I wrote down a structural demand model, simulated data for exogenous variables (product features and consumer characteristics), and generated data for endogenous variables (observed consumption choices). I then estimate the model with the data using a maximum likelihood estimator. However, the estimates are very different from the true parameters used for simulation. Why does this happen and what should I do?

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    $\begingroup$ This question is unanswerable without some details of the structural model and the econometric model. $\endgroup$
    – Herr K.
    Oct 6 '20 at 5:47
  • $\begingroup$ In general, if there is no coding error, should we expect to recover true parameters by doing what I describe in the question? $\endgroup$ Oct 6 '20 at 6:27
  • $\begingroup$ @DavidXiaoyuXu there are too many reasons to count. Let me give you one example. Suppose you generate system of equations in a way that you on purpose make sure the series are non-stationary and then you will without differencing apply VAR model that requires stationarity in order to produce unbiased estimates. You wont reproduce true parameters just because the model is not able to do so because assumptions of the model are not satisfied. Furthermore, you cant expect the parameters to be estimated precisely as true parameters can be only obtained asymptotically if you generate only few obs. $\endgroup$
    – 1muflon1
    Oct 6 '20 at 8:36
  • $\begingroup$ then estimated parameters may differ greatly from the true values. It could even be just a coding errorThere are myriad of other things that could go wrong without knowing detail of how you generated the values, what model you are using etc its impossible to know. Also its not just enough to say you are using maximum likelihood estimator - that does not narrow it any more down than if you would ask us to guess what your pet is and just said its mammal. You should provide at least minimal reproducible example. $\endgroup$
    – 1muflon1
    Oct 6 '20 at 8:38
  • $\begingroup$ what 1muflon1 said was great but, also, if you estimate using MLE, then the error term assumptions are extremely crucial and how one obtains the likelihood to maximize ( given the equations ) can be tricky, especially if there are endogenous variables. For example, are the endogenous variables correlated with the error term ? So, as 1 muflon1 said, if you don't give more details, you probably won't get any useful answers. $\endgroup$
    – mark leeds
    Oct 7 '20 at 2:06

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