Maximum Likelihood Estimation using Grid Searching Gauss file(s) max_grid.g Matlab file(s) max_grid.m Consider the regression model set out in Exercise 1.

(a) Simulate the model for T = 5 observations using the parameter values θ = {β = 1, σ2 = 4}.

(b) Derive an expression for the gradient with respect to β, GT (β).

(c) Choosing σ 2 = 4 perform a grid search of β over GT (β) with β = {0.5, 0.6, · · · , 1.5} and thus find the maximum likelihood estimator of β conditional on σ 2 = 4.

(d) Repeat part

(c) except set σ 2 = 3.5. Find the maximum likelihood estimator of β conditional on σ 2 = 3.5.