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Forecasting 165

where Q* denotes the forecast, m is the number of forecasts, and Q is the

realized future value. An equation’s root mean squared error (RMSE) is sim-

ilarly defined:

Like the goodness-of-fit measures discussed earlier in this chapter, the RMSE

depends on the sum of squared errors. Here, however, the issue is the error in

forecasting future values rather than how well the equation fits the past data.

Note that the “average” is based on degrees of freedom, that is, on the number

of forecasts minus the number of estimated coefficients (k).

Forecasts suffer from the same sources of error as estimated regression

equations. These include errors due to (1) random fluctuations, (2) standard

errors of the coefficients, (3) equation misspecification, and (4) omitted vari-

ables. In addition, forecasting introduces at least two new potential sources of

error. First, the true economic relationship may change over the forecast

period. An equation that was highly accurate in the past may not continue to

be accurate in the future. Second, to compute a forecast, one must specify val-

ues of all explanatory variables. For instance, to predict occupancy rates for its

hotels in future years, Disney’s forecasters certainly would need to know aver-

age room prices and expected changes in income of would-be visitors. In this

sense, its forecasts are conditional—that is, they depend on specific values of

the explanatory variables. Uncertainty about any of these variables (such as

future regional income) necessarily contributes to errors in demand forecasts.

Indeed, an astute management team may put considerable effort into accu-

rately forecasting key explanatory variables.

RMSE

A

g(QQ*)^2

mk

.

Forecasting

Performance

In light of the difficulties in making economic predictions, it is important to

examine how well professional forecasters perform. Stephen McNees, an econ-

omist at the Federal Reserve Bank of Boston, has analyzed the track records of

major forecasters and forecasting organizations. The methods examined

include sophisticated econometric models, barometric methods, time-series

analysis, and informal judgmental forecasts. Thus, his analysis strives for an

even-handed comparison of a wide variety of forecasting methods. He has come

to several interesting conclusions.^11

First, forecast accuracy has improved over time as a result of better data

and better models. Forecasters did better in the 1990s than in the 1980s. They

have made reasonably accurate forecasts of annual real GDP (though they have

(^11) See S. K. McNees, “An Assessment of the ‘Official’ Economic Forecasts;” New England Economic
Review(July–August 1995): 13–23, and S. K. McNees, “How Large Are Economic Forecast Errors?”
New England Economic Review(July–August 1992): 25–42.
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