Fixed Effects Estimation and Inconsistency

Consider estimation of the following population regression function: $$G{Y_{it}} = {\beta _0} + {\beta _1}IN{F_{it}} + {\beta _2}DE{M_i} + {\beta _3}POI{L_t} + {\varepsilon _{it}}$$

Where: $$GY_{it}$$ = percentage growth in real GDP per capita in country $$i$$ in year $$t$$

$$INF_{it}$$ = percentage rate of inflation in country $$i$$ in year $$t$$

$$DEM_i$$ = 1 if country $$i$$ is a democracy, 0 otherwise

$$POIL_t$$ = a price index of crude oil on the world market.

If you were to explore estimation with fixed effects both for countries and for years of observation. Which coefficients in the above model could be estimated? Suppose that INF and POIL are correlated over time, and INF is correlated with DEM across countries. Do the omitted variables in the fixed effects estimate result in inconsistent estimates? Why?

My guess is that the estimates are biased and consistent but I haven't been able to figure out why.

• Omitted variable bias doesn't lead to inconsistent estimates in this case, because we are separating out the effects of the omitted variable with respect to time and across countries. If that is the case then suppose that the omitted variable is only correlated across time. Is fixed effects inappropriate in this case? And how should the regression be estimated? – Jaffar Jan 2 '19 at 4:14