A 70 sector CGE model for Germany

Andreas Mense∗ and Konstantin A. Kholodilin†

April 28, 2011

Abstract

This paper describes the development of a CGE model for the Germaneconomy. Compared to a standard model this model was extended in twoways. These are the high level of sectoral disaggregation and a detailedmodeling of consumption taxes, both of which are useful when analyzingthe impact of subsidies and taxes on a certain industry. In addition, thespecification of variables and model parameters for the German economyare outlined. The model uses German data from the most recent input-output data of 2007.

Keywords: Computable general equilibrium; Germany; social account-ing matrix; input-output tables.

JEL classification: D57; D58.

∗DIW Berlin, Mohrenstraße 58, 10117 Berlin, Germany, e-mail:

andreas.mense@phil.stud.uni-erlangen.de†DIW Berlin, Mohrenstraße 58, 10117 Berlin, Germany, e-mail: kkholodilin@diw.de

I

Contents

1 Introduction 1

2 The Basic Structure 1

3 Specification of the Model 23.1 Extensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23.2 Data and Parameter Estimation . . . . . . . . . . . . . . . . . . 4

4 Conclusion 8

5 Appendix 11

II

List of Tables

1 Structure of the Matrix . . . . . . . . . . . . . . . . . . . . 122 Sets and Variables . . . . . . . . . . . . . . . . . . . . . . . . 133 SAM: CESAM balancing . . . . . . . . . . . . . . . . . . . . . . . 134 Mapping of Industry Classifications . . . . . . . . . . . . . 145 Estimation of the CES production function - country data* 156 Estimation of the CES production function - Results . . 167 Estimation of CES Armington Elasticities . . . . . . . . 188 Estimation of CET Trade Elasticities . . . . . . . . . . . 20

List of Figures

1 Scheme of the EcoMod7 Model . . . . . . . . . . . . . . . . 11

III

1 Introduction

Computable general equilibrium (CGE) models are a widely used tool to analyzethe impact of various policy options on the economy. Thanks to improvementsin the availability of sectoral data it is now possible to go into greater detailwhen estimating the consequences of policy decisions for specific industries.Moreover, advances in computational capacities have made the use of biggermodels possible even on standard PCs. Even more true today than in 1984, “acomputer removes the need to work in small dimension. Much more detail andcomplexity can be incorporated than in simple analytic models.” (Shoven andWhalley, 1984, p. 1008). The goal of this paper is to elaborate a model for theGerman economy with a high degree of complexity on the producers’ side.

The CGE model described below includes 70 sectors and is designed toestimate the impact of different tax policies, subsidies or labor-market shockson prices for goods and services, output and wealth.

First of all, for these tasks a high degree of sectoral aggregation is desirable, ifwe want to make statements about policy-induced effects for different producers.Secondly, emphasis on taxation is crucial for sectoral analysis. We thereforeimplemented a very specific consumption tax that allows the modeler to treateach flow of goods independently.

To the best of our knowledge, a model with a comparable level of sectoraldisaggregation does not exist for Germany to date. Next to frequently arisingquestions of taxation, the model could be used to estimate effects of the expectedshrinkage of the German workforce in the upcoming years on different industries.

The remainder of this paper is structured as follows. In section 2, the model’sanalytical structure and core functions are outlined. Section 3 is devoted to thespecification of the model. This includes a discussion of the data used as wellas the model’s size and treatment of consumption taxes. A conclusion is drawnand possible extensions of the model are sketched in section 4.

2 The Basic Structure

The EcoMod7 model Bayar was used as a point of departure, being a standardCGE model, which compactly and parsimoniously describes the whole economy.Below its structure is briefly described. There are two producers with constantelasticity of substitution (CES) production functions:

Vi(K,L) = γP[βPK

σP−1σP + (1− βP )L

σP−1σP

] σPσP−1 , (1)

where γP is the factor productivity, βP is the share parameter, and σP is theelasticity of substitution. Factors are capital and labor (while unemployment isallowed), and the firms use an aggregator function of Leontief-type to combinevalue-added and intermediate aggregate inputs.

Demand side is represented by one household with Stone-Geary linear ex-penditure system (LES) utility function:

U =∏i

(Xi − Ci)αi , (2)

where Xi and Ci are quantities and αi is a share parameter. Government andbanking sector are modeled using a simple Cobb-Douglas utility function.

1

The economy is open, with one trading partner (Rest Of the World). Theshare of exports is determined by a Constant Elasticity of Transformation (CET)function:

X(E,D) = γE[βEE

σE−1σE + (1− βE)D

σE−1σE

] σEσE−1 , (3)

where E are exports, D are domestically sold products, and X(E,D) is thetotal domestic production.

The utility from imports and domestically produced goods is of CES Armington-type:

U(M,D) = γM[βMM

σM−1σM + (1− βM )D

σM−1σM

] σMσM−1 , (4)

where U(M,XD) is the utility over imports, M , and domestically producedgoods, D.

There are five different types of government revenue: Commodity taxes (i)are uniform for all buyers of a specific commodity, no matter whether the gov-ernment, investment, a producer or the household is the agent. Taxes on capital(ii) and labor (iii) are allowed to vary between the different sectors, so are tar-iffs (iv). Income tax is paid on the household’s total income (v). Furthermore,capital and labor are exogenously fixed and perfectly mobile among sectors, butcannot be traded. Unemployment, savings and investment are endogenously de-termined. Exported and imported goods have an effect on the flexible exchangerate. A full scheme of the model is presented in figure 1 in the appendix.

3 Specification of the Model

The standard model outlined above was modified and specified so that the modelrepresents the German economy. This section is divided into two parts. Firstly,the model’s extensions are outlined in subsection 3.1. Secondly, the specificationof the model for Germany is discussed in detail, which includes a description ofthe data used and of the parameter estimation for the different model functionsin subsection 3.2.

3.1 Extensions

Extension of the Model Size

Since we decided to focus on a sectoral analysis of the German economy, weaimed at extending the size of the model. Data availability is both a limit anda guide for a sectoral extension. German input-output tables are published bythe Federal Statistical Office (Destatis) with 71 sectors on the CPA 2-digitslevel. Since we were not able to estimate all parameter based on the sameclassification, it might be argued that a smaller model would yield more reliableresults (cf. Table 4). However, especially the estimates for the substitutionelasticities of capital and labor inputs are based on a comparable number ofsectors and on the same classification. In addition, we decided to change thehousehold’s LES utility function to a simple Cobb-Douglas form in order toavoid sloppy estimates due to missing data. Albeit objections of this sort haveto be kept in mind, this approach allows a very close look at specific sectors.

2

Consumption Tax Diversification

The second important change to the model concerns taxation. As already notedabove, different recipients of goods cannot be treated individually when apply-ing commodity taxes in the basic framework. We split commodity taxes forsector i, tci, into four sub-groups, namely taxation on household consumption,tci,H ; on investments, tci,S ; on government consumption, tci,G; and on inter-mediate demand, tci,j , of sector j. The formal application of these changes isstraightforward.

The input-output table lists tax revenue from the total consumption byevery agent (defined here as “column-wise”, see below), and total tax revenuefrom consumption of every good (“row-wise”). Additionally, commodity flowsare known, such that we can use their relations to get an idea of how highthe relative tax burden should be. The missing piece are the total tax ratesper sector since the distribution of taxation within household government, andinvestment demand per good was not reported in the Input-Output table. Weused data from Destatis to approximate these distributions (Destatis, 2010b).

One solution to the above estimation problem is to fix “row” and “column”tax revenues and scale per-flow taxation by using the relative quantity consumedby agents k = [1, . . . , 74] and the relative quantity produced in sectors i =[1, . . . , 71].

Let ρ be a vector of total tax revenues per sector (“row-wise”) and ζ be avector of total tax revenues per agent (“column-wise”)

ρ =

r1...ri

, ζ =[c1 . . . ck

], where i are sectors and k are agents.

Also, let CX be a i× k matrix of relative commodity flows (i.e. coefficients):

CX =

f1,1 . . . f1,k...

...fi,1 . . . fi,k

such that∑k fi,k = 1 holds for all i.

Multiplying ρ with CX yields a first estimate of tax flows for each entry ofT , the tax flows matrix. Row sums of T obviously equal ρ (since

∑i fi,k = 1),

but column sums are different from ζ. In order to obtain correct values on bothrow and column sums, the coefficient matrix CX has to be updated to yield:

CT =

t1,1∑iti,1

. . .t1,k∑iti,1

......

ti,1∑iti,k

. . .ti,k∑iti,k

where∑i

ti,k∑iti,k

= 1 for all k.

Finally, ρCT = T , where T is a matrix of tax revenues per sector i and agentk and both

∑i ti,k = ζ and

∑k ti,k = ρ hold.

These estimated tax revenues lead to much more realistic tax rates for thedifferent agents. For example, in 2007 households paid a total of e 144 billiontaxes on the consumption of goods (Destatis, 2010a). However, if the total con-sumption tax revenue of approximately e 251 billion were distributed amongagents using a uniform tax rate on consumption per sector, households would

3

end up with less than e 90 billion. The same is true for tax revenues on gov-ernment consumption: While the input-output table of 2007 reports a total ofapproximately e 5.6 billion, a uniform tax would leave the government with aburden more than three times as high.

Another advantage of more specific consumption taxes is the possibility to“raise taxes” applying only to certain agents (e.g., investment or households),while leaving other recipients to face unaltered tax rates. This allows for ananalysis of sectoral subsidies (e.g., the exemption of energy-intensive industriesfrom the energy and electricity tax), which only apply to certain industries, orcomparable policies where several agents are treated individually.

3.2 Data and Parameter Estimation

The Social Accounting Matrix

In the next step, the initial equilibrium of the German economy had to bespecified. The 2007 input-output table with 71 industrial sectors and goods(CPA 2003) published by Destatis (2010a) served as a basis. We used a SocialAccounting Matrix (SAM) to assemble the data. A social accounting matrixis a convenient way of ordering commodity flows and factor use in the model’sinitial situation. The SAM contains as rows the consumption of all goods andas columns all use of factors in terms of values. Row sums (consumption orrevenue) and column sums (input) have to be equal, so that the CGE model isin an equilibrium condition (with all prices equal to unity) if no further changes(e.g., shocks) are introduced. All parameters are then calculated to match thisequilibrium.

The intra-industrial and final use of goods (section A, cf. Table 1) can befound in the top row of the I-O-table. The original SAM values are net flows,however, for the model, gross flows are needed. The estimated consumptiontaxes were applied to each commodity flow.

Section B contains the total output per sector minus exports (section C).Factor use by sectors and government is reported in D, the totals of the con-sumption tax revenues per sector can be found in part E. Additionally, importtariffs are reported in E, which were evenly distributed over all sectors. Part Fholds the taxation of labor and capital. For labor, this is the employers’ contri-bution to social security1. Taxes on capital were taken from the I-O table. Theincome tax contains social security payments of the employees, self-employedand unemployed as well as imputed social security payments (Destatis, 2010b,account II.c). The households’ income, government payments and factor use ofthe government (G and D) all stem from the national account (Destatis, 2010b,accounts II.1.2, II.2 and II.1.2.2). Finally, G also contains the household’sendowment of capital and labor. Labor is measured as total wage payments,capital equals total revenue from capital. Both were taken from the I-O table2007.

Section H contains imports at c.i.f. minus tariffs (Destatis, 2010a). Invest-ment and savings of households and government as well as the trade balance isreported in part I of the SAM (Destatis, 2010c, account III.1.2) 2.

1The total stems from account II.c of the national account 2007 (Destatis, 2010c)2Household savings equals net asset change through savings plus equity transfers plus

write-offs. Trade balance is the mean of trade and payments balance (Bundesbank, 2008, p.

4

Usually, SAM’s cannot be completed by use of one input-output table, sothat different data sources are necessary. Due to this fact, row and columnsums do not always cancel out in all cases. In that case, the SAM has to bebalanced numerical numerically. A cross-entropy procedure was applied whichworks through a minimization of the difference in information entropy betweenthe unbalanced and the balanced SAM (Golan et al. 1996; Robinson et al. 2001,the GAMS-Code CESAM is based on the work of Robinson et al. 2001).

Due to the high disaggregation of the model, there arose another numericalproblem: In five cases, production for the German market by German firms wasnegative because net exports were higher than net production. As a solution,we reduced exports to the necessary amount and set production for home to asmall positive number before balancing the matrix. A similar problem occurredin the coal and lignite mining sector (CPA 10). Subsidies were so high that netcapital input (i.e. revenue from capital) was negative for that sector. We setthe capital use to a value higher than the subsidy payments.

The balancing of the matrix was successful, with minor deviations fromequilibrium. Results are reported in Table 3.

Parameter Estimation

Due to the fact that the EcoMod7-model uses calibration as its method to obtainthe initial equilibrium, several parameters have to be estimated beforehand.Since the Stone-Geary utility function of household consumption was changedto the simpler Cobb-Douglas type, which does not need parameter estimatesbefore calibration, three CES-type functions (CES production, CET trade, andCES Armington) remain, with three elasticities to be estimated. Given theseestimates, the CES functions can be solved for all other parameters.

Calibration methods have come under serious criticism for their weak em-pirical foundations, since the initial equilibrium rests on data from one baseyear only, without taking the uncertainty in the data from input-output tablesinto account (cf. Roberts, 1994; McKitrick, 1998; Cardenete and Sancho, 2004).However, the alternative approach of an entropy-based estimation for the initialbenchmark equilibrium is in need of a time series of subsequent SAM’s that arenot available in the desired frequency and number for Germany on the levelof sectoral disaggregation at hand. McKitrick (1998, p. 549) uses a 29-yearstime series, whereas for Germany only eight years are available. It is thus veryimportant to focus on the estimation of the necessary parameters. Addition-ally, despite its shortcomings, the calibration approach has the advantage of theshortest possible time distance between the benchmark year and today.

CES Input Elasticities The elasticities of the CES production function wereestimated using the Arrow et al. (1961) approach. The advantage of this methodis that data on capital use and capital revenue are not necessary. The estimationis based on the relationship between labor input, wage rates and gross output.Arrow et al. (1961) developed the CES production function from the followingequation:

lnViLi

= a+ b lnwi + ei (5)

22)

5

where Vi is gross output in value added, Li is labor input, wi represents thewage rate and b is the elasticity of substitution σp of a given sector in countryi (cross-sectional data).

This equation can be estimated with a ordinary least square (OLS) regres-sion. Data were taken from 23 national input-output tables provided by Euro-stat (cf. Table 5). With 58 sectors, the level of disaggregation is high, althoughsmaller than the German national table. Fortunately, all tables use the samesectoral classification (CPA 2003) 3 Value added and wage rates are measuredin local currency, Li is the number of employees in an industry i. Wage rateswere computed from the ratio of total labor costs of a sector to hour equiva-lents worked in that industry, Li. The number of employees had to be takenfrom different sources since only eight input-output tables contain informationon labor input (cf. Table 5).

The results lie within the expected range reported in Table 6. All elasticitiesare significantly different from 0 at the 1% level and 17 coefficients are signif-icantly different from unity at the 10% level. The number of observations isrelatively small and standard errors naturally are highest in those cases witha small number of observations (e.g., CPA 11, petroleum, and 13, iron ore).In most cases, however, confidence intervals are relatively small. These esti-mates confirm the widely-accepted assumption of sectorally differing elasticitiesof substitution close to unity.

CES Armington Elasticities The Armington trade elasticities measure theextent to which a relative price change in the domestic market compared tothe foreign market’s price affects the relative amount of imports to domesticallyproduced goods sold in the domestic market, such that for a unitary elasticity,a one per cent change of the relative price leads to a one per cent change of therelative quantity consumed.

We are therefore looking at a relationship between relative prices and rela-tive consumption of the belonging goods. This rationale follows the approachoutlined by Blonigen and Wilson (1999) and others. The CES Armington utilityfunction in equation (4) is to be maximized subject to the budget constraint

Y = MPM +DPD (6)

where PD are the domestic price; PM are the foreign prices; M are imports, andD are domestically produced goods. From the first-order condition

M

D=(

βM1− βM

PDPM

)σM, (7)

we obtain a log-linear form easily estimated by OLS:

ln

[Mt

Dt

]= α+ σM ln

[PDtPMt

]+ εt (8)

where α = σM ln( βM1−βM ) and t is a time subscript. Since we used monthly

data with only 35 observations (1/2008 - 11/2010), dummies for seasonal effects3For sector 12, uranium and thorium ores, no estimate was needed, since Ger-

many does not have any reported flows in this sector. All data sets are available fordownload at: http://epp.eurostat.ec.europa.eu/portal/page/portal/esa95_supply_use_

input_tables/data/database.

6

were not included. There is no argument that would necessitate such a stepsince these effects should in theory apply to both markets in the same way andtherefore not alter relative prices or amounts.

Data had to be compiled from different time series provided by Destatis.The quantities of goods produced for the domestic market were taken fromthe domestic sales of the manufacturing and related sectors, domestic pricesstem from the index of producer prices. Data on import prices and volumesare available on the SITC 2-digits level, which was most appropriate comparedto the level of aggregation of both the CGE model and the other time series.Two problems remained. First of all, goods classifications of the time series didnot match in detail. This is a problem since it might distort results in somecases. Secondly, there are no data available for trade of services on this level ofdisaggregation. As a preliminary solution, we decided to estimate one elasticityfor all service related sectors from the relative volume and price of an aggregateof all service sectors, using quarterly data (Destatis, 2011a,b).

Results are reported in Table 7 and lie within the expected range. Durbin-Watson and Breusch-Pagan tests were performed. Whereas there did not seemto occur problems of heteroskedasticity, autocorrelation of the residuals was aproblem in three OLS regressions (CPA 11, 25.2, and 27.1-27.3). However, noneof the three corresponding σM -estimates was significantly different from zero ona 5% confidence level.

Due to the relatively high frequency of the data, elasticities have to beinterpreted as short-term elasticities which are assumed to be smaller than long-term estimates. We would expect that in the short run, a shift from consumptionof domestic to foreign goods is less likely than after a prolonged period of pricedifferentials. This is an important aspect with regard to the interpretation ofmodeling results.

CET Export Elasticities The CET function models the firm’s decision tosell its products on the home versus the foreign market. Like the CES productionand CES Armington utility functions, it is a constant elasticity function. Thus,elasticity estimates can be obtained in the same way. The only difference liesin the fact that rising prices lead to the desire to sell more (and not a smallerconsumption) of the product in question, such that an increase in the relativeprice on the domestic compared to the foreign market leads to an increase ofrelative sales on the domestic market compared to the foreign market.

Firms maximize their profits π from exports E and domestic sales D subjectto the CET function stated above (equation 3):

π = EPE +DPD. (9)

Analogously to the CES Armington case, the first order condition can bestated as:

E

D=(

β

1− βPEPD

)σE, (10)

where E denotes the foreign and D the domestic market, and σE is the elasticityof substitution. Compared to equation (7), the relation of prices is reversed,reflecting the aim of the firm to maximize profits (versus the maximization ofconsumption desired by the households). Equation (10) can be estimated by

7

ln

[Dt

Et

]= α+ σEln

[PMt

PEt

]εt. (11)

We used the same data as for the Armington estimation, substituting thecorresponding export figures for the import volumes and prices. Results arereported in Table 8. Durbin-Watson test indicated problems with serial cor-relation for two sectors (CPA 11 and 27.1-27.3). Both estimates of σE werenot significantly different from zero anyhow. Additionally, there seemed to beproblems of heteroskedasticity in two cases (CPA 17 and 24). Since these twoestimates were highly significant, we do not expect higher standard errors tochange our result.

4 Conclusion

The model described in this paper is well suited to analyze sectoral policiesand the impact of shocks on single sectors. Both the disaggregational extensionand the modeling of consumption taxes allow for a very close look at price andfactor cost developments that the basic model could not provide. Although weare aware of the criticism against the calibration method, the estimates reportedin the appendix are of an acceptable quality for the most part, so that the moreserious charges usually leveled against calibration models do not apply.

There are many possibilities to extend the model in the future. A focus onregions, such as the German NUTS-1 regions (Lander), would allow to estimatethe impact of both regional and national policies on regional industries andother economic agents. Another desirable extension would be a distinctionbetween small and large firms, which would enable the modeler to “look inside”an industry. In order to show effects on the distribution of income, furtherhouseholds could be introduced to represent different social classes.

8

References

Kenneth J. Arrow, Hollis B. Chenery, Bagicha S. Minhas, and Robert M. Solow.Capital-Labor Substitution and Economic Efficiency. The Review of Eco-nomics and Statistics, 43(3):225–250, 1961.

Ali H. Bayar. EcoMod7: Global Economic Modelling. GAMS Code.

Bruce A. Blonigen and Wesley W. Wilson. Explaining Armington: What De-termines Substitutability between Home and Foreign Goods? The CanadianJournal of Economics, 32(1):1–21, 1999.

Alejandro M. Cardenete and Ferran Sancho. Sensitivity of CGE SimulationResults to Competing SAM Updates. The Review of Regional Studies, 34(1):37–56, 2004.

Amos Golan, George G. Judge, and Douglas Miller. Maximum Entropy Econo-metrics: Robust Estimation With Limited Data. Wiley and Sons, 1996.

Ross R. McKitrick. The econometric critique of computable general equilibriummodeling: the role of functional forms. Economic Modeling, 15(4):543–573,1998.

Barbara M. Roberts. Calibration procedure and the robustness of CGE models:Simulations with a model for Poland. Economics of Planing, 27(3):189–210,1994.

Sherman Robinson, Andrea Cattaneo, and Moataz El-Said. Updating and Esti-mating a Social Accounting Matrix Using Cross Enthropy Methods. EconomicSystems Research, 13(1):47–64, 2001.

John B. Shoven and John Whalley. Applied General-Equilibrium Models ofTaxation and International Trade: An Introduction and Survey. Journal ofEconomic Literature, 22(3):1007–1051, 1984.

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Data

Bundesbank. German Balance of Payments in 2007. Deutsche Bundesbank,2008.

Destatis. Finance an Taxation: Tax Budget 2007. Federal Statistical Office,Wiesbaden, 2008.

Destatis. National Accounts. Input-Output-Table with 71 ProductGroups/Industries 2007. Federal Statistical Office, Wiesbaden, 2010a.

Destatis. National Accounts. Production- and Import Taxes plus Subsidies 2008.Sectoral Organization. Federal Statistical Office, Wiesbaden, 2010b.

Destatis. National Accounts. Sectoral Accounts. Yearly Results 1991 - 2010.Federal Statistical Office, Wiesbaden, 2010c.

Destatis. National Accounts. Exports and Imports, SITC 2-digits, 01/2008-11/2010. Federal Statistical Office, Wiesbaden, 2011a.

Destatis. Producer Price Index: Germany, Months, GP2009 2-digits, 01/2008-11/2010. Federal Statistical Office, Wiesbaden, 2011b.

10

5 Appendix

Figures

Figure 1: Scheme of the EcoMod7 Model

Source: EcoMod Network.

11

Tables

Table 1: Structure of the Matrix

Households Invest-Goods Sectors Factors Government Taxes ment Exports

Goods A A A

Sectors B C

Factors D D

Households G GGovernment

Taxes E F F

Invest-ment I I

Imports H

12

Table 2: Sets and Variables

Setsj recipientsi goods/sectors, i ∈ j

Endogenous Variables Exogenous VariablesPL, PK factor prices K,L endowment of capital, laborLU unemploymentK(j) primary factor demand tK(i) taxes on the use ofL(j) of agent j tK(i) capital and laborY household income tY income taxP (i) domestic price of iX(i) domestic sales of i tC(i, j) consumption tax on i,

paid by jPE(i) export price of iXE(i) exports of iPM (i) import price of i tM (i) tariff on iXM (i) imports of iCY (i) household demandCG(i) government demandCI(i) investment demandXD(i) domestic production of iI, S savings and investment

Table 3: SAM: CESAM balancing

Normalized Entropy difference 0.969Entropy Difference 0.117Squared Error measure 3.09e-5Highest deviation of row-colum totals 0.150Number of deviations > 1% 15 of 151

13

Table 4: Mapping of Industry Classifications

CPA2003 CPA2008 SITC CPA2003* CPA2003 CPA2008 SITC CPA2003*GP2009 GP2009

01 101 00 01 24 201 51 24104 01202 52109 08 203 53

20 204 5641 20642 205 59

02 02 24.4 211 54 2405 102 03 05 212 5510 051 32 10 25.1 221 23 25

052 6211 061 33 11 25.2 222 57 25

062 34 58091 26.1 231 26

12 NA 26.2-26.8 232 66 2613 071 13 233

072 23414 081 28 14 235

089 236099 27 239237 192

15 103 43 15 27.1-27.3 241 67 27105 07 242106 02 243107 04 27.4 244 68 27108 05 27.5 245 27

06 28 251 69 2809 252

15.9 110 11 15 25316 120 12 16 25417 131 26 17 255

132 65 256133 257139 259

18 141 84 18 29 281 71 29142 85 282 72143 283 73152 284 74

19 151 21 19 28961 331

20 161 24 20 332162 63 30 262 75 30

21.1 171 25 21 31 271 81 3121.2 172 64 21 272 7722.1 181 22 273

22.2-22.3 182 22 27423 191 23 279

14

Table 4 continuedCPA2003 CPA2008 SITC CPA2003* CPA2003 CPA2008 SITC CPA2003*

GP2009 GP200932 275 76 32 35 301 79 35

263 302264 303

33 265 87 33 304266 88 309267 36 310 82 36268 321325 322

34 291 78 34 323292 324 etc.293

* The CPA2003 2-digit classification contains 58 sectors, while the71-sector model based on CPA2003 has several sub-sectors. To each ofof these sub-sectors, the same elasticity estimate was applied.

Table 5: Estimation of the CES production function - country data*

Country Year Source of labor input Approximation**Belgium 2005 I-O table 2005 -Bulgaria 2004 I-O table 2004 - lc n04num1 -Denmark 2006 I-O table 2006 -Germany 2007 I-O table 2007 -Estonia 2006 Employees 2008 - lc n08num1 r2 yesFinland 2007 I-O table 2007 -France 2007 I-O table 2007 -Ireland 2006 Employees 2008 - lc n08num1 r2 yesLatvia 2004 Employees 2004 - lc n04num1 -Lithuania 2006 Employees 2008 - lc n08num1 r2 yesNetherlands 2006 Employees 2008 - lc n08num1 r2 yesNorway 2007 Employees 2004 - lc n04num1 yesAustria 2006 Employees 2004 - lc n04num1 yesPoland 2006 Employees 2004 - lc n04num1 yesRomania 2006 Employees 2008 - lc n08num1 r2 yesSweden 2006 I-O table 2006 -Slovakia 2006 Employees 2008 - lc n08num1 r2 yesSlovenia 2006 Employees 2008 - lc n08num1 r2 yesSpain 2006 Employees 2008 - lc n08num1 r2 yesCzech Republic 2007 Employees 2004 - lc n04num1 yesUK 2003 Employees 2004 - lc n04num1 noPortugal 2006 I-O table 2006 -Macedonia 2007 I-O table 2007 -* All data taken from Eurostat.

** For approximation, the data set “Employees, sex, age and sectoral classification

(1998-2008, NACE Rev.1.1) (1000)” (Eurostat) was used. By making use of the sectoral

growth rate, a yearly growth rate of employment was calculated.

15

Table 6: Estimation of the CES production function - Results

CPA a b Std.Err.(b) Obs.01 Agriculture 1,721 0,870** 0,089 1902 Forestry 1,777 0,850** 0,097 1905 Fishing 1,308 0,930 0,115 1110 Coal and lignite mining -0,341 1,139 0,114 1411 Petroleum and natural gas 0,058 1,360 0,365 1013 Iron ores -0,373 1,301 0,215 914 Other mining 0,911 0,966 0,050 2115 Food and beverage 0,821 0,954* 0,038 2316 Tobacco products 0,156 1,180 0,151 1317 Textiles 0,556 0,958** 0,030 2318 Clothing 0,370 1,006 0,031 2119 Leather and shoes 0,384 1,007 0,031 2120 Wooden products (w/o furniture) 0,701 0,961* 0,031 2321 Paper products 0,793 0,952* 0,039 2322 Print products 0,884 0,918*** 0,040 2323 Coke and fuels 1,280 0,995 0,136 1624 Chemicals 0,717 1,024 0,051 2325 Rubber and plastic products 0,757 0,945** 0,035 2326 Other petroleum products 0,699 0,989 0,035 2327 Metals 0,726 1,011 0,061 2328 Processed metals 0,634 0,961** 0,027 2329 Machinery and equipment 0,435 1,006 0,027 2330 Office equipment and computers 1,062 0,876*** 0,042 2031 Electric machinery and equipment 0,281 1,046 0,041 2332 Telecommunication equipment 0,750 0,926* 0,082 2133 Precision mechanics 0,623 0,975 0,031 2234 Vehicles 0,606 0,973 0,044 2335 Other vehicles 0,310 0,998 0,025 2336 Furniture and processed products 0,597 0,948*** 0,027 2237 Secondary raw materials 1,876 0,792*** 0,088 2040 Electricity 0,714 1,122 0,064 2241 Water supply 0,693 1,006 0,063 2245 Construction 0,920 0,918*** 0,047 1850 Automobile trade and maintenance 0,884 0,950* 0,048 2351 Wholesale 0,864 0,968 0,050 2252 Retail 0,641 0,991 0,045 2255 Hospitality industry 0,796 0,926*** 0,041 1860 Transportation (overland) 0,455 1,033 0,041 2361 Transportation (water) 1,043 0,965 0,092 2162 Transportation (air) 0,237 1,013 0,184 2163 Transportation services 1,036 0,946* 0,060 23

*** b < 1 with α < 0.05, left-sided test,** b < 1 with α < 0.10, left-sided test,* b < 1 with α < 0.20, left-sided test.

16

Table 6 continued.

CPA a b Std.Err.(b) Obs.64 Telecommunication services 1,215 0,941* 0,053 2365 Financial services 1,699 0,796*** 0,074 2366 Insurances 0,659 1,016 0,082 2367 Other financial services 1,411 0,855*** 0,076 2270 Housing and renting 3,320 0,879** 0,082 2271 Renting of mobile objects 1,708 0,953 0,066 2272 Services of the IT-sector 0,795 0,938** 0,046 2373 Research services 0,416 0,957* 0,035 2274 Other business services 0,776 0,950** 0,031 2275 Public administration and defense 0,260 0,991 0,024 1580 Education 0,105 1,000 0,009 1785 Health services 0,351 0,969* 0,018 1890 Sewage and garbage disposal 0,569 1,029 0,029 2391 Organizations and associations 0,206 0,992 0,022 2192 Entertainment and cultural services 0,525 1,018 0,036 2293 Other services 1,052 0,990 0,048 2295 Services of private households -0,076 1,077 0,134 12

*** b < 1 with α < 0.05, left-sided test,** b < 1 with α < 0.10, left-sided test,* b < 1 with α < 0.20, left-sided test.

17

Table 7: Estimation of CES Armington Elasticities

CPA σA StdErr Durbin-Watson Breusch-Pagan1 0.416 0.098 1.883 0.086

(0.000) (0.399) (0.769)5 0.165 0.075 2.193 2.083

(0.036) (0.727) (0.149)10 0.000 0.082 2.215 1.083

(0.997) (0.7680 (0.298)11 0.234 0.134 0.972 0.551

(0.090) (0.001) (0.458)14 0.536 0.075 2.727 0.048

(0.000) (0.989) (0.827)15 0.600 0.108 2.680 0.354

(0.000) (0.983) (0.552)15.9 0.912 0.070 2.767 0.101

(0.000) (0.992) (0.751)16 0.276 0.067 3.343 0.151

(0.000) (1.000) (0.698)17 0.278 0.059 2.017 4.808

(0.000) (0.568) (0.028)18 0.100 0.071 1.636 1.893

(0.168) (0.154) (0.169)19 0.605 0.076 2.607 0.075

(0.000) (0.971) (0.785)20 0.330 0.121 2.768 0.100

(0.011) (0.991) (0.751)21.1 0.161 0.101 1.577 0.891

(0.121) (0.120) (0.345)21.2 0.169 0.058 2.440 0.032

(0.006) (0.921) (0.859)24 0.799 0.167 3.121 1.079

(0.000) (1.000) (0.299)24.4 0.730 0.114 3.066 0.020

(0.000) (1.000) (0.888)25.1 0.012 0.057 1.934 0.054

(0.840) (0.466) (0.816)25.2 0.286 0.067 1.141 0.005

(0.000) (0.005) (0.943)26.2-26.8 0.233 0.109 2.093 0.054

(0.040) (0.613) (0.816)27.1-27.3 -0.035 0.106 1.090 0.059

(0.745) (0.003) (0.809)27.4 0.081 0.093 1.217 0.852

(0.390) (0.011) (0.356)28 0.219 0.078 2.473 0.129

(0.009) (0.929) (0.720)P-values in parentheses (H0: σA = 0).

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Table 7 continuedCPA σA StdErr Durbin-Watson Breusch-Pagan29 0.292 0.055 2.913 0.112

(0.000) (0.998) (0.738)30 0.185 0.065 2.984 0.031

(0.007) (0.999) (0.861)31 0.433 0.078 2.564 0.677

(0.000) (0.960) (0.411)32 0.325 0.117 2.456 0.177

(0.009) (0.912) (0.674)33 0.445 0.072 2.621 0.747

(0.000) (0.972) (0.388)34 0.205 0.052 2.657 0.161

(0.000) (0.978) (0.688)35 0.848 0.050 2.766 1.215

(0.000) (0.993) (0.270)36 0.257 0.062 2.080 0.013

(0.000) (0.611) (0.909)Services 0.021 0.011 2.38 1.279

(0.070) (0.884) (0.258)P-values in parentheses (H0: σA = 0).

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Table 8: Estimation of CET Trade Elasticities

CPA σE StdErr Durbin-Watson Breusch-Pagan1 -0.387 0.094 1.615 0.070

(0.000) (0.145) (0.792)5 -0.607 0.044 2.422 0.054

(0.000) (0.905) (0.816)10 0.011 0.051 2.403 0.897

(0.826) (0.895) (0.344)11 -0.180 0.114 0.657 0.015

(0.125) (0.000) (0.903)14 -0.605 0.047 2.651 0.534

(0.000) (0.977) (0.465)15 -0.727 0.063 2.239 0.315

(0.000) (0.753) (0.575)15.9 -0.898 0.045 2.885 2.230

(0.000) (0.998) (0.135)16 -0.025 0.061 3.200 0.251

(0.677) (1.000) (0.617)17 -0.364 0.097 2.941 6.954

(0.001) (0.999) (0.008)18 -0.597 0.104 1.510 0.351

(0.000) (0.080) (0.554)19 -0.515 0.101 2.840 0.002

(0.000) (0.996) (0.963)20 -0.334 0.079 2.190 0.066

(0.000) (0.726) (0.798)21.1 -0.382 0.131 2.120 3.243

(0.006) (0.636) (0.072)21.2 -0.177 0.105 2.568 2.26

(0.101) (0.961) (0.133)24 -0.518 0.135 2.367 7.594

(0.001) (0.869) (0.006)24.4 -0.384 0.157 2.789 0.462

(0.020) (0.993) (0.497)25.1 0.026 0.083 2.98 0.751

(0.756) (0.999) (0.386)25.2 -0.260 0.088 1.359 1.695

(0.006) (0.029) (0.193)26.2-26.8 -0.015 0.156 1.906 0.204

(0.923) (0.418) (0.652)27.1-27.3 -0.087 0.105 0.655 0.070

(0.411) (0.000) (0.792)27.4 -0.242 0.134 1.930 0.269

(0.080) (0.449) (0.604)28 -0.241 0.072 1.786 0.338

(0.002) (0.279) (0.561)P-values in parentheses (H0: σE = 0).

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Table 8 continuedCPA σE StdErr Durbin-Watson Breusch-Pagan29 -0.223 0.083 2.533 0.874

(0.011) (0.947) (0.350)30 -0.060 0.057 2.43 1.158

(0.300) (0.912) (0.282)31 -0.253 0.0870 2.793 1.069

(0.007) (0.994) (0.301)32 -0.127 0.129 2.508 5.960

(0.333) (0.942) (0.015)33 -0.607 0.086 3.017 1.503

(0.000) (0.999) (0.220)34 -0.150 0.092 3.125 1.336

(0.115) (1.000) (0.248)35 -0.811 0.047 2.940 1.626

(0.000) (0.999) (0.202)36 -0.373 0.070 2.854 0.874

(0.000) (0.997) (0.350)Services 0.122 0.063 2.310 0.220

(0.065) (0.818) (0.639)P-values in parentheses (H0: σE = 0).

21