A polyhedral approximation approach to concave numerical dynamic programming

This paper introduces a numerical method for solving concave continuous state dynamic programming problems which is based on a pair of polyhedral approximations of concave functions. The method is globally convergent and produces computable upper and lower bounds on the value function which can in theory be made arbitrarily tight. This is true regardless of the pattern of binding constraints, the smoothness of model primitives, and the dimensionality and rectangularity of the state space. We illustrate the method's performance using an optimal firm management problem subject to credit constraints and partial investment irreversibilities.     

Exact computation of GMM estimators for instrumental variable quantile regression models

We show that the generalized method of moments (GMM) estimation problem in instrumental variable quantile regression (IVQR) models can be equivalently formulated as a mixed‐integer quadratic programming problem. This enables exact computation of the GMM estimators for the IVQR models. We illustrate the usefulness of our algorithm via Monte Carlo experiments and an application to demand for fish.     

The performance of estimators based on the propensity score

We investigate the finite sample properties of a large number of estimators for the average treatment effect on the treated that are suitable when adjustment for observed covariates is required, like inverse probability weighting, kernel and other variants of matching, as well as different parametric models. The simulation design used is based on real data usually employed for the evaluation of labour market programmes in Germany. We vary several dimensions of the design that are of practical importance, like sample size, the type of the outcome variable, and aspects of the selection process. We find that trimming individual observations with too much weight as well as the choice of tuning parameters are important for all estimators. A conclusion from our simulations is that a particular radius matching estimator combined with regression performs best overall, in particular when robustness to misspecifications of the propensity score and different types of outcome variables is considered an important property.     

A family of empirical likelihood functions and estimators for the binary response model

The minimum discrimination information principle is used to identify an appropriate parametric family of probability distributions and the corresponding maximum likelihood estimators for binary response models. Estimators in the family subsume the conventional logit model and form the basis for a set of parametric estimation alternatives with the usual asymptotic properties. Sampling experiments are used to assess finite sample performance.     

Testing for stochastic dominance using the weighted McFadden-type statistic

We demonstrate that when testing for stochastic dominance of order three and above, using a weighted version of the Kolmogorov–Smirnov-type statistic proposed by McFadden [1989. In: Fomby, T.B., Seo, T.K. (Eds.), Studies in the Economics of Uncertainty. Springer, New York, pp. 113–134] is necessary for obtaining a non-degenerate asymptotic distribution. Since the asymptotic distribution is complex, we discuss a bootstrap approximation for it in the context of a real application.     

An alternative to the weighted score card approach to measuring performance: An analysis of English and Welsh probation boards

The UK government published a weighted score card approach in 2003 to analyse the performance of Probation Boards in England and Wales. However, there has not been a thorough analysis of whether non-parametric methods could provide more advanced options for analysing performance than the standard Weighted Score Card approach – a variant of the Balanced Score Card. Our results show there is considerable divergence in the ranks of Probation Boards from that of the WSC when we include the input variable ‘resource expenditure’ within a DEA model, calling into question recent policy initiatives to increase efficiency in the national probation service.     

A simple ordered data estimator for inverse density weighted expectations

We consider estimation of means of functions that are scaled by an unknown density, or equivalently, integrals of conditional expectations. The “ordered data” estimator we provide is root n$n$ consistent, asymptotically normal, and is numerically extremely simple, involving little more than ordering the data and summing the results. No sample-size-dependent smoothing is required. A similarly simple estimator is provided for the limiting variance. The proofs include new limiting distribution results for functions of nearest-neighbor spacings. Potential applications include endogenous binary choice, willingness to pay, selection, and treatment models.     

A Gaussian approximation scheme for computation of option prices in stochastic volatility models

We consider European options on a price process that follows the log-linear stochastic volatility model. Two stochastic integrals in the option pricing formula are costly to compute. We derive a central limit theorem to approximate them. At parameter settings appropriate to foreign exchange data our formulas improve computation speed by a factor of 1000 over brute force Monte Carlo making MCMC statistical methods practicable. We provide estimates of model parameters from daily data on the Swiss Franc to Euro and Japanese Yen to Euro over the period 1999–2002.     

Riesz estimators

We consider properties of estimators that can be written as vector lattice (Riesz space) operations. Using techniques widely used in economic theory and functional analysis, we study the approximation properties of these estimators paying special attention to additive models. We also provide two algorithms RIESZVAR(i-ii) for the consistent parametric estimation of continuous multivariate piecewise linear functions.     

Data-based ranking of realised volatility estimators

This paper presents new methods for comparing the accuracy of estimators of the quadratic variation of a price process. I provide conditions under which the relative accuracy of competing estimators can be consistently estimated (as T→∞), and show that forecast evaluation tests may be adapted to the problem of ranking these estimators. The proposed methods avoid making specific assumptions about microstructure noise, and facilitate comparisons of estimators that would be difficult using methods from the extant literature, such as those based on different sampling schemes. An application to high frequency IBM data between 1996 and 2007 illustrates the new methods.     

Simulating the Reform of Means‐tested Benefits with Endogenous Take‐up and Claim Costs*

Microsimulation models are commonly used to examine the distributional impact of reforms of the means‐tested benefit system. Take‐up behaviour is related to the level of entitlement, so reform may induce changes in take‐up. We develop a stochastic simulation method and apply it to a probit model of ‘income support’ take‐up by the UK pensioners. The method allows us to adjust net income for the welfare losses because of tangible or intangible claim costs. Endogenous take‐up and claim costs both have an important impact on the simulated outcomes of the policy reform.     

Evaluating PcGets and RETINA as Automatic Model Selection Algorithms*

The paper describes two automatic model selection algorithms, RETINA and PcGets, briefly discussing how the algorithms work and what their performance claims are. RETINA's Matlab implementation of the code is explained, then the program is compared with PcGets on the data in Perez‐Amaral, Gallo and White (2005 , Econometric Theory, Vol. 21, pp. 262–277), ‘A Comparison of Complementary Automatic Modelling Methods: RETINA and PcGets’, and Hoover and Perez (1999 , Econometrics Journal, Vol. 2, pp. 167–191), ‘Data Mining Reconsidered: Encompassing and the General‐to‐specific Approach to Specification Search’. Monte Carlo simulation results assess the null and non‐null rejection frequencies of the RETINA and PcGets model selection algorithms in the presence of nonlinear functions.     

Estimating Nonlinear Models with Multiple Fixed Effects: A Computational Note*

In this paper we consider estimation of nonlinear panel data models that include multiple individual fixed effects. Estimation of these models is complicated both by the difficulty of estimating models with possibly thousands of coefficients and also by the incidental parameters problem; that is, noisy estimates of the fixed effects when the time dimension is short contaminate the estimates of the common parameters due to the nonlinearity of the problem. We propose a simple variation of existing bias‐corrected estimators, which can exploit the additivity of the effects for numerical optimization. We exhibit the performance of the estimators in simulations.     

Edgeworth expansions for realized volatility and related estimators

This paper shows that the asymptotic normal approximation is often insufficiently accurate for volatility estimators based on high frequency data. To remedy this, we derive Edgeworth expansions for such estimators. The expansions are developed in the framework of small-noise asymptotics. The results have application to Cornish–Fisher inversion and help setting intervals more accurately than those relying on normal distribution.     

Estimation and inference in two-stage,semi-parametric models of production processes

Many papers have regressed non-parametric estimates of productive efficiency on environmental variables in two-stage procedures to account for exogenous factors that might affect firms’ performance. None of these have described a coherent data-generating process (DGP). Moreover, conventional approaches to inference employed in these papers are invalid due to complicated, unknown serial correlation among the estimated efficiencies. We first describe a sensible DGP for such models. We propose single and double bootstrap procedures; both permit valid inference, and the double bootstrap procedure improves statistical efficiency in the second-stage regression. We examine the statistical performance of our estimators using Monte Carlo experiments.     

The core can be accessed with a bounded number of blocks

We show the existence of an upper bound for the number of blocks required to get from one imputation to another provided that accessibility holds. The bound depends only on the number of players in the TU game considered. For the class of games with non-empty cores this means that the core can be reached via a bounded sequence of blocks.     

Tikhonov regularization for nonparametric instrumental variable estimators

We study a Tikhonov Regularized (TiR) estimator of a functional parameter identified by conditional moment restrictions in a linear model with both exogenous and endogenous regressors. The nonparametric instrumental variable estimator is based on a minimum distance principle with penalization by the norms of the parameter and its derivatives. After showing its consistency in the Sobolev norm and uniform consistency under an embedding condition, we derive the expression of the asymptotic Mean Integrated Square Error and the rate of convergence. The optimal value of the regularization parameter is characterized in two examples. We illustrate our theoretical findings and the small sample properties with simulation results. Finally, we provide an empirical application to estimation of an Engel curve, and discuss a data driven selection procedure for the regularization parameter.     

Asymptotic properties of Monte Carlo estimators of diffusion processes

This paper studies the limit distributions of Monte Carlo estimators of diffusion processes. We examine two types of estimators based on the Euler scheme, one applied to the original processes, the other to a Doss transformation of the processes. We show that the transformation increases the speed of convergence of the Euler scheme. We also study estimators of conditional expectations of diffusions. After characterizing expected approximation errors, we construct second-order bias-corrected estimators. We also derive new convergence results for the Mihlstein scheme. Illustrations of the results are provided in the context of simulation-based estimation of diffusion processes.     

A decision model for bank branch site selection: Define branch success and do not deviate

Site selection is one of the most important decision making processes for firms since, if done correctly, it provides access to the best customers and the greatest market potential. In contrast, poor location choices are costly and difficult to reverse.This paper deals with the single branch site selection problem in the banking context. Due to the high level of complexity (several factors have to be taken into consideration in the decision making process as well as a wide range of entities' internal requirements), to date there is no single procedure that fits all needs. This paper attempts to provide a solution to this problem by proposing a unified method based on minimizing the distance from the candidate-branch to the most successful branches, taking into account each banking institution’ notion of branch success. This methodology would work well at the lowest possible cost.