Monday, December 12, 2016

Labor, capital, productivity and immigration In New Zealand and Australia

In a previous blog I showed that Kiwis supply more labor (hour worked) than the Australians and the Americans. The supply of labor depends on the marginal income tax rate, the share of factors in production, the relative price of leisure, and consumption-income ratio. In addition to higher supply of labor, estimated reservation wage has been falling over time, which increased employment and hours worked. That explains why the average real wages is relatively low in New Zealand. However, both the supply and the demand curves, and the elasticities affect wages. Let us look closer. 

The share of labor is relatively larger in New Zealand.[1]

Here I plot estimates of the demand for labor for New Zealand and Australia.

The marginal productivity of labor is on the vertical axis and the change in log working age population is on the horizontal axis.The Australian and the New Zealand curves look similar. The Australian curve is slightly flatter. These curves suggest that shifts in the supply of labor (imagine a positively slopped supply of labor cutting through the dots and shifting up or down) are not associated with very large changes in the real wage of labor productivity.

However, there are two observations in the New Zealand data that are extremely large and I cannot explain why. One observation is in the 2000 and the other is in 2012. Removing these observations gives us this:

The New Zealand demand for labor curve becomes infinitely flat. It means that employment is totally irresponsive and unrelated to wages and marginal productivity. As the supply of labor shifts up, wages and productivity do not significantly change in New Zealand.  

What do we know about the supply and demand for capital?

New Zealand has a shallow level of capital stock. Here are the shares for New Zealand and Australia.

Australia should substitute more capital for labor in production because the share of capital is relatively larger. The marginal rate of technical substitution (MRTS) is the ratio of the marginal productivity of labor (MPL) to the marginal productivity of capital (MPK). Here are the estimated marginal productivity for labor and capital.

The MPL is higher in Australia.

The MPK is higher in Australia, but the gap between the two countries is narrowing.

The MRTS measures the substitution between capital and labor along the Isoquant, i.e., output is unchanged. Whatever they have been producing remains the same, but the combinations of factors used in the production change. Clearly, it says that as time goes by both Australia and New Zealand have been substituting more capital for labor to produce the same output. Australia substitutes relatively more capital for labor than us, probably because they have more of it and thus the real cost of capital has been lower than the marginal productivity of capital. The gap, however, is widening. Australia continues to substitute more capital for labor than New Zealand. Adding more capital will increase labor productivity over time. These productivity changes have been happening, but less so in New Zealand. These endogenous processes continue until the rates of returns to factors equal to the marginal productivity.

Given the shallow supply of capital in New Zealand, we should have an excess demand for capital in New Zealand. Here is a graph of the estimated demand for capital in both countries. Indeed, the demand for capital is higher in New Zealand, and the curve is relatively steeper.

 Excess demand for capital (excess demand for investments) puts upward pressure on the real interest rate. This is consistent with the observed high level of real interest in New Zealand.

The real interest rate is determined in the market not by the Reserve Banks. Monetary policy plays no role in the productivity debate. However, there is a role for fiscal policy, i.e., taxes. On average, taxes are similar across the Tasman. Thus, the after-tax real returns on factors probably differ not because of the tax rates, but because of differences in the real interest rates and real wages, which are determined in the markets not in Treasuries.

Why does immigration to New Zealand increase when the demand for labor is low or flat, and the supply of labor is high?

From the immigrant’s standpoint, immigrants consider the New Zealand real wage rate when they immigrate. Why do people immigrate to New Zealand if the real wage is lower than Australia? Everything else constant, they should not come to New Zealand. However, immigrants take many more factors into account that could outweigh the low real wage factor when they make their decision such as taste, family connections, etc. It is also possible that they do not have full information and do not know what the real wage rate in New Zealand is. Sooner, they learn that Australia offers a better real wage so they immigrate / relocate again across the Tasman. I do not have statistics on the number of immigrants to New Zealand who re-settled in Australia.

It is more difficult to explain why the New Zealand immigration policy objective is to increase immigration if New Zealand has been substituting away from labor towards capital (albeit less so than Australia). In this case, adding more people cannot increase labor productivity. The data suggest that in order to increase productivity we should focus more on adding more capital not more labor, perhaps increasing savings. 

[1] The average share of labor is the ratio of compensations to employee / nominal GDP ratio over the sample from 1987 to 2015. Assuming a constant return to scale Cobb-Douglas production function implies that the average share of labor is also 1-the share of capital, where the share of capital is measured as the ratio of gross operating surplus / nominal GDP ratio. To compute the MPL and MPK I assume a constant return to scale Cobb-Douglas production function. I take the derivatives with respect to labor, hence the MPL, and with respect to capital, i.e.,MPK. I use the average of the shares over the sample and the observations for GDP, capital stock and working age population to compute the marginal productivity. 

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