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1 Changes across Cohorts in Wage Returns to Schooling and Early Work Experiences: Distinguishing Price and Composition Effects J.Ashworth, V.J.Hotz, A.Maurel & T.Ransom North American Winter Meeting of the Econometric Society 2014, Philadelphia January 3, 2014 Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

2 Motivation Substantial increase in estimated returns to schooling in the U.S. over the 80 s and 90 s (see e.g. Katz and Murphy, 1992; Katz and Autor, 1999; Card and Lemieux, 2001; Goldin and Katz, 2007). Typically thought of as reflecting changes in prices of skills accumulated while in school. Significant changes in characteristics of youth over the past 20+ years (Altonji, Bharadwaj and Lange, 2012), and how some of these characteristics are associated with schooling (e.g. Belley and Lochner, 2007: family income and college attendance; Carneiro and Lee, 2011: decrease in quality of college grads). Also increase in amount of in-school work experiences, in particular college employment (Bacolod and Hotz, 2006; Scott-Clayton, 2012). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

3 Motivation Substantial increase in estimated returns to schooling in the U.S. over the 80 s and 90 s (see e.g. Katz and Murphy, 1992; Katz and Autor, 1999; Card and Lemieux, 2001; Goldin and Katz, 2007). Typically thought of as reflecting changes in prices of skills accumulated while in school. Significant changes in characteristics of youth over the past 20+ years (Altonji, Bharadwaj and Lange, 2012), and how some of these characteristics are associated with schooling (e.g. Belley and Lochner, 2007: family income and college attendance; Carneiro and Lee, 2011: decrease in quality of college grads). Also increase in amount of in-school work experiences, in particular college employment (Bacolod and Hotz, 2006; Scott-Clayton, 2012). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

4 Motivation (Cont d) Aside from changes in composition, changes in prices of skill correlates (e.g. AFQT, unobserved ability, work experiences) are also likely to play a role. Taber, 2001: increase during the 80s in returns to unobserved ability; Castex and Dechter, 2013: decrease (between NLSY79 and 97) in returns to AFQT. Most of the literature abstracts from the (potentially important) role played by early labor market experiences. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

5 Motivation (Cont d) Aside from changes in composition, changes in prices of skill correlates (e.g. AFQT, unobserved ability, work experiences) are also likely to play a role. Taber, 2001: increase during the 80s in returns to unobserved ability; Castex and Dechter, 2013: decrease (between NLSY79 and 97) in returns to AFQT. Most of the literature abstracts from the (potentially important) role played by early labor market experiences. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

6 Motivation (Cont d) How important are changes in composition of skills vs. changes skill prices in accounting for the evolution of schooling and work experiences (early career) wage premia over the past 30 years? What are the roles played by change in prices of skills accumulated while in school, or in the labor market, vs. skill correlates? Answers to above questions important to understand the sources of changes in U.S. wage structure over the last 30 years. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

7 Motivation (Cont d) How important are changes in composition of skills vs. changes skill prices in accounting for the evolution of schooling and work experiences (early career) wage premia over the past 30 years? What are the roles played by change in prices of skills accumulated while in school, or in the labor market, vs. skill correlates? Answers to above questions important to understand the sources of changes in U.S. wage structure over the last 30 years. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

8 This paper We estimate, using panel data on males for two groups of cohorts (NLSY79 and NLSY97), a dynamic model of schooling and work decisions. We model work-school activity choices over young men s life cycle, controlling for observed determinants (AFQT, family background, experiences) and unobserved persistent characteristics (factor structure). Hourly wages: flexible functions of schooling and (in and out of school) work experiences. We use selection-corrected wage estimates to decompose across-cohort changes in wage premia into changes in skill prices and skill composition. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

9 Data 1979 and 1997 National Longitudinal Surveys of Youth (NLSY). Sample is restricted to males from ages 13 to 28 (Rounds 1-15 for both surveys). We drop the four oldest cohorts from the NLSY79, resulting in the following birth cohort groups: (NLSY79) and (NLSY97). 2, 666 individuals in the NLSY79, 4, 559 in the NLSY97. Sample Selection Track schooling attendance, employment and military activities, as well as wages, on monthly basis. Use comparable AFQT scores for both cohorts (following Altonji, Bharadwaj and Lange, 2012). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

10 Data 1979 and 1997 National Longitudinal Surveys of Youth (NLSY). Sample is restricted to males from ages 13 to 28 (Rounds 1-15 for both surveys). We drop the four oldest cohorts from the NLSY79, resulting in the following birth cohort groups: (NLSY79) and (NLSY97). 2, 666 individuals in the NLSY79, 4, 559 in the NLSY97. Sample Selection Track schooling attendance, employment and military activities, as well as wages, on monthly basis. Use comparable AFQT scores for both cohorts (following Altonji, Bharadwaj and Lange, 2012). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

11 Schooling attendance Figure: Average Months of Schooling Attended (since age 13) by Age & Cohort Months Months Age NLSY 1979 NLSY Age NLSY 1979 NLSY 1997 (a) School Only (b) School and Work Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

12 Educational attainment Table: Graduation probabilities by age 28 Variable y79 y97 Pr(grad HS) ** Pr(start col) *** Pr(grad BA) * Pr(grad BA start col) Note: Significance reported at the 1% (***), 5% (**), and 10% (*) levels Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

13 Work experiences Figure: Average Months of (Non-School) Work Experience by Age & Cohort Months Months Age NLSY 1979 NLSY Age NLSY 1979 NLSY 1997 (a) Part-time (b) Full-time Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

14 Work experiences (Cont d) Figure: Work Experiences by Age & Cohort Months Age NLSY 1979 NLSY 1997 (a) Total Work Experience Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

15 Evolution of Median AFQT y79 y97 Education HS Dropout HS Graduate BA Dropout BA Graduate In-School Work Experience No HS Work HS Work No Col Work Col Work Overall Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

16 Family background characteristics Table: Change in family background characteristics across cohorts Variable HS Dropouts HS Grad BA Grad Mother s education (in years) 1.19*** 1.13*** 1.16*** Father s education (in years) 1.38*** 0.86*** 0.61*** Family Income (in $1, 000s dollars) ** 4.72** Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

17 Choice sets Three choice (or risk) sets: before HS grad; HS grads; BA grads. Within each choice set, agents choose among the following alternatives: Activity number Description 1 School only 2 Work in school 3 Work PT (no school) 4 Work FT (no school) 5 Military 6 Residual 7 Graduate and advance risk set (only for the first two risk sets) Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

18 School & work experiences The vector of accumulated school and work experiences (from age 13 on) enters both the alternative-specific payoff and (potential) wage functions. For individual i at age a, this vector is given by: x ia = ( x 1ia, x 2ia, x 3ia,... x 6ia ) where numbers 1 through 6 correspond to the choice alternatives in the previous slide. Payoffs and wages also depend on HS and BA graduation status (returns to degree). In the following, the model is presented for a given cohort group (NLSY79 or NLSY97). In practice, value and wage functions are specific to each group of cohorts. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

19 School & work experiences The vector of accumulated school and work experiences (from age 13 on) enters both the alternative-specific payoff and (potential) wage functions. For individual i at age a, this vector is given by: x ia = ( x 1ia, x 2ia, x 3ia,... x 6ia ) where numbers 1 through 6 correspond to the choice alternatives in the previous slide. Payoffs and wages also depend on HS and BA graduation status (returns to degree). In the following, the model is presented for a given cohort group (NLSY79 or NLSY97). In practice, value and wage functions are specific to each group of cohorts. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

20 Alternative-specific value functions Value function to individual i at age a associated with alternative j in risk set r (Viaj r ) depends on: 1 family background characteristics (f i ). 2 personal characteristics (z i ). 3 local labor market conditions at age a (m ia ). 4 accumulated schooling and work experiences at age a (x ia ). 5 individual-specific unobserved factors (ξ i = (ξ i1, ξ i2 ) ). 6 idiosyncratic & age-varying preference shocks (ω iaj ). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

21 Alternative-specific value functions Value function to individual i at age a associated with alternative j in risk set r (Viaj r ) depends on: 1 family background characteristics (f i ). 2 personal characteristics (z i ). 3 local labor market conditions at age a (m ia ). 4 accumulated schooling and work experiences at age a (x ia ). 5 individual-specific unobserved factors (ξ i = (ξ i1, ξ i2 ) ). 6 idiosyncratic & age-varying preference shocks (ω iaj ). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

22 Alternative-specific value functions (Cont d) For computational simplicity, V r iaj (j = 1,..., J r ) is approximated as a linear function of these characteristics augmented with higher order and interaction terms (see Heckman, 1981 and Eckstein and Wolpin, 1989): where V r iaj = α r fj f i + α r zjz i + α r mjm ia + k {w,b,h} +α r x2j x2 ia + α r ξj1 ξ i1 + α r ξj2 ξ i2 + ω iaj, I i (k) [ α0jk r + αr xjk x ] ia I i (k) is indicator function that i is in race group k {w, b, h}, (αξj1 r, αr ξj2 ) are alternative-specific factor loadings. Individual i chooses activity diaj r = k yielding the highest value function: j r ia = arg maxviak r k Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

23 Alternative-specific value functions (Cont d) For computational simplicity, V r iaj (j = 1,..., J r ) is approximated as a linear function of these characteristics augmented with higher order and interaction terms (see Heckman, 1981 and Eckstein and Wolpin, 1989): where V r iaj = α r fj f i + α r zjz i + α r mjm ia + k {w,b,h} +α r x2j x2 ia + α r ξj1 ξ i1 + α r ξj2 ξ i2 + ω iaj, I i (k) [ α0jk r + αr xjk x ] ia I i (k) is indicator function that i is in race group k {w, b, h}, (αξj1 r, αr ξj2 ) are alternative-specific factor loadings. Individual i chooses activity diaj r = k yielding the highest value function: j r ia = arg maxviak r k Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

24 Wages The log wage (for work activity j {2, 3, 4}) is specified as follows: where w iaj = β 0j + β m m ia + β z z i + g (x r ia) + β ξj ξ i2 + ɛ iaj g ( ) is a cubic polynomial in all types of experience that also includes pairwise interactions across school and work experience variables (see Heckman, Lochner and Todd, 2006). ξ i2 is an individual-specific productivity factor, and ɛ iaj is an idiosyncratic productivity shock. Family background characteristics are excluded from wage equations (see also Taber, 2001). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

25 Wages The log wage (for work activity j {2, 3, 4}) is specified as follows: where w iaj = β 0j + β m m ia + β z z i + g (x r ia) + β ξj ξ i2 + ɛ iaj g ( ) is a cubic polynomial in all types of experience that also includes pairwise interactions across school and work experience variables (see Heckman, Lochner and Todd, 2006). ξ i2 is an individual-specific productivity factor, and ɛ iaj is an idiosyncratic productivity shock. Family background characteristics are excluded from wage equations (see also Taber, 2001). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

26 Estimation Individual-specific factors (ξ i1, ξ i2 ) i are assumed to be distributed following a standard bivariate normal distribution. Preference shocks (ω iaj ) i,a,j follow a Type-1 Extreme Value distribution; productivity shocks (ɛ iaj ) i,a,j are normally distributed (variances allowed to differ across work activities). Those idiosyncratic shocks are mutually independent, and independent from the heterogeneity factors. Estimation via MLE, separately for each group of cohorts (NLSY79 and NLSY97). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

27 Across-cohort changes in high school and college wage premia Variable Raw Mincerian Flexible Mincerian +Background, AFQT, Unobs. Het HS grad *** *** *** *** (0.0019) (0.0021) (0.0023) (0.0022) BA grad *** *** *** *** (0.0029) (0.0028) (0.0037) (0.0036) (a) NLSY79 Variable Raw Mincerian Flexible Mincerian +Background, AFQT, Unobs. Het HS grad *** *** *** *** (0.0018) (0.0020) (0.0021) (0.0023) BA grad *** *** *** *** (0.0023) (0.0023) (0.0030) (0.0031) (b) NLSY97 Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

28 Across-cohort changes in high school and college wage premia (Cont d) Variable Raw Mincerian Flexible Mincerian +Background, AFQT, Unobs. Het HS grad 0.012*** *** *** *** (0.0026) (0.0029) (0.0031) (0.0032) BA grad *** *** *** *** (0.0037) (0.0036) (0.0048) (0.0048) (c) Across-cohort change These results are sensitive to the cohort groups included within the NLSY79 sample. Across-cohort variation in (raw) college wage premium: if we consider instead the earliest birth cohorts (individuals born from 1957 to 1960), goes up to pp.! Substantial across-cohort variation within the NLSY79 data. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

29 Across-cohort changes in returns to work experiences Variable Raw Flexible Mincerian +Background, AFQT, Unobs. Het Work in HS ** *** 0.023*** (0.0163) (0.0027) (0.0026) Work in college ** *** *** (0.0095) (0.0044) (0.0037) Work PT *** *** (0.0156) (0.0027) (0.0025) Work FT * 0.012*** 0.007*** (0.0068) (0.0010) (0.0008) (d) Across-cohort change (evaluated at age 28) Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

30 Price versus composition effects Full-time wage decompositions at age 28 for school, work experiences, and degree attainment: Obs. Price Obs. Comp. Unobs. Price Unobs. Comp. School -11% 108% 46% -43% Work in HS 46% -33% 65% 23% Work in College 25% 9% 66% 1% Work PT -22% 77% 132% -87% Work FT -70% -30% 204% -5% HS grad 11% -10% 113% -14% BA grad 34% -11% 63% 14% Note: each row sums to 100%. Overall, relatively minor contribution of price of skill of interest...only accounts for less than half of the variation in obs. price. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

31 Price versus composition effects Full-time wage decompositions at age 28 for school, work experiences, and degree attainment: Obs. Price Obs. Comp. Unobs. Price Unobs. Comp. School -11% 108% 46% -43% Work in HS 46% -33% 65% 23% Work in College 25% 9% 66% 1% Work PT -22% 77% 132% -87% Work FT -70% -30% 204% -5% HS grad 11% -10% 113% -14% BA grad 34% -11% 63% 14% Note: each row sums to 100%. Overall, relatively minor contribution of price of skill of interest...only accounts for less than half of the variation in obs. price. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

32 Sample selection Category NLSY79 NLSY97 Starting persons 12,686 8,984 Drop females 6,283 4,599 Drop older birth cohorts 3,386 0 Drop non-race oversamples a Drop other race 0 40 Resulting persons 2,666 4,559 Survey rounds Survey person-years b 35,834 64,856 Add retrospective data years c 6,822 5,354 Potential person-years 42,656 70,210 Potential person-months 511, ,027 Drop missing interview months d 19, ,639 Final months 492, ,388 Final T months months Final max T 192 months 192 months a This refers to the oversamples of military personnel and disadvantage white individuals, both of which are excluded. b This refers to the number of survey rounds available before an individual turns 28. c This refers to adding retrospective data for the years or (if applicable). d This refers to dropping any right-censored missing interview spells or any observations during or after a spell of 3+ missed interviews. Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

33 Sample selection (Cont d) Category NLSY79 NLSY97 Potential wage observations a 275, ,297 Drop self-employed wages 13,872 23,699 Drop outlying wages b 5,358 28,259 Drop non-reported wages 22,076 56,766 Final wage observations 234, ,573 a Potential wage observations refers to the the number of person-months choosing a work alternative. b We drop wages below $2 and above $50 (in $). Ashworth, Hotz, Maurel & Ransom (Duke) Changes in Wage Returns: Price vs. composition January 3, / 24

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