5. Re-estimation of NZIER model

5.1 Key discussion points

5.1.1 Explanatory variables

5.1.2 Econometric techniques

5.1.3 Re-Estimation of NZIER equations

The final stage in the process was to discuss with Covec how our differing forecasts might be reconciled in order to produce a set of estimates for z that would be acceptable to MED from both a theoretical and practical point of view. During these discussions, NZIER re-estimated the forecasting equations using identical data sets.

5.1 Key discussion points

5.1.1 Explanatory variables

It was agreed that a population-based model should be used to estimate z.

5.1.2 Econometric techniques

In their original report of October 2003, Covec used an econometric technique known as ordinary least squares (OLS) to estimate a linear relationship. NZIER embraced a slightly different approach, known as error correction modelling.

Stated in very simple terms, OLS estimates relationships between two or more variables of interest - in this case, advertising revenues and population. Covec used a linear model. Data on each variable were fed into a statistical program, which estimated a linear equation showing how the dependent variable (advertising revenue) is correlated with the explanatory variable (population). Population forecasts were then used in conjunction with the estimated equation to derive forecasts of advertising revenue in 2030.

Error correction models (ECM) can also use OLS. They also start by estimating a relationship between two or more variables - once again, advertising revenues and population. However, they then estimate a second equation, relating the dependent variable to the error on the first equation (i.e. the difference between the actual value and the estimate from the first equation). This second equation is often called the "error correction equation". It seeks to explain how a temporary "disequilibrium" between the dependent and explanatory variables is resolved. ECMs are therefore useful when one wishes to understand short-run dynamics or if forecasts are required over relatively short timeframes.

The choice of either a linear regression or ECM as the final modelling method is often a case of modeller preference. Indeed, they usually produce fairly similar results. When selecting an approach, the modeller must take into account the objectives of the exercise, which in this case was to obtain the most accurate possible forecast of advertising revenues out to 2030.

5.1.3 Re-Estimation of NZIER equations

In NZIER's initial forecasting exercise - presented in section 4 of this report - we attributed the reasons for the difference between our results and those of Covec to a combination of:

• Rounding of the data
• The definition of a year (i.e. calendar or March years)
• The data (explanatory variables) used for forecasting.

Following discussions with Covec related to these issues, we re-estimated both sets of equations using data from Statistics New Zealand (previously data had been obtained from the Economist Intelligence Unit). By ensuring that both regressions used identical data and assumptions, any differences in results could therefore be solely attributable to the difference modelling techniques.

In our re-estimation we used calendar years, rather than the March years we used in our initial estimation. We also used population projections for our forecasts that incorporate a net inflow of 5,000 migrants, as opposed to the 10,000 inflow employed in our initial estimates. Finally some other minor differences related to rounding were eliminated.

The advertising revenue growth forecasts resulting from the re-estimated model are shown in Table 2.

Table 2 Compound average annual growth in advertising revenue: Revised estimates