1. Rates of Return to Wheat breeding Research in Canada: the Results from the infinite lag Model Viktoriya Galushko & Richard Gray
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

2. Does agricultural research yield a high pay-off to society?
Wheat sector in Western Canada as an example
Zentner, Peterson (1984) – 30-39%
Klein (1996) – 27-39%
Guzel, Furtan and Gray (2005) – 24%
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

3. Research Costs and Benefits
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

4. Research expenditures and Yield Index
B is the breeding effort directed at producing that specific variety, G is previously developed germplasm used in the program, K is knowledge stock existing at the time when the variety was being developed.
Breeding effort is a function of breeding expenditures over the years of the program.
I – is incremental investment that adds to the stock of knowledge. Therefore, the stock of knowledge is an infinite sum of knowledge flows at a point in time. The flow of knowledge is going to be a function of the average research productivity that is in turn a function of ‘the state of art’. The state of art is a function of past R&D expenditures including both breeding expenditures and research related to plant physiology, decease resistance, etc. Combining all of this, stock of knowledge will be a function of all past breeding and basic research expenditures.
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

5. Research expenditures and yield index
Therefore, the average yield index in year t is a function of R&D expenditures over infinite number of years
Incorporating all of the above equations into the average yield function tells us that the average yield function is a function of R&D expenditures over infinite number of years.
Specifying average index as a function of expenditures over the last 10 years only would be a significant conceptual error because that would imply imposing a restriction that after some years knowledge depreciates completely. From the econometric estimation point of view, truncation of the research lag is the same as omitting variables and any truncation will simply reduce the overall size of the stream of gross and net benefits thus producing misleading estimates of rate of return to plant breeding.
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

6. Infinite lag model estimation
Step 1: Impose structure on weights
Modified Almon Distributed Lag (Schmidt (1974))
A distinguishing feature of the equation for the average yield is that it has an infinite number of terms and obviously with finite data it is not directly estimable. So the first step is to impose a lag structure.
Modified Almon Polynomial is a combination of a geometric lag (that is always declining) and Almon lag (that is always increasing). Combining the two allows to model a desirable probability distribution for the lag structure – first increasing and then declining. This is a desirable distribution because we know that developed varieties first spread out reaching a maximum adoption at some point of time and then their popularity starts declining. Thus, we would expect the impact of breeding effort to follow a similar pattern with the initial build up before the decline.
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

7. Infinite lag model estimation cont’d
Step 2: Decompose an infinite sum into two terms: one that contains the observed sample information and the one that contains unobserved elements
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

8. Infinite lag model estimation cont’d
Modified Almon Distributed Lag:
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

9. Infinite lag model estimation cont’d
Modified Almon Distributed Lag:
Here, we’re making a substitution j=i-t
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

10. Infinite lag model estimation
Equation to be estimated econometrically:
Alpha, gamma and mu are the paratemers to be estimated. The value of lambda cannot be estimated econometrically as it enters the equation in a highly non-linear fashion. A grid search is performed over lambda: we construct the explanatory variable for different values of lambda and choose that lambda that yields the minimum residual sum of squares – this will give us maximum likelihood estimators of the parameters. As is mentioned in Maddala (1977) estimates of alpha and lambda are consistent while those of mu are not. But for the purpose of calculating the rate of return we only need gammas.
Initial conditions
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

11. Econometric estimation
Analyze time-series properties of the data
If non-stationary a cointegration test is performed:
Engle and Granger [H0: nonstationary – no cointegration]
Laybourne and McCabe (1993) [H0: stationary]
Sephton (1996) reports the critical values
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

12. Data description
Wheat yield index – Gray, Malla (2000), – author’s calculations
Wheat breeding effort (PPY)– Inventory of Canadian Agri-Food Research
Wheat breeding expenditures ($) – Klein, Freeze, Walburger (1996), extrapolated, WGRF reports
Quantity, price, CPI – Statistics Canada, CANSIM
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

13. Econometric estimation: results
Time-series properties: Both yield index and knowledge stock variables are I(1)
co-integration analysis is important!
λ=0.83
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

14. Estimation results
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

15. Estimation results: the impact of adding one PPY
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

16. Cointegration test
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

17. Benefits from wheat breeding
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

18. Does agricultural research still yield a high pay-off to society cont’d?
IRR is calculated under the assumption that one professional person year is added in 2005
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

19. Does agricultural research still yield a high pay-off to society cont’d?
IRR is calculated under the assumption that one professional person year is added every year in
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

20. Does agricultural research yield a high pay-off to society?
Returns to agricultural research are high!!!
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

21. Limitation of the study
Period of time under consideration
Lack of reliable data on wheat breeding expenditures
Pooling of all wheat classes to estimate the average yield index
We were constrained by data. We were able to construct the yield index for different classes of wheat but research expenditures were unavailable.
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

22. Conclusions
New approach: infinite lag models have never been applied to rates of return estimation
The results support the findings in the previous literature about high rates of return to wheat research.
Our estimates are a little bit higher but it is explained by the fact that we incorporate more than 50 years of impact
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS

23. THANK YOU FOR YOUR ATTENTION! 
QUESTIONS?
44th Annual CEA Conference, Quebec City, 29 May 2010
UNIVERSITY OF REGINA, DEPARTMENT OF ECONOMICS