Parameter Restrictions Research Articles

How useful are no-arbitrage restrictions for forecasting the term structure of interest rates?

We develop a general framework for analyzing the usefulness of imposing parameter restrictions on a forecasting model. We propose a measure of the usefulness of the restrictions that depends on the forecaster’s loss function and that could be time varying. We show how to conduct inference about this measure. The application of our methodology to analyzing the usefulness of no-arbitrage restrictions for forecasting the term structure of interest rates reveals that: (1) the restrictions have become less useful over time; (2) when using a statistical measure of accuracy, the restrictions are a useful way to reduce parameter estimation uncertainty, but are dominated by restrictions that do the same without using any theory; (3) when using an economic measure of accuracy, the no-arbitrage restrictions are no longer dominated by atheoretical restrictions, but for this to be true it is important that the restrictions incorporate a time-varying risk premium.

Transmission of evanescent wave modes through a slab of negative-refractive-index material

There has been a long-standing argument about Pendry's suggestion that a plane harmonic evanescent (surface) wave along the interface between free space and a slab of ɛ=-1, μ=-1 double-negative (DNG) medium will emerge on the far side with recovery of phase and amplitude. While this is possible, it is subject to parameter restrictions. This work generalizes previous work and now gives analytical criteria for when to expect such a recovery in a Smith-Kroll DNG medium. Basically this requires, among other things, a relatively narrow bandwidth and relatively small transverse-mode component. There also is a very strong dependence on the ratio of slabwidth to plasma wavelength.

Bounds on revenue distributions in counterfactual auctions with reserve prices

Measuring auction revenues under counterfactual reserve prices or formats requires knowledge of distributions of bidders' values and private signals. This poses a challenge when bids are observed from first‐price, common‐value auctions. I bound counterfactual revenue distributions without imposing parametric restrictions on the model structure. Using data from U.S. municipal bond auctions, I find first‐price and second‐price auctions under optimal reserve prices lead to little improvement in revenues over existing first‐price formats. The number of bidders has a more significant impact on revenues in optimal auctions. I also find invoking an incorrect assumption of private values in counterfactual analyses results in small errors in predicting revenues from optimal second‐price auctions.

Discrete time Wishart term structure models

This paper reveals that the class of Affine Term Structure Models (ATSMs) introduced by Duffie and Kan (1996) is larger than previously considered in the literature. In the framework of risk factors following a Wishart autoregressive process, we define the Wishart Term Structure Model (WTSM) as an extension of a subclass of Quadratic Term Structure Models (QTSMs), derive simple parameter restrictions that ensure positive bond yields at all maturities, and observe that the usual constraint on affine processes requiring that the volatility matrix be diagonal up to a path independent linear invertible transformation can be considerably relaxed.

Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

Optimal Trading Execution with Nonlinear Market Impact: An Alternative Solution Method

We consider the optimal trade execution strategies for a large portfolio of single stocks proposed by Almgren (2003). This framework accounts for a nonlinear impact of trades on average market prices. The results of Almgren (2003) are based on the assumption that no shares of assets per unit of time are trade at the beginning of the period. We propose a general solution method that accomodates the case of a positive stock of assets in the initial period. Our findings are twofold. First of all, we show that the problem admits a solution with no trading in the opening period only if additional parametric restrictions are imposed. Second, with positive asset holdings in the initial period, the optimal execution time depends on trading activity at the beginning of the planning period.

Household Income Uncertainties Over Three Decades

We study the trend in household income uncertainty using a novel approach that measures income uncertainty as the variance of forecast errors at each future horizon separately without imposing parametric restrictions on the underlying income shocks. We find that household income uncertainty has risen significantly and persistently since the early 1970s. For example, our measure of near-future uncertainty in total family non-capital income rose about 40 percent between 1971 and 2002. This rising uncertainty is likely due to the increase in variances of both persistent and transitory income shocks. Although the increase in uncertainty was widespread, the increase was most pronounced among single-earner households and high-income households. A parsimoniously calibrated Aiyagari (1994) model is solved to illustrate how rising income uncertainty affects aggregate saving.

Stability of rigid rotor–aerostatic bearings with double compensations caused by orifice and inherence in series

This study elucidates the coupled effects of pressure compensation that is caused by orifice and inherence in series on static and dynamic characteristics of a rigid rotor that is supported by orifice-restricted aerostatic bearings. The load capacity and stability threshold are analyzed and compared to those obtained with separate orifice and inherence restrictions for various eccentricities, rotor speeds and restriction parameters and numbers of feeding holes. The simulation results have revealed clearly that the effects of orifice and inherence in series on bearing performance cannot be ignored in the design of aerostatic bearings.

Profit Maximization In The National Football League

<p class="MsoBodyText" style="text-align: justify; margin: 0in 0.5in 0pt; mso-pagination: none;"><span style="font-style: normal; font-size: 10pt;"><span style="font-family: Times New Roman;">This paper investigates if NFL teams maximize profits with respect to ticket price.<span style="mso-spacerun: yes;">  </span>We modify Ferguson et al’s (1991) NHL paper as it pertains to the NFL.<span style="mso-spacerun: yes;">  </span>A profit function incorporating variable revenue and cost factors such as gate receipts and player expenses is employed.<span style="mso-spacerun: yes;">  </span>A systems model is used as the estimation procedure to identify the determinants of ticket prices for NFL franchises.<span style="mso-spacerun: yes;">  </span>The model implies a Kuhn-Tucker based cross equation parameter restriction that result from attendance capacity constraints.<span style="mso-spacerun: yes;">  </span>Results from the regression are then used in conjunction with other data to numerically test the first order necessary profit maximization conditions.<span style="mso-spacerun: yes;">  </span>The results indicate that over 80% of NFL teams set ticket prices in a manner consistent with gate receipt and profit maximization.</span></span></p>

Testing multivariate mean collinearity via latent variable modelling

A procedure for testing mean collinearity in multidimensional spaces is outlined, which is applicable in settings with missing data and can be used when examining group mean differences. The approach is based on non-linear parameter restrictions and is developed within the framework of latent variable modelling. The method provides useful information about the constellation of multiple response centroids in the populations studied, and is illustrated with an example.

Identification and Semiparametric Estimation of Equilibrium Models of Local Jurisdictions

We develop a new model of household sorting in a system of residential neighborhoods. We show that this model is partially identified without imposing parametric restrictions on the distribution of unobserved tastes for neighborhood quality and the shape of the indirect utility function. The proof of identification is constructive and can be used to derive a new semiparameteric estimator. Our empirical application focuses on residential choices in the Pittsburgh metropolitan area. We find that sorting of households with children exhibit more stratification by income than sorting of households without children. (JEL C51, D12, H41, J12, R21, R23)

A class of coupled nonlinear Schrödinger equations: Painlevé property, exact solutions, and application to atmospheric gravity waves

The Painleve integrability and exact solutions to a coupled nonlinear Schrodinger (CNLS) equation applied in atmospheric dynamics are discussed. Some parametric restrictions of the CNLS equation are given to pass the Painleve test. Twenty periodic cnoidal wave solutions are obtained by applying the rational expansions of fundamental Jacobi elliptic functions. The exact solutions to the CNLS equation are used to explain the generation and propagation of atmospheric gravity waves.

Block-Conditional Missing at Random Models for Missing Data

Two major ideas in the analysis of missing data are (a) the EM algorithm [Dempster, Laird and Rubin, J. Roy. Statist. Soc. Ser. B 39 (1977) 1–38] for maximum likelihood (ML) estimation, and (b) the formulation of models for the joint distribution of the data Z and missing data indicators M, and associated “missing at random” (MAR) condition under which a model for M is unnecessary [Rubin, Biometrika 63 (1976) 581–592]. Most previous work has treated Z and M as single blocks, yielding selection or pattern-mixture models depending on how their joint distribution is factorized. This paper explores “block-sequential” models that interleave subsets of the variables and their missing data indicators, and then make parameter restrictions based on assumptions in each block. These include models that are not MAR. We examine a subclass of block-sequential models we call block-conditional MAR (BCMAR) models, and an associated block-monotone reduced likelihood strategy that typically yields consistent estimates by selectively discarding some data. Alternatively, full ML estimation can often be achieved via the EM algorithm. We examine in some detail BCMAR models for the case of two multinomially distributed categorical variables, and a two block structure where the first block is categorical and the second block arises from a (possibly multivariate) exponential family distribution.

Using Historical Vital Statistics to Predict the Distribution of Under-Five Mortality by Cause

Cause-specific mortality data is essential for planning intervention programs to reduce mortality in the under age five years population (under-five). However, there is a critical paucity of such information for most of the developing world, particularly where progress towards the United Nations Millennium Development Goal 4 (MDG 4) has been slow. This paper presents a predictive cause of death model for under-five mortality based on historical vital statistics and discusses the utility of the model in generating information that could accelerate progress towards MDG 4. Over 1400 country years of vital statistics from 34 countries collected over a period of nearly a century were analyzed to develop relationships between levels of under-five mortality, related mortality ratios, and proportionate mortality from four cause groups: perinatal conditions; diarrhea and lower respiratory infections; congenital anomalies; and all other causes of death. A system of multiple equations with cross-equation parameter restrictions and correlated error terms was developed to predict proportionate mortality by cause based on given measures of under-five mortality. The strength of the predictive model was tested through internal and external cross-validation techniques. Modeled cause-specific mortality estimates for major regions in Africa, Asia, Central America, and South America are presented to illustrate its application across a range of under-five mortality rates. Consistent and plausible trends and relationships are observed from historical data. High mortality rates are associated with increased proportions of deaths from diarrhea and lower respiratory infections. Perinatal conditions assume importance as a proportionate cause at under-five mortality rates below 60 per 1000 live births. Internal and external validation confirms strength and consistency of the predictive model. Model application at regional level demonstrates heterogeneity and non-linearity in cause-composition arising from the range of under-five mortality rates and related mortality ratios. Historical analyses suggest that under-five mortality transitions are associated with significant changes in cause of death composition. Sub-national differentials in under-five mortality rates could require intervention programs targeted to address specific cause distributions. The predictive model could, therefore, help set broad priorities for interventions at the local level based on periodic under-five mortality measurement. Given current resource constraints, such priority setting mechanisms are essential to accelerate reductions in under-five mortality.

Solitons in Relativistic Plasmas by He’s Variational Principle

The dynamics of electromagnetic solitons in relativistic plasmas is studied in this paper by the aid of He's semi-inverse variational principle. Both Kerr law as well as power law nonlinearity are studied in this paper. The domain restriction of the soliton parameters and the perturbation coefficients are identified.

A Misspecification-Robust Impulse Response Estimator

This paper proposes an alternative methodology to estimating impulse response function. The proposed method does not impose parametric restrictions on the estimated impulse response function as the conventional method does. Instead, the impulse responses are estimated by regressing the series of interest on the residuals obtained from prior-stage “long autoregression”. Our Monte Carlo simulations demonstrate that the proposed estimator is capable of capturing the shapes of a wide range of impulse response functions without requiring that a correctly specified model be used in estimating the innovations. On the other hand, the inference under the conventional impulse response estimator can be quite misleading if the estimation models are misspecified. The advantage of the proposed impulse response estimator over the conventional one is most relevant when the true impulse response function exhibits rich dynamics, but the size of the sample proscribes the use of large-order estimation models.

Sign Restrictions in Structural Vector Autoregressions: A Critical Review

Structural Vector Autoregressions (SVARs) have become one of the major ways of extracting information about the macro economy. One might cite three major uses of them in macro-econometric research.1. For quantifying impulse responses to macroeconomic shocks.2. For measuring the degree of uncertainty about the impulse responses or other quantities formed from them.3. For deciding on the contribution of different shocks to fluctuations and forecast errors through variance decompositions.To determine this information a VAR is first fitted to summarize the data and then a structural VAR (SVAR) is proposed whose structural equation errors are taken to be the economic shocks. The parameters of these structural equations are then estimated by utilizing the information in the VAR. The VAR is a reduced form which summarizes the data; the SVAR provides an interpretation of the data. As for any set of structural equations, recovery of the structural equation parameters (shocks) requires the use of identification restrictions that reduce the number of parameters in the structural equations to the number that can be recovered from the information in the reduced form.Five major methods for recovering the structural equation parameters (identifying the shocks) are present in the literature. Four of these explicitly utilize parametric restrictions. These involve the nature of the structuralequations. Parametric restrictions on these equations can vary according to whether particular variables appear in the latter (Cowles Commission), whether there is a recursive causal structure (Wold (1951), Quenouille (1957) and Sims (1980)), and whether shocks have known short-run (Gali (1992)) or long-run (Blanchard and Quah (1989)) effects. In each case the parametric restrictions free up enough instruments for the contemporaneous endogenous variables in the structural equations, thereby enabling the parameters of those equations to be estimated. Recently, a fifth method for estimating SVARs has arisen that employs sign restrictions upon the impulse responses as a way of identifying shocks - Faust (1998), Uhlig (2005), Canova and De Nicolo (2002). Applications of this method have been growing, as seen in the papers listed in Table 1. The table is a sub-set of published studies and adopts a taxonomy which distinguishes between cases where only sign restrictions are used (often there are mixtures of sign and parametric restrictions), the type of shock (permanent or transitory), the number of shocks identified, and whether the sign restrictions come from a formal model or not. Consequently, it is worth examining this literature in more detail, and the aim of our paper is to exposit how the method works and to identify some of the difficulties that can arise in its application.

Numerical Solution of Dynamic Equilibrium Models Under Poisson Uncertainty

We propose a simple and powerful numerical algorithm to compute the transition process in continuous-time dynamic equilibrium models with rare events. In this paper we transform the dynamic system of stochastic differential equations into a system of functional differential equations of the retarded type. We apply the Waveform Relaxation algorithm, i.e., we provide a guess of the policy function and solve the resulting system of (deterministic) ordinary differential equations by standard techniques. For parametric restrictions, analytical solutions to the stochastic growth model and a novel solution to Lucas' endogenous growth model under Poisson uncertainty are used to compute the exact numerical error. We show how (potential) catastrophic events such as rare natural disasters substantially affect the economic decisions of households.

Testing for Rational Bubbles in a Co-Explosive Vector Autoregression

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The analysis for the no-bubble case is done within the traditional Johansen model for I(1) variables, while the bubble model is analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000.

Time-Oriented Synthesis for aWTAContinuous-Time Neural Network Affected by Capacitive Cross-Coupling

A continuous time neural network built with nonlinear amplifiers which selects the largest item of a list (WTA) is considered. The network receives and processes lists admitted one by one. If the processing and resetting times are imposed, our paper gives a method to find the circuit parameters assuring a correct operation. We take into account the capacitive coupling between input terminals and present complete existence and convergence results on the differential model. The main achievement consists of simple bounds for the processing and resetting times. They are inferred by an original method of decoupling the system model into solvable linear differential inequalities. Also, a new procedure to impose the stationary WTA state is given. All these results are valid under various parameter restrictions. They lead to a neat design procedure which starts from imposed processing and resetting time and list density to determine the WTA threshold, the interconnection conductance, the amplifier gain, the bias current. Numerical examples check and interpret the results.