This paper extends the Pearson chi-square testing method to nondynam ic parametric econometric models, in particular, to models with covar iates. The paper establishes the asymptotic distribution of the test statistic when the test statistic is based on data-dependent random cells of a general form and on an arbitrary asymptotically normal estimator. These results a re attained by extending recent probabilistic results for the weak convergence of empirical processes indexed by sets. The chi-square test that is introduced can be used to test goodness-of-fit of a parametric model, as well as to test particular aspects of the parametric model that are of interest. Copyright 1988 by The Econometric Society.

A market composed of pairwise trading under incomplete information is modeled in order to analyze how resources are allocated among competing uses when information about trade gains is incomplete. Contrary to the results from studying a single such trade, sufficient homogeneity across potential trades guarantees that efficiency obtains. This is analogous to simple first-price auctions with homogeneous bidders, where bidders have a common bid function and, as a result, the high bidder also places the highest value on the auctioned object. With enough symmetry, the decentralized bilateral trades in the present model occur as if they were made in a first-price auction that occurs through time. The robustness of the efficiency result to heterogeneities among agents and to nontrivial search intensity decisions is then considered.

[A market composed of pairwise trading under incomplete information is modeled in order to analyze how resources are allocated among competing uses when information about trade gains is incomplete. Contrary to the results from studying a single such trade, sufficient homogeneity across potential trades guarantees that efficiency obtains. This is analogous to simple first-price auctions with homogeneous bidders, where bidders have a common bid function and, as a result, the high bidder also places the highest value on the auctioned object. With enough symmetry, the decentralized bilateral trades in the present model occur as if they were made in a first-price auction that occurs through time. The robustness of the efficiency result to heterogeneities among agents and to nontrivial search intensity decisions is then considered.]

The authors derive a model of money demand for an optimizing consumer with rational expectations in a discrete time infinte hortizon framework under uncertainty. Mone y demand responds to unanticipated changes in income, one period expe ctations of future bond and money interest rates, unanticipated curre nt interest rates, and past anticipations of current rates. The deriv ed consumption function mirrors money demand behavior. Joint estimati on of the consumption and money demand equations by weighted nonlinea r least squares corroborates the predicted effects, particularly inco me neutrality. This money demand model substantially outperforms a co nventional specification in post-sample simulation over 1975-85. Copyright 1988 by MIT Press.

This research provides improved techniques for analyzing the after-tax risk exposure of taxable institutions holding amortizing instruments such as commercial, real estate, and consumer loans. We derive after-tax duration for amortizing instruments and analyze it for sensitivity to tax rates, coupon, and maturity. Taxable investors who hedge and ignore the effects of taxes on amortizing instruments will underestimate differences in durations on bonds versus amortizing instruments of equal maturities; bond durations increase much faster as tax rates increase. One unexpected result shows that, unlike bond duration, amortizing instrument duration often increases with coupon rate, and sometimes is independent of coupon rate.

Dissatisfaction occasionally has been expressed with traditional measures of duration for immunization on conceptual grounds. However, more elegant duration measures have not been found to be superior to the traditional ones in empirical tests of immunization efficacy. Under the assumption that the term structure of continuously compounded interest rates can be expressed as a polynomial, Chambers and Carleton (1981) demonstrate that the finite and noninstantaneous return of a default-free bond can be expressed as a vector product of a duration vector and a shift vector. This study derives immunization strategies from the model and tests them. The results of the portfolio tests indicate that the traditional duration approach of Macaulay provides enhanced immunization relative to maturity approaches or naive approaches. However, the duration vector approach produces further improvements.

This paper extends the classical test for structural change in linear regression models (see Chow (1960)) to a wide variety of nonlinear models, estimated by a variety of different procedures. Wald, Lagrange multiplier-like, and likelihood ratio-like test statistics are introduced. The results allow for heterogeneity and temporal dependence of the observations. In the process of developing the above tests, the paper also provides a compact presentation of general unifying results for estimation and testing in nonlinear parametric econometric models.