5  Monetary conditions

5.1  Inflation

A change in the model since documentation in Szeto (2002) is inflation (inf) is now forecast as separate tradable (inftr) and non-tradable components (infnt). These components are then weighted (based on the respective weightings in the CPI) to give an overall inflation figure. The inflation equations in NZTM are similar to the Reserve Bank's Forecasting and Policy System (see Hargreaves et al., 2006) with the key exception that expectations are assumed to be formed differently in the two models (see section 5.2).

where infnt_c and inftr_c are the average non-tradable inflation rate and the average tradable inflation rate respectively.

Non-tradable inflation depends on inflation expectations (infe) and the first and second lags of the output gap (lgap),[17] implying firms set their domestic prices on what they expect inflation to be plus any adjustment firms choose to make based on demanded resource pressures. The delayed response of inflation to resource pressures (ie, output gap) reflects sticky prices. Sticky prices in response to resource pressures arise because the costs of changing prices mean that firms are reluctant to change prices too often. The term algap introduces asymmetry into the Phillips curve relationship (the relationship between the output gap and inflation) meaning an increase in a negative output gap will have less impact on inflation in absolute terms than the equivalent increase in a positive output gap (see Razzak, 1997, for evidence of such a relationship in the New Zealand context).

where inf_tar is the central bank's inflation target andif lgap>0 then algap = lgap otherwise algap = 0.

Tradable inflation depends on changes in the exogenous world price of intermediate imports (pimof) and consumption imports (pimcf), the trade-weighted exchange rate (etwit), inflation expectations and the output gap. Inflation expectations are included to reflect that importers do have some price-setting ability (or more correctly, margin-setting) based on what they expect price changes to be. The output gap is assumed to influence tradable inflation given that a lot of non-tradables resources are involved in distributing and retailing tradable goods within New Zealand − therefore pressure on New Zealand resources can influence the domestic price of imported goods sold here. The coefficient (pa20_5) on inflation expectations is set at 0.5 in NZTM, compared to 1.0 in the Reserve Bank of New Zealand's Forecasting and Policy System (Hargreaves et al., 2006) reflecting a different judgement on the relative impact of domestic versus international influences on tradables prices.

where α=0.15 and β=(0.18/4)

Note that inflation sourced from imports is disaggregated into inflation that comes from consumption good imports and inflation from intermediate imports. As discussed, previously NZTM assumed that all imports were intermediate materials in the production process, meaning it did not explicitly model imported consumption goods and services. One clear advantage of the inclusion of consumption imports is that it allows a way that fluctuations in imported consumption goods prices can influence inflation. The importance of the impact of consumption import prices on inflation cannot be understated. The early part of this decade was characterised by the emergence of China and other economies (for example, India) as exporters of low-priced goods and thereby lowering inflationary pressures in countries that import from them, such as New Zealand.

The tradables inflation equation imposes a restriction that a 1% increase in the nominal exchange rate has the same long-run effect on CPI as a 1% decrease in world import prices. Combining all the coefficients suggests that a 10% increase in the nominal exchange rate would lead to about a 0.2% decrease in CPI within the first quarter and a 0.8% decrease in CPI in the long run.

5.2  Inflation expectations

Inflation expectations (infe) are formed by a weighted average of current inflation and inflation expectations one period ahead (weighted 0.05 and 0.95 respectively).

The inflation expectation process in NZTM is based on the expectations theory of the term structure of interest rates. In particular, the expectations theory of the term structure of interest rates states that the yields on financial assets of different maturities are related primarily by market expectations of future yields, otherwise arbitrage is possible. For example, if the risk premium is zero (or constant) then the expected 40-quarter (ie, 10 year) nominal interest rate is equal to the average over the next 40 quarters of the one-quarter interest rates expected to prevail. If this did not hold (for example the long-term 10-year rate was lower) one could simply borrow at the 10-year rate and invest continually in short term rates and make a riskless profit. NZTM slightly modifies this theory to simplify computation, as well as removing the artificial cut off dates by giving expectations further into the future less weight (rather than equal as implied by the theory). Powell and Murphy (1997) show that under the assumptions outlined above:

where b is the distributed lead (as opposed to lag), rl is the 10-year interest rate, rcs is the 90-day rate and E is the expectations operator. Powell and Murphy (1997) show that under certain assumptions (namely the mean lead is 20 quarters) b is equal to 0.95.

Assuming a constant real interest rate equation and remembering the nominal interest rate is equal to the real interest rate plus inflation expectations, it can be shown that:

This is the NZTM inflation expectation process.