Random Effects Estimator - an introduction

in this video I'm going to talk about another panel data estimation technique which is known as random effects so to talk about random effects I'm going to use an example and it's the example which we've been using in the last few videos so we're looking at the various factors which influence a house price in a given City I at a particular point in time so these time periods could be years they could be months could be decades etc and we say that that's equal to some constant beta naught plus beta 1 times the crime rate in that city I at that time T plus beta 2 times the unemployment rate in that city I at that time period t and furthermore we're assuming that we explicitly controlled for the time dependent factors which don't vary across city by including dummy variables for the different time periods and I'm just not going to include them here so that we don't have to write too much but we're still going to include our unobserved heterogeneity term this alpha right here as well as our idiosyncratic error uoit and we spoke about how it was appropriate to use fixed effects or first differences if we thought that this unobserved term alpha right was correlated with one or more of our independent variables so the reason being that if we were to estimate this above model via pooled OLS in the circumstance where this assumption is true then we would have some sort of endogenous so we definitely can't use poor pulled OLS if this assumption is true so we have to use the techniques which remove this alpha right term here which are known as first differences or fixed effect estimation however if we were to assume that the covariance between alpha ROI and any of the independent variables was in fact equal to 0 then we wouldn't necessary need to use either of these two techniques the first differences or first or fixed effects estimation right because we haven't got this issue of in dodging and plaguing the situation so when might it be reasonable to assume that the Cobra ends between the fixed effect alpha line and any of the independent variables was in fact equal to zero well it might be reasonable in circumstances where by we think we have essentially controlled for all factors which are important in determining our dependent variable so we've controlled explicitly by including them in our equation for all those factors which we think are at least in vast majority important for determining house prices or another way of sort of thinking about this is if we assume that the effect alpha R I is very small so in other words there is some unobserved heterogeneity between different cities but it is its effect is relatively small relative to the other variables perhaps in those two circumstances this second assumption might be a better assumption to go under so if we assume that there is no covariance between alpha R I and the independent variables so that's crime and unemployment in this example what should we then do well you might be tempted to think that what we could actually do is we could just use ordinary least squares on the original model right because the problem with using ordinary squares or pulled OLS on this and regional model was that because the fact we had this unobserved heterogeneity it was going to be both biased and inconsistent but if we don't have this issue whereby there is some correlation between alpha and the independent variables then actually it turns out that called OLS is itself consistent or produces consistent estimates so using pooled OLS is an absolutely fine thing to do and similarly as it turns out so is using first differences and fixed effects estimation both of these two types of estimator are themselves consistent whether or whether we know have this issue of unobserved heterogeneity which is correlated with independent variables but it turns out that essentially these to the fixed effects and the first difference is estimation techniques are a little bit too extreme we don't need to do as much as either of these two techniques dictate essentially the first difference is the problem with that is it throws away one of the observations because we end up with t minus 1 periods for estimation rather than T periods and fixed effects estimates are just a little bit too extreme we don't need to go necessarily that far however called OLS has itself some problems even if we assume that all the conditions which we assumed for first differences and fixed effects are true except of course for this particular assumption here then it turns out that there is going to be some issue with pooled OLS and to see that we are going to write our error up here our composite error which is the thing which we don't actually see are as e to write e so e to I T here is equal to alpha I plus UI T and when we look at the covariance of ETA IT with eta is so that the error in for one city I at some point in time T with the error for the same city I at some other time s then we can write that this is equal to the covariance of alpha Ryne plus UI T with alpha I plus you I s where I've just used this definition for e to righty and even if we assume that there is no covariance between the alphas and the use so both of these two terms in the expansion of this covariance bracket are themselves zero and if we assume that there is no covariance in this idiosyncratic errors uit in us then we're still going to be left with the term which is the covariance between alpha I and alpha I and that particular term the covariance of a pariah now Frey is just the variance of alpha I which I'm gonna call Sigma Alpha squared and the variance is necessarily greater than zero so in circumstances even if we do have this particular assumption being true whereby alpha right isn't correlated with the independent variables if we estimate this above equation via pooled OLS then our errors are going to be civilly correlated with one another and when we have serially correlated errors typically we were in the past we've spoken about how we can use another technique to actually correct for this to a correlation of errors and that particular technique is feasible generalized least squares estimate it's feasible because of the fact that we have to estimate the degree of serial correlation errors and it's gr GLS because essentially we are correcting or we're going to transform a model to correct for this particular serial correlation and in panel models in this particular example the feasible generalized least squares estimator takes on the name of the random effects estimator and because we've corrected for this serial correlation it turns out that random effects models will actually be more efficient than both pulled OLS and fixed effects or first differences

Channel: Ben Lambert

Views: 87,659

Rating: 4.9237289 out of 5

Keywords: Random Effects Model, Econometrics (Field Of Study), fixed effects, first differences

Id: bQampZBzU9Q

Length: 8min 9sec (489 seconds)

Published: Fri Oct 04 2013