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.     

Bias in estimates of discrimination and default in mortgage lending: The effects of simultaneity and self-selection

The common practices of estimating single-equation models of mortgage rejection to test for discrimination in mortgage markets or single-equation ex ante mortgage default equations to validate underwriting criteria produce biased and inconsistent parameter estimates. This is due to problems of simultaneous equations bias which arise because, in a world of imperfect information, mortgage terms are not exogenous to the rejection or default decision. In addition, mortgage default estimates are also subject to selection bias. Monte Carlo experiments are used to study the nature and extent of likely bias in single-equation estimation results. We find that rejection equation estimates indicate discrimination when none exists and that estimated coefficients of mortgage terms, such as the loan-to-value ratio, are also subject to significant bias in both rejection and default equations.     

MC's for MCMC'ists

We develop a minimum amount of theory of Markov chains at as low a level of abstraction as possible in order to prove two fundamental probability laws for standard Markov chain Monte Carlo algorithms:
1. The law of large numbers explains why the algorithm works: it states that the empirical means calculated from the samples converge towards their "true" expected values, viz. expectations with respect to the invariant distribution of the associated Markov chain (=the target distribution of the simulation).
2. The central limit theorem expresses the deviations of the empirical means from their expected values in terms of asymptotically normally distributed random variables. We also present a formula and an estimator for the associated variance.     

ON THE CONSISTENCY OF REGRESSION‐BASED MONTE CARLO METHODS FOR PRICING BERMUDAN OPTIONS IN CASE OF ESTIMATED FINANCIAL MODELS

In many applications of regression‐based Monte Carlo methods for pricing, American options in discrete time parameters of the underlying financial model have to be estimated from observed data. In this paper suitably defined nonparametric regression‐based Monte Carlo methods are applied to paths of financial models where the parameters converge toward true values of the parameters. For various Black–Scholes, GARCH, and Levy models it is shown that in this case the price estimated from the approximate model converges to the true price.     

Determinacy in the Linear Model: Gauss to Bose and Koopmans

Gauss showed that least squares fails to produce a unique solution only when the problem is indeterminate. This note considers his argument and the notion of indeterminacy underlying it. It also relates the argument to twentieth-century discussions of estimability and identifiability.     

Block recursion and structural vector autoregressions

In applications of structural VAR modeling, finite-sample properties may be difficult to obtain when certain identifying restrictions are imposed on lagged relationships. As a result, even though imposing some lagged restrictions makes economic sense, lagged relationships are often left unrestricted to make statistical inference more convenient. This paper develops block Monte Carlo methods to obtain both maximum likelihood estimates and exact Bayesian inference when certain types of restrictions are imposed on the lag structure. These methods are applied to two examples to illustrate the importance of imposing restrictions on lagged relationships.     

Design of limited-stop bus service with capacity constraint and stochastic travel time

This paper develops a mathematical model for the optimal stopping design of limited-stop bus service, which allows each bus vehicle to skip some stops. To better reflect the reality, this paper considers the vehicle capacity and stochastic travel time. Also, vehicles are all allowed to skip stops whereas any stop is not allowed to be skipped by two consecutive vehicles. A hybrid artificial bee colony (ABC) and Monte Carlo method is developed to solve the optimal stopping strategy. Finally, the model and solution method are validated by a numerical example, and a sensitivity analysis is performed on the passenger demand.     

Doing Least Squares: Perspectives from Gauss and Yule

Gauss introduced a procedure for calculating least squares estimates and their precisions. Yule introduced a new system of notation adapted to correlation analysis. This paper describes these formalisms and compares them with the matrix and vector space formalisms used in modern regression analysis.     

An analysis of the companies’ compliance with the EU disclosure requirements and corporate characteristics influencing it: A case study of Turkey

One of the factors shaping accounting disclosure of countries in Europe is the EU Fourth Directive (EUFD) which addresses individual company accounts. The EUFD has been claimed to have had an impact on accounting, including accounting disclosure, of not only the EU countries but also non-EU member European countries. Turkey is one of the non-EU member European countries claimed to be influenced by the EUFD and this study examined Turkish companies’ level of compliance with the disclosure requirements of the EUFD over the years (1986, 1987, 1991, 1992 and 1995), and assessed whether companies’ level of compliance had been influenced by their corporate characteristics, such as company size, listing status and industry type.Turkish companies’ level of compliance with the disclosure requirements of the EUFD was measured by an index (i.e. EUFD Disclosure Compliance Index—EUFDCDI). The index was developed by; constructing disclosure scoring sheet; obtaining annual reports of 61 sampled Turkish companies over the years; completing scoring sheet for each companies’ annual report; and creating disclosure index. The index (EUFDCDI) scores was, than, analysed for each year to assess the companies’ compliance with the EU disclosure requirements and both parametric and non-parametric test, were conducted to determine if there were significant changes in the extent of disclosure in compliance with the EUFD over the years. Furthermore, using the companies EUFDCDI score as dependent variable and corporate characteristics as independent variables, the Ordinary Least Square regression was run for each year to find out if the companies’ level of compliance with the EU disclosure requirements were influenced by their corporate characteristics.The results of this study revealed that Turkish companies’ compliance with the required disclosure by the EUFD varied within the range of 30–85%, but their compliance increased significantly from one year to another throughout the selected period. The results further revealed that listing status is one of the important corporate characteristics of the Turkish companies affecting their compliance with the EU disclosure requirements.     

Adjoint-based Monte Carlo calibration of financial market models

Adjoint methods have recently gained considerable importance in the finance sector, because they allow to quickly compute option sensitivities with respect to a large number of model parameters. In this paper we investigate how the efficiency of adjoint methods can be exploited to speed up the Monte Carlo-based calibration of financial market models. After analyzing the calibration problem both theoretically and numerically, we derive the associated adjoint equation and propose its application in combination with a multi-layer method, for which we prove convergence to a stationary point of the underlying optimization problem. Detailed numerical examples illustrate the performance of the method. In particular, the proposed algorithm reduces the calibration time for a typical equity market model with time-dependent model parameters from over three hours to less than ten minutes on a usual desktop PC.