Estimate Log(wage) As A Function Of Education, Experience, I ✓ Solved

Estimate log(wage) as a function of educ, exper, IQ, KWW, bl

Estimate log(wage) as a function of educ, exper, IQ, KWW, black, SMSA, and south. Use heteroskedastic-robust SEs. Interpret the coefficient on black and identify which variables are individually significant at alpha=0.10. Q2: Add interaction black*south; does the racial wage gap depend on living in the South? Q3: Create nonblack_south (nonblack in South) and black_nonsouth (black not in South); re-estimate using three interaction terms (drop variables as needed); how much less do black men in the South earn compared to non-black men not in the South? Q4: Repeat Q2 using urban (SMSA) interaction with black. Q5: Repeat Q3 using urban and black variables. Q6: Summarize overall conclusions from this exercise.

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Introduction

This assignment analyzes racial differences in log wages using the wage2 dataset, estimating log(wage) on education, experience, IQ, KWW (Knowledge of the World of Work), and demographic dummies for black, SMSA (urban), and south. The analysis emphasizes heteroskedasticity-robust inference, interaction terms to evaluate whether the racial wage gap varies by region (South) or by urban status, and alternative parameterizations using group dummies. Methods follow standard microeconometric practice for linear models (Wooldridge, 2016; Cameron & Trivedi, 2005).

Data and Base Model

Specify the baseline linear model: ln(wage) = β0 + β1 educ + β2 exper + β3 IQ + β4 KWW + β5 black + β6 SMSA + β7 south + u. Estimate by OLS and compute heteroskedasticity-robust standard errors (White/sandwich). Robust SEs are required because wage residuals typically exhibit heteroskedasticity (Wooldridge, 2016; Greene, 2018). Report coefficient estimates, robust t-statistics, and p-values. Test joint significance of schooling and experience with an F-test using robust covariance (Cameron & Trivedi, 2005).

Q1 — Interpretation and Significance

Interpretation of β5 (coefficient on black): β5 is the conditional difference in log wages between black and nonblack men, holding education, experience, IQ, KWW, SMSA, and south constant. In percentage terms, a coefficient β5 ≈ -0.05 implies that, ceteris paribus, black men earn about exp(β5)-1 ≈ -4.9% less than nonblack men (approx β5*100% for small β5). Statistical significance: evaluate each coefficient’s t-statistic against a two-sided alpha = 0.10 threshold. Variables with |t| > t_{n-k,0.95} (or p-value

Q2 — Interaction: black*south

Augment the model with an interaction term: ln(wage) = ... + β5 black + β7 south + β8 (black*south) + u. Here β8 captures the differential racial gap in the South relative to the non-South. The racial wage gap for non-South equals β5; for the South it equals β5 + β8. Test whether the racial gap depends on living in the South by testing H0: β8 = 0 versus H1: β8 ≠ 0 using robust SEs. A significant β8 (p

Q3 — Group Dummies: nonblack_south and black_nonsouth

Create mutually exclusive group indicators to identify four groups: (1) nonblack_nonsouth (reference), (2) nonblack_south, (3) black_nonsouth, and (4) black_south. To identify effects, include three dummies (drop the reference). The model becomes ln(wage) = β0 + β1 educ + ... + γ1 nonblack_south + γ2 black_nonsouth + γ3 black_south + u. The coefficient γ3 − 0 (or γ3 − γ1 etc.) gives the difference between black men in the South and reference nonblack non-South. Specifically, the wage gap between black South and nonblack non-South equals γ3. Interpret in log points and convert to percent via exp(γ3)-1. This parameterization avoids multicollinearity and makes subgroup comparisons straightforward (Oaxaca, 1973). If instead using original black and south plus interactions, the same contrasts can be constructed from βs: black_south gap = β5 + β8. Report robust standard errors and p-values for the subgroup contrasts.

Q4 — Interaction: black*SMSA (urban)

Repeat Q2 replacing south with SMSA: include black, SMSA, and black*SMSA. The interaction coefficient indicates whether the racial gap differs between urban and non-urban areas. Test H0: coefficient on the interaction = 0 with robust SEs. Empirical expectations are ambiguous: urban labor markets may show larger or smaller gaps depending on sorting, measured skills, and local labor demand (Card & Krueger; Bertrand & Mullainathan, 2004).

Q5 — Group Dummies for Urban/Suburban Status

As in Q3, construct mutually exclusive dummies: nonblack_nonurban (reference), nonblack_urban, black_nonurban, black_urban, include three dummies, and interpret coefficients relative to reference. This yields direct estimates of the black/nonblack gaps by urban status. Compare magnitudes and statistical significance to determine whether urban residency amplifies or reduces the racial wage gap. Use robust inference for contrasts.

Q6 — Overall Conclusions and Policy Implications

Overall, the exercise assesses whether racial wage differences persist after conditioning on human capital and whether those differences vary by region or urban status. If β5 remains negative and significant after controls, this suggests residual wage discrimination or omitted factors (unobserved quality, experience heterogeneity) (Altonji & Blank, 1999; Becker, 1957). Significant interactions indicate heterogeneity of the gap: a significant negative black*south implies deeper disadvantages for black men in the South; a non-significant interaction suggests the gap is geographically uniform. Group-dummy parameterizations facilitate clear comparisons and policy targeting (Oaxaca, 1973).

Methodological notes: always report robust standard errors, present percentage interpretations from log coefficients, and where possible supplement OLS with decomposition analyses (Oaxaca) or robustness checks (controls for job characteristics). Limitations include potential omitted variable bias (unobserved ability or occupation), measurement error in test scores, and sample selection. Future work could employ decomposition methods, quantile regressions, or experimental designs to strengthen causal claims (Angrist & Pischke, 2009; Bertrand & Mullainathan, 2004).

References

• Altonji, J. G., & Blank, R. M. (1999). Race and gender in the labor market. In O. Ashenfelter & D. Card (Eds.), Handbook of Labor Economics (Vol. 3, pp. 3143–3259). Elsevier.
• Angrist, J. D., & Pischke, J.-S. (2009). Mostly Harmless Econometrics: An Empiricist's Companion. Princeton University Press.
• Becker, G. S. (1957). The Economics of Discrimination. University of Chicago Press.
• Bertrand, M., & Mullainathan, S. (2004). Are Emily and Greg More Employable than Lakisha and Jamal? A Field Experiment on Labor Market Discrimination. American Economic Review, 94(4), 991–1013.
• Cameron, A. C., & Trivedi, P. K. (2005). Microeconometrics: Methods and Applications. Cambridge University Press.
• Greene, W. H. (2018). Econometric Analysis (8th ed.). Pearson.
• Juhn, C., Murphy, K. M., & Pierce, B. (1993). Wage Inequality and the Rise in Returns to Skill. Journal of Political Economy, 101(3), 410–442.
• Oaxaca, R. L. (1973). Male-Female Wage Differentials in Urban Labor Markets. International Economic Review, 14(3), 693–709.
• StataCorp. (2019). Stata Statistical Software: Release 16. StataCorp LLC.
• Wooldridge, J. M. (2016). Introductory Econometrics: A Modern Approach (6th ed.). Cengage Learning.