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I have some elementary problems understanding the consequences of using/adding a lagged dependent variable in my predictive model. I’m trying to predict values $Y_{i,t+\tau}$ for $\tau=1-3$ with:

$Y_{i,t+1}=a+bY_{i,t}+cX_{i,t}+e_{i,t+1}$

$Y_{i,t+2}=a+bY_{i,t}+cX_{i,t}+e_{i,t+2}$

$Y_{i,t+3}=a+bY_{i,t}+cX_{i,t}+e_{i,t+3}$

I already performed a pooled regression where you basically ignore individual firm effects and time-effects and treat every subject equally. As I am trying to forecast different levels (in USD) and my data appears to be extremely tailed as it covers a few extremely large subjects (with extremely high values) but also many small subjects the predictions of the model perform rather poor as the intercept $a$ that is equal for all subject seems largely responsible for this. A fixed model however with individual intercepts is not valid with Lagged dependent variables as the LDV is correlated with the within errors. To account for the heavy tailed errors I already estimated the pooled model with the rlm package (robust lm) that produced slightly better results but overall they appear still very unsatisfactory.

I further read that adding LDV’s results in biased and inconsistent estimators as there is severe correlation between the predictor variables and the model errors and that regular procedures for autocorrelation are not valid anymore. One solution I came across is the use of Instrumental Variables with an Anderson-Hsiao Estimator (i.e using a lag -2 that is not correlated with the error term (with non-autocorrelation assumed but how can you assume no autocorrelation if you incorporate a lag?) Another one is the Arellano Bond GMM estimator, however applying GMM you have to set up moment conditions and I have no idea how to do that and I don’t know exactly how this methods work. What I care about is to obtain an unbiased estimator with valid coefficients and not about standard errors as I don’t do inference. Are there any other strategies to cope with LDV’s I am currently unaware of and what is the best/ideal/easiest way to deal with such matter? Do you best take care of some issues while you ignore others (e.g. autocorrelation)? I’m a little bit lost here.

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  • $\begingroup$ Can i somehow improve the question? ie. narrow it down further so that people are more likely to help? $\endgroup$
    – Gritti
    Jul 17, 2014 at 6:39
  • $\begingroup$ To be honest, it's just a bit hard to read. Maybe put the actual question in bold? Also maybe look into autoregressive distributed lag models. $\endgroup$
    – shadowtalker
    Aug 2, 2014 at 15:39
  • $\begingroup$ I guess you could improve the question by showing some of the steps you took in R as it is kind of hard to visualise what you're actually trying to do. It is not really clear what you're really asking. With regard to the use of LDV's this paper by Beck and Katz came to my mind and might be of some help. Also given the tailed data this paper by Shor et al. on Bayesian multilevel modeling approach might be of interest. $\endgroup$
    – horseoftheyear
    Aug 2, 2014 at 18:43

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