EC 571 Advanced Econometrics

Homework 1

This homework studies the money demand function for the Unites States. In economic literature, a "money demand equation" is usually specified by a log-log linear relationship of real balance with real GDP and one or two interest rate variables. Real GDP is served as a scale variable in the money demand equation, which has positive coefficient. Interest rates are used to reflect the opportunity cost of holding money, which should have a negative impact on the amount of money held.

Take a look at two Excel data files USMoney.xls and USGDP.xls. USMoney.xls contains U.S. monetary monthly time series data (seasonally adjusted, from 1959 until the latest [data may be updated as part of homework]). USGDP.xls consists of U.S. GDP quarterly time series data (seasonally adjusted, from 1947 until the latest [data may be updated as part of homework]). All time series data are obtained from Federal Reserve Bank at St. Louis (http://research.stlouisfed.org/fred2 or http://www.quandl.com). Data description is given as follows:

M1: U.S. MONEY SUPPLY M1 IN BILLIONS OF DOLLARS
M2: U.S. MONEY SUPPLY M2 IN BILLIONS OF DOLLARS
RTB: 3-MONTH TREASURY BILL INTEREST RATE IN PERCENT
GDP: GROSS DOMESTIC PRODUCT IN BILLIONS OF DOLLARS
PGDP: GDP IMPLICIT PRICE DEFLATOR (INDEX, YEAR 2009=100)

Given data on the U.S. money aggregates (M1 and M2), 3 month treasury bills interest rate (RTB), gross domestic product (GDP) and its deflator (PGDP), define all money aggregates and GDP in their real terms (that is, in billions of 2009 dollars) as follows:

RM1=(M1./PGDP)*100
RM2=(M2./PGDP)*100
RGDP=(GDP./PGDP)*100

Two data sets USMoney.xls and USGDP.xls are not compatible in their length and frequency of the series. In particular, the former is in monthly while the later is quarterly. First, convert or transform the monthly monetary data series into their quarter average so that they are compatible with GDP quarterly series from 1959. Further, for the alternative annual version of the anaysis, convert both monetary and GDP seires into their annual average.

Question 1

Using both annual and quaterly time series, estimate and interpret the following money demand equation (Note: we study both M1 and M2 in this homework):

ln(RM1) = α₁ + α₂ln(RGDP) + α₃ln(RTB) + ε
ln(RM2) = β₁ + β₂ln(RGDP) + β₃ln(RTB) + ε

Do you get consistent results from the annual and quarterly versions of money demand equation? Why? Why not?

Question 2

Do you find any problem of autocorrelation in the estimated annual and quarterly versions of money demand equation?

Use the following tests to detect the existence of autocorrelated disturbances if any:
1. Durbin-Watson Bounds Test
2. Breusch-Godfrey LM Test
3. Box-Pierce and Ljung-Box Q Tests
Compute, compare, and explain the heteroscedasticity-autocorrelation-consistent robust variance-covariance matrix of the estimated parameters.
Correct for the first-order autocorrelation in the disturbances of money demand equations using:
1. Cochrane-Ocutt Procedure
2. Prais-Winsten Procedure