Life cycle productivity in academic research: evidence from cumulative publication histories of academic economists.

• Author: Goodwin, Thomas H.

1. Introduction

   Casual observation suggests that the temporal pattern of productivity varies dramatically across individuals, particularly in risky endeavors such as a research career in academia. Some individuals remain productive researchers throughout their career. Others who show early promise become deadwood before their time. Some authors produce papers like a well oiled machine, while others publish at a highly erratic rate.

   Opposing this is a widely held view that there is a common life-cycle component underlying individual productivity. The aging process itself is thought to lead to the initial rise and eventual decline of creative productivity. In addition, human capital models typically imply that investment in skills will decline with age [7]. Both of these ideas suggest that output will be hump-shaped over the life cycle.

   Econometric studies of life cycle productivity have addressed this with regressions which are quadratic functions of age or experience [1; 5]. The quadratic conveniently delivers the sought after hump-shaped pattern in productivity. There are conceptual problems with the quadratic however. It implies a symmetric output path centered on its peak, which is inappropriate if productivity peaks early in the career but remains significant thereafter.

   In addition, data on publishing productivity is heavily affected by the "zeros problem:" the most common number of publications for an active professor in any given year is zero. This requires an estimation procedure designed to accommodate a high probability mass at zero. Levin and Stephan [5] address this problem with the tobit regression. The tobit is a truncated regression model, where in this context publications are distributed as a truncated normal random variable if a vector combination of attributes and coefficients exceeds a threshold level, and are zero otherwise. Although the truncated normal model handles the zeros problem, recent methods have been developed which are designed explicitly for integer counts such as article publications [2]. In this paper we use a Poisson-based regression method which is ideal for count data with a high frequency of zeros.

   This paper studies the temporal distribution of research productivity for a sample of academic economists. Our purpose is descriptive: we do not propose or test a particular theory of productivity. Rather, we measure the variation in productivity over time with methods which are designed to let the data speak. Fortunately, these methods allow the data to say quite a bit, and we take the liberty to speculate on the forces which generate these patterns.

   The data are cumulative histories of research publications obtained from individual vitae. The method relaxes curvature restrictions and imposes distributional assumptions appropriate for integer count data. Specifically, we model article publication as a time dependent Poisson process. Curvature restrictions are relaxed by assuming independence in the probabilities of publishing in successive years. We attempt to characterize the temporal distribution of productivity with a smooth curve only after estimating unrestricted Poisson parameters for each year.

   Our investigation indicates that productivity in economic research rises sharply in the initial stages of a career before encountering a slow decline. Productivity remains significant long after reaching its peak in the early years of a career. We also examine variation in career publication profiles. We document differences in life cycle profiles between high and low-rate publishers. We also consider the effects of different attributes of individuals as manifested in career choices. Some individuals take academic positions such as a department head or journal editor; others spend some portion of their career in government or business. We find that these attributes are strongly related to the timing and level of research productivity.

2. Estimation of the Distribution of Life Cycle Productivity

   The Data

   The sample we analyze consists of 140 tenured professors at 7 research oriented departments.(1) Sauer [10] studied the returns to publishing for this sample with a flexible hedonic wage equation. The data were extracted from individual vitae dated 1982. Our measure of productivity is articles published in refereed journals.(2) The data are right-censored, encompassing the cumulative history of these authors through 1982. Sauer [10] showed that adjustments for article quality and number of authors helped to explain salary variation in this sample, as one would expect. The case that article quality or frequency of co-authorship varies predictably over the life cycle is not as apparent. Although we examined adjustments for quality and co-authorship, we found no evidence that they matter.(3) Hence the data used in this paper count both single-authored and co-authored papers as one publication, with no adjustment for article quality.

   The sample consists of survivors - successful researchers who have been granted tenure at research oriented universities.(4) There are good reasons for studying such a group. First and foremost, we know that publishing productivity is heavily skewed in samples of Ph.D. recipients: the modal number of articles for individuals with at least one article is, in fact, one [11]. A study of life cycle productivity based on a sample of all Ph.D. economists who received their degree in 1960 would be severely compromised by this fact. Hence, to study life cycle productivity in research, it makes sense to focus our attention on scholars at research-oriented institutions where journal publication is important. In light of this, we further restrict our sample to authors with at least 1 refereed article. This leaves us with a sample of 132 individuals with one or more lifetime articles.

   Table I provides summary statistics for the sample, disaggregated into life cycle periods. Each row in the table corresponds to a five or ten year period in the life cycle, with year 0 denoting the year the Ph.D. was received. For each period, Indiv indicates the number of individuals with experience at least equal to the minimum year in each range. The table lists the mean number of articles published per year (per active person), the variance, and the relative frequency of article counts for each period. Moving down the third column of the table, we find that the mean number of publications is highest in the first two post-Ph.D. periods, and is sharply lower, though still significant thereafter. The most common number of publications for a given year is zero throughout the life cycle.

   Estimation of a Compound Poisson Model

   Table I clearly indicates that productivity declines in the latter stages of the life cycle. We now attempt a more precise and comprehensive documentation of this pattern. We do this by modeling publishing as a time dependent Poisson process. Let [A.sub.i[Tau]] represent the number of articles published by individual i in period [Tau]. The Poisson model gives the probability that individual i publishes A articles at period [Tau] as:

   [Mathematical Expression Omitted]!

   The model implies that the expected number of articles published in year [Tau] for individual i is E[[A.sub.i[Tau]]] = [[Lambda].sub.i[Tau]]. Let [X.sub.i[Tau]] be a vector of individual characteristics and [Beta] a coefficient vector. We incorporate individual and time specific effects through

   [[Lambda].sub.i[Tau]] = exp([X.sub.i[Tau]] [center dot] [Beta])

   which ensures non-negativity of [[Lambda].sub.i[Tau]]. We consider four sources of variation in [[Lambda].sub.i[Tau]] at this stage of estimation: the scholar's ability, vintage of her Ph.D., academic affiliation, and stage of the life cycle.

   More able researchers clearly have a higher probability of publishing in any given year. If all individuals had complete careers of, say 40 years, we could control for individual ability by including total lifetime publications as a regressor. This is the approach of Hausman, Hall, and [TABULAR DATA OMITTED] Griliches [4] in their study of patents. However, our sample consists of right-censored careers of varying lengths, with the publication rate varying over the career. We must therefore use an imperfect control for ability. We define quintile rankings based on publication rates within each cohort of experience. Thus, individuals in the top quintile of the youngest cohort receive...