Time Dummies and Time Trend in the same equation.

[Riju Joshi]

Hello,

Can we run this regression:

Y_it = a + bX_it + c₂Time₂ + ... + c_TTime_T + ht + U_it

i = 1,2,..., N ; t = 1,2,3...,T

Where

Time_t are time dummies

t is the time trend.

In other words, can we run a regression with both time dummies and and a time trend? I suspect that we cannot, but am looking for a more formal explanation.

Thank you!

[Rich Goldstein]

of course you can - which you would know if you had tried it; some people use this as a "test" of linearity: if the dummies are statistically significant then there is at least some non-linearity though the form might not be obvious

[Jeff Wooldridge]

No, it doesn't make sense to include a full set of time dummies along with any function of time. Putting in time dummies allows for any kind of trend, of which a linear trend is a special case. A program like Stata will drop either the linear time trend or one of the dummies. Now, if h gets an i subscript then the model makes sense.

Incidentally, it's not just a linear time trend or other functions of time that are redundant. Any macro variables that don't change across i are perfectly collinear with a full set of time dummies. That's an advantage of including the time dummies: one need not restrict the time trend or collect data on aggregate variables.