Weak Instruments Gauss file(s) linear_weak.g Matlab file(s) linear_weak.m This exercise extends the results on weak instruments in Example 5.10. Consider the model y1,t = y2,t

Weak Instruments Gauss file(s) linear_weak.g Matlab file(s) linear_weak.m This exercise extends the results on weak instruments in Example 5.10. Consider the model y1,t = βy2,t + u1,t y2,t = φxt + u2,t, ut ∼ N  0 0  ,  1.00 0.99 0.99 1.00  , where y1,t and y2,t are dependent variables, xt ∼ U(0, 1) is the exogenous variable and the parameter values are β = 0, φ = 0.5. The sample size is T = 5 and 10, 000 replications are used to generate the sampling distribution of the estimator.

(a) Generate the sampling distribution of the IV estimator and discuss its properties.

(b) Repeat part

(a) except choose φ = 1. Compare the sampling distribution of the IV estimator to the distribution obtained in part (a).

(c) Repeat part

(a) except choose φ = 10. Compare the sampling distribution of the IV estimator to the distribution obtained in part (a).

(d) Repeat part

(a) except choose φ = 0. Compare the sampling distribution of the IV estimator to the distribution obtained in part (a). Also compute the sampling distribution of the ordinary least squares estimator for this case. Note that for this model the ordinary least squares estimator has the property (see Stock, Wright and Yogo, 2002) plim(βbOLS) = σ12 σ22 = 0.99 .

(e) Repeat parts

(a) to

(d) for a larger sample of T = 50 and a very large sample of T = 500. Are the results in parts

(a) to

(d) affected by asymptotic arguments?