The Marginal Product of Capital

Capital per worker varies by a factor of 100 in this paper’s data, which makes it tempting to conclude that returns to capital must vary enormously too, and therefore that something – credit frictions – stops capital from flowing to poor countries. The paper measures returns directly instead of calibrating them. Under constant returns and competitive domestic capital markets the rental rate equals the marginal product, so aggregate capital income is the marginal product times the capital stock, and the marginal product can be backed out of output, the capital stock and the capital share alone, with no need to measure human capital or TFP and no functional-form assumption beyond linear homogeneity. Doing this for 53 countries with Penn World Table data, the “naive” estimate looks like a decisive win for the credit-friction view: it averages 27 percent among the 29 lower-income countries, with a standard deviation of 9 percent, against 11 percent and a standard deviation of 3 percent among the 24 higher-income ones, and the implied deadweight loss from failing to equalise returns is 2.9 percent of world output – about a quarter of the aggregate GDP of the developing countries in the sample, which account for roughly 12 percent of sample GDP. Two corrections overturn it. First, the conventional capital share (one minus the labour share) conflates rent on land and natural resources with the return on accumulated capital, whereas the perpetual-inventory capital stock contains only the latter; using World Bank wealth data to strip out natural capital – roughly half of total wealth in the average country, nearly 70 percent when weighted by capital stocks – cuts the poor-country average to 11.9 percent against 7.5 percent for rich countries. Second, frictionless world credit markets equalise the value of the marginal product divided by the price of capital goods, not the physical marginal product, and capital goods are relatively dearer in poor countries; correcting for that alone gives 15.7 against 12.6 percent. With both corrections the poor-country average is 6.9 percent and the rich-country average 8.4 percent – the ordering reverses, the difference is significant only at the 10 percent level, and the deadweight loss falls to 0.1 percent of world output, with counterfactual reallocation actually moving capital out of poor countries. Returning to Lucas’s question, the paper sides with his scepticism about credit frictions but qualifies his answer: decomposing the variance of capital per worker gives a roughly 54-46 split between the relative price of capital and the complementary-factor/TFP term he emphasised. The scope conditions are stated carefully: the decomposition assumes each country produces one good (“admittedly very strong”), the counterfactuals are not policy proposals, adjustment costs to capital are ruled out, and the time-series evidence that the cost of credit frictions has fallen is offered as “tentative.”

James Feyrer | Macro Paper Warehouse

The Marginal Product of Capital