Nonparametric methods with applications to hedonic models

Current real estate statistical valuation involves the estimation of parameters within a posited specification. Suchparametric estimation requires judgment concerning model (1) variables; and (2) functional form. In contrast,nonparametric regression estimation requires attention to (1) but permits greatly reduced attention to (2). Parametric estimators functionally model the parameters and variables affectingE(y¦x) while nonparametric estimators directly modelpdf(y, x) and henceE(y¦x).This article applies the kernel nonparametric regression estimator to two different data sets and specifications. The article shows the nonparametric estimator outperforms the standard parametric estimator (OLS) across variable transformations and across data subsets differing in quality. In addition, the article reviews properties of nonparametric estimators, presents the history of nonparametric estimators in real estate, and discusses a representation of the kernel estimator as a nonparametric grid method.     

Modeling daily price limits

This paper characterizes the behavior of observed asset prices under price limits and proposes the use of two-limit truncated and Tobit regression models to analyze regression models whose dependent variable is subject to price limits. Through a proper arrangement of the sample, these two models, the estimation of which is easy to implement, are applied only to subsets of the sample under study, rather than the full sample. Using the estimation of simple linear regression model as an example, several Monte Carlo experiments are conducted to compare the performance of the maximum likelihood estimators (MLEs) based on these two models and a generalized method of moments (GMM) estimator developed by K. C. John Wei and R. Chiang. The results show that under different price limits and various distributional assumptions for the error terms, the MLEs based on the two-limit Tobit and truncated regression models and the GMM estimator perform reasonably well, while the naive OLS estimator is downward biased. Overall, the MLE based on the two-limit Tobit model outperforms the other estimators.     

Parametric,semiparametric, and nonparametric estimation of characteristic values within mass assessment and hedonic pricing models

Parametric estimators, such as OLS, attain high efficiency for well-specified models. Nonparametric estimators greatly reduce specification error but at the cost of efficiency. Semiparametric estimators compromise between these dual goals of efficiency and specification error. Semiparametric estimators can assume general forms within classes of functional forms. This paper applies OLS, the kernel nonparametric regression estimator, and the semi-parametric estimator of Powell, Stock, and Stoker (1989) to a data set, which should, based on theory and previous empirical work, yield positive coefficients. The semiparametric estimator, on average, displayed the performance most consistent with prior expectations followed by the nonparametric and parametric estimators. In addition, the paper shows how the semiparametric estimator can provide insights into the form of misspecification and suggest data transformations.     

Two-step estimation of the volatility functions in diffusion models with empirical applications

In this article, we develop a two-step estimation procedure for the volatility function in diffusion models. We firstly estimate the volatility series at sampling time points based on high-frequency data. Then, the volatility function estimator can be obtained by using the kernel smoothing method. The resulting estimators are presented based on high-frequency data, and are shown to be consistent and asymptotically normal. We also consider boundary issues and then propose two methods to handle them. The asymptotic normality of two boundary-corrected estimators is established under some suitable conditions. The proposed estimators are illustrated by Monte Carlo simulations and real data.     

Estimating and testing beta pricing models: Alternative methods and their performance in simulations

We conduct a simulation analysis of the Fama and MacBeth[1973. Risk, returns and equilibrium: empirical tests. Journal of Political Economy 71, 607–636.] two-pass procedure, as well as maximum likelihood (ML) and generalized method of moments estimators of cross-sectional expected return models. We also provide some new analytical results on computational issues, the relations between estimators, and asymptotic distributions under model misspecification. The generalized least squares estimator is often much more precise than the usual ordinary least squares (OLS) estimator, but it displays more bias as well. A “truncated” form of ML performs quite well overall in terms of bias and precision, but produces less reliable inferences than the OLS estimator.     

Estimation of risk contributions with MCMC

Determining risk contributions of unit exposures to portfolio-wide economic capital is an important task in financial risk management. Computing risk contributions involves difficulties caused by rare-event simulations. In this study, we address the problem of estimating risk contributions when the total risk is measured by value-at-risk (VaR). Our proposed estimator of VaR contributions is based on the Metropolis-Hasting (MH) algorithm, which is one of the most prevalent Markov chain Monte Carlo (MCMC) methods. Unlike existing estimators, our MH-based estimator consists of samples from the conditional loss distribution given a rare event of interest. This feature enhances sample efficiency compared with the crude Monte Carlo method. Moreover, our method has consistency and asymptotic normality, and is widely applicable to various risk models having a joint loss density. Our numerical experiments based on simulation and real-world data demonstrate that in various risk models, even those having high-dimensional (≈500) inhomogeneous margins, our MH estimator has smaller bias and mean squared error when compared with existing estimators.     

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.     

Using Cointegration Restrictions to Improve Inference in Vector Autoregressive Systems

An improved way of dealing with uncertain prior information in the context of vector autoregressive systems of equations is proposed. The procedure is appropriate when inference about parameters of a cointegrated system is the aim of the analysis. The estimator uses uncertain prior information about the existence of trends and co-trends in the time series to improve parameter estimation within these systems. The improved estimator eliminates the need to carry out the unit root, cointegration, and parameter restriction pretests and is shown in our Monte Carlo experiments to have good statistical properties in small samples. The pretest, maximum likelihood, and restricted maximum likelihood estimators are compared to the proposed estimator based on squared error risk, mean square error of prediction risk, and out-of-sample root-mean-square forecast error. The Monte Carlo simulations are based on actual economic data collected for eurodollar futures contracts. The evidence suggests that the parameters of vector autoregressive systems can be estimated with lower mean square error with the new estimator even when prior guesses about the nature of the cointegrating vector(s) are incorrect. In-sample prediction is likewise improved. The Monte Carlo simulations are based on eurodollar spot and futures market data that has been used to test the unbiased expectations hypothesis.Marjory B. Ourso Center for Excellence in Teaching Professor     

An analysis of contagion among Asian countries using the canonical model of contagion

Understanding the dependence among economies is relevant to policy makers, central banks and investors in the decision-making process. One important issue for study is the existence of contagion among economies. This work considers the Canonical Model of Contagion by Pesaran and Pick (Journal of Economic Dynamics and Control, 2007), which differentiates contagion from interdependence. The ordinary least squares estimator of this model is biased by the endogenous variables in the model. In this study, instrumental variables are used to decrease the bias of the ordinary least squares estimator. The model is extended to the case of heteroskedastic errors, features that are generally found in financial data. We postulate the conditional volatility of the performance indices as instrumental variables and analyze the validity of these instruments using Monte Carlo simulations. Monte Carlo simulations estimate the distributions of the estimators under the null hypothesis. Finally, the canonical model of contagion is used to analyze the contagion among seven Asian countries.     

Estimating Cointegrated Panels with Common Factors and the Forward Rate Unbiasedness Hypothesis

This article proposes a bias-adjusted estimator for use in cointegratedpanel regressions when the errors are cross-sectionally correlatedthrough an unknown common factor structure. The asymptotic distributionof the new estimator is derived and is examined in small samplesusing Monte Carlo simulations. For the estimation of the numberof factors, several information-based criteria are considered.The simulation results suggest that the new estimator performswell in comparison to existing ones. In our empirical application,we provide new evidence suggesting that the forward rate unbiasednesshypothesis cannot be rejected.     

Measuring consumption smoothing in CEX data

A new method of measuring the degree of consumption smoothing is proposed and implemented using data from the Consumer Expenditure Survey. The structure of this Survey is such that estimators previously used in the literature are inconsistent, simply because income is measured annually and consumption is measured quarterly. An AR(1) structure is imposed on the income process to obtain a proxy for quarterly income through a projection on annual income. By construction, this proxy gives rise to a measurement error which is orthogonal to the proxy itself—as opposed to the unobserved regressor—leading to a consistent estimator. Our estimates are contrasted with the output of two estimators used in the literature. This comparison shows that while the first (OLS) estimator tends to overstate the degree of risk sharing, the second (IV) estimator grossly understates it.     

Alternative beta risk estimators and asset pricing tests in emerging markets: The case of Pakistan

This paper tests and compares the applicability of two asset pricing models specifically, the CAPM and the Fama–French three factor models for an emerging stock market namely, Pakistan. The paper analyses a number of beta risk estimators, including OLS, the Dimson thin trading estimator, a trade-to-trade estimator and a sample selectivity estimator. To uncover any possible influence of the return interval and the type of the market index, the analysis is carried out on three data frequencies namely daily, weekly and monthly as well as for a value and an equally weighted market index. The alternative beta estimators appear to correct thin trading bias but their effects on asset pricing tests are not visible. Moreover contrary to the expectations the test results for monthly and weekly frequencies are not promising. Instead for daily data the cross-section of returns are explained by a number of risk factors and trading volume.     

Estimation employing a priori information within mass appraisal and hedonic pricing models

Both statistical appraisal and hedonic pricing models decompose houses into a set of individual characteristics. Regression estimates yield the contribution of each characteristic to total value. Unfortunately, straightforward application of OLS may produce untenable results such as implausible coefficient magnitudes or incorrect signs. Often the suspected cause is multicollinearity. This article examines the effect on estimation efficiency of differing levels of multicollinearity, R², and a priori information in the form of sub-market cost data, by comparing inequality restricted least squares (IRLS) with OLS in a series of Monte Carlo experiments. The IRLS procedure investigated here hybridizes the statistical market approach implemented by OLS, and the more traditional cost approach. The experiments show dramatic gains in estimation efficiency from exploiting a priori information through IRLS.     

Sensitivity estimates for portfolio credit derivatives using Monte Carlo

Portfolio credit derivatives are contracts that are tied to an underlying portfolio of defaultable reference assets and have payoffs that depend on the default times of these assets. The hedging of credit derivatives involves the calculation of the sensitivity of the contract value with respect to changes in the credit spreads of the underlying assets, or, more generally, with respect to parameters of the default-time distributions. We derive and analyze Monte Carlo estimators of these sensitivities. The payoff of a credit derivative is often discontinuous in the underlying default times, and this complicates the accurate estimation of sensitivities. Discontinuities introduced by changes in one default time can be smoothed by taking conditional expectations given all other default times. We use this to derive estimators and to give conditions under which they are unbiased. We also give conditions under which an alternative likelihood ratio method estimator is unbiased. We illustrate the application and verification of these conditions and estimators in the particular case of the multifactor Gaussian copula model, but the methods are more generally applicable.      

Export Sophistication: A Dynamic Panel Data Approach

In this article, we analyze export sophistication based on a large panel dataset (2001–2015; 101 countries) and using various estimation algorithms. Using Monte Carlo simulations, we evaluate the bias properties of estimators and show that GMM-type estimators outperform instrumental-variable and fixed-effects estimators. Based on our analysis we document that GDP per capita and the size of the economy exhibit significant and positive effects on export sophistication; weak institutional quality exhibits negative effect. We also show that export sophistication is path-dependent and stable even during a major economic crisis, which is especially important for emerging and developing economies.     

Multilevel dual approach for pricing American style derivatives

In this article we propose a novel approach to reduce the computational complexity of the dual method for pricing American options. We consider a sequence of martingales that converges to a given target martingale and decompose the original dual representation into a sum of representations that correspond to different levels of approximation to the target martingale. By next replacing in each representation true conditional expectations with their Monte Carlo estimates, we arrive at what one may call a multilevel dual Monte Carlo algorithm. The analysis of this algorithm reveals that the computational complexity of getting the corresponding target upper bound, due to the target martingale, can be significantly reduced. In particular, it turns out that using our new approach, we may construct a multilevel version of the well-known nested Monte Carlo algorithm of Andersen and Broadie (Manag. Sci. 50:1222–1234, 2004) that is, regarding complexity, virtually equivalent to a non-nested algorithm. The performance of this multilevel algorithm is illustrated by a numerical example.     

CONSISTENT ESTIMATION OF RESIDUAL VARIANCE IN REGULATORY EVENT STUDIES

This study presents new evidence on alternative methods used to test for abnormal returns in regulatory event studies where cross-sectional correlation in residuals is significant. Results contradict earlier studies that find no advantages to using joint generalized least squares (JGLS) methods over ordinary least squares (OLS). We find that in an actual regulatory event study cross-correlation is significant, and that failing to correct for this correlation results in substantially higher calculated F-statistics. In Monte Carlo simulations we find that OLS test statistics are not well specified when residuals exhibit cross-sectional correlation at levels that are reasonable to expect in daily return data, while JGLS test statistics are well specified. The study includes tests of the effective power of the OLS and JGLS statistics.     

The Stambaugh bias in panel predictive regressions

This paper analyzes predictive regressions in a panel data setting. The standard fixed effects estimator suffers from a small sample bias, which is the analogue of the Stambaugh bias in time-series predictive regressions. Monte Carlo evidence shows that the bias and resulting size distortions can be severe. A new bias-corrected estimator is proposed, which is shown to work well in finite samples and to lead to approximately normally distributed t-statistics. Overall, the results show that the econometric issues associated with predictive regressions when using time-series data to a large extent also carry over to the panel case. The results are illustrated with an application to predictability in international stock indices.     

Jackknifing stock return predictions

We show that the general bias-reducing technique of jackknifing can be successfully applied to stock return predictability regressions. Compared to standard OLS estimation, the jackknifing procedure delivers virtually unbiased estimates with mean squared errors that generally dominate those of the OLS estimates. The jackknifing method is very general, as well as simple to implement, and can be applied to models with multiple predictors and overlapping observations. Unlike most previous work on inference in predictive regressions, no specific assumptions regarding the data generating process for the predictors are required. A set of Monte Carlo experiments show that the method works well in finite samples and the empirical section finds that out-of-sample forecasts based on the jackknife estimates tend to outperform those based on the plain OLS estimates. The improved forecast ability also translates into economically relevant welfare gains for an investor who uses the predictive regression, with jackknife estimates, to time the market.     

Corporate governance in banking: The role of the board of directors

We use a sample of large international commercial banks to test hypotheses on the dual role of boards of directors. We use a suitable econometric model (two step system estimator) to solve the well-known endogeneity problem in corporate governance literature, and demonstrate the empirical and theoretical superiority of system estimator over OLS and within estimators. We find an inverted U-shaped relation between bank performance and board size, and between the proportion of non-executive directors and performance. Our results show that bank board composition and size are related to directors’ ability to monitor and advise management, and that larger and not excessively independent boards might prove more efficient in monitoring and advising functions, and create more value. All of these relations hold after we control for the measure of performance, the weight of the banking industry in each country, bank ownership, and regulatory and institutional differences.