Question

Suppose you believe that different months have different effects on sales tax collections. Please write a regression model that would capture this.

Answer 1

There are 12 months in a year.

The sales tax collection is compiled at the annual level.

Create 12 dummy variables, one dummy variable for each of the 12 months, such as D1, D2, D3, D4, D5, D6, D7, D8, D9, D10, D11, and D12.

Assume a given month (say, month of Jan) as the base month.

So, the regression model should be:

Annual_Sales_tax = b0 + b2*D2 + b3*D3 + b4*D4 + b5*D5 + b6*D6 + b7*D7 + b8*D8 + b9*D9 + b10*D10 + b11*D11 + b12*D12 + e

Where, Annual_Sales_tax is the dependent variable

e = Residual term

It shall be noted that D1 is the base dummy variable considered, such that expected Annual_Sales_tax in month of Jan is indicated by the regression coefficient b0