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Unformatted text preview: 1 Determinants of Wages Berndt Chapter 5 1.1 Human Capital Theory and Log Wage Equation equalizing di/erence: returns to schoolingpost-schooling investments need to equalize the costs and gains from schoolingpost-schooling investments max ( life-time wealth ) = max f s g lim T !1 R T s W ( s ) e & rt dt = & W ( s ) e & rt =r & & 1 s = W ( s ) e & rs =r where W ( s ) is wage that is associated with schooling s and r is a discount rate so W ( s ) e & rs =r & W ( s ) e & rs = 0 , or marginal gain minus marginal cost thus optimal level of schooling is given by W ( s ) =W ( s ) = r . suppose that the only costs of schooling are those of forgone earnings the rate of return on the &rst year of education r 1 is then computed as incremental bene&ts divided by incremental costs, r 1 = ( W 1 & W ) =W it can be rewritten as W 1 = W (1 + r 1 ) similarly, for year 2 of schooling, the rate of return r 2 is de&ned as r 2 = ( W 2 & W 1 ) =W 1 it implies that W 2 = W 1 (1 + r 2 ) = W (1 + r 1 ) (1 + r 2 ) after s years of schooling, W s = W (1 + r 1 ) (1 + r 2 ) (1 + r s ) in general, r s is decreasing in s meaning that there is some optimal level of schooling, which is r (given above) assume that r 1 = r 2 = ::: = r s = & (we will relax this later) and approximate (1 + & ) by e & (it is a good approximation as long as & is small) then we have W s = W e &s in real world, wage is determined by many things other than schooling incorporate those things by append a multiplicative disturbance term e u so we have W s = W e &s e u take log and obtain the log wage equation log W s = log W + &s + u rewrite this in a standard linear regression setting y i = + 1 s i + u i , for an individual i , where y i = log W i , and 1 are intercept and slope parameter in log wage equation model, 1 has an interpretation of returns to schooling (will see this later) sometimes, we can incorporate other variables into the equation one example is adding experience and its square y i = + 1 s i + 2 x i + 3 x 2 i + u i when there are more than 1 explanatory variables, we call it multiple regression 1 before we talk about multiple regression, we talk about simple regression where there is only 1 explanatory variable 1.2 Simple Regression regression analysis e.g. the heights of fathers and their sons e.g. schooling and log wage we have n subjects indexed by i = 1 ;:::;n & two data variables ( x;y ) a data variable stores a value for each subject: ( x i ;y i ) explain a dependent variable...
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This note was uploaded on 06/05/2008 for the course ECON 483 taught by Professor Seikkim during the Spring '08 term at University of Washington.
- Spring '08