2.3 Block structure and Structural equations (continued)

The domestic price variable (p^c) is the difference between the log of the domestic Consumers’ Prices Index and its trend value. It is therefore a measure of the extent to which prices are growing faster or slower than trend growth. The equation for domestic prices can be interpreted as a reduced form equation capturing mark-up on cost pricing by domestic firms and the direct price effects of final tradeable goods that are consumed domestically, similar to that estimated by Hampton (2001).

The production costs of domestic firms include prices of imported intermediate production inputs, labour costs and productivity. Labour costs are assumed to be determined by a Phillips curve that relates wage inflation to demand pressure and expected inflation. Demand pressure is proxied by the deviation of real GNE from trend (d). Expected inflation which is determined by a combination of current and lagged deviation of prices from trend (p^c). Domestic currency prices of imported intermediate goods are captured by the world price of imports (pz^w) and the exchange rate (e), while the domestic currency prices of final tradeable goods consumed locally are captured by foreign prices for exports, imports and the exchange rate (px^w, pz^w, e).

Dummy variables are used to account for the effect on domestic prices of two goods and services taxation (GST) increases in 1986:4 and 1989:3. The first dummy variable takes the value 1 in 1986:4 and zero in all other quarters; the second takes the value 1 in 1989:3 and zero in all other quarters.

Real returns on domestic equities (q), represented by the NZSE40 gross return index and deflated by the New Zealand Consumers’ Price Index, are specified as a function of contemporaneous foreign real output (y^w), foreign real asset returns (q^w) and the exchange rate (e) to reflect the globalisation of international asset markets. Real domestic equity returns are also specified as being influenced by variables considered likely to affect expectations of domestic real output growth (px^w, pz^w, y) and returns from alternative financial assets (i).

The equation for domestic interest rates (i) is intended to capture the monetary authority’s reaction function. For reasons explained in Section 3, this reaction function is modelled as a forward-looking Taylor-rule. This specification appears to successfully identify monetary policy shocks.

2.4  Data and variables

The quarterly data series used to represent the 13 variables contained within the four blocks are as follow. Foreign real output is represented by the log of trade weighted world industrial production (y^w).[7] Foreign nominal interest rates (i^w) are represented by a weighted average of Australian, United States, United Kingdom, Japan and German 90 day interest rates, where the weights are determined by the ratio of country GDP to the sum of GDP for all these economies. Foreign real asset returns are represented by the log of the Morgan Stanley World Capital Index of gross equity returns (p^w) deflated by an index of United States consumer prices.

The foreign currency price of New Zealand exports is calculated by multiplying Statistics New Zealand’s domestic currency export price index by the trade weighted exchange rate and expressed in logs (px^w). The foreign currency price of New Zealand imports is calculated by multiplying Statistics New Zealand’s domestic currency import price index by the trade weighted exchange rate, and expressed in logs (pz^w). The domestic exchange rate is represented by the nominal trade weighted exchange rate for New Zealand, expressed in logs (e).

Domestic real aggregate output is represented by Statistics New Zealand’s chained measure of production based quarterly real GDP that has been calibrated back to 1978 by Haugh (2001) and expressed in logs (y). Domestic real aggregate demand is represented by Statistics New Zealand’s chain-linked measure of quarterly real GNE backdated to 1982:2, expressed in logs (d).[8] Domestic real exports are represented by Statistics New Zealand’s System of National Accounts measure of real exports of goods and services, expressed in logs (x).[9]

Domestic prices are represented by Statistics New Zealand’s Consumers’ Price Index for New Zealand, expressed in logs (pc). The domestic interest rate is represented by the New Zealand 90-day interest rate (i). Real returns on domestic equities are represented by the NZSE40 gross return index available from Datastream, deflated by the New Zealand Consumers’ Price Index and expressed in logs (q). Domestic climate is represented by the number of days of soil moisture deficit in each quarter estimated by the National Institute of Water and Atmospheric Research Limited (NIWA) (2001), and is denoted as (c). This soil moisture variable is calculated from the daily water balance. It measures the net impact of rainfall entering the pasture root zone in the soil and that which is lost from this zone as a result of evapotranspiration or use of water by the plants.

Each data series enters the structural VAR as a deviation from long-run trend, where the trend is estimated using the Hodrick-Prescott filter, with the smoothing parameter λ=1600.[10] An exception is the climate variable which is detrended by removing from each quarterly value the long-run average value for that quarter. This is done to measure climatic conditions that differ from the normal seasonal pattern to model the impact of climatic conditions above and below the norm on the New Zealand economy. The climate variable therefore represents the soil moisture deficit level above or below the normal seasonal level. The model is estimated using quarterly data from 1983:1 to 2002:1.

2.5  Estimation

The selection of lag length was restricted to between one and four because when we estimated the model using five lags the variance-covariance matrix was singular. On the basis of both the Akaike Information criterion (AIC) and the Bayesian Information Criterion (BIC), the sample evidence for the entire reduced form VAR system suggested a lag length of one. A series of sequential likelihood ratio tests for a shorter lag length versus a longer lag length, suggested a lag length of two. A lag length of one or two is quite short compared with other New Zealand VAR studies.

Given these considerations, the reduced form VAR was estimated with three lags using Seemingly Unrelated Regression (SUR). SUR estimators were used because the inclusion of zero restrictions on some lagged variables renders ordinary least squares estimators inefficient. The Durbin H statistic suggested the reduced form VAR with three lags was absent of serial correlation.

The contemporaneous matrix, B₀ , was estimated using maximum likelihood. Initial starting values for B₀ were found using the genetic algorithm. The estimates from the genetic algorithm were then used as starting values to find the final parameter estimates for B₀ using the Broyden, Fletcher, Goldfarb and Shanno (BFGS) algorithm. As part of the sensitivity analysis, the model was estimated over sample sub-periods to test the robustness of coefficient estimates. The estimation results from different sub-periods suggested the model was robust to changes in the sample period.[11]