Proof Gauss Markov Theorem

From a previous posts on the Gauss Markov Theorem and OLS we know that the assumption of unbiasedness must full fill the following condition Continue reading Proof Gauss Markov Theorem

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CLRM – Assumption 1: Linear Parameter and correct model specification

Assumption 1 requires that the dependent variable \textbf{y} is a linear combination of the explanatory variables \textbf{X} and the error terms \epsilon. Assumption 1 requires the specified model to be linear in parameters, but it does not require the model to be linear in variables. Equation 1 and 2 depict a model which is both, linear in parameter and variables. Note that Equation 1 and 2 show the same model in different notation.

Continue reading CLRM – Assumption 1: Linear Parameter and correct model specification

Capital Adjustment Costs

Understanding investment activity in an economy is not trivial. The erratic nature of firm level investment activity is somewhat of a mystery to me and it took me quite some time to get a vague idea of what could be the generating process behind such an erratic behavior. I think understanding capital adjustment costs was the key to understand why it can be rational for firms to invest in a spasmodic way. In this post I would like to shortly summarize part of what I learnt so far and list different types of capital adjustment costs found in the literature.

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Unbiased Estimator of Sample Variance – Vol. 2

Lately I received some criticism saying that my proof (link to proof) on the unbiasedness of the estimator for the sample variance strikes through its unnecessary length. Well, as I am an economist and love proofs which read like a book, I never really saw the benefit of bowling down a proof to a couple of lines. Actually, I hate it if I have to brew over a proof for an hour before I clearly understand what’s going on. However, in order to satisfy the need for mathematical beauty, I looked around and found the following proof which is way shorter than my original version.

Continue reading Unbiased Estimator of Sample Variance – Vol. 2

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“In God we trust; all others must bring data.” W. Edwards Deming

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