Download Homework Assignment 3

Homework Assignment 3
Economics 514
Macroeconomic Analysis
Assigned: November 30, 2006
1.
Estimate the Money Demand Function
The Baumol-Tobin model, in its general form suggest that the demand for money can
M
Y
M
be written as t  A t  ln t  ln A   ln Yt   ln it . Estimate a statistical model
Pt
it
Pt
of the form
M
ln t   0  1 ln Yt   2 ln it   t
Pt
where β1 =  and β2 = -μ for the USA to find out how sensitive. Annual data on US
money supply, M1, the GDP deflator, Pt, real GDP, Yt, and the short-term interest
rate, it is available in spreadsheet form here.
i.
Estimate the above model with the Excel statistical regression package for the
period 1959-2005. Are the signs of the coefficients consistent with the
Baumol-Tobin model?
ii.
Estimate a Dynamic OLS model of money demand. Control for the short-term
dynamics of the money demand equation by including 1 lead and 1 lag of each
of the right hand-side variables. Construct the leads and lags for each time
period.
1
yt  ln(Yt 1 )  ln(Yt ); yt0  ln(Yt )  ln(Yt 1 ); yt1  ln(Yt 1 )  ln(Yt 2 )
iit1  ln(it 1 )  ln(it ); iit0  ln(it )  ln(it 1 ); iit1  ln(it 1 )  ln(it 2 )
Estimate the model of the form
Mt
ln
  0  1 ln Yt   2 ln it  3yt1   4 yt0  5 yt1   6 iit1   7 iit0  8 iit1   t
Pt
This model can only be estimated using time periods t = 1960 to 2004. Estimate
this model and report your estimates of β1 =  and β2 = -μ. Are these estimates consistent
with the Baumol-Tobin theory.
2.
Estimate the Lucas Supply curve
The aggregate supply curve for short-run models is written as  t   tE    yt  y 
where  t is the inflation rate;  tE is the forecast of inflation; yt is the natural log
of real GDP; and y is potential output. Output is above potential output only
when inflation is above expected inflation. Estimate this model for Hong Kong.
i.
Download the Data. Use annual data on GDP at constant (2000) prices
for Yt and the implicit price deflator, Pt. Data from Hong Kong for
1961-2005 can be downloaded (in an Excel file) at the following web
page.
National Income Data: Hong Kong
Calculate output, yt = ln(Yt) and inflation,  t  ln( Pt )  ln( Pt 1 ) .
ii.
Estimate the gap between output and potential output. Treat potential
output is the path of output if output grew smoothly over time. Define
1961 as t = 1, 1962 as t = 2, 1963 as t = 3, and so on. Estimate the
statistical model, yt   0  1  t   2  t 2  t with least square
regression. Use the estimates of  0 ; 1 and  2 from your regression to
estimate yt  0  1  time  2  time2 so that t =  yt  y  . [Note:
Excel regression gives an option to display fitted residuals so you can
have it directly calculate the output gap, t , for you]
Pt
iii.
Calculate the inflation rate as  t  ln(
iv.
its lag so  t   tE =  t   t 1
For periods t = 20 to t = 44 (i.e. 1980-2004), estimate the statistical
model  t   t 1   0   1  yt  y   ut where  1 is an estimate of  .
Pt 1
) and expected inflation as
3.
Estimate PPP
Calculate the average deviations of PPP for three developed economies (for
France, Germany, and the UK) and describe the short-term dynamics.
i.
Download the Data. Get Data on exchange rates, St, and price levels,
Pt
PPPt  US
in each country in domestic currency relative to US price
Pt
levels in US dollars from the Penn World Tables for the period 19502004.
Penn World Tables
http://pwt.econ.upenn.edu/php_site/pwt62/pwt62_form.php
The data on the exchange rate is available in series XR, the data on
PPP is available on series PPP. Calculate the real exchange rate,
S
st  t . Calculate the average real exchange rate for these
PPPt
economies for the period 1990-2004. Are goods in the European
economies more or less expensive than in the US economies?
ii.
Estimate the short-run dynamics of the real exchange rate Estimate and
auto-regressive model in the real exchange rate
ln st  0  1  ln st 1  t using data from 1951-2004. Typically, the
estimate 1 < 1 indicating that the effects of a shock will dissipate
over time. A measure of how quickly shocks dissipate is the half-life.
Calculate the half life of deviations from PPP using the formula
ln(2)
T12 
for each country.
1