Call:
lm(formula = gsp ~ emp + unemp + hwy, data = Produc)
Residuals:
Min 1Q Median 3Q Max
-28643 -5580 1075 3605 61194
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) -4646.9944 1039.8829 -4.469 8.98e-06 ***
emp 32.4206 0.7370 43.988 < 2e-16 ***
unemp -222.8670 148.2528 -1.503 0.133
hwy 1.0266 0.1483 6.921 9.10e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 9283 on 812 degrees of freedom
Multiple R-squared: 0.9825, Adjusted R-squared: 0.9824
F-statistic: 1.516e+04 on 3 and 812 DF, p-value: < 2.2e-16
Do the estimated coefficients make sense (direction, magnitude, statistical significance)?
Yes, the directions and sizes of the coefficients match what I’d expect, and the main coefficients are highly significant outside of unemployment.
Could there be omitted variable bias that could potentially be reduced by throwing in fixed effects?
Unobserved and state-specific factors such as geography, policies, or demographics could affect both GSP and the predictors. This could potentially be biasing OLS estimates.
# Demean variables by statedemeaned <-within(Produc, { gsp_dm <-ave(gsp, state, FUN =function(x) x -mean(x)) emp_dm <-ave(emp, state, FUN =function(x) x -mean(x)) unemp_dm <-ave(unemp, state, FUN =function(x) x -mean(x)) hwy_dm <-ave(hwy, state, FUN =function(x) x -mean(x))})manual_fe <-lm(gsp_dm ~ emp_dm + unemp_dm + hwy_dm -1, data = demeaned)summary(manual_fe)
Call:
lm(formula = gsp_dm ~ emp_dm + unemp_dm + hwy_dm - 1, data = demeaned)
Residuals:
Min 1Q Median 3Q Max
-16456.4 -712.5 -53.8 717.3 20705.5
Coefficients:
Estimate Std. Error t value Pr(>|t|)
emp_dm 41.1813 0.3336 123.463 < 2e-16 ***
unemp_dm 59.3055 55.0415 1.077 0.282
hwy_dm -1.0868 0.1520 -7.151 1.92e-12 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 2617 on 813 degrees of freedom
Multiple R-squared: 0.9581, Adjusted R-squared: 0.958
F-statistic: 6199 on 3 and 813 DF, p-value: < 2.2e-16
Do your coefficients change? Why or why not?
Yes the coefficients changes because fixed effects control for all the state level characteristics that stay constant over time. This helps eliminate bias from omitted variables that do not change across the years.
What are the fixed effects controlling for?
The fixed effects model controls for all time-invariant characteristics of each state.
Do you get the same coefficient if you specify the Fixed Effect in an alternative way?
Yes, we can see in the three models used above that the coefficients were the same. For example, emp = 41.18, unemp= 59.3, and hwy = -1.09 in all three models.