Monte Carlo experiment.^* Ten individuals had weekly permanent income as follows: $200, 220, 240, 260, 280, 300, 320, 340, 380, and 400. Permanent consumption (Y^∗_i) was related to permanent income X^∗_i as

Y^∗_I = 0.8X^∗_i                                                           (1)

Each of these individuals had transitory income equal to 100 times a random number u_i drawn from a normal population with mean = 0 and σ2 = 1 (i.e., standard normal variable). Assume that there is no transitory component in consumption. Thus, measured consumption and permanent consumption are the same.

a. Draw 10 random numbers from a normal population with zero mean and unit variance and obtain 10 numbers for measured income X_` (= X^∗_I + 100u_i).

b. Regress permanent (= measured) consumption on measured income using the data obtained in (a) and compare your results with those shown in Eq. (1). A priori, the intercept should be zero (why?). Is that the case? Why or why not?

c. Repeat (a) 100 times and obtain 100 regressions as shown in (b) and compare your results with the true regression (1). What general conclusions do you draw?