Tag Archive for 'Marginal product of capital'

Article Summary: The Marginal Product of Capital

This paper (forthcoming in the QJE) by Francesco Caselli (one of my professors at LSE) and James Feyrer (of Dartmouth) has floored me. Here’s the abstract:

Whether or not the marginal product of capital (MPK) differs across countries is a question that keeps coming up in discussions of comparative economic development and patterns of capital flows. Attempts to provide an empirical answer to this question have so far been mostly indirect and based on heroic assumptions. The first contribution of this paper is to present new estimates of the cross-country dispersion of marginal products. We find that the MPK is much higher on average in poor countries. However, the financial rate of return from investing in physical capital is not much higher in poor countries, so heterogeneity in MPKs is not principally due to financial market frictions. Instead, the main culprit is the relatively high cost of investment goods in developing countries. One implication of our findings is that increased aid flows to developing countries will not significantly increase these countries’ incomes.

… which seems reasonable enough. Potentially important for development, but not necessarily something to knock the sense out of you. What blew me away was how simple and after-the-fact obvious their adjustments are. They are:

  1. Estimates of MPK depend on first estimating national income (Y), the capital stock (K) and capital’s share of the national income (?): MPK = ?Y/K. National income figures are fine. A country’s capital stock is typically calculated using the perpetual inventory method, which only counts reproducible capital. Capital’s share of income is typically calculated as one minus the labour share of income (which is easily estimated), but this includes income attributable to both reproducible and non-reproducible capital (i.e. natural resources). Therefore estimates of MPK are too high if they are meant to represent the marginal product of reproducible capital. This error will be more severe in countries where non-reproducible capital makes up a large proportion of a country’s total capital stock. Since this is indeed the case in developing countries (with little investment, natural resources are often close to the only form of capital they possess), this explains quite a lot of the difference in observed MPK between rich and poor countries.
  2. Estimates of MPK based on a one-sector model implicitly assume that prices are not relevant to it’s calculation. However, the relative price of capital goods (i.e. their price relative to everything else in the particular economy) is frequently higher in developing countries. This will force the necessary rate of return higher in poor countries because the cost of investing will be higher.

They give the following revised estimates (Table II in their paper, standard deviations in parentheses):

Measure of MPK Rich countries Poor countries
“Naive” 11.4 (2.7) 27.2 (9.0)
Adjusted only for land and natural resources 7.5 (1.7) 11.9 (6.9)
Adjusted only for price differences 12.6 (2.5) 15.7 (5.5)
Adjusted for both 8.4 (1.9) 6.9 (3.7)

The fact that the adjusted rate of return appears lower in poor countries then goes some way to explaining why the market flow of capital is typically from poor countries to rich countries and, as they say, has some serious implications for development.But that first adjustment! How on earth can that have skipped attention over the years? It seems like something that should have been noticed and dealt with in the ’50s!

The second adjustment managed to shed more light (for me) on just how terrible price controls can be. Under the assumption that if inflation is going to happen, it’s going to happen no matter what you do, if you put a cap on the prices of some goods (or services) then the prices of the rest will simply rise commeasurately further. When Messers Chavez and Mugabe institute price caps in an attempt to hold back inflation, they invariably put them on consumer goods because that’s where the populist vote lies. However, that means that inflation in capital goods will be higher still, making them more expensive relative to everything else in the economy. That will increase the rate of return demanded by investors and — in the meantime — chase investment away. By easing the pain in the short run, they are shooting themselves in the foot in the long run.

Caselli and Feyrer’s results also make me wonder about the East Asian NICs. What attracted the flood of foreign capital if not their higher MPKs? Remember that their TFPs were not growing any faster than those of the West. Their human capital stocks were certainly rising, but – IIRC – no where near as quickly as their capital stocks were growing.

Update (11 Oct):
Of course, the NICs also had – and continue to have – very high savings rates, which at first glance goes a long way to explaining their physical capital accumulation. There are two responses to this:

  1. Even with their high savings rates, they were still running current account deficits. I understand, although I haven’t looked at the figures, that these were driven by high levels of investment rather than high levels of consumption.
  2. Did their savings rates suddenly rise at the start of their growth periods? If so, that is extraordinary and needs explaining in itself; at the very least it raises the question that their savings rates (or, if you prefer, their rate of time preference) were endogenously determined. If not, then we still need to explain why their savings were originally being invested overseas, then domestically and now (that they’ve “caught up”) overseas again.