggregate labor hours as a function of wages, non-labor income, and

the shocks ϕjrt. As noted above, the zjr are not separately identified in the complete model. The

linearization allows us to obtain estimates of the zjr, but it is difficult to know what these estimates

mean; for instance, the estimates will in part simply reflect the approximation error.57

I make two additional simplifications motivated by preliminary estimation. First, I discretize

the parameter space of the land quality variance parameters γ.58 For the estimates below, I

constrain γ to be identical across regions, and perform a grid search to locate a maximum of the

likelihood function. Second, and more importantly, I placed upper bounds on the value of ρ1 and

ρ2. Such a bound proved necessary because the maximum value of the likelihood function was

actually achieved at values of 1 for both parameters. This seems highly implausible, based on a

consideration of the economics behind these parameters; perfect substitutability in any agricultural

sector is clearly unlikely. Given this consideration, as well as the fact that imposing constraints

from economic theory is especially important with such small samples and limited variation, I chose

to impose upper bounds. I use 0.6 as an upper bound, where the choice was informed by the range

of values seen in the simple regression results from estimates of the labor productivity equations

above.57The estimates of zjr are of relatively small magnitudes, which provides some comfort; however, this does not

speak fully to the concern here.58Preliminary estimation attempts allowed this parameter to be continuous and vary by region. Due possibly to

practical constraints on identification with the given data, optimization algorithms failed to locate a local maximum,

though each region’s values of γ at the termination of algorithms were close to one another, and quite close to the

estimate presented below.

39

5.3 Estimates of the Model

A final change to the estimation procedure described above concerns the likelihood function used

for the individual-level data. In the expression for those who choose to work, Pr(κ4z|h) appears.

This is the probability that the individual has a particular value for the unemployment preference

shifter, conditional on hours of work. In estimation, I use the simpler unconditional probability

Pr(κ4z). The implications of this for the estimates are uncertain.

With these caveats in mind, Tables 9-12 show the estimates of the model. Standard errors

are not shown here. While asymptotic standard errors would be meaningful for the estimates

of the labor supply parameters – which rely on a large number of individual-level observations

from the PNAD data – they would be potentially very misleading for the production parameter

estimates. These latter parameters are estimated from only 10 years of data, necessitating small

sample corrections that are not pursued here.

To begin with, Table 9 display estimates of all the parameters affecting labor supply, except for

the region-sector preference shifters. The estimation was performed using 168 as the total number

of possible hours one could work; that is, the estimation was performed on a weekly basis, rather

than an annual basis. Therefore, the estimates of the ψhi parameters give the threshold level of

leisure for one week, and the estimates of the non-labor income distribution parameters refer to

non-labor income for one week.59

The first column of the table addresses preferences for leisure. The estimates there suggest that

workers in other agriculture or non-agriculture obtain a slightly higher marginal utility of leisure

than workers in sugarcane, and have a slightly higher requirement for leisure. The second column

speaks to the propensity to be unemployed and the income of the unemployed. The estimate of

κ4, in combination with the estimates of the region-sector preference shifters in the following table,

suggest that the data are consistent with the population being divided into two groups, one of

people who always work, and one of people who almost never work. The estimate of d1|l means

that, conditional on being a low permanent income person (i.e., having θ = θ2), that person is

always in the work force. Conditional on being a high income person, the probability of being

in the work force is about 0.52. The third column of the table described the non-labor income

distribution further. The unconditional probability of being the high type of non-labor income is

0.7421. Based on the estimate of θ2, there are then about 25% of people who are estimated to

have essentially zero non-labor income. Given limited access to land and other assets in Brazil, this

seems entirely reasonable.

Table 10 presents the remaining non time-varying parameters determining labor supply choices.

The table contains estimates of the region-sector preference shifters. While a full understanding

of preferences for region-sector would require seeing the estimates of the ϕjrt and their means, the

59This choice does not produce any consistency problems when it comes to the aggregate data; weekly labor supply

is simply multiplied by 52 to form annual labor supply where necessary. At the same time, using weekly hours helped

computationally.

40

estimates in Table 10 begin to suggest a few points: The sugarcane sector is much less desirable

than the other sectors; non-agriculture tends to be the most preferred sector within any region;

and the first three regions – which form the South and Southeast of the country – tend to be the

most desirable to work in.

Estimates of the parameters common to all regions and using the aggregate data appear in

Table 11. The fact that the ρ parameters both hit their upper bounds suggest a high degree of

substitutability between effective land units and labor. This is surprising in at least sugarcane, and

I looked extensively at portions of the parameter space where ρ1 < 0. This region of the parameter

space yielded lower values of the likelihood function, though I have not attempted formal tests to

see if the differences are statistically significant. Moreover, policy simulations using values of ρ1

that were negative led to unreasonable conclusions; in particular, they showed unreasonably large

increases in median sugarcane land allocations with almost negligible increases in the median value

of total sugarcane production. These results are available upon request, but they suggest that the

positive values of ρ1 are more likely. Considering the degree to which the labor hours needed can

vary with land type – for example, harvesting sugarcane on the hilly landscapes in areas of the

Northeast may involve many more hours of labor per amount harvested than harvesting sugarcane

in Sao Paulo – perhaps the degree of substitutability between effective land units and labor hours

should not be so surprising. Moreover, flatter landscapes permit mechanization; in areas like Sao

Paulo, a small though not insignificant share of the harvest is mechanized.

Next, I turn to the remaining parameters in Table 11. The value of γ is at the upper bound of

the discretized parameter space that I considered. This indicates a large amount of variance in land

quality within each region. The remaining parameters in the first column describe the variance

to shocks to agricultural land or productivity. The second column deals with ethanol and sugar

production. The estimates of αe and αs suggest that each metric ton of sugarcane can produce

slightly more cubic meters of ethanol than metric tons of sugar. The estimates of βe and βs imply

that ethanol requires much more capital than sugar. This result is reasonable qualitatively, but

the magnitude of the difference is disconcerting. The estimates appear to be relatively insensitive

to allowing the values of ρ1,ρ2, and γ to differ, but this warrants exploration into more flexible

production functions in the future. Finally, the estimates in the third column relate to aggregate

consumption, and show that people on average spend their budget shares in highest to lowest order

on capital, the other agricultural good, ethanol, and sugar. The variance estimates suggest that

substantial volatility in budget shares comes from the shocks to the sugar parameter, though one

must remember that these shocks result in changing budget shares for all goods because of the

functional form assumptions used here.

Table 12 shows the estimates of the remaining parameters, which vary by region. One must be

very cautious in comparing the agricultural parameters across regions because of the normalizations

made above. The first two rows show that the Center-South of Brazil holds large advantages

in TFP over the Northeast (Bahia, Pernambuco, and Maranhao) in both sugarcane and other

41

agriculture. That is, conditional on the same number of labor hours, same amount of effective

land units, and same values of αjr, one parcel yields more output in the Center-South than in

the Northeast regions. The third row, for λ1r, shows that Sao Paulo and Pernambuco have the

highest estimates for sugarcane land quality, while Mato Grosso has the lowest. Similarly to the

case of TFP, differences in these parameters across regions are difficult to interpret in terms of land

yields because of regional differences in the values of the normalized α1r. However, going back to

the definition of total effective land units in each sector from Chapter 3, it is clear that higher

values of λ1r correspond to a higher ratio of effective land units in sugarcane to total hectares in

sugarcane. Moreover, one can show that the derivative of sugarcane output divided by sugarcane

land with respect to α1r is negative. This means that if a high labor share region like Bahia has a

lower estimate of λ1r, then holding land shares and wages constant across regions, Bahia will have

a lower sugarcane yield than the comparison region. Similar statements can be made in regards

to λ2r. The estimates of κ suggest that Parana and Sao Paulo have a bias toward sugarcane land,

while Mato Grosso in particular has a bias toward other agricultural land.

Moving on to the remaining parameters in the table, the estimates of φor imply that Pernam-

buco and Maranhao’s composite good sectors have low relative total factor productivity, and the

estimates of βor show that these two regions also tend to have the highest labor shares in com-

posite good production. Finally, the estimates of the zjr parameters confirm the suggestion of the

region-sector preference shifter estimates from above that sugarcane is a highly undesirable sector,

conditional on constant wages across sectors. Nevertheless, the large negative estimates in non-

agriculture – especially in Sao Paulo – should make us wary about the other tentative conclusions

from the region-sector preference shifter estimates.

For all of the parameter estimates, it is difficult to provide intuitive interpretations. For that

reason, I avoid further discussion of the estimates and move to the simulations that use these

parameter estimates.

6 Simulations

The primary goal of this paper is to use the estimates to simulate the effect of changes in inter-

national ethanol policies on Brazil. In order to do so, I use the parameter estimates to form the

system of nonlinear equations implied by the equilibrium conditions, the system identical to that

used in FIML estimation. I first solve the nonlinear system in the baseline case, where interna-

tional demand for sugar and ethanol is treated as inelastic and the price of ethanol is determined

domestically. Then I simulate three alternative environments. In the first, international demand

for ethanol becomes perfectly elastic at a world price that is 10% higher than the price in the

baseline. In the second and third, demand again becomes elastic, but now at a world price that is

12% and 15% higher than the baseline price. For reasons discussed below, the simulations increase

the world sugar price by the same percentage as the world ethanol price. The first section discusses

details behind the method of simulation, and compares the 2005 data with baseline simulations of

42

the model. The second section covers the results of the simulations of alternative trade regimes.

6.1 Simulation Methods

In running the baseline simulations, I need to make several choices. In what follows, I list the key

choices, along with a short description of each:

• “Baseline” year. Simulating the model first requires making a choice of which year’s

exogenous variables to use. As a reminder, the exogenous variables are: the total number

of individuals, the world sugar price, the world agricultural price, the world composite good

price, the level of ethanol exports, the total amount of land available in each region, the total

capital stock, and the level of government taxes/spending. I choose to use the most recent

values in my data, from 2005.

• Number of draws. The structural model has stochastic elements. One simulated equilib-

rium involves drawing one vector of error terms from the normal distributions in Chapter 5,

and then solving the system of equilibrium equations for the endogenous variables. Since any

resulting vector of endogenous variables is random, it is important to have multiple realiza-

tions of this vector to ascertain something about the characteristics of the distribution. This

necessitates multiple draws of the vector of error terms, with the equilibrium system solved

at each draw. I make 300 such draws.

• Fixing particular error terms. There is no guarantee that a unique equilibrium exists for

any given draw. Initial experimentation with the simulations suggested that it would be very

difficult to find equilibria if I were to draw all 84 error terms. However, as noted above, FIML

guarantees the existence of a unique equilibrium in the neighborhood of the 2005 values for

the error terms. Therefore, loosely speaking, the more error terms that are fixed at their 2005

values, the better the chance of finding an equilibrium. With this in mind, I fix the error

terms for composite good production, ethanol and sugar production, and aggregate good

consumption. I take error draws for all the agricultural parameters and all the labor supply

region-sector preference parameters.

• Restrictions on equilibria. I confine myself to equilibria that have strictly positive land

shares for all uses in all regions, strictly positive wages bounded above by the value of 6 Reais,

strictly positive quantities of production for all goods in all regions, and strictly positive

agricultural profits in both sugarcane and other agriculture in all regions.

• Summary measure. Each simulated equilibrium yields one possible realization of the en-

dogenous variables. It is therefore necessary to have some measure that can summarize the

results of a large number of simulations. Because of concerns about the sensitivity of the mean

43

to outliers, I use the median as a summary measure below.60 Importantly, this method of

summarizing the outcomes means that equilibrium constraints will not in general hold across

the medians presented in the tables below. For instance, the median sugarcane land share

across simulated equilibria, plus the median other agriculture land share, plus the median

non-agriculture land share will not in general sum to 1. However, within any one simulated

equilibrium, the three land shares will sum to one in a region, and all other equilibrium

constraints will hold as well.

6.2 Baseline Simulations

I now turn to the results of the baseline simulations. Of the 300 sets of simulated draws of the error

terms, 253 resulted in equilibria. Tables 13 and 14 compare the median outcomes from the baseline

set of 300 simulations with the actual 2005 data. In doing these comparisons, it is important to

keep in mind that there is no reason to think that the ideal model would have median outcomes

that replicate the 2005 data. My intention here is only to show that the median outcomes are

reasonable in magnitude, where their reasonableness is suggested by their closeness to the actual

2005 outcomes.

Table 13 illustrates that key aggregate quantities in the 2005 data are quite close to the median

of these aggregates from the baseline simulations. As expected, the most comparable aggregates

involve endogenous variables that are primarily determined from equations that hold the error draws

fixed at 2005 values. For example, note the closeness of the median composite good production

and rental rate to the 2005 analogues. However, even the median sugarcane and other agricultural

production amounts – which should be more affected by the stochastic elements of the system –

are fairly close to the 2005 values.

The next table, Table 14 looks at the medians of regional outcomes from the baseline simulations.

In particular, the table examines land shares and wages in sugarcane, other agriculture, and non-

agriculture. The actual 2005 outcomes appear under the columns labeled “2005”, while the medians

of the baseline simulations appear under the column “Base”. Note that the other agriculture land

shares are almost identical to three digits, and the other agriculture wages differ by only small

amounts. The largest discrepancies between the 2005 and median baseline values are for sugarcane

land shares and wages. This should be expected, given that land quality and TFP in sugarcane

have higher estimated variances than their other agriculture counterparts (see 11). Of particular

note is that the Mato Grosso land share is higher than what is seen in the data in most years. As

we will see below, this leads to a higher number of median acres in sugarcane production across

Brazil than the actual 2005 value. Still, most sugarcane values from the baseline simulations appear

reasonably close to their 2005 counterparts.60Conceivably, one would also be interested in other aspects of the distribution of simulated outcomes, such as the

variance or 75th percentile. Depending on how risk averse one is, a policy choice could be made on the basis of a

higher percentile or lower percentile.

44

A comparison of variables not shown in these tables also reveals a fairly close correspondence

between the median of the baseline simulations and the 2005 data. I next use the model to simulate

the effect of expanding ethanol export opportunities on median outcomes, with the primary out-

comes of interest being ethanol production, sugarcane production, and declines in non-agricultural

areas.

6.3 Simulations of Alternative Policy Regimes

The primary goal of this paper is to determine whether a removal of US barriers to ethanol imports

would lead to enough deforestation in Brazil to offset the positive environmental impacts of the

Brazilian ethanol that could be exported. That is, how large would the increase in the supply of

Brazilian ethanol to the US be relative to the increase in land clearing of environmentally sensitive

areas?

This section answers this question. I represent the removal of US barriers in the simple way

noted in Chapter 3. I consider the following policy changes in the simulations: The international

(essentially US) demand for ethanol becomes perfectly elastic at a price 10%, 12%, and 15% above

the 2005 price, while the world sugar price increases by the same percentage as the ethanol price

in each of the three cases.61 A sharp increase in the ethanol price amid falling trade barriers could

certainly lead to increased sugar prices, as sugarcane in Brazil and elsewhere could be diverted to

the production of ethanol. Nevertheless, in the third sub-section, I address concerns about this

assumption.

Are these price increases for ethanol reasonable? As a point of reference, the 2005 price of

ethanol in the data is about US$1.77 per gallon. Considering that the energy equivalent of 1 gallon

of ethanol is around 0.7 gallons of petroleum (see Wolak (2007)), the cost of an amount of ethanol

equivalent to one gallon of petroleum in 2005 is $2.53. It is hard to know how this price relates

to the hypothetical price at the pump in the US, since the ethanol price in my data are derived

from the export price of ethanol. Still, this suggests that the 10%, 12%, and 15% price increases on

the 2005 level could keep ethanol competitive with petroleum in times of relatively high petroleum

prices.

As a final note, for each of the three alternative policy environments, I take 300 draws of the

error vector, try to find an equilibrium for each draw, and then calculate the median of outcomes

over all the equilibria. In particular, for all the alternatives, I use the same draws of 300 vectors

that were used in the baseline simulations. Equilibria were found in 269, 254, and 249 of the error

draws for the 10%, 12% and 15% alternatives, respectively.

The simulation results broadly suggest that Brazil could supply the US with a significant amount

of ethanol without posing an extreme risk to forested areas and other environmentally sensitive parts61Importantly, I do not consider any endogenous changes in Brazilian government policy, producer productivity, or

land quality in response to the policy change. For instance, Hay (2001) and Muendler (2002) find that in Brazilian

manufacturing, productivity tended to improve as firms faced increased competition due to changes in the tariff

structure.

45

of the country. Below, I make this statement precise. The discussion relies on the median values

of key variables over all the equilibria that appear in Tables 15-18. The medians of the baselines

simulations appear in rows or columns denotes “Base”, while the medians for the simulations with an

x% change in ethanol/sugar prices appear in the rows or columns denoted “x%”, for x = 10, 12, 15.

Note that the medians from the baseline simulations – rather than the actual 2005 data – serve as

the proper points of comparison with the medians from the alternative regime simulations.

6.3.1 Ethanol Production and Exports Increase Substantially

The comparison between the medians for the baseline and the alternative regimes reveals that

all three alternatives lead to a substantial increase in ethanol production and exports. Table

15 displays the medians of key aggregate quantities under each policy environment. The initial

movement from the baseline to the 10% regime leads to a massive increase in the median amount

of ethanol produced. The median production increases from 4.1 to 8.9 billion gallons, allowing

exports of ethanol to jump from a baseline level of 684 million gallons to 5.5 billion gallons. To

gauge the size of this number, note that in 2007, total US production of ethanol was 6.5 billion

gallons.

The projected increases are much larger for the 12% and 15% regimes. Median ethanol produc-

tion and exports are predicted to jump to 15.9 billion and 12.4 billion gallons, respectively, in the

12% regime. An export total of 12.4 billion gallons would make a sizeable impact on the US fuel

mix. As noted in the introduction, with 13 billion gallons of ethanol the US could have used ten

percent ethanol blends in all of its 2007 gasoline consumption. In the 15% regime, median ethanol

exports move to 21.2 billion gallons, which by itself falls just short of the 2016 renewable fuels

mandate in the 2007 US energy bill. These predictions suggest that Brazil could have a significant

impact on the shift to low-carbon fuels in the US.62

6.3.2 Less Sugar and More Sugarcane Enable Greater Ethanol Exports

This substantial increase in ethanol exports comes from the movement of sugarcane away from

sugar production and into ethanol production, as well as an increase in total sugarcane production.

The third column of Table 15 illustrates the decline in sugar production. Median sugar production

falls from 27.8 million metric tons (MT) in the baseline to 19.5 million MT in the 10% regime and

essentially zero in the 12% and 15% regimes. Correspondingly, median net exports of sugar also

fall dramatically, as seen in the seventh column of the table. The fact that median net exports are

slightly higher than median sugar production should not be disconcerting, since one must remember

that these two values do not come from the same equilibrium.62One must keep in mind that these results assume nothing is changing in terms of domestic ethanol consumption

within Brazil; if domestic preferences for ethanol increased at the same time as the policy change (because of increased

purchases of flex fuel vehicles, for instance) one would expect significant implications for the amount of ethanol

exported.

46

The increase in ethanol exports also comes from an increase in total sugarcane production. The

first column of Table 15 shows that sugarcane production jumps from a median of 355 million MT

in the baseline to 392, 424 and 478 million MT in the 10%, 12%, and 15% regimes. In principle,

these increases could come through intensified cultivation of existing sugarcane land. Alternatively,

they could come through extensive changes in land allocated to sugarcane.

The results in Table 16 suggest that the production increases actually come through the latter

channel. This table shows the millions of acres allocated to each use under each regime, for all seven

regions. In moving from the baseline simulations to the 10% regime, median sugarcane acreages

increase in every region. In terms of absolute number of acres, the largest changes occur in Mato

Grosso, followed by Sao Paulo. The increases in Mato Grosso – despite the low land quality in

sugarcane, and the strong preference not to work in sugarcane there – are helped along by the

low land quality in other agriculture, the high TFP levels in sugarcane, and the high degree of

substitutability between effective land units and labor. As we next move to the 12% and 15%

regimes, the sugarcane land allocation changes in all the regions are massive, with particularly

large absolute changes in Mato Grosso, Minas Gerais, and Maranhao.

Interestingly, these large shifts of land to sugarcane occur even as median aggregate sugarcane

production increases by a relatively small amount. The high variance of land quality – and low

mean levels of land quality in many regions – implies that the marginal land coming into play is

relatively ineffective in sugarcane production. Moreover, as we will see below, labor hours per acre

in sugarcane appears to drop as sugarcane production expands, putting further downward pressure

on yields.

6.3.3 Consequences for Land Clearing are Non-Linear

Given that Table 15 shows median values of other agricultural production to be stable or increasing

across regimes, and that sugarcane land expands greatly across regimes, the natural concern is that

all these changes are happening at the expense of a great deal of non-agricultural land. However,

the picture is a bit more subtle than this. The sugarcane expansion is accompanied by a decrease

in at least some land for other agriculture in many regions. The net result is that a large expansion

of ethanol exports happens at the expense of relatively little non-agricultural land in the 10% and

12% regimes, but the marginal increase in exports from a shift to the 15% regime comes at the

expense of a large amount of non-agricultural land.

Again, Table 16 shows the relevant results. By looking at the second and third panel, for

other agriculture and non-agriculture median land use respectively, it is clear that the sugarcane

expansion is being absorbed to some extent by decreases in other agricultural land in all regimes.

For instance, looking again at Mato Grosso, median sugarcane land increases about 20 million

acres from the baseline to the 12% regime. At the same time, median other agricultural land falls

by about 10 million acres under this policy change, as does non-agricultural land. The degree to

which other agricultural land absorbs the sugarcane expansion varies across regions, ranging from

47

very strong decreases in Parana and Sao Paulo to apparent increases across regimes in Maranhao.

An increase in other agricultural labor hours (see below), and perhaps a shift of other agricultural

production across areas, keeps total other agricultural production from falling.

What are the ultimate implications of the sugarcane expansions and accompanying changes in

other agricultural land for non-agricultural land clearing? To make the size of non-agricultural

land clearing concrete, it is useful to think about the quantity of non-agricultural land traded off

for a quantity of ethanol exports. The 12$ regime leads to an increase in ethanol exports from the

baseline of about 12 billion gallons, while moving from the 12% regime to the 15% regime leads

to a further increase of 8.7 billion gallons (for a total increase of about 21 billion gallons relative

to the baseline). The first 12 billion gallons of additional ethanol exports come at a median cost

of 37 million acres of non-agricultural land over all of Brazil. This is large (an area about the size

of New York), but seemingly manageable if it is distributed across the country. However, the next

8.7 billion gallons of exports come at a median cost of an additional 86 million acres, which should

cause great concern.

The situation is especially worrisome in Mato Grosso and Maranhao, two regions containing at

least portions of the Amazon Rainforest. The first 12 billion gallons of ethanol exports come at a

cost of 10 million acres of non-agricultural land in Mato Grosso, and 9 million acres in Maranhao.

The next 9 billion gallons of exports come at a further cost of 29 million acres and 24 million acres

in Mato Grosso and Maranhao, respectively. This dramatic non-linearity in land clearing with

respect to exports suggests that there could be a substantial amount of ethanol exported without

causing concern, but that moving to very high levels could pose a serious environmental risk.

6.3.4 Labor Supply Plays a Role

Labor supply to the agricultural sectors plays an important role in the results seen above. Tables

17 and 18 describe the changes in median wages and median annual labor hours across the regimes.

Two points emerge from these tables. First, the ability to substitute labor for land in other agricul-

ture facilitates decreases in other agricultural land area (by facilitating more intensive agriculture).

Movements in median other agricultural labor hours help to stabilize other agricultural production

levels across regimes, even as land allocations to the sector fall. This is most apparent in the move

from the baseline to the 15% regime. This is also true for particular regions in the 10% and 12%

regimes.63 In practice, this means more intensive cultivation of each acre. One way in which this

could be achieved in practice is by switching from pasture to high value export crops, for instance.

As we would expect, Table 17 shows a corresponding increase in the other agricultural wage relative

to the non-agricultural wage across regimes, necessary to draw in labor.63Note that this is likely not the whole story in the 10% and 12% regimes, since some regions do not show labor

hour increases. There may be a composition effect, wherein the land being brought out of other agriculture was

relatively unproductive, so that total production does not fall much. There could also be a re-allocation of other

agricultural production across regions.

48

The second point in the tables is that sugarcane production uses dramatically less labor per

acre in the alternative regimes, likely because of inelastic labor supply to the sugarcane sector.

Table 18 shows that relative to land allocations, median annual labor hours in sugarcane increase

by a relatively small amount.64 Therefore, as we move from the baseline to the various regimes,

median hours per median number of acres fall sharply. In practice, this could be facilitated by

less intensive harvesting of each acre, or use of more land suitable for mechanical harvesting, or a

combination of both. The amount by which labor hours per acre fall appears to be so large that

this may warrant further refinement of the model. But the central point is that labor supply to

sugarcane is inelastic and sugarcane producers can economize on labor by choosing more land and

more appropriate land.

6.3.5 Caveats

The results present a compelling story. Still, it may be possible that the inflexibility in production

and trade relationships for ethanol and sugar influences the results in important ways. One issue

is that one may think that the flooding of the ethanol market with Brazilian ethanol would help

dampen the price increase; given this, 15% may be “too large” a price increase to expect, though

it is difficult to say without a more complete model of international ethanol demand. Another

issue is that the zero-profit conditions impose a tight relationship between the prices of ethanol,

sugar, sugarcane, and capital. Once the ethanol price becomes internationally determined, the two

zero-profit conditions completely determine the price of sugarcane and capital.

The tight relationship imposed by the zero-profit conditions has two implications. First, it

necessitates strong assumptions on the joint movement of sugar and ethanol prices. One can show

that an increase in the ethanol price that holds the sugar price constant must have an opposite effect

on the sugarcane price from an increase in the sugar price that holds the ethanol price constant.

Given the estimates, an increase in the ethanol price holding the sugar price constant will actually

decrease the sugarcane price in our case. It is this fact that necessitates the assumption of increasing

sugar prices along with increasing ethanol prices.65

The other implication of the tight relationship in these prices is that the increase in ethanol

and sugar prices causes the capital price to rise, which causes wages in the composite good sectors

to fall through the composite good zero-profit conditions. Indeed, median wages in non-agriculture

fall monotonically as one moves across regimes in the third panel of Table 17. The falling wages

in non-agriculture allow the sugarcane and other agriculture sectors to draw in more labor hours

without sizable increases in the absolute level of wages in those sectors. This is critical because it

helps keep sugarcane and other agriculture profitable on land parcels that would otherwise not be

profitable. These considerations suggest that making ethanol and sugar production more flexible64Again, as in other agriculture, median sugarcane wages increase relative to non-agricultural wages to draw in

labor.65The zero-profit conditions guarantee that after the policy change, an increase of x% in the ethanol and sugar

price leads to exactly an increase of x% in the sugarcane price.

49

could have important effects on the simulation results.

7 Conclusion

The quest for alternative sources of energy in the US has led to greater interest in ethanol and other

bio-fuels. This interest has crystallized into stringent renewable fuel mandates in the 2007 energy

bill. Under that law, renewables must constitute steadily increasing amounts of total US trans-

portation fuel each year, with a requirement of 36 billion gallons by 2022. As bio-fuels requirements

increase, corn-based ethanol has so far been the primary bio-fuel source and corn producers have

been the primary beneficiaries. Under current policies, the only serious technological alternatives

to corn-based ethanol may still be years away from being cost effective.

Of course, current policies could change. The US protects its ethanol producers with significant

import restrictions. The Brazilian government has been pushing – with no success – to lift them. By

allowing free entry of Brazil’s lower-cost sugarcane-based ethanol, the US government could make

it easier to move the US transportation fuel mix away from petroleum and avoid the economic side

effects of the current reliance on corn in the process.

However, there is a crucial tradeoff for the environment involved. Freeing the US ethanol

market could have substantial environmental benefits, as the lower cost of ethanol could encourage

movement away from petroleum and, equally importantly, the net carbon savings of sugarcane-

based ethanol are several times greater than corn-based ethanol. On the other hand, the sugarcane

necessary to produce ethanol has to be produced somewhere in Brazil. What carbon could be saved

by shifting energy consumption of vehicles to ethanol could be quickly lost through deforestation of

the Amazon or Atlantic Rainforests. Moreover, deforestation and clearing of other environmentally

sensitive areas could have important effects on bio-diversity and eco-system functioning.

This paper addresses this tradeoff by answering the question: Would freely importing Brazilian

ethanol into the US lead to enough land clearing to offset the environmental benefits of using larger

quantities of more energy efficient ethanol?

In short, I find that Brazil could increase ethanol exports sharply in response to a removal of

US import restrictions. The cost in terms of land clearing could be manageable until exports reach

a very high level, at which point there would be a strong risk of destructive land clearing. More

concretely, the results indicate that an additional 12 billion gallons of ethanol exports could come

at a median cost of only 37 million acres of non-agricultural land. However, if the international

ethanol price were higher, Brazil would export more and the next 9 billion gallons of exports would

require an additional decline of approximately 86 million acres. In absolute terms, the greatest

damage would occur in the Mato Grosso region, the region of the model that includes the Amazon

Rainforest.

Of course, the model defines regions very broadly. For instance, my Mato Grosso region contains

the very large states of Mato Grosso, Mato Grosso do Sul, Goias, and Tocantins. Consequently,

a predicted decline in non-agricultural land in the Mato Grosso region may not necessarily come

50

from the Amazon, just as a predicted decline in Parana may not come from the Atlantic Rainforest.

Importantly, in the event of a US policy change, exactly where such a decline comes from will – to

a large extent – be under the control of the Brazilian government in the coming years. This is not

only because of decisions over the enforcement of forest regulations. A number of other decisions

could also influence exactly where land is cleared in an ethanol boom. For instance, permitting a

new distillery to be constructed in Parana but not Mato Grosso will increase the appropriateness

of land for sugarcane production in Parana and, potentially, keep pressure off Mato Grosso.

Determining the consequences of such policy choices within Brazil is not so straightforward, due

to the possibility of simply displacing other agricultural producers to Mato Grosso. More generally,

to determine the effects of such policy choices will require an adequate consideration of the linkages

between land use decisions, labor markets and product markets. This is exactly the value of the

framework developed in this paper; and while I used the framework to address a stylized change in

US trade policy, it has the potential to serve as a foundation for more detailed policy analysis in

the future.

51

A Tables and Figures

Figure 1: Sugarcane Cultivation Area, Eight Quantiles in 2007

Figure 2: Sugarcane Cultivation Area, Eight Equal-Sized Intervals in 2007

52

Figure 3: Regional ClassificationEnvironmentally Sensitive Areas

p

Sriniketh Nagavarapu Brazilian EthanolFigure 4: Amazon and Atlantic Rainforests

53

Figure 5: Prices in the Sugarcane Industry, 1981-2005

1520

2530

35P

rice

(200

0 R

eais

/MT

)

1980 1985 1990 1995 2000 2005

Sugarcane

200

400

600

800

1000

Pric

e (2

000

Rea

is/M

T)

1980 1985 1990 1995 2000 2005

Sugar50

060

070

080

090

0P

rice

(200

0 R

eais

/m3)

1980 1985 1990 1995 2000 2005

Ethanol

2040

6080

100

Pric

e (2

000

Rea

is/B

arre

l)

1980 1985 1990 1995 2000 2005

Petroleum

Figure 6: Prices, Relative to 1995

12

34

5P

rice

(Rel

ativ

e to

199

5)

1980 1985 1990 1995 2000 2005

Sugarcane SugarEthanol Petroleum

54

Figure 7: Agricultural Prices in 1981-2005, Relative to 1981

11.

52

2.5

Pric

e (R

elat

ive

to 1

990)

1980 1985 1990 1995 2000 2005

Sugarcane Other Ag.

55

Figure 8: Regional Sugarcane Land Shares Relative to 1990

0.5

11.

52

2.5

Can

e La

nd S

hare

(R

elat

ive

to 1

990)

1980 1985 1990 1995 2000 2005

Parana Sao Paulo Minas Mato Grosso

Center−South Regions

Figure 9: Regional Sugarcane Land Shares Relative to 1990

0.5

11.

52

2.5

Can

e La

nd S

hare

(R

elat

ive

to 1

990)

1980 1985 1990 1995 2000 2005

Bahia Pernambuco Maranhao

Northeast Regions

56

Figure 10: Regional Sugarcane Production Relative to 1990

0.5

11.

52

2.5

Can

e P

rodu

ctio

n (R

elat

ive

to 1

990)

1980 1985 1990 1995 2000 2005

Parana Sao Paulo Minas Mato Grosso

Center−South Regions

Figure 11: Regional Sugarcane Production Relative to 1990

0.5

11.

52

2.5

Can

e P

rodu

ctio

n (R

elat

ive

to 1

990)

1980 1985 1990 1995 2000 2005

Bahia Pernambuco Maranhao

Northeast Regions

57

Figure 12: Median Hourly Wages, Center-South 1981-2005

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 1

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 20

.51

1.5

22.

5W

age

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 3

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 5

Figure 13: Median Hourly Wages, Northeast 1981-2005

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 4

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 6

0.5

11.

52

2.5

Wag

e

1980 1985 1990 1995 2000 2005

Cane OthAg NonAg

Region 7

58

Table 2: Land Usage and Production, 2005

Land (Mill. Hectares) Production

Region Sugarcane Other Ag. Other Sugarcane Other Ag.

Parana 0.454 46.733 9.154 31.228 35348.059

Sao Paulo 3.085 14.705 7.028 254.810 12482.325

Minas Gerais 0.582 39.517 27.541 37.181 19310.408

Bahia 0.118 29.430 29.075 7.370 6737.708

Mato Grosso 0.543 122.708 65.124 37.939 27539.441

Pernambuco 0.933 12.625 10.018 49.101 3884.236

Maranhao 0.077 30.846 41.971 4.403 6307.208

Note: Cane production in millions of metric tons;

other agriculture in millions of 2000 Reais

Table 3: Ethanol and Sugar Production, 2005

Region Sugarcane Eth. Quant. Eth. Value Sug. Quant. Sug. Value

Parana 31.228 1.079 923.332 1.582 563.626

Sao Paulo 254.810 9.654 8259.898 16.920 6028.224

Minas Gerais 37.181 1.241 1061.645 2.089 744.248

Bahia 7.370 0.135 115.753 0.224 79.764

Mato Grosso 37.939 2.022 1730.309 1.712 610.121

Pernambuco 49.101 1.424 1218.738 4.034 1437.392

Maranhao 4.403 0.108 92.198 0.019 6.743

Note: Sugarcane and sugar quantities in metric tons,

ethanol quantity in cubic meters. Ethanol and sugar values

in 2000 Reais. All values in millions of respective units.

59

Table 4: Median Hours and Number of Workers by Sector, 2005

Cane Other Ag. Non Ag.

Region Hours Number Hours Number Hours Number

Parana 46 30173 40 2720925 44 9567751

Sao Paulo 48 151129 44 820975 42 15725917

Minas Gerais 48 55817 40 2296550 42 13301037

Bahia 48 26977 40 2172985 40 3783111

Mato Grosso 48 23542 44 1163488 44 4665797

Pernambuco 48 223194 35 1702326 40 4452067

Maranhao 40 35155 30 2499108 40 4070798

Table 5: Median Hourly Wages in 2005 (2000 Reais)

Region Sugarcane Other Ag. Non Ag.

Parana 1.234 1.212 1.914

Sao Paulo 1.740 1.252 2.169

Minas Gerais 1.044 0.957 1.722

Bahia 1.116 0.816 1.276

Mato Grosso 1.640 1.276 1.722

Pernambuco 0.957 0.765 1.276

Maranhao 0.765 0.696 1.148

60

Table 6: Sugarcane Labor Prod. Regressions

Covariates OLS IV-PA IV-PT OLS IV-P IV-T

Log Cane Wage 0.251 0.302 -2.269

[0.170] [0.610] [4.294]

Log Cane Price -0.027 -0.047 0.872

[0.151] [0.331] [1.716]

Log(Wage/Price) Cane 0.111 -0.095 0.328

[0.138] [0.285] [0.438]

Sao Paulo 0.282** 0.255 1.609 0.356*** 0.464** 0.242

[0.132] [0.336] [2.266] [0.121] [0.179] [0.250]

Minas -0.492*** -0.493*** -0.467*** -0.491*** -0.489*** -0.493***

[0.096] [0.097] [0.160] [0.097] [0.097] [0.098]

Bahia -0.456*** -0.457*** -0.394* -0.453*** -0.448*** -0.458***

[0.126] [0.127] [0.228] [0.126] [0.128] [0.128]

Mato Grosso 0.486*** 0.468* 1.379 0.536*** 0.609*** 0.459**

[0.114] [0.237] [1.530] [0.108] [0.140] [0.183]

Pernambuco -0.683*** -0.684*** -0.604** -0.678*** -0.672*** -0.685***

[0.126] [0.127] [0.241] [0.126] [0.128] [0.128]

Maranhao -0.644*** -0.624** -1.629 -0.698*** -0.779*** -0.614***

[0.142] [0.270] [1.691] [0.137] [0.169] [0.213]

Year 0.052*** 0.051*** 0.096 0.052*** 0.058*** 0.046***

[0.006] [0.013] [0.078] [0.006] [0.009] [0.013]

Year*NE -0.038*** -0.038*** -0.054* -0.039*** -0.041*** -0.038***

[0.007] [0.008] [0.028] [0.007] [0.007] [0.007]

Constant 2.075*** 2.157* -1.668 2.309*** 1.566 3.089*

[0.531] [1.261] [6.974] [0.505] [1.031] [1.579]

Observations 154 154 154 154 154 154

NOTE: Dependent variable is the log of the ratio of sugarcane production (metric tons) to total annual labor hours

in sugarcane. “P”, “A”, and “T” indicate that the log of the petroleum price, other agriculture price, and total

population are used as instruments, respectively. Standard errors in brackets – * significant at 10%; ** significant at

5%; *** significant at 1%

61

Table 7: Otherag Labor Prod. Regressions

Covariates OLS IV-T IV-P OLS IV-A IV-P

Log(OthagWage) 1.409*** 4.057*** 2.294***

[0.197] [1.428] [0.417]

Log(OthagPrice) -0.625 -1.033 -0.761*

[0.377] [0.735] [0.430]

Log(Wage/Price) 1.257*** 0.483 2.434***

[0.183] [0.504] [0.507]

Sao Paulo 0.208** -0.255 0.053 0.235** 0.370*** 0.029

[0.089] [0.293] [0.118] [0.089] [0.128] [0.137]

Minas -0.229*** 0.136 -0.107 -0.250*** -0.356*** -0.088

[0.086] [0.249] [0.109] [0.087] [0.116] [0.125]

Bahia 0.156 1.575* 0.630* 0.074 -0.341 0.705*

[0.232] [0.858] [0.324] [0.233] [0.358] [0.378]

Mato Grosso 0.123 -0.049 0.065 0.133 0.183* 0.056

[0.083] [0.179] [0.096] [0.084] [0.098] [0.109]

Pernambuco 0.328 2.071** 0.911** 0.228 -0.282 1.002**

[0.244] [1.017] [0.361] [0.243] [0.406] [0.425]

Maranhao 0.169 2.099* 0.814** 0.058 -0.506 0.915**

[0.252] [1.110] [0.384] [0.249] [0.436] [0.453]

Year 0.024 -0.042 0.002 0.054*** 0.047*** 0.065***

[0.018] [0.048] [0.022] [0.007] [0.009] [0.010]

Year*NE -0.053*** -0.083*** -0.063*** -0.051*** -0.042*** -0.064***

[0.011] [0.026] [0.013] [0.011] [0.013] [0.015]

Constant 3.567** 6.896** 4.680*** 5.923*** 2.403 11.272***

[1.489] [3.275] [1.740] [0.844] [2.296] [2.310]

Observations 84 84 84 84 84 84

NOTE: Dependent variable is the log of the ratio of other agricultural production to annual labor hours in other

agriculture. “P”, “A”, and “T” indicate that the log of the petroleum price, other agriculture price, and total

population are used as instruments, respectively. Standard errors in brackets – * significant at 10%; ** significant at

5%; *** significant at 1%

62

Table 8: Sugarcane Land Share Regressions

Covariates OLS IV OLS-NE IV-NE OLS IV-PA

Log(P1) -0.203 -0.049 -0.122 0.048 0.261*** 0.475***

[0.146] [0.292] [0.197] [0.592] [0.085] [0.179]

Log(P1) ∗NE -0.233 -0.661 -0.187 -0.445

[0.297] [0.942] [0.137] [0.426]

Log(W1r) 0.048 0.926 0.038 -0.268 -0.004 -0.44

[0.156] [1.668] [0.231] [2.503] [0.106] [0.404]

Log(W1r) ∗NE 0.034 2.197 0.373** 1.022

[0.317] [3.420] [0.155] [0.741]

Log(PA) 0.485** 1.026*** 0.502* 1.043**

[0.194] [0.341] [0.270] [0.520]

Log(PA) ∗NE -0.115 -0.098

[0.389] [0.742]

Log(W2r) -0.054 -1.737 0.16 -0.8

[0.171] [1.440] [0.300] [3.031]

Log(W2r) ∗NE -0.252 -1.191

[0.365] [3.365]

Log(S1r, t− 1) 1.221*** 1.294***

[0.074] [0.102]

Sao Paulo 2.549*** 2.402*** 2.515*** 2.855*** -0.951*** -0.933***

[0.100] [0.643] [0.121] [0.812] [0.219] [0.302]

Minas -0.063 -0.268 -0.038 -0.147 -0.699*** -0.733***

[0.073] [0.205] [0.079] [0.390] [0.056] [0.068]

Bahia -1.406*** -1.761*** -0.228 1.015 -0.183 0.883

[0.100] [0.335] [1.589] [5.027] [0.478] [1.618]

Mato Grosso -1.746*** -1.959*** -1.745*** -1.560** -0.395*** -0.146

[0.101] [0.563] [0.115] [0.776] [0.106] [0.225]

Pernambuco 2.019*** 1.354** 3.190** 4.078 -0.625 0.207

[0.115] [0.595] [1.602] [5.009] [0.533] [1.477]

Maranhao -2.031*** -2.386*** -0.852 0.752 -0.097 1.092

[0.115] [0.284] [1.623] [5.399] [0.505] [1.858]

Year 0.017*** 0.026** 0.015* 0.027 -0.009** -0.004

[0.006] [0.011] [0.008] [0.026] [0.004] [0.007]

Year*NE -0.041*** -0.044*** -0.040*** -0.057* 0.004 -0.003

[0.005] [0.008] [0.011] [0.031] [0.005] [0.011]

Constant -5.538*** -8.762*** -5.804*** -9.175** 2.177*** 1.771**

[0.771] [1.896] [1.047] [3.548] [0.503] [0.764]

Observations 145 145 145 145 145 145

NOTE: Dependent variable is the log of the ratio of share of land in sugarcane production to share of land in

non-agriculture. “P”, “A”, and “T” indicate that the log of the petroleum price, other agriculture price, and total

population are used as instruments, respectively. Standard errors in brackets – * significant at 10%; ** significant at

5%; *** significant at 1%

63

Table 9: Utility Function Parameter Estimates I

β 0.4165 p4 11.9696 θ1 5.1842

ψh1 0.0111 d1|h 0.5219 θ2 -5.1141

ψh2 0.0520 d1|l 1 π1 0.7421

ψh3 0.0533 σ 0.5037

Table 10: Utility Function Parameter Estimates II: κjr

Region Cane Other Ag Non Ag

Parana 2.630 6.290 7.036

Sao Paulo 3.480 5.140 10.744

Minas 2.875 6.127 7.442

Bahia 1.836 6.093 6.369

Mato Grosso 1.327 5.419 6.433

Pernambuco 4.107 5.809 6.574

Maranhao 2.252 6.290 6.519

Table 11: Estimates of Parameters Common to Regions

ρ1 0.600 αe -2.202 ae -4.385

ρ2 0.600 αs -2.464 as -5.870

γ 0.995 βe -1.605 aa -2.033

σ2ε1 0.093 βs 1.204 ak -1.073

σ2ε2 0.029 σ2

e1 0.090 σ2δe 0.019

σ2ν1 0.340 σ2

s 0.022 σ2δs 0.362

σ2ν2 0.146 σ2

ε2 0.078 σ2δa 0.019

σ2ν3 0.046 σ2

δk 0.018

64

Tab

le12

:E

stim

ates

ofR

egio

n-Sp

ecifi

cP

aram

eter

s

Par

amet

erP

aran

aSa

oP

aulo

Min

asB

ahia

Mat

oG

ross

oP

erna

mbu

coM

aran

hao

φ1r

-1.4

16-0

.662

-1.6

29-2

.162

-0.3

87-2

.339

-2.7

98

φ2r

-2.8

91-2

.506

-3.3

30-4

.171

-2.6

90-4

.212

-4.4

39

λ1r

-4.5

51-2

.497

-4.5

07-5

.407

-6.7

56-2

.188

-5.5

75

λ2r

-0.6

65-0

.943

-1.0

86-1

.098

-2.6

71-0

.508

-1.2

47

λ3r

0.16

30.

749

0.59

80.

651

0.98

40.

365

0.54

5

κ0.

719

0.37

31.

012

1.73

02.

288

1.10

81.

744

φor

-0.4

50-0

.378

-0.4

61-0

.474

-0.4

27-0

.810

-0.8

91

βor

1.05

01.

072

1.07

41.

196

1.15

10.

711

0.66

4

z 1r

-3.4

53-3

.031

-3.0

09-2

.852

-2.9

84-2

.053

-2.4

90

z 2r

-1.9

14-2

.521

-1.5

64-1

.214

-2.1

01-1

.076

-0.9

01

z 3r

-2.6

18-5

.891

-2.6

21-2

.392

-2.7

17-2

.378

-2.3

45

σ2 νk

0.01

60.

087

0.02

90.

046

0.08

90.

158

0.22

3

σ2 εop

0.02

30.

020

0.01

70.

023

0.01

60.

028

0.02

5

σ2 εob

0.03

50.

043

0.02

00.

028

0.01

80.

019

0.01

7

σ2 z1r

1.42

30.

257

0.48

80.

929

1.09

50.

532

1.23

9

σ2 z1r

0.07

60.

066

0.02

00.

066

0.04

40.

380

0.09

8

σ2 z1r

0.43

60.

397

0.42

90.

341

0.54

10.

252

0.59

8

65

Tab

le13

:C

ompa

riso

nof

2005

and

Med

ian

Bas

elin

eP

rodu

ctio

nan

dP

rice

s

Pro

duct

ion

(Mill

ions

ofU

nits

*)P

rice

s(2

000

Rea

is)

Can

eE

than

olSu

gar

Oth

erA

gC

ompo

site

Can

eE

than

olR

enta

lR

ate

2005

422.

0341

37.8

726

.58

937.

0610

180.

0820

.38

855.

6111

0.42

Bas

elin

e35

5.42

4130

.94

27.8

098

1.00

1016

1.52

20.3

985

4.29

110.

22

*Not

e:C

ompo

site

good

isac

tual

lyin

billi

ons

ofun

its;

unit

sof

suga

rcan

ean

dsu

gar

are

met

ric

tons

,w

hile

unit

sof

etha

nol

are

US

gallo

ns.

Tab

le14

:C

ompa

riso

nof

2005

and

Med

ian

Bas

elin

eL

and

Shar

esan

dW

ages

Lan

dSh

ares

Wag

es(2

000

Rea

is)

Can

eO

thA

gO

ther

Can

eO

thA

gN

onA

g

Reg

ion

2005

Bas

e20

05B

ase

2005

Bas

e20

05B

ase

2005

Bas

e20

05B

ase

Par

ana

0.00

80.

016

0.82

90.

829

0.16

20.

154

1.23

41.

027

1.21

21.

074

1.91

41.

926

Sao

Pau

lo0.

124

0.12

80.

593

0.59

20.

283

0.28

01.

740

1.41

11.

252

1.29

82.

169

2.18

4

Min

as0.

009

0.01

50.

584

0.58

40.

407

0.40

11.

044

0.90

30.

957

0.94

71.

722

1.73

4

Bah

ia0.

002

0.00

80.

502

0.50

20.

496

0.49

01.

116

0.82

50.

816

0.79

01.

276

1.28

5

Mat

oG

ross

o0.

003

0.01

90.

651

0.65

10.

346

0.33

01.

640

1.35

71.

276

1.18

01.

722

1.73

4

Per

nam

buco

0.04

00.

042

0.53

50.

535

0.42

50.

423

0.95

70.

788

0.76

50.

704

1.27

61.

281

Mar

anha

o0.

001

0.00

50.

423

0.42

30.

576

0.57

20.

765

0.55

50.

696

0.65

01.

148

1.15

3

66

Tab

le15

:C

ompa

riso

nof

Med

ian

ofA

ggre

gate

sin

Bas

elin

ean

dSi

mul

ated

Env

iron

men

ts

Pro

duct

ion

(Mill

ions

ofU

nits

*)N

etE

xpor

ts(M

illio

nsof

Uni

ts*)

Env

iron

men

tSu

garc

ane

Eth

anol

Suga

rO

ther

Ag

Com

posi

teE

than

olSu

gar

Oth

erA

g

Bas

e35

5.42

4130

.94

27.8

098

1.00

1016

1.52

684.

7513

.07

92.8

2

Sim

10%

392.

3489

44.9

519

.48

978.

8111

103.

7554

87.0

610

.74

92.8

8

Sim

12%

423.

9115

927.

840.

0098

7.02

1121

3.64

1242

8.72

1.31

92.9

1

Sim

15%

477.

8024

768.

540.

0610

11.2

211

397.

3921

188.

55-8

.61

92.9

4

*Not

e:C

ompo

site

quan

titi

esar

ein

billi

ons

ofun

its.

Uni

tsof

etha

nol

are

US

gallo

ns,

whi

leun

its

ofsu

garc

ane

and

suga

rar

em

etri

cto

ns.

Tab

le16

:L

and

Allo

cati

ons

Und

erth

eB

asel

ine

and

Sim

ulat

edE

nvir

onm

ents

(Mill

ions

ofA

cres

)

Suga

rcan

eO

ther

Ag.

Non

-Agr

icul

ture

Reg

ion

Bas

e10

%12

%15

%B

ase

10%

12%

15%

Bas

e10

%12

%15

%

Par

ana

2.23

4.03

9.10

22.2

311

5.47

114.

2910

8.77

101.

1821

.51

22.0

220

.91

15.5

2

Sao

Pau

lo7.

8510

.35

14.1

724

.46

36.3

335

.70

33.0

526

.61

17.1

516

.08

14.5

010

.55

Min

as2.

494.

4011

.27

26.7

597

.65

97.6

496

.06

93.4

267

.00

66.2

359

.96

47.3

0

Bah

ia1.

142.

767.

2617

.03

72.7

272

.72

73.0

674

.61

71.0

070

.32

64.6

752

.48

Mat

oG

ross

o8.

8215

.61

29.9

376

.64

303.

2430

3.14

293.

2027

5.37

153.

4215

2.06

143.

2711

4.21

Per

nam

buco

2.43

3.82

6.32

13.1

231

.20

31.2

029

.89

27.4

824

.63

24.0

722

.06

17.3

8

Mar

anha

o0.

952.

818.

4918

.19

76.2

276

.22

77.9

882

.88

102.

9510

1.42

93.3

776

.95

67

Tab

le17

:W

ages

Und

erth

eB

asel

ine

and

Sim

ulat

edE

nvir

onm

ents

Suga

rcan

eO

ther

Ag.

Non

-Agr

icul

ture

Reg

ion

Bas

e10

%12

%15

%B

ase

10%

12%

15%

Bas

e10

%12

%15

%

Par

ana

1.02

71.

071

1.02

00.

941

1.07

41.

104

1.07

71.

044

1.92

61.

359

1.27

41.

158

Sao

Pau

lo1.

411

1.55

51.

500

1.43

21.

298

1.30

01.

268

1.23

62.

184

1.49

31.

391

1.25

4

Min

as0.

903

0.92

70.

893

0.82

70.

947

0.94

40.

933

0.91

31.

734

1.22

41.

148

1.04

4

Bah

ia0.

825

0.89

60.

862

0.83

70.

790

0.79

20.

784

0.77

21.

285

0.86

40.

802

0.72

0

Mat

oG

ross

o1.

357

1.35

41.

291

1.17

31.

180

1.19

31.

187

1.15

91.

734

1.20

21.

123

1.01

7

Per

nam

buco

0.78

80.

823

0.81

60.

806

0.70

40.

716

0.70

30.

700

1.28

11.

022

0.98

10.

922

Mar

anha

o0.

555

0.60

10.

597

0.58

70.

650

0.65

70.

655

0.65

31.

153

0.93

60.

900

0.85

1

Tab

le18

:A

nnua

lL

abor

Hou

rsU

nder

the

Bas

elin

ean

dSi

mul

ated

Env

iron

men

ts(M

illio

ns)

Suga

rcan

eO

ther

Ag.

Non

-Agr

icul

ture

Reg

ion

Bas

e10

%12

%15

%B

ase

10%

12%

15%

Bas

e10

%12

%15

%

Par

ana

6473

9613

251

5850

9550

6254

4820

761

3073

530

459

2665

9

Sao

Pau

lo40

340

950

775

217

1117

3119

1021

1334

672

4403

140

671

2476

7

Min

as13

214

318

024

643

2043

1245

1049

9728

523

3859

237

897

3354

8

Bah

ia54

5668

9637

7337

7038

0640

6678

1012

703

8756

173

Mat

oG

ross

o40

5468

9323

8223

5723

6725

6010

157

1729

316

294

9736

Per

nam

buco

551

549

618

874

2941

2933

2861

2890

9326

1746

830

744

5465

8

Mar

anha

o69

6873

108

3995

3990

3977

4050

8463

4174

272

214

1607

61

68

B Methodological Details

B.1 Product and Labor Supply Expressions

In the main text, I state expressions for the fraction of land used for a particular purpose, as well

as the total effective land units used for that purpose. Here, I provide a more complete derivation

of those expressions. Beginning with the land shares, and using the same notation as used in the

main text:

Sj = Pr(cj + uj > ck + uk, cj + uj > cp + up)

=∫ ∞−∞

∫ cj−ck+uj

−∞

∫ cj−cp+uj

−∞(1γ

)3e−1γuj− 1

γuk− 1

γupe−e

− 1γ uj−e−

1γ uk−e−

1γ up

dupdukduj

=∫ ∞−∞

∫ cj−ck+uj

−∞(1γ

)2e−e− 1γ (cj−cp+uj)

e− 1γuj− 1

γuke−e

− 1γ uj−e−

1γ uk

dukduj

=∫ ∞−∞

1γe−e

− 1γ (cj−cp+uj)

e−e− 1γ (cj−ck+uj)

e− 1γuje−e

− 1γ uj

duj

=ecjrtγr∑3

i=1 ecirtγr

Total effective land units in use j, j=1, 2 can be derived as follows:

Aj = SjA∗E(eλj+uj |cj + uj > ck + uk, cj + uj > cp + up)

= SjA∗∫ ∞−∞

eλj+uj

∫ cj−ck+uj−∞

∫ cj−cp+uj−∞ f(uj , uk, up)

Sjduj

= A∗∫ ∞−∞

∫ cj−ck+uj

−∞

∫ cj−cp+uj

−∞(1γ

)3eλj+uje−1γuj− 1

γuk− 1

γupe−e

− 1γ uj−e−

1γ uk−e−

1γ up

d~u

=1γA∗eλj

∫ ∞−∞

e−uj( 1

γ−1)

e−e− 1γ uj (1+e

− 1γ (cj−cp)

+e− 1γ (cj−ck)

)duj

= A∗eλj∫ ∞

0v−γe−v(1+e

− 1γ (cj−ck)

+e− 1γ (cj−cp)

)dv

= A∗rteλjrt(Sjrt)1−γrΓ(1− γr)

The expressions for aggregate product supply and aggregate labor demand follow immediately.

Finally, the expression for aggregate labor supply comes from the following. Let x = θ+µ, and

69

use the same notation as in the main text. Then:

LSst = NstE(hist|i ∈ s)

= Nst(1− β)(T − ψhs)−Nstβ

wstE(ex|i ∈ s)

= Nst(1− β)(T − ψhs)−Nstβ

wst

∫ ∞−∞

exPr(i ∈ s|x)Pr(i ∈ s)

f(x)dx

= Nt(1− β)(T − ψhs)∫ ∞−∞

Pr(i ∈ s|x)f(x)dx−Ntβ

wst

∫ ∞−∞

exPr(i ∈ s|x)f(x)dx

= Nt

∫ ∞−∞

[(1− β)(T − ψhs)−β

wstex]Pr(i ∈ s|x)f(x)dx

= Nt

2∑i=1

∫ ∞−∞

[(1− β)(T − ψhs)−β

wstex]Pr(i ∈ s|x)

1σ√

2πe−12

(x−θiσ

)2πidx

= Nt

2∑i=1

∫ ∞−∞

[(1− β)(T − ψhs)−β

wsteµ+θi ]Pr(i ∈ s|µ, θi)

1σ√

2πe−12

(µσ

)2πidµ

= Nt

2∑i=1

2∑j=1

πidj|i

∫ ∞−∞

[(1− β)(T − ψhs)−β

wsteµ+θi ]Pr(i ∈ s|µ, θi, p4j)

e−12

(µσ

)2

σ√

2πdµ

B.2 Construction of Variables

I begin by describing in more detail the data on prices and land allocations, and then conclude by

describing how these data – along with the other data mentioned in the text – are used to construct

the analogues to all the aggregate quantities in the model.

B.2.1 Prices

• Price of Sugarcane: I take the price of sugarcane directly from the FGV-provided prices,

which cover 17 states at one point or another during the period of study. FGV provides

prices on a month-by-month basis. I use an average over these monthly prices. In a case

in which a region includes more than one state with a sugarcane price provided, I use the

average of the prices of all the states in that region. In a case in which no states within a

region have a sugarcane price, I use the sugarcane price of the closest region geographically.

For the estimation and simulations, I assume one sugarcane price exists for all of Brazil. For

this purpose, I use the median price of sugarcane across the regions.

• Price of Sugar: I use the FGV-provided price of a pound of sugar from the New York market,

as provided by the FGV. To translate this into Reais from US dollars, I use contemporaneous

exchange rate data from the Central Bank of Brazil.

• Price of Ethanol: The FGV provides a price index for ethanol. I benchmark this index

using the implied price of a cubic meter of exported ethanol in a particular year. I obtained

this price using data from SECEX.

70

• Price of Other Agricultural Good: The FGV provides a price index for all of agricul-

ture. Using sugarcane prices and data on the share of agricultural production resulting from

sugarcane (from IBGE sources), I calculate a price index for “other agriculture.” Since such

a price has no natural units, I simply set the 2000 value to 100 Reais. This defines a “unit”

of non-sugarcane agricultural production.

• Petroleum Prices: The FGV provides historical series of the price of a barrel of oil in US

dollars at various points of origin. I use the prices for the Texas and Nigeria points of origin,

relying on the Central Bank exchange rate series to convert these into Reais.

• Sectoral Hourly Wages: To construct the hourly wage, I multiply re-ported monthly

earnings by 730 , and then divide the result by reported hours of work. In the analysis, I

use the unconditional median hourly wage in the sugarcane sector and other agricultural

sector in a particular region as the regional wage for those sectors. In calculating the wage,

I use only the earnings of hired workers in the relevant sector. In particular, I do not use

self-employment earnings.

B.2.2 Land Use

• Land Cultivated for Sugarcane: The Producao Agricola Municipal (PAM) data provide

information on the number of acres on which sugarcane was harvested in a given year. It is

important to note that the PAM data refers to the calendar year, rather than the sugarcane

harvesting year (which differs depending on the region of the country).

• Land Cultivated for Other Agricultural Uses: I impute the total amount of land used

for other agricultural purposes due to data limitations. In the period extending to 1990, I

only have PAM data on the acreage for the ten major crops. After 1992, the available PAM

data include a much larger range of temporary and permanent crops. I use this information in

combination with data from the agricultural censuses of 1980, 1985, 1995, and 2005-06 which

provide more complete information. In particular, I use a scale factor defined by the ratio of

the PAM acreage to the agricultural census acreage in a census year to estimate total acreages

for non-census years. The agricultural censuses also provide information on total land used

for pasture and privately owned forests. To interpolate pasture values for a region between

census years, I first run a regression on time trends and total cattle raised in a region in a

year (available in PPM data), allowing for region-specific intercepts. Not surprisingly, the

resulting standard errors are large, but as the purpose is only to obtain reasonable predictions,

I use the regression equation to predict values for pasture land for each non-census year in

each region. In the small number of cases with negative predicted values, I set pasture land

to zero. I use IBGE data on the value of forest production in each year to conduct a similar

imputation procedure. I then sum the values for crop land, pasture land, and private forest

land across all states. Further details are available upon request.

71

• Non-Agricultural Land: Non-agricultural land in a region is simply the residual resulting

from subtracting sugarcane and other agricultural land from the total land area of the region.

Data on total land area is obtained from the Brazilian government. A given region may

become slightly larger or smaller over time due to changes in method of measurement, changes

in state boundaries, etc. Because of the difficulty in knowing the sources of this variation, I

simply use the given land area for each year.

It is useful to clearly delineate what quantities are available in the data sources and what can

be constructed from the these data sources, with the help of supplementary assumptions. Table 19

provides the quantities available from the raw data, categorized according to the labels in the first

column. An asterisk in a superscript indicates that the item is referring to Brazil as a whole, rather

than just the non-North regions that are the subject of this paper. A superscript “N” indicates

aggregates specific to the North Census region, while aggregates without a superscript refer to the

non-North portions of the country. When a quantity appears with the subscript “r”, it should

be understood to represent that quantity for all regions. The item G∗t refers to total government

spending. The quantity V Prt denotes the total value of production in each region.

Table 19: Raw Data

Category Available in Data

Production Y S1rt, YS2rt, Y

Sert, Y

Ssrt

Prices p1t, pet, rt, pst, p2t, pot, wjrt

Labor Hours L1rt, L2rt, L3rt

GDP Components KD∗t , Y X∗et , Y X∗st , Y X∗2t , G∗t , V Prt, GDPrt

Land Shares S1rt, S2rt, S3rt

I use the data from Table 19, along with supplementary assumptions, to construct empirical

analogues of key quantities in the model. Table 20 summarizes this construction process. Each

row in the first column provides the raw data variables and assumptions that I use to construct the

item in the second column of that row.

The first set of assumptions is necessary to divide up national quantities between the North

Census region and the non-North Census regions that are the subject of my analysis. I make several

assumptions to use the asterisked national-level items to construct the corresponding quantities for

only the non-North regions. These assumptions are:

• Net exports from the North Census region are zero for the intermediate good of sugarcane

and for each final good

• Agricultural profits, net transfers from the government, and capital do not flow in or out of

the North Census region

72

Table 20: Use of Raw Data to Construct Quantities

Can Use To Construct

GDPrt GDPt, GDPNt , GDP ∗t

Y X∗et , Y X∗st , Y X∗2t , zero North net ex. for each good Y Xet , Y Xst , Y X2t

G∗t , government budget balance τ∗t

τ∗t , GDPt, GDPNt , GDP ∗t τNt , τt

Y Sert, YXet , Y Ssrt, Y

Xst , Y S2rt, Y

X2t Y Det , Y Dst , Y D2t

rtKD∗t , GDP ∗t , τ∗t , GDPt, τt rtK

Dt

GDPt, YDet , Y Dst , Y D2t , KD

t , p1t, pet, rt, pst, p2t, pot Y Dot

Y Xet , Y Xst , Y X2t , p1t, pet, rt, pst, p2t, pot, trade balance Y Xot

Y Xot , Y Dot Y Sot

L1rt, L2rt, L3rt, w1rt, w2rt, w3rt WBt

GDPt, WBt, τt Mt

Mt, p2t, w2rt, YS2rt, p1t, w1rt, Y

S1rt, τt, rt K̄t (capital stock)

V Prt, petYSert, pstY

Ssrt, p2tY

S2rt, p1tY

S1rt, potY

Sot potY

Sort

• Net taxes in each super-region (the North, and the rest of Brazil) are proportional to GDP

in that super-region

Together, these assumptions ensure both the North economy and the non-North economy are

coherent, in the sense that the spending, production, and income methods of income accounting all

yield the same values for GDP in the North Census region and in the total of the non-North Census

regions. The assumptions also ensure that we can construct the amount of capital demanded and

the amount of non-labor income in each of the two areas.

As a final note on Table 20, two new expressions appear there. First, WBt is defined as

WBt =∑

r,j wrjtLrjt (total wage bill for all regions and sectors). Second, the table lists the

quantity V Prt. This piece of data from the regional income accounts represents the total value of

production in a region. It does not have a directly analogous item in the model, since it incorporates

the value of taxes and some fraction of the value of newly produced capital goods.

Under one additional assumption, I can use V Prt to construct the total supply of the composite

good in each region. First note:

V Prt = potYSort + petY

Sert + pstY

Ssrt + patY

S2rt + p1tY

S1rt +OVrt

where OVrt is the value of taxes and counted capital in the region. Assume that OVrt is a fixed

proportion ω of potY Sort across regions. Then we have:

V Prt − (petY Sert + pstY

Ssrt + p2tY

S2rt + p1tY

S1rt)∑

r(V Prt − (petY Sert + pstY S

srt + p2tY S2rt + p1tY S

1rt))=

(1 + ω)potY Sort

(1 + ω)∑

r potYSort

=potY

Sort∑

r potYSort

73

Multiplying the result by total supply of the composite good then yields the region-specific supply

of the composite good for every region.66 Below, I discuss the methods used to construct the

key variables utilized in the analysis. The description is divided up by the type of variable under

consideration. The programs used to construct the variables and perform the estimation can be

provided upon request.

References

Alix-Garcia, J. (2007): “A Spatial Analysis of Common Property Deforestation,” Journal of

Environmental Economics and Management, 53(2), 141–157.

(2008): “An Exploration of the Positive Effect of Inequality on Common Property Forests,”

Journal of Development Economics, 87, 92–105.

Amemiya, T. (1985): Advanced Econometrics. Harvard University Press, Cambridge, Mas-

sachusetts.

Assuncao, J. (2006): “Land Reform and Landholdings in Brazil,” UNU-WIDER Research Paper,

2006/137.

Bardhan, P., and C. Udry (1999): Development Microeconomics. Oxford University Press, New

York.

Barros, A. R., T. V. de V. Cavalcanti, F. M. Dias, and A. M. Magalhaes (2005): “The

Impact of Sugar’s World Trade Liberalization on Poverty in Brazil,” Unpublished manuscript.

Barros, G. S. D. C., and M. A. F. D. D. Moraes (2002): “A Desregulamentacao do Setor

Sucroalcooleiro,” Revista de Economica Politica, 22(2-86), 156–173.

Berry, S. (1994): “Estimating Discrete-Choice Models of Product Differentiation,” The RAND

Journal of Economics, 25(2), 242–262.

Berry, S., J. Levinsohn, and A. Pakes (1995): “Automobile Prices in Market Equilibrium,”

Econometrica, 63, 841–890.

(2004): “Differentiated Products Demand Systems from a Combination of Micro and

Macro Data: The New Car Market,” Journal of Political Economy, 112(1), 68–105.

Blundell, R., and T. MaCurdy (2007): “Labour Supply,” Forthcoming in Palgrave’s Dictionary

of Economics.66I should note here that the GDP values calculated in this manner will not necessarily correspond with GDP

values from the national income accounts. The sum of regional GDP measures differs somewhat from the national

totals.

74

Borrell, B., J. R. Bianco, and M. D. Bale (1994): “Brazil’s Sugarcane Sector: A Case of

Lost Opportunity,” World Bank Policy Research Working Paper, 1363.

Bovenberg, L. A., L. H. Goulder, and M. R. Jacobsen (2006): “Costs of Alternative

Environmental Policy Instruments in the Presence of Industry Compensation Requirements,”

Working Paper.

Bussolo, M., J. Lay, and D. van der Mensbrugghe (2004): “Structural Change and Poverty

Reduction in Brazil: The Impact of the Doha Round,” Draft of ch. 9 in Hertel and Winters, eds.,

”‘Putting Development Back into the Doha Agenda: Poverty Impacts of a WTO Agreement”’.

de Rezende, G. C. (2002): “Ocupacao Agricola e Estrutura Agraria no Cerrado: O Papel do

Preco da Terra, dos Recursos Naturais e da Tecnologia,” IPEA Texto Para Discussao, 913.

de Souza Ferreira Filho, J. B., and M. Horridge (2005): “The Doha Round, Poverty and

Regional Inequality in Brazil,” in Putting Development Back into the Doha Agenda: Poverty

Impacts of a WTO Agreement, ed. by T. W. Hertel, and L. A. Winters. World Bank, Forthcoming.

Deaton, A., and J. Muellbauer (1983): Economics and Consumer Behavior. Cambridge Uni-

versity Press, New York.

Eckstein, Z., and K. I. Wolpin (1999): “Why Youths Drop Out of High School: The Impact

of Preferences, Opportunities, and Abilities,” Econometrica, 67(6), 1295–1339.

Edmonds, E. (2002): “Government Initiated Community Resource Management and Local Re-

source Extraction from Nepal’s Forests,” Journal of Development Economics, 68(1), 89–115.

Elobeid, A., and S. Tokgoz (2008): “Removing Distortions in the U.S. Ethanol Market: What

Does it Imply for the United States and Brazil?,” American Journal of Agricultural Economics,

90(4), 918–932.

Fair, R., and W. Parke (1980): “Full-Information Estimates of a Nonlinear Macroeconometric

Model,” Journal of Econometrics, 13, 269–291.

Fair, R., and J. Taylor (1983): “Solution and Maximum Likelihood Estimation of Dynamic

Nonlinear Rational Expectations Models,” Econometrica, 51(4), 1169–1185.

Foster, A., and M. Rosenzweig (2003): “Economic Growth and the Rise of Forests,” The

Quarterly Journal of Economics, pp. 601–637.

Hay, D. (2001): “The Post-1990 Brazilian Trade Liberalization and the Performance of Large

Manufacturing Firms: Productivity, Market Share, and Profits,” Economic Journal, 111, 620–

641.

Heckman, J., and B. Singer (1984): “A Method for Minimizing the Impact of Distributional

Assumptions in Econometric Models for Duration Data,” Econometrica, 52(2), 271–320.

75

Heckman, J. J., L. Lochner, and C. Taber (1998): “Explaining Rising Wage Inequality:

Explorations with a Dynamic General Equilibrium Model of Labor Earnings with Heterogeneous

Agents,” Review of Economic Dynamics, 1, 1–58.

Heckman, J. J., and G. Sedlacek (1985): “Heterogeneity, Aggregation, and Market Wage

Functions: An Empirical Model of Self-Selection in the Labor Market,” The Journal of Political

Economy, 93(6), 1077–1125.

Helfand, S. M. (2003): “The Impact of Agricultural Policy Reforms on the Agricultural Sector

in Brazil in the 1990s: Implications for Pro-Poor Agricultural Policies,” in OECD Global Forum

on Agriculture: Designing and Implementing Pro-Poor Agricultural Policies.

Helfand, S. M., and G. C. de Rezende (2004): “The Impact of Sector-Specific and Economy-

Wide Policy Reforms on the Agricultural Sector in Brazil: 1980-98,” Contemporary Economic

Policy, 22(2), 194–212.

Judd, K. (1998): Numerical Methods in Economics. The MIT Press, Cambridge, Massachusetts.

Lee, D., and K. I. Wolpin (2006): “Intersectoral Labor Mobility and the Growth of the Service

Sector,” Econometrica, 74(1), 1–46.

Lopes, M. D. R., and I. V. Lopes (1998): “Fatores Que Afetam a Competitividade da Cadeia

da Cana,” Centro de Estudos Agricolas, FGV and IBRE.

Mas-Colell, A., M. D. Whinston, and J. R. Green (1995): Microeconomic Theory. Oxford

University Press.

Moraes, M. A. F. D. D. (2007): “The Sugarcane Agro-System in Brazil: Labor Market Indicators

and Wage Formation Model,” Mimeo.

Mroz, T. A. (1999): “Discrete Factor Approximations in Simultaneous Equation Models: Esti-

mating the Impact of a Dummy Endogenous Variable on a Continuous Outcome,” Journal of

Econometrics, 92, 233–274.

Muendler, M. (2002): “Trade, Technology, and Productivity: A Study of Brazilian Manufactur-

ers, 1986-1998,” University of California, Berkeley mimeo.

Nelson, G. C., and J. Geoghegan (2002): “Deforestation and Land Use Change: Sparse Data

Environments,” Agricultural Economics, 27, 201–216.

Nelson, G. C., and R. D. Robertson (2008): “Green Gold or Green Wash: Environmental

Consequences of Biofuels in the Developing World,” Review of Agricultural Economics, 30(3),

517–529.

Nunberg, B. (1986): “Structural Change and State Policy: The Politics of Sugar in Brazil Since

1964,” Latin American Research Review, 21(2), 53–92.

76

Pfaff, A. (1999): “What Drives Deforestation in the Brazilian Amazon?,” Journal of Environ-

mental Economics and Management, 37, 26–43.

Pfaff, A., and et al. (2007): “Road Investments, Spatial Spillovers, and Deforestation in the

Brazilian Amazon,” Journal of Regional Science, 47(1), 109–123.

Ravallion, M. (2004): “Looking Beyond Averages in the Trade and Poverty Debate,” World

Bank Policy Research Working Paper Series, 3461.

Sargan, J. (1975): “Asymptotic Theory and Large Models,” International Economic Review,

16(1), 75–91.

Timmins, C. (2006): “Endogenous Land Use and the Ricardian Valuation of Climate Change,”

Environmental and Resource Economics, 33, 119–142.

Valdes, A., and J. A. Mistiaen (eds.) (2003): Rural Poverty Alleviation in Brazil: Toward an

Integrated Strategy, vol. World Bank Country Study. The International Bank for Reconstruction

and Development / The World Bank.

Wolak, F. (2007): “An Ethanol Policy That Benefits All Americans,” SIEPR Policy Brief.

77