CohortsandWages2011A

# CohortsandWages2011A - Econ145. John Pencavel COHORTS AND...

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Econ145.CohortsandWages2011A John Pencavel COHORTS AND WAGES With physical capital, if specific productivity improvements are embodied in each new generation of machinery, then the machines need to be distinguished according to their vintage. A similar notion is used in human capital research where cohort effects identify wage differences (or, indeed, any other differences) that are associated with people who belong to the same birth year or to the same year of entry into the labor force. What is the source of these cohort effects? 1. Recent cohorts may work better (are more complementary) with new technology than earlier cohorts. 2. In some fields (engineering, medical science), the content of material taught has changed as the state of technology has advanced. If each new generation of graduates is exposed to the latest ideas and methods, a corresponding obsolescence of earlier vintages is implied. If cohort effects on log(w) move linearly over time, then we might propose specifying a wage equation of the following form to describe a cross- section of workers (1) ln w i = α 0 + α 1 X i + α 2 C i + α 3 S i + g i where X i is the labor market experience of individual i , C i is the birth cohort of this individual (i.e., the year the individual was born), and S i is individual

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2 i ’s years of schooling. If A i stands for i ’s age, then it is common to define X i as equal to A i - (S i + 6), that is, the years estimated to be in the labor force after finishing schooling. I neglect the familiar quadratic term in X i to simplify the analysis. It can be added without undermining the basic point about lack of identification. Let T* be the year in which these cross-section observations are collected. Then, for every individual in the data, his or her value for C i is given by T* - A i in which case, using this and X i = A i - (S i + 6) : ln w i = α 0 + α 1 [A i - (S i + 6)] + α 2 ( T* - A i ) + α 3 S i + g i ln w i = α 0 - α 1 .6 + α 2 T* + ( α 1 - α 2 )A i + ( α 3 - α 1 )S i + i (2) ln w i = β 0 + β 1 .A i + β 2 .S i + i where β 0 = α 0 - α 1 .6 + α 2 T* , a constant, β 1 =( α 1 - α 2 ) and β 2 =( α 3 - α 1 ). In other words, the three concepts of time (birth year, age, and year of the data, T *) are linearly dependent: an individual’s C i = T* - A i and in a cross- section T* is fixed and is the same for everyone. Hence, in a single year’s cross-section, differences across individuals in C i are perfectly correlated with differences in age, A i . The experience effects on wages (given by α 1 ) cannot be unscrambled from the cohort effects on wages (given by α 2 ). There are three slope coefficients in
3 equation (1), but as equation (2) makes clear there are really just two independently-varying right-hand side variables so all three coefficients ( α 1 , α 2 , and α 2 ) are not separately identified and cannot be estimated. Another way of expressing the point is: a single year’s cross-section cannot distinguish between (i.e., cannot identify) both cohort effects and age (or experience) effects (unless some basic nonlinearity in the form of the effects is imposed on the observations). Panel data or pseudo-panel data provide another degree of freedom, i.e., different cohorts can be examined at

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## This note was uploaded on 01/16/2012 for the course ECON 145 at Stanford.

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CohortsandWages2011A - Econ145. John Pencavel COHORTS AND...

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