Economists' salaries and lifetime productivity.

I. Introduction

One of the advantages of studying academic labor markets is that many facets of productivity are easily measured. This makes it possible to study the relationship between pay and productivity. There has been some debate whether labor markets are auction markets, where salaries equal expected near-term productivity, or are characterized by implicit long-term contracts. In this paper, we test these propositions directly, and perhaps for the first time, using data from the academic labor market. We show that economists' salaries are best described as reflecting implicit long-term contracts.

Weiss and Lillard [14] modelled the determination of academic salaries when a professor's productivity changes over time, perhaps due to luck in creativity or shifts in opportunities for productive research. They concluded that if there are no costs to mobility, then the salary must equal the professor's immediate expected productivity. Competition among universities for faculty forces salaries to equal expected productivity in the near term. With positive costs of mobility, this spot market relationship is severed, causing salaries to be less sensitive to new information about expected productivity. In particular, the cost of mobility creates a wedge that allows increases (decreases) in expected near term productivity to not always be matched by wage increases (decreases). In fact, if mobility is sufficiently costly, "the contract provides perfect insurance against individual failure and a stable salary stream over time" [14, 162]. Since salary does vary over an academic's career, the stable salary stream scenario is empirically irrelevant. The question then is whether professors are paid according to their expected near-term productivity or according to some implicit long-term contract that might place a greater weight on early productivity.

What factors determine a faculty member's productivity in a university? Let us assume that universities are concerned with their contribution to the advancement of knowledge (or their reputation for doing so) and teaching. A university's current reputation for advancing knowledge depends on its current publications and citations.(1) A university is not directly interested in rewarding faculty for previous publications and citations, since these do not enhance its current reputation. In the university's struggle for prestige, contributions to academic debates two decades ago that are forgotten (i.e., no longer cited) count for little. A faculty member's current productivity thus is a function of his current articles, current citations, current contribution to teaching, and the role he plays in running the school.

We use a rich data set of economists from 10 large public universities, which has life cycle data on publications and citations taken from the Social Science Citation Index. To test the zero-mobility-cost hypothesis that salaries are determined by currently expected near-term productivity, we create estimates of expected biennial publications and citations for each economist. Our method uses individual-specific quadratic time-trend regressions to predict the flow of current publications and citations. To capture costly mobility, we create discounted stocks of articles and citations and find the discount rates that best explain salaries. With these discounted stocks, earnings are potentially less sensitive to fluctuations in productivity over the life cycle, as would be the case with costly mobility. We then compare the fit obtained using our measures of predicted articles and citations with the fit obtained using these measures of how salaries might be determined under implicit contracts and find that the costly mobility estimates perform better.

Our discounted stock specification is a novel approach to describing the relationship between salaries and productivity. As Hamermesh, Johnson, and Weisbrod [6, 474] note, "it is unclear a priori whether a lifetime stock or a current or recent flow is the more appropriate measure of a scholar's contribution to the intellectual community." Many studies have found a positive relationship between salaries and the undiscounted stock of publications. Also, Holtman and Bayer [8], Hamermesh, Johnson, and Weisbrod [6], Diamond [3], and Sauer [13] have shown that the flow of recent citations also affects earnings, and Hamermesh, Johnson, and Weisbrod [6, 487] furthermore conclude that "it is not worthwhile to build measures of the lifetime stock of references." Does the literature's practice of applying a zero discount rate to past publications and an infinite discount rate to past citations create discounted stocks of articles and citations that best explain academic salaries? We search for the discount rates that do and then probe the underpinnings of this specification further by testing whether salaries are better explained by the currently expected flows of citations and publications. We hope that by shedding some light on the specification issue, we will also gain insight into the more fundamental question of whether or not academic labor markets are spot markets.(2)

The other thrust of our work is to examine the impact of journal quality on salary. When Sauer [13] found that publishing in a higher quality journal is rewarded, he used an impact-adjusted citation frequency ranking, developed by Liebowitz and Palmer [11], to measure journal quality. They ranked 108 journals as of 1980. Since then, many new economic journals have sprung up, such as Journal of Economic Behavior, Journal of Health Economics, Journal of International Money and Finance, Journal of Labor Economics, Journal of Labor Research, and Journal of Economic Perspectives. A quality measure that is easily updated would be useful. A broader measure that includes journals less commonly utilized by economists also would be useful. Liebowitz and Palmer's [11] ranking excludes American Political Science Review, AREUEA Journal, Decision Sciences, Harvard Law Review, American Journal of Agricultural Economics, Journal of Forecasting, Management Science, and Science, for example. The quality measure we will use in this study satisfies both these concerns. The Social Science Citation Index (SSCI) annually publishes an impact factor for each journal [5]. The present study uses the 1986 impact factor, which equals the number of citations in 1986 to a journal's articles in 1984 and 1985 divided by the number of articles written in the journal in 1984 and 1985.(3) Some representative impact factors are 2.146 for Econometrica, 1.881 for American Economic Review, 1.231 for Journal of Money, Credit, and Banking, .808 for Journal of Human Resources, .652 for Canadian Journal of Economics, .433 for Southern Economic Journal, .284 for Applied Economics, and .184 for Cato Journal. Levin and Stephan [10] have found salary growth in physics and earth science to be related to SSCI's measure of publication quality. We provide perhaps the first evidence on the relationship between this quality variable and academic salaries in the social sciences.

II. Data Set

Taking advantage of "public access" provisions found in many state governments, we obtained nine month salary data for 1987-88 for economics departments in ten large public universities. These departments ranked from the low teens to the high seventies, with a mean rank of 40 [7].(4) We then gathered detailed data from the Social Science Citation Index [9] on the timing of publications and citations over their careers. The number of publications (adjusted for the number of authors), the quality of journals in which they were published, the number of citations, and the quality of the journals in which the citations appeared were collected for the following nine periods: 1966-70, 1971-72, 1973-74, 1975-76, 1977-78, 1979-80, 1981-82, 1983-84, and 198586.(5) To make the task manageable, we started with the year in which the professor received his or her Ph.D. and thus deleted a small number of economists for whom we could not ascertain the date of degree. In order to have enough life cycle observations for our time trend predicting regressions, we restricted our sample to those who received their Ph.D.s prior to 1979 (i.e., those with more than 8 years of "experience"). We also dropped individuals who, 1) because of a common last name and initials were difficult to isolate in the Social Science Citation Index [9]; 2) specialized in other fields, such as anthropology, finance, geography, or marketing; 3) held or had held administrative posts other than chairman, such as chancellor, president, or dean; 4) were vice-chairmen; 5) were institute directors and whose salary increment for these additional duties was unavailable; or 6) were members of the editorial board of a journal in which the editors published frequently.(6)

III. Quality Specification

Before turning to the empirical results, let us consider how best to specify the quality relationship. There are several reasons why a transformation of the impact factor may provide a better measure of quality than the raw impact factor. A journal with double the impact factor of another journal might not be valued doubly by universities. Also, some journals and all articles in books were not given an impact factor in the Social Science Citation Index or in the Science Citation Index [5]; we assigned to these a zero impact factor even though they certainly have some value.

We therefore report results based on the following weighted transformation of the impact factor:

[QUAL.sub.cij] = [Beta] [center dot] IMPACT [FACTOR.sub.cij] + (1 - [Beta]) [center dot] 1

[QUAL.sub.aij] = [Beta] [center dot] IMPACT [FACTOR.sub.aij] + (1 - [Beta]) [center dot] 1.

To illustrate, [QUAL.sub.cij] is the transformed average impact factor for citations received in period i by economist j, and IMPACT [FACTOR.sub.cij] is the average impact factor of the journals in which economist j's citations were received in period i.(7) [QUAL.sub.aij] is similarly defined for publications. This formulation assigns (1 - [Beta]) to articles in uncited journals or to articles in unlisted journals or in books, for which there is no impact factor. A unit rise in the impact factor leads to a [Beta] increase in this quality measure. Our search over [Beta] for the value that minimized the mean squared errors in the salary regressions will be described in more detail below.

IV. Predicting Publication and Citation

Individual Time Trend Regressions

Our best predictions of articles and citations published in 1987-88 are based on quadratic time-trend citation and publication regressions that have been estimated for each of the economists in our sample. We first estimate:

[Mathematical Expression Omitted]

[Mathematical Expression Omitted]

for each economist j, where [QUAL.sub.aij] is the transformed average impact factor for articles published in period i by economist j and [ART.sub.ij] represents the number of articles published in period i by economist j.(8) ELAPSED [TIME.sub.i] equals the time (in two year units) between period i and 1987-88; for example, ELAPSED TIME equals 2 for 1983-84. These regressions, which are illustrated in Figure 1, allow us to take advantage of the fact that publication and subsequent citation often rise and then fall over academic careers. The regressions can accommodate wide variation among our academics in the shapes of their publication and citation profiles. Of course, there is a great deal of noise in publications over time, which makes many of the estimates of [[Tau].sub.2j] and [[Tau].sub.3j] insignificant.

Since very little is published in the year in which the Ph.D. was received and in the subsequent year, these years were not included in our regressions. As noted above, productivity data have been gathered in two year intervals. Since we required at least four data points for each regression, our sample consists of those with at least 9 years of experience; our experience measure [EXPERIENCE.sub.87] equals the number of years as of 1987 since receiving the Ph.D.(9) This yields a sample of 145 senior economists, who have an average of 18 years of experience and up to 41 years of experience.

The spot market time trend regressions utilize all the life cycle data available as of 1987 and are based on between four and nine observations.(10) The results of the 145 individual time trend publication regressions and 145 individual time trend citation regressions are illuminating. Summary statistics for these coefficients and for other variables used in our study are reported in Table I.

The estimated annual change in quality-adjusted publications (as of 1987-88, when ELAPSED TIME=0) equals - [[Tau].sub.2j]/2. Eighty eight percent of these estimates are negative, indicating that for the vast majority of this sample there has been a decline in publication in recent years. The mean and median rates of decline in quality adjusted publications are, however, quite small (.081 and .035, respectively). Eighty eight percent of those whose publications are estimated to be declining (i.e., those with -[[Tau].sub.2j] [less than] 0) have publications that are estimated to have peaked sometime earlier in their career. For this group, publication peaked -[[Tau].sub.2j]/(2 [multiplied by] [[Tau].sub.3j]) two year periods, or [[Tau].sub.2j]/[[Tau].sub.3j] [TABULAR DATA FOR TABLE I OMITTED] years, earlier. This estimate can be combined with the individual's current labor market experience to arrive at an estimate of how long the faculty member had been working before his rate of publication peaked.(11) Three quarters of these estimates fall between 5.1 and 9.2 years after the professor received his Ph.D.

The coefficients from the citation regressions can be utilized in the same fashion. For ninety six percent of these economists, citations are estimated to have been falling in recent years. The mean and median estimates of the annual rate of recent decline in citations equal .714 and .394, respectively. The citations for ninety nine percent of those with declining citations are estimated to have peaked earlier. For three quarters of this subsample, citations peaked 6.8 to 12.6 years after receiving the Ph.D. Given the lag between publication and citation, it is reassuring that citations are estimated to peak later in the academic career than publications.

Discounted Stock Regressions

Predictions of the flow of new publications (citations) also could be based on the discounted stock of an economist's publications (citations). For example, define

DISC ART [STOCK.sub.79-84,j] = QUAL [ART.sub.83-84,j]/[(1 + [r.sub.a]).sup.2] + QUAL [ART.sub.81-82,j]/[(1 + [r.sub.a]).sup.4] + QUAL [ART.sub.79-80,j]/[(1 + [r.sub.a]).sup.6]

where DISC ART [STOCK.sub.79-84,j] equals the discounted stock of publications over 1979-84 of economist j, QUAL [ART.sub.i,j] equals his quality weighted publications in period i ([QUAL.sub.aij] [multiplied by] [ART.sub.ij]), and [r.sub.a] is the discount rate applied to every economist's stream of publications. The discounted stock of citations, with discount rate [r.sub.c], is similarly defined. We searched for the discount rates on past publications and citations that best explain publications and citations, respectively, in 1985-86. Since the stocks are being used to explain recent flows, the stocks are based on only those years in which all in our sample had left graduate school.

For publications, the best fit was obtained with a discount rate of 65 percent. This implies that, to explain publications in 1985-86, a publication in 1983-84 is equivalent to 8 publications in 1981-82 and 67 publications in 1979-80.

[Mathematical Expression Omitted]

where [Beta] = .88, OBSERVATIONS = 145, ADJUSTED [R.sup.2] = .3577, ROOT MEAN SQ ERROR = .981, and T-statistics are in parentheses. The stock of past publications clearly has some success in explaining current publications.

For citations, the fit continued to improve as the discount rate increased, and we stopped searching at a discount rate of 99 percent. Basically, only the most recent citations are useful for predicting current citations, and this relationship is quite significant.

[Mathematical Expression Omitted]

where [Beta] = .88, OBSERVATIONS = 145, ADJUSTED [R.sup.2] = .8460, and ROOT MEAN SQ ERROR = 8.221.

We do not claim that the predictions of current flows of articles and citations based on discounted stocks of articles and citations are the best predictions. These predictions suffer from being based on a common discount rate for all academics and from coming out of regressions that do not fully utilize the individual's time pattern of citation or publication. Nevertheless, these predictions make it possible to compare the discount rates that best explain salaries with the discount rates that best predict citation and publication, which provides some insight into whether academic salaries reflect spot pay or an implicit long-term contract.

V. Salary Regressions

The 1987-88 salary regressions that are found in Table II are the product of some specification testing. We report regressions with the natural logarithm of salary as the dependent variable, because a Box-Cox test showed it to dominate salary as a regressand [12, 178-79]. We found no evidence that the absolute value of the errors increased with experience; our productivity measures seem to have kept this form of heteroskedasticity under control. Our independent variables include the various productivity measures, experience, two dummies indicating whether the individual is the department chair or a female, and nine university dummies. We also estimated regressions which included experience squared and dummy variables for fields of specialization; these variables were quite insignificant, and the regressions are not reported. Apparently, any field effects are picked up by the productivity measures. We, like others working in this area, are unable to control for individual differences in teaching and service effectiveness across universities.

Quadratic Time Series Predictions: Spot Market Specification

Predicted values for publications in 1987-88 [E ([ARTICLES.sub.87-88)TS = [[Tau].sub.1j]]] and citations in 1987-88 [E [([CITATIONS.sub.87-88).sub.TS] = [[Rho].sub.1j]]] that are based on the 145 individual quadratic time-series [TABULAR DATA FOR TABLE II OMITTED] regressions described in section IV are used in the first regression in Table II.(12) The use of this set of predicted values is based on the assumption that salaries are determined in a spot market, in which rewards are based on the best estimate of expected near term productivity.

We searched for the quality parameter [Beta] that produced the best fit under this specification and estimated [Beta] to be .25, which implies

[QUAL.sub.ij] = .75 + .25 [multiplied by] IMPACT [FACTOR.sub.ij].

Accordingly, weights of .75, .95, and 1.22, respectively, are assigned to articles in a book, the Journal of Human Resources, and the American Economic Review. A likelihood ratio test accepts the null hypothesis that journal quality is unimportant (i.e., [Beta] = 0); the [[Chi].sup.2] statistic equals 0.53, with one degree of freedom. Our use of the SSCI impact factor to measure the quality of publication therefore receives little support in this sample.(13)

The significantly positive coefficients on expected publications for 1987-88 [E [([ARTICLES.sub.87-88)TS]]] and on expected citations [E [([CITATIONS.sub.87-88)TS]]] and the significantly negative coefficients on their squared terms imply that these quality measures have positive but diminishing effects on the log of salary. A doubling of quality-adjusted predicted biennial citations from 9 to 18 is associated with an 10 percent increase in salaries on average. Similarly, roughly doubling the number of quality-adjusted publications for 1987-88 (from 1 to 2) leads to a 9 percent higher salary. Publications and citations together account for 20 percent of salaries on average in this sample.(14)

Why are these productivity relationships quadratic? If schools were only concerned with advancing knowledge, the reward for publications and citations would be constant. But in fact expected publication and citation have a diminishing effect on salaries. We interpret this as reflecting the diminishing effect that one scholar's annual productivity has on a school's reputation. For example, Stanford's reputation would be altered less if Stiglitz published one more article each year than if a more typical professor published one more article annually.

Linear Time Series Predictions: Spot Market Specification

The second regression in Table II utilizes publication and citation predictions that are based on a simpler linear time series specification, which restricts [[Tau].sub.3j] and [[Rho].sub.3j] to equal 0. These predictions are less successful in explaining economists' salaries, with a 10 percent lower adjusted [R.sup.2], than are the predictions derived from the quadratic time series regressions. The linear and quadratic specifications can be more formally compared using the J test for nonnested models, which was proposed by Davidson and McKinnon [2]. Predicted values are generated from the first and second regressions in Table II, and each model is reestimated using the predicted values from the competing model as an additional regressor. When a variable representing predicted values from the linear specification is included in the quadratic specification, its coefficient is insignificant, with a t-statistic of 1.11, indicating that the quadratic specification is the correct model. Conversely, a variable representing predicted values from the quadratic specification has a t-statistic of 4.40 in the linear model, leading us to reject the linear time series model in favor of the quadratic specification. Academic institutions apparently show some sophistication in determining faculty salaries.

Distributed Lags: Implicit Contract Specification

With costly mobility, early productivity may receive more weight than would be justified under a spot market. We capture this aspect of implicit long-term contracts by relating professors' salaries to discounted stocks of citations and publications over their career, instead of to the expected flows of citations and publications in 1987-88 used in the first two regressions in Table II. Define

[DISC ART STOCK.sub.j] = [QUAL ART.sub.85-86,j]/[(1 + [r.sub.a]).sup.2] + [QUAL ART.sub.83-84,j]/[(1 + [r.sub.a]).sup.4] + . . . + [QUAL ART.sub.66-70,j]/[(1 + [r.sub.a]).sup.19.5]

The third regression in Table II reports the outcome of a search over values of the discount rates [r.sub.a] and [r.sub.c] and the weight on quality [Beta] for the triplet that produced the best fit. [Beta] was found to equal .88. That is, in the discounted stock specification, each article is worth .12 +. 88 [multiplied by] IMPACT FACTOR. Once again, however, the restriction that [Beta] equal zero is not rejected in a likelihood ratio test ([[Chi].sup.2] = 2.53, 1 d.f.). That is, this regression provides little evidence that publishing in a better journal is indeed rewarded.

We found that the discount rate on citations ([r.sub.c]) was zero and that the discount rate on articles ([r.sub.a]) was .28. An article written 5 years ago thus receives only 19 per cent of the compensation for an article written today. Likelihood ratio tests strongly reject the restrictions that the discount rate on citations equals the discount rate that we found for publications (.28) [[[Chi].sup.2] = 11.08, 1 d.f.] and that [r.sub.a] equals zero [[[Chi].sup.2] = 8.39, 1 d.f.]. Another likelihood ratio test rejects at the 95 percent confidence level the restrictions that the discount rates are equal (.07) [[[Chi].sup.2] = 6.36, 2 d.f.; [Mathematical Expression Omitted]].

In section IV, a discounted stock of past publications (citations) was used to explain current publications (citations). Current productivity was best explained using discount rates of .66 and .99 for publications and citations, respectively. The fourth regression in Table II examines how successful these current productivity discount rates are in explaining salaries. A likelihood ratio test strongly rejects the restrictions that these are the appropriate discount rates for determining salaries ([[Chi].sup.2] = 24.36). Much lower discount rates (.28, .00) are used to determine salaries than to explain current productivity. Thus, academic salaries extend the influence of early productivity well past the point at which it has lost its usefulness in explaining current productivity.

The first regression in Table II utilizes better estimates of current productivity, based on individual time series regressions, than does the fourth regression. These better estimates of current productivity are more successful in explaining economists' salaries than the discounted stock current productivity estimates employed in the fourth regression but still do not explain salaries as well as the unrestricted discounted stock specification in the third regression. The explanatory power of the specifications in the first and third regressions can be compared using a J test. Predicted values from the unrestricted discounted stock specification (regression 3) are significant (t = 3.11) when added to the predicted flow specification, and predicted values from the first regression are an insignificant addition (t = 0.86) to the unrestricted distributed lag specification of the third regression. Together these results imply that academic salaries are better characterized as being determined by discounted stocks of publications and citations than by expected near-term productivity. These markets do not appear to be spot markets.

Finally, we compare our discounted stock specification with the specification commonly utilized in the academic salary literature. The practice in this literature of simply adding up publications and of utilizing only recent citations amounts to assuming that the discount rates on publication and citation are zero and infinity, respectively. These restriction are incorporated in the fifth regression in Table II and are rejected by a likelihood ratio test ([[Chi].sup.2] = 17.82, 2d.f.). In the academic market, prior citations have a longer influence and prior publications have a shorter influence than the literature would suggest.

Let's now consider the productivity coefficients of the preferred third regression. Doubling the discounted stock of articles from 1.5 to 3 is estimated to result in 8.6 percent higher wages. Similarly, doubling the undiscounted stock of citations from 60 to 120 leads to a 11.6 percent higher salary. Citations appear to be more important than publications in determining salary.

Other Results

Turning to the other results for these regressions, we find that department heads (HEAD = 1) receive a large compensation for their unusual administrative skills or the time spent running the department.(15) Salaries are estimated to rise as [EXPERIENCE.sub.87] increases at about 1 percent per year, perhaps because of expanding responsibilities in supervising students or running the university. The coefficient of FEMALE in the third regression is not quite significant at the 10 percent level using a 2-tailed test, suggesting that females earn no less than males when article production, citations, and time since Ph.D. are held constant. The results for the nine school dummies are not reported in Table II; these dummies control for differences in the cost of living, locational amenities, and job conditions (e.g., quality of students and colleagues, teaching load).

VI. Conclusion

This research yields a number of interesting results for the traditional academic salary literature. Although the Social Science Citation Index's [5] impact factor improves the fit, it does not significantly do so. Liebowitz and Palmer's [11] measure of the quality of economics journals may be more useful for determining salaries in economics. We also find that salaries continue to rise with experience in this sample of senior economists, after adjusting for citations and publications. Since this is past the point when most would expect there to be improvements in teaching performance, this may reflect a growing effectiveness in supervising students or administering the university. Finally, we find no strong evidence of sexual discrimination.

Our research has focused on the correct specification of the relationship between academic salaries and life cycle measures of productivity. After searching over discount rates associated with discounted stocks of past publications and citations, we found that salaries are best explained using a zero rate of discount on citations and a moderately high (28%) rate of discount on publications. The empirical literature on academic salaries uses recent flows of citations and undiscounted life cycle stocks of articles to explain academic salaries, which gives too little weight to early citations and too much weight to early publications.

With costless mobility, salaries should be based on expected productivity at that moment. Costly mobility, in contrast, makes salaries less sensitive to fluctuations over time in expected productivity. Indirect evidence on the cost of mobility comes from comparing the fits obtained with the different specifications. The distributed lag specification discounts past citations and publications at lower rates than would predict current productivity and thus is compatible with an implicit long-term contract. This long-term contract specification is more successful in explaining salaries than is a spot market specification that utilizes individual-specific predicted publications and citations. Academic markets give early citations and publications more weight than they would warrant under a spot market. Thus, we have indirect evidence that academic mobility is costly, which seems necessary to explain the institution of tenure.

Joy Czerwonky, Subhasis Das, Valerie Hartung, Chiang Kim, and Brian Thomas assisted in gathering the data. We have benefitted from comments from James Adams, Jeff Biddle, George Borjas, Arthur Diamond Jr., David Denslow Jr., Mary Horney, Prakash Loungani, G. S. Maddala, John McDowell, Mark Rush and Nachum Sicherman.

1. The total number of citations is a flawed measure of a university's prestige, since some citations criticize the article being cited. Nevertheless, Cole and Cole [1] suggest that this problem is unimportant empirically.

2. See also Diamond [4], who utilizes wage growth data to distinguish between incentive and learning models of salary determination.

3. The drawback to using the impact factor is that it is not sensitive to the economic content of a journal. It assigns, for example, a greater weight to a citation in the Harvard Law Review than to one in the Quarterly Journal of Economics.

4. The universities are Arizona State, Auburn, Florida, Florida State, Houston, Illinois, Iowa, Michigan State, North Carolina, and North Carolina State.

5. Following Sauer [13], each article is weighted by one over the number of authors. Book reviews, editorials, letters, and meeting abstracts are not included as publications. Self-citations are not counted. The Social Science Citation Index [9] does not list books as publications, but Sauer [13] and others have found that books do not significantly affect economists' salaries. In the Social Science Citation Index [9], citations are only accorded to the first author of a multiple-authored article; Diamond [3] found no improvement in the fit when he corrected for this deficiency.

6. Two economists, who received many more citations than any others in our sample, were dropped because of the unjustifiably large cost in gathering data on their citations, which would have produced two outliers in our sample.

7. We also tried the exponential transformation used by Sauer [13]:

[Mathematical Expression Omitted]

The disadvantage of this transformation is that it places no value on articles published in uncited or unlisted journals or published in books. Similar results were obtained from both quality measures.

8. Note that for those who received their Ph.D. before 1966 the dependent variables for the period 1966-70 have been divided by 2.5, so that all observations measure biennial productivity.

9. Difficulties associated with eliminating the year in which the Ph.D. was received and the subsequent year from these regressions in the five year interval 1966-70 also necessitated dropping those with 19 to 21 years of experience from the sample.

10. The nine observation regressions utilize all publication or citation data for 1966-86.

11. This equals experience as of 1987-88 ([EXPERIENCE.sub.87] + .5) less -[[Tau].sub.2j]/[[Tau].sub.3j].

12. All predicted publications and citations are constrained to be non-negative. This worsens the fit slightly but does not appreciably affect the results.

13. Note that the impact factor significantly improves the fit in regressions based on a larger sample that also includes younger economists.

14. That is, applying the article and citation coefficients to mean values for these variables produces a salary differential that equals 21 percent of the average wage in the sample.

15. The large compensation chairmen receive could reflect the present value of a significant drop in research productivity.

References

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