The marginal product of capital, and policy irrelevance

The May 2007 Quarterly Journal of Economics offers up a fun piece on the marginal product of capital, earlier version here.  The bottom line is startling, though it requires only a simple model:

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.

The rough equality of MPKs [correction: financial rates of return] means that capital can flow to where it is most productive.  That means if a country receives some aid, and converts that aid into useful capital goods, less capital flows into your country.  A version of neutrality holds.  Of course there is no reason to focus on aid in this argument.  Most one-off improvements (or destructions) wash out in the longer run, due to subsequent adjustments in the capital stock.  The one-off improvements matter only if liquidity and credit imperfections hinder the international mobility of capital; such imperfections would mean that transfers could bring about a permanently higher level of capital.

No, I’m not ready to "press the yes button" on this model (should I be?), but it is a good example of how open economy considerations can overturn our expectations, or how easily economics can generate a counterintuitive conclusion.  You also may have noticed Borjas and Rodrik using a version of this model lately, attempting a Brad DeLong Smackdown.  I am suspicious.  It’s not a model they believe in, or if they do I am waiting for Borjas to stop warning us about capital destruction costs more generally… 


They do not claim a rough equality for MPKs, the rough equality is of financial rate of return.

So, the difference between the two is due to the relatively high cost of investment goods. I assume this is relative to the cost in developed countries. Could someone give me an idea of why this is?

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Re: "They do not claim a rough equality for MPKs, the rough equality is of financial rate of return. So, the difference between the two is due to the relatively high cost of investment goods. I assume this is relative to the cost in developed countries. Could someone give me an idea of why this is?"

It's Balassa-Samuelson.

This is the way that Larry Summers and I understood it back in the early 1990s, and I haven't changed my mind:

"Begin with the large divergence between purchasing power parity and current exchange rate measures of relative GDP per capita levels. The spread between the highest and lowest GDP per capita levels today, using current exchange rate-based measures, is a factor of 400; the spread between the highest and lowest GDP per capita levels today using purchasing power parity-based measures is a factor of 50. If the purchasing power parity-based measures are correct, real exchange rates vary by a factor of eight between relatively rich and relatively poor economies. And the log GDP per capita level accounts for 80 percent of the cross-country variation in this measure of the real exchange rate, with each one percent rise in GDP per capita associated with an 0.34 percent rise in the real exchange rate.

"Why? Because real exchange rates are such as to make the prices of traded manufactured goods roughly the same in the different nation-states of the world, putting to one side over- or undervaluations produced by macroeconomic conditions, tariffs and other trade barriers, and desired international investment flows. Thus the eight-fold difference in real exchange rates between relatively rich and relatively poor economies is a reflection of an approximately eight-fold difference in the price of easily-traded manufactured goods: relative to the average basket of goods and prices on which the "international dollar" measure is based, the real price of traded manufactures in relatively rich countries is only one-eighth the real price in relatively poor countries.

"This should come as no surprise. The world's most industrialized and prosperous economies are the most industrialized and prosperous because they have attained very high levels of manufacturing productivity: their productivity advantage in unskilled service industries is much lower than in capital- and technology-intensive manufactured goods.

"And a low relative price of technologically-sophisticated manufactured goods has important consequences for nation-states' relative investment rates. In the United States today machinery and equipment account for half of all investment spending; in developing economies--where machinery and equipment, especially imported machinery and equipment is much more expensive--it typically accounts for a much greater share of total investment spending (see Jones, 1994; DeLong and Summers, 1991).

"Consider the implications of a higher relative price of capital goods for a developing economy attempting to invest in a balanced mix of machinery and structures. There is no consistent trend in the relative price of structures across economies: rich economies can use bulldozers to dig foundations, but poor economies can use large numbers of low-paid unskilled workers to dig foundations. But the higher relative price of machinery capital in developing countries makes it more and more expensive to maintain a balanced mix: the poorer a country, the lower is the real investment share of GDP that corresponds to any given fixed nominal savings share of GDP.

"The gap between nominal savings and real investment shares of GDP that follows from the high relative price of machinery and equipment in poor countries that wish to maintain a balanced mix of investment in structures and equipment is immense. For a country at the level of the world's poorest today--with a real exchange rate-based GDP per capita level of some $95 a year--saving 20% of national product produces a real investment share (measured using the "international dollar" measure) of only some 5% of national product.

"In actual fact poor economies do not maintain balanced mixes of structures and equipment capital: they cannot afford to do so, and so economize substantially on machinery and equipment. Thus here are two additional channels by which relative poverty is a cause slow growth: first, relative poverty is the source of a high real price of capital, a low rate of real investment corresponding to any given nominal savings effort, and a low steady-state capital-output ratio; second, to the extent that machinery and equipment are investments with social products that significantly exceed the profits earned by investors (see DeLong and Summers, 1991), the price structures in relatively poor developing economies lead them to economize on exactly the wrong kinds of capital investment."

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The QJE version and the Working Paper are quite different.

In the abstract to the Working Paper they write:
"We find that the MPK is much higher on average in poor countries."

In the QJE they changed it to:
"Using easily accessible macroeconomic data we find that MPKs are remarkably similar across countries."

The results depend on the correction for "land and natural-resources" and for relative prices.

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