Estimating a Regression with Multiple Treatment Effects

[Anupam Ghosh]

I want to estimate a linear model to estimate the effect of hurricane exposure (T's are windspeeds) in the past on a present outcome variable. I have 20 lagged treatment variables. Can I fit them all in one regression along with my other demographic and economic controls?

Ex:

Y = a + b1 T_1 + .... +b20 T_20 + cX +E

If I run this model, then can I interpret the effect of short-term (past 3 years) hurricane exposure on my outcome variable as the sum of regression coefficients b1+b2+b3?

[Clyde Schechter]

Can I fit them all in one regression along with my other demographic and economic controls?

I'm not sure what your specific concern is here. Unless you have a staggeringly large number of "controls", you are very unlikely to exceed the limit on the length of a command--and if you do have that many variables you probably wouldn't be able to make any use or sense of the output anyway. Not to mention that the sample size you would need to regress on that many variables would probably make the data set unable to fit in the memory of most computers.

The only real issue I can think of here is whether your data set has enough observations to support a regression with that many variables. There are various rules of thumb, but I think the most liberal of those says you need 10 observations per variable to avoid overfitting noise in the data. And other rules of thumb say you should have 30, or 50, or even 100.

The other thing I will say is that while you can have your 20 lagged variables and include them all in the regression, you can also do this in long layout with a single variable T containing the windspeed for that year. Then you can include the term L(1/20).T in the regression, and all 20 lags will be included as regressors.

[Anupam Ghosh]

Hi Clyde,
Can you please elaborate as to how I can include the term L(1/20)? I am not exactly sure what you mean by that and how to implement it.

Secondly, can you please answer if, "I can interpret the effect of short-term (past 3 years) hurricane exposure on my outcome variable as the sum of regression coefficients b1+b2+b3?"

[Clyde Schechter]

Can you please elaborate as to how I can include the term L(1/20)? I am not exactly sure what you mean by that and how to implement it.

If your data is in long form, and T is your windspeed variable, X is your other variable or variables, do this:

regress outcome_variable L(1/20).T X

Secondly, can you please answer if, "I can interpret the effect of short-term (past 3 years) hurricane exposure on my outcome variable as the sum of regression coefficients b1+b2+b3?"

Well, you can define anything however you want, but the question is whether others will consider it reasonable and useful to do so. I think, however, that the answer here is no. What might be useful and reasonable is to define the effect of short-term hurricane exposure on outcome as b1*T1 + b2*T2 + b3*T3. This will take into account the actual occurrence of hurricanes during those three years, which b1 + b2 + b3 does not do. You can calculate that expression for each observation in your data set using the -lincom- command (see -help lincom- if you are unfamiliar with this).