Expansions of GMM statistics that indicate their properties under weak and/or many instruments and the bootstrap

We construct higher order expressions for Wald and Lagrange multiplier (LM) GMM statistics that are based on 2step and continuous updating estimators (CUE). We show that the sensitivity of the limit distribution to weak and many instruments results from superfluous elements in the higher order expansion. When the instruments are strong and their number is small, these elements are of higher order and result in higher order biases. When instruments are weak and/or their number is large, they are, however, of zero-th order and influence the limiting distributions. Edgeworth approximations do not remove the superfluous elements. The expansion of the LM-CUE statistic, which is Kleibergen's (2003) K-statistic, does not contain the superfluous higher order elements so it is robust to weak or many instruments. An Edgeworth approximation of its finite sample distribution shows that the bootstrap reduces the size distortion. We compute power curves for tests on the autocorrelation parameter in a panel autoregressive model to illustrate the consequences of the higher order.terms and the improvement that results from applying the bootstrapGMM, weak instruments, bootstrap, Panel AR(1)

Finite-sample instrumental variables inference using an asymptotically pivotal statistic

This paper is concerned with investigating the role of accounting practices in radical change processes. The institutional framework has been taken as a starting point in investigating these processes. The research has been carried out at the Dutch Railways. This company was forced by the Dutch government to change from a public company into a private company. This decision by the Dutch Government has had radical consequences for Dutch Railways’ position in the (rail) transport market and for the way of managing the company. The research focuses on the processes in which the company has changed its template as a public company into a profit-oriented template. This paper examines the interaction of accounting practices with the environmental and organisational context. Emphasis is placed on how these mutual processes of interaction change internal and external positioning, create new visibilities, transform perspectives on organisational activities and performance and modify conditions for organisational change. Existing institutional concepts regarding change processes are evaluated in the light of the case findings and building blocks are developed for a comprehensive change framework.

Finite-sample instrumental variables inference using an asymptotically pivotal statistic

The paper considers the K-statistic, Kleibergen’s (2000) adaptation of the Anderson-Rubin (AR) statistic in instrumental variables regression. Compared to the AR-statistic this K-statistic shows improved asymptotic efficiency in terms of degrees of freedom in overidenti?ed models and yet it shares, asymptotically, the pivotal property of the AR statistic. That is, asymptotically it has a chi-square distribution whether or not the model is identi?ed. This pivotal property is very relevant for size distortions in ?nite-sample tests. Whereas Kleibergen (2000) focuses especially on the asymptotic behavior of the statistic, the present paper concentrates on finite-sample properties in a Gaussian framework. In that case the AR statistic has an F-distribution. However, the K-statistic is not exactly pivotal. Its finite-sample distribution is affected by nuisance parameters. Here we consider the two extreme cases, which provide tight bounds for the exact distribution. The first case amounts to perfect identification —which is similar to the asymptotic case—where the statistic has an F-distribution. In the other extreme case there is total underidentification. For the latter case we show how to compute the exact distribution. Thus we provide tight bounds for exact con?dence sets based on the efficient K-statistic. Asymptotically the two bounds converge, except when there is a large number of redundant instruments.

Reduced Rank Regression using Generalized Method of Moments Estimators with extensions to structural breaks in cointegration models

Generalized Method of Moments (GMM) Estimators are derived for Reduced Rank Regression Models, the Error Correction Cointegration Model (ECCM) and the Incomplete Simultaneous Equations Model (INSEM). The GMM (2SLS) estimators of the cointegrating vector in the ECCM are shown to have normal limiting distributions. Tests for the number of unit roots can be constructed straightforwardly and have Dickey-Fuller type limiting distributions. Two extensions of the ECCM, which are important in practice, are analyzed. First, cointegration estimators and tests allowing for structural shifts in the variance (heteroscedasticity) of the series are derived and analyzed using a Generalized Least Squares Estimator. Second, cointegrating vector estimators and tests are derived which allow for structural breaks in the cointegrating vector and/or multiplicator. The resulting cointegrating vectors estimators have again normal limiting distributions while the cointegration tests have limiting distributions which differ from the standard Dickey-Fuller type

Identification Robust Inference for the Risk Premium in Term Structure Models

We propose identification robust statistics for testing hypotheses on the risk premia in dynamic affine term structure models. We do so using the moment equation specification proposed for these models in Adrian et al. (2013). We extend the subset (factor) Anderson-Rubin test from Guggenberger et al. (2012) to models with multiple dynamic factors and time-varying risk prices. Unlike projection-based tests, it provides a computationally tractable manner to conduct identification robust tests on a larger number of parameters. We analyze the potential identification issues arising in empirical studies. Statistical inference based on the three-stage estimator from Adrian et al. (2013) requires knowledge of the factors' quality and is misleading without full-rank beta's or with sampling errors of comparable size as the loadings. Empirical applications show that some factors, though potentially weak, may drive the time variation of risk prices, and weak identification issues are more prominent in multi-factor models

Bayesian Analysis of ARMA Models

Root cancellation in Auto Regressive Moving Average (ARMA) models leads tolocal non-identification of parameters. When we use diffuse or normal priorson the parameters of the ARMA model, posteriors in Bayesian analyzes show ana posteriori favor for this local non-identification. We show that the priorand posterior of the parameters of an ARMA model are the (unique)conditional density of a prior and posterior of the parameters of anencompassing AR model. We can therefore specify priors and posteriors on theparameters of the encompassing AR model and use the prior and posterior thatit implies on the parameters of the ARMA model, and vice versa. Theposteriors of the ARMA parameters that result from standard priors on theparameters of an encompassing AR model do not lead to an a posteriori favorof root cancellation. We develop simulators to generate parameters fromthese priors and posteriors. As a byproduct, Bayes factors can be computedto compare (non-nested) parsimonious ARMA models. The procedures are appliedto the (extended) Nelson-Plosser data. For approximately 50% of the seriesan ARMA model is favored above an AR model

Bayesian and Classical Approaches to Instrumental Variables Regression

We estabilsh the relationships between certain Bayesian and classical approaches to instrumental variables regression. We determine the form of priors that lead to posteriors for structural paameters that have similar properties as classical 2SLS and LIML and in doing so provide some new insight to the small sample behavior of Bayesian and classical procedures in the limited information simultaneous equations model. Our approach is motivated by the relationship between Bayesian and classical procedures in linear regression models: i.e., Bayesian analysis with a diffuse prior leads to posteriors that are identical in form to the finite sample density of classical least squares estimators. We use the fact that the instrumental variables regression model can be obtained from a reduced rank restriction on a multivariate linear model to determine the priors that give rise to posteriors that have properties similar to classical 2SLS and LIML. As a by-product of this approach we provide a novel way to dtermine the exact finite sample density of the LIML estimator and theprior that corresponds with classical LIML. We show that the traditional Dreze (1976) and a new Bayesian Two Stage approach are similar to 2SLS whereas the approach based on the Jeffreys' prior corresponds to LIML.Bayesian, diffuse prior, instrumental variables, Jeffreys prior, limited information maximum likelihood, reduced rank, two stage least squares,

Priors, posteriors and Bayes factors for a Bayesian analysis of cointegration

Cointegration occurs when the long run multiplier of a vector autoregressive model exhibits rank reduction. Priors and posteriors of the parameters of the cointegration model are therefore proportional to priors and posteriors of the long run multiplier given that it has reduced rank. Rank reduction of the long run multiplier is modelled using a decomposition resulting from its singular value decomposition. It specifies the long run multiplier matrix as the sum of a matrix that equals the product of the adjustment parameters and the cointegrating vectors, i.e. the cointegration specification, and a matrix that models the deviation from cointegration. Priors and posteriors for the parameters of the cointegration model are obtained by restricting the latter matrix to zero in the prior and posterior of the unrestricted long run multiplier. The special decomposition of the long run multiplier results in unique posterior densities. This theory leads to a complete Bayesian framework for cointegration analysis. It includes prior specification, simulation schemes for obtaining posterior distributions and determination of the cointegration rank via Bayes factors. We illustrate the analysis with several simulated series, the UK data of Hendry and Doornik (1994) and the Danish data of Johansen and Juselius (1990)

Bayesian Analysis of ARMA models using Noninformative Priors

Parameters in AutoRegressive Moving Average (ARMA) models are locally nonidentified, due to the problem of root cancellation. Parameters can be constructed which represent this identification problem. We argue that ARMA parameters should be analyzed conditional on these identifying parameters. Priors exploiting this feature result in regular posteriors, while priors which neglect it result in posteriori favor of nonidentified parameter values. By considering the implicit AR representation of an ARMA model a prior with the desired proporties is obtained. The implicit AR representation also allows to construct easily implemented algorithms to analyze ARMA parameters. As a byproduct, posteriors odds ratios can be computed to compare (nonnested) parsimonious ARMA models. The procedures are applied to two datasets, the (extended) Nelson-Plosser data and monthly observations of US 3-month and 10 year interest rates. For approximately 50% of the series in these two datasets an ARMA model is favored above an AR model

Unit roots in the Nelson-Plosser data: Do they matter for forecasting?

In this paper we compare two univariate time series models, i.e. one with and one without an imposed unit root, in a forecasting experiment for the fourteen annually observed US data analyzed by Nelson and Plosser (1982, Journal of Monetary Economics 10, 139–162). Our main result is that the unit root model is regularly preferred. This result holds for a variety of sample sizes and forecast horizons as well as for one-step and multi-step ahead forecasts