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David Rose is a Research Advisor at the Bank of Canada. This paper has benefitted from discussions with Bob Amano, Tamim Bayoumi, Steven Braun, Paula De Masi, Bill English, Bill Lee, Tiff Macklem, Guy Meredith, Eswar Prasad, Carmen Reinhart, John Roberts, Steven Symansky, Bob Tetlow, Chris Towe, and Simon van Norden. The views expressed in this paper are those of the authors and do not necessarily reflect those of the International Monetary Fund or the Bank of Canada.
We measure output gaps such that positive values are associated with excess demand and upward pressure on inflation. Some researchers follow Arthur Okun’;s convention and define gaps the other way round.
Eisner’;s model uses unemployment gaps. He finds that a reduction in unemployment is less inflationary if the economy is booming and unemployment is initially below the natural rate than if unemployment is initially above the natural rate. The statement in the text assumes that there is a direct relationship between excess demand conditions in the goods market and excess demand conditions in the labor market.
Laxton, Rose, and Tetlow (1993a) present Monte Carlo evidence that reliance on traditional detrending techniques to measure gaps can explain why some researchers may have falsely rejected asymmetries.
Of course, asymmetry in the output-inflation nexus will have implications for other endogenous macro variables, such as interest rates. Indeed, one of concerns voiced by Chairman Greenspan is that bumping into capacity limits increases the uncertainty about future inflation and creates more volatility in financial markets.
The other countries for which Turner finds significant asymmetry are Canada and Japan. Laxton, Rose, and Tetlow (1993b) also provide evidence for asymmetry in the Canadian Phillips curve.
We focus on modelling price dynamics in this paper and our empirical work uses the output gap. This is not to deny that there are interesting issues in linking labor and output markets in macro models and discussions of inflation. However, we have chosen to keep our macro model as simple as possible and do not include a separate treatment of the labor market.
In the simulations presented in Section III, we adopt the pure intrinsic dynamics interpretation of equation (2). That is, we simulate under the assumption of model-consistent expectations and treat the backward-looking component of the equation as coming entirely from intrinsic rigidities and not expectations.
Output is measured in logarithms so that in a growing economy gaps constructed with a symmetric two-sided filter will have a zero mean in large samples.
See Eichenbaum (1990) for an excellent discussion of why econometric techniques cannot provide reliable estimates of the relative variance of demand and supply shocks. We pursue this issue in Section IV.3.
We have noted already and will argue more formally later in the paper that the extent of this shift will depend on the nature of the monetary reaction function and the consequent cyclical properties of the economy. There may be good reason to doubt that the same monetary reaction function has been operating throughout our estimation sample. However, we leave this complication to future research and interpret the estimated shift parameter as reflecting average historical behavior.
See Section IV.2 for a discussion of the statistical properties of asymmetric models when researchers fail to account for their logical implications.
This choice of lag structure does not affect our conclusions. We obtain basically the same results if we estimate an unrestricted model with 4 lags on inflation and inflation expectations or impose a triangular distribution on lagged inflation expectations.
The notional restriction on β is necessary so that α is identified under the null hypothesis. This avoids the necessity to compute a more complicated test of the restriction when there is a nuisance parameter. See, for example, Andrews and Ploberger (1994).
The simulations reported here are deterministic. Although these types of experiments are useful for developing the basic intuition behind the model, they do not do justice to the full policy implications. See Clark, Laxton and Rose (1995) for a more extensive analysis of the policy implications of asymmetry in inflation dynamics in a stochastic environment.
These simulations were carried out using the “stacked time” algorithm in TROLL. See Armstrong, Black, Laxton and Rose (1995) for a description of this algorithm and its properties.
This argument is developed more formally in Laxton, Rose and Tetlow (1993c) using stochastic simulations of a small macro model.
A good example of this is provided in Chadha, Masson and Meredith (1992). These authors present a statistical test of a restriction of an asymmetric Phillips curve to a linear formulation, which rejects the restriction at the 95 percent confidence level, but not at the 97.5 percent confidence level. Because they had placed the linear model on the pedestal, they concluded that this was not strong enough evidence to reject the simpler linear version, and they went on to do policy analysis with the linear model. Had they taken the perspective that there was good reason to put the asymmetric model on the pedestal, in view of the importance this would have for the policy analysis, the statistical evidence would likely have been interpreted as supporting the asymmetric model.
We remind the reader that we consider these tests biased. We think that the statistical case for the presence of an asymmetry is stronger than discussed here. The point here is that there is no strong case against asymmetry even in the analysis based on biased tests.
Kuttner (1991) implements a Kalmon filter procedure to provide model-consistent estimates of the gap when the Phillips Curve is linear. An obvious extension of our work is to develop a similar procedure that can be used for nonlinear models.
It is not uncommon for researchers to use such techniques and then discard level gap variables because their estimated coefficients are not significantly different from zero, despite the implications this has for monetary policy. The lack of any level gap effects in the Phillips Curve is sometimes interpreted as evidence of hysteresis.
HP filler estimates (
For an example of the segmented-trend approach, see Braun (1990), with details in Table A.2, page 302.
We thank Paula De Masi and Michael Funke for supplying us with these estimates.
This conclusion also holds if we add further lags of the relative price of oil.
We consider it self-evident that the Lucas critique is important for monetary policy analysis, that is, in counterfactual simulations where monetary policy is presumed to change. Representations of expectations with fixed-parameter, backward-looking dynamics can be dangerously misleading in such cases. We offer some examples later in this section. However, for estimation of the rest of the parameters of the Phillips curve, such representations may inefficient but still admissible.
Ericson and Irons (1995) have recently provided an assessment of the quantitative significance of the Lucas critique. These authors argue that despite the fact that most economists presume that the Lucas critique is valid, direct empirical evidence to support this presumption is rarely offered. They go on to claim that, in fact, “virtually no evidence exists that empirically substantiates the Lucas Critique.” We think that there is plenty of evidence, but that debate must await a separate paper.
In Gordon’;s model inflation expectations always lag behind actual inflation. In this model, the integral of the output gaps or unemployment gaps must always sum to zero as long as the terminal inflation rate is equal to the initial value of inflation. For this reason we follow Summers (1988) and refer to this model as the integral gap model so that it will not be confused with the natural rate model.
This observation is also consistent with measures of inflation expectations from countries that have conventional and indexed bonds and similar inflation experiences. For example, in Canada despite the fact that monetary policy has delivered 2 percent inflation for three years now, long-term inflation expectations are still around 4.5 percent by this measure.