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Economics 123B

Winter 2023

Lab Assignment 1

Due by 5 pm on Feb 3 rd , 2023

1.  Generate a covariate matrix X of dimension n x k, where n = 500 and k = 4. The fi rst column in X should be a column of ones and the other three columns can be generated from a relatively diffuse normal or uniform distribution.  Let β = (1, 1.25, 1.5, 1.75)  and let σ 2  = 1.  Simulate y from the model y = Xβ + ε, where ε ~ N (0, σ2 In).  Estimate β by ordinary least squares.  Report βˆ 0Ls  and the standard errors of βˆ 0Ls . Also submit your computer codes.

For this exercise , the TA has provided support on coding in MATLAB ( free on Apporto at https :// uci . apporto . com / ), but you can use any software you are comfortable with . The idea behind this exercise is not to use statistical packages or click on buttons , but to do the coding from scratch , following the theoretical derivations presented in class . Deriving βˆ OLS and its standard errors by using statistical packages will result in 0 points .