You Want to Find the Determinants of Suicide Rates in the United

You want to find the determinants of suicide rates in the United States. To investigate the issue, you collect state level data for ten years. Your first idea, suggested to you by one of your peers from Southern California, is that the annual amount of sunshine must be important. Stacking the data and using no fixed effects, you find no significant relationship between suicide rates and this variable. (This is good news for the people of Seattle.)However, sorting the suicide rate data from highest to lowest, you notice that those states with the lowest population density are dominating in the highest suicide rate category. You run another regression, without fixed effect, and find a highly significant relationship between the two variables. Even adding some economic variables, such as state per capita income or the state unemployment rate, does not lower the t-statistic for the population density by much. Adding fixed entity and time effects, however, results in an insignificant coefficient for population density.
(a)What do you think is the cause for this change in significance? Which fixed effect is primarily responsible? Does this result imply that population density does not matter?
(b)Speculate as to what happens to the coefficients of the economic variables when the fixed effects are included. Use this example to make clear what factors entity and time fixed effects pick up.
(c)What other factors might play a role?