# Economics of Purchasing Behavior by vhl14259

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```									                     Economics 827 - Economic Forecasting
Summer, 1999 - Exercise III - Leading Indicators?
August 5th, 1999
Due: August 17th, 1999
Frequently in the press or in policy discussions you will encounter claims that some economic
measure will change in the future based on the observed behavior to date of some other economic
variable. Explicitly or implicitly the assertion is that one variable is functioning as a “leading
indicator” of the other variable, i.e. that the first variable has “predictive causality” for the
second variable.

The data set exer3.xls is an Excel worksheet that contains monthly time series on the following
variables for the U.S. economy:

UNRATE = the unemployment rate
INDPRO = the index of industrial production
CPI = the consumer price index
PPI = the producer price index for finished goods
PPI_CRD = the producer price index for crude materials
NAPM = the National Association of Purchasing Managers Index
TRSP500 = a total returns index for S&P 500 stocks (this is not a rate of return, but the S&P 500 index

In addition it includes the following transformations of the above variables:

QINDPRO = the log of the index of industrial production
QCPI = the log of the consumer price index
QPPI = the log of the producer price index for finished goods
QPPI_CRD = the log of the producer price index for crude materials
QNAPM = the log of the Purchasing Managers Index
QSP500 = the log of the S&P 500 total returns index

DUNRATS = the first difference of the unemployment rate
DQINDPRO = the first difference of the log (growth rate) of the index of industrial production
INFCPI = the first difference of the log of the consumer price index (the CPI inflation rate
INFPPI = the first difference of the log of the producers price index (the PPI inflation rate
INFPPI_CRD = the first difference of the log of the producers price index for crude materials (the inflation
rate of crude materials prices)
DQNAPM = the first difference of the log (growth rate) of the Purchasing Managers Index
DQSP500 = the first difference of the log (total rate of return) of the S&P 500 total returns index

DINFCPI = the first difference of the CPI inflation rate
DINFPPI = the first difference of the PPI inflation rate
DINFPPI_CRD = the first difference of the inflation rate in Crude Materials Prices.

All of the original data series and their logged values, except for TRSP500 begin in January,
1948. TRSP500 and QSP500 begin in January, 1970. The differenced series start one
observation later and the changes in the inflation rate series start two observations later. All
series end in December, February 1999.

======================================
1) Each team is to investigate a two variable leading-indicator VAR model in the specified
variable (or transformations thereof) and assess the evidence for a leading indicator relationship.
Note: Only use the date up to 1997,12 : Do not use the data for 1998 and 1999.

Team I.
Look for leading indicators of the unemployment rate.

Team II.

2) Each team is to take the mathematical model which they estimated in part 1, and use it, via
Excel, to predict the series’ behavior for the period January 1998 to February 1999.

How? Trim down the Excel file until it only contains the variables you need, then create a pair of
new columns for whichever variables you worked with in part 1.

E.g.: if your best model for (say for inflation) was a VAR[1,1] with a constant of 2.6, a
coefficient of 0.7 on the first lag of unemployment and a coefficient of -0.55 on the first lag of
inflation, then you would enter, for the predicted value for inflation in January 1998:

=2.6+(0.7*X627)+(-0.55*Y627)

…where I’m assuming that December 1997’s actual unemployment rate was located in cell X627
and December 1997’s actual inflation rate was located in cell Y627. You can then repeat the
process to generate the forecast for the other variable. These two forecasts will then provide the
“history” for the next forecast.

The simplest way to do this is to copy and paste the actual data up to 12/97 into the new
columns, and then in the 1/98 cell, using formulas like the one above, create your forecasts for
January 1998.Drag that pair of forecast cells down to create the forecasts for February and on
(which will thus be based on actual events before 1998 and forecasts events during and after
1998).

3) Evaluate your model’s performance. Plot the real and estimated behavior, and determine
where (and if possible, why) your model was imperfect. Generate prediction:realization diagrams
(remembering that they show the predicted and actual changes in the outcomes). If possible, give
a qualitative estimate of the Theil inequality proportions for your model.

If your forecasts appear to be accurate in the short term, but become inaccurate in the long term,
it may be worthwhile to see how accurate your model would have been at forecasting one period
ahead after January 1998 (i.e. to make a series of 1-period forecasts, first using only data to
12/97, then using data to 1/98 and so on). Some models which perform poorly in the long term
may nonetheless have useful information in the short run.

Where appropriate, discuss what changes should be made to your model in light of its successes
or failures.

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