Detrending in a Poisson Panel Model with many zeros in earlier years

[Max Bertoldi]

Hello Stata community,
I have a panel data set of regions within a country and regress the mortality rate due to drug abuse (deaths per 100,000) on the unemployment rate. For the moment I use a log-linear model with the following stata code:

reg ln(mortality) unemployment controls i.year region##c.year [iw=region_population], vce(cluster region)

So far, so good (I hope). Now I want to results by age and sex. However, this is somewhat difficult because by slicing my sample into different sub-groups by age and sex I create some sub-groups with some 0s. Thus my idea to use a Poisson model for the analysis of these sub-groups, something along the lines of:

ppml mortality unemployment controls year_dummies region_dummies region_trends [iw=region_population] ,cluster(region)

(I hard code the dummies this time so ppml can work better with them).

So far this is very straight forward. But I think there might be a problem with the linear trend specification because most of the 0s in the mortality data happen to be in earlier years before the trend lifts them up. Thus, I think a linear trend might not be a good approximation for the mortality data per sub-group due to the 0s. In other words, there is no trend (or seasonality for that matter) as long as mortality is equal to 0 but, as soon as mortality takes up the first positive value, it exhibits a linear trend.

Do you have any recommendations of what to do in such a case? Should I just use a non-linear detrending method before running the regression, eg. a Hodrick-Prescott filter (although Hamilton says we should never use one)?

Any suggestions would be much appreciated
Thanks,
Max

[Phil Bromiley]

No one responded quickly to your question. You'll increase your chances of a helpful answer if you follow the FAQ on asking questions - provide Stata code in code delimiters, Stata output, and sample data. Most of the folks on this list do not open files. Also, try to simplify your code to what is necessary to demonstrate the problem.

First, instead of reg, I'd be inclined to xtreg. You have panel data. Second, you are using a user-written procedure. Why are you not using the xtpoisson routine? You're much more likely to get help with a Stata provided procedure than a user written one.

Why are you forcing the effect of years to be linear? Why not allow year dummies? Why would zeros lead to poisson rather than tobit?

[Max Bertoldi]

Thank you very much for your answer Phil. I can switch to the built-in commands.

I have year dummies AND region-specific linear trends. For the OLS regression of the big groups, I believe a linear trend to be accurate. When I analyse smaller sub-groups, that is not the case anymore. My question is, whether I need to pay to anything specifically when detrending within a Poisson model.

I though my underlying process would be more accurately modeled by Poisson distribution, as the mortality rate is count data divide by population size. The only reason I have 0s in the data is that the underlying population is not big enough for positive count values. Should I really consider Tobit for such a case?

[Tom Zylkin]

Hi Max,
That's an interesting question. My experience with Poisson FE models is from working with trade data and may not be universal. But I often find that PPML gives similar results with versus without zeroes. I would suggest checking how your results change when you only use non-zero observations. If they are still similar, you probably do not need to worry about this.

Tom