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...shock, inflation persistence can be interpreted as the tendency of the rate of inflation to converge slowly toward its long-run value. Thus, knowledge of the degree of inflation persistence is important. Uncertainties from price fluctuations are usually associated with the degree of inflation persistence, and this is valuable information for both monetary policy and macroeconomic modeling.
Different macroeconomic models are able to generate alternative explanations for the main sources of inflation persistence (see e.g., Taylor 1980, Rotemberg 1982, Calvo 1983, Mankiw and Reis 2002, Minford et al. 2005). However, these models are generally silent with respect to what frequency the data should be sampled. Models at different levels of time aggregation are interpreted as being theoretically equivalent. In the light of this background, one relevant problem that deserves attention is the relationship between temporal aggregation and inflation persistence. By temporal aggregation we mean the process of moving from one unit of time measurement (e.g., monthly) to larger unit (e.g., quarterly). In this paper, the question we want to explore is the following: does the unit of time adopted in empirical work on inflation persistence matter and, if so, by how much?
The econometric literature has accumulated evidence showing that temporal aggregation may affect the properties and information content of the data-generating process. (2) For instance, models estimated with high frequency data (e.g., monthly or quarterly) show fewer signs of persistence than models estimated with lower frequency data (e.g., annual data). One important implication of this is that results using temporally aggregated data can be need funreliable, making it more difficult to distinguish empirically between alternative explanations of inflation persistence. For this reason, in this paper we depart from the approaches mentioned above and, specifically, concentrate on the impact of temporal aggregation on alternative definitions of inflation persistence.
In applied work the persistence of a stochastic process is determined by the Impulse Response Function (IRF), which is not invariant to time aggregation effects (see Rosssana and Seater 1995). These authors have also pointed out three main effects for a temporally aggregated ARIMA(p, d, q) process. The first effect, due to Brewer (1973), defines a limit for the MA structure of the aggregated series. The second effect, due to Tiao (1972), shows how all the AR coefficients and all but the first d MA coefficients go to zero as aggregation increases, that is, as we move from high to low frequency data. Consequently, the limiting aggregated model of an ARIMA process is an IMA(d, d). The third effect is due to small sample sizes. If the autocorrelations of the aggregated time series rise by proportionally less than n 1/2 they may become insignificant and suggest a model of order IMA(d, [d.sup.*]), where [d.sup.*] < d.
In addition to the above effects, there are three issues that need further consideration: (i) The statistical theory is not definitive because some of the results are asymptotic and leave open the question of what happens with actual data, for which the aggregation span is finite. (ii) Empirical research usually takes logs of the price level series to analyze inflation. However, the existing statistical theory of temporal aggregation applies only to unlogged data. (iii) There is no unique definition of persistence, and alternative measures of persistence might be affected differently by time aggregation and small sample effects, specially when the AR structure of the series is higher than one.
Within this context, our aim in this paper is to shed some light on the effect of time aggregation on inflation persistence. In particular, we use data for the United States, and to avoid the potential effects of the above-mentioned issues on our empirical application, we also run Monte Carlo simulations with artificially created data.
The rest of the paper is organized as follows. Section 1 describes alternative measures of persistence commonly used in the literature. Section 2 presents the results, and Section 3 gives the conclusions.
1. ALTERNATIVE MEASURES OF...
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