Mister
1. Interpreting the regression results obtained by pooled OLS method
log (rentit) = β0 + β1*log (popit) + β2*log (avgincit) + β3*pctstuit + δ*y90t + αi +uit log = -1.500 + 0.407*log (pop) + 0.571*log (avginc) + 0.005*pctstu + 0.262*y90 se = (0.535) (0.023) (0.053) (0.001) (0.348) t = (-1.06) (1.81) (10.76) (4.95) (7.54) p = (0.073) (0.009) (0.000) (0.000) (0.000) r2 = 0.861 adj r2 = 0.857 df = 123 = 0.016
The regression table shows that 100% increase in city population will result in 4% increase in average rental prices, while holding all other variables constant. Similarly, 100% increase in average income will lead to 57% increase in dependent variable, holding other variables constant. 100% increase of student population in total population will result in 0.5% increase in rental prices, holding other variables constant. Since we have variable αi (which captures all the unobserved, time constant factors affecting rent prices) in our equation, we have fixed problem. In other words, αi is unobserved rent effect or rent price fixed effect. αi represents all factors affecting rent prices that don’t change over time. We can see that “y90” is dummy variable, which only counts observations for 1990 while in our regression model we have 128 observations, which means that observations for 1980 we also included in the model.
2. Estimating the first-difference model of equation (a) using OLS method xtset city year, delta(10) panel variable: city (strongly balanced) time variable: year, 80 to 90 delta: 10 units
log = 0.386 + 0.072*log (pop_d) + 0.310*log (avginc_d) + 0.011*pctstu_d se = (0.368) (0.088) (0.066) (0.004) t = (10.47) (0.82) (4.66)
log (rentit) = β0 + β1*log (popit) + β2*log (avgincit) + β3*pctstuit + δ*y90t + αi +uit log = -1.500 + 0.407*log (pop) + 0.571*log (avginc) + 0.005*pctstu + 0.262*y90 se = (0.535) (0.023) (0.053) (0.001) (0.348) t = (-1.06) (1.81) (10.76) (4.95) (7.54) p = (0.073) (0.009) (0.000) (0.000) (0.000) r2 = 0.861 adj r2 = 0.857 df = 123 = 0.016
The regression table shows that 100% increase in city population will result in 4% increase in average rental prices, while holding all other variables constant. Similarly, 100% increase in average income will lead to 57% increase in dependent variable, holding other variables constant. 100% increase of student population in total population will result in 0.5% increase in rental prices, holding other variables constant. Since we have variable αi (which captures all the unobserved, time constant factors affecting rent prices) in our equation, we have fixed problem. In other words, αi is unobserved rent effect or rent price fixed effect. αi represents all factors affecting rent prices that don’t change over time. We can see that “y90” is dummy variable, which only counts observations for 1990 while in our regression model we have 128 observations, which means that observations for 1980 we also included in the model.
2. Estimating the first-difference model of equation (a) using OLS method xtset city year, delta(10) panel variable: city (strongly balanced) time variable: year, 80 to 90 delta: 10 units
log = 0.386 + 0.072*log (pop_d) + 0.310*log (avginc_d) + 0.011*pctstu_d se = (0.368) (0.088) (0.066) (0.004) t = (10.47) (0.82) (4.66)