Semiparametric estimation of multinomial discrete‐choice models using a subset of choices

Nonlogit maximum‐likelihood estimators are inconsistent when using data on a subset of the choices available to agents. I show that the semiparametric, multinomial maximum‐score estimator is consistent when using data on a subset of choices. No information is required for choices outside of the subset. The required conditions about the error terms are the same conditions as for using all the choices. Estimation can proceed under additional restrictions if agents have unobserved, random consideration sets. A solution exists for instrumenting endogenous continuous variables. Monte Carlo experiments show the estimator performs well using small subsets of choices.     

Nonparametric density estimation and tests of continuous time interest rate models

I study the finite sample distribution of one of Ait-Sahalia's(1996c) nonparametric tests of continuous-time models of theshort-term riskless rate. The test rejects true models too oftenbecause interest rate data are highly persistent but the asymptoticdistribution of the test (and of the kernel density estimatoron which the test is based) treats the data as if it were independentlyand identically distributed. To attain the accuracy of the kerneldensity estimator implied by its asymptotic distribution with22 years of data generated from the Vasicek model in fact requires2755 years of data.     

Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels

This paper proposes an asymmetric kernel-based method for nonparametric estimation of scalar diffusion models of spot interest rates. We derive the asymptotic theory for the asymmetric kernel estimators of the drift and diffusion functions for general and positive recurrent processes and illustrate the advantages of the Gamma kernel for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed nonparametric estimators for bond and option pricing are evaluated using actual and simulated data for U.S. interest rates.     

A computationally fast estimator for random coefficients logit demand models using aggregate data

This article proposes a computationally fast estimator for random coefficients logit demand models using aggregate data that Berry, Levinsohn, and Pakes ( 1995 ; hereinafter, BLP) suggest. Our method, which we call approximate BLP (ABLP), is based on a linear approximation of market share functions. The computational advantages of ABLP include (i) the linear approximation enables us to adopt an analytic inversion of the market share equations instead of a numerical inversion that BLP propose, (ii) ABLP solves the market share equations only at the optimum, and (iii) it minimizes over a typically small dimensional parameter space. We show that the ABLP estimator is equivalent to the BLP estimator in large data sets. Our Monte Carlo experiments illustrate that ABLP is faster than other approaches, especially for large data sets.     

Nonparametric estimation and testing of stochastic discount factor

This paper attempts to estimate stochastic discount factor (SDF) proxies nonparametrically using the conditional Hansen–Jagannathan distance. Nonparametric estimation can not only avoid misspecification when dealing with nonlinearity in the model but also provide more precise information about the local properties of the estimators. Empirical studies show that our method performs better than the alternative parametric polynomial models, and furthermore, we find that the return on aggregate wealth can sufficiently explain the SDF proxies when one deals with nonlinearity appropriately.     

Nonparametric mean and variance estimation from truncated data

Abstract

This paper considers situations where a known number of the smallest values of a sample and a known number of the largest values have been truncated. The problem is to obtain an estimate of the population mean, an estimate of the standard deviation of this estimate of the mean, and an estimate of the population standard deviation. This paper derives a nonparametric estimate for each of these three cases. These estimates are approximately valid for most continuous statistical populations of practical interest when a small number of sample values are truncated and the sample size is not too small. The mean estimate consists of a linear function of the ordered values of the truncated sample, while each standard deviation estimate is the square root of a quadratic function of these observations.     

Nonparametric realized volatility estimation in the international equity markets

Using high-frequency intraday data, we construct, test and model seven new realized volatility estimators for six international equity indices. We detect jumps in these estimators, construct the jump components of volatility and perform various tests on their properties. Then we use the class of heterogeneous autoregressive (HAR) models for assessing the relevant effects of jumps on volatility. Our results expand and complement the previous literature on the nonparametric realized volatility estimation in terms of volatility jumps being examined and modeled for the international equity market, using such a variety of new realized volatility estimators. The selection of realized volatility estimator greatly affects jump detection, magnitude and modeling. The properties each volatility estimator tries to incorporate affect the detection, magnitude and properties of jumps. These volatility-estimation and jump properties are also evident in jump modeling based on statistical and economic terms.     

Computing finite-time survival probabilities using multinomial approximations of risk models

We consider the problem of computing finite-time survival probabilities for various risk models. We develop an approximating discrete-time multinomial lattice that mimics the evolution of the corresponding continuous risk process. A simple recursive algorithm to compute survival probabilities is described. Numerical results show that the proposed scheme yields accurate values in all the considered cases.     

On choice of statistics in credibility estimation

Abstract

The question on what statistics to base our credibility estimators, is discussed in a general model. We introduce concepts of sufficiency, completeness, θ-sufficiency, and θ-completeness that are useful in this connection, and use methods of Rao-Blackwell type. Some of the present results are closely related to results by Taylor (1977).     

Nonparametric efficiency estimation in stochastic environments: Noise-to-signal estimation,finite sample performance and hypothesis testing

This study considers the issues of noise-to-signal estimation, finite sample performance and hypothesis testing for a new nonparametric and stochastic efficiency estimation technique. We apply the technique for analyzing the efficiency of European banks from various regions and with various specializations. The technique seems well suited for this application area because banking inputs and outputs generally are measured with error, the banking production technology is not well-defined and large banking data sets such as BankScope allow for a nonparametric approach.     

Binary choice models and corporate takeover

This paper utilizes four different classification procedures (binary choice models) and compares their ability to predict corporate takeovers. Specifically, the paper develops logit, probit, discriminant, and recursive partitioning, models to predict which firms will be taken over. The original classification accuracy and the validation test results indicate that the recursive partitioning model outperforms the other models (although its accuracy drops significantly in the validation test). The results also indicate the difficulty in predicting corporate takeovers.     

Optimal consumption and investment for markets with random coefficients

We consider an optimal investment and consumption problem for a Black–Scholes financial market with stochastic coefficients driven by a diffusion process. We assume that an agent makes consumption and investment decisions based on CRRA utility functions. The dynamic programming approach leads to an investigation of the Hamilton–Jacobi–Bellman (HJB) equation which is a highly nonlinear partial differential equation (PDE) of the second order. By using the Feynman–Kac representation, we prove uniqueness and smoothness of the solution. Moreover, we study the optimal convergence rate of iterative numerical schemes for both the value function and the optimal portfolio. We show that in this case, the optimal convergence rate is super-geometric, i.e., more rapid than any geometric one. We apply our results to a stochastic volatility financial market.     

Nonparametric estimation for i.i.d. paths of a martingale-driven model with application to non-autonomous financial models

Finance and Stochastics - This paper deals with a projection least squares estimator of the function $J_{0}$ computed from multiple independent observations on $[0,T]$ of the process $Z$ defined by...     

Local identification in DSGE models

The issue of identification arises whenever structural models are estimated. Lack of identification means that the empirical implications of some model parameters are either undetectable or indistinguishable from the implications of other parameters. Therefore, identifiability must be verified prior to estimation. This paper provides a simple method for conducting local identification analysis in linearized DSGE models, estimated in both full and limited information settings. In addition to establishing which parameters are locally identified and which are not, researchers can determine whether the identification failures are due to data limitations, such as lack of observations for some variables, or whether they are intrinsic to the structure of the model. The methodology is illustrated using a medium-scale DSGE model.     

Bayesian estimation of financial models

This paper outlines a general methodology for estimating the parameters of financial models commonly employed in the literature. A numerical Bayesian technique is utilised to obtain the posterior density of model parameters and functions thereof. Unlike maximum likelihood estimation, where inference is only justified in large samples, the Bayesian densities are exact for any sample size. A series of simulation studies are conducted to compare the properties of point estimates, the distribution of option and bond prices, and the power of specification tests under maximum likelihood and Bayesian methods. Results suggest that maximum–likelihood–based asymptotic distributions have poor finite–sampleproperties.     

Finite sample accuracy and choice of sampling frequency in integrated volatility estimation

We consider the properties of three estimation methods for integrated volatility, i.e. realized volatility, Fourier, and wavelet estimation, when a typical sample of high-frequency data is observed. We employ several different generating mechanisms for the instantaneous volatility process, e.g. Ornstein–Uhlenbeck, long memory, and jump processes. The possibility of market microstructure contamination is also entertained using models with bid-ask bounce and price discreteness, in which case alternative estimators with theoretical justification under market microstructure noise are also examined. The estimation methods are compared in a simulation study which reveals a general robustness towards persistence or jumps in the latent stochastic volatility process. However, bid-ask bounce effects render realized volatility and especially the wavelet estimator less useful in practice, whereas the Fourier method remains useful and is superior to the other two estimators in that case. More strikingly, even compared to bias correction methods for microstructure noise, the Fourier method is superior with respect to RMSE while having only slightly higher bias. A brief empirical illustration with high-frequency GE data is also included.     

The effect of estimation risk on optimal portfolio choice

This paper determines the effect of estimation risk on optimal portfolio choice under uncertainty. In most realistic problems, the parameters of return distributions are unknown and are estimated using available economic data. Traditional analysis neglects estimation risk by treating the estimated parameters as if they were the true parameters to determine the optimal choice under uncertainty. We show that for normally distributed returns and ‘non-informative’ or ‘invariant’ priors, the admissible set of portfolios taking the estimation uncertainty into account is identical to that given by traditional analysis. However, as a result of estimation risk, the optimal portfolio choice differs from that obtained by traditional analysis. For other plausible priors, the admissible set, and consequently the optimal choice, is shown to differ from that in traditional analysis.     

On the estimation of beta-pricing models

An integrated econometric view of maximum likelihood methodsand more traditional two-pass approaches to estimating beta-pricingmodels is presented. Several aspects of the well-known 'errors-in-variablesproblem' are considered, and an earlier conjecture concerningthe merits of simultaneous estimation of beta and price of riskparameters is evaluated. The traditional inference procedureis found, under standard assumptions, to overstate the precisionof price of risk estimates and an asymptotically valid correctionis derived. Modifications to accommodate serial correlationin market-wide factors are also discussed.     

Consistent estimation of cross-sectional models in event studies

Event studies often include cross-sectional regressions of announcementeffects on exogenous variables. If the event is voluntary andinvestors are rational, then standard OLS and GLS estimatorsare inconsistent. Consistent ML estimators are constructed fora cross-sectional model of horizontal mergers relating announcementeffects to exogenous characteristics of firms and industries.The OLS and ML estimates differ dramatically for bidders butnot for targets. The evidence suggests that manager of bidders,but not targets, have valuable private information about thepotential synergies from proposed mergers.