Interpreting coefficients in log-linear model when independent var is percent

[Jarron VanCeylon]

If I run a model where the dependent variable is log sales price of a home and the independent variable in question is (for example) the percent unemployment in the town where the home is located, how do I interpret the coefficient?

Example) ln(sales price) = Bo + B1 * %Unemployed ..........

And say the coefficient on B1 is -0.0014


Do I treat this as log-log model where a 1% increase in unemployment is associated with a 0.0014% decrease in sales price (on avg, all else equal)?

Or do I treat it as log-linear and transform B1*100 to interpret?

I am confusing myself to no end.

Thank you!
-j

[Clyde Schechter]

Do I treat this as log-log model where a 1% increase in unemployment...

No, you can't say anything about a 1% increase in unemployment with this model--the effect of that would depend on the baseline percent unemployment. You can say something about a 1 percentage point difference in unemployment.

Reason it through. When the unemployment rate changes by 1 percentage point, because B1 = -0.0014, the associated difference in ln sales_price is -0.0014. A difference of -0.0014 in ln sales_price corresponds mathematically to a decrease of sales_price itself to its original value * exp(-0.0014). Now exp(-0.0014) = 0.9986 (to four decimal places). So, expressed in the percentage metric, the associated change in sales price is to 99.86% of its original value, i.e. a decrease of 0.14%.

So, summing it up in a single sentence: a 1 percentage point increase in the unemployment rate is associated with a 0.14% decrease in sales price.

[Jarron VanCeylon]

Got it, thank you!