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Appendix

This Appendix reviews an econometric analysis of wage formation in Denmark. The analysis is based on hourly wages in manufacturing. The following section gives a brief discussion of alternative models to explain wage formation, as the basis for the econometric analysis. Then follows a description of data and methodology. The article then reviews the estimation of each model separately, and tests the models against each other. Finally, the statistical properties of the preferred model are discussed, including stability and forecast properties.

Model framework

As mentioned previously, the basis for the analysis is alternative hypotheses, each of which has played a central role in existing empirical studies of the development in both Danish and foreign wages. The Phillips curve comes first chronologically and describes the rate of wage increases as a function of inflation and the unemployment rate. It has played a central role in many macroeconometric models, although it is often criticized for a lack of theoretical basis and sometimes also for empirical instability. The counterpart of the Phillips curve is equations which describe a relationship between real wages/wage share and e.g. unemployment. Chart 4 indicates that both Phillips curves and real-wage models might be of empirical interest, since both the rate of wage increases and the wage share appear to

have a negative correlation with the unemployment rate. However, in recent years this correlation appears to be broken. Whether there is a structural break will be investigated in the following.

In essence, the Phillips curve describes the rate of wage increases, w, as a function of expected inflation, p^e, and the unemployment rate, UR, and possibly also the change in the unemployment rate, UR,

Expected inflation is normally approximated by lagged values of actual inflation, p. Other explanatory variables might well be included. As previously stated the Phillips curve has been criticized for giving a too simple description of wage formation. One of the most important points of criticism is that it does not explain the level of real wages at a given unemployment rate, but only the rate of increase in nominal wages. However, in a wider model context the Phillips curve does not necessarily imply that real wages are indeterminate. They may very well be included in both supply and demand for labour. In that case the Phillips curve will merely be the mechanism ensuring adjustment of real wages and creating equilibrium in the labour market. It should also be stated that the existence of a well-
determined long-term level of unemployment does not necessarily imply a vertical Phillips curve, i.e. =1. With fixed exchange rates, unemployment in equilibrium must result in the same rate of wage increase as in the anchor area. This appears from e.g. multiplier simulations using the Nationalbank's macroeconometric model¹⁾.

Wage bargaining models represent a more recent theory of wage formation. Real wages are determined by negotiation between trade unions and employers and will therefore depend on the relative bargaining power of the unions. The unemployment rate is used as a proxy, so that W/P=g(UR), g'<0. Real wages are normally also influenced by other factors such as payroll and corporate taxes, productivity, the replacement ratio of unemployment benefits, etc.²⁾ As the basis for empirical determination of a model for real wages we will use the following log-linear specification where the expected sign of the parameters is stated:

p_C indicates consumer prices, p_Y producer prices, q labour productivity, h weekly working hours, t_i average income-tax rate, t_p payroll taxes, i.e. employers' indirect wage costs³⁾, and r the replacement ratio. The wedge, WW, between the employers' product real wages, W₁=W·T_p /P_Y , and the employees' consumption real wages, W₂=W·T_i /P_C, i.e. ww =p_C-p_Y+t_p-t_i , is of relevance since employers and employees do not normally focus on the same wage concepts. The relevance of the wedge can be illustrated by the following wage equation with disposable consumption real wages on the lefthand side:

If µ₁=µ₂=µ₃=0, the consumption real wages will be invariant to changes in the wedge components, whereas product real wages are invariant if µ₁=µ₂=-µ₃=1. Ultimately, the size of the coefficients is determined by the bargaining power of the unions, i.e. their ability to pass on changes in income tax and consumer prices to wages, and equivalently prevent business enterprises from passing on changes in indirect wage costs to wages. A tax symmetry in the wage formation might be envisaged, i.e. µ₁=µ₂=-µ₃, so that a simple restructuring of the tax system has no real effects through changes in real wages, although this need not be the case.

Data and methodology

Quarterly data from the Nationalbank's Mona model are used. The estimation period is from the 1st quarter of 1975 to the 4th quarter of 1995, whereas data until end-1997 is used for out-of-sample predictions. The following series are used:

W hourly wage index for workers in manufacturing⁴⁾

P_C private consumption deflator

P_Y deflator for GDP at factor prices for the private sector, excluding agriculture, energy and housing

T_p payroll taxes⁵⁾

T_i average income tax, including gross tax⁶⁾

UR unemployment rate

Q average hourly productivity in the private non-agricultural sector, excluding energy

H maximum agreed annual working hours

R average replacement ratio

In the first instance a unit root test is used to study the integration order of the time series. For this purpose an augmented Dickey-Fuller test based on the following equation is used. A time trend, t, is included when relevant in economic terms as an alternative to a stochastic trend.

The study of the series' order of integration indicates, cf. Table 1, that it is uncertain whether the nominal wage is integrated of first or second order, whereas the other nominal variables, consumer and producer prices, are more unequivocally integrated of first order. The working hypothesis is that all nominal variables are integrated of first order. The real variables such as real wages, wedge, unemployment, working hours and payroll and income taxes are integrated of first order⁷⁾. In view of the test statistics productivity might appear to be stationary, but is assumed to be integrated of the same order as the other real variables.

The empirical analysis will be based on Johansen's multivariate cointegration model⁸⁾. A p-dimensional VAR model, written in the error-correction form, is given as

k is the number of lags in the VAR model and t is an index of time. D signifies the deterministic terms. The error term is assumed to be identically, independently and normally distributed with the covariance matrix . Relevant variables in the long-term correlation are nominal wages, consumer prices, average hourly productivity, rate of unemployment, the wedge between enterprises' product real wages and the disposable consumption real wages, and the average replacement ratio, i.e. X={w, p_C, q, UR, ww, r}.

The long-term multipliers of the model are contained in the 6*6 matrix . As mentioned above X_t is integrated of first order, i.e. X_t ~I(1). The assumptions behind the VAR model imply that the above model describes a balanced system where all elements are stationary. Hence this means that must be of reduced rank, rank ()=, and can thereby be divided into two matrices, and ?, both 6* matrices of full column rank, where . In other words <6, when X is non-stationary. The situation =0 corresponds to no cointegration and the model is reduced to a traditional VAR model in first differences, whereas in a situation where 0<<6, independent cointegrating relationship can be found between the I(1) variables in X.

Each column in describes a cointegration relationship, and the corresponding loadings, i.e. the coefficients of the cointegration relationships in the individual equations. If there is more than one cointegration relationship the coefficients in and will not be identified and identifying restrictions must be imposed on the system in order to derive correlations which can be given an economic and structural interpretation.

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Footnotes