Question

Consider the following model used to explain the growth path of the monetary aggregate M2:

ln(M2_t) = ?_o + ?₁time_t + ?₂D1_t + ?₃D2_t +?₄D3_t + … + ?₁₂D11_t + u_t

where: M2 = M2 measure of the money supply in month t
           time_t = time (in months)
           D1_t, D2₂, …, D11_t = monthly dummy variables corresponding to January through November
A) In this specification, what is the interpretation of the coefficient on time_t?

B) What is the interpretation of the coefficients on each of the monthly dummy variables in the equation above?

C) In the model above, why is a dummy variable for the month of December omitted?

Answer 1

A) For the given log-linear regression equation; the dependent variable is monetary aggregate M2 which is a measure of currency, checkable and saving deposits over the given months.

when explanatory variable is the time in months, the slope coefficient of time t implies that on average the rate of growth of M2 will change by the amount of the slope for one month change in time, ceteris paribus.

B)In the equation above, each dummy variable implies different months from January to November. For example, if D1t=1 and rest zero implies the rate of growth of M2 for the month of January.

C) The dummy for the month of December is omitted because otherwise, it would lead to dummy variable trap which implies that if there are n categories to be estimated then n-1 dummy variables are always used and one is kept as benchmark variable. Here December is the benchmark variable when all dummies are zero.