Fabio Busetti

Testing against stochastic trend and seasonality in the presence of unattended breaks and unit roots

This paper considers the problem of testing against stochastic trend and seasonality in the presence of structural breaks and unit roots at frequencies other than those directly under test, which we term unattended breaks and unattended unit roots respectively. We show that under unattended breaks the true size of the Kwiatkowski et. al. (1992) [KPSS] test at frequency zero and the Canova and Hansen (1995) [CH] test at the seasonal frequencies fall well below the nominal level under the null with an associated, often very dramatic, loss of power under the alternative. We demonstrate that a simple modification of the statistics can recover the usual limiting distribution appropriate to the case where there are no breaks, provided unit roots do not exist at any of the unattended frequencies. Where unattended unit roots occur we show that the above statistics converge in probability to zero under the null. However, computing the KPSS and CH statistics after pre-filtering the data is simultaneously efficacious against both unattended breaks and unattended unit roots, in the sense that the statistics retain their usual pivotal limiting null distributions appropriate to the case where neither occurs. The case where breaks may potentially occur at all frequencies is also discussed. The practical relevance of the theoretical contribution of the paper is illustrated through a number of empirical examples.

Variance Shifts, Structural Breaks, and Stationarity Tests

This article considers the problem of testing the null hypothesis of stochastic stationarity in time series characterized by variance shifts at some (known or unknown) point in the sample. It is shown that existing stationarity tests can be severely biased in the presence of such shifts, either oversized or undersized, with associated spurious power gains or losses, depending on the values of the breakpoint parameter and on the ratio of the prebreak to postbreak variance. Under the assumption of a serially independent Gaussian error term with known break date and known variance ratio, a locally best invariant (LBI) test of the null hypothesis of stationarity in the presence of variance shifts is then derived. Both the test statistic and its asymptotic null distribution depend on the breakpoint parameter and also, in general, on the variance ratio. Modifications of the LBI test statistic are proposed for which the limiting distribution is independent of such nuisance parameters and belongs to the family of Cramér–von Mises distributions. One such modification is particularly appealing in that it is simultaneously exact invariant to variance shifts and to structural breaks in the slope and/or level of the series. Monte Carlo simulations demonstrate that the power loss from using our modified statistics in place of the LBI statistic is not large, even in the neighborhood of the null hypothesis, and particularly for series with shifts in the slope and/or level. The tests are extended to cover the cases of weakly dependent error processes and unknown breakpoints. The implementation of the tests are illustrated using output, inflation, and exchange rate data series.

Main Drivers of the Recent Decline in Italy's Non-Construction Investment

This paper examines the causes of the exceptionally marked fall in non-construction investment in Italy since 2007. Non-financial private services were the main driver of the decline in the aggregate investment rate, but all sectors weighed in negatively; the reallocation of value added away from industry was a further drag on investment. In concordance with survey findings, an aggregate model of investment indicates that even during the recent double recession the most important driver of capital accumulation was demand conditions. The user cost of capital had a substantial negative impact in the acute phases of the sovereign debt crisis, but since 2013 its contribution has been positive, thanks to the ECB’s expansionary monetary policy. The constraints on capital accumulation imposed by tight credit supply conditions were particularly severe in 2009 and 2012. Finally, uncertainty provided a sizeable drag on investment growth not only during the global financial crisis but also in the last two years. The significance of these determinants of investment is confirmed also by a disaggregated model for the thirteen manufacturing branches.

STATIONARITY TESTS FOR IRREGULARLY SPACED OBSERVATIONS AND THE EFFECTS OF SAMPLING FREQUENCY ON POWER

In this paper, starting from continuous-time local level unobserved components models for stock and flow data we derive locally best invariant (LBI) stationarity tests for data available at potentially irregularly spaced points in time. We demonstrate that the form of the LBI test differs between stock and flow variables. In cases where the data are observed at regular intervals throughout the sample we show that the LBI tests for stock and flow data both reduce to the form of the standard stationarity test in the discrete-time local level model. Here we also show that the asymptotic local power of the LBI test increases with the sampling frequency in the case of stock, but not flow, variables. Moreover, for a fixed time span we show that the LBI test for stock (flow) variables is (is not) consistent against a fixed alternative as the sampling frequency increases to infinity. We also consider the case of mixed frequency data in some detail, providing asymptotic critical values for the LBI tests for both stock and flow variables, together with a finite sample power study. Our results suggest that tests which ignore the infra-period aspect of the data involve rather small losses in efficiency relative to the LBI test in the case of flow variables, but can result in significant losses of efficiency when analysing stock variables.

Trust, But Verify. De-Anchoring of Inflation Expectations Under Learning and Heterogeneity

The paper studies how a prolonged period of subdued price developments may induce a de-anchoring of inflation expectations from the central banks objective. This is shown within a framework where agents form expectations using adaptive learning, choosing among a set of alternative forecasting models. The analysis is accompanied by empirical evidence on the properties of inflation expectations in the euro area. Our results also suggest that monetary policy may lose effectiveness if delayed too much, as expectations are allowed to drift away from target for too long. JEL Classification: E31, E37, E58, D83

Deflationary Shocks and De-Anchoring of Inflation Expectations

A prolonged period of low inflation, particularly in a situation of monetary policy rates near the zero lower bound, can heighten the risk of inflation expectations de-anchoring from the central bank objective. The purpose of this paper is to assess the effects of a sequence of deflationary shocks, such as those that hit the euro area in 2013-14, on expected/realized inflation and output. To do so we consider a simple New Keynesian model where agents, rather than being endowed with rational expectations, have incomplete information about the working of the economy and form expectations through an adaptive learning process (in the sense that they behave like econometricians, using regressions to anticipate the future value of the variables of interest). The model is simulated with euro area data over the period 2014-16 under the assumption both of rational expectations and of learning. The main findings are the followings: (i) under learning, price dynamics in 2015-16 is on average 0.6 percentage points lower than in the case of fully rational agents, as inflation expectations are strongly affected by the repeated deflationary shocks; (ii) the learning process implies a (data-driven) de-anchoring of inflation expectations from the central bank target, which would be perceived by economic agents to fall to 0.8% at the end of 2016; (iii) output expectations would also be lower in the case of learning, resulting in a slower recovery of economic activity.