2.3 The real exchange rate

In specifying the dynamics of the real exchange rate, I begin by setting its medium-term anchor. In the long run, the nominal exchange rate is thought to move in such a way that prices between two countries are equalised. That is to say that capital will flow between countries such that relative unit labour costs are equalised and that the relative demand for currency acts to push the nominal exchange rate so that price differentials gradually erode, albeit with a wedge arising from transport costs. Such a medium-term relationship is known as relative purchasing power parity (PPP) where, the nominal exchange rate is given by the ratio of domestic to foreign prices and a permanent wedge. Linearising around this steady state and taking logs gives the long-run PPP steady state condition,

      (2.15)

The short-run dynamics of the nominal exchange rate, e_t, are given by the uncovered interest rate parity condition (UIP),

      (2.16)

where the nominal exchange rate gap is given by the expected nominal exchange rate one period ahead and the relative interest rate between New Zealand and a foreign country.

Substituting in the real exchange rate identity, , gives the real-UIP (RUIP) condition,

      (2.17)

And solving for the real exchange rate gives

      (2.18)

Gali & Monacelli (2005) include a similar equation in their open-economy model and convergence with a steady state is achieved by iterating forward, such that the expectations term drops out of the equation. Because they linearise around long-run PPP this is consistent with agents in the economy expecting long-run PPP to hold in subsequent periods. In practise, deviations of the observed real exchange rate from that consistent with long-run PPP can persist for long periods of time and it is thought that convergence with PPP is slow. To allow for this empirical observation I include a convergence parameter, ψ_q, which weakens the pull from the steady state in the short term. Compared with the G&M model, this specification increases the responsiveness of the exchange rate to interest and inflation shocks, consistent with the high degree of volatility associated with the New Zealand Dollar.

Taking the RUIP equation, linearising around long-run PPP and introducing a convergence term gives the equation,

      (2.19)

The equation is based on the notion that, if a real interest rate differential exists, the real rate of return on domestic and foreign assets is equalised by movements in the exchange rate.The assumption of convergence with long-run PPP is consistent with more sophisticated models. For example, in macro-balance models of the exchange rate, short-run dynamics are typically governed by some version of real or nominal uncovered interest parity. But, in the medium term, the real exchange rate moves to stabilise a country's net international investment position.[13]

In this model, foreign interest rates follow an autoregressive process and, in steady-state, are equal to the steady-state domestic nominal interest rate,

      (2.20)

For the purposes of including changes in the real exchange rate in the IS relation it is necessary to have a forecast of foreign inflation. This too follows an autoregressive process and is assumed to have a steady-state rate consistent with the domestic inflation target, a similar assumption to that made by Carlin & Soskice (2010),

      (2.21)

Given the share of primary goods in New Zealand's exports, it is perhaps unsurprising that commodity price changes influence the exchange rate. To allow for the effect of persistent commodity price changes on the exchange rate, I introduce persistence to the shock term,

      (2.22)