Econometric Models for Count Data with an Application to the Patents-R&D Relationship

This paper focuses on developing and adapting statistical models of counts (non-negative integers) in the context of panel data and using them to analyze the relationship between patents and RD persistent individual (fixed or random) effects, and "noise" or randomness in the Poisson probability function. We apply our models to a data set previously analyzed by Pakes and Griliches using observations on 128 firms for seven years, 1968-74. Our statistical results indicate clearly that to rationalize the data, we need both a disturbance in the conditional within dimension and a different one, with a different variance, in the marginal (between) dimension. Adding firm specific variables, log book value and a scientific industry dummy, removes most of the positive correlation between the individual firm propensity to patent and its R&D intensity. The other new finding is that there is an interactive negative trend in the patents - R&D relationship, that is, firms are getting less patents from their more recent R&D investments, implying a decline in the "effectiveness" or productivity of R&D.

[1]  Z. Griliches,et al.  Who Does R&D and Who Patents? , 1982 .

[2]  J. Neyman,et al.  Consistent Estimates Based on Partially Consistent Observations , 1948 .

[3]  Erling B. Andersen,et al.  The Numerical Solution of a Set of Conditional Estimation Equations , 1972 .

[4]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[5]  H. Chernoff,et al.  The Use of Maximum Likelihood Estimates in {\chi^2} Tests for Goodness of Fit , 1954 .

[6]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[7]  D. Cox,et al.  A General Definition of Residuals , 1968 .

[8]  M. Greenwood,et al.  An Inquiry into the Nature of Frequency Distributions Representative of Multiple Happenings with Particular Reference to the Occurrence of Multiple Attacks of Disease or of Repeated Accidents , 1920 .

[9]  Jerry A. Hausman,et al.  Panel Data and Unobservable Individual Effects , 1981 .

[10]  E. B. Andersen,et al.  Asymptotic Properties of Conditional Maximum‐Likelihood Estimators , 1970 .

[11]  J. Hausman.  Specification tests in econometrics , 1978 .

[12]  David R. Cox.  The analysis of binary data , 1970 .

[13]  A. Pakes,et al.  The Estimation of Distributed Lags in Short Panels , 1980 .

[14]  Y. Mundlak.  On the Pooling of Time Series and Cross Section Data , 1978 .

[15]  Shelby J. Haberman,et al.  Maximum Likelihood Estimates in Exponential Response Models , 1977 .

[16]  Calyampudi R. Rao,et al.  Advanced Statistical Methods in Biometric Research. , 1953 .

[17]  P. McCullagh,et al.  Generalized Linear Models , 1984 .

[18]  D. McFadden.  Conditional logit analysis of qualitative choice behavior , 1972 .

[19]  A. Pakes,et al.  Patents and R&D at the Firm Level: A First Look , 1984 .