Identifying Age, Cohort and Period Effects in Scientific Research Productivity: Discussion and Illustration Using Simulated and Actual Data on French Physicists Bronwyn H. HALL (UC Berkeley and NBER) [ [email protected] ] Jacques MAIRESSE (CREST and NBER) [ [email protected] ] Laure TURNER (ENSAE and CREST) [ [email protected] ] 26 June 2005 AbstractHall-Mairesse-Turner June 2005 2 Identifying Age, Cohort and Period Effects in Scientific Research Productivity: Discussion and Illustration Using Simulated and Actual Data on French Physicists1 Bronwyn H. HALL, Jacques MAIRESSE, and Laure TURNER 1 Introduction Empirical studies in the social sciences often rely on data and models where a number of individuals born at different dates are observed at several points in time, and interest centers on the identification of age, cohort, and time or period effects in the relationship of interest. However, modeling and identification of such relationships has proved to be problematic, largely because of the obvious impossibility of observing two individuals at the same point in time that have the same age but were born at different dates. The identification problem is further aggravated if one uses standard panel data estimators in which one takes first differences (or within individual differences) of the variables, in order to control for unobserved individual effects. In this case, the cohort effect disappears completely (because it is collinear with the individual effects), which obscures but does not eliminate the problem of identifying year and age effects simultaneously. A number of “solutions” to this identification problem have been offered in the literature in different contexts (e.g., R. E. Hall 1971, Mason et al. 1973, Rodgers 1982a,b, Mason and Fienberg 1985, Berndt and Griliches 1991), all of which assume restrictions on the specification of the general underlying model, usually by imposing some sort of functional form assumption on the way the three effects enter. Hall (1971) was concerned with disentangling depreciation (the age effect), embodied technical change (the cohort effect), and disembodied technical change (the period effect) in a vintage capital model applied to trucks, in which he imposed the constraint that the two most recent vintages were identical in order to identify the model. Berndt and Griliches (1991) were interested in a problem similar to that 1This is a revision of a paper prepared for the SPRU Conference in Memory of Keith Pavitt at the University of Sussex, 13-15 November, 2003. We are extremely grateful to Serge Bauin and Michele Crance from UNIPS-CNRS, France for their invaluable help in constructing the database of condensed matter physicists.Hall-Mairesse-Turner June 2005 3 confronting Hall: the construction of a hedonic pricing model of personal computers that incorporates technical change, vintage, and age effects. Unlike Hall, they explored and exposited the full range of assumptions available for identification of the additive dummy variable model. At the same time, the problem had not gone unnoticed in the sociological literature, especially as it related to the interpretation of cohort effects. In a series of papers William Mason and his co-authors proposed estimating cohort-age-period models using identification assumptions similar to the one used by Hall (1971). This work culminated in a conference volume published in 1985 (Mason and Fienberg 1985) that provides an excellent overview of the state of the art and the views of sociologists, statisticians, and economists on the problems associated with this kind of modeling, both conceptual and methodological. One of the many domains in which this identification problem is prevalent is the study of the scientific productivity of researchers, where we would like simultaneously to take account of differing productivity over time, as a function of age, and as a function of the vintage of the researcher. Scholars in the sociology of science, and more recently economists, have tried to measure the age-related productivity curve, and to purge it of effects due to the vintage of the researchers and the periods in which they are being observed. A major problem in such analysis is the need to take into account two major tendencies: the exogenous increase of publications with time and with cohort. Descriptive statistics on scientific publications suggest that they tend to increase over time more or less rapidly in many scientific fields, overall but also per researcher. A way to capture such time effects, as well as any general changes in the state of art and work environment is simply to introduce period (year) indicators in the model. In the same manner, it seems that younger cohorts tend to publish more than older ones when they were the same age, which may be related to the fact that there are increased incentives and competition for the younger generations, and/or they are more motivated and better trained, and/or that the cost of publishing is less (with the use of computers and internet, and growing numbers of journals, etc.). However, including cohort indicators (or for that matter individual effects) together with period indicators in the model introduces the aforementioned identification problem with the age variable. In this paper we give an overview of the general identification problem of age, cohort, and period effects in a panel data regression model, of the estimation and interpretation difficultiesHall-Mairesse-Turner June 2005 4 it raises, and propose what we think a practical approach to deal with them (second section); we illustrate these difficulties and the suggested solutions on simulated data (third section), and on a rich longitudinal database of the publications over 20 years (1980-2002) of about 500 French condensed matter physicists (fourth section). We have three goals in undertaking this work: 1) to illustrate the potential for such data to lead to misleading inference if the identification problem is overlooked or not confronted; 2) to discuss the estimation and interpretation of cohort-age-period models when there are individual