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I have a question concerning the GMM equation specification.

Say we partition each day in 7 intraday intervals. We want to estimate the 7 intraday interval moments for a variable Y observed in those 7 intervals over a period of T days meaning we have t = T*7 total observations for Y.

I first estimate the following model:

Y(t) = c + c(1)*dummy1+c(2)*dummy2+c(6)*dummy6+c(7)*dummy7 +error(t)

(where c represents a constant and dummy1-7 represent dummy variables taking the value of 1 and 0, indicating if the observation occurrs in the according period) I use dummy1 dummy2 dummy6 dummy7 as instrument variables (in moment conditions)

in order to see if the observations in periods 1, 2, 6, 7 (in the morning and or afternoon) are statistically different from the variables in the intervals 3-5. The results will be very similar to OLS regression results except for error homscedasticity and no auto correlation in errors.

QUESTION: Is it legitimate to add another variable -- c(8)*X(t) -- (with the same amount of obseravtions t as Y) as moment such that the equation takes the form ???

Y(t) = c + c(1)*dummy1+c(2)*dummy2+c(6)*dummy6+c(7)*dummy7 +c(8)*X(t) + error(t)

- With OLS this is clearly no problem but with GMM? I am not sure if one can use moment -- c(8)*X(t) -- that does enter the estimation for each the Y(t) observations. as i enter X as additional instrument variable for the orthogonality conditions, i get an error message: near singular matrix ...

thanx for advice

f. :rofl: :rofl: