Interpreting stata result

[Tita Kusuma]

Hello Everyone,
I would like to ask about how to interpreting my estimation result.
I am using panel data with GLS, Fixed Effect.

The model is :
logYit=logCAPit+logLFit+SPit+SSit+STit+e ,

whereas Y, CAP and LF are real number of GDP, Capital and Labor force;
and SP, SS, ST are, respectively, share of laborforce that completed primary, secondary and tertiary school.

the result is as below:
logY= 12.8288 + 0.0377063 logCAP + 0.3179409 logLF + 1.763282 SS + 1.510425 ST

sigma_u | .84891852
sigma_e | .08279592
rho | .99057732

SP is not significant.

Would you please show me how to interpret the result in such " 10% increase of..." and also how the logic works?
Thank you in advance.

[Clyde Schechter]

The model is :
logYit=logCAPit+logLFit+SPit+SSit+STit+e ...

the result is as below:
logY= 12.8288 + 0.0377063 logCAP + 0.3179409 logLF + 1.763282 SS + 1.510425 ST

No, that is not the result. You have omitted the term for SP. Even though it is not "significant" it is still a part of the model, and, indeed, if you re-ran the model omitting SP you would get somewhat different results. This is a serious mis-interpretation of what it means for an effect to be not statistically significant.

Turning to your original question, this is a matter of high school algebra.

A 10% increase in CAP means that CAP is multiplied by 1.10. Since the log of a product is the sum of the logarithms, it means that log CAP is increased by log 1.10, which is 0.0953 to four decimal places. The increase of 0.0953 in logCAP is then associated with an expected increase in logY of 0.0377063*0.0953, which, again to four decimal places, is 0.0036. Again because the sum of two logarithms is the logarithm of the product, this increase in logY corresponds to a multiplication of Y by a factor of e^0.0036, which, again to four decimal places, is 1.0036. So if Y has gone up by a factor of 1.0036, one can also say that it has increased by 0.36 percent.

It is common in this situation to use a shortcut approximation. When the regression coefficients are small in magnitude (generaly speaking, if they are less than 0.1) it is approximately true that when the coefficient is b, a 10% increase in the predictor variable will be associated with a 10b% increase in the outcome variable. As you can see, had we applied this shortcut approximation, we would have gotten 0.38 percent, which is fairly close. The larger b is, the poorer the approximation, and when b > 0.1 (or < -0.1) it is too inaccurate to be useful. It is never exactly correct unless b = 0.

[Phil Bromiley]

You are likely to find it helpful to use the margins command after your estimation to look at changes in predicted values (or functions of predicted values like exp(ln(y))) for changes in x's.