RDP 9105: Inflation in Australia: Causes, Inertia and Policy 3. Testing the Exogeneity of Nominal Wage Growth

In this section we test for the exogeneity of nominal wage growth. We do so by reporting, for each country, the variance decompositions of wage and money growth obtained from a vector autoregression (VAR) estimated over the period 1964–1989.^[7]

Consider the autoregressive process y_t = b(L)y_t + u_t. y is an n×1 vector of stationary variables, u is an n×1 vector of innovations (forecast errors) and b(L) is an nxT matrix of autoregressive parameters, where L is the lag operator and T is the lag length of the autoregression. Wold's representation theorem states this process can be expressed as the vector moving average y_t = a(L)u_t + E(u_t) where the coefficients of the matrix a(L) are functions of the estimated autoregressive parameters b(L). a(L) at lag 0 is the identity matrix. Each variable is therefore expressed as the sum of current and past innovations of all the variables in the system. The variance decomposition assigns the total variance of the k-step ahead forecast error to innovations in the variables of the system, via the MA representation.

The forecast variance of a variable which is essentially exogenous will be largely explicable by the variance of its own innovations.^[8] With little feedback to it from the other variables, its forecast variance will be largely unaffected by innovations to the other variables.

For each country, we estimate a five variable VAR, the variables being domestic price inflation, domestic nominal wage inflation, world price inflation, money growth and productivity growth.^[9] Since a VAR is just a set of reduced form equations, the estimation results are not open to structural inferences.^[10] However, the ordering of the variables in the VAR does impose some structure on the contemporaneous relationships between the variables, which affects the variance decompositions. We place the variables in the following order: world inflation, productivity growth, money growth, nominal wage growth and price inflation. This reflects our prior view that world inflation is contemporaneously exogenous to all the other variables, world inflation and productivity growth are together exogenous to the remaining variables etc. (Reversing the order of money and wages does not alter the results in any important way.)

In Table 1 we report the variance decompositions of nominal wage growth in each country. Each entry in Table 1 represents the proportion of nominal wage growth, at each time lag, associated with shocks to each variable in the model. By construction, these shocks are uncorrelated, so the proportions sum to 100 per cent. We use two lags of each variable in each VAR.

The exogenous nature of nominal wages in Australia is quite apparent, with wage growth explaining a very large proportion of its own forecast variance i.e. there appears to relatively little feedback from the other variables to nominal wage inflation, even after five years, although we leave open the possibility that it might be affected by factors determined outside the model, such as expected inflation.

The results for New Zealand are very similar to Australia. In Japan, the United Kingdom and the United States nominal wages also appear to be largely exogenous, though to a lesser extent than Australia and New Zealand, with shocks to wage inflation explaining about half of the forecast variance after 3–5 years. Unlike Australia and New Zealand, however, innovations to productivity growth appear to be important determinants of nominal wage growth in these three countries, as do shocks to world inflation. Interestingly, and significantly, shocks to money growth do not appear to be important determinants of wage inflation in any country, except perhaps initially in the United Kingdom.

Footnotes

Because of data limitations, the estimation period for New Zealand starts in 1965. [7]

Strictly speaking, such a variable will not be Granger caused by other variables. Granger non-causality and econometric exogeneity are related, but distinct, concepts. In general, Granger non-causality neither implies nor is implied by weak exogeneity. However, we show in Appendix 1 that under weak assumptions Granger non-causality does imply weak exogeneity in this model. [8]

Appendix 2 contains details of data methods and sources. [9]

The estimated VAR parameters are available on request. [10]