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.     

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.     

Bayesian estimation of agent-based models

We consider Bayesian inference techniques for agent-based (AB) models, as an alternative to simulated minimum distance (SMD). Three computationally heavy steps are involved: (i) simulating the model, (ii) estimating the likelihood and (iii) sampling from the posterior distribution of the parameters. Computational complexity of AB models implies that efficient techniques have to be used with respect to points (ii) and (iii), possibly involving approximations. We first discuss non-parametric (kernel density) estimation of the likelihood, coupled with Markov chain Monte Carlo sampling schemes. We then turn to parametric approximations of the likelihood, which can be derived by observing the distribution of the simulation outcomes around the statistical equilibria, or by assuming a specific form for the distribution of external deviations in the data. Finally, we introduce Approximate Bayesian Computation techniques for likelihood-free estimation. These allow embedding SMD methods in a Bayesian framework, and are particularly suited when robust estimation is needed. These techniques are first tested in a simple price discovery model with one parameter, and then employed to estimate the behavioural macroeconomic model of De Grauwe (2012), with nine unknown parameters.     

基于AEPD分布和ALD分布的VaR模型

本文以成熟市场和新兴市场的六个主要的市场指数为例,将更精确反映金融资产收益率典型事实的AEPD分布和ALD分布运用于股票市场VaR的度量。并与其它常见的非参、半参和参数法VaR模型进行全面比较。实证表明,对于参数法模型,误差项服从ALD分布和正态分布的GARCH族模型分别当且仅当在度量低分位数和高分位数水平下的VaR值时表现优异;而误差项服从AEPD分布的GARCH族模型在度量各种分位数水平下的VaR值时均取得不错的效果。另外对于CAViaR模型,它们在度量VaR时与参数法中表现最好的AR-GJR-GARCH-AEPD(ALD)两个模型效果相当。     

Bayesian modeling of joint and conditional distributions

In this paper, we study a Bayesian approach to flexible modeling of conditional distributions. The approach uses a flexible model for the joint distribution of the dependent and independent variables and then extracts the conditional distributions of interest from the estimated joint distribution. We use a finite mixture of multivariate normals (FMMN) to estimate the joint distribution. The conditional distributions can then be assessed analytically or through simulations. The discrete variables are handled through the use of latent variables. The estimation procedure employs an MCMC algorithm. We provide a characterization of the Kullback–Leibler closure of FMMN and show that the joint and conditional predictive densities implied by the FMMN model are consistent estimators for a large class of data generating processes with continuous and discrete observables. The method can be used as a robust regression model with discrete and continuous dependent and independent variables and as a Bayesian alternative to semi- and non-parametric models such as quantile and kernel regression. In experiments, the method compares favorably with classical nonparametric and alternative Bayesian methods.     

Testing non-nested semiparametric models: an application to Engel curves specification

This paper proposes a test statistic for discriminating between two partly non-linear regression models whose parametric components are non-nested. The statistic has the form of a J-test based on a parameter which artificially nests the null and alternative hypotheses. We study in detail the realistic case where all regressors in the non-linear part are discrete and then no smoothing is required on estimating the non-parametric components. We also consider the general case where continuous and discrete regressors are present. The performance of the test in finite samples is discussed in the context of some Monte Carlo experiments. The test is well motivated for specification testing of Engel curves. We provide an application using data from the 1980 Spanish Expenditure Survey. © 1998 John Wiley & Sons, Ltd.     

The Extended Generalized Gamma Model and its Special Cases: Applications to Modeling Marriage Durations

The paper demonstrates how various parametric models for duration data such as the exponential, Weibull, and log-normal may be embedded in a single framework, and how such competing models may be assessed relative to a more comprehensive one. To illustrate the issues addressed, the survival patterns of marriages among 1203 Swedish men born 1936–1964 are studied by parametric and non-parametric survival methods. In particular, we study the sensitivity of model-choice with respect to level of aggregation of the time variable; and of covariate-effects with respect to the model chosen. In accordance with previous works our empirical results indicate that the choice of a parametric model for the duration variable is affected by the level of time aggregation. In contrast to previous results, however, our analysis shows that estimates of covariate effects are not always robust to distributional assumptions for the duration variable.     

The importance of flexible hazard functions in the analysis of organizational survival data -- experiences from a cohort of Swedish commercial banks

The survival pattern of Swedish commercial banks during the period 1830--1990 is studied by parametric and non-parametric event-history methods. In particular we study the sensitivity of the conclusions reached with respect to the model used. It is found that the hazard is inversely U-shaped, which means that models that cannot allow for this type of hazard run into difficulties. Thus two of the most popular approaches in the analysis of event history data, the Gompertz and the Weibull models produce misleading results regarding the development of the death risk of banks over time. As regards the effect of explanatory variables on survival, on the other hand, most models are found to be robust and even in cases of misspecified baseline hazards, the estimated effects of the explanatory variables do not seem to be seriously wrong.     

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.     

Nonparametric specification tests for conditional duration models

This paper deals with the testing of autoregressive conditional duration (ACD) models by gauging the distance between the parametric density and hazard rate functions implied by the duration process and their non-parametric estimates. We derive the asymptotic justification using the functional delta method for fixed and gamma kernels, and then investigate the finite-sample properties through Monte Carlo simulations. Although our tests display some size distortion, bootstrapping suffices to correct the size without compromising their excellent power. We show the practical usefulness of such testing procedures for the estimation of intraday volatility patterns.     

Local multiplicative bias correction for asymmetric kernel density estimators

We consider semiparametric asymmetric kernel density estimators when the unknown density has support on [0,∞)$[0,\infty )$. We provide a unifying framework which relies on a local multiplicative bias correction, and contains asymmetric kernel versions of several semiparametric density estimators considered previously in the literature. This framework allows us to use popular parametric models in a nonparametric fashion and yields estimators which are robust to misspecification. We further develop a specification test to determine if a density belongs to a particular parametric family. The proposed estimators outperform rival non- and semiparametric estimators in finite samples and are easy to implement. We provide applications to loss data from a large Swiss health insurer and Brazilian income data.     

Non-Linearities in Electricity Demand and Temperature: Parametric Versus Non-Parametric Methods

This paper investigates the relationship between outside air temperature and the residential demand for space heating energy. These non-linearities are investigated empirically using high frequency panel data for a sample of UK households, and both parametric and non-parametric methods for identifying non-linearities are examined. The econometric evidence finds support for important non-linearities across the range of observed temperatures and points to limitations in the use of parametric functional forms.     

Ultimate Controllers,Ownership and the Probability of Insolvency in Financially Distressed Firms

This paper investigates the impact of corporate ownership and control on the outcome of financial distress. It is argued that the likelihood of financial distress resulting in insolvency depends on whether firms have controllers, the type of controllers and their cash flow ownership. Using a sample of 484 UK firms, 81 of which filed for insolvency, we show that financially distressed firms with controllers are more likely to be insolvent than widely held firms, where the probability of insolvency is greater when controllers are family or financial institutions. However, the probability of insolvency reduces significantly as the controllers' cash flow ownership increases beyond 10%. Copyright © 2013 John Wiley & Sons, Ltd.     

Modelling and Forecasting Gas Flow on Exits of Gas Transmission Networks

The flow of natural gas within a gas transmission network is studied with the aim to optimize such networks. The analysis of real data provides a deeper insight into the behaviour of gas in‐ and outflow. Several models for describing dependence between the maximal daily gas flow and the temperature on network exits are proposed. A modified sigmoidal regression is chosen from the class of parametric models. As an alternative, a semi‐parametric regression model based on penalized splines is considered. The comparison of models and the forecast of gas loads for very low temperatures based on both approaches is included. The application of the obtained results is discussed.     

Discrete time duration models with group-level heterogeneity

Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration in the current state as a covariate. We propose estimators that allow for group-specific effect in parametric and semiparametric versions of the model. The proposed method is illustrated by an empirical analysis of job durations allowing for firm-level effects.     

A comparison of parametric and non-parametric efficiency measures: The case of Norwegian ferries

The trunk road system in Norway has to be supplemented by a number of ferries due to the long coastline with numerous islands and fjords. Most of the ferries are run by private companies, but at a loss. The deficit are covered by the Ministry of Transport. The subsidies have risen rapidly in the last years and have focussed attention on whether the ferries are really run as efficiently as possible. To change the incentives to economize, a lump-sum payment is considered. To implement such a system, an initial assessment of reasonable input requirements is needed. The aim of this article is to provide such a yardstick by establishing a best practice frontier. Both a non-parametric and a parametric approach to a deterministic frontier are tried and differences of results discussed. Peculiarities due to choice of methods are revealed. The efficiency distributions are quite similar for the two methods except for scale efficiency, where the parametric method indicates substantial unrealized scale economies, while the non-parametric approach shows the largest and some small ferries to be scale efficient. The results indicate a substantial rationalization potential of about 30 percent in total.I am indebted to three referees for forcing me to improve significantly the quality of the study. Any remaining shortcomings are, of course, my responsibility.     

The Ordinal Controversy Revisited

We present a discussion of the different dimensions of the ongoing controversy about the analysis of ordinal variables. The source of this controversy is traced to the earliest possible stage, measurement theory. Three major approaches in analyzing ordinal variables, called the non-parametric, the parametric, and the underlying variable approach, are identified and the merits and drawbacks of each of these approaches are pointed out. We show that the controversy on the exact definition of an ordinal variable causes problems with regard to defining ordinal association, and therefore to the interpretation of many recently designed models for ordinal variables, e.g., structure equation models using polychoric correlations, latent class models and ordinal response models. We conclude that the discussion with regard to ordinal variable modeling can only be fruitful if one makes a distinction between different types of ordinal variables. Five types of ordinal variables were identified. The problems concerning the analysis of these five types of ordinal variables are solved in some cases and remain a problem for others.     

A non-parametric statistical model for the control of Italian insurance companies

The problem of evaluating the solvency of insurance companies is tackled through the use of a non-parametric statistical model, constructed using decision-tree techniques. The model is tested on a sample of Italian non-life insurance companies and its performance over the test period compared with those of linear and quadratic parametric models.

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Riassunto Il problema della valutazione della solvibilità delle imprese di assicurazione è affrontato con l'impiego di un modello statistico non parametrico, costruito con le tecniche degli alberi delle decisioni. Viene proposta una sperimentazione del modello su un campione di imprese assicuratrici italiane operanti nei rami nonvita ed effettuata una analisi comparata intertemporale con gli standards di efficienza registrati su modelli parametrici lineare e quadratico.