I am refreshing my understanding of econometrics and have a question regarding interpretation of square of logarithm-transformed term in linear regression. The interpretation of a square term or a logarithm-transformed term is standard. But what does it mean when we have a variable that is first logarithm-transformed and then taken square? For example, suppose we are interested in the relationship between income and household expenditure. We want to predict how income affects household expenditure decision. The LHS of the regression is
log (yearly household expenditure)
measured by dollars and the RHS variable is
log(income), (log(income))^2, and a vector of covariates.
Traditional double-log model's coefficient means how unit percentage change in independent variable is associated with percentage change in dependent variable. But do you have any ideas how to interpret regression results from a squared logarithm specification?
Thanks for your help!