4. Initial NZIER estimates of z
We were then asked to develop our own forecasting equations for advertising revenue for television and radio, exploring some of the questions raised in our peer review. The aim was to establish whether we would derive estimates of z that were significantly different to those suggested by Covec, and if so, whether our forecasts would be more reliable.
We explored a number of options for the regression equations. In particular, we considered the prospect of using some combination of a per capita income variable (GDP per capita), a population variable and a price variable to explain changes in advertising revenue.
The problem with including each of these variables separately is that they are probably correlated. Although in concept GDP per capita and population are not related (since we think of the first as being controlled for the effect of population), in practice they are inextricably linked. In fact in the sample that we used they had a correlation coefficient of 0.914.6 The reason for the correlation can be explained as economies of scale - as more people populate an economy they generate additional income directly and indirectly so that everyone is slightly better off. This makes it difficult to separately identify the effect each of these two variables has if both are included in the same regression, though the resulting estimates are not biased.
In order to get around the problem of correlation between the separate variables we chose to use a single variable that combines the three elements in which we are interested (income per capita, population and a price variable). We used nominal aggregate GDP as our single variable. This had the additional benefit of reducing the number of explanatory variables in the model and hence increasing the degrees of freedom (and our confidence in the explanatory power of our results).
We used a technique known as error correction modelling. This is generally regarded as the best way to deal with cointegrated variables. As Covec noted in their report, advertising and population are non-stationary. This means that the mean and/or variance of these variables changes over time. This is very common in economic data since a lot of series exhibit a trend. This phenomenon can be observed in GDP data. Cointegration describes a special relationship between non-stationary variables. In particular, it describes the case where a pair of non-stationary variables move in such a way that over time they do not drift too far apart. Error correction models (ECMs) exploit this relationship.
We used logarithms for all data. This allows us to interpret the coefficients as elasticities. In other words, the coefficient indicates the percentage change in advertising revenue that results from a 1% change in the value of the explanatory variable (either population or GDP).
We also examined the relationship between population alone and advertising revenue using an ECM. The aim was to compare our population-based estimates with those developed by Covec.
Once the population-based and nominal GDP-based equations were estimated, we used projections of population and nominal GDP out to 2030 to forecast advertising revenue for TV and radio.
Table 1 reports Covec's results alongside those of NZIER's initial modelling.
Table 1 Compound average annual growth in advertising revenue: Initial estimation
|Covec population model||1.95||2.02|
|NZIER population model||2.6-2.8||1.6-1.9|
|NZIER GDP model||2.8-3.0||1.6-1.9|
- The upper and lower bounds represent the compound annual rate of growth between 1990-2030 and 2010-2030. The latter is the lower figure in each case.
- The figures that we have presented for the radio-GDP model are not based directly on the model. The reason for this is that the coefficient on the error results in an over-correction (i.e. it is less than -1). The growth presented includes a manual correction for this. If the equation were used directly the forecast growth would be between 3.7%-4.1%.
While it is on the face of it surprising that there was such a marked difference between NZIER and Covec's population-based equations, there are several possible explanations:
- The data are for different years. We used the year ending in March.
- The data have been rounded. Our population estimates were in thousands.
- The data used for forecasting are different. We used Statistics New Zealand's medium population projections with an annual net inflow of 10,000 migrants.7
Using a population-based model, advertising revenue growth can be forecast at a regional level, down to growth in specific transmitter areas. This is because Statistics New Zealand's population forecasts are available at a very low level of regional disaggregation. Thus we need to consider how a nominal GDP-based forecasting methodology could also be used to determine regional advertising revenue growth.
In order to disaggregate the growth factors to a transmitter level, we could suppose that the relationships described in the national equation are invariant between regions (this assumption is also required for a population-based method).
Instead of using national nominal GDP data, transmitter area nominal GDP figures could be estimated for each region. NZIER currently forecasts regional nominal GDP for 14 regions across New Zealand. Nominal GDP per capita in the relevant regional council area could be calculated by dividing each region's nominal GDP by the regional population. This figure could then be multiplied by the relevant transmitter area population (as per the data obtained for Covec) to obtain transmitter area nominal GDP.
Essentially this assumes that nominal GDP per capita is constant within each region (across all of that region's transmitter areas). The variation between nominal GDP in each region's transmitter areas is thus due to population differences.
NZIER's initial modelling report identified some alternative modelling techniques that could be used to forecast advertising revenue growth for TV and radio. After completing this process and examining the differences in results obtained by Covec's and NZIER's population-based methods and by NZIER's nominal GDP-based method, we suggested that there was not sufficient difference between the practical results of the two equations we derived to justify adopting the more complex nominal GDP method.
6A correlation coefficient indicates the strength of the (linear) relationship between two variables. A coefficient of one indicates perfect correlation.
7Note that if we use the assumption of an annual net inflow of 5,000 migrants, the NZIER population model suggests growth of 2.0 - 2.5% for radio advertising revenue and 1.3 - 1.6% for TV advertising revenue.