Monday, February 3, 2014

Unemployment, wages, productivity and monetary policy in New Zealand

At the microeconomic level, the firm hires more labour as long as the marginal product of labour exceeds the real wage. Hiring stops when the marginal product of labour is equal to the real wage. When the wage rate is higher than marginal product of labour, the firm lays off labour, hence unemployment increases. There are some challenging issues to reconcile the microeconomic and the macroeconomics of wage dynamics. Blanchard and Katz (1991), among other papers, is an excellent discussion of this issue.

That been said, the neoclassical theory is quite intuitive and empirically verifiable at the macro level, which I will show graphically. I graph below the business cycle fluctuations of the real wage and the marginal product of labour in New Zealand.[1] The cyclical fluctuations are deviations from an HP filter’s trends. Clearly there is a wedge.

Figure 1

The wedge between the real wage and the marginal product of labour can result for a number of reasons (see Thurow, 1968). First, taxes create a wedge if the incidence of the indirect taxes is on labour. Second, monopoly power can explain differences between the marginal product of factor inputs and their prices. Third, there is a constant substitution between factor inputs along growth path. Although there is some evidence that the stock of capital is shallow in New Zealand (but it has a positive trend, nevertheless). As the stock of capital rises, labour is displaced. That might cause the returns to labour to fall below its marginal productivity. Wages fall below the marginal product of labour if the transition cost is high. When labour is not paid its marginal productivity, the optimal stock of capital is less than it would be if labour were paid its marginal productivity; the opposite can be true too. Fourth, if firms set the wage rate by the marginal product of the marginal worker rather than the marginal product of the average worker, due to heterogeneity. Maré and Hyslop, (2008) provide evidence that less skilled labour is hired at the up-turn of the New Zealand business cycle. If this were the case then wages will have to be lower than the marginal product of the average worker. Fifth, some of the wedge between the marginal products and the returns could be explained by risk premiums. Sixth, when social returns are not equal to private returns, actual returns must be corrected for taxes when possible. And, seventh, endogenous growth models assume an increasing return to scale rather (i.e., less than doubling factor inputs is needed to double output), which means that capital and labour will more than exhaust total output. Thus, the marginal product of labour will not equal the real wage. 

The second figure plots the wedge between the real wage and the marginal product of labour, and the unemployment gap (the HP filtered unemployment rate). The increase in the real wage over the marginal product of labour opens a positive wedge, and unemployment increases above its long-run trend level. The correlation coefficient is nearly 70 percent. The wedge between the wage rate and the marginal product of labour is a predictor of unemployment in New Zealand as the neoclassical model suggests.

Figure 2

The unemployment rate in New Zealand is expected to be declining as the marginal product of labour continues to improve and to rise above the real wage over the business cycle. This seems to be happening now. The unemployment rates during the last three quarters of 2013 were 3.7, 3.9 and 4.2, and have been close to the natural rate of unemployment. Razzak (2014) provides a number of estimates of the natural rate of unemployment in New Zealand, which are between 3.5 and 4.5 percent. The actual annual inflation rate since January 2012 has been below the mid-point of the target. If the wedge between the wage rate and marginal productivity of labour is expected to continue to decline, i.e., productivity is higher than wages, unemployment will be expected to decline as firms will hire more labour, and hence more expected inflationary pressures. These stylized facts must have implications for future monetary policy.

 Figure 3 is a 95-percent chi-squared confidence ellipse. It shows that the correlation between the wage-marginal product of capital wedge and the unemployment gap is significant.

Figure 3


Blanchard, O. J., and L. Katz, (1999), “Wage Dynamics: Reconciling Theory and Evidence,” American Economic Review 89 (3), 69-74.

Maré, D. C., and D. R. Hyslop, (2008), “Cyclical Earnings Variation and the Composition of Employment,” Working paper, Statistics New Zealand, Wellington, New Zealand.

Razzak, W A, (2014), “New Zealand Labour Market Dynamics – pre and post global financial crisis,” Forthcoming Working Paper, New Zealand Treasury, Wellington, New Zealand.    

Thurow, L. C., (1968), "Disequilibrium and Marginal Productivity of Capital and Labor," Review of Economics and Statistics Vol 50, No.1, 23-31.        

[1] All the data are taken from Statistics New Zealand online. The sample is March 1991to September 2013. GDP data are only available to September 2013. The marginal product of labour is a calibrated derivative of output (real GDP) with respect to labour of the Cobb-Douglas production function. I assume a simple Cobb-Douglas production function, where real GDP is a function of capital and labour with the shares fixed at 0.4 and 0.6 for capital and labour respectively. Capital stock is measured by the Perpetual Inventory equation with the assumption that the initial period capital stock equal to 3 times GDP and a depreciation rate 0.08. Labour is measured by working age population (15-64. Gross capital formation is deflated by the capital price index. Wages are average hourly total ordinary wage minus expected inflation, which I measure as a 6 quarter moving average of the inflation rate. The inflation rate is the log-difference of the CPI. Different functional forms and assumptions could be used, e.g., differentiating between skilled and unskilled labour in a CES production function. The business cycle fluctuations are deviations from trend measured by the HP filter. So unemployment fluctuations are the deviations of unemployment from trend.