Homework 3
Homework 3
Eco 4306 Economic and Business Forecasting
Spring 2020
Due: Thursday, Fe
uary 27, before the class
Problem 1
The Federal Reserve Act of 1977 specified that the goals of the Fed are to promote stable prices and maximum
employment. The maximum employment in this context is understood as the employment level such that the
GDP is at its potential level. The high inflation in 1960s and 1970s then led the Fed under Paul Volcker, as
Chairman of the Federal Reserve from August 1979 to August 1987, to focus on lowering the inflation. But
since the inflation and GDP respond to monetary policy only with a lag, the Fed has to make decisions based
on its forecasts of future inflation and future GDP growth. The inevitable forecast e
ors are costly, which
leads to the concept of the loss function we discussed in class. This problem will ask you to investigate some
properties of the Fed’s loss function for inflation forecasts under Paul Volcker.
Download the quarterly time series of the price index based on the GDP deflator, i.e. PGDP, during the
Paul Volcker period, 1979Q4-1987Q3, obtained from https:
fred.stlouisfed.org/series/GDPDEF. Calculate
the growth rate of PGDP to get the inflation rate gPGDP. In addition download Fed’s 1-quarter-ahead
forecasts for that inflation rate gPGDPF1, obtained from www.philadelphiafed.org
esearch-and-data
eal-
time-cente
greenbook-data/philadelphia-data-set. On the Philadelphia Fed website, click on Philadelphia
Fed’s Greenbook Data Set: Row Format to download the excel file. Within the file GBweb_Row_Format.xlsx,
we are interested in column gPGDPF1 of sheet gPGDP.
Note the time shift between the two variables: the first observation of gPGDPF1, for 1979Q4, is the forecast in
1979Q4 of the inflation in 1980Q1, the actual value of which is the second observation of gPGDP, and so on.
(a) Create a time series plot showing together actual values gPGDP and 1-step ahead forecasts GPGDP_F1,
after adjusting for the time shift, i.e. GPGDP_F1 ≡ lag(gPGDPF1,1). Is there any trend? Does one time
series appear to be above the other one most of the time?
(b) Generate 1-quarter-ahead forecast e
ors et,1 = yt+1 − ft,1 as gPGDP_E1 = gPGDP - gPGDP_F1. Create
a time series plot for forecast e
ors. Do they appear to be distributed more or less symmetrically
around zero, or are they positive or negative most of the time?
(c) Obtain histogram and descriptive statistics for forecast e
ors gPGDP_E1. Are they normally distributed?
(d) Estimate the regression et,1 = β0 + εt where et,1 is the 1-step-ahead forecast e
or, i.e. regress gPGDP_E1
on constant only. Is β̂0 statistically significantly different from zero here? Recall that under symmetric
quadratic loss function forecast is unbiased, ft,1 = µt+1|t and E(et,1) = 0, which would imply β̂0 = 0.
(e) Estimate the regression yt+1 = β0 +β1ft,1 + εt+1 where yt+1 is the actual value and ft,1 is the 1-quarter-
ahead forecast, i.e. regress gPGDP on constant and gPGDP_F1. Recall that under symmetric quadratic
loss function the forecast is unbiased, ft,1 = µt+1|t, and so in this case the regression would yield β̂0 = 0
and β̂1 = 1. Perform an F-test for the joint hypothesis H0 : β0 = 0, β1 = 1 to confirm
eject this.
(f) Obtain the co
elogram for forecast e
ors. Do you observe any time dependence in the forecast e
or,
or are the components of the AC and PAC functions within the 95% confidence interval around zero?
(g) If the forecast is optimal under symmetric quadratic loss function, ft,1 = µt+1|t, and the forecast e
ors
should be white noise with no time dependence, unbiased, with zero mean. Summarize the results from
(a)-(e). Was the Fed under Paul Volcker producing forecasts which are optimal under the assumption of
a symmetric quadratic loss function, or is there some evidence that Fed’s loss function was asymmetric?
1
https:
fred.stlouisfed.org/series/GDPDEF
https:
www.philadelphiafed.org
esearch-and-data
eal-time-cente
greenbook-data/philadelphia-data-set
https:
www.philadelphiafed.org
esearch-and-data
eal-time-cente
greenbook-data/philadelphia-data-set
https:
www.philadelphiafed.org/-/media
esearch-and-data
eal-time-cente
greenbook-data/documentation/gbweb_row_format.xlsx?la=en
https:
www.philadelphiafed.org/-/media
esearch-and-data
eal-time-cente
greenbook-data/documentation/gbweb_row_format.xlsx?la=en
Problem 1