CAPITAL‐ AND LABOR‐SAVING TECHNICAL CHANGE IN AN AGING ECONOMY

• Published date: 01 February 2017
• DOI: http://doi.org/10.1111/iere.12216
• Date: 01 February 2017
• Author: Andreas Irmen

INTERNATIONAL ECONOMIC REVIEW

Vol. 58, No. 1, February 2017

CAPITAL- AND LABOR-SAVING TECHNICAL CHANGE IN AN AGING

ECONOMY∗

BYANDREAS IRMEN1

CREA, University of Luxembourg, and CESifo, Munich, Germany

Does population aging and the associated increase in the old-age dependency ratio affect economic growth? The

answer is given in a novel analytical framework that allows for population aging to affect endogenous capital- and

labor-saving technical change. In a steady state capital-saving technical progress vanishes, and the economy’s growth

rate of per-capita variables reflects only labor-saving technical change. The mere possibility of capital-saving technical

change is shown to imply that the economy’s steady-state growth rate becomes independent of its age structure: Neither

a higher life expectancy nor a decline in fertility affects economic growth in the long run.

1. INTRODUCTION

Population aging, defined as the process by which older individuals become a proportionally

larger fraction of the total population, has been the predominant demographic phenomenon

in many countries over the last decades and is forecast to reach unprecedented heights. As

a concomitant phenomenon the United Nations predicts a substantial increase in the old-age

dependency ratio (OADR) of many countries and regions. Whereas the current level of this

ratio is around 0.2 in the United States and 0.24 in Europe, the respective predictions for 2050

are 0.36 and 0.47.2

There is widespread consensus that these trends have two main causes, a decline in fertility

and an increase in longevity (see, e.g., Weil, 2008).3This article starts from this premise and asks

whether and how population aging and the associated increase in the OADR affect economic

growth. In particular, I argue that firms adjust their innovation investments in aging economies.

Since these investments constitute a crucial determinant of the speed of technical progress,

population aging has the potential to affect the growth performance of an economy both in the

short run and in the long run.

I address this issue in a novel growth model that allows for endogenous capital- and labor-

saving technical change. This feature turns out to substantially modify the predicted effects

∗Manuscript received February 2015; revised October 2015.

1This article is a revised version of my CREA Discussion Paper (Irmen, 2013a). Financial support from the University

of Luxembourg under the program “Agecon C—Population Aging: An Exploration of Its Effect on Economic Perfor-

mance and Culture” is gratefully acknowledged. I would like to thank two anonymous referees and an associate editor

for helpful comments. I thank D´

eborah Schwartz and Amer Tabakovic for competent research assistance. This article

also benefited from useful suggestions provided by Volker B¨

ohm, Raouf Boucekkine, Oded Galor, Hendrik Hakenes,

Burkhard Heer, Johanna Kuehnel, Anastasia Litina, Isabel Schnabel, Robert Stelter, Gautam Tripati, Edgar Vogel,

Benteng Zou, and seminar audiences at several academic institutions. Please address correspondence to: Andreas

Irmen, CREA, Faculty of Law, Economics and Finance, University of Luxembourg, 162a, avenue de la Fa¨

ıencerie,

L-1511 Luxembourg, Luxembourg. E-mail: airmen@uni.lu.

2Here, the OADR is expressed as the ratio of the population aged 65 or over to the population aged 15–64. The

predicted numbers correspond to the “medium fertility variant” presented in United Nations (2013). For countries like

China, India, Japan, and for the entire planet, the predicted increase of the OADR over the same period is even more

pronounced. I focus on the OADR as an indicator of population aging since this measure has a natural counterpart in

the theoretical analysis that follows.

3During a demographic transition, a decline in fertility will increase the OADR because fewer young people enter

the labor force than there are old workers leaving it. A higher longevity means an increase in the number of years an

individual is old. This increases the OADR by raising the number of retired persons alive.

261

C

(2017) by the Economics Department of the University of Pennsylvania and the Osaka University Institute of Social

and Economic Research Association

262 IRMEN

of population aging on economic growth. The production side of the economy builds on and

extends ideas of the so-called “induced innovations” literature (see, e.g., Hicks, 1932; Drandakis

and Phelps, 1966). According to this literature, relative factor prices reflect the relative scarcity

of factors and induce innovations that raise the productivity of the relatively scarcer and more

expensive factor. In line with this reasoning, my framework highlights that population aging

increases the relative scarcity of labor with respect to capital. This tendency increases the real

wage relative to the real rental rate of capital and induces more labor-saving and less capital-

saving technical change.4However, unlike the “induced innovations” literature, the investment

behavior of competitive firms is fully microfounded in this article. To accomplish this, I introduce

a production function defined over “types of tasks” performed by either capital or labor.

The household side has two-period lived overlapping generations (OLGs) as in Allais (1947),

Samuelson (1958), or Diamond (1965). Individuals face a survival probability when they enter

the second period of their lives. This framework allows for a straightforward representation of

population aging as an increase in the OADR. Both a decline in fertility and an increase in the

survival probability of the current young augment this ratio in the next period.

The main result of my analysis concerns the relationship between population aging and

economic growth in the long run. I establish that the steady-state growth rate of per-capita

variables is given by the growth rate of labor-saving technological knowledge alone. Moreover,

this growth rate is independent of population aging. The latter property is shown to be due to

the mere possibility of endogenous capital-saving technical change.

The intuition behind this finding is linked to the logic of the generalized steady-state growth

theorem devised in Irmen (2013b). This theorem generalizes Uzawa’s steady-state growth

theorem (Uzawa, 1961) to endogenous-growth economies including the one studied in this

article. Roughly speaking, it states that only labor-saving technical change can occur in the

steady state of a neoclassical economy that uses some of its current output to generate technical

progress. Thus, asymptotically, capital-saving technical change must vanish. For the steady state

of the economy under scrutiny, here this requires that the stock of capital-saving technological

knowledge remains constant over time. Hence, the steady state must induce capital-saving

technical progress just sufficient to offset the depreciation of this stock. This requirement

determines a time-invariant steady-state level of the “efficient capital intensity,” the economy’s

state variable. The determination of this level reflects two facets of the production sector,

namely, the way capital-saving technological knowledge accumulates and the conditions for

profit maximization of firms that undertake capital-saving innovation investments. Population

aging does not interfere with its determination. As the steady-state level of the efficient capital

intensity also determines the growth rate of labor-saving technical progress, the steady-state

growth rate of the economy does not hinge on population aging either.

There are at least two ways to link this finding to the recent experience of the U.S. economy.

First, the evolution of the OADR and of per-capita GDP growth over the period 1960–2012

appear uncorrelated in the data.5Whereas the OADR trends upward, the evolution of the

growth rate of per-capita GDP is driven by short-run fluctuations around a constant trend.

These features are consistent with the near steady-state behavior of the economy under scrutiny

here. Since the steady-state growth rate is independent of the OADR, there is a neighborhood

of the locally stable steady state where fluctuations of per-capita GDP growth remain small

even if the OADR increases. Second, as shown by Klump et al. (2007) for the period 1953–1998,

4This chain of reasoning associates the phenomenon of population aging with the famous contention of John Hicks

(1932, pp. 124–125) on induced inventions according to which “a change in the relative prices of the factors of production

is itself a spur to invention, and to invention of a particular kind—directed to economizing the use of a factor that

has become relatively expensive. The general tendency to a more rapid increase of capital than labor that has marked

European history during the last few centuries has naturally provided a stimulus to labor-saving inventions.”

5To confirm this statement, I regressed U.S. per-capita GDP on the OADR and a time trend using data from the

World Bank (2013) for the above-mentioned period. The coefficient on OADR is statistically insignificant with a p-

value greater than 0.6. The same qualitative finding obtains if, in the regression, per-capita GDP growth is replaced by

labor productivity growth. The detailed regression results are available from the author upon request.