tag:blogger.com,1999:blog-2198942534740642384.post8491821970380945482..comments2023-10-24T03:16:41.009-07:00Comments on Econometrics Beat: Dave Giles' Blog: Another Gripe About the Linear Probability ModelDave Gileshttp://www.blogger.com/profile/05389606956062019445noreply@blogger.comBlogger24125tag:blogger.com,1999:blog-2198942534740642384.post-4278309238457807762019-03-29T11:36:26.207-07:002019-03-29T11:36:26.207-07:00There is no such thing as the "true marginal ...There is no such thing as the "true marginal effect", because the marginal effect depends on x. It is the researcher who chooses to calculate it for the mean x, but why should we care about the derivative at this particular point? This is just one possible x, no better and no worse than any other. LPM (OLS) gives you a weighted-average of marginal effects at different values of x. Of course it will be a different number! (And even more if the distribution of x is ugly). This is like an apples-to-oranges comparison. But this is not a problem of OLS per se, it is a problem of the choice of mean x as the point where marginal effect was calculated. A somewhat fairer test could be to at least calculate the average partial effect of MLE and then compare it to OLS - these are the two competing ways of aggregating marginal effects into one single parameter of interest. OLS can be seen as a more convenient one, especially since MLE (and hence average partial effects) relies on untestable distributional assumptions to identify the parameter of interest: here you even simulated a normal epsilon and selectively picked a model that assumes a normal epsilon, but in real data we would never know...Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-56497517883268865662019-02-18T00:05:20.862-08:002019-02-18T00:05:20.862-08:00Dave: thank you for your prompt reply and feedback...Dave: thank you for your prompt reply and feedback.Federico Belottinoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-30938223063324129312019-02-15T14:29:28.131-08:002019-02-15T14:29:28.131-08:00Frederico - I have now amended the EViews code and...Frederico - I have now amended the EViews code and updated the blog post. Again - much appreciated.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-25741585730409782912019-02-14T09:55:57.562-08:002019-02-14T09:55:57.562-08:00Frederico - you are right! How silly of me. The st...Frederico - you are right! How silly of me. The structure I used would have been correct if it had been the Logit model, and U'd used the cumulative logistic instead of the cumulative Normal. I'll have to fix this at some stage, even though this post is ancient history. Second, it's moot as to whether one reports the marginal effect at the mean, or the average of the marginal effects. Of course, you do get different answers. Finally, the X variable was just artificially generated - it's in the EViews workfile alreadt and wasn't generated in the program. DGDave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-2346854863949221972019-02-14T08:03:18.615-08:002019-02-14T08:03:18.615-08:00Dear Dave,
I'd like to jump in here, even tho...Dear Dave,<br /><br />I'd like to jump in here, even though this is an old thread.<br />In particular, I'd like to ask for two clarifications on the Eviews code you used for the Monte Carlo analysis. I might be wrong or missing something since I don't know the Eviews syntax very well but it seems to me that marginal effect of x (at means) in a probit model should be<br /><br />@dnorm(c(1)+c(2)*@mean(x))*c(2)<br /><br />instead of<br /><br />@cnorm(c(1)+c(2)*@mean(x))*(1-@cnorm(c(1)+c(2)*@mean(x)))*c(2)<br /><br />Am I wrong?<br />Second: Why did you consider the marginal effect at mean instead of the average marginal effect? How the regressor x is generated? I wasn't able to find it looking at the code.<br /><br />Many thanks,<br />Federico<br /><br /><br /><br /><br /><br /><br />Federico Belottinoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-53402437619015955232016-06-03T17:43:38.892-07:002016-06-03T17:43:38.892-07:00I'd discriminate between the two using one the...I'd discriminate between the two using one the of the available information criteria. A useful paper on this is: G. Chen & H. Tsurumi, "Probit and Logit MOdel Selection", Communications in Statisics - Theory & Methods, 2010, 40, 159-175. Here's the abstract:<br /><br />Abstract:<br />"Monte Carlo experiments are conducted to compare the Bayesian and sample theory model selection criteria in choosing the univariate probit and logit models. We use five criteria: the deviance information criterion (DIC), predictive deviance information criterion (PDIC), Akaike information criterion (AIC), weighted, and unweighted sums of squared errors. The first two criteria are Bayesian while the others are sample theory criteria. The results show that if data are balanced none of the model selection criteria considered in this article can distinguish the probit and logit models. If data are unbalanced and the sample size is large the DIC and AIC choose the correct models better than the other criteria. We show that if unbalanced binary data are generated by a leptokurtic distribution the logit model is preferred over the probit model. The probit model is preferred if unbalanced data are generated by a platykurtic distribution. We apply the model selection criteria to the probit and logit models that link the ups and downs of the returns on S&P500 to the crude oil price."Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-15287064473372509142016-06-02T00:24:25.059-07:002016-06-02T00:24:25.059-07:00Great posting! I have a quick question for you. Wh...Great posting! I have a quick question for you. What if there is no a priori reason for preferring the probit model (e.g., we are not doing a simulation and not knowing it to be the true model)..how can we choose between the probit model and the logit model?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-55727922891779446082014-12-12T09:13:39.410-08:002014-12-12T09:13:39.410-08:00This comment has been removed by a blog administrator.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-46974577291650295782014-11-01T01:11:03.319-07:002014-11-01T01:11:03.319-07:00Very useful posting since I am now dealing with bi...Very useful posting since I am now dealing with binary dependent variable. I am still learning your another post about robust standard error for Probit and Logit. Very helpful!! TonyAnonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-74682616157637621372013-02-06T05:48:12.497-08:002013-02-06T05:48:12.497-08:00Trying simulatating a model in which there is a tr...Trying simulatating a model in which there is a true "absolute treatment effect", e.g. <br /><br />y = a0 + a1*x + e in which e ~ bernoulli<br /><br />Then run LPM and logit.<br /><br />Better yet add a covariate to the equation above (e.g. a2*w) and show how logit will suggest that "a1" varies with w when it actually doesn't.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-46769429987419328972013-02-05T11:54:49.619-08:002013-02-05T11:54:49.619-08:00How did your estimates of B2 turn out?How did your estimates of B2 turn out?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-81186730601729032722013-01-13T14:02:32.372-08:002013-01-13T14:02:32.372-08:00Thanks. A follow-up if I could...
If I use the lo...Thanks. A follow-up if I could...<br /><br />If I use the logistic link function, then maximizing (1-a)*(1-p) + ap (MLE?) in the binary response case seems to be identical to minimizing absolute error. Is this true?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-9666530148242014392013-01-12T10:07:25.007-08:002013-01-12T10:07:25.007-08:00Personally, I'd see more sense in that than ju...Personally, I'd see more sense in that than just using OLS.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-68561132490235240462013-01-11T20:32:54.174-08:002013-01-11T20:32:54.174-08:00Dave, if I use a logistic link function but minimi...Dave, if I use a logistic link function but minimize MSE instead of using MLE, do I still have the same problems?Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-64065432151598424062012-09-06T10:35:49.069-07:002012-09-06T10:35:49.069-07:00Rose - I have some sympathy with that, but there&#...Rose - I have some sympathy with that, but there's a good literature on how to do things properly, even in that case. For example:<br /><br />http://www.unc.edu/~enorton/AiNorton.pdf<br /><br />and<br /><br />http://www.sciencedirect.com/science/article/pii/S0165176510000777Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-53932092152837939082012-09-06T10:07:54.153-07:002012-09-06T10:07:54.153-07:00Hi Dave,
What about when you have many interacted...Hi Dave, <br />What about when you have many interacted independent variables and a binary dependent variable? (for example interacting many independent variables with a set of dummies) Given that calculating marginal effects of interactions is complex when there are so many. Could you be justified in using LPM in this situation?<br />RoseAnonymoushttps://www.blogger.com/profile/03163427526599405122noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-58482615481929212282012-07-18T13:37:41.962-07:002012-07-18T13:37:41.962-07:00Scott: Thanks for the comments. First one - fair e...Scott: Thanks for the comments. First one - fair enough.<br /><br />Second one - Yes, MLE will also be inconsistent if the Probit DGP is wrong. However, other work I've played around with shows that the asymptotic bias associated with the LPM is often greater than that associated with an incorrect nonlinear model. For example, if the data are generated according to Probit, and then we fit either LPM or Logit.<br /><br />This is something I'm currently working on more seriously - see one of my responses at http://davegiles.blogspot.ca/2012/07/more-comments-on-use-of-lpm.html#comment-form<br /><br />This certainly deserves proper investigation.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-19028855767001934402012-07-18T10:30:08.545-07:002012-07-18T10:30:08.545-07:00Well, Dave, you mention that panel data you would ...Well, Dave, you mention that panel data you would consider the use of LPM, but not cross-section... but there are many cases of using lots of FE in cross-section data, and I think it is *really* hard to defend non-linear models in cases such as these. FE account for variation in the data in a completely general way -- the non-linear model relies on the functional form.<br /><br />Also, your monte carlo example is a bit of a cherry pick; the LPM is the "wrong" model in this case. MLE will be inconsistent if the probit model is wrong, too.Scott Bnoreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-71146312839879446792012-06-02T23:14:00.232-07:002012-06-02T23:14:00.232-07:00Alan: Thanks! Glad it was helpful.Alan: Thanks! Glad it was helpful.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-6440398194306858352012-06-02T18:52:02.016-07:002012-06-02T18:52:02.016-07:00This post has some very useful information about L...This post has some very useful information about LPM. Thanks for the effort you put into this and your other interesting (and often entertaining!) blog posts. <br /><br />I try to do my bit by being as DEMONSTRATIVE as possible in telling my Econ 345 students why they must use probit or logit instead of LPM.Alan Mehlenbacherhttp://web.uvic.ca/~amehlen/noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-43409867900475937552012-06-01T11:42:54.491-07:002012-06-01T11:42:54.491-07:00Brian: See J. A. Angrist, "Estimation of Limi...Brian: See J. A. Angrist, "Estimation of Limited Dependent Variable Models With Dummy Endogenous Regressors: Simple Strategies for Empirical Practice", Journal of Business & Economic Statistics, 2001, 19, 2-28 (includes discussion & response). email me directly if you have trouble getting this.Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-60398031276992543522012-06-01T11:41:56.297-07:002012-06-01T11:41:56.297-07:00Dimitriy: We'd need to model the het. in the L...Dimitriy: We'd need to model the het. in the Logit or Probit model, because we know that the MLE for the PARAMETERS in these models is inconsistent if there is het. I think you've already seen my earlier post on this point. I'd still avoid the LPM!Dave Gileshttps://www.blogger.com/profile/05389606956062019445noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-10811656610738812502012-06-01T11:36:36.426-07:002012-06-01T11:36:36.426-07:00Would you still do this if heteroscedasticity was ...Would you still do this if heteroscedasticity was an issue?Dimitriyhttps://www.blogger.com/profile/02728704178088861714noreply@blogger.comtag:blogger.com,1999:blog-2198942534740642384.post-21276586726714432892012-06-01T11:23:56.000-07:002012-06-01T11:23:56.000-07:00Dave: Can you suggest a reference for the endogen...Dave: Can you suggest a reference for the endogenous dummy covariate case?Brian Fergusonhttp://cocktailpartyeconomics.com/blogs/noreply@blogger.com