Wages and Market Potential in Germany

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... Sabine Böckem, Heinz Holländer, Klaus Wälde,. Heiko Zuchel and the participants at the ”Jahrestagung des Vereins für Socialpolitik” for helpful comments. 1 ...
Wages and Market Potential in Germany Michael Roos¤ Universität Dortmund Graduiertenkolleg ”Allokationstheorie, Wirtschaftspolitik und kollektive Entscheidungen” 44221 Dortmund [email protected] Abstract Using a market potential function, we examine the spatial correlation of wages and consumer purchasing power across regions in West Germany. The market potential function can be regarded as a reduced form of several new economic geography models. Thus, the estimation results provide some …rst evidence on the validity of these models for European regions. We …nd that the wage in one region is indeed positively related to purchasing power in other regions. However, this relationship only holds for skilled workers’ salaries and wages, whereas it does not for the wages of untrained workers. JEL codes: F12, R12 Keywords: economic geography, market potential function, empirical evaluation ¤

I am grateful to Lutz Arnold, Sabine Böckem, Heinz Holländer, Klaus Wälde, Heiko Zuchel and the participants at the ”Jahrestagung des Vereins für Socialpolitik” for helpful comments.

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1

Introduction

In the past decade, a new literature evolved: ”new economic geography”. This literature analyzes some of the centrifugal and centripetal forces that shape the economic landscape. To date, there exist a number of theoretical models which explain large-scale agglomeration phenomena by linkages between …rms and consumers or vertical linkages between …rms. All these models are based on increasing returns, imperfect competition, and trade costs (for a recent survey, see Schmutzler 1999). Despite the attained level of theoretical sophistication the empirical evaluation of these models has been scant. This led some authors (Ottaviano/Puga 1998: 726) to claim that empirical testing of the models is the ”single most important direction” of further research. In order to progress in the task of re…ning the still very abstract theoretical models one must try to weigh the e¤ects that have been prosposed to explain the economic geography. This can be achieved only by looking at the data. We aim to provide some new evidence. Our work is based on the work of Hanson (1999), who was the …rst to test Helpman’s version of Krugman’s ”core-periphery model” (Krugman 1991a). Krugman (1992: 351) himself pointed out that one of the equilibrium conditions of his model closely resembles to a concept which is known in regional science since the 1950s: the market potential function. Harris (1954) identi…ed the access to product and factor markets as an important force creating agglomeration of manufacturing …rms. In order to have a measure of this force he constructed the so-called market potential index M Pj =

K X

Yk f (djk )

(1)

k

which de…nes the market potential of location j as the sum of purchasing power Yk in the accessible regions k, weighted by a function of distance f (djk ) between j and k. It is a nice property of this ad-hoc index that in the new economic geography framework it can be interpreted as a spatial labor demand function. In equilibrium the nominal wage in a region is also a weighted sum of the purchasing power in other regions. The models predict that the wage gradients of an economy follow a centerperiphery structure. Thus, Hanson regards the market potential function as a reduced form of the Krugman model. Using U.S. county data, he estimates this equation as a preliminary excercise before actually estimating the structural parameters from a structural equation. For the U.S., he is able to con…rm the theoretical model. Hanson’s work is important because his …ndings are favorable to the 2

new analytical framework. However, as some authors emphasize (Brülhart 1998: 796-798, Fujita et al. 1999: 347), much more empirical work is needed to get to …rm conclusions which new economic geography model is appropriate in which context. Although Hanson concludes that the Helpman version of the core-periphery model …ts the U.S. data well, one might doubt that it is a good description of European economies. Hanson’s empirical test of the model basically consists in verifying whether the model’s other variables can explain the observed wage gradients. He relates the wage in a region to a complex combination of wages, purchasing power, and the housing stock in other regions. For several reasons, this relation might not describe European conditions well. First, wages in Europe are likely to depend on other factors than in the United States. In European countries wage setting is much more centralized and in‡uenced by unions (Layard et al. 1991: 87). Also, European countries currently have high and persistent unemployment (Layard et al. 1991:222-225). These factors could have an in‡uence on the wage, but are not considered by the Helpman model. Second, it is well known that labor mobility is higher in the United States than in Europe (Decressin/Fatás 1995: 1644-1650, Nickell 1997: 59). Yet, the Helpman model assumes perfect labor mobility, which leads to equalized real wages in all regions. In order to assess whether the Helpman model can serve to analyze the economic geography of European countries despite these objections, we try to estimate its parameters using German data. Since the results are not favorable, we estimate the relationship between market potential and wages as well. As stated above, the market potential function can be regarded as a reduced form of several new economic geography models. Therefore, one can expect that if this theory has relevance for the economic landscape in Germany, at least this less elaborate relation between wages and purchasing power should hold. We …nd that wages are indeed positively related with market potential. However, market potential explains only little of the variation in average wages and market linkages are limited in space. Market potential is a determinant of salaries and wages of skilled workers, whereas it is not of untrained workers’ wages. The remainder of the paper is organized as follows: In the second section, we summarize the Helpman model, describe the empirical speci…cation and mention some econometric issues. In the third section, we describe the data. Section 4 contains the estimation results and in the last section, we draw conclusions.

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2 2.1

Theory The Theoretical Model

The theoretical model behind the empirical analysis is the Helpman (1998) version of Krugman’s so-called core-periphery model. While the models have di¤erent theoretical implications, their structure is similar. The main di¤erence is that the immobile factor in Krugman’s model is farm workers, while it is housing in the Helpman model. The Helpman model is more suitable for estimation, because data on housing is available, while it appears di¢cult to identify data that serves as a good proxy for immobile labor producing a freely traded homogeneous good. The model’s structure is as follows. The economy consists of J regions. In total there are L individuals, who are perfectly mobile across regions in the long run. All individuals are identical and each of these individuals supplies inelastically one unit of labor. They maximize CobbDouglas utility functions over two types of goods, manufacturing goods Cm and housing services Ch , ¹ 1¡¹ U = Cm Ch :

(2)

All consumers’ expenditure share on manufactures is ¹: Cm is a CES function of consumption of individual manufactured product varieties with Cm =

"

n X

¾¡1 ¾

ci

i

#

¾ ¾¡1

; ¾ > 1;

(3)

where ¾ is the elasticity of substitution between varieties and n the number of available varieties. Manufactured goods are traded across space and incur iceberg transport costs when shipped from location k to location j. The transportation cost per distance unit is ¿ and djk is the distance between j and k: ”Iceberg costs” means that only a fraction vjk of the shipped good reaches its destination vjk = e¡¿ djk :

(4)

Transport costs are borne by consumers. There are increasing returns to scale in the production of manufactures, since the labor requirement for any variety i is given by Lim = a + bxi ;

a; b > 0:

(5)

Let xi be the quantity of variety i which is produced, a and b are constants. We assume that the number of …rms is large, so that there is 4

no strategic interaction between …rms. Because of increasing returns to scale, every …rm produces only one variety. In equilibrium, every …rm produces the same quantity of its variety. Firms can freely choose where to locate. There is a stock of housing services Hj in every region j; which is inelastically supplied in housing markets with perfect competition. Housing stocks are equally owned by all individuals in the economy. As in every new economic geography model, there are agglomeration and dispersion forces. The forces working towards agglomeration are the forward and backward linkages between individuals and …rms. The forward and backward linkages create pecuniary externalities. Because of increasing returns to scale, every manufacturing variety is produced at one location only. Thus, …rms want to locate where demand is highest. Since consumers must pay the transport costs, manufactured goods are cheaper for them if they do not have to be imported. Therefore, individuals migrate to regions where many varieties of manufactured goods are produced. However, living at a manufacturing center is costly for individuals because of the high competition for the …xed stock of housing, which is the dispersion force. The model is in equilibrium if neither …rms nor individuals have an incentive to move to another region. Individuals do not want to move if real wages are equal in all regions1 : wj 1¡¹ ¹ Pj Tj

=

wk 1¡¹ ¹ ; Pk Tk

8j 6= k:

(6)

The nominal wage wj is de‡ated by the cost-of-living price index Pj1¡¹ Tj¹ , where Pj is the price of housing, and Tj is the price index for manufactures in region j: The price of housing Pj is determined by the condition that housing income must equal housing expenditure (7)

Pj Hj = (1 ¡ ¹)Yj ; 8j:

Total income Yj in each region equals labor income earned in the region and the housing rents of every individual: (8)

Yj = ¸j L(wj + ½); 8j;

where ¸j = nnj is the equilibrium share of …rms (and of workers) in region j; and ½ is every individual’s share of the total housing income. The price index in region j is given by Tj = 1

"

J X

¸k (wk e¡¿ djk )1¡¾

k=1

1 # 1¡¾

; 8j:

(9)

In Helpman (1998) the equilibrium condition is that indirect utilities be equal.

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This is the standard Dixit-Stiglitz price index corresponding to (3). We have the nominal wage in the index instead of the price of manufactures because the model allows a normalization so that the price equals the wage. Market clearing on the market for manufactured goods implies that the wage in every region must satisfy the following condition wj =

"

J X

Yk (Tk e¡¿ djk )¾¡1

k=1

# ¾1

(10)

; 8j:

The so-called wage-equation (10) plays a crucial role in the analysis of many new economic geography models. It can be interpreted as a spatial labor demand function, because it gives the wage at which …rms in region j break even, given the income levels and price indices in all locations and the transportation costs (Fujita et al. 1999: 53). The wage equation is especially important because, in principle, it could be estimated empirically. Krugman (1992: 351) noted that is has a similar structure to Harris’ market potential index (1). The major di¤erence between Harris’ index and the wage equation (10) is that the former is constructed as an ad-hoc measure of a location’s attractiveness for …rms, while the latter comes out of a general equilibrium model as an equilibrium condition. In e¤ect, the wage equation relates the wage to the market potential of a region.

2.2

The Empiricial Model

The wage equation (10) intuitively relates the wage level in a region to the attractiveness of this region as a location of production. If a location has good access to large product markets, it is attractive for a …rm. Since the wage equation comes out of several models, we would like to …nd out whether it is supported by the data. Unfortunately, data for the price index Tk in (10) is not available on a disaggregated geographical level. Hence, (10) cannot be estimated directly. In order to eliminate Tk , Hanson proposes to use the other equilibrium conditions of the model. This can be done by isolating Pj in (7) and plugging this into (6). From the resulting relation we can isolate Tk , which delivers a substitute for Tk in (10). After factoring out a constant c and adding an error term ²j , we obtain "

wj = c

J X

¾(¹¡1)+1 ¹

Yk

(1¡¹)(¾¡1) ¹

Hk

k=1

¾¡1 ¹

wk

e¡¿(¾¡1)djk

# ¾1

+ ²j :

(11)

This relationship contains only variables for which data is available. From (11) we can estimate the structural parameters of the Helpman 6

model, ¾; ¹; and ¿ : If the model …ts the data well, all of them should be positive. Furthermore, the model requires that ¹ be less and ¾ be greater than unity. In the introduction, we mentioned reasons why the Helpman model might not …t the German data. To date the literature does not provide an alternative model which allows to eliminate the price index in (10) in a similar way. Assuming that the price index is equal in all regions and taking logarithms, we obtain log(wj ) = log(T

¾¡1 ¾

1 ¾

)+

= ®0 + ®1 log(

log(

J P

k=1

J X

Yk e¡¿ (¾¡1)djk ) + ²j

Yk e¡®2 djk ) + ²j ;

(12)

k=1

which we refer to as market potential function. The assumption that the price index T is equal in all regions is a bit problematic. Exactly the di¤erentials in the costs of living between regions are a crucial element that help to cause agglomeration in the core-periphery models. Although we lose the so-called forward linkage by setting T equal to a constant, there is still the backward linkage as the second centripetal force. Backward linkage means that …rms want to locate where purchasing power is high. This force is captured by the market potential function (12). The estimation of (12) is attractive because it is a relationship with few parameters. Since (12) can be derived from several theoretical models it is a fairly fundamental test on the validity of the new economic geography theory. If this relationship does not hold, the observed agglomeration patterns are rather due to other factors than to the pecuniary externality stressed in this theory. There are several important estimation issues. In principle, it would be appropriate to estimate a system of equations but because of data limitations this is not possible. Estimating (11) and (12), one has to be aware of the endogeneity problem that arises from having the dependent variable wj among the independent variables in (11) and included in Yk both in (11) and (12). This problem could lead to inconsistent coe¢cient estimates. In order to minimize the e¤ects of endogeneity, Hanson proposes to subtract own region values from the independent variables, which we do, too. An additional device to reduce endogeneity e¤ects is to aggregate the independent variables. If the dependent variable is measured at a …ner geographic level than the independent variables, it is less likely that a shock to a lower level region greatly a¤ects the aggregate of regions. While we use county level data for the dependent

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variable, we add up the income of counties in an administrative district. The number of summation terms J in (11) and (12) is therefore 30 (the number of districts) instead of 327 (the number of counties). The aggregation also solves a more practical problem. Because of the summation of the independent variables, the …ner the level of geographical detail is, the bigger the input matrices get. This is especially true for the distance matrix, which, in principle, should have an entry for every pair of regions under consideration. Without any aggregation on the RHS this matrix would be (327£327) with more than 53,000 di¤erent entries only for the west German counties. The aggregation facilitates greatly the data editing and the computations.

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Data Description

Counties (by ”counties” we mean ”Landkreise and kreisfreie Städte”) are the …nest geographical units at which the necessary data is available in Germany. We only use data for West Germany for two reasons. First, a part of the data is not available for the former GDR. Second, we think that inference on general economic conditions is dangerous from data of an economy still in transition. For the estimations data are necessary on wages, income, and the housing stock. We also need a distance measure. The data on wages and salaries were provided by the Bundesanstalt für Arbeit. We use the average annual nominal wage of workers who pay compulsory social security contributions. Total disposable income of all private income in a region serves as proxy for the regions purchasing power. Complete sets of all variables were only available for 1992 and 1996. In order to measure distances between regions, one must assign a center to every county. In most cases, this is simply the administrative center of the county. In some cases, however, we choose the biggest city or a city which is centrally located. The distance between two counties is de…ned as the direct geodesic distance between the regions’ centers, which we calculate using Gauss-Krueger coordinates. Table A1 in the appendix contains summary statistics of the main variables. In order to obtain a …rst impression of the data, we draw some maps of western Germany. Figure 1 shows the quintiles of the nominal wage distribution in 1992. The wage distribution in 1996 di¤ers only slightly from the one in 1992. The regions in black represent the highest quintile, the white regions the lowest. The map shows that there are three major regions in which wages are highest: the Ruhr area, the Frankfurt am Main region, and the region around Stuttgart. In several cities, wages are high, too, for example Hamburg, Wolfsburg, Kassel and Munich. It is also obvious that these high wage centers are surrounded by regions 8

of the second highest quintile. The regions in the lowest quintile are mostly rural areas, especially in the northern part of Germany and in Bavaria. Many of these low wage regions are in the German periphery in border or coastal regions. Almost all Bavarian counties at the Czech border belong to the lowest quintile. Notice that the only border to a non-EU (or non-EFTA) country is the one to the Czech republic. Figure 1 here Not surprisingly, wages are closely matched by personal income. Figure 2 here Figure 2 shows the quintiles of the distribution of total disposable income in German administrative districts (”administrative district” stands for ”Regierungsbezirk”). The counties in the highest quintile of wages lie in the districts which are in the highest income quintile. However, the income is also relatively high in several northern districts where wages are low. This might be due to …nancial support by regional policy or other redistributive mechanisms.

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Results

4.1

The Helpman Model

As it was said before, it is unlikely that the combination of the housing stocks, personal incomes and wages in (11) can exclusively explain the wage level in a county. Other variables, that do not appear in the model, will have an e¤ect as well. In order to obtain good estimates of the structural parameters of the Helpman model, one must control for these other variables. Assuming that they are time invariant, this can be done by time di¤erencing the log of (11). This yields 1 ¢ log(wjt ) = ¾

2

Ã

J P

¾(¹¡1)+1 ¹

(1¡¹)(¾¡1) ¹

¾¡1 ¹

6 log Ykt Hkt wkt e 6 6 Ãk6=j ¾(¹¡1)+1 (1¡¹)(¾¡1) 6 ¾¡1 J P 4 ¹ ¹ ¹

¡ log

k6=j

Ykt¡1

Hkt¡1

¡¿ (¾¡1)djk

wkt¡1 e

! 3

7 7 ! 7+¢²jt : 7 ¡¿ (¾¡1)djk 5

(13) Table 1 presents the results from a non-linear least squares estimation2 of (13). Table 1 here 2

The estimated intercept is not shown.

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The signs of ¾; ¹ and ¿ are positive, as predicted by theory. However, the other theoretical restrictions that ¾ be greater and ¹ be less than unity are only partly satis…ed. At the 5%-level only ¹ is signifcantly di¤erent from one, whereas ¾ is not. Furthermore, ¿ is not signi…cantly di¤erent from zero either (at 5%). If these estimates were reliable, the price-cost margin ¾=(¾ ¡ 1) > 1 would indicate the presence of increasing return to scale (Krugman 1991a). ¾(¹ ¡ 1) is a stability condition for agglomeration. If it were greater than unity, there would be centipetal forces from the housing sector instead of centifugal ones. Since it is less than one, this would imply a strong sensitivity of industrial agglomeration to the level of transport costs (Hanson 1999, Helpman 1998). Both results would con…rm Hanson’s …ndings. The empirical violation of the restrictions on ¾ and ¿ con…rms the conjecture that the Helpman model is not suitable to describe the German economic geography. Of course, the estimation of (11) is not really a rigorous test of one model against an alternative one. This makes it di¢cult to explain why the model does not …t. An explanation might be that labor mobility in Germany is far from being perfect. The model as it is presented here assumes that in the long run workers move towards regions with the highest real wages. This leads to the equilibrium condition (6) that wages are equalized. If real wages are not approximately equal across regions we cannot use (6) to eliminate T in (10) in the way described in Section 2.2. But then, there is no theoretical reason why (11) should hold. With ¾ equal to unity, both the housing variable and the wage variable in (11) drop out and the estimated equation is only a version of the market potential function (12). Thus it seems that this more fundamental relationship is not rejected by German data. The following subsection contains the results of explicit estimations of (12).

4.2

The Market Potential Function

In order to eliminate region-speci…c time invariant features, that are not explicitly modelled, we estimate the time di¤erenced version of (12) 2

6 6 ¢ log(wjt ) = ®0 + ®1 6 4

log(

J P

k6=j J P

¡ log(

Ykt exp(¡®2 djk )) Ykt¡1 exp(¡®2 djk ))

k6=j

3

7 7 7 + ¢"jt : 5

(14)

Table 2 contains the results of the nonlinear least squares estimation. Table 2 here 10

The sample size is 327 counties. Estimating the market potential function in time di¤erences means that we relate the change in wages to the change in market potential. Since distances do not change over time, we in fact relate the wage change to the change in personal income. Row (a) contains the results of an estimation with an intercept. The inclusion of an intercept seems reasonable because an estimation without an intercept assumes that the price indices in 1992 and 1996 were unchanged. In addition, excluding the intercept would assume that there were no time varying in‡uences on the wage except for the market potential. In fact, the exclusion of the intercept worsens the model …t considerably. The interesting coe¢cient estimates ®1 and ®2 are negative, which contradicts theory. The Box-Pierce statistic indicates that the residuals are correlated, so that the calculated t-values are not reliable (the 5% critical value is 25). Thus, the estimates could be zero as well. The negative estimates are surprising not only with respect to theory but also with regard to the data. Both wages and income rose from 1992 to 1996 so that we regressed a positive wage change on an increase of market potential. An explanation could be that the parameters ®1 and ®2 are not stable over time. In order to analyze the hypothesis that the parameters changed over time, we estimate the market potential function not in time di¤erenced form but equation (12) directly for 1992 and 1996. The results of the nonlinear least square estimation are shown in Table 3. Table 3 here Now, in accordance with the theory, both ®1 and ®2 are positive. Again, the t-statistics are not reliable because of correlated residuals. The correlation3 probably explains why the t-statistics are quite high. For both dates, ®1 and ®2 are almost identical, but the estimated intercepts di¤er. Wages seem to be positively related to ”market potential” as de…ned by the weighted sum of purchasing power in other regions. From (12) we can interpret the slope estimate ®1 as the reciprocal value of ¾: Hence, from the estimated ®1 we can calculate the measure of returns to scale ¾ ¾ : From the results in Table 3, we obtain ¾¡1 = 1:087, which indicates ¾¡1 that there are increasing returns to scale. The size of ®2 is harder to interpret. ®2 can be understood as a spatial discount factor. Table 4 3

For the correlation of the residuals the ordering of the sample is important. Here, counties are ordered according to their code number in the German o¢cial statistics, which is lexicographic. This means that neighboring counties in the sample order are not necessarily neighboring in space. We chose to calculate the Box-Pierce statistic for 15 values because a county’s direct neighbors almost always fall in this range.

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contains some computations how purchasing power is weighted with different values of the transport cost parameter4 . For example, with an ®2 of 0.028 purchasing power in a region 100 km apart from another region gets a weight of 0.0608. The corresponding weight for 300 km is 0.0002. Table 4 Put di¤erently, for a …rm a personal income of one billion marks is worth DM 60,800,000 if it is 100 km away, and only DM 200,000 at a distance of 300 km. Hence, purchasing power in regions far apart is not so important as purchasing power in regions nearby. In order to illustrate the meaning of the estimation results, we perform a similar simulation experiment as Hanson. Based on the estimated coe¢cients in the market potential function for 1992, we compute how the predicted wages would change if the total personal income in the district Frankfurt5 was increased by 10 percent. Figure 3 shows the results. Figure 3 here For instance, at Gießen, which is 51 km away from Frankfurt am Main, the predicted wage would increase by 0.31 percent. At Worms at a distance of 58 km, the predicted wage would be 0.21 percent higher, and 133 km away at Zweibrücken the wage would rise by 0.057 percent. Beyond 200 km the wage increase is less than 0.01%. These e¤ects are rather small. A 10% increase to personal income in a district is a major shock to the economy. The small simulation e¤ects to predicted wages suggest that market potential does matter for wages but maybe less than the new economy geography literature asserts. Another way to understand what the estimated coe¢cients mean is to perform a second estimation. Using ®2 ; we calculate the market potential for every region. Then, we regress the wage (in levels) on the calculated market potential. The result is an intercept of 39,777 (120.7) and a slope coe¢cient of 61.6 (12.6)6 , i.e. for every billion marks of market potential the estimated wage would rise by DM 61.6. It is 4

Note that Hanson (1999) obtains estimates for ®2 which are much larger than unity. He obtains parameter values between 1.4 and 13. For a distance of 50 km an ®2 of 2 leads to a weight of 3.72¢10¡44 . 5 Frankfurt am Main lies in the district Darmstadt, but we treat Frankfurt as the economic center of this district. 6 t-values in parenthesis.

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helpful to know that the 1992 market potentials range from DM 8.19 billion to DM 206.59 billion and have a mean of DM 55.93 billion. As on can see in Tables 2 and 3, the estimation residuals are highly correlated. A reason for this might be the aggregation of the independent variables. For each of the 327 observations on the county level, the independent variable is the sum of 30 total personal incomes on the district level. Each income is weighted with the transport cost term between the respective county’s center and the center of the district. For counties that are close together and have only a small purchasing power7 , the independent variables are almost identical. Neither the aggregate incomes nor the distances to the district centers di¤er much. If the wages in those counties di¤er greatly this could cause correlated residuals. In order to check whether the aggregation of the independent variables in‡uences the estimation results, we do the estimation again with a restricted sample. We choose the Bundesland Nordrhein-Westfalen (NRW), because of its size (it has 54 counties), its central location, and the variation in the dependent variable. Table 5 shows the results, when we do not aggregate the incomes at all. Only the wages and incomes of the 54 NRW counties are used. For each observation j the sum in (12) runs from 1 to J = 54 and excludes the income of region j. The distance matrix contains 1404 di¤erent non-zero distances between the centers of the 54 NRW counties. Table 5 here The Box-Pierce Q-statistic shows that the estimation residuals are uncorrelated now. Row (a) corresponds to row (a) of Table 2. Again, when the market potential function is estimated in time di¤erenced form, ®1 and ®2 are negative. But now, the t-statistics indicate that the estimates are not signi…cantly di¤erent from zero. Estimating (12) at one point in time yields positive and signi…cant8 estimates (except for ®2 in 1996). Compared to the values in Table 3, the estimates of ®1 and ®2 changed drastically. ®1 more than halved and ®2 is four to …ve times higher than before. Restricting the sample to the NRW counties alone reduces the estimated market potential of these counties relative to the actual one. The border of a Bundesland is neither a hindrance for labor nor for goods 7

Remember that we subtract own county income from the respective district income. 8 ”Signi…cant” always means signi…cantly greater than zero at the 5% level in a one-sided t-test.

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or …rms. Thus, the non-NRW counties should be included in the estimation. As a compromise between the aggregation problem and the loss of information, we partially aggregate the independent variables. The NRW incomes are not aggregated, while the non-NRW counties are aggregated on the district level. With the data of the other regions as well, the number of summation terms is 79 (53 NRW counties plus the 26 non-NRW districts). The results of this estimation, shown in Table 6, are similar to the ones in Table 5. Table 6 here The inclusion of non-NRW regions in the restricted sample does not alter the estimates much. This could be interpreted as evidence that the market linkages are fairly limited in space. Purchasing power from markets outside NRW in‡uences the NRW wages only slightly. The Helpman model assumes that labor is homogeneous. In the preceeding analysis, we have treated labor as if it was homogeneous, too. However, in reality it is not. Workers di¤er in their formal quali…cations and their job experience. These factor in‡uence the wage. The wage statistics also show that male workers earn more than their female colleagues. In Germany - and probably in most other countries, too - in cities the quali…cation level of labor is higher than in rural areas (Wagner 1989). The unequal distribution of heterogeneous labor alone, thus, might explain a lot of the distribution of wages. To check whether wages are related to market potential even after controlling for the heterogeneity of labor we perform the following estimation using the NRW data from 1996 P log(wj ) = ®0 + ®1 log( k Yk exp(¡®2 djk )) + q1 trainingj + q2 universityj + q3 oldj + q4 malej + ²j :

(15)

The variables training; university, old, and male designate the percentages of trained workers, employees with a university degree9 , workers older than 50 years, and male workers of the total laborforce in a region. The results can be seen in Table 7. All estimates are positive and signi…cant. Compared to the previous estimations, the R2 and the BIC are much higher now. The quali…cation variables, thus, improve the model …t strongly. Regressing the wage rate only on the quali…cation variables yields a good …t, too, as column (c) shows. However, this estimation is 9

”Trained workers” are persons with a ”Berufsausbildung”, ”university degree” includes ”Fachhochschuldiplom” as well.

14

not as good as the ones which include the market potential. We therefore conclude that even after controlling for the regions’ quali…cation strukture wages are positively related to market potential. In comparison with the results in Table 5 and Table 6, the size of ®2 has decreased remarkably. It is puzzling that ®2 varies so much depending on whether we include all regions (column (a)) or restrict the sample on the NRW regions (column (b)). Table 7 here The preceeding estimation shows that the use of average wages without controlling for quali…cation di¤erences might be misleading. For one thing, the unequal distribution of quali…cations in‡uences the wage irrespective of any market potential in‡uence. In addition, it is known that there exists a positive correlation between the mobility of workers and their education level (Wagner 1989: 99). This means that high-skilled workers have a geographically larger labor market than low-skilled ones. Forslid (1999) assumes that only skilled workers are mobile, while unskilled labor is completely immobile. Hence, in his model, only the wage of skilled workers is determined by the wage equation (10). We repeat the estimations of the market potential function with wages and salaries of workers with di¤erent quali…cation levels. Table 8 here Table 8 contains the results of an estimation of (12) using salaries of employees with a university degree instead of average wages of all workers. Again, all estimates are positive and signi…cant at the 5%-level. Note that the R2 is fairly high. The implied mark-up ratios that can be calculated from the values of ®1 are between 1.03 and 1.04. Hence, there are only small increasing returns to scale. The estimated values of ®2 are smaller than the ones in Tables 5 and 6 but higher than those in Table 7. Higher values of ®2 mean higher spatial discounting. The higher ®2 is, the weaker are the spatial linkages between markets. Table 9 shows the results when we use the wages of trained workers as the independent variable. The estimates are similar to the ones in Table 8. The main di¤erence is that the ®2 estimates are higher, which means that the backward linkages are more local than for high-skilled workers. Table 9 here 15

As before, we perform a simulation experiment, now based on the estimates in row (d) of Table 8. We increase income in the city of Essen by 10 percent and calculate how the predicted wage would change. Figure 4 shows the results. Figure 4 here The e¤ects are small. The predicted wage increases by 0.067 percent at most. This is little relative to a 10% increase of total personal income of a big city with a total personal income of DM 18.35 billion in 1996. Also, the e¤ects do no spread far in space. The radius within which the simulated wage change is greater than 0.01 percent is approximately 50 km. We did not perform such a simulation experiment for the predicted wages based on the estimation results in Tables 5, 6, and 9. Since the estimated values of ®1 are of similar size whereas the transport cost parameter estimates ®2 are higher in the estimations with wages we can conclude that the e¤ects would be even smaller and much more spatially limited. In the Forslid model, only the wage of skilled workers is related to market potential, while the wage of unskilled workers is determined by other factors. The preceeding estimation supports the former result. To …nd out whether the data back the second one, too, we repeat the estimation with wages of untrained workers. Table 10 contains the results. Table 10 here The …rst thing to notice is that the partial aggregation matters now. In columns (c) and (d), we …nd correlated residuals again. Therefore, we ignore these results. In the other two estimations, we do not …nd correlation in the residuals. In both cases, ®2 is not signi…cantly di¤erent from zero. In addition, with the 1992 data, ®1 is not signi…cant either. Thus, market potential does not help to explain these wages. We regard this as a con…mation of the Forslid model. At least in the European context, a new economic geography model should distinguish between skilled (mobile) and unskilled (immobile) labor. What have we learned from the market potential estimations? Almost every estimation we have performed shows that market potential and wages are positively related. In most cases the market potential parameters ®1 and ®2 are signi…cantly positive, as predicted by theory. The size of the estimates, however, varies considerably, depending on the data and the estimation procedure used. Since the aggregation causes correlation in the residuals, we regard the estimation with all counties only as 16

tentative evidence for the strength of the backward linkages in Germany. Accordingly, we base our conclusions on the results from the estimations with the restricted sample. Here, the various estimations demonstrate that it is crucial to consider the quali…cation level when making statements about wages and market potential. Both average wages and the wage of untrained workers are rather determined by other factors than by market potential. In contrast, the market potential of a region can explain quite well the level of wages of skilled workers. The simulation experiment and the ®2 estimates in Table 8 and Table 9 indicate that the market potential of a region mostly consists of the purchasing power in regions nearby.

5

Conclusions

In this paper, we analyze the empirical relationship between the wage in a region and purchasing power in other regions. Many new economic geography models contain such a relationship as an equilibrium condition. Using German county data, we estimate the so-called wage-equation in two forms: one which is derived from Helpman’s version of the coreperiphery model, and another which is not directly linked to a single model. We …nd that in the Helpman version of the wage equation important theoretical restrictions are violated empirically . This model, thus, is not really suitable to describe the economic landscape in Germany. Imperfect labor mobility in Germany might explain, why the estimated relationship does not …t. The so-called market potential function which can be derived from several models assuming that the price index is equal in all regions yields more favorable results. Our estimations show that the average wage in a region is positively related to the market potential of that region. We estimate the market potential function in di¤erent ways. First, we use data of all German counties and aggregate the dependent variables on the level of administrative districts. A simulation experiment shows that the estimates imply fairly weak linkages between wages and incomes in other regions. In addition, these linkages are limited in geographic scope. Then, we estimate the market potential function with a sample restricted to the counties of the Bundesland Nordrhein-Westfalen and without aggregation of the independent variables. To account for the heterogeneity of labor, we include several quali…cation variables in the estimation. We …nd that although the quali…cation variables alone explain much of the variation in wages, market potential improves the model …t. 17

Three other estimation are performed using salaries of high-skilled employees and wages of trained and untrained workers instead of average wages of all workers. Salaries and wages of trained workes are related to market potential whereas the wages of the untrained are not. This is exactly what the Forslid model (Forslid 1999) predicts. In the model, the di¤erent mobility of high-skilled and low-skilled labor is the reason for this. The analysis performed here is not a rigorous test of a model against another or even of a theory. Nevertheless, it is possible to say that there is evidence of backward linkages described by Krugman-type new economic geography models. This supports the view that the new economic geography literature not only makes a theoretical contribution to explaining agglomerations, but also has empirical relevance.

18

Appendix

Table 11 here References Brülhart, M. (1998), ”Economic Geography, Industry Location and Trade: The Evidence” The World Economy 21: 775-801 Decressin, J., A. Fatás (1995), ”Regional labor market dynamics in Europe” European Economic Review 39: 1627-1655 Forslid, R. (1999), ”Agglomeration with Human and Physical Capital: An Analytically Solvable Case” CEPR Discussion Paper No. 2102 Fujita, M., P. Krugman, A. J. Venables (1999), ”The Spatial Economy” MIT Press, Cambridge MA Hanson, G. (1998), ”Market Potential, Increasing Returns, and Geographic Concentration” NBER Working Paper No. 6429 Hanson, G. (1999), ”Market Potential, Increasing Returns, and Geographic Concentration” University of Michigan mimeo Harris, C. D (1954), ”The Market as a Factor in the Localization of Industry in the United States” Annals of the Association of American Geographers 44: 315-348 Helpman, E. (1998), ”The Size of Regions” in: D. Pines, E. Sadka, and I. Zilcha, eds., Topics in Public Economics, Cambridge University Press, Cambridge, pp. 33-54 Keeble, D., P. L. Owens, C. Thomson (1982), ”Regional Accessibility and Economic Potential in the European Community” Regional Studies 16: 419-432 Krugman, P. (1991a), ”Increasing Returns and Economic Geography” Journal of Political Economy 99: 483-499 Krugman, P. (1991b), ”Geography and Trade” MIT Press, Cambridge MA Krugman, P. (1992), ”A Dynamic Spatial Model” NBER Working Paper No. 4219 19

Layard, R., S. Nickell, R. Jackman (1991), ”Unemployment - Macroeconomic Performance and the Labour Market” Oxford University Press, Oxford Nickell, S. (1997), ”Unemployment and Labour Market Rigidities: Europe versus North America” Journal of Economic Perspectives 11(3): 55-74 Ottaviano, G., D. Puga (1998), ”Agglomeration in the Global Economy - A Survey of the ’New Economic Geography‘” The World Economy 21: 707-731 Schmutzler, A. (1999), ”The New Economic Geography”, Journal of Economic Surveys 13: 355-379 Wagner, M. (1989), ”Räumliche Mobilität im Lebensverlauf”, Enke Verlag, Stuttgart

20

Figures Figure 1: Distribution of average wages in 1992

21

Figure 2: Distribution of total disposable income in 1992

22

Figure 3: Simulated wage changes

23

Figure 4: Simulated wage change in NRW

24

Tables Table 1: Parameter estimates of the Helpman model Estimate ¾ 6.198 ¹ 0.863 0.003 ¿ adj. R2 0.28 Q(15) 18.5 ¾=(¾ ¡ 1) 1.192 ¾(1 ¡ ¹) 0.849

Std.Error 3.66 0.07 0.002

Q(p): Box-Pierce statistic = T

Pp

2 k=1 rk

Table 2: Market potential function, West Germany, di¤erences ®0 ®1 (a) 0.433 -3.407 t-stat. (6.26) (-4.87) (b) 1.152 t-stat. (128.8)

®2 BIC Q(15) adj. R2 -0.005 -1826 56.6 0.23 (-4.75) 0.003 -1766 248.5 0.05 (3.71)

BIC: Bayesian (Schwarz) information criterion =-2*log(likelihood)+(#parameter)*log(#observations)

Table 3: Market potential function, West Germany, levels ®0 (a) 1992 10.36 (198.3) t-stat. (b) 1996 10.47 t-stat. (193.3)

®1 0.080 (8.30) 0.080 (8.13)

®2 Q(15) adj. R2 0.028 67.1 0.33 (7.89) 0.028 73.1 0.31 (7.75)

Table 4: Implied weights by the transport cost estimates km ®2 10 0.028 50 100 200 300

e¡®2 d ®2 0.7558 0.073 0.2466 0.0608 0.0037 0.0002

e¡®2 d 0.4819 0.0260 0.0007 4.6¢10¡7 2.1¢10¡13

25

®2 e¡®2 d 0.12 0.3012 0.0025 6.1¢10¡6 3.8¢10¡11 2.3¢10¡16

Table 5: Market potential function, NRW only ®0 (a) ¢ 0.126 t-stat. (8.25) (b) 1992 10.69 (179.8) t-stat. (c) 1996 10.81 t-stat. (173.5)

®1 -0.177 (-1.14) 0.029 (2.48) 0.025 (2.01)

®2 -0.297 (-0.64) 0.128 (1.83) 0.138 (1.56)

BIC Q(15) adj. R2 -313 15.6 0.03 -160 16.9

0.37

-153 13.8

0.29

Table 6: Market potential function, NRW plus other regions ®0 (a) ¢ 0.012 t-stat. (0.11) (b) 1992 10.68 t-stat. (162.1) (c) 1996 10.80 t-stat. (158.5)

®1 1.031 (0.91) 0.032 (2.46) 0.027 (2.01)

®2 0.012 (0.92) 0.115 (1.88) 0.125 (1.56)

BIC Q(15) adj. R2 -315 18.7 0.07 -160 18.2

0.38

-153 14.6

0.29

Table 7: Market potential function, NRW, quali…cation variables ®0 ®1 ®2 q1 q2 q3 q4 BIC Q(15) adj. R2

(a) NRW+other 9.46 (50.4) 0.050 (1.76) 0.022 (2.04) 0.004 (4.45) 0.020 (14.9) 0.009 (6.53) 0.010 (9.75) -247 14.5 0.90

(b) NRW only 9.63 (91.2) 0.020 (2.92) 0.057 (1.96) 0.004 (4.48) 0.020 (14.5) 0.010 (6.78) 0.010 (10.0) -247 9.2 0.90

t-statistics in parenthesis

26

(c) NRW only 9.69 (83.8)

0.002 0.021 0.011 0.011 -234 10.7 0.86

(2.31) (13.0) (7.00) (9.67)

Table 8: Market potential function, NRW, university degree ®0 (a) 92, NRW 11.04 t-statistics (215.3) (b) 96, NRW 11.15 (188.7) t-statistics (c) 92, NRW+ 10.97 t-statistics (105.2) (d) 96, NRW+ 11.13 t-statistics (148.7)

®1 0.026 (2.95) 0.028 (2.78) 0.039 (2.17) 0.032 (2.45)

®2 0.071 (1.96) 0.083 (1.87) 0.045 (1.76) 0.073 (1.85)

Q(15) adj. R2 9.0 0.38 8.8

0.37

13.4

0.41

10.0

0.37

”NRW+” means NRW counties plus non-NRW districts as regressors

Table 9: Market potential function, NRW, trained workers ®0 (a) 92, NRW 10.70 t-statistics (177.5) (b) 96, NRW 10.82 t-statistics (166.8) (c) 92, NRW+ 10.67 t-statistics (146.1) (d) 96, NRW+ 10.80 t-statistics (139.0)

®1 0.036 (3.24) 0.034 (2.89) 0.041 (3.07) 0.039 (2.74)

®2 0.100 (2.25) 0.101 (2.00) 0.085 (2.29) 0.087 (2.06)

Q(15) adj. R2 15.5 0.47 14.6

0.41

17.9

0.47

16.6

0.42

Table 10: Market potential function, NRW, unskilled ®0 (a) 92, NRW 10.39 t-statistics (96.0) 10.50 (b) 96, NRW t-statistics (107.1) (c) 92, NRW+ 8.10 t-statistics (7.15) (d) 96, NRW+ 9.07 t-statistics (12.36)

®1 0.030 (1.64) 0.032 (1.93) 0.386 (2.35) 0.256 (2.34)

27

®2 0.063 (1.08) 0.061 (1.27) 0.007 (2.67) 0.009 (2.91)

Q(15) adj. R2 19.5 0.13 18.5

0.18

33.1

0.27

27.4

0.28

Table 11: Descriptive statistics of the data

unit avg. wages 92 DM avg. wages 96 DM wages 92 NRW DM wages 96 NRW DM salaries¤ 92 DM DM salaries¤ 96 t wages 92 DM t wages 96 DM wagesu 92 DM u wages 96 DM bill. income 92 full income 96 full bill. income 92 NRW bill. income 92 NRW bill. avg. distance km avg. dist. NRW km

DM DM DM DM

min 34,249 38,203 40,624 45,494 62,133 66,227 42,181 47,741 29,962 34,362 10.9 13.1 2.9 3.2 211 60

max 60,676 64,404 57,278 64,404 74,796 86,468 58,689 66,416 43,737 48,871 149.7 159.9 28.5 30.8 479 157

mean 43,224 48,492 45,589 50,814 66,805 74,499 47,447 53,085 35,591 39,896 56.7 62.6 8.9 9.6 289 85

std.dev 4,044 4,580 2,887 3,250 2,552 3,504 2,840 3,236 2,313 2,382 35.0 37.4 4.7 5.0 57.5 24.0

obs. 327 327 54 54 54 54 54 54 54 54 30 30 54 54 327 54

* Salaries of employees with a university degrees. t Wages of trained workers. u Wages of untrained workers. Wages and salaries are measured at the county level. West Germany without Berlin has 327 counties and the Bundesland NordrheinWestfalen has 54 counties. Total personal income is measured on the level of administrative districts and on the county level. There are 30 administrative districs in West Germany. In the full sample, average distance is the mean of distances from one county to all districts. In the restricted sample, it is the mean of distances between one county and all other counties in NRW. The Bundesanstalt für Arbeit provided the wage data. The CDROM ”Statistik regional” of the German statistics o¢ce is the data source of total disposable income of private households and the number of apartments in every county. Further data on income and housing was provided by the Gesellschaft für Konsumforschung (GfK) from their CD-ROM ”Basisdaten”. The coordinates for the calculation of distances were provided by the CD-ROM ”Top 200” of the German o¢ce of cartography. 28