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Recall the linear model y = Xβ + ε where X is an NxK design matrix (observed 'independent' K variables), Nis the number of observations, K is the number of covariates, y is an N-dimensional vector of observed dependent variable, a is an N-dimensional vector of unobserved random errors, and β is a K-dimensional vector of unknown parameters to be determined from the data The OLS estimator is
β^LS = (X' X)-1 X'y
where β^LS, or b, is the estimator of this linear statistical model, and "≡" stands for definition. Show that this estimator does not exist if the number of observations is smaller than the number of explanatory variables (including the constant): N<K. What is the rank of X'X in this case (where stands for transpose)?
This is a technical question where insufficient rank will lead to a poor OLS solution. There is a canonical proof of this either online or in Gujarati, Stock and Watson, Greene or other texts that they should find for me and use, with matrix algebra notation. It just involves researching or looking up the right matrix solution in a text and typing it up so it''s not a lot of work to do, except maybe the typing.
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In response, she has proposed legislation that would award each existing firm 20 percent of a contract for 600 units at a contracted price of $100 per unit. If this legislation is passed, by how much should you expect your profits to change?
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