R&D and Productivity: Estimating Endogenous Productivity

TLDR: In this article, the authors developed a model of endogenous productivity change to examine the impact of investment in knowledge on the productivity of firms and derived a novel estimator for production functions in this setting.

Abstract: We develop a model of endogenous productivity change to examine the impact of the investment in knowledge on the productivity of firms. Our dynamic investment model extends the tradition of the knowledge capital model of Griliches (1979) that has remained a cornerstone of the productivity literature. Rather than constructing a stock of knowledge capital from a firm’s observed R&D expenditures, we consider productivity to be unobservable to the econometrician. Our approach accounts for uncertainty, nonlinearity, and heterogeneity across firms in the link between R&D and productivity. We also derive a novel estimator for production functions in this setting. Using an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s, we provide evidence of nonlinearities as well as economically significant uncertainties in the R&D process. R&D expenditures play a key role in determining the differences in productivity across firms and the evolution of firm-level productivity over time.

Figures

Figure 3: Persistence and uncertainty.

Figure 1: (cont’d) Distribution of expected productivity.

Figure 2: Distribution of expected productivity. Exogenous Markov process.

Figure 1: (cont’d) Distribution of expected productivity.

Figure 4: Return to R&D and uncertainty.

Full text

University of Pennsylvania University of Pennsylvania
ScholarlyCommons ScholarlyCommons
Business Economics and Public Policy Papers Wharton Faculty Research
2-2013
R&D and productivity: Estimating endogenous productivity R&D and productivity: Estimating endogenous productivity
Ulrich Doraszelski
University of Pennsylvania
Jordi Jaumandreu
Follow this and additional works at: https://repository.upenn.edu/bepp_papers
Part of the Economics Commons
Recommended Citation Recommended Citation
Doraszelski, U., & Jaumandreu, J. (2013). R&D and productivity: Estimating endogenous productivity.
Review of Economic Studies,
80
(4), 1338-1383. http://dx.doi.org/10.1093/restud/rdt011
This paper is posted at ScholarlyCommons. https://repository.upenn.edu/bepp_papers/109
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R&D and productivity: Estimating endogenous productivity R&D and productivity: Estimating endogenous productivity
Abstract Abstract
We develop a model of endogenous productivity change to examine the impact of the investment in
knowledge on the productivity of >rms. Our dynamic investment model extends the tradition of the
knowledge capital model of Griliches (1979) that has remained a cornerstone of the productivity
literature. Rather than constructing a stock of knowledge capital from a >rm’s observed R&D expenditures,
we consider productivity to be unobservable to the econometrician. Our approach accounts for
uncertainty, nonlinearity, and heterogeneity across >rms in the link between R&D and productivity. We also
derive a novel estimator for production functions in this setting.
Using an unbalanced panel of more than 1800 Spanish manufacturing >rms in nine industries during the
1990s, we provide evidence of nonlinearities as well as economically signi>cant uncertainties in the R&D
process. R&D expenditures play a key role in determining the differences in productivity across >rms and
the evolution of >rm-level productivity over time.
Keywords Keywords
R&D, productivity, knowledge capital model
Disciplines Disciplines
Economics
This journal article is available at ScholarlyCommons: https://repository.upenn.edu/bepp_papers/109

R&D and productivity: Estimating endogenous productivity
∗
Ulrich Doraszelski
†
University of Pennsylvania
Jordi Jaumandreu
‡
Boston University
December 3, 2011
Abstract
We develop a model of endogenous productivity change to examine the impact of
the investment in knowledge on the productivity of firms. Our dynamic investment
model extends the tradition of the knowledge capital model of Griliches (1979) that
has remained a cornerstone of the productivity literature. Rather than constructing
a stock of knowledge capital from a firm’s observed R&D expenditures, we consider
productivity to be unobservable to the econometrician. Our approach accounts for
uncertainty, nonlinearity, and heterogeneity across firms in the link between R&D and
productivity. We also derive a novel estimator for production functions in this setting.
Using an unbalanced panel of more than 1800 Spanish manufacturing firms in nine
industries during the 1990s, we provide evidence of nonlinearities as well as economically
significant uncertainties in the R&D process. R&D expenditures play a key role in
determining the differences in productivity across firms and the evolution of firm-level
productivity over time.
∗
Earlier versions of this paper were circulated as “R&D and productivity: The knowledge capital model
revisited” and “R&D and productivity: Estimating production functions when productivity is endogenous.”
We thank Dan Ackerberg, Manuel Arellano, Steve Berry, Michaela Draganska, Ivan Fernandez-Val, David
Greenstreet, Dale Jorgenson, Ken Judd, Saul Lach, Jacques Mairesse, Rosa Matzkin, Ariel Pakes, Amil
Petrin, Zhongjun Qu, Mark Roberts, Marc Rysman, Mark Schankerman, and Jim Tybout for helpful com-
ments and discussions as well as Laia Castany and Nilay Yilmaz for excellent research assistance. Doraszelski
gratefully acknowledges the hospitality of the Hoover Institution during the academic year 2006/07. Do-
raszelski and Jaumandreu gratefully acknowledge financial support from the National Science Foundation
under Grant No. 0924380.
†
Wharton School, University of Pennsylvania, 3620 Locust Walk, Philadelphia, PA 19104, USA. E-mail:
doraszelski@wharton.up enn.edu.
‡
Department of Economics, Boston University, 270 Bay State Road, Boston, MA 02215, USA. E-mail:
jordij@bu.edu.

1 Introduction
A firm invests in R&D and related activities to develop and introduce process and product
innovations. These investments in knowledge enhance the productivity of the firm and
change its competitive position relative to that of other firms.
Our goal in this paper is to assess the role of R&D in determining the differences
in productivity across firms and the evolution of firm-level productivity over time. To
achieve this goal, we develop a model of endogenous productivity change resulting from
investment in knowledge. We also derive an estimator for production functions in this
setting. With these tools in hand we study the link between R&D and productivity in
Spanish manufacturing firms during the 1990s.
Our starting point is a dynamic model of a firm that invests in R&D in order to improve
its productivity over time in addition to carrying out a series of investments in physical cap-
ital. Both investment decisions depend on the current productivity and the capital stock
of the firm as do the subsequent decisions on static inputs such as labor and materials.
Productivity follows a Markov process that can be shifted by R&D expenditures. The evo-
lution of productivity is thus subject to random shocks. These innovations to productivity
capture the factors that have a persistent influence on productivity such as absorption of
techniques, modification of processes, and gains and losses due to changes in labor com-
position and management abilities. For a firm that engages in R&D, the productivity
innovations additionally capture the uncertainties inherent in the R&D process such as
chance in discovery, degree of applicability, and success in implementation.
Our model of endogenous productivity change is not the first attempt to account for
investment in knowledge. In a very influential paper, Griliches (1979) proposed to augment
a standard production function with “a measure of the current state of technical knowledge,
determined in part by current and past research and development expenditures” (p. 95). In
practice, a firm’s observed R&D expenditures are used to construct a proxy for the state of
knowledge. This knowledge capital model has remained a cornerstone of the productivity
literature for more than 25 years and has been applied in hundreds of studies on firm-level
productivity (see the surveys by Mairesse & Sassenou (1991), Griliches (1995, 2000), and
Hall, Mairesse & Mohnen (2010)).
In a departure from the previous literature we do not attempt to construct a stock of
knowledge capital from the available history of R&D expenditures and with it control for
the impact of R&D on productivity. Instead, we consider productivity to be unobservable to
the econometrician and in this way relax the assumptions on the R&D process in a natural
fashion. We recognize that the outcome of the R&D process is likely to be subject to a high
degree of uncertainty. Once discovered, an idea has to be developed and applied, and there
are the technical and commercial uncertainties linked to its practical implementation. We
further recognize that current and past investments in knowledge are likely to interact with
each other in many ways. Since there is little reason to believe that features such as com-
2

plementarities and economies of scale in the accumulation of knowledge or the obsolescence
of previously acquired knowledge can be adequately captured by simple functional forms,
we model the interactions between current and past investments in knowledge in a flexible
fashion.
To retrieve productivity at the level of the firm, we have to estimate the parameters
of the production function. However, if a firm adjusts to a change in its productivity by
expanding or contracting its production depending on whether the change is favorable or
not, then unobserved productivity and input usage are correlated and biased estimates result
(Marschak & Andrews 1944). Recent advances in the structural estimation of production
functions, starting with the dynamic investment model of Olley & Pakes (1996) (OP), tackle
this endogeneity problem.
1
The insight of OP is that if observed investment is a monotone
function of unobserved productivity, then this function can be inverted to back out—and
thus control for—productivity. This line of research has been extended by Levinsohn &
Petrin (2003) (LP) and Ackerberg, Caves & Frazer (2006) (ACF).
Instead of relying on the firm’s dynamic programming problem as OP do, we use the fact
that static inputs are decided on with current productivity known and therefore contain in-
formation about it. As first shown by LP, the input demands resulting from short-run profit
maximization are invertible functions of unobserved productivity. We use this insight to
control for productivity and obtain consistent estimates of the parameters of the production
function. In addition, we recognize that, given a parametric specification of the production
function, the functional form of the inverse input demand functions is known. Because we
fully exploit the structural assumptions, we do not have to rely on nonparametric methods
to estimate these functions. Our parametric inversion yields a particularly simple estimator
for production functions.
We apply our estimator to an unbalanced panel of more than 1800 Spanish manufactur-
ing firms during the 1990s. Our data is of notably high quality and combines information
on production with information on firms’ R&D activities in nine industries. This broad
coverage of industries is uncommon and allows us to examine the link between R&D and
productivity in a variety of settings that differ greatly in the importance of R&D. At the
same time, it allows us to put to the test our model of endogenous productivity change and
the estimator we develop for it.
Somewhat unusually we have firm-level wage and price data.
2
The fact that the wage
and prices vary across firms is at variance with the often-made assumption in the literature
following OP that all firms face the same wage and prices and that these variables can
therefore be replaced by a dummy. Instead, as LP point out, the wage and prices must be
1
See Griliches & Mairesse (1998) and Ackerberg, Benkard, Berry & Pakes (2007) for reviews of this and
other problems that arise in the estimation of production functions.
2
There are other data sets such as the Colombian Annual Manufacturers Survey (Eslava, Haltiwanger,
Kugler & Kugler 2004) and the Longitudinal Business Database at the U.S. Census Bureau that contain
separate information about prices and quantities, at least for a subset of industries (Roberts & Supina 1996,
Foster, Haltiwanger & Syverson 2008).
3

Frequently asked questions

Q1. What have the authors contributed in "R&d and productivity: estimating endogenous productivity" ?

The authors develop a model of endogenous productivity change to examine the impact of the investment in knowledge on the productivity of firms. Rather than constructing a stock of knowledge capital from a firm ’ s observed R & D expenditures, the authors consider productivity to be unobservable to the econometrician. Their approach accounts for uncertainty, nonlinearity, and heterogeneity across firms in the link between R & D and productivity. Using an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s, the authors provide evidence of nonlinearities as well as economically significant uncertainties in the R & D process. ∗Earlier versions of this paper were circulated as “ R & D and productivity: The knowledge capital model revisited ” and “ R & D and productivity: Estimating production functions when productivity is endogenous. ” the authors thank Dan Ackerberg, Manuel Arellano, Steve Berry, Michaela Draganska, Ivan Fernandez-Val, David Greenstreet, Dale Jorgenson, Ken Judd, Saul Lach, Jacques Mairesse, Rosa Matzkin, Ariel Pakes, Amil Petrin, Zhongjun Qu, Mark Roberts, Marc Rysman, Mark Schankerman, and Jim Tybout for helpful comments and discussions as well as Laia Castany and Nilay Yilmaz for excellent research assistance. 

Q2. How much of the output of R&D is derived from the firms with intermediate or high?

In addition, the authors estimate that firms that perform R&D contribute between 65% and 90% of productivity growth in the industries with intermediate or high innovative activity. 

Q3. What is the advantage of equation (5)?

In considering instruments, it is important to remember that because equation (5) models the law of motion for productivity it has an advantage over equation (1): Instruments have to be uncorrelated with the innovation to productivity ξjt but not necessarily with the level of productivity ωjt. 

Q4. What is the elasticity of output with respect to already attained productivity?

Since a change in the conditional expectation function g(·) can be interpreted as the expected percentage change in total factor productivity,∂g(ωjt−1,rjt−1) ∂rjt−1 is the elasticity of output with respectto R&D expenditures or a measure of the return to R&D.30 Similarly, ∂g(ωjt−1,rjt−1)∂ωjt−1 is theelasticity of output with respect to already attained productivity. 

Q5. What is the elasticity of output with respect to the stock of knowledge capital?

The elasticity of output with respect to the stock of knowledge capital tends to be small and rarely significant in the gross-output version but becomes larger in the value-added version. 

Q6. What is the conditional expectation function g()?

The conditional expectation function g(·) is not observed by the econometrician and must be estimated nonparametrically along with the parameters of the production function. 

Q7. What is the link between R&D and productivity?

Applying their approach to an unbalanced panel of more than 1800 Spanish manufacturing firms in nine industries during the 1990s, the authors show that the link between R&D and productivity is subject to a high degree of uncertainty, nonlinearity, and heterogeneity. 

Q8. What is the reason why productivity is less persistent in an industry where a large part of its?

That is, productivity is less persistent in an industry where a large part of its variance is due to random shocks that represent the uncertainties inherent in the R&D process. 

Q9. Does g() depend on already attained productivity?

While the conditional expectation function g(·) depends on already attained productivity ωjt−1 and R&D expenditures rjt−1, ξjt does not: by construction ξjt is mean independent (although not necessarily fully independent) of ωjt−1 and rjt−1. 

Q10. What is the reason why the authors reject the parameter restrictions in equation (4)?

the functional form of the inverse labor demand function in equation (4) may be inappropriate if the labor decision has dynamic consequences. 

Q11. What is the role of R&D in determining the differences in productivity across firms?

To assess the role of R&D in determining the differences in productivity across firms and the evolution of firm-level productivity over time, the authors examine five aspects of the link between R&D and productivity in more detail: productivity levels and growth, the return to R&D, the persistence in productivity, and the rate of return. 

Q12. How does the estimator differ from LP?

Their estimator differs from LP by recognizing that, given a parametric specification of the production function, the functional form of the input demand functions (and their inverses) is known. 

Q13. Why do the authors use nonparametric methods to estimate production functions?

Because the authors fully exploit the structural assumptions, the authors do not have to rely on nonparametric methods to estimate these functions. 

Q14. How much of the variance in productivity is explained by innovations?

The authors estimate that, depending on the industry, between 25% and 75% of the variance in productivity is explained by innovations that cannot be predicted when decisions on R&D expenditures are made. 

Q15. How many performers and nonperformers are in the test?

Because the tests tend to be inconclusive when the number of firms is small, the authors limit them to cases in which the authors have at least 20 performers and 20 nonperformers.