Price Differences and the Structure of Urban-Rural ...€¦ · Resumen: This paper estimates the growth of Big Mac prices for urban and rural areas in the United States. We find that

Price Differences and the Structure of Urban-Rural Transmission: Exploratory

Analysis using the Big Mac Index

Autores y e-mail de la persona de contacto:

Alberto Díaz, Scott Loveridge y Dusan Paredes,

Departamento: Economía Aplicada, Economía y Agricultural, Food, and Resource

Economics.

Universidad: Universidad de Oviedo, Michigan State University y Universidad

Catolica del Norte.

Área Temática: Crecimiento desarrollo, competitividad y desigualdades territoriales.

Resumen: This paper estimates the growth of Big Mac prices for urban and rural areas

in the United States. We find that 2014 prices grew slightly faster in rural areas in

comparison to urban areas. Our results are robust to spatial econometrics

specification. We also find that most of the differences in price change patterns are due

to localized effects rather than spillovers.

Palabras Clave: Big Mac, urban rural price differential, price index, spatial

econometrics, stratified random sample.

Clasificación JEL: D22, E31, O18, R11, R12.

Running Head : Price Differences and the Structure of Urban-Rural Transmission

1. Introduction

The rural areas of the United States and other highly developed countries face

continuing out-migration. This phenomenon is typically explained as the result of

numerous factors pulling people towards the cities. Among others, the factors often

cited include the lure of the city’s entertainment and shopping; better job prospects; ease

of finding two jobs in an era of dual-earner households. These factors can be broadly

lumped into a general term: agglomeration economies. Congestion costs offset

agglomeration economies. As people move from low density areas to high density

areas, congestion costs rise, and one would expect costs to converge as agglomeration

economies are exhausted and congestion costs begin to dominate. In theory, costs

should equilibrate across space until new shocks (e.g., technical change) disturb the

system. After declining for much of the last half of the 20th century, many US cities

recently experienced a resurgence. Setting aside the property bust of 2008-09, urban

land rents prices have recently tended to rise while rural areas were more stable,

indicating a lack of convergence. To what extent do land rents reflect trends in the

broader economy? Most evidence on rural prices and costs is based on housing.

The pace of rural-urban price convergence is not well known in the United

States due to lack of data on rural prices. Through well-known principles established

long ago by Von Thunnen, it is recognized that land rents will typically be cheaper

outside of urban areas, so housing costs (the one rural price data point that is

consistently available) may not be a good indicator of price convergence. House prices

are also influenced by Federal monetary goals as changes in policy quickly work their

way into mortgage rates, changing the amount of money consumers can afford to

borrow for housing. To the extent that places vary in their level of churn in the housing

market, house prices some places may respond more quickly to changes in Federal rates

than others. Relying solely on housing prices is problematic, and prices of other goods

are readily measured, but Loveridge and Paredes (2016) produce several arguments

against attempting to measure prices for a rural basket of goods. When considering

convergence, taking the time to measure a basket could produce lags in the information.

Such lags could reduce the value of understanding relative movements.


In this paper, we explore the use of an easily collected price (the Big Mac

sandwich from McDonald’s) for examining the dynamics of price across the urban-rural

space. Using two rounds of Big Mac price observations from a national sample, we

compute same-store price changes. We use spatial models to explore patterns in price

changes, including estimates of direct and indirect impacts. We find spatial

autocorrelation in price changes, and controlling for other factors, that rural prices rose

faster than urban prices (albeit from a lower base) during the observation interval.

Spatial relationships in prices seem to be limited to very localized effects, meaning the

prices increases are likely not due to urban spillover effects.

2. Literature Review

A well-established body of work related to spatial prices focuses on price

transmission and movement of commodities (e.g., Fackler and Goodwin, 2001; Burke

and Myers, 2014; Vitale and Bessler, 2006), land rents (e.g. Capozza and Helsley,

1989), or price discrimination (e.g. Guo and Lai, 2014). Less well-studied is the spatial

dynamics of cost of living or price indices. In the United States, the consumer price

index is based on prices of a basket of goods, but is measured only in cities. While a

basket of goods is a robust approach to determining prices, it still has shortcomings,

namely issues that arise when consumers substitute out of expensive goods (Araya and

Rivera, 2011), or when an item in the basket becomes obsolete (Erikson and Pakes,

2011).

Price/cost comparisons become even more problematic when done across countries

due to the vagaries of exchange rates, leading The Economist to propose a

“lighthearted” approach to measuring purchasing power parity via the Big Mac in 1986

(The Economist, 2014). Since that time, authors of over forty refereed journal articles

have used the index to study a variety of price comparison issues in the international

context; recent studies include O’Brien and Vargas, (2016), Cavallo and Rigobon

(2016) or Clements, et al. (2012).

Less studied is how Big Mac prices vary across places within a country. There are

two contributing factors. First, in some countries, such as Chile, prices appear to be set

at the corporate level rather than by individual location managers (Paredes, 2016), as is


done in the US (Ater and Rigbi, 2015). Second, while the company operates over

30,000 locations in more than 100 countries, in many parts of the world, McDonald’s

restaurants are found only in large metropolitan areas (McDonald’s Corporation, 2016),

so regional analysis in many countries would be hindered by a lack of ability to obtain

observations outside of major cities.

An exception to the lack of academic products relating to regional Big Mac price

variation is a study by Loveridge and Paredes (2016) that explored regional variation in

Big Mac prices. The Big Mac differs from commodity studies in a subtle way. It is a

higher value-added product intended to be consumed within minutes of production, so

spatial arbitrage is less feasible than it would be with a commodity such as maize or

some other grain. The Big Mac is thus more appropriate for the study of local costs

than other standardized products. We borrow from methods employed in Loveridge and

Paredes (2016)to develop analysis of determinants of price change in the United States.

3. Method

We use a regression approach to estimate trends in the urban-rural price

differential in United States. In particular, we use the Big Mac price differential

between August 2014 and December 2014 as the dependent variable, and we use a set

of control variables to take into account the characteristics of the particular restaurant as

well as a dummy variable indicating urban-rural condition. This strategy recovers the

price index effect through the marginal effect associated with the urban-rural dummy.

As with any OLS approach, its accuracy rests on the exogeneity of the control variables,

as well as the absence of selection bias or any another source of endogeneity. We build

our identification strategy carrying out an analysis of a stratified random sample of Big

Mac prices in McDonald’s restaurants across United States. The homogeneity of the

Big Mac, as well as services provided by McDonald’s restaurants, helps to avoid

problems with the econometric specification (Loveridge and Paredes, 2016). We include

control variables to take into account any unobservable factor affecting the fixed costs

in the stores and supply of additional services.

While the price of a Big Mac is set by the individual location’s manager, not

centrally (Ater and Rigbi, 2015), the spatial econometrics literature provides several


reasons to expect Big Mac price spatial correlation among restaurants. First, we can

expect scale and agglomeration economies in large urban areas. There are increments in

productivity when the firms are close enough through the spillover interaction of

knowledge as well as through the better match between supply and demand in larger

labor markets (see Rosenthal and Strange, 2004; Combes, 2000; Ciccone, 2002;

Combes et al., 2008 or Artis et al., 2012). The improvement in productivity can be

within the industry, namely location economies, or between sectors, also known as

urbanization economies. In both cases, economics of agglomeration would push up

wages, increasing firm costs, and maybe also affecting local prices of nearby stores.

A second reason to expect spatial autocorrelation is the role played by functional

areas instead of administrative division (Bellandi, 2002; Dei Ottati, 2002; Boix and

Galleto, 2008). An administrative spatial division, e.g., county line, does not necessarily

fit with the underlying economic forces shaping the economic interaction between

spatial units. For example, core-periphery structures could generate important

externalities – see Lambert et al. (2012) - which are not taken into account in the

administrative division. This implies that we could observe weaker correlation among

counties than what might exist between functional areas.

A final argument has to do with a popular topic in regional science--spatial

competition between firms (Biscaia and Mota, 2011). Previous articles (Hotelling, 1929;

Hakimi, 1983; Lederer and Thisse, 1990) indicate that firms choose the price and the

location where they can maximize profits. In addition, Porter (1979) explains that scale

economies can be developed easily in territories with a bigger local market. In this case,

strong spatial competition could push down prices in large urban areas, while the

opposite condition could result in monopolistic power in rural areas. Chirco et al.

(2003) provide insights as to how the structure of demand can influence prices and

products over space.

Due to these spatial considerations, we complement the Ordinary Least Squares

(OLS) estimation with a spatial econometric approach to improve the efficiency and

consistency of estimates (Anselin, 1988; LeSage and Pace (2009). We produce our

estimates using the Spatial Autoregressive Model (SAR) and Spatial Error Model


(SEM). 1 While the SAR model assumes the spatial autocorrelation in the dependent

variable (equation 1) - SEM includes the spatial effect in the error (equation 5).

In both models we capture spatial dependence with a spatial lag. This spatial lag

is a linear combination of the values of the variable in all the j neighbors .

The weights are placed in an matrix as in equation (1). Two types of

spatial weights are used to generate the matrix. The first weight uses the inverse linear

distance between stores while in the second it is the inverse-quadratic distance between

stores.2 Returning to the specification, we set the SAR model as:

(1)

where is the spatial average of the dependent variable and is the spatial

autoregressive parameter. The marginal effect in these spatial models differs from OLS.

In OLS, the coefficient of the variable is equal to the marginal effect of the variable.

However, for the SAR model, there may be an increment of the variable in the area, but

also in the neighbors. Following LeSage and Pace (2009) or Elhorst (2014). This effect

can be seen in equation (2).

(2)

The expansion of is a geometric series that can be expanded as in

equation (3):

(3)

In this expression, the increment of the independent variable affects the

neighboring territories through infinite, but decreasing rounds. So

generates two types of effects: direct and indirect impact. The direct impact is the effect

of the dependent variable in a territory due to the increment of the independent variable

in that same territory, but also including a possible feedback effect through the

neighbors. On the other hand, the indirect impact would be the effect over the dependent

1 Model SARMA and SDM were also estimated (Apendix I) and were not significantly different from

spatial lag results with SARMA; the spatial effect in the urban variable with SDM was also not

significantly different. 2 Alternative weight matrixes for polygons - Queen, Rook, k-neighbours, etc. were discarded due to the

configuration of our database of restaurants as points over the territory.


variable in a particular area caused by the increment of the independent variable in the

other regions. If we decompose both effects, then we can measure the relevance of

spatial transmission among stores. As in LeSage and Pace (2009) or Elhorst (2014), we

estimate both effects obtained through equation (4), while the standard deviation is

obtained through Monte Carlo Simulation.

Average Total Impact (ATI) = =

Average Direct Impact (ADI) = =

Average Indirect Impact = = ATI-ADI

(4)

On the other hand, as equation (5) shows, the SEM includes a spatial lag in the

error term instead the dependent variable. Here, in the case of SEM, we assume that

the omission of the spatial interactions is just a problem of efficiency because the spatial

autocorrelation would exist only on unobservable factors. In this setup, the

autocorrelation does not change the interpretation of the coefficients of the variables.

However, we should have to take into account that the standard deviations may change

the significance of these coefficients. Equation (5) shows the model specification.

(5)

4. Application to the US

4.1 Data

We carry out the empirical analysis using collected data from a stratified random

sample of McDonald’s restaurants. Our sample includes 3,440 restaurants from a total

of approximately 14,000 stores across the 48 contiguous US states plus Washington

DC. In particular, we built a stratified sample over-representing rural areas. From US


Census information we estimated the population shares to build a weight probability for

urban and rural counties. Of course, these weights only affect the standard errors, not

the size of our estimated coefficients. Figure 1 shows the spatial distribution of these

restaurants.3 We repeated the data collection capture time variation. The first round

survey took place in late July- early September 2014, while the second round, covering

the same sampled restaurants, was carried out in December 2014, with a 93%

completion rate for the two observations. With both periods of time, we can track the

price change across time for each restaurant in our sample.

Figure 1. McDonald’s in the Sample

Source: Own computation.

Note. We intentionally excluded Alaska, Hawaii, Puerto Rico, Guam, Virgin Islands, American Samoa

Following Loveridge and Paredes (2016), we control for characteristics of the

restaurant address the possibility of different fixed cost across outlets. Our controls,

provided by Aggdata4, include the availability of: a play area for kids, a drive-through

window, Wi-Fi, as well as whether the location accepts arch cards (prepaid McDonalds

debit card). The rurality of each restaurant’s location was assigned using the USDA

Economic Research Service 2013 Rural-Urban Continuum Classification (RUCC) code.

The RUCC code is a commonly used grouping variable in urban research (for example,

Rickman and Wang, 2015; Porter, 2016). The RUCC categories are provided in

Appendix Table A1. For our analysis we consider a county urban if the county’s RUCC

3 Additional details about the survey method can be found in Loveridge and Paredes (2016). 4 www.aggdata.com.


code is less than 3 based on Loveridge and Paredes’ (2016) finding of little price

difference across the higher RUCC codes.

We provide a set of summary statistics in Table 1. First of all, we detect an

average price increase of about 1.2% during the roughly four months between data

collection periods. The reported Big Mac price range (including both periods) was

between $1.19 and $6.00. Table 1 also includes the Aggdata information about different

services available in each store. Most outlets are quite similar in characteristics: 92.5%

include a drive-through window, 99.1% accept the arch card and 95.4% provide Wi-Fi.

There is more variability in the play area for children, with only 30.2% of restaurants

providing this. While there is little variation in several of these features, we include

them as control factors to evaluate the urban-rural price differential. Finally, Table 1

shows 32.3% of the sample is located in an urban area, while 67.7% are in rural areas.

Table 1

Summary statistics

Variable Definition Mean Std. Dev. Min Max

Percentage price increase 1.227 11.099 -71.93 232.56

Play place Restaurant with an area for kids (binary) .302 .459 0 1

Drive thru Restaurant with drive-in window (binary) .925 .264 0 1

Arch card Restaurant accepts arch cards (binary) .991 .096 0 1

Wi-Fi Restaurant with Wi-Fi (binary) .954 .210 0 1

Urban Restaurant in urban area: (binary RUCC<3) .323 .468 0 1

4.2 Results

We start with OLS estimations and we compare the performance against SAR

and SEM models to evaluate the potential bias and efficiency problems. The first

column of Table 2 contains the OLS estimations. The OLS estimator suggests that rural

areas had a higher price increase than urban areas across the study period, rounding to


1.27%. As we also expected, the proxies for fixed cost are not significant in explaining

the price change variation. We use the predicted error term from OSL to test if we find

evidence of spatial using the Moran’s I.

The Moran’s I row in Table 2 shows that OLS is clearly affected by bias and

efficiency problems because the spatial autocorrelation is positive and significant. In

practical terms, we should not trust the price change differences determined by the OLS

price index, namely 1.27% because this could be affected by bias and efficiency

problems.

Table 2

OLS, SEM and SAR estimations with robust deviation

OLS SAR SEM

Urban -1.27*** -1.12*** -1.34***

Play place 0.06 0.17 0.28

Drive thru -0.91 -0.97 -1.05

Arch card -2.18 -1.88 -1.53

Wifi 2.16** 1.84* 1.54

Constant 2.57 2.22 2.57

0.25***

0.25***

N 3194 3194 3194

Moran's I test 9.12***

LM test 82.011*** 83.082***

Robust LM test 2.84* 1.16

Note. *, ** and *** represent estimates significantly different from

zero at 10%, 5% and 1%, respectively.


Even if we reject the use of OLS, we still have to decide if SAR or SEM have a

better fit for our model as well as the appropriate spatial weight matrix for this analysis.

For most of our estimations, we find that inverse quadratic distance matrix fits the data

– see table 3 - possibly indicating that the spatial autocorrelation has a local character.

Table 3

Spatial diagnostics of linear vs quadratic distance

W(distance) W(distance2)

Moran's I 9.12*** 8.31***

LM (SEM) 82.011*** 62.365***

Robust

LM (SEM) 1.385 0.015

LM (SAR) 83.082*** 62.53***

Robust

LM (SAR) 2.456 0.183*

Note. *, ** and *** represent estimates

significantly different from zero at 10%, 5% and

1%, respectively.

Returning to Table 2, columns 2 and 3 report the SAR and SEM, respectively, as well as

the Lagrange Multiplier (LM) to evaluate both models. Both the SAR and SEM models

produce a slightly different price index for urban areas, but the estimates are not

substantially different than OLS. The estimated price change index now ranges

between 1.12% and 1.34%, and except for Wi-Fi in the SAR model, the rest of the

control variables are still not significant. The interesting result appears with the LM test;

the test does not reject both models. As Anselin (1988) suggest, in this case we need the

robust version of the LM test to evaluate both models. The robust LM test suggests that

we find spatial autocorrelation to support the SAR model, but not SEM. In other words,

the spatial autocorrelation comes from the price transmission among restaurants more


than autocorrelation between unobservable factors. Next section uses the SAR estimates

to estimate the price index and the direct and indirect impact.

We use equation (4) to identify the marginal effect of the urban-rural dichotomy

on price change. The estimated average effects for our sample and are shown in Table 4.

Table 4

Marginal urban effects - SAR model,

Mean Std. Dev. Z P-value

Average Total Impact -1.490*** 0.501 -2.985 0.000

Average Direct Impact -1.134*** 0.372 -3.057 0.000

Average Indirect Impact -0.357*** 0.161 -2.230 0.000

Note. *, ** and *** represent estimates significantly different from zero at 10%, 5%

and 1%, respectively.

As we discussed in the first section, the marginal effect is not similar to the

estimated OLS coefficient. The SAR model reveals that Big Mac prices in rural areas

grew 1.49% faster than urban areas. In this scenario we could think than rural areas

have higher price growth because they are close to urban areas. In other words, rural

areas are not getting more expensive on their own; it only would be a spillover effect

from urban areas. Now, the estimates for direct and indirect impact help us to evaluate

this question. As Table 3 shows, from the 1.4% price change, fully 1.13% is attributable

to the rural area itself or equivalently, 76% of the total price change appears to be due to

sources from within rural areas.

Clearly the indirect effect depends on the distance, due to the presence of the

weight matrix in the estimation, combined with the spatial parameter – see equation

(1). As a robustness check, we evaluate the role of distance to assess the geographic

spread of this process. To estimate the area which influences a restaurant we created a

cumulative indirect effect for the distance to each restaurant. To create this variable, we

calculated the percentage of each indirect effect in the total indirect effect over each

store. Then, we sorted these percentages using the distance from the source. Finally, all


these percentages are added up for each distance to create a cumulative effect. Figure 2

represents in a histogram distribution of the cumulative indirect effect of each store

within a ring of one kilometer. The Y-Axis in figure 2 can be interpreted in terms of the

usual density. It represents the coefficient of the absolute frequency and the width of the

intervals in the histogram.

Figure 2. Histogram of the proportion of indirect effects in 1 km - SAR model

Source: Own computation.

Figure 2 indicates that most of the restaurants accumulate more than 70% of the indirect

effect within one km. So, it seems, as this process is local, without much interaction

outside the borders of the city.

5. Conclusions


This paper first documents how Big Mac prices changed, and how that change differed

between rural and urban areas in mid- to late 2014, and then explores the influence of

localized processes over prices. The econometric analysis of the collected survey data

revealed a significant negative effect of being in an urban area over the increase in

prices. This significant effect seems to indicate that urban areas in US were

experiencing slower price increases relative to rural areas. We compute indirect effects

and determine that most of the rural price change is likely due to localized effects.

Several factors could be behind the relative difference in change. First, there may be

transitory influences that are causing faster rural price increases. A commodity boom,

for example, could affect rural areas more than urban areas. Rural areas have lower

labor force participation than urban areas, but at the same time rural markets are thin, as

evidenced by the fact workers may travel great distances for high paying jobs, such as

those found in the natural gas extraction industry during the time period of our data

collection (Brown, 2014). On the other hand, it is possible that urban cost structures are

becoming more efficient. While urban rents are rising, many core urban areas are

experiencing a renaissance and concomitant population increase that could help

restaurants spread their fixed costs over more customers or that could increase the

spatial competition with other McDonald’s locations or new non-McDonald’s

competitor restaurants. Finally, it is possible that high volume outlets are simply

innovating faster in an effort to reduce costs and stay competitive.

Our approach demonstrates the utility of using a single, standardized, widely

available, but relatively complex item to collect price change information. We provide

insights on the structure of rural price transmission, showing that spillovers, at least in

the case of this item, can be highly localized.

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Appendix

Table A1

RUCC classification

Code Description

1 Counties in metro areas of 1 million population or more

2 Counties in metro areas of 250,000 to 1 million population

3 Counties in metro areas of fewer than 250,000 population

4 Urban population of 20,000 or more, adjacent to a metro area

5 Urban population of 20,000 or more, not adjacent to a metro area

6 Urban population of 2,500 to 19,999, adjacent to a metro area

7 Urban population of 2,500 to 19,999, not adjacent to a metro area

8 Completely rural or less than 2,500 urban population, adjacent to a metro area

9 Completely rural or less than 2,500 urban population, not adjacent to a metro

area

Table A2

Different spatial specifications

SAR SEM SARAR SDM

Play place 0.17 0.28 0.23 0.285

Drive thru -0.97 -1.05 -1.03 -1.067

Arch card -1.88 -1.53 -1.68 -1.619

Wifi 1.84 1.54 1.69 1.799*

Urban -1.12*** -1.34*** -1.23*** -1.433*


Play

place_W

-1.724**

Drive

thru_W

0.587

Arch card_W -4.839

Wifi_W 3.53**

Urban_w 0.589

Constant 3.05 3.32 3.17 3.403

0.25*** 0.14** 0.248***

0.25*** 0.13

N 3194 3194 3194 3194

Note. *, ** and *** represent estimates significantly different

from zero at 10%, 5% and 1%, respectively.

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Price Differences and the Structure of Urban-Rural ...€¦ · Resumen: This paper estimates the growth of Big Mac prices for urban and rural areas in the United States. We find that