6.3 Estimates using an Almon lag structure
Table 7 summarises the results from running equation 10 using second order polynomials for both domestic and foreign research. The lag lengths were chosen by first searching over all lags from 1 to 60 years (except when the dummy was included which meant it was only possible to search up to 55 lags). This involved running up to 3,600 regressions for each model to allow for every possible combination of domestic and foreign lag lengths. The search over lag lengths was conducted without fixing the sample period. The effects of fixing the sample period compared to allowing the sample period to vary according to the lag length is discussed below. The combination of lag lengths which gave the minimum value of the Akaike Information Criterion (AIC) was chosen as the preferred model.
When human capital is excluded, the sum of domestic R&D lags is negative and not significant, but becomes significant when the dummy is included. The sum of the lags of US patent numbers is always positive and significant, affecting New Zealand agricultural productivity even after 59 lags (when the dummy is not included). However, when human capital is included, the number of lags on this foreign research variable which effect MFP shortens to 13, while domestic R&D still affects MFP after 59 lags, compared with only 17 lags when human capital is not included. This indicates that the results are subject to considerable variation depending on the particular specification of the model.
The results are also sensitive to the choice of lag length. For example, if we instead of the AIC we were to chose the optimal lag lengths using the adjusted R-squared of each model, for Model 2 (i.e. excluding human capital and the dummy variable) we obtain a positive and significant number for the lagged contributions of domestic R&D (0.25), with a lag length of 24, as well as a positive and significant number for the sum of the lagged contributions for foreign patent numbers (0.21), although only with a lag length of 1. For model 1 (when we include human capital), human capital is negative and significant (with a coefficient equal to -0.55), and domestic R&D is positive and significant, with contributions over a period of 37 years (and the sum of the lagged contributions equal to 0.97). The sum of the contributions from our foreign spill-in variable becomes negative and significant (-0.83), with a lag length of 15.
We also ran this model by using a first order polynomial for the lags of the education variable (see models 5 and 6 in Table 7). The sum of the contributions from both domestic and foreign research become insignificant when we include human capital in this way, while the sum of the lagged contributions from education is significant in both models.
|Model 1||Model 2||Model 3||Model 4||Model 5||Model 6|
|No. of lags : domestic||59||17||12||11||46||46|
|No. of lags: foreign||13||59||54||54||32||32|
|No. of lags: education||31||31|
Note: The coefficients for domestic R&D, foreign R&D, and education are computed as the sum of the coefficients on the individual lags.
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%.
When estimating models with different lag lengths the sample period varies according to the length of the lag as observations are lost from the start of the series to accommodate the lagged effect. It is therefore possible that differences which might appear to arise from different lag lengths in fact arise from different sample periods.
Table 8 compares the results of regressions using the Almon second order distributed lags when we fix the sample period and when we allow the sample period to vary. We have minimised the search over different lag lengths by restricting both the domestic and foreign research variables to have the same lag length. Again, the number of lag lengths which gave the minimum value of the Akaike Information Criterion (AIC) was chosen as the preferred model.
Table 8 shows that fixing the sample period can have a large effect on the number of lags chosen as the preferred model. In turn, the lag length appears to change the results significantly. For example, in Model 1, when we use a fixed sample period for the regression, a lag length of 18 years is chosen as that which minimises the AIC, resulting in a significantly positive coefficient on foreign R&D and human capital. Alternatively, when we allow the sample period to vary with the lag length, the AIC suggests a lag length of 59 years, with a negative and not significant coefficient on both foreign R&D and human capital. This highlights the sensitivity of results to the lag specification.
|Model 1||Model 4||Model 5|
|Fixed Sample||Unconstrained Sample||Fixed Sample||Unconstrained Sample||Fixed Sample||Unconstrained Sample|
|No. of lags : domestic||18||59||34||45||24||59|
|No. of lags: foreign||18||59||34||45||24||59|
|No. of lags: education||24||59|
- Only searching over 46 lags due to memory constraints in eviews.