An Application of Nonlinear Bounded Influence Estimation to Aggregate Bank Borrowing from the Federal Reserve

Abstract

Forecasting aggregate discount window borrowing has posed difficulties for the Federal Reserve, due in part to outliers resulting from numerous institutional changes and special borrowing situations. This article applies bounded influence estimation and influence diagnostics to identify and adjust for outliers in the case of discount window borrowing. Since most banks borrow from the Federal Reserve infrequently, the model is nonlinear and of the switching regression class. We perform case-deletion diagnostics, modifying the empirical influence function of Reid and Crepeau (1985) for the nonlinear regression. The bounded influence estimator (BIE) extends Carroll and Ruppert (1985, 1987). Influence diagnostics and bounded influence estimation contribute to the investigation of discount window borrowing in a number of ways. Examination of weights generated by the estimator reveals that the BIE downweights observations during periods of known institutional change affecting the discount window. Consequently, the relative importance of institutional events can be inferred. Examples of institutional circumstances creating outliers in this application include the Monetary Control Act of 1980, the threatened bond defaults of late 1982, the February 1984 change to Contemporaneous Reserve Accounting, solvency problems of the Continental Bank of Illinois during 1984, and borrowing in May 1985 by Maryland thrift institutions affected by bank runs. Influence diagnostics in turn provide information concerning what parameter estimates have been most altered as a result. An interesting intuitive finding arises from use of the switching regression model: outlying observations tend to influence estimated parameters only from the same regime. When compared with maximum likelihood, we find that the BIE substantially alters some parameter estimates, including the estimated switchpoints. Identifying and correcting for outliers by the BIE improves the ability of the model to discriminate among regimes. Moreover, bounded influence estimation in discount window borrowing increases estimator efficiency, reduces residual pattern, discriminates outliers from large estimated residuals, and slightly improves the goodness of fit. The overall findings indicate that influence diagnostics and bounded influence estimation could significantly assist the Federal Reserve in explaining and predicting discount window borrowing.

Key Words:

• Aggregate discount window borrowing
• Empirical influence function
• Gross-error sensitivity
• Outlier
• Switching regression
• Weighted maximum likelihood