Matthew L. Higgins

A CLASS OF NONLINEAR ARCH MODELS

A class of nonlinear autoregressive conditional heteroskedasticity models is suggested. The proposed class encompasses several functional forms for autoregressive conditional heteroskedasticity which have been put forth in the literature. A Lagrange multiplier test is developed to test Engles autoregressive conditional heteroskedasticity specification against the wider class of models. This test provides an easily computed disgnostic check of the adequacy of an autoregressive conditional heteroskedasticity model after it has been estimated. The theory is applied to a number of weekly exchange rate series and the authors find strong evidence of nonlinear autoregressive conditional heteroskedasticity. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Exchange-rate uncertainty and workers' remittances

A panel of nine Western Hemisphere nations is employed to test the proposition that the remittances of immigrants respond to risk variables, in particular to exchange-rate uncertainty. To estimate annual exchange-rate uncertainty, a nonparametric estimator based on monthly exchange rate returns is used. Also the instrumental variables procedure of Pagan and Ullah (Journal of Applied Econometrics, 3, 87–105, 1988) is employed to insure that the conclusions are robust to possible error in the measurement of exchange-rate uncertainty. The results give credence to the ‘new economics of migration’ approach which argues that immigrants are highly motivated by portfolio variables.

ARCH and Bilinearity as Competing Models for Nonlinear Dependence

In this article we consider whether the wide acceptance of autoregressive conditional heteroscedasticity (ARCH) models may be at the expense of other nonlinear processes, such as bilinear models. We first propose a joint test for ARCH and bilinearity. A nonnested test is then suggested to determine whether nonlinear dependence should be attributed to ARCH or bilinearity. The tests are then applied to three series. When generalized ARCH (GARCH) models are taken as the null hypothesis, we fail to reject it for all the data series. When bilinearity is taken as the null, however, it is rejected in two cases. Moreover, an out-of-sample forecasting exercise shows that the GARCH model is superior. The results, therefore, indicate a strong preference for the GARCH model.

A joint test for arch and bilinearity in the regression model

In this paper we argue that a simultaneous test for ARCH and bilinearity should be used to test for the possible nonlinearity of the error process in the regression model. We suggest such a joint test statistic. An empirical example shows that the individual tests of ARCH and bilinearity may not be conclusive while a joint test clearly rejects the linearity hypothesis. Our results are also applicable to pure time series models.

Inflation uncertainty and money demand

We enter inflation uncertainty into error-correction models (EC) of US M1 and M2 money demand. We estimate the models using an instrumental variables procedure that is robust to mis-specification of inflation uncertainty. We find inflation uncertainty has a negative effect on M1 demand and a positive effect on M2 demand. Our results suggest that when confronted with increased inflation uncertainty, agents substitute away from M1 and to the interest bearing components of M2.

Computation of the GLS estimator of a model with anticipated and unanticipated effects

Abstract This paper demonstrates that the two-step GLS estimator of a model with current anticipated and unanticipated effects can be computed from an artificial double length regression using any standard econometric software. This computational procedure follows from a simple matrix inversion result.

A monte carlo study of tests for non-nested models estimated by generalized method of moments

Finite sample properties of two robust tests based on the Cox and encompassing principles are investigated using Monte Carlo simulations. The tests are constructed from generalized method of moments estimators and are robust to heteroskedastic and serially correlated errors of unknown form. Non-nested linear regression models that are estimated by the method of instrumental variables are used in the simulation. Size and power of the tests are found with control parameters which include the degree of serial correlation and heteroskedasticity, the degree of correlation between regressors across models, the degree of correlation between regressors and instrumental variables within models, the error distribution, the sample size and the number of regressors.