I'm analyzing some panel data that show how the percentage of the workforce as well as median wages have changed over time (hryear4) across major industry groupings (prmjind1). The data look like this:
If I do a simple OLS regression where
This model says that for every 1 unit increase in the percent of the workforce that are minorities, you get a 21 cent drop in the median wage. Now, if I do a fixed-effect regression assuming that there exist unobserved time-invariant differences across industries, the results change completely:
This model says that every 1 unit increase in the percent of the workforce that are minorities results in a 36 cent increase in the median wage. Lastly, if I do another fixed-effect regression but this time assume that there exist constant differences across industries that vary over time, the results again change dramatically:
Now we're back to a decrease in the median wage, and a much bigger decrease than the one estimated from OLS. I'm looking for advice regarding how to interpret these findings and what next steps would be. If the coefficient always had the same sign, it would be much easier but I don't understand how it can flip from positive to significantly negative like it's doing here.
Code:
Row │ hryear4 prmjind1 prcnt_minority median_wage wage_10 median_age
│ Int64 Int64 Float64 Float64 Float64 Float64
─────┼─────────────────────────────────────────────────────────────────────
1 │ 2010 1 54.9525 10.0 8.0 36.0
2 │ 2010 2 28.5844 18.0 11.0242 40.0
3 │ 2010 3 38.9158 16.0 10.0 37.0
4 │ 2010 4 37.2013 14.5 9.0 43.0
5 │ 2010 5 33.117 10.0 7.5 34.0median_wage = a + b * percent_minority, I get the following output:
Code:
Continuous Response Model
Number of observations: 143
Null Loglikelihood: -366.63
Loglikelihood: -353.41
R-squared: 0.1689
LR Test: 26.43 ∼ χ²(1) ⟹ Pr > χ² = 0.0000
Formula: median_wage ~ 1 + prcnt_minority
Variance Covariance Estimator: OIM
──────────────────────────────────────────────────────────────────────────────
PE SE t-value Pr > |t| 2.50% 97.50%
──────────────────────────────────────────────────────────────────────────────
(Intercept) 23.5535 1.62157 14.5251 <1e-29 20.3478 26.7593
prcnt_minority -0.211443 0.0395056 -5.35222 <1e-06 -0.289543 -0.133343
Code:
Continuous Response Model
Number of observations: 143
Null Loglikelihood: -366.63
Loglikelihood: -180.77
R-squared: 0.9261
Wald: 162.53 ∼ F(1, 129) ⟹ Pr > F = 0.0000
Formula: median_wage ~ 1 + prcnt_minority + absorb(prmjind1)
Variance Covariance Estimator: OIM
──────────────────────────────────────────────────────────────────────────────
PE SE t-value Pr > |t| 2.50% 97.50%
──────────────────────────────────────────────────────────────────────────────
(Intercept) 0.0584638 1.17216 0.0498769 0.9603 -2.26068 2.37761
prcnt_minority 0.367398 0.0288186 12.7486 <1e-23 0.31038 0.424417
──────────────────────────────────────────────────────────────────────────────
Code:
Continuous Response Model
Number of observations: 143
Null Loglikelihood: -366.63
Loglikelihood: -317.78
R-squared: 0.4969
Wald: 87.84 ∼ F(1, 131) ⟹ Pr > F = 0.0000
Formula: median_wage ~ 1 + prcnt_minority + absorb(hryear4)
Variance Covariance Estimator: OIM
──────────────────────────────────────────────────────────────────────────────
PE SE t-value Pr > |t| 2.50% 97.50%
──────────────────────────────────────────────────────────────────────────────
(Intercept) 27.9752 1.40108 19.9668 <1e-40 25.2035 30.7469
prcnt_minority -0.320378 0.0341831 -9.37241 <1e-15 -0.388001 -0.252756
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