Province Specific Linear Trend

[Adriano Ruggiero]

Hello, I'm a student of a master in applied economics. The problem I come to you with is that I am trying to replicate an analysis methodology from a paper but I do not understand how I can insert a model element within the analysis:
ln(Mkjt) = α_{jt} + U_{kjt}γ + λ_{kt} + H_j ∗ t + ε_{kjt}.
Whereas this is a model for examining the effect of the unemployment rate on the mortality rate, where k denotes the different causes of death, j denotes the provinces and t denotes time. The problem I encountered in the analysis on stata is on how to fit the province-specific linear trend represented by H_j * t, into the analysis on Stata. In addition to it, during the analysis within the paper it is confirmed that the analysis is also controlled for fixed effect years and fixed effect provinces, in addition to the province specific linear trend. I did in this way:
reg ln_Mortality_Rate Unemployment_rate i.num_id##c.years i.years i.num_id, vce(robust).
Where num_id is the id of the provinces.
I'm not sure if it is correct, because i used the same command for all of the cause of deahts and the results are not statistically significant, and this is a problem. Can someone help me?

[George Ford]

reg ln_Mortality_Rate Unemployment_rate years i.num_id#c.years i.id , vce(robust)

cleaner options:

areg ln_Mortality_Rate Unemployment_rate years i.num_id#c.years , absorb(num_id) vce(robust)

reghdfe ln_Mortality_Rate Unemployment_rate years i.num_id#c.years , absorb(num_id) vce(robust)


might need to cluster the SE on province (need at least 30 or so)

Statistical (in)significance is not a problem, it just "is".

[Adriano Ruggiero]

But, if you don't put i.id, you don't take into account the year fixed effect. Am I wrong? George Ford

[George Ford]

you can put year in absorb in reghdfe or areg, or add i.year in reg.

[Adriano Ruggiero]

I have just other two questions. Do you think is better to transform years (2010 2011 2012) in years_ ( 1 2 3) ? I have data from 2004 to 2014.
I tried the methodology that you suggested me, but nothing is change. I tried also to generate a new variable as years_num_id = years * num_id and put it as interaction and not as num_id#c.years. In this way I found statistically significant results. Do you think that is also correct the methodology? George Ford

[George Ford]

Then you got it right the first time. Good job.

The alternative is not correct. The num_id is a category. The multiplication of the two is meaningless and you are not estimating province specific trends.

It appears, once correcting for trends, the unemployment has no effect on the mortality rate, though I suspect there are other variables you need in your model. Time and the unemployment rate are not the sole, nor primary, causes of mortality.

[George Ford]

Did the paper you mention find something?

[George Ford]

You might think about whether you want the between or within estimator. I can see where persistently high unemployment might affect mortality, but less so where a change in unemployment would lead to a contemporaneous change in mortality.

[Adriano Ruggiero]

I want the within estimator. Also, could be possible that if I used the Panel regression (with the function of FE) and not the simple reg the results are different?

xtreg ln_Mortality_Rate Unemployment_rate i.num_id#c.years, fe vce(robust).

[George Ford]

All you have done is panel regression. xtreg is just another way to do it. in your xtreg command, you don't have a year fixed effect. xtreg ..., fe only account for the num_id FE.

Honestly, I'd be shocked if the within estimator was non-zero.