Assessing the contribution of R&D to total factor productivity—a Bayesian approach to account for heterogeneity and heteroskedasticity
Tóm tắt
This paper proposes a hierarchical Bayes estimator for a panel data random coefficient model with heteroskedasticity to assess the contribution of R&D capital to total factor productivity. Based on Hall (1993) data for 323 US firms over 1976–1990, we find that there appear to have substantial unobserved heterogeneity and heteroskedasticity across firms and industries that support the use of our Bayes inference procedure. We find much higher returns to R&D capital and a more pronounced downswing for the 1981–1985 period, followed by a more pronounced upswing than those yielded by the conventional feasible generalized least squares estimators or other estimates. The estimated elasticities of R&D capital are 0.062 for 1976–1980, 0.036 for 1981–1985 and 0.081 for 1986–1990, while the estimated elasticities of ordinary capital are much more stable over these periods.
Tài liệu tham khảo
Amemiya, T.: The estimation of the variance in a variance-component model. Int. Econ. Rev. 12, 1–13 (1971)
Baltagi, B.H.: An alternative heteroscedastic error component model, problem 88.2.2. Econom. Theory 4, 349–350 (1988)
Baltagi, B.H., Griffin, J.M.: A generalized error component model with heteroscedastic disturbances. Int. Econ. Rev. 29, 745–753 (1988)
Baltagi, B.H., Bresson, G., Pirotte, A.: Adaptive estimation of heteroskedastic error component models. Econom. Rev. 24, 39–58 (2005)
Baltagi, B.H., Bresson, G., Pirotte, A.: Joint LM test for homoskedasticity in a one-way error component model. Econom. J. 134, 401–417 (2006)
Basu, S., Chib, S.: Marginal likelihood and Bayes factors for Dirichlet process mixture models. J. Am. Stat. Assoc. 98, 224–235 (2003)
Bresson, G., Hsiao, C., Pirotte, A.: Assessing the contribution of R&D to total factor productivity. A Bayesian approach to account for heterogeneity and heteroscedasticity, Working paper 07-08, Ermes, Université Paris II (2007)
Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer Series in Statistics. Springer, Berlin (1991)
Carlin, B.P., Louis, T.A.: Bayes and Empirical Bayes Methods for Data Analysis. Chapman & Hall/CRC Press, London/Boca Raton (2000)
Chib, S.: Panel data modeling and inference: a Bayesian primer. In: Màtyàs, L., Sevestre, P. (eds.) The Econometrics of Panel Data: Fundamentals and Recent Developments in Theory and Practice, pp. 479–516. Kluwer Academic, Norwell (2008)
Friedman, M.: Essays in Positive Economics. University of Chicago Press, Chicago (1953)
Gelfand, A.E., Smith, A.F.M.: Sampling-based approaches to calculating marginal densities. J. Am. Stat. Assoc. 46, 84–88 (1990)
Griliches, Z.: Issues in assessing the contribution of research and development to productivity growth. Bell J. Econ. 10, 92–116 (1979)
Hall, B.H.: Industrial research during the 1980s: did the rate of return fall? Brookings papers on Economic Activity. Microeconomics 2, 289–343 (1993)
Hsiao, C.: Statistical inference for a model with both random cross-sectional and time effects. Int. Econ. Rev. 15, 12–30 (1974)
Hsiao, C.: Some estimation methods for a random coefficient model. Econometrica 43, 305–325 (1975)
Hsiao, C.: Analysis of Panel Data, Econometric Society Monographs. Cambridge University Press, Cambridge (2003)
Hsiao, C.: Panel data analysis—advantages and challenges. Test 16, 1–22 (2007)
Hsiao, C., Pesaran, M.H.: Random coefficients panel data models. In: Màtyàs, L., Sevestre, P. (eds.) The Econometrics of Panel Data: Fundamentals and Recent Developments in Theory and Practice, pp. 185–214. Kluwer Academic, Norwell (2008)
Hsiao, C., Tahmiscioglu, A.K.: A panel analysis of liquidity constraints and firm investment. J. Am. Stat. Assoc. 92, 455–465 (1997)
Hsiao, C., Appelbe, T.W., Dineen, C.R.: A general framework for panel data analysis—with an application to Canadian customer dialed long distance service. Econom. J. 59, 63–86 (1993)
Hsiao, C., Pesaran, M.H., Tahmiscioglu, A.K.: Bayes estimation of short-run coefficients in dynamic panel data models. In: Hsiao, C., Lahiri, K., Lee, L.-F., Pesaran, M.H. (eds.) Analysis of Panels and Limited Dependent Variable Models, pp. 268–296. Cambridge University Press, Cambridge (1999)
Klein, L.R.: The statistical approach to economics. Econom. J. 37, 7–26 (1988)
Li, Q., Stengos, T.: Adaptive estimation in the panel data error component model with heteroskedasticity of unknown form. Int. Econ. Rev. 35, 981–1000 (1994)
Lindley, D.V., Smith, A.F.M.: Bayes estimates for the linear model. J. R. Stat. Soc. B 34, 1–41 (1972)
Magnus, J.R.: Multivariate error components analysis of linear and non-linear regression models by maximum likelihood. Econom. J. 19, 239–285 (1982)
Mairesse, J., Sassenou, M.: R&D and productivity: a survey of econometric studies at the firm level. Sci. Technol. Ind. Rev. 8, 317–348 (1991)
Mazodier, P., Trognon, A.: Heteroskedasticity and stratification in error components models. Ann. INSEE 30–31, 451–482 (1978)
Murtazashvili, I., Wooldridge, J.M.: Fixed effects instrumental variable estimation in correlated random coefficient panel data models. Econom. J. 142, 539–552 (2008)
Phillips, R.F.: Estimation of a stratified error-components model. Int. Econ. Rev. 44, 501–521 (2003)
Randolph, W.C.: A transformation for heteroscedastic error components regression models. Econ. Lett. 27, 349–354 (1988)
Rao, S.R.S., Kaplan, J., Cochran, W.C.: Estimators for the one-way random effects model with unequal error variances. J. Am. Stat. Assoc. 76, 89–97 (1981)
Roy, N.: Is adaptive estimation useful for panel models with heteroskedasticity in the individual specific error component? Some Monte Carlo evidence. Econ. Rev. 21, 189–203 (2002)
Swamy, P.A.V.B.: Efficient inference in a random coefficient regression model. Econometrica 38, 311–323 (1970)
Wakefield, J.C., Smith, A.F.M., Poon, A.R., Gelfand, A.E.: Bayesian analysis of linear and non-linear population models by using the Gibbs sampler. Appl. Stat. 43, 201–221 (1994)
Wansbeek, T.J.: An alternative heteroscedastic error components model, solution 88.1.1. Econom. Theory 5, 326 (1989)
Zellner, A.: Bayesian analysis in econometrics. Econom. J. 37, 27–50 (1988)