The Marginal Product of Capital

TLDR: The authors showed that the marginal product of capital (MPK) is remarkably similar across countries and there is no prima facie support for the view that international credit frictions play a major role in preventing capital flows from rich to poor countries.

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. Using easily accessible macroeconomic data we find that MPKs are remarkably similar across countries. Hence, there is no prima facie support for the view that international credit frictions play a major role in preventing capital flows from rich to poor countries. Lower capital ratios in these countries are instead attributable to lower endowments of complementary factors and lower efficiency, as well as to lower prices of output goods relative to capital. We also show that properly accounting for the share of income accruing to reproducible capital is critical to reach these conclusions. One implication of our findings is that increased aid flows to developing countries will not significantly increase these countries’ capital stocks and incomes. I. INTRODUCTION Is the world’s capital stock efficiently allocated across countries? If so, then all countries have roughly the same aggregate marginal product of capital (MPK). If not, the MPK will vary substantially from country to country. In the latter case, the world foregoes an opportunity to increase global GDP by reallocating capital from low to high MPK countries. The policy implications are far reaching. Given the enormous cross-country differences in observed capital-labor ratios (they vary by a factor of 100 in the data used in this paper) it may seem obvious that the MPK must vary dramatically as well. In this case we would have to conclude that there are important frictions in international capital markets that prevent an efficient cross-country allocation of capital. 1 However, as Lucas [1990] pointed out in his celebrated article, poor countries also have lower endowments of factors complementary with physical capital, such as human capital, and lower total

Figures

Table A-1: Data and Implied Estimates of of the MPK (cont.)

Table 3: Average Changes in Equilibrium Capital Stocks under MPK Equalization

Figure 2: Counterfactual Capital per Worker with Equalized Returns to Capital

Figure A-2: Relative Prices

Table 5: World Output Gain from MPK Equalization

Figure A-1: Capital per Worker

Full text

CEP Discussion Paper No 735
August 2006
The Marginal Product of Capital
Francesco Caselli and James Feyrer

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. We use easily accessible macroeconomic data to shed light on this issue, and
find that MPKs are remarkably similar across countries. Hence, there is no prima facie
support for the view that international credit frictions play a major role in preventing capital
flows from rich to poor countries. Lower capital ratios in these countries are instead
attributable to lower endowments of complementary factors and lower efficiency, as well as
to lower prices of output goods relative to capital. We also show that properly accounting for
the share of income accruing to reproducible capital is critical to reach these conclusions.
One implication of our findings is that increased aid flows to developing countries will not
significantly increase these countries' incomes.
JEL classifications: E22, O11, O16, O41.
Keywords: investment, capital flows
This paper was produced as part of the Centre’s Macro Programme. The Centre for
Economic Performance is financed by the Economic and Social Research Council.
Acknowledgements
We would like to thank Robert Barro, Tim Besley, Maitreesh Ghatak, Berthold Herrendorf,
Jean Imbs, Faruk Khan, Pete Klenow, Michael McMahon, Nina Pavcnik, Bob Solow, Alan
Taylor, Mark Taylor, Silvana Tenreyro and three anonymous referees for useful comments
and suggestions.
Francesco Caselli is an Associate of the Macro Programme at the Centre for Economic
Performance, London School of Economics (f.caselli@lse.ac.uk
). James Feyrer is assistant
professor in the economics department at Dartmouth College, New Hampshire, USA (james.
feyrer@dartmouth.edu
).
Published by
Centre for Economic Performance
London School of Economics and Political Science
Houghton Street
London WC2A 2AE
All rights reserved. No part of this publication may be reproduced, stored in a retrieval
system or transmitted in any form or by any means without the prior permission in writing of
the publisher nor be issued to the public or circulated in any form other than that in which it
is published.
Requests for permission to reproduce any article or part of the Working Paper should be sent
to the editor at the above address.
© F. Caselli and J. Freyrer, submitted 2006
ISBN 0 7530 2032 7

1 Introduction
Is the world’s capital stock efficiently allocated across countries? If so, then all countries
have roughly the same aggregate marginal product of capital (MP K). If not, the MP K
will vary substantially from country to country. In the latter case, the world foregoes
an opportunity to increase global GDP by reallocating capital from low to high MP K
countries. The policy implications are far reaching.
Given the enormous cross-country differences in observed capital-labor ratios
(they vary by a factor of 100 in the data used in this paper) it may seem obvious that the
MP K must vary dramatically as well. In this case we would have to conclude that there
are important frictions in international capital markets that prevent an efficient cross-
country allocation of capital.
1
However, as Lucas (1990) pointed out in his celebrated
article, poor countries also have lower endowments of factors complementary with
physical capital, such as human capital, and lower total factor productivity (TFP).
Hence, large differences in capital-labor ratios may coexist with MP K equalization.
2
It is not surprising then that considerable effort and ingenuity have been de-
voted to the attempt to generate cross-country estimates of the MP K. Banerjee and
Duflo (2005) present an exhaustive review of existing methods and results. Briefly,
the literature has followed three approaches. The first is the cross-country compar-
ison of interest rates. This is problematic because in financially repressed/distorted
economies interest rates on financial assets may be very poor proxies for the cost of
capital actually borne by firms.
3
The second is some variant of regressing ∆Y on ∆K
for different sets of counties and comparing the coefficient on ∆K. Unfortunately, this
approach typically relies on unrealistic identification assumptions. The third strategy
1
The credit-friction view has many vocal supporters. Reinhart and Rogoff (2004), for example,
build a strong case based on developing countries’ histories of serial default, as well as evidence by
Alfaro, Kalemli-Ozcam, and Volosovych (2003) and Lane (2003) linking institutional factors to capital
flows to poorer economies. Another forceful exposition of the credit-friction view is in Stulz (2005).
2
See also Mankiw (1995), and the literature on development-accounting [surveyed in Caselli (2005)],
which documents these large differences in human capital and TFP.
3
Another issue is default. In particular, it is not uncommon for promised yields on “emerging
market” bond instruments to exceed yields on US bonds by a factor of 2 or 3, but given the much
higher risk these b onds carry it is possible that the expected cost of capital from the perspective of
the borrower is considerably less. More generally, Mulligan (2002) shows that with uncertainty and
taste shocks interest rates on any particular financial instruments may have very low – indeed even
negative – correlations with the rental rate faced by firms.
1

is calibration, which involves choosing a functional form for the relationship between
physical capital and output, as well as accurately measuring the additional complemen-
tary factors – such as human capital and TFP – that affect the MP K. Since giving a
full account of the complementary factors is quite ambitious, one may not want to rely
on this method exclusively. Both within and between these three broad approaches
results vary widely. In sum, the effort to generate reliable comparisons of cross-country
MP K differences has not yet paid off.
This paper presents estimates of the aggregate MP K for a large cross-section of
countries, representing a broad sample of developing and developed economies. Rela-
tive to existing alternative measures, ours are extremely direct, impose extremely little
structure on the data, and are extremely simple to calculate. The general idea is that
under conditions approximating perfect competition on the capital market the MP K
equals the rate of return to capital, and that the latter multiplied by the capital stock
equals capital income. Hence, the aggregate marginal product of capital can be easily
recovered from data on total income, the value of the capital stock, and the capital
share in income. We then combine data on output and capital with data on the capital
share to back out the MP K.
4
Our main result is that MP Ks are essentially equalized: the return from invest-
ing in capital is no higher in poor countries than in rich countries. This means that one
can rationalize virtually all of the cross-country variation in capital per worker without
appealing to international capital-market frictions. We also quantify the output losses
due to the (minimal) MP K differences we observe: if we were to reallocate capital
across countries so as to equalize MP Ks the corresponding change in world output
would be negligible.
5
Consistent with the view that financial markets have become
more integrated worldwide, however, we also find some evidence that the cost of credit
frictions has declined over time.
The path to this result offers additional important insights. We start from a
“naive” estimate of the MP K that is derived from the standard neoclassical one-sector
model, with labor and reproducible capital as the only inputs. Using this initial mea-
sure, the average MP K in the developing economies in our sample is more than twice
4
Mulligan (2002) performs an analogous calculation to identify the rental rate in the US time series.
He finds implicit support for this method in the fact that the rental rate thus calculated is a much
better predictor of consumption growth than interest rates on financial assets.
5
Our counter-factual calculations of the consequences of full capital mobility for world GDP are
analogous to those of Klein and Ventura (2004) for labor mobility.
2

as large as in the developed economies. Furthermore, within the developing-country
sample the MP K is three times as variable as within the developed-country sample.
When we quantify the output losses associated with these MP K differentials we find
that they are very large (about 25 percent of the aggregate GDP of the developing
countries in our sample). These results seem at first glance to represent a big win for
the international credit-friction view of the world.
Things begin to change dramatically when we add land and other natural re-
sources as possible inputs. This obviously realistic modification implies that standard
measures of the capital share (obtained as 1 minus the labor share) are not appropriate
to build a measure of the marginal productivity of reproducible capital. This is because
these measures conflate the income flowing to capital accumulated through investment
flows with natural capital in the form of land and natural resources. By using data
recently compiled by the World Bank, we are able to separate natural capital from re-
producible capital and calculate the share of output paid to reproducible capital that
is our object of interest. This correction alone significantly reduces the gap between
rich and poor country capital returns. The main reason for this is that poor countries
have a larger share of natural capital in total capital, which leads to a correspondingly
larger overestimate of the income and marginal-productivity of reproducible capital
when using the total capital-income share. The correction also reduces the GDP loss
due to MP K differences to a fraction of the amount implied by the naive calculation.
6
The further and final blow to the credit-friction hypothesis comes from gener-
alizing the model to allow for multiple sectors. In a multi-sector world the estimate of
MP K based on the one-sector model (with or without natural capital) is – at best –
a proxy for the average physical MP K across sectors. But with many sectors physical
MP K differences can be sustained even in a world completely unencumbered by any
form of capital-market friction. In particular, even if poor-country agents have access to
unlimited borrowing and lending at the same conditions offered to rich-country agents,
the physical MP K will be higher in poor countries if the relative price of capital goods
is higher there. Intuitively, poor-country investors in physical capital need to be com-
pensated by a higher physical MP K for the fact that capital is more expensive there
6
We are immensely grateful to Pete Klenow and two referees for bringing up the issue of land
and natural resources. Incidentally, these observations extend to a criticism of much work that has
automatically plugged in standard capital-share estimates in empirical applications of models where
all capital is reproducible. We plan to pursue this criticism in future work.
3

Frequently asked questions

Q1. How much of the capital in the US is reproducible?

In the average country in their sample, reproducible capital represents roughly one half of total capital, while various forms of “natural” capital account for the other half. 

Q2. What is the variance of log(k) for PMPKL?

The variance of log(k∗) for their PMPKL case is 2.46, the variance of log(Π) is 0.82, the variance of log(Λ) is 0.61, and the covariance term is 0.52. 

Q3. What is the general approach to estimating rents from a particular form of capital?

The general approach is to estimate the value of rents from a particular form of capital and then capitalize this value using a fixed discount rate. 

Q4. What is the naive version of the MPKN?

To recap, the naive version, MPKN , does not account for difference in prices of capital and consumption goods, and also uses the total share of capital, not the share of reproducible capital. 

Q5. What is the proportion of reproducible capital’s share of total capital income?

Reproducible capital’s share of total capital income is therefore going to be proportional to reproducible capital’s share of wealth (since all units of wealth pay the same return). 

Q6. What is the ultimate cause of differences in capital per worker?

The ultimate cause of differences in capital per worker may therefore be productivity differences if productivity differences are the ultimate cause of differences in capital costs and the share of capital. 

Q7. What is the preferred estimate of a private company?

Their preferred estimates are reported in the column labeled “Actual OSPUE,” and they are constructed by assigning to labor a share of the Operating Surplus of Private Unincorporate Enterprises equal to the share of labor in the corporate (and public) sector. 

Q8. How much is the deadweight loss from inefficient allocation of capital?

This result implies that the deadweight loss from inefficient allocation of capital is in the order of one quarter of the aggregate (and hence also per capita) income of developing countries. 

Q9. What are the common words used in the paper?

Since the World Bank’s data on land and natural-resource wealth is by far thenewest and least familiar among those used in this paper, a few more words to describe these data are probably in order. 

Q10. How much of the total GDP of the sample is in the order of 0.03?

To put it in perspective, consider that the 28 developing countries in their sample account for 12 percent of the aggregate GDP of the sample. 

Q11. What is the likely explanation for the decline in the deadweight losses in the 1980s?

When one starts think-ing about unobservables, however, it appears quite likely that their estimates are still25The acceleration in the decline of the deadweight losses during the 1980s may reflect historically low MPKs in developing countries during that decade’s crisis.