How Important Are Scale Effects for Growth When Knowledge Is a Public Good?

• Author: Fernando Sánchez‐Losada
• DOI: http://doi.org/10.1111/sjoe.12273
• Date: 01 April 2019
• Published date: 01 April 2019

Scand. J. of Economics 121(2), 763–782, 2019

DOI: 10.1111/sjoe.12273

How Important Are Scale Effects for Growth

When Knowledge Is a Public Good?*

Fernando S´anchez-Losada†

University of Barcelona, 08034 Barcelona, Spain

fernando.sanchezlosada@ub.edu

Abstract

In this paper, byproposing an R&D accumulation law for an economy with an expanding number

of firms, I seek to reconcile the following three facts: the positiverelationship between the fraction

of income allocated to R&D expenditureand g rowth;the positive relationship between the number

of firms and total factor productivity growth; and knowledge as a non-rival and non-excludable

good. There are scale effects because of the public nature of knowledge, but the economy also

grows in the absence of population growth. I find that population growth explains one-fifth of

market income growth but only one-sixteenth of efficient income growth.

Keywords: Efficientgrowth; market growth; population growth

JEL classification:O30; O40; O41

I. R&D-Variety Growth Models and Scale Effects

In recent years, there has been some discussion as to which of the

following growth models provides a better explanation of technological

progress: R&D-variety growth models or Schumpeterian models. In R&D-

based models of growth (see Jones, 1995), a positive increase in R&D

resources is required to maintain sustained growth, given the assumption of

diminishing returns to knowledge. Hence, a rising supply of researchers is

needed. This implies that growth is explained exclusively by scale effects

and, therefore, an economy with zero population growth experiences zero

income growth. In contrast, in Schumpeterian models (see Dinopoulos and

Thompson, 1998), there is a positive relation between the fraction of income

allocated to R&D expenditure and economic growth. This implies growth

without scale effects.

*I acknowledge useful comments received from one anonymous referee, the participants at the

UB Macro Internal Seminar, Daniel Cardona, David Cuberes, Patricio Garc´ıa-M´ınguez, Vahagn

Jerbashian, Charles I. Jones, Xavier Raurich, andAusias Rib ´o, and wouldespecially like to thank

Edgar Cruz for his time. I am grateful for financial support from the Ministerio de Econom´ıa y

Competitividad and Fondo Europeo de Desarrollo Regional through grant ECO2015-66701-R

(MINECO/FEDER, UE) and from the Government of Catalonia through grant 2014SGR493.

†Affiliated with the Center for Research in Welfare Economics (CREB) and the Barcelona

Economics Analysis Team(BEAT).

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The editors of The Scandinavian Journal of Economics 2017.

764 Scale effects and knowledge as a public good

In principle, the empirical evidence supports Schumpeterian models

(see Zachariadis, 2003; Madsen, 2008). However, these papers suggest

that this conclusion could also be reached by the diminishing returns to

knowledge assumed in the R&D-variety growth models and, as such, they

support the findings of Madsen (2007) and Venturini (2012). While the

former concludes that R&D might be characterized by constant returns to

scale, the latter reports that knowledge production functions based on the

expansion of variety overlook some relevant institutional and policy factors.

Indeed, developed countries during the 20th century were characterized by

a negative relationship between population growth and economic growth

(see Galor and Weil, 2000). To reconcile the R&D-variety growth model

and this circumstance, Strulik et al. (2013) introduce the Beckerian child

quantity–quality trade-off.1

However, for growth, the importance of scale effects in their own right

as well as via agglomeration economies has been broadly documented. For

example, Nickell (1996) shows that an increase in the number of firms is

associated with a higher rate of total factor productivity (TFP) growth.

Likewise, ´

Alvarez-Pel´aez and Groth (2005) highlight the importance of

the returns to specialization for growth. Ciccone and Hall (1996) find

that doubling employment density increases average labor productivity

by 6 percent, whereas Davis et al. (2014) estimate that the impact of

local agglomeration on the growth rate is about 10 percent. Therefore,

because competition increases as the number of firms grows, competition

drives growth, as Nickell (1996) has shown empirically. In other words,

an increased number of competitors in the same industry is positively

correlated with TFP growth. Thus, an R&D-variety growth model should

at least explain a significant part of this growth.

It seems clear that because knowledge is non-rival and non-excludable,

population matters in the determination of growth. The rationale is that an

increase in population makes an increase in knowledge more likely, which

is to the benefit of the population. From an economic point of view, it is

therefore clear that as knowledge is a public good, endogenous growth

exhibits some kind of scale effects.2This positive correlation between

growth and technological advancement or knowledge, and population

growth, has been empirically shown in Kremer (1993) for the very long

run.

In this paper, I seek to reconcile these three facts (the positive

relationship between the fraction of income allocated to R&D expenditure

and growth; the positive relationship between the number of firms and

1The connection between growth, human capital, and the child quantity–quality trade-off had

previously been shown byZhang (1995) and Zhang and Zhang (2003), among many others.

2See Jones (1999) for an exhaustive reviewof this body of literature.

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The editors of The Scandinavian Journal of Economics 2017.