Coefficient interpretation difference log - difference log in fixed effects model

[Lisanne Spiegelaar]

Dear Statalist,

I have a question with regards to the coefficient interpretation of my model.

I am doing a fixed effects model on the effect of house price changes on consumption.

My house price index variable, hpilagthree, looks as follows:

gen loghpi = ln(housepriceindex201206100)
by facilityid, sort: gen hpi=loghpi[_n]-loghpi[_n-1]
by facilityid: gen hpilagthree = hpi[_n-3]

My consumption variable, growthcons1, looks as follows:

gen logcons1 = ln(cons1)
by facilityid, sort: generate growthcons1=logcons1[_n]-logcons1[_n-1]

To analyze the effect, I am running the following regression:

xtreg growthcons1 hpilagthree lti savingsrate incomerate age unemp lendingrate, fe vce(cluster facilityid)

I receive the following output:

My question is how I interpret the 7.54. I know that with a log-log model, the coefficient is an elasticity with interpretation: a one percent increase in x results in a beta percent increase in y. However, my model isn't log-log, but delta log - delta log.

My guess is that I should divide the coefficient by 100, as the 'growth rates' (delta log variables) are not in percentages (so not 5%) but in units (so 0.05). Then the interpretation would be a one percent increase in the house price index three months previously increases current consumption by 0.075 percent. I am not sure whether this is correct.

Could anyone advise me whether this is the best way to specify the model and whether my interpretation is correct? Would it perhaps be better if I simply estimate a log log model, so

xtreg logcons1 loghpi[_n-3] lti savingsrate incomerate age unemp lendingrate, fe vce(cluster facilityid)

In that way the coefficient for loghpi would simply be the elasticity, but I am not sure whether I am incorporating house price growth in that case, because my research is centered around the effect of house price growth.


Thanks a lot and kind regards,

Lisanne Spiegelaar

[Phil Bromiley]

You'll increase your chances of a useful answer by following the FAQ on asking questions - provide Stata code in code delimiters, readable Stata output, and sample data using dataex. Also, shorten the post to the minimum needed to demonstrate the problem.

While I suspect there are smarter ways to handle this, a simple way is to use margins. You can back out from change in logs to change in original variables and from the log dv to the original variable.

I'm not sure you need all these change variables. The parameter on a normal regression is just the effect of a change in the iv on the predicted dv. What you're estimating is the effect of a change in the change in the iv on the predicted change in the dv. Seems hard to keep straight.

[Lisanne Spiegelaar]

Thank you Phil. I will see if I can figure out the margins.

[Carlo Lazzaro]

Lisanne:
as Phil wisely pointed out, things can be made simpler starting from you code: provide that you -xtset- your data with a -timevar- too, you can create difference, lags and leads via -tsvarlist- options.

More substantively, if you have (as it seems) panel data, you have repeated measures on regressand and regressor for a given number of measurement episodes (say, years).
Besides, you chose a fixed effect approach: assuming that the user-written command -xtoverid- (unfortunately, -hausman- test does not support non-default satndard errors, nor adding robust/cluster standard errors after -hausman- with default standard errors will pass the muster with any decent reviewer) outcome pointed you in that way, you are focusing on the variation of the conditional mean of the dependent variable within each panel.
All that said, why differenciating the regressand by hand when -xtreg,fe- wil demean it for you?
At the top of that, with such a large sample, the withih R-sq (which is the most relevant under -fe-) is pretty negligible: are you sure that you gave a fair and true view of the data generating process (ie, have you ruled out non-linear relationships between regressor(s) and regressand and/or that no relevant predictor has been excluded from the right-hand side of your regression equation)?