Monte Carlo tests with nuisance parameters: A general approach to finite-sample inference and nonstandard asymptotics

The technique of Monte Carlo (MC) tests [Dwass (1957, Annals of Mathematical Statistics 28, 181–187); Barnard (1963, Journal of the Royal Statistical Society, Series B 25, 294)] provides a simple method for building exact tests from statistics whose finite sample distribution is intractable but can be simulated (when no nuisance parameter is involved). We extend this method in two ways: first, by allowing for MC tests based on exchangeable possibly discrete test statistics; second, by generalizing it to statistics whose null distribution involves nuisance parameters [maximized MC (MMC) tests]. Simplified asymptotically justified versions of the MMC method are also proposed: these provide a simple way of improving standard asymptotics and dealing with nonstandard asymptotics.     

Pitfalls in the estimation of a cost function that ignores allocative inefficiency: A Monte Carlo analysis

In the stochastic frontier literature, it is a widely held view that allocative inefficiency can be lumped together with technical inefficiency in the estimation of cost frontiers. Therefore, a one-sided error term in the cost function is believed to capture the cost of overall (technical plus allocative) inefficiency. In this paper we challenge that view through a detailed Monte Carlo investigation. The results show that failure to include the cost of allocative inefficiency explicitly in the cost function biases the estimates of: (i) the cost function parameters, (ii) returns to scale, (iii) input price elasticities, and (iv) cost-inefficiency.     

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.     

Testing for short- and long-run causality: A frequency-domain approach

The framework of Geweke (1982. Journal of the American Statistical Association 77, 304–324.) and Hosoya (1991. Probability Theory and Related Fields 88, 429–444.) is adopted to construct a simple test for causality in the frequency domain. This test can also be applied to cointegrated systems. To study the large sample properties of the test, we analyze the power against a sequence of local alternatives. The finite sample properties are investigated by means of Monte Carlo simulations. Our methodology is applied to investigate the predictive content of the yield spread for future output growth. Using quarterly US data we observe reasonable leading indicator properties at frequencies around one year and typical business cycle frequencies.     

Nonparametric stochastic frontiers: A local maximum likelihood approach

This paper proposes a new approach to handle nonparametric stochastic frontier (SF) models. It is based on local maximum likelihood techniques. The model is presented as encompassing some anchorage parametric model in a nonparametric way. First, we derive asymptotic properties of the estimator for the general case (local linear approximations). Then the results are tailored to a SF model where the convoluted error term (efficiency plus noise) is the sum of a half normal and a normal random variable. The parametric anchorage model is a linear production function with a homoscedastic error term. The local approximation is linear for both the production function and the parameters of the error terms. The performance of our estimator is then established in finite samples using simulated data sets as well as with a cross-sectional data on US commercial banks. The methods appear to be robust, numerically stable and particularly useful for investigating a production process and the derived efficiency scores.     

Information measures for generalized gamma family

The objective of this paper is to integrate the generalized gamma (GG)$(\mathit{GG})$ distribution into the information theoretic literature. We study information properties of the GG$\mathit{GG}$ distribution and provide an assortment of information measures for the GG$\mathit{GG}$ family, which includes the exponential, gamma, Weibull, and generalized normal distributions as its subfamilies. The measures include entropy representations of the log-likelihood ratio, AIC, and BIC, discriminating information between GG$\mathit{GG}$ and its subfamilies, a minimum discriminating information function, power transformation information, and a maximum entropy index of fit to histogram. We provide the full parametric Bayesian inference for the discrimination information measures. We also provide Bayesian inference for the fit of GG$\mathit{GG}$ model to histogram, using a semi-parametric Bayesian procedure, referred to as the maximum entropy Dirichlet (MED). The GG$\mathit{GG}$ information measures are computed for duration of unemployment and duration of CEO tenure.     

Endogeneity in quantile regression models: A control function approach

This paper considers a linear triangular simultaneous equations model with conditional quantile restrictions. The paper adjusts for endogeneity by adopting a control function approach and presents a simple two-step estimator that exploits the partially linear structure of the model. The first step consists of estimation of the residuals of the reduced-form equation for the endogenous explanatory variable. The second step is series estimation of the primary equation with the reduced-form residual included nonparametrically as an additional explanatory variable. This paper imposes no functional form restrictions on the stochastic relationship between the reduced-form residual and the disturbance term in the primary equation conditional on observable explanatory variables. The paper presents regularity conditions for consistency and asymptotic normality of the two-step estimator. In addition, the paper provides some discussions on related estimation methods in the literature.     

Short and long run causality measures: Theory and inference

The concept of causality introduced by Wiener [Wiener, N., 1956. The theory of prediction, In: E.F. Beckenback, ed., The Theory of Prediction, McGraw-Hill, New York (Chapter 8)] and Granger [Granger, C. W.J., 1969. Investigating causal relations by econometric models and cross-spectral methods, Econometrica 37, 424–459] is defined in terms of predictability one period ahead. This concept can be generalized by considering causality at any given horizon h$h$ as well as tests for the corresponding non-causality [Dufour, J.-M., Renault, E., 1998. Short-run and long-run causality in time series: Theory. Econometrica 66, 1099–1125; Dufour, J.-M., Pelletier, D., Renault, É., 2006. Short run and long run causality in time series: Inference, Journal of Econometrics 132 (2), 337–362]. Instead of tests for non-causality at a given horizon, we study the problem of measuring causality between two vector processes. Existing causality measures have been defined only for the horizon 1, and they fail to capture indirect causality. We propose generalizations to any horizon h$h$ of the measures introduced by Geweke [Geweke, J., 1982. Measurement of linear dependence and feedback between multiple time series. Journal of the American Statistical Association 77, 304–313]. Nonparametric and parametric measures of unidirectional causality and instantaneous effects are considered. On noting that the causality measures typically involve complex functions of model parameters in VAR and VARMA models, we propose a simple simulation-based method to evaluate these measures for any VARMA model. We also describe asymptotically valid nonparametric confidence intervals, based on a bootstrap technique. Finally, the proposed measures are applied to study causality relations at different horizons between macroeconomic, monetary and financial variables in the US.     

Measuring correlations of integrated but not cointegrated variables: A semiparametric approach

Many macroeconomic and financial variables are integrated of order one (or I(1)) processes and are correlated with each other but not necessarily cointegrated. In this paper, we propose to use a semiparametric varying coefficient approach to model/capture such correlations. We propose two consistent estimators to study the dependence relationship among some integrated but not cointegrated time series variables. Simulations are used to examine the finite sample performances of the proposed estimators.     

A semi-parametric Bayesian approach to the instrumental variable problem

We develop a Bayesian semi-parametric approach to the instrumental variable problem. We assume linear structural and reduced form equations, but model the error distributions non-parametrically. A Dirichlet process prior is used for the joint distribution of structural and instrumental variable equations errors. Our implementation of the Dirichlet process prior uses a normal distribution as a base model. It can therefore be interpreted as modeling the unknown joint distribution with a mixture of normal distributions with a variable number of mixture components. We demonstrate that this procedure is both feasible and sensible using actual and simulated data. Sampling experiments compare inferences from the non-parametric Bayesian procedure with those based on procedures from the recent literature on weak instrument asymptotics. When errors are non-normal, our procedure is more efficient than standard Bayesian or classical methods.     

Knowledge spillovers in US patents: A dynamic patent intensity model with secret common innovation factors

During the past two decades, innovations protected by patents have played a key role in business strategies. This fact enhanced studies of the determinants of patents and the impact of patents on innovation and competitive advantage. Sustaining competitive advantages is as important as creating them. Patents help sustaining competitive advantages by increasing the production cost of competitors, by signaling a better quality of products and by serving as barriers to entry. If patents are rewards for innovation, more R&D should be reflected in more patent applications but this is not the end of the story. There is empirical evidence showing that patents through time are becoming easier to get and more valuable to the firm due to increasing damage awards from infringers. These facts question the constant and static nature of the relationship between R&D and patents. Furthermore, innovation creates important knowledge spillovers due to its imperfect appropriability. Our paper investigates these dynamic effects using US patent data from 1979 to 2000 with alternative model specifications for patent counts. We introduce a general dynamic count panel data model with dynamic observable and unobservable spillovers, which encompasses previous models, is able to control for the endogeneity of R&D and therefore can be consistently estimated by maximum likelihood. Apart from allowing for firm specific fixed and random effects, we introduce a common unobserved component, or secret stock of knowledge, that affects differently the propensity to patent of each firm across sectors due to their different absorptive capacity.     

Distribution-free tests of stochastic monotonicity

This article proposes a nonparametric test of monotonicity for conditional distributions and its moments. Unlike previous proposals, our method does not require smooth estimation of the derivatives of nonparametric curves. Distinguishing features of our approach are that critical values are pivotal under the null in finite samples and that the test is invariant to any monotonic continuous transformation of the explanatory variable. The test statistic is the sup-norm of the difference between the empirical copula function and its least concave majorant with respect to the explanatory variable coordinate. The resulting test is able to detect local alternatives converging to the null at the parametric rate n^−1/2$n^{-1/2}$, with n$n$ the sample size. The finite sample performance of the test is examined by means of a Monte Carlo experiment and an application to testing intergenerational income mobility.     

Nonparametric estimation of an instrumental regression: A quasi-Bayesian approach based on regularized posterior

We propose a quasi-Bayesian nonparametric approach to estimating the structural relationship φ$\phi$ among endogenous variables when instruments are available. We show that the posterior distribution of φ$\phi$ is inconsistent in the frequentist sense. We interpret this fact as the ill-posedness of the Bayesian inverse problem defined by the relation that characterizes the structural function φ$\phi$. To solve this problem, we construct a regularized posterior distribution, based on a Tikhonov regularization of the inverse of the marginal variance of the sample, which is justified by a penalized projection argument. This regularized posterior distribution is consistent in the frequentist sense and its mean can be interpreted as the mean of the exact posterior distribution resulting from a Gaussian prior distribution with a shrinking covariance operator.     

Confidence intervals for the quantile of treatment effects in randomized experiments

In this paper, we explore partial identification and inference for the quantile of treatment effects for randomized experiments. First, we propose nonparametric estimators of sharp bounds on the quantile of treatment effects and establish their asymptotic properties under general conditions. Second, we construct confidence intervals for the bounds and the true quantile by using the approach in Chernozhukov et al. (2009). Third, under additional conditions, we develop a new approach to construct confidence intervals for the bounds and the true quantile and refer to it as the order statistic approach. A simulation study is conducted to investigate the finite sample performance of both approaches.     

Method of moments estimation and identifiability of semiparametric nonlinear errors-in-variables models

This paper deals with a nonlinear errors-in-variables model where the distributions of the unobserved predictor variables and of the measurement errors are nonparametric. Using the instrumental variable approach, we propose method of moments estimators for the unknown parameters and simulation-based estimators to overcome the possible computational difficulty of minimizing an objective function which involves multiple integrals. Both estimators are consistent and asymptotically normally distributed under fairly general regularity conditions. Moreover, root-n consistent semiparametric estimators and a rank condition for model identifiability are derived using the combined methods of the nonparametric technique and Fourier deconvolution.     

Measuring volatility with the realized range

Realized variance, being the summation of squared intra-day returns, has quickly gained popularity as a measure of daily volatility. Following Parkinson [1980. The extreme value method for estimating the variance of the rate of return. Journal of Business 53, 61–65] we replace each squared intra-day return by the high–low range for that period to create a novel and more efficient estimator called the realized range. In addition, we suggest a bias-correction procedure to account for the effects of microstructure frictions based upon scaling the realized range with the average level of the daily range. Simulation experiments demonstrate that for plausible levels of non-trading and bid–ask bounce the realized range has a lower mean-squared error than the realized variance, including variants thereof that are robust to microstructure noise. Empirical analysis of the S&P500 index-futures and the S&P100 constituents confirms the potential of the realized range.     

A martingale approach for testing diffusion models based on infinitesimal operator

I develop an omnibus specification test for diffusion models based on the infinitesimal operator. The infinitesimal operator based identification of the diffusion process is equivalent to a “martingale hypothesis” for the processes obtained by a transformation of the original diffusion model. My test procedure is then constructed by checking the “martingale hypothesis” via a multivariate generalized spectral derivative based approach that delivers a N(0,1) asymptotical null distribution for the test statistic. The infinitesimal operator of the diffusion process is a closed-form function of drift and diffusion terms. Consequently, my test procedure covers both univariate and multivariate diffusion models in a unified framework and is particularly convenient for the multivariate case. Moreover, different transformed martingale processes contain separate information about the drift and diffusion specifications. This motivates me to propose a separate inferential test procedure to explore the sources of rejection when a parametric form is rejected. Simulation studies show that the proposed tests have reasonable size and excellent power performance. An empirical application of my test procedure using Eurodollar interest rates finds that most popular short-rate models are rejected and the drift misspecification plays an important role in such rejections.     

Stale and Scale Effects in Markets-Based Accounting Research: Evidence from the Valuation of Dividends

Abstract

This study revisits prior research on the valuation of dividends in an accounting-based valuation framework. Using a battery of tests, we show that market value deflation is essential in market-based tests of dividend displacement and signalling because it controls for ‘stale’ information in addition to scale (size) differences across firms. For US firms, we show that after controlling for ‘stale’ information, the empirical association between dividends and market values switches from positive to negative. This switch is not explained by scale differences across firms. Further, we show that after controlling for staleness, the valuation of dividends remains positive for European firms. This result is explained by the relatively stronger association of dividends with future earnings in these settings (i.e. signalling). Lastly, our country-specific estimates of dividend valuation provide a potentially valuable index for studies aimed at examining the effects of accounting and securities regulation on information asymmetries in an international context.     

Taking a new contour: A novel approach to panel unit root tests

The paper introduces a novel approach to testing for unit roots in panels, which takes a new contour that is drawn along the line given by the equi-squared-sum instead of the traditional one given by the equi-sample-size. We show in the paper that the distributions of the unit root tests are asymptotically normal along the new contour under both the null and the local-to-unity alternatives. Subsequently, we demonstrate that this startling finding may be exploited constructively to invent tools and methodologies for effective inferences in panel unit root models. Simulations show that our approach works quite well in finite samples.