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...relationship, nonlinear Phillips curve. To accommodate this potentially important departure from linearity, a vector autoregression (VAR) model of output, inflation, and the terms of trade is augmented with logistic smooth transition autoregression specifications. My empirical results indicate that the model captures the nonlinear features present in the data well. Based on this nonlinear approximation, the output costs for reducing inflation are found to vary, depending critically on the state of the economy, the size of intended inflation change, and whether policymakers seek to disinflate or prevent inflation from rising. This implies that inferences based on the conventional linear Phillips curve may provide misleading signals about the cost of lowering inflation and thus the appropriate policy stance.
1. Introduction
One of the key costs of achieving low inflation is the short-term output loss that generally accompanies a permanent decline in inflation. Particularly stark examples of this output cost were seen in the early 1980s and 1990s where disinflations in both periods were accompanied by severe recessions. Obviously, policymakers' decisions on the timing and extent of inflation reduction depend on balancing the costs and benefits of moving to a new, lower level of inflation. The issue has become more relevant since the beginning of the 1990s, when several countries, including Australia, explicitly committed themselves to low inflation targets. With the advent of this inflation targeting regime, an increasingly important issue is the output cost of preventing inflation from rising. As incipient inflation pressures gain momentum, tighter monetary policy can slow the economy and thereby preemptively forestall the rise in actual inflation. This could avoid costly recessions down the track, but slower output growth would be the cost of resisting inflationary pressures. Together, these two output costs of fighting inflation play important roles in determining how to seek further disinflation toward price stability and how best to maintain low inflation. Undoubtedly, only with accurate measures can the net benefits of fighting inflation reliably be assessed.
A standard approach in the literature is to use the Phillips curve and estimate the so-called sacrifice ratio, which measures how much output would be lost by lowering inflation one percentage point. Traditionally, this short-run trade-off between output and inflation is assumed to be constant under the proposition that the shape of the Phillips curve is linear. However, a strand of the theoretical literature suggests the nonlinear nature of the Phillips curve. Empirical evidence supporting a variety of asymmetries in the output-inflation relationship has also mounted in recent times. Ball (1994) and Jordan (1997), for example, find that the output costs for reducing inflation vary with the states of the economy for the majority of OECD countries, including Australia. In these studies, they identified periods of disinflation and inflation episodes a priori and then estimated the output costs for each period separately. Recently, Filardo (1998) presents a more general approach by employing nonlinear modeling a long the line of Tong's (1983) threshold autoregression models. In this setup, the data itself define different regimes and determine the transition process between the regimes. The output costs of lowering inflation are allowed to vary with the signs and sizes of the shocks and the initial strength of the economy. With application to the U.S. data, he finds that the output costs of lowering inflation are indeed dependent on those factors.
The purpose of this paper is to extend Filardo's study to the case of Australia. There is a key difference, however. My vector autoregression (VAR) model is constructed to accommodate a potentially important departure from linearity through a logistic smooth transition autoregression (LSTAR) specification. The LSTAR specification allows the model to alternate between different regimes, with linear and discrete nonlinear cases as extreme ends. Importantly, the transition is carried out in a smooth manner so that there can be a continuum of states between the regimes. This contrasts with Filardo's model, where regime switching is discrete. The use of an LSTAR model in this paper is particularly justified by the fact that slow adjustments in inflation and consumers' expectations are the main reasons for the output cost of lowering inflation. Inflation tends to move slowly over time, generating a great deal of persistence and inertia. Consumers' expectations may also adjust slowly over time, perhaps being based o n some sort of adaptive mechanism. Because decisions about wages and prices depend on expectations of future changes, slow adaptation is self-fulfilling, creating inertia. Further, consumers may exert different degrees of inertia and so will adjust with different time lags. When considering aggregate behavior, the time path of regime changes is likely to be better captured by a model that permits gradual rather than instantaneous adjustment.
My baseline VAR model consists of real GDP, the inflation rate, and the terms of trade in line with Gordon and King (1982), Cecchetti (1994), King and Watson (1994), and Cecchetti and Rich (1999). The additional inclusion of the terms-of-trade variable in the model is motivated by Schelde-Anderson (1992) and Ball (1994), who identified the changes in that variable as a potentially important factor influencing the output costs through the inflationary process.' The model is assumed to be characterized by three structural shocks: a terms-of-trade shock, a domestic supply shock, and a domestic demand shock. Following previous studies, the output cost of lowering inflation is defined as a ratio of the output response relative to the inflation response with respect to an innovation to domestic demand. Hereafter, this is referred to as the cost of fighting inflation (COFI) ratio, following Filardo. Calculation of the COFI ratio then requires identification of the structural shocks in the model. In this paper, I ext end the identification procedure by Shapiro and Watson (1988) to the case involving LSTAR specifications. The underlying shocks in the model are identified by imposing long-run restrictions and exogeneity conditions of the type used for VAR models. In their paper, King and Watson (1994) find that structural estimates on the Phillips curve are quite sensitive to the directions of contemporaneous restrictions imposed for identification. Using long-run identifying restrictions will allow the data to determine the contemporaneous interactions between the two rather than imposing them a priori. This also differs from Filardo's paper, which adopted Cholesky-type contemporaneous identifying restrictions.
The remainder of this paper is organized as follows. Section 2 presents some preliminary analysis on the output-inflation relationship, together with discussions of the issues the paper seeks to answer. Section 3 discusses a structural model that constitutes my empirical analysis. The empirical results of this study are given in section 4. Section 5 draws policy implications from the empirical results and presents some conclusions.
2. Some Preliminary Considerations
In their paper, King and Watson (1994) find that for postwar U.S. data, the Phillips correlation between inflation and unemployment is alive and well, once one recognizes that it lives at the business cycle frequencies. After decomposing both data into three parts using the Baxter and King (1995) band-pass filter, there is a remarkably strong presence of this correlation at business cycle frequencies that is masked by low (i.e., trend) and high (i.e., irregular) frequency components. Figure 1 shows the results from passing real GDP and the (annualized) inflation rate of Australia through the same band-pass filter that isolates fluctuations at business cycle periodicities, six quarters to eight years. Also depicted in the figure is a dating scheme for Australian business cycle fluctuations constructed by the Melbourne Institute of Applied Economic and Social Research (MIAESR) at the University of Melbourne. (2) The shaded areas measure the time between the peaks and troughs of Australian growth cycles. Note th at by viewing the band-pass-filtered data as deviations from a local trend, I applied growth cycle peak and trough dates rather than classical cycle peak and trough dates. See Harding and Pagan (1999) for a detailed exposition of this distinction.
Figure 1 suggests that the Australian experience accords with King and Watson's observation. The cyclical components of the series vary, as the Phillips curve would suggest, with real GDP and the inflation rate falling in most cases during the MIAESR-dated growth recessions. To shed more light on this, Table 1 reports the cross-correlation coefficients of cyclical inflation at various lags and leads with cyclical real GDP. I also considered several subsamples to look at the stability of the relationship, including the break point of 1973:Q3, which was chosen to reflect the first major oil shock in October 1973. Looking at the full sample first, the presence of the Phillips curve relationship between GDP and...
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