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open 3 si Pubblicato come working paper: Geraci, Andrea ; Fabbri, Daniele ; Monfardini, Chiara (2014) Testing exogeneity of multinomial regressors in count data models: does two stage residual inclusion work? Bologna: Dipartimento di Scienze economiche DSE, p. 37. DOI 10.6092/unibo/amsacta/3937 . In: Quaderni - Working Paper DSE (921). ISSN 2282-6483. We study a simple exogeneity test in count data models with possibly endogenous multinomial treatment. The test is based on Two Stage Residual Inclusion (2SRI), an estimation method which has been proved to be consistent for a general class of nonlinear parametric models. Results from a broad set of simulation experiments provide novel evidence on important features of this approach. We find differences in the finite sample performance of various likelihood-based tests, analyze their robustness to misspecification arising from neglected over-dispersion or from incorrect specification of the first stage model, and uncover that standardizing the variance of the first stage residuals leads to better results. An original application to testing the endogeneity status of insurance in a model of healthcare demand corroborates our Monte Carlo findings. partially_open embargoed_20171108 Geraci, Andrea; Fabbri, Daniele; Monfardini, Chiara Geraci, Andrea; Fabbri, Daniele; Monfardini, Chiara

In this paper we discuss general identification results for Structural Vector Autoregressions (SVARs) with external instruments, considering the case in which r valid instruments are used to identify g Ï 1 structural shocks, where r Ï g. We endow the SVAR with an auxiliary statistical model for the external instruments which is a system of reduced form equations. The SVAR and the auxiliary model for the external instruments jointly form a "larger" SVAR characterized by a particularly restricted parametric structure, and are connected by the covariance matrix of their disturbances which incorporates the "relevance" and "exogeneity" conditions. We discuss identification results and likelihood-based estimation methods both in the "multiple shocks" approach, where all structural shocks are of interest, and in the "partial shock" approach, where only a subset of the structural shocks is of interest. Overidentified SVARs with external instruments can be easily tested in our setup. The suggested method is applied to investigate empirically whether commonly employed measures of macroeconomic and financial uncertainty respond on-impact, other than with lags, to business cycle fluctuations in the U.S. in the period after the Global Financial Crisis. To do so, we employ two external instruments to identify the real economic activity shock in a partial shock approach.

Building on the literature on regularization and dimension reduction methods, we have developed a quarterly forecasting model for euro area GDP. This method consists in bridging quarterly national accounts data using factors extracted from a large panel of monthly and quarterly series including business surveys and financial indicators. The pseudo real-time nature of the information set is accounted for as the pattern of publication lags is considered. Forecast evaluation exercises show that predictions obtained through various dimension reduction methods outperform both the benchmark AR and the diffusion index model without pre-selected indicators. Moreover, forecast combination significantly reduces forecast error.

This paper explores the potential of bootstrap methods in the empirical evalu- ation of dynamic stochastic general equilibrium (DSGE) models and, more generally, in linear rational expectations models featuring unobservable (latent) components. We consider two dimensions. First, we provide mild regularity conditions that suffice for the bootstrap Quasi- Maximum Likelihood (QML) estimator of the structural parameters to mimic the asymptotic distribution of the QML estimator. Consistency of the bootstrap allows to keep the probability of false rejections of the cross-equation restrictions under control. Second, we show that the realizations of the bootstrap estimator of the structural parameters can be constructively used to build novel, computationally straightforward tests for model misspecification, including the case of weak identification. In particular, we show that under strong identification and boot- strap consistency, a test statistic based on a set of realizations of the bootstrap QML estimator approximates the Gaussian distribution. Instead, when the regularity conditions for inference do not hold as e.g. it happens when (part of) the structural parameters are weakly identified, the above result is no longer valid. Therefore, we can evaluate how close or distant is the esti- mated model from the case of strong identification. Our Monte Carlo experimentations suggest that the bootstrap plays an important role along both dimensions and represents a promising evaluation tool of the cross-equation restrictions and, under certain conditions, of the strength of identification. An empirical illustration based on a small-scale DSGE model estimated on U.S. quarterly observations shows the practical usefulness of our approach.

Forecasting-volatility models typically rely on either daily or high frequency (HF) data and the choice between these two categories is not obvious. In particular, the latter allows to treat volatility as observable but they suffer of many limitations. HF data feature microstructure problem, such as the discreteness of the data, the properties of the trading mechanism and the existence of bid-ask spread. Moreover, these data are not always available and, even if they are, the asset’s liquidity may be not sufficient to allow for frequent transactions. This paper considers different variants of these two family forecasting-volatility models, comparing their performance (in terms of Value at Risk, VaR) under the assumptions of jumping prices and leverage effects for volatility. Findings suggest that GARJI model provides more accurate VaR measures for the S&P 500 index than RV models. Furthermore, the assumption of conditional normality is shown to be not sufficient to obtain accurate risk measures even if jump contribution is provided. More sophisticated models might address this issue, improving VaR results.

A specific concept of structural model is used as a background for discussing the structurality of its parameterization. Conditions for a structural model to be also causal are examined. Difficulties and pitfalls arising from the parameterization are analyzed. In particu- lar, pitfalls when considering alternative parameterizations of a same model are shown to have lead to ungrounded conclusions in the lit- erature. Discussion of observationally equivalent models related to different economic mechanisms are used to make clear the connection between an economicall meaningful parameterization and an econom- ically meaningful decomposition of a complex model. The design of economic policy is used for drawing some practical implications of the proposed analysis.

This paper focuses on the dynamic misspecification that characterizes the class of small-scale New-Keynesian models and provides a `natural' remedy for the typical difficulties these models have in accounting for the rich contemporaneous and dynamic correlation structure of the data, generally faced with ad hoc shock specifications. We suggest using the `best fitting' statistical model for the data as a device through which it is possible to adapt the econometric specification of the New-Keynesian model. The statistical model may feature an autocorrelation structure that is more involved than the autocorrelation structure implied by the structural model's reduced form solution under rational expectations, and it is treated as the actual agents' expectations generating mechanism. A pseudo-structural form is built from the baseline system of Euler equations by forcing the state vector of the system to have the same dimension as the state vector characterizing the statistical model. We provide an empirical illustration based on U.S. quarterly data and a small-scale monetary New Keynesian model.

The problem of instrument proliferation and its consequences (overfitting of the endogenous explanatory variables, biased IV and GMM estimators, weakening of the power of the overidentification tests) are well known. This paper introduces a statistical method to reduce the instrument count. The principal component analysis (PCA) is applied on the instrument matrix, and the PCA scores are used as instruments for the panel generalized method-of-moments (GMM) estimation. This strategy is implemented through the new command pca2.

In this article, we investigate the behaviour of a number of methods for estimating the co-integration rank in VAR systems characterized by heteroskedastic innovation processes. In particular, we compare the efficacy of the most widely used information criteria, such as Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) , with the commonly used sequential approach of Johansen [Likelihood-based Inference in Cointegrated Vector Autoregressive Models (1996)] based around the use of either asymptotic or wild bootstrap-based likelihood ratio type tests. Complementing recent work done for the latter in Cavaliere, Rahbek and Taylor [Econometric Reviews (2014) forthcoming], we establish the asymptotic properties of the procedures based on information criteria in the presence of heteroskedasticity (conditional or unconditional) of a quite general and unknown form. The relative finite-sample properties of the different methods are investigated by means of a Monte Carlo simulation study. For the simulation DGPs considered in the analysis, we find that the BIC-based procedure and the bootstrap sequential test procedure deliver the best overall performance in terms of their frequency of selecting the correct co-integration rank across different values of the co-integration rank, sample size, stationary dynamics and models of heteroskedasticity. Of these, the wild bootstrap procedure is perhaps the more reliable overall as it avoids a significant tendency seen in the BIC-based method to over-estimate the co-integration rank in relatively small sample sizes.

This paper proposes a testing strategy for the null hypothesis that a multivariate linear rational expectations (LRE) model may have a unique stable solution (determinacy) against the alternative of multiple stable solutions (indeterminacy). The testing problem is addressed by a misspecification-type approach in which the overidentifying restrictions test obtained from the estimation of the system of Euler equations of the LRE model through the generalized method of moments is combined with a likelihood-based test for the cross-equation restrictions that the model places on its reduced form solution under determinacy. The resulting test has no power against a particular class of indeterminate equilibria, hence the non rejection of the null hypothesis can not be interpreted conclusively as evidence of determinacy. On the other hand, this test (i) circumvents the nonstandard inferential problem generated by the presence of the auxiliary parameters that appear under indeterminacy and that are not identifiable under determinacy, (ii) does not involve inequality parametric restrictions and hence the use of nonstandard inference, (iii) is consistent against the dynamic misspecification of the LRE model, and (iv) is computationally simple. Monte Carlo simulations show that the suggested testing strategy delivers reasonable size coverage and power against dynamic misspecification in finite samples. An empirical illustration focuses on the determinacy/indeterminacy of a New Keynesian monetary business cycle model of the US economy.

In this article we propose a Monte Carlo algorithm for sequential parameter learning for a stochastic volatility model with leverage, nonconstant conditional mean and jumps. We are interested in estimating the time invariant parameters and the nonobservable dynamics involved in the model. Our simple but effective idea relies on the auxiliary particle filter algorithm mixed together with the Markov Chain Monte Carlo (MCMC) methodology. Adding an MCMC step to the auxiliary particle filter prevents numerical degeneracies in the sequential algorithm and allows sequential evaluation of the fixed parameters and the latent processes. Empirical evaluation on simulated and real data is presented to assess the performance of the algorithm. A numerical comparison with a full MCMC procedure is also provided. We also extend our methodology to superposition models in which volatility is obtained by a linear combination of independent processes.

I exploit the potential of latent class models for proposing an innovative framework for financial data analysis. By stressing the latent nature of the most important financial variables, expected return and risk, I am able to introduce a new methodological dimension in the analysis of financial phenomena. In my proposal, (i) I provide innovative measures of expected return and risk, (ii) I suggest a financial data classification consistent with the latent risk-return profile, and (iii) I propose a set of statistical methods for detecting and testing the number of groups of the new data classification. The results lead to an improvement in both risk measurement theory and practice and, if compared to traditional methods, allow for new insights into the analysis of financial data. Finally, I illustrate the potentiality of my proposal by investigating the European stock market and detailing the steps for the appropriate choice of a financial portfolio.

Goal of this paper is to analyze and forecast realized volatility through nonlinear and highly persistent dynamics. In particular, we propose a model that simultaneously captures long memory and nonlinearities in which level and persistence shift through a Markov switching dynamics. We consider an efficient Markov chain Monte Carlo (MCMC) algorithm to estimate parameters, latent process and predictive densities. The insample results show that both long memory and nonlinearities are significant and improve the description of the data. The out-sample results at several forecast horizons, show that introducing these nonlinearities produces superior forecasts over those obtained from nested models.

In this paper we examine the formal implications of international risk sharing among a set of countries in the presence of market frictions and forward-looking behaviour. We show that if frictions prevent consumption to adjust instantaneously to its optimal long run level, consumption streams in the countries belonging to the risk sharing pool change over time according to a dynamic disequilibrium model which can be nested within an error-correcting vector autoregressive process. Econometric methods for testing the restrictions imposed by the theory at both short and long horizons are proposed and discussed. The empirical analysis of a set of core European countries suggest that consumption data do not seem to contrast neither with the existence of risk sharing against permanent income fluctuations and integrated capital markets, nor with a gradual and interrelated process of adjustment towards the equilibrium. The apparent lack of risk sharing in Europe documented in earlier works might depend not only on the misspecification of the short run dynamics of consumption, but also on the relatively low speed of adjustment toward the equilibrium. Adjustment costs, Consumption risk sharing, Cointegrated,VAR models, Financial market integration, Market frictions.

In this paper we analyze the consequences of model overidentification on testing exogeneity, when maximum likelihood technique for estimation an inference are used. This situation is viewed as a particular case of the more general problem of considering how restrictions on "nuisance" parameters could help in making inference on the parameters of interest. At first general model is considered. A suitable likelihood function factorization is used which permits to easily derive the information matrix and other tools useful for constructing hoint tests for exogeneity and overidentifying restrictions both of Wald and Lagrange Multiplier type. The asymptotic local power of the exogeneity test in the justidentified model is compared with that of the overidentified one, when we assume that this last is the true model. Then the pseudolikelihood framework is proposed for appreciating the consequences of working woth a model where overidentifying restrictions are erroneously imposed. The inconsistency introduced by imposing false restrictions is analysed and the consequences of the misspecification on the exogeneity test are carefully examined.