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Wooldridge (Intro Econometric book) he states that seasonal dummy variables (say a dummy for the calendar month) satisfy the strict exogeneity assumption because "they follow a deterministic pattern. For example, the months do not change based upon whether the explanatory variables or the dependent variable changes ".

Why is this? What does the explanation have to do with the error term (data not included in the regression that influence the dependent variable) being correlated with any of the seasonal dummies?

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  • $\begingroup$ Although it's true that "winter is winter", it is not true that the variable called winter is a constant. It is 1 in the winter and 0 in the spring, summer, and fall. I don't know the answer to the OP's question. In my limited understanding, for a seasonal dummy to be strictly exogenous, it would have to be the case that for every year, the variation in the error term during the entire year would have to be the same as the variation in the error term in each season of that year. But each year only has one winter and so it seems to me that the variation in the single error term for a ... $\endgroup$ – Lifetime Beginner May 24 '17 at 2:09
  • $\begingroup$ ... year's winter is zero while the variation in the four error terms for an entire year may not be zero. Obviously, my thinking is wrong, but I don't know where my mistake is $\endgroup$ – Lifetime Beginner May 24 '17 at 2:09
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Strict exogeneity means that the error $u_t$ is uncorrelated with all past and future values of the seasonal dummies. This means that such variables cannot react to shocks to $y$ in the past or the future. Suppose consumers feel worried about the economy in December and such sentiments are unobserved. This means there was a negative shock to Amazon sales that month as people cut back on presents. Big negative error. I don't get my pony. But Amazon just cannot decide to have a Christmas season again in January. Contrast this to the effect of police on crime example from earlier in that chapter. If there was a gang war in December, the police force would jump $n$ months later as the mayor gets tough on crime and the cadets graduate. Now that would violate the strict exogeneity assumption.

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  • $\begingroup$ For the first example (Amazon), what if the error tended to be larger (prediction too low) each December? Would that not show a correlation between that seasonal dummy (for December) being "1" and the error? I guess that is what confused me - how could you know if a dummy tends to be correlated with error in advance? $\endgroup$ – B_Miner Nov 29 '12 at 20:13
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    $\begingroup$ Wooldridge makes the (strong) assumption that the seasonal patterns are constant across time. So if there was systematic error in December, that coefficient should pick that up. $\endgroup$ – Dimitriy V. Masterov Nov 29 '12 at 20:56
  • $\begingroup$ Here's the link to the text: books.google.com/… $\endgroup$ – Dimitriy V. Masterov Nov 29 '12 at 21:03
  • $\begingroup$ Dimitriy, so your Amazon example is related to the feedback example on page 348? So we just are arguing that $u_{t}$ (the deviation of Y at time t above or below its average value) does not effect the value of a future X - which makes sense. Especially given your point that if there was a systematic error in December, that the coefficient would pick it up and the error would not be there... $\endgroup$ – B_Miner Nov 30 '12 at 1:51
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    $\begingroup$ I would stick a coefficient on that lagged $x$, but otherwise that sounds reasonable to me. $\endgroup$ – Dimitriy V. Masterov Nov 30 '12 at 3:14
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A seasonal dummy is nonrandom: Whatever sample you draw, winter is winter, never summer. The covariance of a random variable and a constant is zero.

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