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I have the following two models. The first is a level-log model, and the second is a log-level model. These models are two separate regressions and are estimated independently.

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Assume that α=0.036 and β=0.549. Based on these values, I want to calculate the economic significance of the effects of my independent variables as follows:

Change in the dependent variables in response to one standard deviation increase in the independent variables.

Suppose that after multiplying α and β with the respective standard deviations, the final values are equal to 0.020 and 0.120.

Will you please tell me how should I interpret these two number? in %? How much change is observed in my dependent variable in levels if the independent variable in log increases by 0.020?

I know how to interpret coefficients in level-log model and log-level models but got a bit confused here.

Will you please share your opinion?

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Interpretation of $\alpha$ : one percent change in $X_{it}$ is associated with $\alpha * \ln\left(\frac{101}{100}\right)$ change in $Y_{it}$.

Interpretation of $\beta$ : an increase of one-unit in the Height would result in $\left(e^\beta - 1\right)*100\%$ change in $Y_{it}$.

For more information, you can see this document

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  • $\begingroup$ Thank you for your message. I do not have problems with interpreting α and β. My question was about its economic significance. Would 0.020 and 0.120 have the same interpretation as α and β? $\endgroup$ – gluark May 27 at 19:14
  • $\begingroup$ I suppose 0.02 is $\frac{\alpha}{sd_\alpha}$. If it's this then, the coefficient $\alpha$ will be significant if 0.02 is greater than $t_{(3),\alpha}$ a student statistic. $\endgroup$ – Abdoul Haki May 27 at 19:27
  • $\begingroup$ I think I could not convey my message in a clear way. My question is about economic significance. Not statistical significance. $\endgroup$ – gluark May 27 at 19:32
  • $\begingroup$ 0.02 is α multiplied by its standard deviation. I assume that the independent variable increases by one standard deviation. $\endgroup$ – gluark May 27 at 19:41
  • $\begingroup$ I don't know if I understand properly. if you are talking about economic significance, it doesn't depend of the values you obtain by it more depend on the litterature review $\endgroup$ – Abdoul Haki May 27 at 19:53

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