Gianni Amisano

Comparing Density Forecasts via Weighted Likelihood Ratio Tests

We propose a test for comparing the out-of-sample accuracy of competing density forecasts of a variable. The test is valid under general conditions: The data can be heterogeneous and the forecasts can be based on (nested or nonnested) parametric models or produced by semiparametric, nonparametric, or Bayesian estimation techniques. The evaluation is based on scoring rules, which are loss functions defined over the density forecast and the realizations of the variable. We restrict attention to the logarithmic scoring rule and propose an out-of-sample “weighted likelihood ratio” test that compares weighted averages of the scores for the competing forecasts. The user-defined weights are a way to focus attention on different regions of the distribution of the variable. For a uniform weight function, the test can be interpreted as an extension of Vuongs likelihood ratio test to time series data and to an out-of-sample testing framework. We apply the tests to evaluate density forecasts of U.S. inflation produced by linear and Markov-switching Phillips curve models estimated by either maximum likelihood or Bayesian methods. We conclude that a Markov-switching Phillips curve estimated by maximum likelihood produces the best density forecasts of inflation.

Profit related pay in Italy

This paper investigates which company characteristics affect the decision to introduce profit‐sharing. Unlike most studies, this paper relies on a ten‐year panel. The results presented in this paper are based on the estimation of a panel data fixed‐effect logit model. Given that they are immune from heterogeneity bias, it is believed that these results are more reliable than those obtained by estimating cross‐sectional models. These results are in line with the common findings of the literature. Companies that are more likely to introduce profit‐sharing (PS) are larger firms which invest more, due to the lower cost of debt, and tend to pay higher wages as an incentive to boost the initially lower productivity. These companies are more likely to undertake investment projects which support the interpretation of PS as a risk‐sharing device.

What goes up sometimes stays up: shocks and institutions as determinants of unemployment persistence

We analyse the determinants of unemployment persistence in four OECD countries by estimating a structural Bayesian VAR with an informative prior based on an insiders/outsiders model. We explicitly insert unemployment benefits and labour taxes so that our identification is not affected by the Faust and Leeper (1997) critique. We find widespread hysteresis: demand shocks play a dominant role in explaining unemployment also in the medium-run. Moreover real wages have low sensitivity to cyclical fluctuations and to labour market disequilibria. Our results emphasise the real power of the unions and their interactions with structural shocks and other institutions as crucial determinants of hysteresis.

Forecasting cointegrated series with BVAR models

In this paper we examine how BVARs can be used for forecasting cointegrated variables. We propose an approach based on a Bayesian ECM model in which, contrary to the previous literature, the factor loadings are given informative priors. This procedure, applied to Italian macroeconomic series, produces more satisfactory forecasts than different prior specifications or parameterizations. Providing an informative prior on the factor loadings is a crucial point: a flat prior on the ECM terms combined with an informative prior on the lagged endogenous variables coefficients gives too much importance to the long-run properties with respect to the short-run dynamics. Copyright

From VAR models to Structural VAR models

In this chapter we introduce the philosophy, the basic concepts and definitions of VAR analysis (sections 1.1 and 1.2). After that, in section 1.3 we discuss the problems of VAR estimation and in section 1.4 we describe the possible uses of VAR models. Then in section 1.5 we start dealing with Structural VAR analysis, pointing out the main features of the different classes of Structural VAR models, their likelihood functions (section 1.6) and their differences with respect to the standard simultaneous equations models (section 1.7). We conclude this chapter by providing examples of Structural VARs taken from the applied econometric literature (section 1.8).

Model selection in Structural VAR analysis

In this chapter we explain how to use the dominance ordering and the likelihood dominance criteria introduced by Pollack and Wales (1991) as model selection devices in Structural VAR analysis1. In section 7.1 we recall the main aspects of model selection and we connect this issue directly to the Structural VAR framework. The next two sections are devoted to explaining the above mentioned model selection criteria.

The problem of non-fundamental representations

The validity of dynamic simulation results obtained from Structural VAR model has been very strongly criticised in two recent papers (Lippi and Reichlin, 1993 and 1994). The content of this criticism is closely connected to the existence and the relevance of non fundamental MA representations (see Hansen e Sargent, 1991, ch. 4). We start this chapter by describing the content of the Lippi and Reichlin criticism. Section 8.1 is devoted to explain the notion of non fundamental representation in time series models. Section 8.2 presents some examples of economic models generating non fundamental representations and section 8.3 connects the issue of the existence of non fundamental representations to Structural VAR analysis, presenting a new way to assess the relevance of these representations in particular applications. An applied example of this procedure is contained in section 8.4.

Two applications of Structural VAR analysis

In this chapter we present the results of two different applications of Structural VAR analysis, which are intended to provide the reader with some evidence of the way in which the techniques described in this book can be concretely applied.

Impulse response analysis and forecast error variance decomposition in SVAR modelling

In this chapter we explain how to use estimated Structural VAR models to perform dynamic simulations, via impulse response analysis (section 5.1) and forecast error variance decomposition (section 5.2). After presenting the asymptotic results which are used to obtain confidence bounds around the estimated coefficient, in section 5.3 we present some discussion about the reliability of these asymptotic results in small samples.

Identification analysis and F.I.M.L estimation for the AB-Model

The K-model1 is completely defined by the following equations and distributional assumptions: n n