‘Phillips Curve’ or ‘Wage Curve’: Is there really a puzzle ? Evidence for West Germany

Markus Pannenberg a * and Johannes Schwarze a, b a

German Institute for Economic Research (DIW), b

University of Bamberg

July 1998

Abstract Is there an inverse relationship between the rate of change of wages and the contemporaneous unemployment rate or rather between the level of both variables ? The former view leads to the Phillips curve, which has been challenged by the latter, named the Wage curve. Exploiting regional data for West Germany, we conclude that none of the two seems to be appropriate. However, there is evidence for a dynamic Wage curve with partial adjustment to equilibrium, at least for the years 1990 to 1994. Hence, the striking puzzle „Phillips curve or Wage curve“ might be more apparent than real.

JEL Classification: E24, J64, C23. Keywords: Phillips Curve, Wage Curve, GMM.

1. Introduction The relationship of unemployment and wages is an evergreen in both theoretical and empirical economics. Based on the famous work by A. Phillips standard macroeconomic textbooks state that there is an inverse relationship between the rate of change of wages and the contemporaneous unemployment rate, i.e. there is a Phillips curve. This common view is grounded on the idea that wages adjust to eliminate any excess supply or demand in the labor market and is supported by a huge amount of empirical work with macroeconomic data for different countries. However, Blanchflower and Oswald (1994) have challenged the theoretical and empirical foundation of the Phillips curve. They argue, that the level of wages rather than the wage change is related to the unemployment rate, i.e. there is a Wage curve. The Wage curve can be derived for example from an efficiency wage framework or from a bargaining approach and is in accordance with the notion that the level of prices is related to the level of quantities. Similar to the Phillips curve, the Wage curve can rely on considerable microeconometric evidence for various countries. Concerning the validity of the Phillips curve, Blanchflower and Oswald claim, that estimates of a dynamic version of the Wage curve show little autoregression in wages. Therefore, from their point of view the „famous Phillips curve is an illusion“ and „the apparent autoregression in macro pay levels may be the result of aggregation error or measurement error or specification error or all three“ (p. 284). Blanchflowers and Oswalds striking conclusion has been disputed by various authors. Blanchard and Katz (1997) argue that there might be a theoretical tension between the Wage curve and the Phillips curve, but that a careful replication of the microeconometric evidence for the US reveals a ‘true’ autoregression coefficient close to one, which is in accordance with the traditional Phillips curve. Card and Hyslop (1996) also present evidence in favor of the Phillips curve for the US. However, since Bell (1997) clearly shows that the aforementioned conclusions might be as premature as Blanchflowers and Oswalds claim, there is need for further empirical analysis. In this paper we pursue to assess the power of the different claims with respect to German wage dynamics, since, thus far, there is hardly any rigorous (nested) test of the competing hypotheses. We are aware of studies using macro or sectoral data, such as Franz and Gordon (1993), Fitzenberger and Franz (1994), or Franz and Smolny (1994), which include the Phillips curve concept into a broader approach, and of microeconomic studies of the Wage curve, such as Wagner (1994) or Pannenberg/Schwarze (1998). By and large, the former studies provide evidence for a mixture of an augmented Phillips curve/real wage bargaining approach, while 1

the latter lend support to the existence of a static Wage curve. Therefore, alike the evidence for the US, the problem is to reconcile macro and micro empirical results, though the evidence for real wage bargaining from macro data in Franz and Gordon (1993) signals that something is going on besides the pure Phillips curve dynamics in Germany. In Section 2, we briefly sketch a convenient framework for testing the Phillips curve against the Wage curve. Using regional panel data for West Germany, our framework requires a dynamic model for panel data. In addition to standard least square dummy variable estimators used in the above cited debate, we employ some instrumental variable estimators, which are discussed in Section 3. Subsequent to a brief description of the data and the variables in Section 4, we will present our results in Section 5. We find neither evidence for a pure Phillips curve nor a static Wage curve. Rather we obtain a dynamic Wage curve with partial adjustment to equilibrium for West Germany. Considering our results, we argue that the above mentioned puzzle is more apparent than real, once we take macroeconomic approaches like Layard/Nickell/Jackman (1991) into account. Actually, regional and macro data seem to mirror the same phenomena for West Germany.

2. Nesting the Phillips Curve and the Wage Curve Following Blanchard and Katz (1997) a simple form of a wage equation within a macroeconometric error correction framework can be written as ∆w t = α 0 + α 1 ∆p t −1 − α 2 ln( u t ) − λ(w t −1 − p t −1 − φ t −1 ) + v t ,

(1)

where w is the logarithm of the nominal wage, p is the logarithm of the price index, φ is the logarithm of the productivity level, u is the unemployment rate, a is a constant, v is an error term and ∆ the usual difference operator. 1 We use the log of the unemployment rate instead of the level to allow direct comparison of the Phillips curve and the Wage curve approach. λ indicates whether a deviation of the real wage from the normal or equilibrium level determined by productivity and the unemployment rate causes variation in wage inflation. Since „there is no such thing as a separate wage equation“ (Franz and Gordon 1993) simultaneity bias is avoided by excluding the contemporaneous price term in equation (1). Note however that the identification problem pointed out by Manning (1993) still exists, since a complete model should consist of a price, a wage and an unemployment equation. 1

Note that all above mentioned macroeconomic studies for Germany essentially rely on a similar error correction type wage equation. 2

Blanchflowers and Oswalds main point is that most of the well-known problems, such as treatment of expected inflation or measurement of productivity growth, which arise when wage equations like (1) are estimated, will vanish by analyzing the relationship of wages and unemployment across space within a country over time. Assuming that price inflation and productivity growth are common to all regions, equation (1) can be rewritten as ∆w rt = α 0 + α 1 ∆p t −1 − α 2 ln(u rt ) − λ (w r ,t −1 − p t −1 − φ t −1 ) + v rt ,

(2)

where r is a region specific index. Employing regional panel data, all terms in equation (2), which do no vary accross regions, can be captured by common time effects. Moreover, unobserved heterogeneity accross regions can be catched by a permanent region-specific effect. Using explicit differences instead of the difference operator, we therefore yield the following standard dynamic Wage curve equation w rt = α 0 − α 2 ln( u rt ) + (1 − λ )w r, t −1 + x *'rt α 3 + µ r + η t + ε rt ,

(3)

where x *'rt is a vector of exogenous variables controlling for observed time variant regional characteristics, µr is a permanent region-specific effect, ηt is a time effect that is common to all regions and εrt is a random disturbance. Appropriate estimation of equation (3) enables us to put the competing hypotheses of the Phillips curve and the Wage Curve to test. If (1-λ) = 0 and α2 > 0 hold, we will observe instantaneous adjustment of wages in response to exogenous shocks in our data, i.e. there is a static Wage Curve. For (1-λ) = 1 and α2 > 0, we will discover a pure disequilibrium adjustment process, i.e. there is a Phillips curve. Intermediate values of λ, λ ∈ ]0, 1[ , imply both an error correction mechanism and considerable nominal inertia in the short run.

3. Econometric specifications Equation (3) can compactly be written as w rt = (1 − λ )w r , t −1 + ~ x 'rt γ + µ r + η t + ε rt ,

(4)

where γ = [ α 0 ,− α 2 , α '3 ] ‘and ~ x 'rt is the extended vector of exogenous variables (observed heterogenity). Furthermore, we assume that µ r is a permanent region-specific fixed effect and

3

ηt is a time fixed effect. Our choice of the two-way fixed effects model is based on the conjecture that µ r is likely correlated with the other regressors 2 and that it is appropriate to capture ηt by a deterministic time fixed effect. Since t is relatively small in our panel data set, it x 'rt with t-1 time dummies to x 'rt . Hence, we consider the following is possible to extend ~ dynamic fixed effects model w rt = (1 − λ )w r , t −1 + x 'rt β + µ r + ε rt ,

(5)

where β = [ γ ’, η1 , ..., η t −1 ]’ and ε rt ∼ N(0, σ 2ε ), E( ε rt ε js ) = 0, r ≠ j or t ≠ s, E( µ r ε jt ) = 0 ∀r,j,t and E( x rt ε js ) = 0 ∀r,j,t,s. As it is well known from the literature (Nickell 1981, Kiviet 1995), the usual least square dummy variable estimator (LSDV) of equation (5) yields an asymptotic (N → ∞) biased estimate of the coefficients, since the lagged dependent variable is correlated with the transformed random disturbance term by construction. The inconsistency is of O(1/T). Several estimators have been suggested to estimate dynamic panel models. (1981, 1982) propose two instrumental variable estimators.

3

Anderson and Hsiao

Firstly, they first difference

equation (5) to wipe out µ r . Secondly, since ∆w r , t −1 is correlated with ∆ε rt , they suggest using ∆w r , t −2 or w r , t −2 as instruments. Applying standard IV-procedures then yields the two Anderson and Hsiao estimators, which we indicate AHD ( ∆w r , t −2 ) and AHL( w r , t −2 ). Arellano (1989) shows that AHD might suffer from identification problems, a fact we have to take into account when applying these estimators to our dynamic Wage curve. Arellano and Bond (1991) propose two GMM-estimators, which exploit more orthogonality conditions than the above mentioned IV-procedures. Alike Anderson and Hsiao, they start with first differencing equation (5). Secondly, they use all available lagged values of the dependent variable as instruments in the empirical application of their study, but make no use of the over-identifying restrictions that follow from the assumption that all exogenous variables are assumed to be strictly exogenous. The form of the GMM estimators is

2

3

Moreover, since we observe our data for all but one region of West Germany for a given period, it seems not appropriate to assume that our regional panel is a random sample from a larger universe of regions, as supposed by a random effects approach. A comprehensive survey is given by Baltagi (1995). 4

δ$ = (X' ZA N Z' X) −1 X' ZA N Z' Y

where:

(6)

X is a stacked N(T-2) * k matrix of x r = [( ∆w r 2 L ∆w r , T −1 )' M( ∆x 'r 3 L ∆x 'rT )' ] , Z is a stacked N(T-2) * m matrix of w r 1 0 zr= M 0

0 w r1 0

0 w r2 0

L

0 0

O

0 w r1

L

L

0 0 0

L

w r ,T − 2

∆x 'r 3 ∆x 'r 4 , M ∆x 'rT

Y is a stacked N(T-2) * 1 matrix of y r = [( ∆w 'r 3 L ∆w 'rT )' ] AN is an m*m optimal weighting matrix (Hansen 1982).

Arellano and Bond (1991) suggest two different choices for AN, where the first one (a) simply takes account of the fact that the first differenced error term is MA(1) with unit root and the second one (b) uses the estimated residuals of the first step estimate of (a) to construct an AN, which yields a two-step GMM estimator, which is robust to general cross section and time series heteroscedasticity. In our applied work we indicate (a) as GMM1 and (b) as GMM2. Alike the standard errors of GMM2, we do compute robut standard erros for GMM1. Since the presented estimators hinge upon the assumption that there is no second-order serial correlation for the disturbances of the first-differenced equations, we employ a robust test of second-order correlation suggested by Arrelano and Bond (1991). In addition we employ a Sargent test of overidentifying restrictions for the GMM-estimates (Arrelano and Bond 1991). Wald tests for all IV-estimators are robut to general heteroscedasticity.

4. The Data Our empirical analysis is based on a balanced regional panel data set of 74 „Raumordnungsregionen“ (ROR) of West Germany for the years 1985 to 1994. The ROR´s are specific regional areas constructed along the administrativ structure below the state level of West Germany (c.f. BfLR 1992). Since before 1990 West Berlins geographical situation was unique and after 1990 the ROR „Berlin“ includes East Berlin as well, we exclude Berlin from our sample. The data is provided by the Federal Institute for Regional Research and Planning

5

(„Bundesanstalt für Landeskunde und Raumordnung (BfLR)“) 4 and is collected from various official statistics.5 The wage measure employed in our analysis is the average monthly labor income in the manufacturing sector with more than 20 employees. In order to capture the composition of our regional labor markets, we include as exogenous variables the following shares, which always refer to the number of employees with mandatory social insurance in the relevant ROR 6: share of the employees without a completed education, share of the employees with high education, share of the over 55-year-old employees, as well as the share of the employed women. Moreover, the industrial structure within the ROR is considered by the shares of employees in the energy, chemistry, metal engineering and the electrical engineering sector. Our measure of labor market slack is the unemployment rate within the ROR´s. Until 1990 the unemployment rate in Germany was calculated roughly as the ratio of the registered unemployed and the sum of registered unemployed and employees. Since 1990 the unemployment rate is calculated along the lines of the official statistic provided by the EC. The two concepts differ with respect to the denominator, since the EC concept includes self employed persons. Unfortunately, in our data regional unemployment rates for the years 1985-1989 are not re-adjusted to the EC framework. Therefore, we have to employ separate different unemployment rates for the periods 1985 to 1989 and 1990 to 1994 in our empirical work. Means and standard deviations for all variables used in our empirical work are given in Table 1.

- Table 1 -

5. Results For sake of comparison, we start our analysis with a replication of the static Wage curve.

- Table 2 Column 1 of Table 2 7 displays the results of a static two-way fixed effects model. We find evidence for the existence of a static Wage curve for the years 1990 to 1994, but no evidence 4

5 6 7

The data used here is a special set of indicators collected by the BfLR for the German Socio Economic Panel Group (GSOEP). The data are available upon request from the German Institute for Economic Research (DIW), GSOEP, 14195 Berlin, Koenigin-Luise-Straße 5, Germany. A detailed description is given by BfLR (1992). About 95 percent of all employees are covered by the mandatory social security system. For reasons of clarity, the estimated coefficients of all shares and the set of time dummies are ommited. All results are available from the authors on request. 6

for the years 1985 to 1989. The estimated elasticity of wages with respect to unemployment (-0.03) is roughly in line with other studies for West Germany, but is remarkably lower than the estimates provided by Blanchflower and Oswald (1994). The estimated auotocorrelation of the residuals is 0.14. Estimating our dynamic wage (equation 5) by means of the LSDV - estimator we obtain a short run elasticity of wages with respect to unemployment of -0.03 for the years 1990 to 1994, which is again significant (column 2). The estimates imply a long run elasticity of -0.04. The estimate of (1-λ) is highly significant with a value of 0.18, which is obviously significantly different from 1. Hence, we find neither evidence for a Phillips curve nor for a static Wage curve in our data using the standard LSDV estimator. The results rather indicate that there exists an inverse long run equilibrium relationship of wages and unemployment, but that in the short run there is notable inertia in wages. As stated in chapter 3, the LSDV estimates in column 2 are biased in short panels. Therefore, we employ four different IV-estimators (AHL, AHD, GMM1 and GMM2) to assess the potential size of the bias. 8 Since all estimators hinge upon the assumption that there is no second-order serial correlation for the residuals of the first-differenced equations, we start with a discussion of the results of various test. With respect to the robust test statistics of m2 in Table 2, we find no evidence which indicates that our assumption of serially uncorrelated errors is not appropriate. Moreover, the Sargant test statistic for the GMM2 estimator provides no evidence that the over-identifying restrictions are not valid. Hence, the exploited specification tests do not lend support for inappropriate assumptions regarding the disturbance term or inproper over-identifying restrictions. Column 3 and column 4 of Table 2 report the estimates employing the two IV-estimators proposed by Anderson and Hsiao. Using AHL there is neither evidence for a Phillips curve nor a Wage curve. With respect to AHD, we observe a weak significant autocorrelation in wages, but no significant elasticity of wages with respect to unemployment. Hence, our results again lend no support for both competing hypotheses. However, as indicated by Arellano and Bond (1991) estimates using AHD and AHL with short panels might be poorly determined, since they do not make use of all available instruments. Therefore, we run appropriate regressions using GMM1 and GMM2 with an instrument set as described in section 3. The results reported in column 5 and 6 display significant autocorrelation in wages. The obtained coefficients [(1-λ)] range from 0.27 to 0.30

8

All estimations are carried out using the DPD for Gauss tool developed by M. Arellano and S. Bond (Arellano/Bond 1988). We thank M. Arellano for providing a copy of DPD for Gauss. 7

and are highly significant. Since they are obviously not close to one, the estimates do not provide evidence for a pure Phillips curve. In addition, with respect to the estimated coefficients employing GMM2, we obtain a significant short run elasticity of wages with respect to unemployment of -0.03 for the years 1990 to 1994. The corresponding long run elasticity is -0.04. Both results provide evidence for the existence of dynamic Wage curve with partial adjustment to a new equilibrium. Since the Monte Carlo study of Arellano and Bond (1991) shows that the standard errors of GMM2 might be plagued by a slight downward bias, care should be exercised in using estimates of GMM2 alone to make inference conclusions. In order to test the behavior of both GMM estimators, we run a series of regressions with more restrictive instrument sets 9, i.e. reducing step by step the number of lagged dependent variables exploited in Z. Employing GMM2, the estimated coefficient of the lagged dependent variable is always significantly positive within a range from 0.12 to 0.26. With respect to GMM1, some regressions yield significantly positive coefficients of the lagged dependent variable within a range from 0.14 to 0.22, but other regressions produce similar results to the set of insignificant estimates reported in column 3 of Table 2. Concerning the estimated elasticity of wages with respect to unemployment for the years 1990 to1994, the results resemble the above presented estimates, i.e. GMM2 produces - with one exception - significant estimates within a range of -0.05 to 0.03. Strikingly, two estimates of the elasticity of wages with respect to unemployment for 1985 to 1989 using GMM2 yield significantly negative estimates of -0.03, but none of the GMM1 estimates do. In order to check the robustness of our results, we pursue two additional tests. Firstly, along the lines of most Phillips curve estimates, we specify our dynamic Wage curve as a linear function of unemployment. Similar to the above presented results, the estimated coefficients of the lagged dependent variable are significantly positive and different from 1 within a range from 0.23 to 0.46. Moreover, along the lines of previous Wage curve studies, there is no evidence for a linear relationship of regional unemployment and regional wages. Our second check of robustness considers potential spatial correlation in regional unemployment. Based on the Queen-criterion (Kelejian/Robinson 1995, pp. 94/95) we construct a row-normalized spatial weighting matrix for regional unemployment to take excess labor supply of adjacent regions into account. Our estimates again reveal significant autocorrelation in wages, which is always different from 1. However, the estimates of the

9

We also try to exploit additional over-identifying restrictions arising from the strict exogeneity of xit. However, we run into identification problems by widening the set of instruments. 8

effects of regional unemployment and unemployment within neighboring regions are plagued by multicollinearity, which renders it impossible to identify the effects of spatially lagged unemployment rates.

6. Much ado about nothing ? Is there a Phillips Curve or a static Wage Curve? Exploiting regional data for West Germany, we conclude that none of the two seems to be appropriate. Rather there is evidence for a dynamic Wage curve with partial adjustment to equilibrium in Germany, at least for the years 1990 to 1994.10 This implies that a higher level of regional unemployment exerts permanently increased downward pressure on regional wages, ceteris paribus. Our results leave us with the problem of reconciling the theoretical tension between the Phillips curve and the Wage curve. Therefore, it might be helpful to take macroeconomic approaches like Layard/Nickel/Jackman (1991) or Bean (1994) into account. At the heart of these approaches is a so-called wage setting function, which apparently resembles our dynamic Wage curve. Using macro data for West Germany for the years 1956 to 1985 to fit a wage equation based on their theoretical framework, Layard/Nickell/Jackman (1991) yield an estimate of the coefficient of the lagged dependent variable of 0.46 and an estimated coefficient for log(u) of -0.019. These estimates are rather similar to our results using regional data for 1985 to 1994. Also, Layard/Nickell/Jackman (1991) demonstrate that their approach is capable of producing a Phillips curve type adjustment process. Hence, though a snapshot of the data sometimes makes one think of a pure Phillips curve mechanism, empirical evidence relying on regional and macro data lends support to the existence of both considerable nominal inertia in wages and a negative long run equilibrium wage-unemployment nexus in Germany.

10

Note that our results resemble the LSDV estimates provided by Bell (1997) for the US. 9

References Anderson, T.W. and C. Hsiao (1981), Estimation of Dynamic Models with Error Components, Journal of the American Statistical Association, 76, 598-606. Anderson, T.W. and C. Hsiao (1982), Formulation and Estimation of Dynamic Models Using Panel Data, Journal of Econometrics, 18, 47-82. Arellano, M. (1989), A Note on the Anderson-Hsiao Estimator for Panel Data, Economics Letters, 31, 337-341. Arellano, M and S. Bond (1988), Dynamic Panel Data Estimation Using DPD - A Guide for Users, Working Paper No. 88/15, Institute for Fiscal Studies, London. Arellano, M and S. Bond (1991), Some Test of Specification of Panel Data: Monte Carlo Evidence and an Application to Employment Equations, Review of Economic Studies, 58, 277-297. Baltagi, B. (1995), Econometric Analysis of Panel Data, Chichester. Bean, C. (1994), European Unemployment: A Survey, Journal of Economic Literature, XXXII, 573-619. Bell, B. (1997), Wage Curve or Phillips Curve, Manuscript, Nuffield College, Oxford. Blanchard, O. and L. F. Katz, (1997), What We Know and Do Not Know about the Natural Rate of Unemployment, Journal of Economic Perspectives 11, 57-72. Blanchflower, D.G. and A.J. Oswald (1994), The Wage Curve, Cambridge (Mass.). Bundesforschungsanstalf für Landeskunde und Raumordnung (BfLR)(1992), Laufende Raumbeobachtungen, in: Materialien zur Raumentwicklung 47. Card, D. and D. Hyslop (1996), Does Inflation ‘Grease the Wheels of the Labor Market’ ?, Working Paper 5538, NBER. Fitzenberger, B. and W. Franz (1994), Dezentrale Versus Zentrale Lohnbildung in Europa: Theoretische Aspekte und empirische Evidenz, in: Gahlen, B., H. Hesse and H.J. Ramser, Europäische Integrationsprobleme aus Wirtschaftswissenschaftlicher Sicht, 321-354. Franz, W. and R. Gordon (1993), German and American Wage and Price Dynamics, European Economic Review, 37, 719-762. Franz, W. and W. Smolny (1994), Sectoral Wage and Price Formation and Working Time in Germany, Zeitschrift für Wirtschafts- und Sozialwissenschaften, 114, S. 507-529. Hansen, L. P. (1982), Large Sample Properties of Generalized Methods of Moments Estimators, Econometrica, 50, 1029-1054. Kelejian, H. H. and D. P. Robinson (1995), Spatial Correlation: A Suggested Alternative to the Autoregressive Model, in: Anselin, L. and R.J.G.M. Florax (eds.), New Directions in Spatial Econometrics, S. 75-95, Springer. Kiviet, J. (1995), On Bias, Inconsistency, and Efficiency of Various Estimators in Dynamic Panel Data Models, Journal of Econometrics, 68, 53-78. Layard, R., S. Nickell and R. Jackman (1991), Unemployment. Macroeconomic Performance and the Labor Market, Oxford. Manning, A. (1993), Wage Bargaining and the Phillips Curve: The Identification and Specification of Aggregate Wage Equations, Economic Journal, 103, 98-118.

10

Nickell, S. (1981), Biases in Dynamic Models with Fixed Effects, Econometrica, 49, 14171426. Pannenberg, M. and J. Schwarze (1998), Labor Market Slack and the Wage Curve, Economics Letters, 58, 351-354. Wagner, J. (1994), German Wage Curves 1979-1990, Economics Letters, 44, 307-311.

11

Table 1 Descriptive Statistics

Variable

Mean

Std.-Dev.

log monthly labor income

8.32

0.18

log unemployment rate 1985-89

2.10

0.40

log unemployment rate 1990-94

1.89

0.36

40.99

3.07

over 55-years-old

8.94

1.04

without education

32.99

3.55

with high education

4.63

1.80

energy

1.75

1.99

chemistry

6.11

3.52

14.84

6.09

8.00

4.60

share of employees female

metall engineering electrical engineering

Note: log’s of unemployment rates are computed for the relevant years. The shares always refer to the number of employees with mandatory social insurance in the relevant ROR.

12

Table 2 West German Wage Curves

LSDVstatic

LSDVdynamic

AHL

AHD

GMM1

GMM2

0.184 (0.219) 0.021 (0.035)

0.468 (0.290) 0.024 (0.041)

0.265 (0.055) 0.010 (0.032)

0.295 (0.026) -0.017 (0.014)

β ln( u r , 85− 89 )

0.009 (0.013)

0.182 (0.042) 0.002 (0.013)

β ln( u r , 90 −94 )

-0.028 (0.014)

-0.030 (0.015)

0.003 (0.039)

0.012 (0.045)

-0.020 (0.031)

-0.031 (0.012)

0.98

0.98

--

--

--

--

Wald1 [χ 2 (11)]

--

--

74.81

29.42

127.24

482.90

Wald2 [χ 2 (8)]

--

--

44.60

22.71

69.94

256.02

m2 [N(0,1)]

--

--

-0.99

0.01

-0.86

-0.63

Sargent[χ 2 (35)]

--

--

--

--

--

46.06

(1-λ)

R2

--

Notes: (Robust) standard errors in parentheses. Wald1: Wald test of joint significance of all exogenous variables, Wald2: Wald test of joint significance of time dummies. m2: Test of second-order correlation of disturbances. The test is distributetd N(0,1) Arellano/Bond (1991). Sargent: Sargent test of over-identifying restrictions. Degrees of freedom for χ2 statistics are reported in parantheses.

13

Markus Pannenberg a * and Johannes Schwarze a, b a

German Institute for Economic Research (DIW), b

University of Bamberg

July 1998

Abstract Is there an inverse relationship between the rate of change of wages and the contemporaneous unemployment rate or rather between the level of both variables ? The former view leads to the Phillips curve, which has been challenged by the latter, named the Wage curve. Exploiting regional data for West Germany, we conclude that none of the two seems to be appropriate. However, there is evidence for a dynamic Wage curve with partial adjustment to equilibrium, at least for the years 1990 to 1994. Hence, the striking puzzle „Phillips curve or Wage curve“ might be more apparent than real.

JEL Classification: E24, J64, C23. Keywords: Phillips Curve, Wage Curve, GMM.

1. Introduction The relationship of unemployment and wages is an evergreen in both theoretical and empirical economics. Based on the famous work by A. Phillips standard macroeconomic textbooks state that there is an inverse relationship between the rate of change of wages and the contemporaneous unemployment rate, i.e. there is a Phillips curve. This common view is grounded on the idea that wages adjust to eliminate any excess supply or demand in the labor market and is supported by a huge amount of empirical work with macroeconomic data for different countries. However, Blanchflower and Oswald (1994) have challenged the theoretical and empirical foundation of the Phillips curve. They argue, that the level of wages rather than the wage change is related to the unemployment rate, i.e. there is a Wage curve. The Wage curve can be derived for example from an efficiency wage framework or from a bargaining approach and is in accordance with the notion that the level of prices is related to the level of quantities. Similar to the Phillips curve, the Wage curve can rely on considerable microeconometric evidence for various countries. Concerning the validity of the Phillips curve, Blanchflower and Oswald claim, that estimates of a dynamic version of the Wage curve show little autoregression in wages. Therefore, from their point of view the „famous Phillips curve is an illusion“ and „the apparent autoregression in macro pay levels may be the result of aggregation error or measurement error or specification error or all three“ (p. 284). Blanchflowers and Oswalds striking conclusion has been disputed by various authors. Blanchard and Katz (1997) argue that there might be a theoretical tension between the Wage curve and the Phillips curve, but that a careful replication of the microeconometric evidence for the US reveals a ‘true’ autoregression coefficient close to one, which is in accordance with the traditional Phillips curve. Card and Hyslop (1996) also present evidence in favor of the Phillips curve for the US. However, since Bell (1997) clearly shows that the aforementioned conclusions might be as premature as Blanchflowers and Oswalds claim, there is need for further empirical analysis. In this paper we pursue to assess the power of the different claims with respect to German wage dynamics, since, thus far, there is hardly any rigorous (nested) test of the competing hypotheses. We are aware of studies using macro or sectoral data, such as Franz and Gordon (1993), Fitzenberger and Franz (1994), or Franz and Smolny (1994), which include the Phillips curve concept into a broader approach, and of microeconomic studies of the Wage curve, such as Wagner (1994) or Pannenberg/Schwarze (1998). By and large, the former studies provide evidence for a mixture of an augmented Phillips curve/real wage bargaining approach, while 1

the latter lend support to the existence of a static Wage curve. Therefore, alike the evidence for the US, the problem is to reconcile macro and micro empirical results, though the evidence for real wage bargaining from macro data in Franz and Gordon (1993) signals that something is going on besides the pure Phillips curve dynamics in Germany. In Section 2, we briefly sketch a convenient framework for testing the Phillips curve against the Wage curve. Using regional panel data for West Germany, our framework requires a dynamic model for panel data. In addition to standard least square dummy variable estimators used in the above cited debate, we employ some instrumental variable estimators, which are discussed in Section 3. Subsequent to a brief description of the data and the variables in Section 4, we will present our results in Section 5. We find neither evidence for a pure Phillips curve nor a static Wage curve. Rather we obtain a dynamic Wage curve with partial adjustment to equilibrium for West Germany. Considering our results, we argue that the above mentioned puzzle is more apparent than real, once we take macroeconomic approaches like Layard/Nickell/Jackman (1991) into account. Actually, regional and macro data seem to mirror the same phenomena for West Germany.

2. Nesting the Phillips Curve and the Wage Curve Following Blanchard and Katz (1997) a simple form of a wage equation within a macroeconometric error correction framework can be written as ∆w t = α 0 + α 1 ∆p t −1 − α 2 ln( u t ) − λ(w t −1 − p t −1 − φ t −1 ) + v t ,

(1)

where w is the logarithm of the nominal wage, p is the logarithm of the price index, φ is the logarithm of the productivity level, u is the unemployment rate, a is a constant, v is an error term and ∆ the usual difference operator. 1 We use the log of the unemployment rate instead of the level to allow direct comparison of the Phillips curve and the Wage curve approach. λ indicates whether a deviation of the real wage from the normal or equilibrium level determined by productivity and the unemployment rate causes variation in wage inflation. Since „there is no such thing as a separate wage equation“ (Franz and Gordon 1993) simultaneity bias is avoided by excluding the contemporaneous price term in equation (1). Note however that the identification problem pointed out by Manning (1993) still exists, since a complete model should consist of a price, a wage and an unemployment equation. 1

Note that all above mentioned macroeconomic studies for Germany essentially rely on a similar error correction type wage equation. 2

Blanchflowers and Oswalds main point is that most of the well-known problems, such as treatment of expected inflation or measurement of productivity growth, which arise when wage equations like (1) are estimated, will vanish by analyzing the relationship of wages and unemployment across space within a country over time. Assuming that price inflation and productivity growth are common to all regions, equation (1) can be rewritten as ∆w rt = α 0 + α 1 ∆p t −1 − α 2 ln(u rt ) − λ (w r ,t −1 − p t −1 − φ t −1 ) + v rt ,

(2)

where r is a region specific index. Employing regional panel data, all terms in equation (2), which do no vary accross regions, can be captured by common time effects. Moreover, unobserved heterogeneity accross regions can be catched by a permanent region-specific effect. Using explicit differences instead of the difference operator, we therefore yield the following standard dynamic Wage curve equation w rt = α 0 − α 2 ln( u rt ) + (1 − λ )w r, t −1 + x *'rt α 3 + µ r + η t + ε rt ,

(3)

where x *'rt is a vector of exogenous variables controlling for observed time variant regional characteristics, µr is a permanent region-specific effect, ηt is a time effect that is common to all regions and εrt is a random disturbance. Appropriate estimation of equation (3) enables us to put the competing hypotheses of the Phillips curve and the Wage Curve to test. If (1-λ) = 0 and α2 > 0 hold, we will observe instantaneous adjustment of wages in response to exogenous shocks in our data, i.e. there is a static Wage Curve. For (1-λ) = 1 and α2 > 0, we will discover a pure disequilibrium adjustment process, i.e. there is a Phillips curve. Intermediate values of λ, λ ∈ ]0, 1[ , imply both an error correction mechanism and considerable nominal inertia in the short run.

3. Econometric specifications Equation (3) can compactly be written as w rt = (1 − λ )w r , t −1 + ~ x 'rt γ + µ r + η t + ε rt ,

(4)

where γ = [ α 0 ,− α 2 , α '3 ] ‘and ~ x 'rt is the extended vector of exogenous variables (observed heterogenity). Furthermore, we assume that µ r is a permanent region-specific fixed effect and

3

ηt is a time fixed effect. Our choice of the two-way fixed effects model is based on the conjecture that µ r is likely correlated with the other regressors 2 and that it is appropriate to capture ηt by a deterministic time fixed effect. Since t is relatively small in our panel data set, it x 'rt with t-1 time dummies to x 'rt . Hence, we consider the following is possible to extend ~ dynamic fixed effects model w rt = (1 − λ )w r , t −1 + x 'rt β + µ r + ε rt ,

(5)

where β = [ γ ’, η1 , ..., η t −1 ]’ and ε rt ∼ N(0, σ 2ε ), E( ε rt ε js ) = 0, r ≠ j or t ≠ s, E( µ r ε jt ) = 0 ∀r,j,t and E( x rt ε js ) = 0 ∀r,j,t,s. As it is well known from the literature (Nickell 1981, Kiviet 1995), the usual least square dummy variable estimator (LSDV) of equation (5) yields an asymptotic (N → ∞) biased estimate of the coefficients, since the lagged dependent variable is correlated with the transformed random disturbance term by construction. The inconsistency is of O(1/T). Several estimators have been suggested to estimate dynamic panel models. (1981, 1982) propose two instrumental variable estimators.

3

Anderson and Hsiao

Firstly, they first difference

equation (5) to wipe out µ r . Secondly, since ∆w r , t −1 is correlated with ∆ε rt , they suggest using ∆w r , t −2 or w r , t −2 as instruments. Applying standard IV-procedures then yields the two Anderson and Hsiao estimators, which we indicate AHD ( ∆w r , t −2 ) and AHL( w r , t −2 ). Arellano (1989) shows that AHD might suffer from identification problems, a fact we have to take into account when applying these estimators to our dynamic Wage curve. Arellano and Bond (1991) propose two GMM-estimators, which exploit more orthogonality conditions than the above mentioned IV-procedures. Alike Anderson and Hsiao, they start with first differencing equation (5). Secondly, they use all available lagged values of the dependent variable as instruments in the empirical application of their study, but make no use of the over-identifying restrictions that follow from the assumption that all exogenous variables are assumed to be strictly exogenous. The form of the GMM estimators is

2

3

Moreover, since we observe our data for all but one region of West Germany for a given period, it seems not appropriate to assume that our regional panel is a random sample from a larger universe of regions, as supposed by a random effects approach. A comprehensive survey is given by Baltagi (1995). 4

δ$ = (X' ZA N Z' X) −1 X' ZA N Z' Y

where:

(6)

X is a stacked N(T-2) * k matrix of x r = [( ∆w r 2 L ∆w r , T −1 )' M( ∆x 'r 3 L ∆x 'rT )' ] , Z is a stacked N(T-2) * m matrix of w r 1 0 zr= M 0

0 w r1 0

0 w r2 0

L

0 0

O

0 w r1

L

L

0 0 0

L

w r ,T − 2

∆x 'r 3 ∆x 'r 4 , M ∆x 'rT

Y is a stacked N(T-2) * 1 matrix of y r = [( ∆w 'r 3 L ∆w 'rT )' ] AN is an m*m optimal weighting matrix (Hansen 1982).

Arellano and Bond (1991) suggest two different choices for AN, where the first one (a) simply takes account of the fact that the first differenced error term is MA(1) with unit root and the second one (b) uses the estimated residuals of the first step estimate of (a) to construct an AN, which yields a two-step GMM estimator, which is robust to general cross section and time series heteroscedasticity. In our applied work we indicate (a) as GMM1 and (b) as GMM2. Alike the standard errors of GMM2, we do compute robut standard erros for GMM1. Since the presented estimators hinge upon the assumption that there is no second-order serial correlation for the disturbances of the first-differenced equations, we employ a robust test of second-order correlation suggested by Arrelano and Bond (1991). In addition we employ a Sargent test of overidentifying restrictions for the GMM-estimates (Arrelano and Bond 1991). Wald tests for all IV-estimators are robut to general heteroscedasticity.

4. The Data Our empirical analysis is based on a balanced regional panel data set of 74 „Raumordnungsregionen“ (ROR) of West Germany for the years 1985 to 1994. The ROR´s are specific regional areas constructed along the administrativ structure below the state level of West Germany (c.f. BfLR 1992). Since before 1990 West Berlins geographical situation was unique and after 1990 the ROR „Berlin“ includes East Berlin as well, we exclude Berlin from our sample. The data is provided by the Federal Institute for Regional Research and Planning

5

(„Bundesanstalt für Landeskunde und Raumordnung (BfLR)“) 4 and is collected from various official statistics.5 The wage measure employed in our analysis is the average monthly labor income in the manufacturing sector with more than 20 employees. In order to capture the composition of our regional labor markets, we include as exogenous variables the following shares, which always refer to the number of employees with mandatory social insurance in the relevant ROR 6: share of the employees without a completed education, share of the employees with high education, share of the over 55-year-old employees, as well as the share of the employed women. Moreover, the industrial structure within the ROR is considered by the shares of employees in the energy, chemistry, metal engineering and the electrical engineering sector. Our measure of labor market slack is the unemployment rate within the ROR´s. Until 1990 the unemployment rate in Germany was calculated roughly as the ratio of the registered unemployed and the sum of registered unemployed and employees. Since 1990 the unemployment rate is calculated along the lines of the official statistic provided by the EC. The two concepts differ with respect to the denominator, since the EC concept includes self employed persons. Unfortunately, in our data regional unemployment rates for the years 1985-1989 are not re-adjusted to the EC framework. Therefore, we have to employ separate different unemployment rates for the periods 1985 to 1989 and 1990 to 1994 in our empirical work. Means and standard deviations for all variables used in our empirical work are given in Table 1.

- Table 1 -

5. Results For sake of comparison, we start our analysis with a replication of the static Wage curve.

- Table 2 Column 1 of Table 2 7 displays the results of a static two-way fixed effects model. We find evidence for the existence of a static Wage curve for the years 1990 to 1994, but no evidence 4

5 6 7

The data used here is a special set of indicators collected by the BfLR for the German Socio Economic Panel Group (GSOEP). The data are available upon request from the German Institute for Economic Research (DIW), GSOEP, 14195 Berlin, Koenigin-Luise-Straße 5, Germany. A detailed description is given by BfLR (1992). About 95 percent of all employees are covered by the mandatory social security system. For reasons of clarity, the estimated coefficients of all shares and the set of time dummies are ommited. All results are available from the authors on request. 6

for the years 1985 to 1989. The estimated elasticity of wages with respect to unemployment (-0.03) is roughly in line with other studies for West Germany, but is remarkably lower than the estimates provided by Blanchflower and Oswald (1994). The estimated auotocorrelation of the residuals is 0.14. Estimating our dynamic wage (equation 5) by means of the LSDV - estimator we obtain a short run elasticity of wages with respect to unemployment of -0.03 for the years 1990 to 1994, which is again significant (column 2). The estimates imply a long run elasticity of -0.04. The estimate of (1-λ) is highly significant with a value of 0.18, which is obviously significantly different from 1. Hence, we find neither evidence for a Phillips curve nor for a static Wage curve in our data using the standard LSDV estimator. The results rather indicate that there exists an inverse long run equilibrium relationship of wages and unemployment, but that in the short run there is notable inertia in wages. As stated in chapter 3, the LSDV estimates in column 2 are biased in short panels. Therefore, we employ four different IV-estimators (AHL, AHD, GMM1 and GMM2) to assess the potential size of the bias. 8 Since all estimators hinge upon the assumption that there is no second-order serial correlation for the residuals of the first-differenced equations, we start with a discussion of the results of various test. With respect to the robust test statistics of m2 in Table 2, we find no evidence which indicates that our assumption of serially uncorrelated errors is not appropriate. Moreover, the Sargant test statistic for the GMM2 estimator provides no evidence that the over-identifying restrictions are not valid. Hence, the exploited specification tests do not lend support for inappropriate assumptions regarding the disturbance term or inproper over-identifying restrictions. Column 3 and column 4 of Table 2 report the estimates employing the two IV-estimators proposed by Anderson and Hsiao. Using AHL there is neither evidence for a Phillips curve nor a Wage curve. With respect to AHD, we observe a weak significant autocorrelation in wages, but no significant elasticity of wages with respect to unemployment. Hence, our results again lend no support for both competing hypotheses. However, as indicated by Arellano and Bond (1991) estimates using AHD and AHL with short panels might be poorly determined, since they do not make use of all available instruments. Therefore, we run appropriate regressions using GMM1 and GMM2 with an instrument set as described in section 3. The results reported in column 5 and 6 display significant autocorrelation in wages. The obtained coefficients [(1-λ)] range from 0.27 to 0.30

8

All estimations are carried out using the DPD for Gauss tool developed by M. Arellano and S. Bond (Arellano/Bond 1988). We thank M. Arellano for providing a copy of DPD for Gauss. 7

and are highly significant. Since they are obviously not close to one, the estimates do not provide evidence for a pure Phillips curve. In addition, with respect to the estimated coefficients employing GMM2, we obtain a significant short run elasticity of wages with respect to unemployment of -0.03 for the years 1990 to 1994. The corresponding long run elasticity is -0.04. Both results provide evidence for the existence of dynamic Wage curve with partial adjustment to a new equilibrium. Since the Monte Carlo study of Arellano and Bond (1991) shows that the standard errors of GMM2 might be plagued by a slight downward bias, care should be exercised in using estimates of GMM2 alone to make inference conclusions. In order to test the behavior of both GMM estimators, we run a series of regressions with more restrictive instrument sets 9, i.e. reducing step by step the number of lagged dependent variables exploited in Z. Employing GMM2, the estimated coefficient of the lagged dependent variable is always significantly positive within a range from 0.12 to 0.26. With respect to GMM1, some regressions yield significantly positive coefficients of the lagged dependent variable within a range from 0.14 to 0.22, but other regressions produce similar results to the set of insignificant estimates reported in column 3 of Table 2. Concerning the estimated elasticity of wages with respect to unemployment for the years 1990 to1994, the results resemble the above presented estimates, i.e. GMM2 produces - with one exception - significant estimates within a range of -0.05 to 0.03. Strikingly, two estimates of the elasticity of wages with respect to unemployment for 1985 to 1989 using GMM2 yield significantly negative estimates of -0.03, but none of the GMM1 estimates do. In order to check the robustness of our results, we pursue two additional tests. Firstly, along the lines of most Phillips curve estimates, we specify our dynamic Wage curve as a linear function of unemployment. Similar to the above presented results, the estimated coefficients of the lagged dependent variable are significantly positive and different from 1 within a range from 0.23 to 0.46. Moreover, along the lines of previous Wage curve studies, there is no evidence for a linear relationship of regional unemployment and regional wages. Our second check of robustness considers potential spatial correlation in regional unemployment. Based on the Queen-criterion (Kelejian/Robinson 1995, pp. 94/95) we construct a row-normalized spatial weighting matrix for regional unemployment to take excess labor supply of adjacent regions into account. Our estimates again reveal significant autocorrelation in wages, which is always different from 1. However, the estimates of the

9

We also try to exploit additional over-identifying restrictions arising from the strict exogeneity of xit. However, we run into identification problems by widening the set of instruments. 8

effects of regional unemployment and unemployment within neighboring regions are plagued by multicollinearity, which renders it impossible to identify the effects of spatially lagged unemployment rates.

6. Much ado about nothing ? Is there a Phillips Curve or a static Wage Curve? Exploiting regional data for West Germany, we conclude that none of the two seems to be appropriate. Rather there is evidence for a dynamic Wage curve with partial adjustment to equilibrium in Germany, at least for the years 1990 to 1994.10 This implies that a higher level of regional unemployment exerts permanently increased downward pressure on regional wages, ceteris paribus. Our results leave us with the problem of reconciling the theoretical tension between the Phillips curve and the Wage curve. Therefore, it might be helpful to take macroeconomic approaches like Layard/Nickel/Jackman (1991) or Bean (1994) into account. At the heart of these approaches is a so-called wage setting function, which apparently resembles our dynamic Wage curve. Using macro data for West Germany for the years 1956 to 1985 to fit a wage equation based on their theoretical framework, Layard/Nickell/Jackman (1991) yield an estimate of the coefficient of the lagged dependent variable of 0.46 and an estimated coefficient for log(u) of -0.019. These estimates are rather similar to our results using regional data for 1985 to 1994. Also, Layard/Nickell/Jackman (1991) demonstrate that their approach is capable of producing a Phillips curve type adjustment process. Hence, though a snapshot of the data sometimes makes one think of a pure Phillips curve mechanism, empirical evidence relying on regional and macro data lends support to the existence of both considerable nominal inertia in wages and a negative long run equilibrium wage-unemployment nexus in Germany.

10

Note that our results resemble the LSDV estimates provided by Bell (1997) for the US. 9

References Anderson, T.W. and C. Hsiao (1981), Estimation of Dynamic Models with Error Components, Journal of the American Statistical Association, 76, 598-606. Anderson, T.W. and C. Hsiao (1982), Formulation and Estimation of Dynamic Models Using Panel Data, Journal of Econometrics, 18, 47-82. Arellano, M. (1989), A Note on the Anderson-Hsiao Estimator for Panel Data, Economics Letters, 31, 337-341. Arellano, M and S. Bond (1988), Dynamic Panel Data Estimation Using DPD - A Guide for Users, Working Paper No. 88/15, Institute for Fiscal Studies, London. Arellano, M and S. Bond (1991), Some Test of Specification of Panel Data: Monte Carlo Evidence and an Application to Employment Equations, Review of Economic Studies, 58, 277-297. Baltagi, B. (1995), Econometric Analysis of Panel Data, Chichester. Bean, C. (1994), European Unemployment: A Survey, Journal of Economic Literature, XXXII, 573-619. Bell, B. (1997), Wage Curve or Phillips Curve, Manuscript, Nuffield College, Oxford. Blanchard, O. and L. F. Katz, (1997), What We Know and Do Not Know about the Natural Rate of Unemployment, Journal of Economic Perspectives 11, 57-72. Blanchflower, D.G. and A.J. Oswald (1994), The Wage Curve, Cambridge (Mass.). Bundesforschungsanstalf für Landeskunde und Raumordnung (BfLR)(1992), Laufende Raumbeobachtungen, in: Materialien zur Raumentwicklung 47. Card, D. and D. Hyslop (1996), Does Inflation ‘Grease the Wheels of the Labor Market’ ?, Working Paper 5538, NBER. Fitzenberger, B. and W. Franz (1994), Dezentrale Versus Zentrale Lohnbildung in Europa: Theoretische Aspekte und empirische Evidenz, in: Gahlen, B., H. Hesse and H.J. Ramser, Europäische Integrationsprobleme aus Wirtschaftswissenschaftlicher Sicht, 321-354. Franz, W. and R. Gordon (1993), German and American Wage and Price Dynamics, European Economic Review, 37, 719-762. Franz, W. and W. Smolny (1994), Sectoral Wage and Price Formation and Working Time in Germany, Zeitschrift für Wirtschafts- und Sozialwissenschaften, 114, S. 507-529. Hansen, L. P. (1982), Large Sample Properties of Generalized Methods of Moments Estimators, Econometrica, 50, 1029-1054. Kelejian, H. H. and D. P. Robinson (1995), Spatial Correlation: A Suggested Alternative to the Autoregressive Model, in: Anselin, L. and R.J.G.M. Florax (eds.), New Directions in Spatial Econometrics, S. 75-95, Springer. Kiviet, J. (1995), On Bias, Inconsistency, and Efficiency of Various Estimators in Dynamic Panel Data Models, Journal of Econometrics, 68, 53-78. Layard, R., S. Nickell and R. Jackman (1991), Unemployment. Macroeconomic Performance and the Labor Market, Oxford. Manning, A. (1993), Wage Bargaining and the Phillips Curve: The Identification and Specification of Aggregate Wage Equations, Economic Journal, 103, 98-118.

10

Nickell, S. (1981), Biases in Dynamic Models with Fixed Effects, Econometrica, 49, 14171426. Pannenberg, M. and J. Schwarze (1998), Labor Market Slack and the Wage Curve, Economics Letters, 58, 351-354. Wagner, J. (1994), German Wage Curves 1979-1990, Economics Letters, 44, 307-311.

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Table 1 Descriptive Statistics

Variable

Mean

Std.-Dev.

log monthly labor income

8.32

0.18

log unemployment rate 1985-89

2.10

0.40

log unemployment rate 1990-94

1.89

0.36

40.99

3.07

over 55-years-old

8.94

1.04

without education

32.99

3.55

with high education

4.63

1.80

energy

1.75

1.99

chemistry

6.11

3.52

14.84

6.09

8.00

4.60

share of employees female

metall engineering electrical engineering

Note: log’s of unemployment rates are computed for the relevant years. The shares always refer to the number of employees with mandatory social insurance in the relevant ROR.

12

Table 2 West German Wage Curves

LSDVstatic

LSDVdynamic

AHL

AHD

GMM1

GMM2

0.184 (0.219) 0.021 (0.035)

0.468 (0.290) 0.024 (0.041)

0.265 (0.055) 0.010 (0.032)

0.295 (0.026) -0.017 (0.014)

β ln( u r , 85− 89 )

0.009 (0.013)

0.182 (0.042) 0.002 (0.013)

β ln( u r , 90 −94 )

-0.028 (0.014)

-0.030 (0.015)

0.003 (0.039)

0.012 (0.045)

-0.020 (0.031)

-0.031 (0.012)

0.98

0.98

--

--

--

--

Wald1 [χ 2 (11)]

--

--

74.81

29.42

127.24

482.90

Wald2 [χ 2 (8)]

--

--

44.60

22.71

69.94

256.02

m2 [N(0,1)]

--

--

-0.99

0.01

-0.86

-0.63

Sargent[χ 2 (35)]

--

--

--

--

--

46.06

(1-λ)

R2

--

Notes: (Robust) standard errors in parentheses. Wald1: Wald test of joint significance of all exogenous variables, Wald2: Wald test of joint significance of time dummies. m2: Test of second-order correlation of disturbances. The test is distributetd N(0,1) Arellano/Bond (1991). Sargent: Sargent test of over-identifying restrictions. Degrees of freedom for χ2 statistics are reported in parantheses.

13