Interactive R&D spillovers: An estimation strategy based on forecasting-driven model selection

This paper proposes an estimation strategy that exploits recent non-parametric panel data methods that allow for a multifactor error structure and extends a recently proposed data-driven model-selection procedure, which has its roots in cross validation and aims to test whether two competing approximate models are equivalent in terms of their expected true error. We extend this procedure to a large panel data framework by using moving block bootstrap resampling techniques in order to preserve cross-sectional dependence in the bootstrapped samples. Such an estimation strategy is illustrated by revisiting an analysis of international technology diffusion. Model selection procedures clearly conclude in the superiority of a fully non-parametric (non-additive) specification over parametric and even semi-parametric (additive) specifications. This work also refines previous results by showing threshold effects, non-linearities, and interactions that are obscured in parametric specifications and which have relevant implications for policy.     

Interpretable Machine Learning Using Partial Linear Models*

Despite their high predictive performance, random forest and gradient boosting are often considered as black boxes which has raised concerns from practitioners and regulators. As an alternative, we suggest using partial linear models that are inherently interpretable. Specifically, we propose to combine parametric and non-parametric functions to accurately capture linearities and non-linearities prevailing between dependent and explanatory variables, and a variable selection procedure to control for overfitting issues. Estimation relies on a two-step procedure building upon the double residual method. We illustrate the predictive performance and interpretability of our approach on a regression problem.     

Rare shocks vs. non-linearities: What drives extreme events in the economy? Some empirical evidence

A small-scale vector autoregression (VAR) is used to shed some light on the roles of extreme shocks and non-linearities during stress events observed in the economy. The model focuses on the link between credit/financial markets and the real economy and is estimated on US quarterly data for the period 1984–2013. Extreme shocks are accounted for by assuming t-distributed reduced-form shocks. Non-linearity is allowed by the possibility of regime switch in the shock propagation mechanism. Strong evidence for fat tails in error distributions is found. Moreover, the results suggest that accounting for extreme shocks rather than explicit modeling of non-linearity contributes to the explanatory power of the model. Finally, it is shown that the accuracy of density forecasts improves if non-linearities and shock distributions with fat tails are considered.     

Non-linear exchange rate relationships: An automated model selection approach with indicator saturation

This paper examines whether the explanatory power of exchange rate models can be improved by allowing for cross-country asymmetries and non-linear effects of fundamentals. Both appear to be crucial. The samples include the USD versus pound and yen from 1982:10 to 2013:10, and automated model selection is conducted with indicator saturation. Several non-linear effects are significant at 1%. Further, many of the indicators present in the linear models are eliminated once allowing for non-linearities; suggesting some of the structural breaks found in previous work were an artifact of the misspecified linear functional form. These conclusions are robust to estimation using principal components.     

Structural estimation of jump-diffusion processes in macroeconomics

This paper shows how to solve and estimate a continuous-time dynamic stochastic general equilibrium (DSGE) model with jumps. It also shows that a continuous-time formulation can make it simpler (relative to its discrete-time version) to compute and estimate the deep parameters using the likelihood function when non-linearities and/or non-normalities are considered. We illustrate our approach by solving and estimating the stochastic AK and the neoclassical growth models. Our Monte Carlo experiments demonstrate that non-normalities can be detected for this class of models. Moreover, we provide strong empirical evidence for jumps in aggregate US data.     

Properties of Census Dual System Population Size Estimators

We study parametric and non‐parametric approaches for assessing the accuracy and coverage of a population census based on dual system surveys. The two parametric approaches being considered are post‐stratification and logistic regression, which have been or will be implemented for the US Census dual system surveys. We show that the parametric model‐based approaches are generally biased unless the model is correctly specified. We then study a local post‐stratification approach based on a non‐parametric kernel estimate of the Census enumeration functions. We illustrate that the non‐parametric approach avoids the risk of model mis‐specification and is consistent under relatively weak conditions. The performances of these estimators are evaluated numerically via simulation studies and an empirical analysis based on the 2000 US Census post‐enumeration survey data.     

Economic freedom as driver of growth in transition

This paper reviews the political economy of economic growth in post-communist economies making the transition to free markets, focusing on the role of economic policy and institutions. We test the hypothesis that better institutions, measured in terms of economic freedom, contribute to growth. To begin with, the empirical results from the cross-section of transition economies confirm this hypothesis. Yet the question is deeper than that since there is an interactive effect between economic freedom and investment. The paper concludes that non-linearities are present in the growth model.     

Statistical Decision Problems and Bayesian Nonparametric Methods

This paper considers parametric statistical decision problems conducted within a Bayesian nonparametric context. Our work was motivated by the realisation that typical parametric model selection procedures are essentially incoherent. We argue that one solution to this problem is to use a flexible enough model in the first place, a model that will not be checked no matter what data arrive. Ideally, one would use a nonparametric model to describe all the uncertainty about the density function generating the data. However, parametric models are the preferred choice for many statisticians, despite the incoherence involved in model checking, incoherence that is quite often ignored for pragmatic reasons. In this paper we show how coherent parametric inference can be carried out via decision theory and Bayesian nonparametrics. None of the ingredients discussed here are new, but our main point only becomes evident when one sees all priors—even parametric ones—as measures on sets of densities as opposed to measures on finite-dimensional parameter spaces.     

Bayesian semiparametric stochastic volatility modeling

This paper extends the existing fully parametric Bayesian literature on stochastic volatility to allow for more general return distributions. Instead of specifying a particular distribution for the return innovation, nonparametric Bayesian methods are used to flexibly model the skewness and kurtosis of the distribution while the dynamics of volatility continue to be modeled with a parametric structure. Our semiparametric Bayesian approach provides a full characterization of parametric and distributional uncertainty. A Markov chain Monte Carlo sampling approach to estimation is presented with theoretical and computational issues for simulation from the posterior predictive distributions. An empirical example compares the new model to standard parametric stochastic volatility models.     

A survey of two-sample location-scale problem, asymptotic relative efficiencies of some rank tests

Here the parametric as well as the non parametric approach to the two-sample location-scale problem are reviewed. Special attention is paid to the quadratic form of the linear rank statistics for the location and the scale suggested by Lepage for testing this problem. Several such quadratic forms are compared through ARE computations.     

Weighted least squares estimators in possibly misspecified nonlinear regression

The behavior of estimators for misspecified parametric models has been well studied. We consider estimators for misspecified nonlinear regression models, with error and covariates possibly dependent. These models are described by specifying a parametric model for the conditional expectation of the response given the covariates. This is a parametric family of conditional constraints, which makes the model itself close to nonparametric. We study the behavior of weighted least squares estimators both when the regression function is correctly specified, and when it is misspecified and also involves possible additional covariates.     

Non-linearities in cross-country growth regressions: a semiparametric approach

In this paper we employ an additive semiparametric partially linear model to uncover the way that initial output and schooling levels affect growth rates. Our results based on marginal integration allow for graphical representation of the non-linearities that characterize the effects that these variables have on growth rates and suggest the presence of multiple regimes (equilibria). Our findings seem to be in agreement with those of Durlauf and Johnson ( 1995 ) and Hansen ( 1996 ) who used a different data set. Copyright © 1999 John Wiley & Sons, Ltd.     

Risk premia in general equilibrium

This paper shows that non-linearities from a neoclassical production function alone can generate time-varying, asymmetric risk premia and predictability over the business cycle. These empirical key features become relevant when we allow for non-normalities in the form of rare disasters. We employ analytical solutions of dynamic stochastic general equilibrium models, including a novel solution with endogenous labor supply, to obtain closed-form expressions for the risk premium in production economies. In contrast to an endowment economy with constant investment opportunities, the curvature of the consumption function affects the risk premium in production economies through controlling the individual's effective risk aversion.     

Nonparametric likelihood ratio model selection tests between parametric likelihood and moment condition models

We propose a nonparametric likelihood ratio testing procedure for choosing between a parametric (likelihood) model and a moment condition model when both models could be misspecified. Our procedure is based on comparing the Kullback–Leibler Information Criterion (KLIC) between the parametric model and moment condition model. We construct the KLIC for the parametric model using the difference between the parametric log likelihood and a sieve nonparametric estimate of population entropy, and obtain the KLIC for the moment model using the empirical likelihood statistic. We also consider multiple (>2)$(>2)$ model comparison tests, when all the competing models could be misspecified, and some models are parametric while others are moment-based. We evaluate the performance of our tests in a Monte Carlo study, and apply the tests to an example from industrial organization.     

Non-parametric Estimator for Conditional Mode with Parametric Features*

We in this paper propose a new approach for estimating conditional mode non-parametrically to capture the ‘most likely’ effect built on local linear approximation, in which a parametric pilot modal regression is locally adjusted through a kernel smoothing fit to potentially reduce the bias asymptotically without affecting the variance of the estimator. Specifically, we first estimate a parametric modal regression utilizing prior information from initial studies or economic analysis, and then estimate the non-parametric modal function based on the additive correction by eliminating the parametric feature. We derive the asymptotic normal distribution of the proposed modal estimator for both fixed and estimated parametric feature cases, and demonstrate that there is substantial room for bias reduction under certain regularity conditions. We numerically estimate the suggested modal regression model with the use of a modified modal-expectation-maximization (MEM) algorithm. Monte Carlo simulations and one empirical analysis are presented to illustrate the finite sample performance of the developed modal estimator. Several extensions, including multiplicative correction, generalized guidance, modal-based robust regression and the incorporation of categorical covariates, are also discussed for the sake of completeness.     

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.     

Specification Testing of Markov Switching Models*

This paper proposes a set of formal tests to address the goodness‐of‐fit of Markov switching models. These formal tests are constructed as tests of model consistency and of both parametric and non‐parametric encompassing. The formal tests are then combined with informal tests using simulation in combination with non‐parametric density and conditional mean estimation. The informal tests are shown to be useful in shedding light on the failure (or success) of the encompassing tests. Several examples are provided.     

On the optimal taxation of common-pool resources

Recent research developments in common-pool resource models emphasize the importance of links with ecological systems and the presence of non-linearities, thresholds and multiple steady states. In a recent paper Kossioris et al. (2008) develop a methodology for deriving feedback Nash equilibria for non-linear differential games and apply this methodology to a common-pool resource model of a lake where pollution corresponds to benefits and at the same time affects the ecosystem services. This paper studies the structure of optimal state-dependent taxes that steer the combined economic-ecological system towards the trajectory of optimal management, and provides an algorithm for calculating such taxes.     

BAYESIAN INFERENCE METHODS FOR UNIVARIATE AND MULTIVARIATE GARCH MODELS: A SURVEY

This survey reviews the existing literature on the most relevant Bayesian inference methods for univariate and multivariate GARCH models. The advantages and drawbacks of each procedure are outlined as well as the advantages of the Bayesian approach versus classical procedures. The paper makes emphasis on recent Bayesian non‐parametric approaches for GARCH models that avoid imposing arbitrary parametric distributional assumptions. These novel approaches implicitly assume infinite mixture of Gaussian distributions on the standardized returns which have been shown to be more flexible and describe better the uncertainty about future volatilities. Finally, the survey presents an illustration using real data to show the flexibility and usefulness of the non‐parametric approach.     

Analysis of failure time using threshold regression with semi‐parametric varying coefficients

Many new statistical models may enjoy better interpretability and numerical stability than traditional models in survival data analysis. Specifically, the threshold regression (TR) technique based on the inverse Gaussian distribution is a useful alternative to the Cox proportional hazards model to analyse lifetime data. In this article we consider a semi‐parametric modelling approach for TR and contribute implementational and theoretical details for model fitting and statistical inferences. Extensive simulations are carried out to examine the finite sample performance of the parametric and non‐parametric estimates. A real example is analysed to illustrate our methods, along with a careful diagnosis of model assumptions.