Natural Resources and Missing Inputs in International Productivity Comparisons*

• Published date: 01 March 2021
• Author: Daan Freeman,Robert Inklaar,W. Erwin Diewert
• Date: 01 March 2021
• DOI: http://doi.org/10.1111/roiw.12451

© 2020 The Authors. Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association for Research in Income and Wealth

1

NATURAL RESOURCES AND MISSING INPUTS IN INTERNATIONAL

PRODUCTIVITY COMPARISONS*

by Daan Freeman and robert Inklaar

University of Groningen

AND

W. erWIn DIeWert

University of British Columbia

Standard theory for cross-country productivity comparisons assumes all countries use the same factor

inputs in production. This assumption is violated when including natural resources, such as oil, gas

and gold, because countries do not extract the full set of resources. In this paper we propose a solution

by viewing it as a “missing goods” problem and assigning missing inputs a reservation price equal to

the world resource price. We show that this has a substantial impact on relative productivity levels for

countries heavily reliant on natural resources for generating their income. Under our new productivity

measure, resource-rich countries are no longer uncommonly productive.

JEL Codes: E22, O13, O57

Keywords: development accounting, missing goods, natural resources, productivity measurement,

reservation prices

1. IntroDuctIon

Development accounting is a popular tool that is used to establish how much

of the differences in income levels across countries can be accounted for by differ-

ences in observed factor inputs—such as buildings, machinery and (skilled) work-

ers—and how much by differences in productivity, the residual.1 This, in turn, can

inform further research to explain why, for instance, investment in capital may be

low or why productivity lags.2 But omission or mismeasurement of factor inputs

will lead to biased measures of productivity. This has motivated researchers to

expand and improve the measurement of inputs, by including additional types of

intangible capital (Chen, 2018), accounting for differences in management

1See Caselli (2005) and Hsieh and Klenow (2010) for overviews of this literature.

2See e.g. Acemoglu et al. (2019), who show that democratization increases income levels by improv-

ing investment, not by improving TFP.

Note: We would like to thank two anonymous referees, participants at the General Conference of

the International Association of Research in Income and Wealth (2018), the SOM PhD conference

(2017) and Society for Economic Measurement conference (2017) for helpful comments.

*Correspondence to: Robert Inklaar, Groningen Growth and Development Centre, Faculty of

Economics and Business, University of Groningen, Nettelbosje 2, 9747 AE Groningen, The Netherlands

(r.c.inklaar@rug.nl).

Review of Income and Wealth

Series 67, Number 1, March 2021

DOI: 10.1111/roiw.12451

This is an open access article under the terms of the Creative Commons Attribution License, which

permits use, distribution and reproduction in any medium, provided the original work is properly cited.

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Review of Income and Wealth, Series 67, Number 1, March 2021

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© 2020 The Authors. Review of Income and Wealth published by John Wiley & Sons Ltd on behalf of

International Association for Research in Income and Wealth

practices (Bloom et al., 2016) and improving estimates of human capital over the

life cycle (Inklaar and Papakonstantinou, 2019; Lagakos et al., 2018). Omitted so

far in these efforts is the role of natural resources, such as oil, gas, iron and gold,

even though natural resources are an important source of income and wealth in

many lower-income countries, as well as some (very) high-income countries (Lange

et al., 2018).3 Inputs of subsoil assets also already fall within the asset boundary of

the System of National Accounts, which means that systematically accounting for

the use of these assets in production does not necessitate changes to measures of

output or investment, unlike with, for instance, intangible capital.

The contribution of this paper is to propose and implement a method for

incorporating natural resources as a factor of production in cross-country com-

parisons of productivity. We build on the work of Brandt et al. (2017) and Diewert

and Fox (2016), who show how natural resources can be incorporated in a “sources

of growth” framework. Many of the measurement considerations of their work,

such as measures of resource rents, apply in a cross-country context. However,

the extension to a cross-country setting faces a notable challenge in that countries

typically extract only a few types of natural resources rather than the full set. Such

missing inputs mean that relative productivity is not defined in the typical produc-

tivity comparison framework, such as that of Diewert and Morrison (1986) and

Inklaar and Diewert (2016).

We propose a solution by drawing a parallel to the literature that deals with

the “new goods” problem.4 New goods complicate inflation measurement because

no price is observed in the period before the new good appears; a solution is to

identify Hicksian reservation prices (Hicks, 1940), the price just high enough for

demand to be zero. In the current context, we can define a producer Hicksian reser-

vation price, which is the input price where that primary input is not used in pro-

duction. Aside from the practical challenge in identifying what that price level

would be, this introduces a conceptual complication in productivity measurement,

because in the Diewert and Morrison (1986) framework, a Törnqvist index of pri-

mary input quantities is used. When a primary input is missing, this would then

require taking the log of zero. To avoid this problem, we will treat natural resources

as intermediate inputs.5 We illustrate this method for incorporating natural

resources in international productivity comparisons for the 116 countries for which

the Penn World Table (version 9.0, Feenstra et al., 2015) provides information on

the input of produced and human capital and for which Lange et al. (2018) pro-

vides information on the production of natural resources—all for the year 2011.

The main unknown variable in applying this method is the reservation price for

natural resources. The unit rent—defined as the resource price minus unit produc-

tion cost—is the central concept, because, as Diewert and Fox (2016) show, the unit

rent is equivalent to the user cost of the natural resource, i.e. the price of the input,

3More specifically, we focus on what is referred to in National Accounts terminology as “subsoil

assets.” Natural resources more broadly can also cover agricultural land and forests, see Lange et al.

(2018).

4See e.g. Diewert and Feenstra (2018), Redding and Weinstein (2019), Feenstra (1994) and Balk

(1999).

5That means that for our productivity computation, the value of output is defined as GDP minus

resource rents and inputs consist of labour and produced capital.