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On the domain of positive real number is OLS on count data a consistent estimator of coefficients? I am trying to understand if the estimator is inefficient or produces biased SEs but is nevertheless a consistent estimator of betas.

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2 Answers2

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It depends on the distribution of the count data. Consider a Poisson regression, or a Negative Binomial Regression, depending on how your counts are distributed.

That said, sometimes you can have OLs with count data: see OLS regression with count data

RandomForestRanger
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In answer to the title question: Yes. The Gauss-Markov Theorem says the OLS estimate is the best linear unbiased estimator of the regression coefficient and this property has nothing to do with the distribution of the outcome (although it doesn't really make a ton of sense if the outcome is not numeric)

https://en.wikipedia.org/wiki/Gauss%E2%80%93Markov_theorem

not_bonferroni
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    Gauss-Markov assumes equal variances among observations. For count data like Poisson, variance increases with the number of counts, so Gauss-Markov might not hold for count data. – EdM Aug 28 '19 at 21:00