Product variety, product quality, and evidence of. Schumpeterian endogenous growth: A note

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1 Product variety, product quality, and evidence of Schumpeterian endogenous growth: A note Francesco Venturini Abstract Using US manufacturing industry data, this paper re-examines empirical evidence of first- and second-generation Schumpeterian models of endogenous growth focusing on innovation (patent) quality. It shows that semi-endogenous growth models behave better than the other strands of Schumpeterian theory especially in the knowledge-intensive section of the economy. Keywords: Fully endogenous growth theory, Semi-endogenous growth theory, Innovation quality, US manufacturing, High-tech industries. JEL classification: O3, O4. francesco.venturini@unipg.it. Department of Economics, Finance and Statistics, University of Perugia, Via Pascoli 20, Perugia (Italy). Tel.: I wish to thank Antonio Minniti, Cristiano Perugini and Paul Segerstrom and the seminar participants at the Middldesex Business School and Università Politecnica delle Marche for helpful comments. 1

2 1 Background In the R&D-based endogenous growth theory, growth in knowledge is expressed as an ideas-based innovation function: A A = λ( X ) σa φ 1 Q (1) where A( ) is the annual flow of new knowledge (ideas) and A the knowledge stock available each year (Ha and Howitt, 2007). The rate of change in knowledge is positively affected by R&D input X, and negatively by the rise in product variety, Q. The latter is the product proliferation effect associated with demographic change L (Q t L β t ), that dilutes R&D expenses over a larger number of projects. β is a duplication parameter which is 0 when innovations are replications of existing products, and 1 when there are no duplicating innovations. Equation (1) incorporates the main innovation mechanisms designed by the growth theory (Table 1). Under σ = 0 and φ = 1, A/A is consistent with the neoclassical prediction that productivity grows exogenously. The R&D-based, fully endogenous growth setup of the first-generation Schumpeterian models (hereafter denoted by FE I) emerges when σ > 0, φ = 1 and β = 0 (Aghion and Howitt, 1992; Romer, 1990). A/A approaches the semi-endogenous, scale-invariant growth framework (SE) in the original version designed by Segerstrom (1998) when σ > 0, φ < 1 and β = 0, or in the hybrid version including a (weak) product proliferation effect when, other things equal, β < 1. Lastly, equation (1) is consistent with the second-generation, fully endogenous, scale-invariant growth mechanism (FE II) of Aghion and Howitt (1998, Ch. 12) when σ > 0, φ = 1 and β = 1. SE and FE II frameworks have been motivated on the basis of the Jones (1995) critique against the prediction of FE I models that economic growth is proportional to the level of R&D. The innovation function (1) has been assessed by several empirical works, most of which found that FE II theories are more consistent with data (Ha and Howitt, 2007; Madsen, 2008). Evidence corroborating the SE framework has been partially reported by Ang and Madsen (2010), Barcenilla-Visús et al. (2010), and more extensively by 2

3 Table 1: Classification of growth models Source: Ha and Howitt (2007). φ β σ Neoclassical NEO =1 - =0 Fully Endogenous I FE I =1 =0 >0 Semi-Endogenous SE <1 [0,1) >0 Fully Endogenous II FE II =1 =1 >0 Venturini (2010) looking at R&D races underlying these models. Findings inconsistent with either branch of the most recent Schumpeterian theories are provided by Madsen (2007). Since Aghion and Howitt (1992), endogenous growth literature has developed as quality ladder theory. However, the role of innovation quality has almost completely been superseded by extant studies, which tested the various setups by estimating equation (1) with patent counts as a measure of innovation output, not controlling for their quality content. This means considering only the horizontal dimension of innovation (product variety). Also, the majority of works rely on country-level data, whereas new growth models are conceived to describe innovation mechanisms occurring at the industry level. Due to this (non-negligible) twofold inconsistency with growth theory, the present work revisits evidence on Schumpeterian endogenous growth by applying US manufacturing industry data on product variety (patent counts), product quality (patent quality) and research engagement (R&D capital) to the innovation framework described by equation (1). The outline of the work is as follows. Section 2 illustrates the econometric specification and the employed data. Section 3 reports results. Section 4 concludes. 2 Econometric specification and data We estimate the steady-state framework where Q t = L β t and equation (1) (in logs) is reworded as: ln A it = α 0i + α 1 ln X it + α 2 ln L it + α 3 A it + T D + ɛ it (2) 3

4 where α 0i = ln λ i, α 1 = σ, α 2 = σβ, α 3 = φ. Subscripts denote time and industry. α 0i are industry fixed-effects, T D common time dummies, and ɛ it stationary error terms. In contrast to the majority of works, A is considered as innovation output, not as TFP, in order to avoid imposing a stationarity condition on productivity growth which is hard to hold on disaggregated industry series (see Venturini, 2007). The cointegration relationship (2) is estimated with the panel dynamic OLS estimator (Mark and Sul, 2003) on twenty US manufacturing industries for the period Data on patent counts (number of applications) and patent quality (forward citations, backward citations, claims) are taken from NBER Patent Data files, industry accounts data from EU KLEMS, and total R&D expenses from the National Science Foundation and OECD ANBERD. Data details and statistical properties of the series are provided in the web appendix. The flow of new ideas A is initially measured by total patent applications; the stock of available knowledge, A, by the cumulative value of the flow of new ideas, obtained with the perpetual inventory method and geometric depreciation. We then discriminate patented innovations by their quality content weighting each patent with the number of forward citations received (scaled on manufacturing mean to control for truncation). Although this is the most commonly used patent quality indicator (Trajtenberg, 1990), as an alternative we also adopt backward citations made to existing patents, and priorities claimed in patent applications. Product proliferation, L, is measured by real gross output; research input, X, by the stock of real R&D expenditure. 1 Industry list (ISIC Rev. 3 categories and OECD technological classes in parentheses): 1) Food, beverage & tobacco (15-16; Low-Tech, LT), 2) Textile, leather & footwear (17-19; LT), 3) Pulp, paper, printing & publishing (21-22; LT), 4) Petroleum, refining & extraction (23; Medium-Low Tech, MLT), 5) Chemicals and chemical products (24; Medium-High Tech, MHT), 6) Pharmaceuticals (2423; High-Tech, HT), 7) Rubber & plastics (25; MLT), 8) Other non-metallic mineral (26; MLT), 9) Basic metals (27; MLT), 10) Fabricated metal products (28; MLT), 11) Machinery (29; MLT), 12) Office, accounting and computing machinery (30; HT), 13) Electrical machinery and apparatus, nec (31; MHT), 14) Electronic valves and tubes (321; HT), 15) Communication equipment (322t3; HT), 16) Scientific instruments (331t3; HT), 17) Other instruments (334t5; HT), 18) Motor vehicles, trailers and semi-trailers (34; MHT), 19) Other transport equipment (incl. aerospace, 35; HT), 20) Wood, furniture and manufacturing nec (20, 36-37; LT). 4

5 3 Results Estimates of eq. (2) are shown on the top of Table 2, the implied coefficient of product proliferation, β, in the middle, while the bottom section sums up the values assumed by the theoretical variables and the growth theory identified by the various specifications. A linear Wald test is used to check the hypothesis of constant returns in the innovation function (φ = 1), a non-linear one based on the delta method to assess whether β equals zero (as in FE I or original SE), or β equals one (as in FE II). In column (1), estimates are obtained with patent counts as a proxy for new ideas A, and their cumulative value for A. The elasticity of A with respect to R&D input, X, is 0.042, that of the ideas stock one (Wald test p-value for φ = 1: 0.65). The coefficient of L is insignificant and the Wald tests performed on the ratio α 2 /α 1 indicate that product proliferation does not sterilise the R&D effort. Unambiguously, this evidence supports FE I (φ = 1, β = 0, σ > 0). The innovation function is then examined across technology-based industry groups. In medium- and low-tech sectors (col. 2), we find decreasing returns and a negative effect of product proliferation which, clearly, is not grounded theoretically. Mixed evidence emerges for the high- and medium-tech group (col. 3): the positive, smaller than unity impact of product proliferation fits the predictions of the hybrid SE framework (β = 0.38), while constant returns are consistent with FE II. 2 When the focus is restricted to high-tech industries only (col. 4), innovation counts turn out to be unrelated to R&D input (β is not definite). Next, columns (5) to (8) show results yielded using forward cites-weighted patents as a proxy for ideas. For the overall sample, results differ from col. (1) because of a smaller elasticity of R&D input (0.019), the presence of decreasing returns (0.937) and a strong (unitary) impact of product proliferation. In the light of such results, it is not possible to establish which new R&D-based growth model is better grounded empirically (φ < 1, β = 1, σ > 0). Though, more valuable information is obtained by separately assessing the two large technology-based groups of industries (cols. 6 and 7). On the one hand, a neoclassic-type framework of growth is found to hold for medium- and low-tech sectors (φ = 1, σ = 0, β non definite). On the other hand, 2 FE I is not compatible with product proliferation. 5

6 evidence consistent with the hybrid version of SE framework emerges for high- and medium-tech industries (φ < 1, σ > 0, β (0, 1)). The latter findings are confirmed when attention is paid to high-tech manufacturing only (col. 8), for which we find a larger impact of R&D capital (0.058) and a stronger sterilisation of R&D by product proliferation (β = 0.74). As robustness checks, backward citations are adopted as an alternative measure of innovation quality, providing scarcely conclusive findings (cols. 9-12). This may depend on the derivative nature of such a patent indicator (Hall et al., 2007), which is a powerful conduit of information on innovation quality only for the most technologically advanced manufacturing industries (col. 12); for high-tech sectors, evidence is partially corroborating both SE and FE II (φ < 1, β = 1, σ > 0). Some key findings obtained with forward cites are reaffirmed weighting patents with claims. First, in technologically backward industries, innovation is found to be independent of R&D input (col. 14). Second, although there is no clear-cut evidence for the wide group of high- and medium-tech sectors (col. 15), the empirical model is fully consistent with the SE framework in its original version when only the most knowledge-intensive sectors are considered (φ < 1, σ > 0, β = 0; col. 16). 6

7 Table 2: Cointegration estimates of innovation function Dep: ln Key results Alternative quality indicators Row counts Forward citations Counts Backward citations Counts Claims Counts All Medium- High- High- All Medium- High- High- All Medium- High- High- All Medium- High- High- Low Medium Tech Low Medium Tech -Low Medium -Tech Low Medium Tech Tech Tech Tech Tech Tech Tech Tech Tech LT+MLT HT+MHT HT LT+MLT HT+MHT HT LT+MLT HT+MHT HT LT+MLT HT+MHT HT Ȧ (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11) (12) (13) (14) (15) (16) α1 ln X 0.042** 0.042** 0.045** ** ** 0.058** * ** ** 0.031** ** 0.026** (0.006) (0.007) (0.008) (0.008) (0.008) (0.010) (0.009) (0.012) (0.003) (0.010) (0.002) (0.003) (0.006) (0.011) (0.008) (0.008) α2 ln L ** * 0.021** * 0.054** ** ** ** ** ** ** * ** (0.008) (0.008) (0.010) (0.008) (0.007) (0.021) (0.008) (0.010) (0.002) (0.025) (0.002) (0.002) (0.007) (0.025) (0.007) (0.006) α3 ln A 1.004** 0.978** 1.011** 0.979** 0.937** 0.991** 0.898** 0.914** 1.002** 1.016** 0.999** 0.995** 1.006** 1.027** 0.987** 0.968** (0.008) (0.009) (0.012) (0.012) (0.013) (0.020) (0.014) (0.015) (0.001) (0.006) (0.001) (0.002) (0.006) (0.012) (0.008) (0.011) Wald test φ = 1 (α3 = 1) p-value β = α2/α ND 0.63 ND ND ND Wald test β=0 p-value Wald test β=1 p-value Industries Obs IMPLIED VALUES FOR THEORETICAL PARAMETERS φ =1 <1 =1 <1 <1 =1 <1 <1 >1 >1 =1 <1 =1 >1 =1 <1 β =0 <0 (0,1) ND =1 ND (0,1) (0,1) =0 <0 ND =1 (0,1) ND (0,1) =0 σ >0 >0 >0 =0 >0 =0 >0 >0 <0 <0 =0 >0 >0 =0 >0 >0 MODEL IDENTIFICATION FE I None SE/FE II None SE/FE II NEO SE SE None None NEO SE/FE II SE/FE II None SE/FE II SE Notes: Industry fixed-effects and common time dummies included. Pre-whitened standard errors in parentheses. ND=not definite. ** and * significant at a 5 and 10% level. 7

8 4 Conclusions This paper examined the innovation functions designed by the most recent Schumpeterian growth theories using US manufacturing industry data. In contrast to existing evidence based on innovation counts, when innovation quality is adequately allowed for (forward citations), semi-endogenous growth models are found to outperform other theories especially for the most knowledge-intensive section of the economy. 8

9 References Aghion, P., Howitt, P., A model of growth through creative destruction. Econometrica 60, , Endogenous growth theory. MIT Press, Cambridge. Ang, J. B., Madsen, J. B., Can second-generation endogenous growth models explain the productivity trends in the Asian miracle economies? Rev Econ Stat, forthcoming. Barcenilla-Visús, S. López-Pueyo, C., Sanaú J., Semi-endogenous growth theory versus fully-endogenous growth theory: A sectoral approach. University of Zaragoza, mimeo. Ha, J., Howitt, P., Accounting for trends in productivity and R&D: A Schumpeterian critique of semi-endogenous growth theory. J Money Credit Bank 39, Hall, B. H., Thoma, G., Torrisi, S., The market value of patents and R&D: Evidence from European firms. NBER Work Pap Ser No Jones, C., Time series tests of endogenous growth models. Q J Econ 110, Madsen, J. B., Are there diminishing returns to R&D? Econ Lett 95, , Semi-endogenous versus Schumpeterian growth models: Testing the knowledge production function using international data. J Econ Growth 12, Mark, N., Sul, D., Cointegration vector estimation by Panel DOLS and long-run money demand. Oxf Bull Econ Stat 65, Romer, P., Endogenous technological change. J Polit Econ 98, Segerstrom, P. S., Endogenous growth without scale effects. Am Econ Rev 88,

10 Trajtenberg, M., A penny for your quotes: Patent citations and the value of innovations. Rand J Econ 21, Venturini, F., ICT and productivity resurgence: A growth model for the Information Age. BE J Macroecon, Contributions, 7, article 31. Venturini, F., Looking into the black box of Schumpeterian growth theories: An empirical assessment of R&D races. Università di Perugia, mimeo. 10

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