Timeline for HAC standard error or missing ARMA terms
Current License: CC BY-SA 3.0
14 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Apr 13, 2017 at 12:44 | history | edited | CommunityBot |
replaced http://stats.stackexchange.com/ with https://stats.stackexchange.com/
|
|
| Mar 14, 2017 at 9:15 | history | edited | Richard Hardy | CC BY-SA 3.0 |
added 643 characters in body
|
| Feb 12, 2017 at 11:12 | history | edited | Richard Hardy | CC BY-SA 3.0 |
added 393 characters in body
|
| Jan 22, 2016 at 5:57 | comment | added | Richard Hardy | Once again, read what I said before: ...including the lagged dependent variable (and lagged independent variable) is equivalent to a regression with AR(1) error. That means that both ways you will get the same coefficient estimates. <...> You get the correct estimates... | |
| Jan 21, 2016 at 21:46 | comment | added | Frank | Hi Richard, in the example model $y_t = a + b x_t + u_t$, I guess the coef $b$ is the "structural" parameter you have in mind. Yes, the 2nd solution you suggested can estimate $b$ correctly (but combining them into one equation seems makeing estimation easier...). But should I say I would disagree with the 1st one? If the lagged dependent variable should be in the model, but instead is left out and hidden in the residual. The HAC won't work because the possible correlation between the lagged dependent variable and the regressor would make the estimate of $b$ inconsistent. | |
| Jan 21, 2016 at 19:28 | comment | added | Richard Hardy | So the argument about interest in structural parameters is not compelling? Perhaps it indeed isn't, I am not sure... | |
| Jan 21, 2016 at 19:12 | comment | added | Frank | I see. I will use the dollar signs for math. Thanks for pointing it out. I am tempted to conclude that never use HAC without investigating adding lagged dependent variables. Otherwise the omitted lagged dependent variables could be correlated with the regressors and lead to biased estimate. | |
| Jan 21, 2016 at 18:32 | comment | added | Richard Hardy | Well, in your long comment you seem to show that including the lagged dependent variable (and lagged independent variable) is equivalent to a regression with AR(1) error. That means that both ways you will get the same coefficient estimates. Isn't that satisfying? You get the correct estimates (as long as regression with ARMA errors is the correct model) and preserve the original model (except for introducing some structure in the error term), which may be desirable if you care about structural coefficients. | |
| Jan 21, 2016 at 18:27 | comment | added | Richard Hardy | @Frank, next time you type an equation, put dollar signs in front and at the end. Then you will get proper-looking output. | |
| Jan 21, 2016 at 18:27 | comment | added | Frank | I wasn't saying adding the AR equation for the residual is wrong. It is correct. But estimation could be tougher than just combining the two equations, which can be estimated by the usual OLS. | |
| Jan 21, 2016 at 18:23 | comment | added | Frank | Thanks for your help, Richard =) But I don't think an extra equation for the error can solve the problem. The key thing is that the lag could be correlated with x_t. If the lag is left out in the residual, the estimate of the coef on x_t is no longer consistent. It is an omitted-variable problem. The suggestion of adding an AR equation for the residual doesn't help. For eample, y_t = a + b * x_t + u_t, u_t = c * u_{t-1} + v_t. Combining this two gives y_t = a(1-c) + c * y_{t-1} + b * x_t - b * c * x_{t-1} + v_t. It still shows that the lag should be in the model to estimate the coef b. | |
| Jan 21, 2016 at 18:17 | comment | added | Richard Hardy | @Frank, How come? As long as the model is well specified, what is the problem with that? The two equations would be estimated simultaneously so that the estimation is efficient etc. Regression with ARMA errors is a valid model by itself, the only question is whether it makes sense in a given application. | |
| Jan 21, 2016 at 18:10 | comment | added | Frank | Thanks for your help, Richard =) But I don't think that including an extra equation for the error process can solve the problem. | |
| Jan 21, 2016 at 17:50 | history | answered | Richard Hardy | CC BY-SA 3.0 |