ECON 645 Empirical Analysis III
Instructor: Ye Zhang
Department of Economics
University of Maryland, College Park
Fall 2021

Problem Set #5

Due: Friday, December 9, at 6:00PM as an upload to ELMS

Instructions: Your problem set will be graded out of 100 points. You may work on it
collaboratively with other members from the class, but I expect each student to write their own
solution, in their own words, using their own STATA do-files, etc. The empirical problems’ data
sets are on ELMS under “Problem Sets, Problem Set 5”.

Please refer my syllabus for details on how to submit this one. Otherwise, the grader reserves the
right to deduct up to 10 points off your final score for not following these guidelines.

For this problem set, you are to upload THREE documents, in this order:
(1) A Microsoft Word file which includes your own answers to and relevant supporting
details for the questions posed below and his is what will be graded;
(2) Your STATA .do file in which your work is conducted; and
(3) The full output of running your STATA .do file (as a .log file- please set STATA to
generate a text log file instead (by simply appending “.log” to your log file name in
your do-file)). Note: we do not accept SMCL files and the system will only allow you to
upload .pdf, .log, .docx and .do files.












Theoretical Problems
1. The Federal Reserve monitors and analyzes the money supply, that is, the total amount of
money – cash, coins, and balances in bank accounts – in circulation. One of the several measures
of money supply is M2. The following graphs are based on monthly data of M2 from 1962 to
2002 and you are interested in forecasting future M2 behavior. The first graph is the time series
of log of M2 level (LnM2) and the second graph is the growth rate of M2 (GRM2).




a. (15 Points) In class, using quarterly GDP data as an example, we’ve seen how to convert
log levels of variables into annualized growth rates by differencing the log levels and
then multiplying these by 400. Now that our M2 data is monthly, how are you planning to
get annualized growth rate of M2?

b. (15 Points) Please describe the specific steps you will take to test for stochastic trend in
LnM2 and GRM2? These steps should include the way you use to determine the number
of lags to be included and whether or not to include a deterministic trend in your test.

c. (20 Points) You decide to conduct an Augmented-Dicky-Fuller test for LnM2, GRM2
and the change in the growth rate ΔGRM2. This results in the following t-statistic on the
parameter of interest.

LnM2
with trend
GRM2
without trend
GRM2
with trend
△ GRM2
without trend
-3.25 -3.46 -4.10 -8.35

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. (20 Points) To forecast the M2 growth rate, you decided to add lags of the monetary base
growth rate (GRMB) into the model to see if you can improve on the forecasting
performance of a chosen AR(10) model in GRM2. You perform a F test on the 9 lags of
GRMB and find a F-statistic of 2.31. Please interpret this result.

Empirical Problems:
2. The STATA program ECON645_PS5_RANDOMWALK.do generates 5 random walks of 100
observations each. In order for the random number generator to work in STATA, you need to
first select a 4-digit seed for the random number generator. For example, you can use the last 4
digits of your Social Security Number. Please select a seed and then run this program. This will
produce a dataset called ECON645_PS5_Q2 with a time index (t) and 5 time series.
a. (15 Points) Load the ECON645_PS5_Q2 data and run 10 different regressions. These
ten regressions include all the unique possible combinations of regressions where the
lowest numbers time series is the dependent variable. That is regress y1 y2;
regress y1 y3; regress y1 y4; regress y1 y5; regress y2
y3 … regress y4 y5. If we define this model as !" = # + $%" + ", of these 10
unique regressions, how many times did you reject the null hypothesis #: $ = 0?

b. (15 Points) Let’s construct the first difference in each series. The first difference for
series 1 can be generated with the commands
gen yl1=y1[_n-1]
gen dy1=y1-yl1
You can call these dy1 – dy5. Run the 10 unique regressions where the lowest
numbered time series is the dependent variable. That is regress y1 y2; regress
y1 y3; regress y1 y4; regress y1 y5; regress y2 y3 …
regress y4 y5. If we define this model as Δ!" = # + $Δ%" + ", of these 10
unique regressions, how many times did you reject the null hypothesis #: $ = 0?