This Selected Issues paper analyzes labor market asymmetries and macroeconomic adjustment in Germany. Empirical work reported shows that in Germany, negative demand shocks increase the unemployment rate by more than the decrease in the unemployment rate caused by a comparable-sized positive demand shock. The contribution of labor costs to explaining the high level of unemployment, particularly since unification, is studied. Empirical estimates are obtained for the wage gap—the deviation of actual labor costs from warranted labor costs based on estimated production functions assuming competitive factor markets and full employment.

Abstract

This Selected Issues paper analyzes labor market asymmetries and macroeconomic adjustment in Germany. Empirical work reported shows that in Germany, negative demand shocks increase the unemployment rate by more than the decrease in the unemployment rate caused by a comparable-sized positive demand shock. The contribution of labor costs to explaining the high level of unemployment, particularly since unification, is studied. Empirical estimates are obtained for the wage gap—the deviation of actual labor costs from warranted labor costs based on estimated production functions assuming competitive factor markets and full employment.

II. Real Labor Costs, Unemployment, and Unification1

72. The ratcheting up of the unemployment rate in Germany from the low levels of the 1960s to the high levels of the 1990s is a well-known and extensively-studied phenomenon. In chapter I, Germany was shown to have the greatest increase in structural unemployment among the G-7 countries and Denmark, Sweden, The Netherlands, Ireland and Spain. The Fund’s staff has estimated the rate of structural unemployment at 8¾ percent for unified Germany in 1995.2

73. According to one view, this poor employment performance has been due in large part to inadequate real wage adjustment to input price shifts (e.g., brought on by the twin oil shocks, globalization, and labor-saving technical change), rather than to insufficient aggregate demand coupled with hysteresis effects in the labor market.3 The observed increase in the unemployment rate and in the dependant labor income share from 1960 to the early 1980s, and their decline in the late 1980s, supports this view (Chart II-1). The wage bargaining process in Germany has been slow to adapt to changing demand conditions and productivity shifts. Indeed, the responsiveness of real wages to higher unemployment rates has been twice as slow in Germany as in France, The United Kingdom, and the United States.4 This evidence, along with the results in chapter I that Germany has a relatively high degree of downward wage rigidity, suggests that real wages in Germany may indeed be too high.5

Chart II-1.
Chart II-1.

Germany: Unemployment and Labor’s Share of Income

(In percent)

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Sources: IMF, World Economic Outlook; and Statisches Bundesamt.1/ Data prior to 1991 refer to West Germany only.

74. Unification in 1990 was a major shock to the factor markets in Germany. The integration of the new Länder resulted in an increase of 28 percent in the labor supply compared with an increase of 13 percent in the capital stock, according to recently released data.6 Consequently, the ratio of capital to labor and labor productivity declined following unification (Chart II-2). If real wages were completely flexible and labor always earned its marginal product, real wages should have dropped with this decline in labor productivity. However, real wages in the eastern Länder rose and the labor’s share of income also rose. In fact, in the period 1990-1995 real wages in the new and old Länder have risen by three percent whereas productivity declined by two percent. At the same time, unemployment rates have risen to record levels. This suggests that real wage rates did not adjust to reflect labor productivity.

Chart II-2.
Chart II-2.

Germany: Capital to Labor Ratio, Wages and Labor Productivity

(Indices: 1970=100)

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Sources: OECD Economic Indicators; and Statisches Bundesamt.1/ Data prior to 1991 refer to West Germany only.2/ Total labor income per hour worked.3/ Based on hours worked.

75. This chapter measures the departure of observed real wages from the real wages “warranted” by a simple model of the German economy under the assumptions of competitive factor markets, flexible real wages, and full employment. This departure is termed the wage gap.7 After the basic theory is presented, this paper explores the main empirical issues and computes a wage gap for Germany for the period 1960-1995. A wage gap is shown to have emerged in western Germany after the two oil price shocks but it had narrowed significantly by 1989. Following unification, the wage gap increased in western Germany but the wage gap for eastern Germany was even greater. The calculated wage gap for unified Germany is found to be significantly correlated with the observed unemployment rate for unified Germany. Halving the wage gap for unified Germany would reduce the German unemployment rate by approximately 3 percentage points.

A. The Theory

76. The model economy has a production technology described by the aggregate production function,

Y=f(K,L)(1)

where Y is output and K and L are the capital and labor inputs, respectively. The production function is concave, increasing in K and L, and has the property that,

limfk(K,L)=,K0limfL(K,L)=,L0(2)

so the firm uses all the available inputs. Hence, the only unemployment in this model would be frictional, resulting from job search, and L corresponds to the natural rate of employment. Assuming that firms maximize profits, and that the markets for labor and capital are competitive, the properties of the production function in (2) imply that the real wage equals the marginal product of labor,

W=fL(K,L)(3)

and the share of total income earned by labor is,

SL=W·LY(4)

77. To illustrate how a wage gap might arise, consider the case where real wages initially reflect labor productivity. If wages are maintained constant by wage bargaining after the economy has been hit by a negative exogenous productivity shock, then real wages would exceed the marginal productivity of labor and a wage gap would develop. The wage gap concept is admittedly simple as many potentially important factors are left out of the model, such as the effects of wage dispersion, skill and regional mismatching, and labor supply. In particular, changes in demographics and labor market policies, such as the level and duration of unemployment benefits, could have considerable influence on labor supply at a given real wage. Thus, the wage gap is only a partial measure of wage rigidity and of the lack of competition in the labor market.

78. Computing the wage gap is a two-step process. First, the parameters of a production function are estimated using data for actual labor supply, L*, output, Y*, capital, K*, and the observed labor’s share of income, SL*.8 In this paper, labor supply is measured by both employment and total hours worked. The second step involves the calculation of the labor’s share of income, SL, when the actual labor supply is equal to the warranted labor supply, L or the natural rate of employment. The natural rate was calculated based on the Fund staffs estimate of the NAIRU. Therefore, L can be computed using,

L=1u1u*L*(5)

where u is the NAIRU, u* is the actual unemployment rate, and L* is the actual labor supply.9 Finally, the wage gap is calculated as,

wagegapSL*SL(6)

B. Wage Gap Estimation

79. In the first part of this section, the widely used Cobb-Douglas (CD) production function with constant returns to scale is estimated. Subsequently, a constant elasticity of substitution (CES) production function is estimated. (The CD production function is a special case of the CES production function corresponding to an elasticity of substitution of one.) The CES specification is frequently preferred to the CD form because under the latter, factor shares are constant over time and are not affected by changes in the capital-labor ratio. These restrictions could produce misleading estimates of the wage gap over time.

80. Assume that the aggregate production function in (1) is a constant returns to scale Cobb-Douglas function,

f(K,L)=γLαK1αwithαε(0,1)(7)

Using (3) and (4), the labor’s share of income is simply,

SL*=α(8)

The marginal product of a factor or its partial elasticity with respect to output is also equivalent to that factor’s income share. The parameter γ is the efficiency parameter or scalar.

81. The log version of (7) could be estimated directly. However, this approach is problematic because the error in measuring factor inputs is likely to be considerable, and because this procedure faces the econometric problems of multicollinearity and heteroskedasticity. To avoid these problems and the need for data on inputs, the factor shares’ approach is often utilized.10 Under the factor shares’ approach the following equation is estimated,11

log(Y*/L*)=logγ+(1α)log(K*/L*)(9)

82. Before estimating (9), an augmented Dickey-Fuller test was performed on the data in levels. This test failed to reject the presence of a unit root. Therefore to produce stationary time series, first differences were taken prior to the estimation.12 The estimation period was 1965-1989, and labor was measured by alternatively employment and hours worked (regressions A and B in Table II-1). Both versions of the estimated equation fit the data quite well (adjusted R2 of more than 0.99), although the fit for hours worked was slightly better gauging by the higher value for the F-statistic. The labor coefficient was 0.70 using employment and 0.66 using hours worked. Both were statistically significant at the 99 percent confidence interval. The mean value of labor’s share of income during the estimation period (1965-89) was 0.714. Using a Wald test, the equality of these estimates to the sample mean were tested. In both cases, the null hypothesis of equality could not be rejected.

Table II-1.

Estimation Results for a CD Production Function

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83. Because the hours worked equation fitted the data marginally better and the value of α=0.66 is closer to the mean of labor’s share of income during the 1960s, the warranted labor’s share of income was set at SL=0.66. The resulting wage gap, SL*-SL, is shown in Chart II-3. The wage gap rose from 1960 to 1982, peaking at around 10 percent before declining to below 5 percent in 1989 prior to unification.

Chart II-3.
Chart II-3.

Germany: Wage Gap

(CD production function, in percent)

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Source: IMF staff estimates.

84. The estimated production function for pre-unification western Germany is then utilized for out-of-sample calculations of the wage gap for unified Germany. This assumes that the measured capital, labor, and the production technology of eastern Germany are the same as for western Germany so that aggregation is possible. To check whether the production function was unchanged after unification, the estimation period was extended from 1965-1989 to 1965-1994 (regression C in Table II-1).13 The estimated value of α is 0.709 when the sample period is 1965-1994 compared with 0.707 for the period 1965-1989. Using a Wald test, the hypothesis that α is the same in both estimations is not rejected at conventional confidence levels.14 This result justifies the use of the same production function to calculate the wage gap since unification. The resulting wage gap for unified Germany was found to have jumped up immediately following unification but it appears to be slowly trending downwards since 1993 (see Chart II-3).

85. The calculated wage gap is sensitive to the definition of labor income. In this study, employee compensation (inclusive of employers’ contributions to social security funds and other social security expenditures by employers) was utilized, which implicitly treats entrepreneurial income as capital income. Changes in the distribution of wage income from entrepreneurial to dependent sources could distort wage gap calculations over time. When the share of labor’s income is adjusted for changes in self employment, the resulting wage gap calculations yield a negative wage gap in the 1990s.15 This result is implausible given the well-documented high wage costs in Germany16, the high structural unemployment and recent wage gap calculations for several European countries.17 Additional evidence is provided below, utilizing the less restrictive constant elasticity of substitution production function.

86. The constant elasticity of substitution (CES) aggregate production function has a constant elasticity which can take a value other than unity. A CES production function with constant returns to scale is written,18

f(K,L)=γ[αLρ+(1α)Kρ]1/ρ(10)

As before, capital and labor are the two factors of production and the technology exhibits constant returns to scale. The parameter α is the distribution parameter as in the CD production function and determines the relative factor shares in production. The other parameter ρ is the substitution parameter and determines the value of the elasticity of substitution. Then, under perfect competition and profit maximization, the real wage is given by,

W=dYdL=γρα(Y/L)1ρ(11)

So the following relation can be estimated,

log(Y*/L*)=a+11ρlog(W*)(12)

where W* is the real wage.19 The coefficient, 1/(1-ρ), is the elasticity of substitution and if it were unity (or if ρ were zero), the CES production function would collapse to a CD production function.

87. As before, first differences were taken to ensure stationarity of the variables. The results for equation (12) using employment and hours worked are shown in regressions A and B in Table II-2. Again both versions yielded good results with the hours-worked equation appearing to have a marginally better fit. The coefficients are statistically significant at the 99 percent confidence interval. Moreover, the coefficients are virtually identical.

Table II-2.

Estimation Results for a CES Production Function

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88. The two parameters, a and ρ, are sufficient to compute SL and the wage gap. This is done by solving for SL from the following equation,

log(Y/L)=a+11ρlog(SL·Y/L)(13)

Here, the relation W=SL·Y/L from equation (4) was used. Therefore, potential output, Y, and full employment labor supply, L, are required to obtain SL from (13) using the parameters estimated from equation (12). Potential output is obtained by adjusting actual output by the Fund staff’s estimate of the output gap, and full employment is obtained using equation (5).20

89. The calculation of the wage gap does not require the estimation of all the parameters of the CES production function in (10), because equation (12), with only two parameters, is estimated instead.21 Since the estimation was performed in first differences, equation (13) cannot be employed directly to obtain SL, rather it yields only changes in SL. Therefore, to construct the SL series a further assumption is needed regarding the level of SL. For example, it could be assumed that SL*-SL for a particular year or for a period of years. For the calculations made in this paper, it was assumed that SL* equals SL during the 1960s when the annual unemployment rate averaged less than 1 percent.22

90. The estimated values of SL are shown in the top panel of Chart II-4, and calculated wage gaps are plotted in the bottom panel. As in the CD specification, the wage gap rose during the 1970s and early 1980s, spiking upwards with the twin oil price shocks and reaching 10 percent in 1983. (Focusing only on the manufacturing sector, previous estimates of the real wage gap in Germany, showed that the gap reached about 10 percentage points in 1982.23) The calculated wage gap then declined to 5 percent in 1990. With unification, the wage gap 64 surged upward to more than 20 percent. This result is obtained when either employment or hours worked are used as the measure of labor supply.24

Chart II-4.
Chart II-4.

Germany: Labor’s Share of Income and Wage Gap

(CES production function, in percent)

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Source: IMF staff estimates.

91. To check whether the production function estimated using 1965-1989 data from the old Länder is unchanged after unification, the sample period of the estimation is extended to 1994 (regression C in Table II-2). A Wald test was used to formally test the equality of the pre- and post-unification production functions, and the coefficients were found not to be significantly different.25

92. To understand the higher wage gap since unification, recall that the wage gap increases with a rise in SL*, which clearly rose in the 1990s, or a decline in SL, which fell sharply after unification. The drop in the warranted share of labor income was due to the fall in labor productivity following unification. This relation between the share of labor and productivity is obtained by rearranging equation (13),

SL=γρα[YL]ρwithρ<0(14)

93. To examine the fraction of the higher wage gap following unification due to the drop in SL (as opposed to the fraction due to the rise in SL*), the wage gap was recalculated assuming that labor productivity remained at its 1990 level. Under this assumption, the wage gap would have been more than halved to 5-10 percent (see Chart II-5).

Chart II-5.
Chart II-5.

Germany: Effect of Unification on Wage Gap

(In percent)

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Source: IMF staff estimates.

94. In addition to estimating the wage gap for unified Germany, the wage gap for the old Länder alone can be estimated. Using the observed labor productivity for the old Länder and the estimated CES production function, a wage gap for the old Länder was calculated at about 5 percent in 1991 (Chart II-6). By 1994 the wage gap in western Germany exceeded 10 percent.26 This analysis suggests that the wage gap problem for unified Germany does not stem from the wage gap in the new Länder alone. Still, the new Länder contribute a disproportionate amount to unified Germany’s wage gap. A disaggregated analysis of developments in wages and labor productivity in the new Länder is presented in the following chapter.

Chart II-6.
Chart II-6.

West Germany: Wage Gap and Labor Productivity

Citation: IMF Staff Country Reports 1997, 101; 10.5089/9781451810318.002.A002

Source: IMF staff estimates; and Statisches Bundesamt.1/ Data prior to 1991 refer to West Germany only.

C. The Unemployment Rate and The Real Wage Gap

95. Under the assumptions of the model, the wage gap measures the magnitude of the discrepancy between actual real wages and real wages warranted by competitive labor markets when wages are perfectly flexible. The large wage gap found for unified Germany points to substantial labor market frictions which are reflected in the high unemployment rate. Indeed, a casual comparison of Charts II-1 and II-4 suggests a positive correlation between the unemployment rate and the wage gap. In addition, the unemployment rate is known to vary over the business cycle, and to be negatively correlated with the output gap.

96. To quantify these correlations, a regression was run with the unemployment rate as the dependant variable, and the following explanatory variables: the estimated wage gap, the Fund staff’s estimate of the output gap, and a dummy in 1990 related to unification. The results are shown in Table II-3. The estimated coefficients for the output and wage gaps have the expected signs and are statistically significant at the 98 percent level. The coefficient on the output gap is negative indicating that the unemployment rate falls as the output gap is closed or rises above potential. A positive correlation exists between the calculated wage gap and the actual unemployment rate. The regression has an adjusted R2 of only 77 percent, which is not surprising given the absence of additional explanatory variables particularly related to labor supply. Although definite statements cannot be made based on these equations alone (since omitted variables could bias the estimates), it is, nonetheless, instructive to observe that a lowering of the wage gap for unified Germany from 20 percent to 10 percent would reduce the unemployment rate in unified Germany by approximately 3¼ percentage points. In contrast, closing the output gap in 1996 would reduce the unemployment rate by almost 1¼ percentage points. The impact of unification, captured by the dummy variable, accounts for approximately 3 percentage points of the unemployment rate.27

Table II-3.

Unemployment and the Wage Gap

article image
1

Prepared by Victor Valdivia.

2

The OECD’s estimate for structural unemployment was even higher: 9 ½ percent (OECD Economic Surveys: Germany 1996, (Paris: OECD)).

3

In this study, wages refer to total worker compensation including employers’ contributions to social security funds and other social security expenditures by employers.

4

The OECD Jobs Study, 1994, (Paris: OECD).

5

A recent study revealed that Germany has the highest hourly compensation costs for production workers in manufacturing of all 28 countries included in the study. Costs in Germany were 80 percent higher than in the U.S. and the OECD average in 1996. See “International Comparison of Hourly Compensation Costs for Production Workers in Manufacturing, 1996”, in News, Bureau of Labor Statistics (Washington, D.C.: U.S. Department of Labor).

6

However, the increase in human and physical capital measured in effective units (i.e., old Länder equivalents) may not be the same.

7

This study is an extension of the earlier work on wage gaps found in: Artus, Jacques, 1984, “The Disequilibrium Real Wage Hypothesis: An Empirical Evaluation,”, Staff Papers, International Monetary Fund, Vol. 31 (June), pp. 249-302; Lipschitz, Leslie, and Susan M. Schadler, 1984, “Relative Prices, Real Wages, and Macroeconomic Policies: Some Evidence from Manufacturing in Japan and the United Kingdom”, Staff Papers, International Monetary Fund, Vol. 31, (June), pp. 303-338; and, more recently, Halikias, loannis, 1997, “An Analysis of the Wage Gap”, in Kingdom of the Netherlands-Selected Issues, Country Report 97/139 (Washington: International Monetary Fund). The first two studies compute a wage gap only for the manufacturing sector, whereas this study and the one by Halikias estimate a wage gap for the whole economy. (Citations to the relevant economic literature can be found in these earlier papers.)

8

In the notation of this paper, X* stands for the actual (observed) value of a variable and X is the value of the variable under the assumptions of the model.

9

When hours worked are used as a measure of labor supply, the series is adjusted using (4) as well.

10

For an overview of alternative econometric approaches to estimating production functions refer to Intriligator, Michael, Bodkin, Ronald and Hsiao, Cheng, 1996, Econometric Models, Techniques, and Applications, second edition (Upper Saddle River: Prentice-Hall).

11

The shares method was used by Artus, Jacques, 1984, op cit., and, more recently, by the U.S. Congressional Budget Office for the United States.

12

If a unit root is indeed present in the data, then the stochastic trend must be removed by first differencing. Incorporating a deterministic trend in the regression fails to remove the stochastic trend and also results in a mis-specification error.

13

The series have a break in 1991 caused by unification and the splicing of the time series. This break is an outlier in the estimation because the estimation is done in first differences. Therefore, 1991 data are omitted from the estimation.

14

Chow tests could not be used to check for the stability of the estimate because the splicing of data for the old Länder and the new Länder in 1990-1991 introduced a series break. When a Chow breakpoint test was applied to the original estimation using the sample period 1965-1989, breaks were also detected in the years 1974-1975 and 1977-1980.

15

Since the adjusted series has a downward trend, it is not surprising that a negative wage gap emerges. Under the CD specification, the wage gap is nothing more than the deviation of the labor’s share of income from its mean. Hence, a decreasing series will have a negative wage gap.

16

See footnote 4.

17

Halikias, Ioannis, 1996, op cit.

18

Artus, Jacques, 1984, op cit., also estimated a CES production function with constant returns to scale. Estimates of aggregate production functions for industrial countries generally exhibited constant returns to scale.

19

Details of the specification are given in Intriligator, Michael, Bodkin, Ronald and Hsiao, Cheng, 1996, op cit.

20

Using actual output instead of potential output introduces only a small error in the value of the wage gap (e.g. the error is less than 2 percent in the 1990s wage gap).

21

A CES production function for western Germany for the period 1971-94 was estimated in Ziebarth, Gerhard, 1995, “Methodology and Technique for Determining Structural Budget Deficits”, Discussion Paper 2/95, Economic Research Group of the Deutsche Bundesbank. He estimates a scalar elasticity (λ) of 1.11, indicating increasing returns to scale. His estimate for the substitution parameter (ρ) differs from the results reported here. Also, the estimated labor share parameter, α, is 0.38, which is considerably lower than would be expected from the data. Possible explanations for these differences in estimated parameters may be the deterministic de-trending use by Ziebarth compared with first differences used here (see footnote 9) and the a priori restriction of constant returns to scale employed in this study.

22

The same assumption was made by Artus, Jacques, 1984, op cit.

23

Artus, Jacques, 1984, op cit.

24

As in the CD case, the estimated wage gap depends on the definition of labor income. The estimated wage is smaller when the labor share of income is adjusted for changes in the distribution of income (from entrepreneurial to dependant workers). This wage gap rose after unification, peaked at 13 percent in 1993, and then dropped to 11 percent by 1995.

25

As before, data for 1991 are excluded from the sample because of the break in the time series associated with unification (and the splicing of time series). This, however, prevents the use of Chow tests to check for the stability of the production function. Alternatively, a Wald test was used to test whether the estimation coefficients from the different sample periods were different. In contrast to the CD case, when a Chow breakpoint test was applied to the original estimate using the sample period 1965-1989, no breaks were detected (see footnote 11).

26

Due to the lack of separate data for the old and new Länder after 1994, the wage gap can only be estimated for unified Germany after this year.

27

Note that the dummy variable and the complete closing of the wage and output gaps would return the unemployment rate to the level prevailing in the 1960s. This result is consistent with the assumption underlying the calculation of the wage gap. Namely, that the unemployment rate in the 1960s corresponds to a zero wage gap.

Germany: Selected Issues
Author: International Monetary Fund
  • View in gallery

    Germany: Unemployment and Labor’s Share of Income

    (In percent)

  • View in gallery

    Germany: Capital to Labor Ratio, Wages and Labor Productivity

    (Indices: 1970=100)

  • View in gallery

    Germany: Wage Gap

    (CD production function, in percent)

  • View in gallery

    Germany: Labor’s Share of Income and Wage Gap

    (CES production function, in percent)

  • View in gallery

    Germany: Effect of Unification on Wage Gap

    (In percent)

  • View in gallery

    West Germany: Wage Gap and Labor Productivity