Quantifying Optimal Growth Policy

• Author: TIMO TRIMBORN,THOMAS M. STEGER,VOLKER GROSSMANN
• Published date: 01 June 2016
• DOI: http://doi.org/10.1111/jpet.12151
• Date: 01 June 2016

QUANTIFYING OPTIMAL GROWTH POLICY

VOLKER GROSSMANN

University of Fribourg

THOMAS M. STEGER

University of Leipzig

TIMO TRIMBORN

University of G¨

ottingen

Abstract

We determine the optimal growth policy within a comprehensive en-

dogenous growth model. The model accounts for important elements

of the tax transfer system and for transitional dynamics. It captures the

three main growth engines based on standard ingredients in order to

understand the quantitative policy and welfare implications of the ex-

isting theory. Our calibrated model indicates that the current policy

leads to severe underinvestment in both R&D and physical capital, im-

plying that both R&D and capital investment subsidies should be in-

creased substantially. We argue that previous research has overlooked a

strong evidence for the welfare significance of the quest for the optimal

growth policy by failing to calibrate the distortionary tax system.

1. Introduction

What does the optimal growth policy in advanced economies look like and what are the

quantitative effects of implementing it? One must acknowledge that, after three decades

of endogenous growth theory, we still do not have a sound answer to this exceptionally

important research question. In this sense, the topic on optimal growth policy in ad-

vanced economies appears heavily underresearched.

Volker Grossmann, Department of Economics, University of Fribourg, Bd. de P´

erolles 90, 1700

Fribourg, Switzerland (volker.grossmann@unifr.ch). Thomas M. Steger, Institute for Theoretical Eco-

nomics, University of Leipzig, Grimmaische Strasse 12, 04109 Leipzig, Germany (steger@wifa.uni-

leipzig.de). Timo Trimborn,Faculty of Economic Sciences, University of G ¨

ottingen, Platz der G¨

ottinger

Sieben 3, 37073 G¨

ottingen, Germany (timo.trimborn@wiwi.uni-goettingen.de).

We are grateful to two anonymous referees as well as to Carl-Johan Dalgaard, Mark Gradstein, Dirk

Krueger,and Holger Strulik for helpful comments and suggestions. We also benefitted from discussions

with seminar participants at the World Congress of the Econometric Society in Shanghai; the Annual

Meeting of the European Economic Association in Glasgow; the Dynamics, Economic Growth, and In-

ternational Trade Conference in Frankfurt (DEGIT XV); the Annual Meeting of German Economists

(Verein f¨

ur Socialpolitik) in Kiel; the CESifo Area Conference in Public Economics in Munich; the An-

nual Meeting of German Macroeconomists (Makro¨

okonomischer Ausschuss—Verein f¨

ur Socialpolitik)

in Hamburg; and research seminars at the University of Heidelberg and University of St. Gallen.

Received November 12, 2014; Accepted November 30, 2014.

C2015 Wiley Periodicals, Inc.

Journal of Public Economic Theory, 18 (3), 2016, pp. 451–485.

451

452 Journal of Public Economic Theory

This paper employs a comprehensive endogenous growth model to quantitatively

derive the optimal policy mix and to determine the potential welfare gain from an op-

timal policy reform. Our model accounts for important elements of the tax transfer

system and for transitional dynamics. It captures the three main growth engines, allow-

ing for investment in physical capital, human capital, and R&D. The modeling of the

growth engines is consciously based on well understood and widely used ingredients

in order to understand the quantitative policy and welfare implications of the existing

theory.

Our results strongly suggest that the current policy mix is suboptimal and there is

potential to realize substantial welfare gains. As will become apparent below, the quan-

titative implications are large and hence the results seem provocative. We conclude that

there is strong indication for the welfare significance of the quest for the optimal growth

policy.

Endogenous growth theory provides a natural analytical framework for studies that

aim at advising policy makers about the design of welfare-maximizing growth policy by

taking into account the general equilibrium dimension and the intertemporal dimen-

sion associated with R&D. However, any such analysis faces the problem of achieving

a balance between maintaining analytical tractability and avoiding a model that is too

stylized to base policy recommendations upon it. It is true that any specific policy advice

(like the calculation of the optimal R&D subsidy rate) requires numerical evaluations

at some stage of the analysis. Nevertheless, for at least two reasons we want to limit

ourselves to models where the steady state can be derived analytically. First, analytical

solutions are generally useful in understanding the mechanics of a model such that nu-

merical results can then be used mainly for quantification purposes. Second, analytical

steady state results are salient for matching endogenous variables to observables when

calibrating the model. Using the steady state as an anchor for calibration appears to be

reasonable strategy in the case of the U.S. economy. This allows us to limit the degree

of freedom in the numerical analysis substantially.

We think that any serious and careful study of optimal growth policy in advanced

economies should at least meet the following two requirements. First, it should capture

important elements of the income tax system. Taxes on labor income, bond yields, cap-

ital gains, and corporate income may be levied for other (e.g., redistributive) purposes

than stimulating economic growth. However, like externalities and market power, they

may directly distort investment decisions. Failing to account for income taxation thus

potentially gives rise to misleading growth policy recommendations. Another reason to

take the public finance side seriously when calculating quantitative policy recommen-

dations results from the requirement of a careful calibration strategy. Setting model

parameters such that endogenous variables match observables requires taking public

policy into account since endogenous variables may depend on public policy. Account-

ing for this fact turns out to have important consequences for our results compared to

the existing literature.

The second requirement in studying our research question is the need to take tran-

sitional dynamics into account in the numerical evaluation of growth policy reforms.

This requires a calculation of the entire transition path in response to policy shocks. It

is well known that, in growth models with decreasing marginal productivity of capital, it

may take a long time after a shock before per capita income adjusts to anywhere near

the new steady state. It is thus salient to compute the policy mix which maximizes the

intertemporal welfare gain from a policy reform and not just focus on maximization

of steady state welfare. Moreover, the underlying R&D-based growth model represents

a non linear, highly dimensional, saddle-point stable, differential algebraic system. For

Quantifying Optimal Growth Policy 453

plausible calibrations, the stable eigenvalues differ substantially in magnitude; hence,

the dynamic system belongs to the class of stiff differential equations. Simulating such

a dynamic model is all but trivial.1We employ a recent procedure, called relaxation

algorithm (Trimborn, Koch, and Steger 2008), which can deal with these conceptual

difficulties.

Our analysis suggests that the current R&D subsidization in the United States leads

to more dramatic underinvestment in R&D than has been previously found in the lit-

erature. The main reason is that by not accounting for capital income taxation, which

distorts incentives to invest in physical capital, households have to be calibrated to be

less patient to match observable income growth than they may actually be. Thus, socially

optimal investment levels are found to be closer to the market equilibrium than may be

the case. According to our preferred calibration, innovating firms should be allowed to

deduct more than twice their R&D costs from sales revenue for calculating taxable cor-

porate income, rather than just 1.1 times their R&D costs as under the current policy.

The U.S. stimulus for investment in physical capital is also suboptimally low. In addi-

tion to capital income taxation, the investment rate is biased downwards because of the

price-setting power of firms. Our calibrated model implies that firms should be allowed

to deduct about 1.5 times their capital costs from sales revenue, rather than full deduc-

tion of their capital costs under the current policy. Investment in human capital should

also be subsidized, roughly to the extent labor income is taxed. A policy reform targeted

simultaneously to all three growth engines may entail huge welfare gains. An appropri-

ate policy reform could achieve an intertemporal welfare gain which is equivalent to a

permanent doubling of per capita consumption. The welfare gain in response to the

implementation of the optimal growth policy program is only slightly smaller if the gov-

ernment adjusts a distortionary tax instead of adjusting a lump-sum tax to achieve a

balanced budget. Although the potential welfare gain varies with the calibration, the

optimal policy mix is remarkably robust to parameter changes.

There is general consensus among economists that private firms in advanced

economies conduct too little R&D. This conviction can be substantiated by noting that

the social rate of return to business enterprise R&D is far above the private rate of re-

turn. The empirical literature has identified social rates of return to R&D between 70%

and more than 100% (e.g., Scherer 1982, Griliches and Lichtenberg 1984). Jones and

Williams (1998) argue that, due to methodical shortcomings, these estimates should in-

deed be viewed as lower bounds. Hall (1996) reports that estimates of the private rate of

return to R&D cluster around 10%–15%. It is also widely believed that this R&D under-

investment bias is likely to cause a substantial welfare loss. Moreover, there is strong ev-

idence showing that fiscal incentives are effective in increasing the economy-wide R&D

intensity (e.g., Bloom, Griffith, and van Reenen 2002). This raises the important ques-

tion addressed in our paper about the level of fiscal intervention which is required to

remove the R&D underinvestment gap.

Our paper is closely related to the theoretical literature on underinvestment gaps

which, however, has focused on a steady state analysis. Our main point of reference is

the innovative study by Jones and Williams (2000). Like we do, they employ a horizontal

innovation model without strong scale effects `

alaJones (1995). However, they neither

consider transitional dynamics nor do they calculate the optimal policy mix. We identify

1The growth literature has used the techniques of linearization, time elimination, or backward inte-

gration. Linearization delivers bad approximations if the deviation from the steady state is large, time

elimination does not work if there are nonmonotonic adjustments, and backward integration fails in

the case of stiff differential equations.