5    Productivity forecasts

5.1 Catching-up and the logistic function

5.2 Technical change—Estimation of the frontier

5.3 Forecasting

In this section we seek to develop projections of technological change in livestock productivity to the year 2005. We do so by making separate projections of the catching-up and technical change portions of productivity.

5.1 Catching-up and the logistic function

In the case of catching-up, we assume that the observable growth in productivity can be modelled as a diffusion process of new technologies. Previous studies (Griliches 1957 and Jarvis 1981) have shown that the cumulative adoption path often follows a logistic curve. Initially, productivity changes slowly because new innovations take some time to be adopted—usually there is the need of adapting the new technologies to different conditions to those of the country that generated the innovation. After this, a period of rapid growth is expected (e.g. as the risk of applying the new technology is reduced). This is illustrated by the case of China’s pork production in the 1990s. Finally, productivity growth slows when nearly all producers who will find the technology profitable have adopted, and the process reaches a stable ceiling.

We specify the following logistic function to represent the catching up process for each of the regions in the sample:

                                                     (5)

In this equation, the parameters and determine the shape of the logistic relationship for each region. The parameter K determines the ceiling, or maximum productivity level, to which the region in question is expected to converge. In estimating this relationship, we use actual observed values for K. These are equal to the maximum productivity value for each sector among all countries in each year.

The parameters of the logistic function are estimated by the following transformation:

                                   (6)

using an iterative Cochrane–Orcutt (C–O) procedure to correct for autocorrelation when necessary. First, a logistic functional form is assumed for all regions and the parameters estimated for periods of different length (all including the last year). The period for which the R² is higher is considered the period for which there is evidence of technology diffusion following the logistic pattern. For some of the regions, the logistic functional form clearly does not describe the diffusion process. According to the results, the regions can be classified in one of the following categories:

• Regions with a good fit of the logistic (high R², highly significant and positive coefficients) were assumed to exhibit diffusion processes of new technology following this pattern.
• Regions with high productivity that resulted in poor fits of the logistic (low R² and non-significant coefficients) were considered ‘frontier regions’. The regions under this group are Japan, EU, North America and Korea in pig production; Australia, New Zealand, North America and EU in poultry production, and Japan in beef production. In pig and poultry production, all the ‘frontier’ regions differ by less than 20% from the region with the maximum productivity value. Productivity in these regions is assumed to grow at the frontier growth rate.
• Regions that resulted in poor fits of the logistic but cannot be considered as being at the frontier, where the exponential functional form is the one that best represents the diffusion process of new technology in general. This is the case of Japan, South-east Asia and sub-Saharan Africa in poultry production and Australia, New Zealand, South-east Asia and North America in beef production.
• None of the commonly used functional forms show a good fit for the diffusion process of beef production in sub-Saharan Africa, where there is little evidence of productivity growth in the past three decades (Table 1). For this particular case, the mean productivity value for the period is used as the forecast, using the errors with respect to the mean to generate a distribution for the forecast.

5.2 Technical change—Estimation of the frontier

While we are able to use actual observations of the frontier in estimating the logistic function, when it comes to forecasting, we need some way of predicting the evolution of this productivity ceiling. We choose to make this a simple function of time, as follows:

                                                                       (7)

Results from estimation of the different models are provided in Tables 3, 4 and 5. The bottom portions of these tables show the results of the estimation procedure of the productivity frontier for pigs, poultry and beef. The coefficients of the logistic and of the exponential reflect the diffusion speed of the technology. The high speed of diffusion of new technology in China, Australia and New Zealand in pig production; China and Korea in poultry production and Korea in beef production can be related with the efficiency gains and catching up of this regions. The relatively high coefficients for Australia, New Zealand, North America and EU in poultry production can be interpreted as the speed of diffusion of new technology in the frontier. The speed of the logistic diffusion process of technology in poultry production in South America is very low probably reflecting the fact that the production ceiling for this region is far below the fitted frontier.

Table 3. Parameters and regression statistics in pig production.

Table 4. Parameters and regression statistics in poultry production.

Table 5. Parameters and regression statistics in beef production.

5.3 Forecasting

For purposes of forecasting, it is useful to have some idea of the possible distribution of outcomes, not just a single point-estimate. A distribution of the forecasts for each sector was approximated using the Efron bootstrapping method (Dorfman et al. 1990). The methodology proceeds in the following steps:

1. The residuals from the regression of Y_t on t (equation 6) are scaled by a factor of (T/(T – k))^1/2 and assigned mass 1/T.
2. ε_t* is chosen by random draw with replacement from (i) and added to the right hand side of equation (6) to generate a new vector of quantities Y_t*.
3. New parameter estimates (a^*, b^*, r^*) are generated from regressing Y_t* on t and then used to generate a forecast.
4. Steps (ii) and (iii) are repeated many times by redrawing from (i) and used to create a distribution for the forecasts.
5. To consider the effect of the frontier’s forecast in China’s productivity forecast, steps (i) to (iv) are used to generate a distribution of the frontier’s forecast. Values of K are chosen by random draw simultaneously with ε*_t in step (ii) and used in (iii) to generate the forecast.

Tables 6, 7 and 8 summarise the mean, standard deviation and implied growth rates for productivity in these sectors. Table 9 decomposes these growth rates into the portion attributable to catching-up and further decomposes that attributable to movement in the frontier. Catching-up in productivity growth is relevant in pig production in China and South-East Asia, in poultry production in China and in beef production in Korea. The change in the distance to the frontier as shown in Table 10 confirms this. In particular, productivity in China’s poultry production is expected to grow twice as fast as for pigs (9.81% vs. 4.5% per year) over the forecasted period. Compare this with the forecasted developing world total production annual growth rate of 3.0% and 2.8% for poultry and pork, respectively for the period 1993–2020 (Delgado et al. 1999). Poultry production is higher on both counts by about three times—that is, the frontier in poultry productivity is projected to grow three times as fast as for pigs over this period—and China is expected to continue rapid catch-up in poultry productivity as well. In the case of pigs, slower growth in the frontier, coupled with current levels of productivity, which are closer to that frontier (66% in 2005), translate into slower overall productivity growth.

Table 6. Productivity forecasts and growth in pig production.

Table 7. Productivity forecasts and growth in poultry production.

Table 8. Productivity forecasts and growth in beef production.

Table 9. Productivity growth decomposition 1995–2005 (percentage).

Table 10. Distance to the technological frontier.