2.2 The Phillips curve

The New Keynesian Phillips Curve (NKPC) relates current inflation to expectations of future inflation and marginal cost pressures. That the inflation process is forward-looking follows from the price-setting behaviour of firms, which is assumed to follow Calvo (1983). The basic premise is that in each period a firm has a fixed probability that it will keep its prices unchanged, so firms set prices now with a view to the future because they know that they may not be able to change their prices in the subsequent period.[9] The probability of changing/not changing price each period is independent of the time elapsed since the firm last changed its price, and this attribute simplifies the aggregation of individual firm behaviour to the whole-economy level. This gives an equation of the form,

      (2.11)

where is the rate of inflation and is the expectation of inflation conditioned on information available at the current time.

I assume that real marginal cost pressures drive the inflation process, consistent with Gali & Gertler (1999) and that these cost pressures are well-represented by the output gap, . There are other measures which could be used - Batini et al. (2005) use the labour share of income in their estimate of the Phillips curve, which has the advantage of being directly observable.[10] But using the labour share for forecasting with this model would not be possible because it does not capture the evolution of the labour market, so the output gap is preferred. The error term, , is an independent, identically-distributed inflation shock.

As with the IS relation, the purely forward-looking version of this equation fits the data poorly - failing to capture the observed inertia of inflation. The equation specification implies that persistence in either movements in the output gap or changes in inflation expectations could produce an inertial path for inflation, but leaves open the possibility of large jumps. It also implies that inflation should lead the output gap, which is the opposite of what we observe in the data; both empirical evidence and conventional wisdom suggests that monetary policy affects inflation only with a lag, rather than instantaneously.[11]

A model that does not adequately capture the persistence of inflation would not fit the data and have misleading simulation properties. Therefore, in what follows, I relax the restrictive assumption that households and firms are completely forward-looking and anchor expectations of inflation to the middle of the Reserve Bank's target range.

The hybrid version of the New Keynesian Phillips Curve, used in a number of empirical estimates of the equation (Gali & Gertler,1999) modifies the standard NKPC formulation by allowing a proportion of firms to use a rule of thumb when setting prices, consistent with a degree of indexation in price setting. This modification provides a theoretical justification for the presence of an inflation lag in the first order condition of the NKPC. Intuitively, the inclusion of lags of inflation serves to act as a proxy for the rational expectation of future values of the driving variable. The resulting equation therefore includes a backward-looking term and a coefficient, β_π, that determines the weight placed on past inflation relative to inflation expectations in the inflation process,

         (2.12)

The restriction placed on the inflation coefficients summing to unity (effectively imposing a discount factor of one) means that money is super-neutral in this model. It also implies that the coefficient, β_π, can be interpreted directly as the proportion of firms in the economy that set prices in a backward/forward looking manner.

In this paper I take a slightly different approach to the Gali & Gertler set-up and adopt the prior expectation that agents in the economy expect that monetary policy is able to return inflation to target at some time horizon (typically assumed to be around two years). Therefore, I use equation 2.12 and set equal to the inflation target, π*,

     (2.13)

To allow for the effect of exchange rate pass-through to prices, I include lags of the change in the real trade-weighted exchange rate.[12] That the Phillips curve can be augmented in this way is demonstrated formally in Batini et al. (2005) and Gali & Monacelli (2005).

Finally, linearising around the target rate of inflation gives the Phillips curve in 'inflation gap' terms.

       (2.14)