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currently I am trying to estimate a simple linear regression: \begin{equation} y_t = X \beta + \varepsilon_t, \end{equation} where I try to find 4 coefficients and one specific predictor is an autoregressive predictor: $y_{t-1}$. OLS will yield biased results so I am attempting to use GMM with the following moment conditions: \begin{equation} E(y_{t-2}\varepsilon_t) = 0 \\ E(y_{t-3}\varepsilon_t) = 0 \\ E(y_{t-4}\varepsilon_t) = 0 \\ E(y_{t-5}\varepsilon_t) = 0 \\ E(y_{t-6}\varepsilon_t) = 0 \\ \end{equation}

After implementing GMM in MATLAB, I get the following warning: "Matrix is close to singular or badly scaled. Results may be inaccurate. RCOND = 1.080661e-21.". Moreover, this warning is quite correct as my estimated GMM coefficients are of the magnitude e+150...

I know that the optimal weighting matrix $W$ is the following: \begin{equation} W = S^{-1} = (E(g(x_t, \beta)g(x_t, \beta)'))^ {-1}, \end{equation} where $g$ are my moment conditions.

Why is my Weighting matrix singular? and how do I prevent it? What advice can you give me to solve the endogeneity problem for estimating my regression?

user326465
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  • Do you think GMM will yield unbiased results? I would doubt that. – Richard Hardy Jun 24 '21 at 16:55
  • @RichardHardy I do not think it will yield unbiased results, GMM is generally biased I know. But is GMM a better way to estimate a regression including an Autoregressive explanatory variable compared to OLS? if not, are there better estimation methods? – user326465 Jun 25 '21 at 06:23
  • I do not know, but I do not remember hearing that GMM would be preferable to OLS in such cases, so perhaps it is not. But I am not sure. Also, see [this](https://stats.stackexchange.com/questions/182592/) and the comments by Glen_b. – Richard Hardy Jun 25 '21 at 08:07

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