World Productivity Growth: A Model Averaging Approach

• DOI: http://doi.org/10.1111/1468-0106.12238
• Author: Robin C. Sickles,Jiaqi Hao,Anders Isaksson,Meryem Duygun
• Date: 01 October 2017
• Published date: 01 October 2017

WORLD PRODUCTIVITY GROWTH: A MODEL

AVERAGING APPROACH

MERYEM DUYGUN Nottingham University Business School

JIAQI HAO Phoenix Finance

ANDERS ISAKSSON United Nations Industrial Development Organization

ROBIN C. SICKLES*Rice University/Economics

Abstract. Policy makers and the economic researchers who provide them estimates of economic ac-

tivity need to have an informative and scientifically-based method to develop a consensus estimate

for the most basic of the productivity measures, total factor productivity (TFP) growth. We discuss

methods to combine the various estimates based on different empirical specifications that model and

estimate productivity growth. We also discuss the various econometric approaches used in the pro-

fession to estimate productivity growth. Our focus is on world TFP growth.

1. INTRODUCTION

The measure of nations’productivity is of great importance for both academics

and policymakers in assessing performance and planning future economic

roadmaps. Strategic decisions require robust indicators that receive broad

consensus from various parties involved in the decision-making process. The

importance of such consensus is further amplified when monitoring bodies,

and lenders such as international organizations or financial and development

institutions (e.g., IMF, World Bank, UN and Regional Development Banks),

are involved. This underscores the long debated and largely unanswered

question in the literature: on which approach do we rely?

A common measure of productivity is the Total Factor Productivity (TFP)

Index. However, the existence of numerous methods and models involved in

TFP measurement make it a cumbersome and puzzling process for policy

makers. This paper proposes a practical yet robust approach that provides an

appealing solution to academics and policy makers alike in their pursuit for a

“consensus”productivity indicator. We propose that instead of relying on a

single approach, one should gather information from a set of measurement

methods and construct a single productivity indicator that is backed by robust

methodological techniques.

To demonstrate our approach, we apply it to a unique data set that covers a

large set of countries across the globe, namely the World Productivity Database

(WPD) developed by the United Nations Industrial Development Organization

(UNIDO). One of the purposes of WPD is to speak to the many approaches to

*Address for Correspondence: Robin C. Sickles, Rice University/Economics, Houston, Texas.

E-mail: rsickles@rice.edu. The authors would like to thank the editors of this special issue as well as

two anonymous referees for their helpful criticisms and for their patience. The authors are indebted

to Shasha Liu for her substantive research assistance and also thank Kevin Bittner for his editorial

assistance. The usual caveat applies.

Pacific Economic Review, 22: 4 (2017) pp. 587–619

doi: 10.1111/1468-0106.12238

© 2017 John Wiley & Sons Australia, Ltd

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TFP measurement and provide productivity analysts across the globe with TFP

estimates based on numerous methods, production function specifications, func-

tional forms, different capital stock and labor input measures, and much more.

The arsenal of approaches available to the researcher today, many of which are

reflected in WPD, is manifold and technically advanced and invites researchers

to provide comparisons of results obtained from applying several methods.

Unfortunately, this approach is seldom the case, as analysts tend to resort to

one method only.

The advantage of having a rich toolkit is, of course, a potential increase in ac-

curacy with which we are able to measure productivity performance. However,

it also constitutes an acknowledgement of uncertainties involved in modeling the

productivity measure. A notable disadvantage is that these different measure-

ment methods yield a range of estimates with sometimes very wide dispersion

or, in the worst case, conflicting results. Furthermore, all models may be subject

to misspecification of unknown form, e.g., researchers might have different in-

formation sets. Moreover, models may be affected differently by structural

breaks caused by institutional change or technological development, to name

but a few possible reasons leading to variation in TFP measurement.

However commendable the work of WPD may be, it is still silent on the issue

of what the “correct”productivity estimate is. Importantly, the question is how

policy makers are going to be able to make the “right”choice from available

alternative approaches. The approach presented in this paper is a step towards

resolving this conundrum.

To demonstrate the strength of our approach, the analysis presented, inter

alia, includes results at the aggregate world level, compares the performance

of six country groups at different stages of development, and decomposes TFP

growth into change in technical efficiency and innovation. Such decomposition

provides policy makers with a richer and more detailed basis for policy making.

Importantly, the analysis introduces a comparison of our consensus estimates

with those provided by common approaches such as growth accounting, pooled

and panel regression analysis, and data envelopment analysis. Our consensus

estimates fare well in comparison and we conclude that it may be advisable to

combine estimates in order to make the best conclusion based on all the

available information.

The paper provides a brief discussion of panel data and productivity analysis

in applied economic modeling. We discuss a variety of modeling scenarios and

justifications for them based on classical economic theory and on more recent

advances in production modeling that formulate methods to decompose produc-

tivity growth based on a Solow-type residual (Solow, 1957) into innovation and

catch-up, the latter referred to as technical efficiency change in the stochastic

and non-parametric frontier literature. We point to a number of innovations

contributed to the panel data literature by those working in the stochastic

frontier productivity discipline. In that literature the focus has been on the inter-

pretation of relative temporal heterogeneity between production units (firms,

countries, etc.) as a measure of relative technical efficiency in the use of the fron-

tier technology. Our paper has an aggregate productivity perspective, focusing

M. DUYGUN ET AL.588

© 2017 John Wiley & Sons Australia, Ltd

on country level productivity, as it better motivates and displays the strong intel-

lectual parallels between the efficiency literature, the economic growth and

development literature, and the literature on panel data econometrics.

The paper is organized in the following way. We first discuss how productivity

growth typically has been measured in classical productivity studies. We then

briefly discuss how innovation and catch-up can be distinguished empirically.

We discuss the econometric methods that accomplish this. In the Appendix we

also provide a set of Monte Carlo simulations that assess the performance of

the model averaging estimators we employ in our empirical work. We detail

the motivation for and the methods used in developing a consensus estimate

from the competing model estimates. We apply these methods to develop con-

sensus estimates for world TFP growth from 1970 to 2000 and then conclude.

2. MEASURING PRODUCTIVITY AND ITS GROWTH

2.1. Solow residual-based methods

In order to account for changing input (X

i

) mix, modern index number analyses

utilize a measure of total factor productivity (TFP) for a single output (Y) tech-

nology that in its simplest form is a ratio of output to a weighted sum of inputs.

A useful construct for a single output technology is thus:

TFP ¼Y

∑aiXi

:(1)

Detailed discussion of the properties and formulation of productivity mea-

sures for single and multiple output technologies are plentiful in the productivity

literature. One relatively early and informative discussion was undertaken by

productivity pioneers Jorgenson and Griliches (1972). Many others have pre-

ceded and followed their work. The literature is deep and extensive and we do

not attempt to list the relevant references in this paper.

Solow’s residual-based measure is based on the Cobb–Douglas production

function with constant returns to scale, Y¼AX α

LX1α

Kand given by:

TFP ¼Y

Xα

LX1α

K

:(2)

Cost-minimization allows one to describe the TFP growth index in terms of

expenditure shares:

T_

FP ¼dY

YαdXL

XL

þ1α

ðÞ

dXK

XK



where the non-negative parameter αis the input expenditure share for labor.

When multiple outputs exist, TFP can also be described as a ratio of an index

number describing aggregate output levels (Y

j

) divided by an index number de-

scribing aggregate input levels (X

i

). As is well-known, since TFP is a function of

index numbers, it derives its properties from the aggregator functions on which it

is based (see, e.g., Good et al., 1997).

WORLD PRODUCTIVITY GROWTH: A MODEL AVERAGING APPROACH 589

© 2017 John Wiley & Sons Australia, Ltd