Homework 3 Eco 4306 Economic and Business Forecasting Spring 2020 Due: Thursday, February 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 errors 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, Le. PGDP, during the Paul Volcker period, 197904-198703, obtained from http://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/research-and-data/real- time-center/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. 118x, 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 197904 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 I-quarter-ahead forocast errors en = 1+1 - f6,1 # gPGDP_E1 = gPGDP - gPGDP_F1. Create a time series plot for forecast errors. 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 errors PGDP_El. Are they normally distributed? (d) Estimate the regression cat = fo + 6: where can is the 1-step-ahead forecast error, i.c. regress gPGDP_E1 on constant only. Is So statistically significantly different from zero here? Recall that under symmetric quadratic loss function forecast is unbiased, t = petit and E(er,1) =0, which would imply A =0. (e) Estimate the regression 91 = As + Pit tent where you is the actual value and fry 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, fo1 = Prije, and so in this case the regression would yield / = 0 and # = 1. Perform an F-test for the joint hypothesis Ho : A = 0,8, = 1 to confirm/reject this. (f) Obtain the correlogram for forecast errors. Do you observe any time dependence in the forecast error, 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, f61 = Ayer, and the forecast errors 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
