Source : NEP (New Economics Papers) | RePEc

**Semiparametric Estimation in Time Series of Simultaneous Equations**

Date: | 2010-09 |

By: | Jiti Gao (School of Economics, University of Adelaide) Peter C. B. Phillips (Cowles Foundation, Yale University) |

URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1769&r=ecm |

A system of vector semiparametric nonlinear time series models is studied with possible dependence structures and nonstationarities in the parametric and nonparametric components. The parametric regressors may be endogenous while the nonparametric regressors are strictly exogenous and represent trends. The parametric regressors may be stationary or nonstationary and the nonparametric regressors are nonstationary time series. This framework allows for the nonparametric treatment of stochastic trends and subsumes many practical cases. Semiparametric least squares (SLS) estimation is considered and its asymptotic properties are derived. Due to endogeneity in the parametric regressors, SLS is generally inconsistent for the parametric component and a semiparametric instrumental variable least squares (SIVLS) method is proposed instead. Under certain regularity conditions, the SIVLS estimator of the parametric component is show n to be consistent with a limiting normal distribution that is amenable to inference. The rate of convergence in the parametric component is the usual /n rate and is explained by the fact that the common (nonlinear) trend in the system is eliminated nonparametrically by stochastic detrending. | |

Keywords: | Simultaneous equation, Stochastic detrending, Vector semiparametric regression |

JEL: | C23 |

**Nonlinear Cointegrating Regression under Weak Identification**

Date: | 2010-09 |

By: | Xiaoxia Shi (Dept. of Economics, Yale University) Peter C. B. Phillips (Cowles Foundation, Yale University) |

URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1768&r=ecm |

An asymptotic theory is developed for a weakly identified cointegrating regression model in which the regressor is a nonlinear transformation of an integrated process. Weak identification arises from the presence of a loading coefficient for the nonlinear function that may be close to zero. In that case, standard nonlinear cointegrating limit theory does not provide good approximations to the finite sample distributions of nonlinear least squares estimators, resulting in potentially misleading inference. A new local limit theory is developed that approximates the finite sample distributions of the estimators uniformly well irrespective of the strength of the identification. An important technical component of this theory involves new results showing the uniform weak convergence of sample covariances involving nonlinear functions to mixed normal and stochastic integral limits. Based on these asymptotics, we construct confi dence intervals for the loading coefficient and the nonlinear transformation parameter and show that these confidence intervals have correct asymptotic size. As in other cases of nonlinear estimation with integrated processes and unlike stationary process asymptotics, the properties of the nonlinear transformations affect the asymptotics and, in particular, give rise to parameter dependent rates of convergence and differences between the limit results for integrable and asymptotically homogeneous functions. | |

Keywords: | Integrated process, Local time, Nonlinear regression, Uniform weak convergence, Weak identification |

JEL: | C13 |

**Identification and Estimation of Semiparametric Two Step Models**

Date: | 2010-05-01 |

By: | Juan Carlos Escanciano (Indiana University) David Jacho-Chavez (Indiana University) Arthur Lewbel (Boston College) |

URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:756&r=ecm |

Let g0(X) be a function of some observable vector X that is identified and can be nonparametrically estimated. This paper provides new results on the identification and estimation of the function F and the vector β0 whenE(Y|X)=F[X⊤β0,g0(X)]. Many models fit this framework, including latent index models with an endogenous regressor, and nonlinear models with sample selection. Our identification results show that identification based on functional form, without exclusions or instruments, extends to this semiparametric model. On estimation we provide a new uniform convergence result that allows for random weighting and data dependent bandwidths and trimming. We include Monte Carlo simulations and an empirical application. | |

Keywords: | Double index models; Two step estimators; Semiparametric regression; Control function estimators; Sample selection models; Empirical process theory; Limited dependent variables; Oracle estimators; Migration |

JEL: | C13 |

**Nonparametric Identification of Multivariate Mixtures**

Date: | 2010-08 |

By: | Kasahara, Hiroyuki Shimotsu, Katsumi |

URL: | http://d.repec.org/n?u=RePEc:hit:econdp:2010-09&r=ecm |

This article analyzes the identifiability of k-variate, M-component finite mixture models in which each component distribution has independent marginals, including models in latent class analysis. Without making parametric assumptions on the component distributions, we investigate how one can identify the number of components and the component distributions from the distribution function of the observed data. We reveal an important link between the number of variables (k), the number of values each variable can take, and the number of identifiable components. A lower bound on the number of components (M) is nonparametrically identifiable if k >= 2, and the maximum identifiable number of components is determined by the number of different values each variable takes. When M is known, the mixing proportions and the component distributions are nonparametrically identified from matrices constructed from the distribution fun ction of the data if (i) k >= 3, (ii) two of k variables take at least M different values, and (iii) these matrices satisfy some rank and eigenvalue conditions. For the unknown M case, we propose an algorithm that possibly identifies M and the component distributions from data. We discuss a condition for nonparametric identi fication and its observable implications. In case M cannot be identified, we use our identification condition to develop a procedure that consistently estimates a lower bound on the number of components by estimating the rank of a matrix constructed from the distribution function of observed variables. | |

Keywords: | finite mixture, latent class analysis, latent class model, model selection, number of components, rank estimation |

**Instrumental Variable Estimation of Dynamic Linear Panel Data Models with Defactored Regressors under Cross-sectional Dependence**

Date: | 2010-02 |

By: | Sarafidis, Vasilis Yamagata, Takashi |

URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:25182&r=ecm |

This paper develops an instrumental variable (IV) estimator for consistent estimation of dynamic panel data models with error cross-sectional dependence when both N and T, the cross-section and time series dimensions respectively, are large. Our approach asymptotically projects out the common factors from regressors using principal components analysis and then uses the defactored regressors as instruments to estimate the model in a standard way. Therefore, the proposed estimator is computationally very attractive. Furthermore, our procedure requires estimating only the common factors included in the regressors, leaving those that influence the dependent variable solely into the errors. Hence aside from computational simplicity the resulting approach allows parsimonious estimation of the model. The finite-sample performance of the IV estimator and the associated t-test is investigated using simulated data. The results show that the bias of the estimator is very small and the size of the t-test is correct even when (T,N) is as small as (10,50). The performance of an overidentifying restrictions test is also explored and the evidence suggests that it has good power when the key assumption is violated. | |

Keywords: | Method of moments; dynamic panel data; cross-sectional dependence |

JEL: | C13 |

**Numerical distribution functions of fractional unit root and cointegration tests**

Date: | 2010-08-03 |

By: | James G. MacKinnon (Queen’s University) Morten Ørregaard Nielsen (Queen?s University and CREATES) |

URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-59&r=ecm |

We calculate numerically the asymptotic distribution functions of likelihood ratio tests for fractional unit roots and cointegration rank. Because these distributions depend on a real-valued parameter, b, which must be estimated, simple tabulation is not feasible. Partly due to the presence of this parameter, the choice of model specification for the response surface regressions used to obtain the numerical distribution functions is more involved than is usually the case. We deal with model uncertainty by model averaging rather than by model selection. We make available a computer program which, given the dimension of the problem, q, and a value of b, provides either a set of critical values or the asymptotic P value for any value of the likelihood ratio statistic. The use of this program is illustrated by means of an empirical example involving opinion poll data. | |

Keywords: | Cofractional process, fractional unit root, fractional cointegration, response surface regression, cointegration rank, numerical distribution function, model averaging. |

JEL: | C12 |

**Model Selection and Testing of Conditional and Stochastic Volatility Models**

Date: | 2010-09-01 |

By: | Massimiliano Caporin Michael McAleer (University of Canterbury) |

URL: | http://d.repec.org/n?u=RePEc:cbt:econwp:10/58&r=ecm |

This paper focuses on the selection and comparison of alternative non-nested volatility models. We review the traditional in-sample methods commonly applied in the volatility framework, namely diagnostic checking procedures, information criteria, and conditions for the existence of moments and asymptotic theory, as well as the out-of-sample model selection approaches, such as mean squared error and Model Confidence Set approaches. The paper develops some innovative loss functions which are based on Value-at-Risk forecasts. Finally, we present an empirical application based on simple univariate volatility models, namely GARCH, GJR, EGARCH, and Stochastic Volatility that are widely used to capture asymmetry and leverage. | |

Keywords: | Volatility model selection; volatility model comparison; non-nested models; model confidence set; Value-at-Risk forecasts; asymmetry, leverage |

JEL: | C11 |

**Model selection, estimation and forecasting in VAR models with short-run and long-run restrictions**

Date: | 2010-09-13 |

By: | Athanasopoulos, George Guillén, Osmani Teixeira de Carvalho Issler, João Victor Vahid, Farshid |

URL: | http://d.repec.org/n?u=RePEc:fgv:epgewp:707&r=ecm |

We study the joint determination of the lag length, the dimension of the cointegrating space andthe rank of the matrix of short-run parameters of a vector autoregressive (VAR) model using modelselection criteria. We consider model selection criteria which have data-dependent penalties aswell as the traditional ones. We suggest a new two-step model selection procedure which is ahybrid of traditional criteria and criteria with data-dependant penalties and we prove its consistency.Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arisefrom the joint determination of lag-length and rank using our proposed procedure, relative to anunrestricted VAR or a cointegrated VAR estimated by the commonly used procedure of selecting thelag-length only and then testing for cointegration. Two empirical applications forecasting Brazilianinflation and U.S. macroeconomic aggregates growth rates respectively show the usefulness of themodel-selection strategy proposed here. The gains in different measures of forecasting accuracy aresubstantial, especially for short horizons. |

**On the Identification of Codependent VAR and VEC Models**

Date: | 2010-09-15 |

By: | Trenkler, Carsten Weber, Enzo |

URL: | http://d.repec.org/n?u=RePEc:bay:rdwiwi:16477&r=ecm |

In this paper we discuss identification of codependent VAR and VEC models. Codependence of order q is given if a linear combination of autocorrelated variables eliminates the serial correlation after q lags. Importantly, maximum likelihood estimation and corresponding likelihood ratio testing are only possible if the codependence restrictions can be uniquely imposed. However, our study reveals that codependent VAR and VEC models are not generally identified. Nevertheless, we show that one can guarantee identification in case of serial correlation common features, i.e. when q=0, and for a single vector generating codependence of order q=1. | |

Keywords: | Codependence; identification; VAR; cointegration; serial correlation common features |

JEL: | C32 |

**Nonparametric Identification of Accelerated Failure Time Competing Risks Models**

Date: | 2010-04-01 |

By: | Sokbae Lee (University College London) Arthur Lewbel (Boston College) |

URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:755&r=ecm |

We provide new conditions for identification of accelerated failure time competing risks models. These include Roy models and some auction models. In our set up, unknown regression functions and the joint survivor function of latent disturbance terms are all nonparametric. We show that this model is identified given covariates that are independent of latent errors, provided that a certain rank condition is satisfied. We present a simple example in which our rank condition for identification is verified. Our identification strategy does not depend on identification at infinity or near zero, and it does not require exclusion assumptions. Given our identification, we show estimation can be accomplished using sieves. | |

Keywords: | accelerated failure time models; competing risks; identifiability. |

**The information content of high-frequency data for estimating equity return models and forecasting risk**

Date: | 2010 |

By: | Dobrislav P. Dobrev Pawel J. Szerszen |

URL: | http://d.repec.org/n?u=RePEc:fip:fedgfe:2010-45&r=ecm |

We demonstrate that the parameters controlling skewness and kurtosis in popular equity return models estimated at daily frequency can be obtained almost as precisely as if volatility is observable by simply incorporating the strong information content of realized volatility measures extracted from high-frequency data. For this purpose, we introduce asymptotically exact volatility measurement equations in state space form and propose a Bayesian estimation approach. Our highly efficient estimates lead in turn to substantial gains for forecasting various risk measures at horizons ranging from a few days to a few months ahead when taking also into account parameter uncertainty. As a practical rule of thumb, we find that two years of high frequency data often suffice to obtain the same level of precision as twenty years of daily data, thereby making our approach particularly useful in finance applications where only short data samples are available or economically meaningful to use. Moreover, we find that compared to model inference without high-frequency data, our approach largely eliminates underestimation of risk during bad times or overestimation of risk during good times. We assess the attainable improvements in VaR forecast accuracy on simulated data and provide an empirical illustration on stock returns during the financial crisis of 2007-2008. |

**Forecasting in an extended chain-ladder-type model**

Date: | 2010-06-24 |

By: | Di Kuang (Aon, 8 Devonshire Square, London EC2M 4PL, U.K.) Bent Nielsen (Nuffield College, Oxford OX1 1NF, U.K.) Jens Perch Nielsen (Cass Business School, City University London, 106 Bunhill Row, London EC1Y 8TZ, U.K.) |

URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:1005&r=ecm |

Reserving in general insurance is often done using chain-ladder-type methods. We propose a method aimed at situations where there is a sudden change in the economic environment affecting the policies for all accident years in the reserving triangle. It is shown that methods for forecasting non-stationary time series are helpful. We illustrate the method using data published in Barnett and Zehnwirth (2000). These data illustrate features we also found in data from the general insurer RSA during the recent credit crunch. | |

Keywords: | Calendar effect, canonical parameter, extended chain-ladder, identification problem, forecasting. |

**Multivariate outbreak detection**

Date: | 2010-09-17 |

By: | Schiöler, Linus (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University) Frisén, Marianne (Statistical Research Unit, Department of Economics, School of Business, Economics and Law, Göteborg University) |

URL: | http://d.repec.org/n?u=RePEc:hhs:gunsru:2010_002&r=ecm |

On-line monitoring is needed to detect outbreaks of diseases like influenza. Surveillance is also needed for other kinds of outbreaks, in the sense of an increasing expected value after a constant period. Information on spatial location or other variables might be available and may be utilized. We adapted a robust method for outbreak detection to a multivariate case. The relation between the times of the onsets of the outbreaks at different locations (or some other variable) was used to determine the sufficient statistic for surveillance. The derived maximum likelihood estimator of the outbreak regression was semi-parametric in the sense that the baseline and the slope were non-parametric while the distribution belonged to the exponential family. The estimator was used in a generalized likelihood ratio surveillance method. The method was evaluated with respect to robustness and efficiency in a simulation study and applied to spatial data for detection of influenza outbreaks in Sweden. | |

Keywords: | Exponential family; Generalised likelihood; Ordered regression; Regional data; Surveillance |

JEL: | C10 |

**Testing for Codependence of Non-Stationary Variables**

Date: | 2010-09-15 |

By: | Trenkler, Carsten Weber, Enzo |

URL: | http://d.repec.org/n?u=RePEc:bay:rdwiwi:16478&r=ecm |

We analyze non-stationary time series that do not only trend together in the long run, but restore the equilibrium immediately in the period following a deviation. While this represents a common serial correlation feature, the framework is extended to codependence, allowing for delayed adjustment. We show which restrictions are implied for VECMs and lay out a likelihood ratio test. In addition, due to identification problems in codependent VECMs a GMM test approach is proposed. We apply the concept to US and European interest rate data, examining the capability of the Fed and ECB to control overnight money market rates. | |

Keywords: | Serial correlation common features; codependence; cointegration; overnight interest rates; central banks |

JEL: | C32 |

**Forecast Combination and Bayesian Model Averaging – A Prior Sensitivity Analysis**

Date: | 2010-09-15 |

By: | Feldkircher, Martin (Oesterreichische Nationalbank) |

URL: | http://d.repec.org/n?u=RePEc:ris:sbgwpe:2010_014&r=ecm |

In this study the forecast performance of model averaged forecasts is compared to that of alternative single models. Following Eklund and Karlsson (2007) we form posterior model probabilities – the weights for the combined forecast – based on the predictive likelihood. Extending the work of Fernández et al. (2001a) we carry out a prior sensitivity analysis for a key parameter in Bayesian model averaging (BMA): Zellner’s g. The main results based on a simulation study are fourfold: First the predictive likelihood does always better than the traditionally employed ‘marginal’ likelihood in settings where the true model is not part of the model space. Secondly, and more striking, forecast accuracy as measured by the root mean square error (rmse) is maximized for the median probability model put forward by Barbieri and Berger (2003). On the other hand, model averaging excels in predicting direction of changes, a finding that is in line with Crespo Cuaresma (2007). Lastly, our recommendation concerning the prior on g is to choose the prior proposed by Laud and Ibrahim (1995) with a hold-out sample size of 25% to minimize the rmse (median model) and 75% to optimize direction of change forecasts (model averaging). We finally forecast the monthly industrial production output of six Central Eastern and South Eastern European (CESEE) economies for a one step ahead forecasting horizon. Following the aforementioned forecasting recommendations improves the out-of-sample statistics over a 30-period horizon beating for almost all countries the first order autoregressive benchmark model. | |

Keywords: | Forecast Combination; Bayesian Model Averaging; Median Probability Model; Predictive Likelihood; Industrial Production; Model Uncertainty |

JEL: | C11 |

**Discrete-valued Levy processes and low latency financial econometrics**

Date: | 2010-06-18 |

By: | Ole E. Barndorff-Nielsen (The T.N. Thiele Centre for Mathematics in Natural Science, Department of Mathematical Sciences, University of Aarhus, Ny Munkegade, DK-8000 Aarhus C, Denmark & CREATES, University of Aarhus) David G. Pollard (AHL Research, Man Research Laboratory, Eagle House, Walton Well Road, Oxford OX2 6ED, UK) Neil Shephard (Oxford-Man Institute, University of Oxford, Eagle House, Walton Well Road, Oxford OX2 6ED, UK, & Department of Economics, University of Oxford) |

URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:1004&r=ecm |

Motivated by features of low latency data in finance we study in detail discrete-valued Levy processes as the basis of price processes for high frequency econometrics. An important case of this is a Skellam process, which is the difference of two independent Poisson processes. We propose a natural generalisation which is the difference of two negative binomial processes. We apply these models in practice to low latency data for a variety of different types of futures contracts. | |

Keywords: | futures markets; high frequency econometrics; low latency data; negative binomial; Skellam distribution. |

**Nonparametric Euler Equation Identification and Estimation**

Date: | 2010-06-01 |

By: | Arthur Lewbel (Boston College) Oliver Linton (London School of Economics) |

URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:757&r=ecm |

We consider nonparametric identification and estimation of consumption based asset pricing Euler equations. This entails estimation of pricing kernels or equivalently marginal utility functions up to scale. The standard way of writing these Euler pricing equations yields Fredholm integral equations of the first kind, resulting in the ill posed inverse problem. We show that these equations can be written in a form that equals, (or with habits, resembles) Fredholm integral equations of the second kind, having well posed rather than ill posed inverses. We allow durables, habits, or both to affect utility. We show how to extend the usual method of solving Fredholm integral equations of the second kind to allow for the presence of habits. Using these results, we show with few low level assumptions that marginal utility functions and pricing kernels are locally nonparametrically identified, and we give conditions for finite set and point identification of these functions. Unlike the case of ill posed inverse problems, the limiting distribution theory for our nonparametric estimators should be relatively standard. | |

JEL: | C14 |

**Pricing with Asymmetric Heteroskedastic Normal Mixture Models**

Date: | 2010-09-01 |

By: | Jeroen Rombouts Lars Peter Stentoft |

URL: | http://d.repec.org/n?u=RePEc:cir:cirwor:2010s-38&r=ecm |

This paper uses asymmetric heteroskedastic normal mixture models to fit return data and to price options. The models can be estimated straightforwardly by maximum likelihood, have high statistical fit when used on S&P 500 index return data, and allow for substantial negative skewness and time varying higher order moments of the risk neutral distribution. When forecasting out-of-sample a large set of index options between 1996 and 2009, substantial improvements are found compared to several benchmark models in terms of dollar losses and the ability to explain the smirk in implied volatilities. Overall, the dollar root mean squared error of the best performing benchmark component model is 39% larger than for the mixture model. When considering the recent financial crisis this difference increases to 69%. <P>Dans le présent document, nous avons recours aux modèles hétéroscédastiques asymétriques avec mélange de distributions normales pour ajuster les données sur les rendements et fixer les prix des options. Les modèles peuvent être estimés directement par le maximum de vraisemblance, ils comportent un ajustement statistique élevé quand ils sont utilisés sur les données de rendement de l’indice S&P 500, et ils permettent de tenir compte d’une asymétrie négative importante et des moments d’ordre élevé variant dans le temps liés à la distribution du risque nul. Dans le cas des prévisions hors-échantillonnage concernant une vaste gamme d’options sur indice entre 1996 et 2009, nous constatons des améliorations substantielles, par rapport à plusieurs modèles de référence, en termes de pertes exprimées en dollars et de capacité d’expliquer le caractère ironique des volatilités implicites. En général, la racine de l’erreur quadratique moyenne du modèle de référence à composantes le plus efficace est 39 % plus grande que dans le cas du modÍ le à mélange. Dans le contexte de la récente crise financière, c ette différence augmente à 69 %. | |

Keywords: | Asymmetric heteroskedastic models, finite mixture models, option pricing, out-of-sample prediction, statistical fit , modèles hétéroscédastiques asymétriques, modèle à mélanges finis, fixation des prix des options, prédiction hors-échantillonnage, ajustement statistique |

JEL: | C11 |

**Regression Discontinuity Marginal Threshold Treatment Effects**

Date: | 2010-08-01 |

By: | Yingying Dong (California State University, Fullerton) Arthur Lewbel (Boston College) |

URL: | http://d.repec.org/n?u=RePEc:boc:bocoec:759&r=ecm |

Consider a standard regression discontinuity model, where an outcome Y is determined in part by a binary treatment indicator T, which always (in sharp designs) or sometimes (in fuzzy designs) equals one when a running variable X exceeds a threshold c, and zero otherwise. It is well known that in these models a local average treatment effect can be nonparametrically identified under very general conditions. We show that the derivative of this treatment effect with respect to the threshold c is also nonparametrically identified in both sharp and fuzzy designs, and can be easily estimated. This marginal threshold treatment effect (MTTE) may be used to estimate the impacts of small changes in the threshold, e.g., we use it to show how raising the age of Medicare eligibility would change the probability of take up of various types of health insurance. | |

Keywords: | regression discontinuity, sharp design, fuzzy design, treatment effects, program evaluation, threshold, running variable, forcing variable, marginal effects, health insurance, Medicare |

JEL: | C21 |

**Testing for rational bubbles in a co-explosive vector autoregression**

Date: | 2010-06-24 |

By: | Tom Engsted (CREATES, School of Economics and Management, Aarhus University, DK-8000 Aarhus C) Bent Nielsen (Nuffield College, Oxford OX1 1NF, U.K.) |

URL: | http://d.repec.org/n?u=RePEc:nuf:econwp:1006&r=ecm |

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The analysis for the no-bubble case is done within the traditional Johansen model for I(1) variables, while the bubble model is analysed using a co-explosive framework. The methodology is illustrated using US stock prices and dividends for the period 1872-2000. | |

Keywords: | Rational bubbles, Explosiveness and co-explosiveness, Cointegration, Vector autoregression, Likelihood ratio tests. |

**Identification of models of the labor market**

Date: | 2010 |

By: | Eric French Christopher Taber |

URL: | http://d.repec.org/n?u=RePEc:fip:fedhwp:wp-2010-08&r=ecm |

This chapter discusses identification of common selection models of the labor market. We start with the classic Roy model and show how it can be identified with exclusion restrictions. We then extend the argument to the generalized Roy model, treatment effect models, duration models, search models, and dynamic discrete choice models. In all cases, key ingredients for identification are exclusion restrictions and support conditions. | |

Keywords: | Labor market |

**Level Shifts in Volatility and the Implied-Realized Volatility Relation**

Date: | 2010-09-09 |

By: | Bent Jesper Christensen (Aarhus University and CREATES) Paolo Santucci de Magistris (University of Pavia and CREATES) |

URL: | http://d.repec.org/n?u=RePEc:aah:create:2010-60&r=ecm |

We propose a simple model in which realized stock market return volatility and implied volatility backed out of option prices are subject to common level shifts corresponding to movements between bull and bear markets. The model is estimated using the Kalman filter in a generalization to the multivariate case of the univariate level shift technique by Lu and Perron (2008). An application to the S&P500 index and a simulation experiment show that the recently documented empirical properties of strong persistence in volatility and forecastability of future realized volatility from current implied volatility, which have been interpreted as long memory (or fractional integration) in volatility and fractional cointegration between implied and realized volatility, are accounted for by occasional common level shifts. | |

Keywords: | Common level shifts, fractional cointegration, fractional VECM, implied volatility, long memory, options, realized volatility. |

JEL: | C32 |

**Integrating spatial dependence into stochastic frontier analysis**

Date: | 2010 |

By: | Areal, Francisco J Balcombe, Kelvin Tiffin, R |

URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:24961&r=ecm |

An approach to incorporate spatial dependence into Stochastic Frontier analysis is developed and applied to a sample of 215 dairy farms in England and Wales. A number of alternative specifications for the spatial weight matrix are used to analyse the effect of these on the estimation of spatial dependence. Estimation is conducted using a Bayesian approach and results indicate that spatial dependence is present when explaining technical inefficiency. | |

Keywords: | Spatial dependence; technical efficiency; Bayesian; spatial weight matrix |

JEL: | C51 |

**Inferring Beliefs as Subjectively Uncertain Probabilities**

Date: | 2010-09 |

By: | Steffen Andersen John Fountain Glenn W. Harrison Arne Risa Hole E. Elisabet RutstrÃ¶m |

URL: | http://d.repec.org/n?u=RePEc:exc:wpaper:2010-14&r=ecm |

We propose a method for estimating subjective beliefs, viewed as a subjective probability distribution. The key insight is to characterize beliefs as a parameter to be estimated from observed choices in a well-defined experimental task, and to estimate that parameter as a random coefficient. The experimental task consists of a series of standard lottery choices in which the subject is assumed to use conventional risk attitudes to select one lottery or the other, and then a series of betting choices in which the subject is presented with a range of bookies offering odds on the outcome of some event that the subject has a belief over. Knowledge of the risk attitudes of subjects conditions the inferences about subjective beliefs. Maximum simulated likelihood methods are used to estimate a structural model in which subjects employ subjective beliefs to make bets. We present evidence that some subjective probabilities are inde ed best characterized as probability distributions with non-zero variance. |

**The Mysteries of Trend**

Date: | 2010-09 |

By: | Peter C. B. Phillips (Cowles Foundation, Yale University) |

URL: | http://d.repec.org/n?u=RePEc:cwl:cwldpp:1771&r=ecm |

Trends are ubiquitous in economic discourse, play a role in much economic theory, and have been intensively studied in econometrics over the last three decades. Yet the empirical economist, forecaster, and policy maker have little guidance from theory about the source and nature of trend behavior, even less guidance about practical formulations, and are heavily reliant on a limited class of stochastic trend, deterministic drift, and structural break models to use in applications. A vast econometric literature has emerged but the nature of trend remains elusive. In spite of being the dominant characteristic in much economic data, having a role in policy assessment that is often vital, and attracting intense academic and popular interest that extends well beyond the subject of economics, trends are little understood. This essay discusses some implications of these limitations, mentions some research opportunities, and brief ly illustrates the extent of the difficulties in learning about trend phenomena even when the time series are far longer than those that are available in economics. | |

Keywords: | Climate change, Etymology of trend, Paleoclimatology, Policy, Stochastic trend |

JEL: | C22 |