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A new algorithm is presented for the discretization of semiconductor models in one space dimension plus time. A complete error analysis is given, showing that the discretization errors do not depend on any derivatives of ill‐behaved quantities such as carrier densities. In this algorithm, the electrostatic potential is updated from a discretization of the equation of total current continuity, and parabolic equations for the current densities are discretized, rather than those for the carrier densities. Projection methods, e.g. simple finite‐element methods, are used for the space discretization. The equations for the current densities are similar to the familiar Scharfetter‐Gummel expressions in the stationary limit. However, the discrete time‐dependent current densities are required here to be H1 functions of x, obtained in a space with at least second order approximation property in L2. This method is fully compatible with recently developed methods for uncoupling the discrete systems to be solved at each time step, for an individual device or when a given problem involves multiple, coupled devices.

When linear simultaneous equations are ‘ill‐conditioned’, small variations in the (usually measured) quantities on the right‐hand sides of the equations are associated with large variations in the values of some of the unknowns. The basic reason for this is that the matrix of the coefficients has at least one small latent root. Associated with each small latent root λr is a quantity Ur, a linear combination of the quantities on the right‐hand sides of the original equations, and the uncertainty associated with the ‘ill‐condition’ is essentially uncertainty as to the values of the quantities Ur; the original equations can be replaced by another set of equations which is not ill‐conditioned but involves the Ur. General methods are used, but applied to two specific cases; in one of these there are two equal small latent roots of the matrix of coefficients and the necessary adjustments for this case are explained. Two alternative methods for determining the small latent roots of a matrix are discussed.

The objective of this research is to identify areas where audit research can assist the Public Company Accounting Oversight Board (PCAOB) in its deliberation of the auditing standard on engagement quality (EQ) review required by the Sarbanes‐Oxley Act of 2002.

The approach used in this paper is a review of the literature.

The paper links academic research on EQ review to issues raised by the PCAOB. It also identifies questions for future research.

The academic research reviewed in this paper provides important information to the PCAOB staff as it considers EQ review.

The chapter reviews and extends the theory of exact and superlative index numbers. Exact index numbers are empirical index number formula that are equal to an underlying theoretical index, provided that the consumer has preferences that can be represented by certain functional forms. These exact indexes can be used to measure changes in a consumer's cost of living or welfare. Two cases are considered: the case of homothetic preferences and the case of nonhomothetic preferences. In the homothetic case, exact index numbers are obtained for square root quadratic preferences, quadratic mean of order r preferences, and normalized quadratic preferences. In the nonhomothetic case, exact indexes are obtained for various translog preferences.

Several lessons learnt from a Bayesian analysis of basic macroeconomic time-series models are presented for the situation where some model parameters have substantial posterior probability near the boundary of the parameter region. This feature refers to near-instability within dynamic models, to forecasting with near-random walk models and to clustering of several economic series in a small number of groups within a data panel. Two canonical models are used: a linear regression model with autocorrelation and a simple variance components model. Several well-known time-series models like unit root and error correction models and further state space and panel data models are shown to be simple generalizations of these two canonical models for the purpose of posterior inference. A Bayesian model averaging procedure is presented in order to deal with models with substantial probability both near and at the boundary of the parameter region. Analytical, graphical, and empirical results using U.S. macroeconomic data, in particular on GDP growth, are presented.

A concise introduction to the normalized quadratic expenditure or cost function is provided so that the interested reader will have the necessary information to understand and use this functional form. The normalized quadratic is an attractive functional form for use in empirical applications as correct curvature can be imposed in a parsimonious way without losing the desirable property of flexibility. We believe it is unique in this regard. Topics covered include the problem of cardinalizing utility, the modeling of nonhomothetic preferences, the use of spline functions to achieve greater flexibility, and the use of a “semiflexible” approach to make it feasible to estimate systems of equations with a large number of commodities.

We compare the finite sample power of short- and long-horizon tests in nonlinear predictive regression models of regime switching between bull and bear markets, allowing for time varying transition probabilities. As a point of reference, we also provide a similar comparison in a linear predictive regression model without regime switching. Overall, our results do not support the contention of higher power in longer horizon tests in either the linear or nonlinear regime switching models. Nonetheless, it is possible that other plausible nonlinear models provide stronger justification for long-horizon tests.

When products are differentiated, applying the standard critical loss formula to assess whether it is profitable for a hypothetical monopolist to impose a common price increase can lead to delineating an antitrust market that is too broad by setting a critical loss threshold that is too low. This error is particularly likely to occur when the products exhibit very different per-unit profits, own price elasticities, and cross price elasticities. In particular, different per-unit profits are a necessary condition for this error to occur and this difference is more likely to be driven by an asymmetry in prices than by an asymmetry in costs when own price elasticities are moderate in magnitude. In contrast, differences in the quantity sold of each product do not tend to lead to errors in market definition. Given the issues associated with the standard critical loss analysis, critical loss analysis with asymmetric price increases and the gross upward pricing pressure index are practical alternative approaches for conducting market definition analysis when products in a candidate market are differentiated.

We analyze fluctuations in inflation and the nominal exchange rate under optimal monetary policy with local currency pricing by developing two-country DSGE local currency pricing and producer currency pricing models. We estimate our models using Bayesian techniques with Japanese and US data, and calculate impulse response functions. Our estimation results show that local currency pricing is strongly supported against producer currency pricing. From the estimated parameters, we show that completely stabilizing consumer price index inflation is optimal from the viewpoint of minimizing welfare costs and that completely stabilizing consumer price index inflation is consistent with completely stabilizing the nominal exchange rate.