Testing for unit roots in time series models with non-stationary volatility

Many of the key macro-economic and financial variables in developed economies are characterized by permanent volatility shifts. It is known that conventional unit root tests are potentially unreliable in the presence of such behaviour, depending on a particular function (the variance profile) of the underlying volatility process. Somewhat surprisingly then, very little work has been undertaken to develop unit root tests which are robust to the presence of permanent volatility shifts. In this paper we fill this gap in the literature by proposing tests which are valid in the presence of a quite general class of permanent variance changes which includes single and multiple (abrupt and smooth-transition) volatility change processes as special cases. Our solution uses numerical methods to simulate the asymptotic null distribution of the statistics based on a consistent estimate of the variance profile which we also develop. The practitioner is not required to specify a parametric model for volatility. An empirical illustration using producer price inflation series from the Stock–Watson database is reported.     

Coordination and the Provision of Discrete Public Goods by Correlated Equilibria

The strategic analysis of the private provision of a discrete public good has shown the existence of multiple Nash equilibria with the efficient number of players voluntarily contributing. However the coordination issue is left unexplained by this literature. The experimental evidence shows that communication among players is helpful in achieving cooperation. We claim that, from the theoretical point of view, this is equivalent to playing correlated equilibria in an extended public good game with communication, modeled as Chicken. We characterize such equilibria as feasible coordination mechanisms to achieve public goods provision in the general contribution game. We further introduce a second kind of game characterized by payoff externalities that may persist after the minimal threshold of contributors is achieved. While it is easy to show the existence of Pareto efficient correlated equilibria in the first game, in the second one players face incentive problems such that a first best cannot always be an equilibrium. Nevertheless there exist correlated equilibria that can qualify as incentive efficient mechanisms, once free riding is seen as a moral hazard issue. Finally, with an example, we discuss the impact of coalition formation in our framework.     

Co‐integration Rank Determination in Partial Systems Using Information Criteria

We investigate the asymptotic and finite sample properties of the most widely used information criteria for co‐integration rank determination in ‘partial’ systems, i.e. in co‐integrated vector autoregressive (VAR) models where a sub‐set of variables of interest is modelled conditional on another sub‐set of variables. The asymptotic properties of the Akaike information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan–Quinn information criterion (HQC) are established, and consistency of BIC and HQC is proved. Notably, the consistency of BIC and HQC is robust to violations of weak exogeneity of the conditioning variables with respect to the co‐integration parameters. More precisely, BIC and HQC recover the true co‐integration rank from the partial system analysis also when the conditional model does not convey all information about the co‐integration parameters. This result opens up interesting possibilities for practitioners who can now determine the co‐integration rank in partial systems without being concerned about the weak exogeneity of the conditioning variables. A Monte Carlo experiment based on a large dimensional data generating process shows that BIC and HQC applied in partial systems perform reasonably well in small samples and comparatively better than ‘traditional’ methods for co‐integration rank determination. We further show the usefulness of our approach and the benefits of the conditional system analysis in two empirical illustrations, both based on the estimation of VAR systems on US quarterly data. Overall, our analysis shows the gains of combining information criteria with partial system analysis.     

A Comparison of Sequential and Information‐based Methods for Determining the Co‐integration Rank in Heteroskedastic VAR Models

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.     

PRIVATIZATION AND EFFICIENCY: FROM PRINCIPALS AND AGENTS TO POLITICAL ECONOMY

Abstract.  We survey the theoretical literature on privatization and efficiency by tracing its evolution from the applications of agency theory to recent contributions in the field of political economy. The former extend the theory of regulation with incomplete information to address privatization issues, comparing state-owned enterprises with private regulated firms. The benefits of privatization may derive either from the constraints it places on malevolent agents or from the impossibility of commitment by a benevolent government because of incomplete contracts. Contributions dealing with political economy issues separate privatization from restructuring decisions. They either explore bargaining between managers and politicians or analyse the impact of privatization shaped by political preferences on efficiency. The theoretical results regarding the relation between privatization and efficiency do not lead to any definitive conclusion. Privatization may increase productive efficiency when restructuring takes place whereas its effects on allocative efficiency still remain uncertain.     

Overcompliance and Voluntary Agreements

Voluntary agreements with industry offer many examplesof overcompliance with respect to environmentalstandards. Such phenomena seem to be irrational butappear less surprising considering firms' strategiesare aimed to internalise environmental quality. Wemodel the choice of the environmental quality ofproducts in a one-shot game between a monopolist andconsumers, to show the existence of inefficientequilibria where quality is low because of moralhazard. The firm can, however, change its' equilibriumstrategy in a repeated but finite game, in order tobuild an environmental reputation if we suppose thatconsumers' information is not only imperfect withregard to quality, but also incomplete with respect toany environmental constraint that may affect thebehaviour of firms (like the threat either of astricter regulation or of potential entry). In atwo-period model, we show the existence of a perfectBayesian equilibrium in mixed strategies where thefirm can revert to the production of green products inorder to influence consumers' beliefs and acquire anenvironmentally friendly reputation. Due to thepeculiarity of environmental information (greenproducts are credence goods), we claim that anexplicit agreement is also necessary in order toestablish monitoring and controlling procedures toverify the performance of firms. These procedures canexplain per se the diffusion of voluntary agreementsthat are nevertheless self-enforcing because of thereputation effect.     

Testing for a change in persistence in the presence of non-stationary volatility

In this paper we consider tests for the null of (trend-) stationarity against the alternative of a change in persistence at some (known or unknown) point in the observed sample, either from I(0)$I\left(0\right)$ to I(1)$I\left(1\right)$ behaviour or vice versa, of, inter alia, [Kim, J., 2000. Detection of change in persistence of a linear time series. Journal of Econometrics 95, 97–116]. We show that in circumstances where the innovation process displays non-stationary unconditional volatility of a very general form, which includes single and multiple volatility breaks as special cases, the ratio-based statistics used to test for persistence change do not have pivotal limiting null distributions. Numerical evidence suggests that this can cause severe over-sizing in the tests. In practice it may therefore be hard to discriminate between persistence change processes and processes with constant persistence but which display time-varying unconditional volatility. We solve the identified inference problem by proposing wild bootstrap-based implementations of the tests. Monte Carlo evidence suggests that the bootstrap tests perform well in finite samples. An empirical illustration using US price inflation data is provided.     

Regional consumption dynamics and risk sharing in Italy

In this paper, we propose a new method for investigating consumption insurance. Differently from the existing literature, we use error correcting VAR models in order to capture simultaneously the occurrence of risk sharing against permanent and transitory shocks. The proposed method is applied to the case of Italian regions. Empirical results obtained over the 1960–2001 period reveal that contrary to previous findings, Italian regions seem to shield against permanent shocks other than transitory ones. Although some biases are detected in the allocation process of resources, deviations from full consumption insurance are not as relevant as claimed in the previous literature on the Italian regions.     

Testing for a Change in Persistence in the Presence of a Volatility Shift*

We consider the impact of a break in the innovation volatility process on ratio‐based persistence change tests. We demonstrate that the ratio statistics used do not have pivotal limiting null distributions and that the associated tests display a considerable degree of size distortion with size approaching unity in some cases. In practice, therefore, on the basis of these tests the practitioner will face difficulty in discriminating between persistence change processes and processes which display a simple volatility break. A wild bootstrap‐based solution to the identified inference problem is proposed and is shown to work well in practice.