Suppose GDP can be described by the following process: GDP_t = GDP_t - 1 + epsil

Question

Suppose GDP can be described by the following process: GDP_t = GDP_t - 1 + epsilon_t What is this process called? Is this process covariance covariance stationary? If not, which condition(s) fail? Suppose we want to estimate whether GDP follows the process in part 4. That is, we want to estimate GDP_t = b_1GDP_t - 1 + e_t and test whether b_1 = 1. Since the process is not covariance stationary if b_1 = 1, we cannot estimate this directly. How can we transform the model so that we can use OLS to test whether beta_1 = 1 (this is called a Dickey-Fuller test)? Suppose we estimate the relationship between government spending and GDP (e.g. do increases in spending increase or decrease GDP?) but do not account for the possibility that both variables are trending upwards over time. If we estimate GDP_t = b_0 + b_1 spending_t + e_t and GDP and spending really are trending upwards, will b_1 capture the true causal relationship between spending and GDP? Why or why not?

Explanation / Answer

4 (a) The process is difference stationary process.

b) This is not covariance stationay. Covariance will always depend on the time lag.

5. GDPt - GDPt-1 = (1-b1) GDPt-1 + et

Ho: 1-b1=0

Test this hypothesis by tau-statistic. If null hypothesis is rejected then GDP estimation is stationary.

6. b1 will not capture the true causal relationship as spending does depends on lag GDP.

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