6.2  Estimates based on the Koyck transformation

The insignificance of the weather variable in both the PIM and Koyck models could be due to the fact that weather only has a short-run impact on productivity in the agricultural sector, whereas we are estimating long-run relationships. Another possibility for the insignificant results is the use of MFP as the dependent variable – if weather has an equal effect on both outputs and inputs, this effect will be netted out when MFP is used.

Table 6 summarises the results from running the regression model using a Koyck transformation. Again we have run the model including and excluding the human capital and the dummy variable for structural change. As with the PIM models above, the dummy variable is always significant, suggesting that there could be a structural break in the data following the reforms. Again, the coefficient on the domestic R&D variable becomes significant when we exclude the human capital index from the regression.[30] The coefficient on the human capital index is never significant. The foreign spill-in variable is again significant for all six models, with an elasticity ranging from 0.10 to 0.14.

We also ran the Koyck transformation specification using education enrolment numbers instead of our human capital index (which is itself constructed from education enrolment numbers). This way we could also have all current and past enrolment levels included in a similar way to the research variables, if we assume that the decay parameter is the same.

We found that by including human capital in this alternative way, domestic R&D remains significant, although the contemporaneous effect of education on MFP is not significant. This is to be expected since the variable is enrolment numbers so will affect MFP with a lag. Thus it is more informative to look at the sum of the current and past enrolment rates by using equation (14), just as it is more informative to look at this sum for the domestic and foreign research variables.

Looking at these long-run estimates, we can see that foreign research is always significantly different from zero, while domestic research is significant in all but one of the models (it is not significant when human capital is included, but is significant when the dummy is added to the equation, even when human capital is still included). That is, once all of the past effects of research on productivity are taken into account, there is a significantly positive association with productivity. However, education is not significant even when we take into account the past effects on MFP. The elasticity of MFP with respect to domestic R&D, once all lags are accounted for, ranges from 0 to 0.21. The long-run elasticity with respect to foreign research ranges from 0.23 to 0.39. The corresponding implied rate of return to domestic R&D lies in the range 0 to 25%, once all of the effects of the R&D expenditure on subsequent output are taken into account.[31] Note that these Koyck models imply a depreciation rate of between 32% and 44%. Once again the weather variable is never significant and extension is always negative, and significant in 2 of the 6 specifications.

The insignificance of the weather variable in both the PIM and Koyck models could be due to the fact that weather only has a short-run impact on productivity in the agricultural sector, whereas we are estimating long-run relationships. Another possibility for the insignificant results is the use of MFP as the dependent variable – if weather has an equal effect on both outputs and inputs, this effect will be netted out when MFP is used.

Note: The coefficients for domestic R&D are computed using equation (15) and its counterpart for the foreign R&D.

Note: The asterisks indicate the degree of significance of the estimated coefficient; *** = 1%; ** = 5%; * = 10% and an absence of asterisk indicates the coefficient was only significant at more than 10%.

a: Significance levels for these long-run coefficients have been calculated using the delta method.

b: This tests whether the coefficient restrictions on the lagged variables in equation (16) (e.g. the coefficient on the lagged weather variable is equal to the coefficient on the weather variable multiplied by the coefficient on the lagged MFP variable) are true. The Wald statistic measures how close the unrestricted estimates come to satisfying the restrictions under the null hypothesis.

The coefficient on the extension variable is consistently negative. Based on concerns that there may be a serious discontinuity in the data (see Figure 2(b)) we re-estimated model 1 using data for a reduced sample period (1926-27 to 1983-84) which eliminated the period of the apparent break in the data series. However the results were similar to those found with the full sample period.

To some extent, the dummy variable could also be picking up this drop in extension numbers after 1984, as well as the drop in enrolment numbers which occurred around this time (as well as the effect of the reforms on agricultural productivity). In short, these changes were in themselves reflections of the many structural reforms that were taking place in the New Zealand economy, and it is not possible to isolate their separate effects within our models.

Figure 4 plots the dependent variable (the log of MFP) against its predicted values using Model 2 in Table 6. The model was run up to 1990 and then out of sample forecasts were computed. The model is found to perform well in this out of sample forecasting, predicting the variable nature of MFP after 1990, recognising that the model contains the lagged value of productivity as an explanatory variable.

Figure 4: Agricultural Productivity: Actual Versus Values based on estimation up to 1990 with projected values beyond 1990