#
Question

4) You collect monthly data on the money supply (M2) for the United States from 1962:1-2002:4 to forecast future money supply behavior.

where *LM2* and *DLM2 *are the log level and growth rate of M2.

(a) Using quarterly data, when analyzing inflation and unemployment in the United States, the textbook converted log levels of variables into growth rates by differencing the log levels, and then multiplying these by 400. Given that you have monthly data, how would you proceed here?

(b) How would you go about testing for a stochastic trend in *LM2* and *DLM2*? Be specific about how to decide the number of lags to be included and whether or not to include a deterministic trend in your test. The textbook found the (quarterly) inflation rate to have a unit root. Does this have any affect on your expectation about whether or not the (monthly) money growth rate should be stationary?

(c) You decide to conduct an ADF unit root test for *LM2*, *DLM2*, and the change in the growth rate Δ*DLM2*. This results in the following *t*-statistic on the parameter of interest.

with trend |
without trend |
with trend |
without trend |

-0.505 |
-4.100 |
-4.592 |
-8.897 |

Find the critical value at the 1%, 5%, and 10% level and decide which of the coefficients is significant. What is the alternative hypothesis?

(d) In forecasting the money growth rate, you add lags of the monetary base growth rate (*DLMB*) to see if you can improve on the forecasting performance of a chosen AR(10) model in *DLM2*. You perform a Granger causality test on the 9 lags of *DLMB* and find a *F*-statistic of 2.31. Discuss the implications.

(e) Curious about the result in the previous question, you decide to estimate an ADL(10,10) for *DLMB* and calculate the *F*-statistic for the Granger causality test on the 9 lag coefficients of *DLM2*. This turns out to be 0.66. Discuss.

(f) Is there any a priori reason for you to be skeptical of the results? What other tests should you perform?