How Biased Are U.S. Government Forecasts of the Federal Debt?

Abstract

Government debt and forecasts thereof attracted considerable attention during the recent financial crisis. The current paper analyzes potential biases in different U.S. government agencies' one-year-ahead forecasts of U.S. gross federal debt over 1984-2012. Standard tests typically fail to detect biases in these forecasts. However, impulse indicator saturation (IIS) detects economically large and highly significant time-varying biases, particularly at turning points in the business cycle. These biases do not appear to be politically related. IIS defines a generic procedure for examining forecast properties; it explains why standard tests fail to detect bias; and it provides a mechanism for potentially improving forecasts.

Detecting Location Shifts during Model Selection by Step-Indicator Saturation

“…Hendry et al [3] derive the null distribution of IIS for independent, identically distributed (IID) data, and [4] generalize that analysis to dynamic regression models (possibly with unit roots). Hendry and Santos [5] propose an IIS-based test of super exogeneity, building on [6]; and [7][8][9][10][11][12] provide empirical applications of IIS.…”

Out-of-sample testing price discovery in commodity markets: the case of soybeans

“…What will the benchmark model be? Giacomini and Rossi (, and also Giacomini, ) suggest time‐varying relative performance of forecast models, whereas Ericsson () suggests different ways of evaluating time‐varying forecast bias.…”

“…As the forecast bias may vary over time (), Ericsson () proposes testing time dependence of the forecast bias by regressing the forecast error term on impulse indicator dummies, that is, a 1‐0 dummy for each out‐of‐sample observation as we will next explain. That is, where the impulse indicator dummy is unit for t = i and zero otherwise.…”

“…IIS adds a 1‐0 dummy variable by each observation as regressor (see Hendry et al., ), it is a procedure for testing parameter constancy. Ericsson () extends the IIS in the context of evaluating forecast bias and includes other types of saturation, in particular, “super‐saturation” and “ultra‐saturation.” In addition to the searching across done by IIS, super saturation searches across all possible one‐of step functions to capture permanent or long‐lasting changes, where is unit for t ≥ i and zero otherwise. Ultra saturation adds broken linear trends to the searching across , where is t – i + 1 for t ≥ i and zero otherwise.…”