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Returns to beef research in Canada: A comparison of time series and mathematical programming approaches
AgriculturalSystems46 (1994)443-459 © 1994Elsevier Science Limited Printed in Great Britain. All rights reserved 0308-521X/94/$07.00 ELSEVIER
Returns to Beef Research in Canada: A Comparison of Time Series and Mathematical Programming Approaches K. K. Klein The University of Lethbridge, Lethbridge, Alberta, Canada, T1K 3M4
B. Freeze* Agriculture Canada Research Station, PO Box 3000, Main, Lethbridge, Alberta, Canada, T1J 4B1
J. Stephen Clark Nova Scotia Agricultural College, Truro, Nova Scotia, Canada
& G. Fox Department of Agricultural Economics and Business, University of Guelph, Guelph, Ontario, Canada, N1G 2Wl (Received 5 March 1993; revised version received 10 November 1993, accepted 25 November 1993)
ABSTRA CT A general equilibrium sectoral model of Canadian agriculture was used to determine whether economic payoffs from investment in beef research might be more completely estimated with mathematical programming than with traditional time series analyses Using this approach, estimated rates of return to beef research were significantly lower than those estimated in earlier studies that used an econometric approach. At a 5% discount rate, benefit-to-cost ratios generated were 37 to I for unadjusted beef research and 30.4 to I for beef research adjusted for concomitant effects of crop research. These compare with a benefit-to-cost ratio of about 48 to 1 in * To whom correspondence should be addressed. This paper is Lethbridge Research Station Contribution no. 3879296. 443
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox earlier econometric studies. Flexibility of the mathematical programming approach provides an opportunity to estimate various secondary impacts of specific agricultural research programs, including regional payoffs, environmental externalities, and interactions with agricultural policies and programs.
BACKGROUND
AND OBJECTIVES
Estimation of the returns to public investments in agricultural research began with the work o f Schultz (1953). Griliches' w o r k on hybrid corn in 1958 followed in this tradition . Since these early studies, an enormous literature has evolved (Ruttan, 1982). F o r the most part, rates of return on agricultural research have been found to be high, much higher than those determined for many other public investment opportunities. R u t t a n 1980) argued that public investments in agricultural research in the United States have generated exceptionally high returns and that these returns contrast with the perception o f public sector inefficiencies. As an example, estimates o f the returns to Canadian public sector agricultural research have been made since the late 1970s. Estimates o f rates of return for Canadian public agricultural research have been found to be high but variable (Table 1). TABLE 1 Summary of Canadian Return to Research Studies Study Nagy & Furtan, 1978 Farrell, Funk & Brinkman, 1984
Commodity
Period
Ulrich, Furtan & Schmitz, 1985
Rapeseed Corn Wheat Barley Canola Rapeseed Wheat Wheat Rapeseed Barley Alfalfa Malt barley
1951-1981
Brown-Andison & Brinkman, 1986 Haque, Fox & Brinkman, 1989 Widmer, Fox & Brinkman, 1988 Horbasz, Fox & Brinkman, 1988 Zachariah, Fox & Brinkman, 1989 Huot, Fox & Brinkman, 1989
Dairy cattle Laying hens Beef cattle Sheep Broilers Swine
1968-1984 1968-1984 1968-1984 1968-1984 1968-1984 1968-1984
Ulrich, Furtan & Downey, 1984 Zentner & Peterson, 1984 Ulrich & Furtan, 1985
1960-1975 1984-2003
1951-1981 1946-1979 1950-1983
Rate of return 101% 20-22% 41% 1540% 17-21% 51% 34-39% 29% 51% 22% 14% Public 50% Private 74% 115% 81-98% 66% 25% 61% 50%
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Previous studies on the social benefits of agricultural research have used an econometric approach based on time series data on outputs and inputs, including research expenditures (Nagy & Furtan, 1978; Zentner & Peterson, 1984; Funk & Farrell, 1985; Horbasz et al., 1988; Widmer et al., 1988; Haque et al., 1989). This approach has several well-known limitations, including the usual need to specify variables in an aggregate manner to preserve degrees of freedom for statistical testing. An alternate approach to estimation of benefits from agricultural research is the use of a general equilibrium industry-wide mathematical programming model. A mathematical programming approach provides virtually limitless opportunities for output and input disaggregation and permits a more thorough analysis of indirect, as well as direct, impacts of agricultural research activities. Chang et al., (1991) used this approach to analyze the potential benefits of rice research, with and without government programs. The overall objective of this study was to assess the usefulness of mathematical programming in estimating returns to investment in agricultural research, using beef research in Canada as an example. Data used in a previously published econometric analysis of returns to investments in beef research in Canada (Fox et al., 1987a) were inserted in a regional linear programming systems model of Canadian agriculture. This permitted a direct comparison between the two approaches. In addition, the process involved in transforming the time series data into input-output coefficients suitable for use in the linear programming model focused attention on the assumptions inherent in both approaches.
The econometric approach Measurement of yearly changes in consumers' and producers' surpluses forms the basis of the econometric approach. A supply function for the commodity is estimated with quantity supplied as a function of several independent variables including lagged research expenditures. Supply is estimated for each time period, with and without research expenditures, to establish a sequence of annual benefits and costs from research. Various net benefit measures, such as net present value, internal rate of return and benefit-cost ratio, can then be calculated. Net present value is the discounted value of the benefit stream minus the discounted value of the cost stream based to the earliest time period in which research expenditures occurred in the data series. Regression analysis is used to estimate parameters of the supply function. The supply function is generally represented as QS = f ( p , G, E, R,_k, T)
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
where Q~ is the level of output in a particular time period, P is a vector of relevant product and input prices, G consists of variables reflecting the impact of government policies, E represents environmental variables such as weather, Rt_k is research expenditures in past time periods, and T consists of other technology-related variables such as levels of education or information. Time series data are used to estimate parameter values for each of the above types of variables once a specific algebraic representation of the supply function is chosen. Many studies have compared the results of variations in the algebraic representation of supply (Fox et al., 1987a,b; Haque et al., 1989). The purpose of the regression analysis is to separate effects of research expenditures on industry output from many other factors that can influence supply. Because the econometric approach uses historical data, estimates are based on what has actually occurred in the industry. The lag structure associated with the development, adoption and obsolescence of new technology is estimated directly, without the use of subjective interview data. Results can be readily compared with the international literature, since this has been the most frequently employed approach. Estimates of returns at the industry level are usually interpreted as average effects from all research activities, including unsuccessful projects. The main limitation of the econometric approach relates to the problem of aggregation. Most studies have focused on single commodities for large regions or whole countries. It is well known that technological change can create ripple effects across markets and within regions. For example, improvements in feed efficiency of beef cattle shift the demand for forages and feed grains. Variations in the supply and price of beef could influence demand and prices in hog markets. Regional patterns of adoption of a new technology can influence the distribution of gains from research. It is difficult to incorporate these interactions into the analysis when using the econometric approach. A second limitation of the econometric approach is that it is difficult to correctly account for all factors that can shift the supply function for a given commodity. Since the inception of empirical analyses of research investments, researchers have attempted to ensure that effects of supplyshifters, such as improvements in the level of education and experience of farm operators, are not falsely attributed to research and technological change. A third limitation of the econometric approach is in the interpretation of results. Not only are results dependent on assumptions employed, they are usually not easily understood by research administrators and research funding agencies Moreover, due to the aggregate nature of variables,
Returns to beef research in Canada
447
econometric analysis usually give no clear prescription of what to do next. For example a high estimated return to beef research gives no indication of what kinds of beef research should be conducted, or even if more expenditures should be devoted to beef research. As a consequence, many econometric studies of returns to agricultural research have largely been seen by research administrators and budget committees as interesting but of little practical use.
The mathematical programming approach Sectoral mathematical programming models select combinations of inputs and levels of outputs to maximize the sum of producers' and consumers' surpluses for a set of interrelated markets, subject to a set of technical input/output relationships and constraints. The outcomes of agricultural research may be inserted directly as changes in input/output coefficients, as changes in product or input prices, or as changes in quality of inputs or outputs. The sector model is solved first with production costs and yields corresponding to the 'old' or 'bench-mark' technology. The costs of production and yields are then adjusted to reflect the 'new' or proposed technology and the model solved a second time. Since the objective function of the model represents the sum of consumers' and producers' surpluses in all agricultural sectors, the difference between model solutions provides an estimate of the annual net benefits to society from development of the new technology. In addition, the model may summarize net earnings of each agricultural sector so that gainers and losers among various groups of producers and consumers can be identified. The mathematical programming approach differs from the econometric approach in the way consumers' and producers' surpluses are calculated. In the econometric approach, only one market is normally considered, while in the mathematical programming approach, markets for all major agricultural products are considered simultaneously. Since these markets are closely linked, a change in one market may affect conditions in other markets. By considering all major agricultural products simultaneously, the mathematical programming approach calculates the change in consumers' and producers' surpluses in the agricultural industry as a whole, thus providing a more complete analysis of the effects of research. Finally, additional output from the mathematical programming approach allows evaluation of the distribution of the benefits in terms of commodities and regions. The assumptions inherent in linear programming also make for some disadvantages to its use in estimating returns to research Optimizing
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
behaviour is assumed and linear programming activities depend on linear, continuous functions which may not always represent production conditions in agriculture. However, the inherent problems in linear programming models may be overcome by using more complex mathematical programming procedures, such as goal programming, stochastic programming or quadratic programming. For example, the quadratic programming approach provides a way to accommodate risk in production. The flow of benefits from new research are uncertain, depending on rate of adoption, time lag and elasticities of demand. Probability distributions of net present values of benefits could be constructed by Monte Carlo simulations performed by repeated solving of the mathematical programming model. Mathematical programming also lacks statistical tests for the estimates. Unlike the econometric approach which provides the analyst with many alternatives for testing hypotheses against known probability distributions, mathematical programming estimates are merely point estimates. No information is available on their distribution. However, sensitivity analyses may be employed to provide some information on the reliability of the estimates.
CANADIAN REGIONAL A G R I C U L T U R A L MODEL (CRAM) To accomplish the study objectives, the Canadian Regional Agricultural Model (CRAM) (Webber et al., 1986) was used to estimate the total return and the rate of return to beef research in Canada over the period 1968-84. These estimates were then compared with results from an econometric study of returns to beef research in Canada conducted over the same time period, as reported by Fox et al. (1987a). CRAM is a regional linear programming model that simulates production, marketing and transportation of the major agricultural commodities produced in Canada. It optimizes production of these commodities within the constraints of available agricultural resources and final demands for products. It is a single-year model based, in its current configuration, on the calendar year 1989. Beef, hogs, dairy and poultry production in Canada is modelled in CRAM for each of the ten provinces. Low and high quality beef are produced, with low quality beef coming from the slaughter of mature dairy and beef cows and bulls. Pork primal cuts are produced in the hog sector of the model. Fluid and industrial milk products are produced in the dairy sector of the model. Eggs, broiler meat, and turkey meat are produced in the poultry sector of the model.
Returns to beef research in Canada
449
Animals are fed grains grown in the crops sector of the model: stored forage, pasture, barley and corn for beef and dairy animals, barley for hogs, and wheat for poultry. Protein supplements are treated as a cash cost. Based on relative prices and nutritional characteristics of feedstuffs, feeder animals and the beef breeding herd can be fed different ratios of feed grains and forages. The model also chooses the optimal rate of growth of feeder animals, within specified constraints. Domestic level demand is specified for low and high quality beef, pork, final dairy products, eggs, broilers and turkeys. Excess supplies can be exported. Both meat and livestock animals can be transported to other provinces and to export locations. Live beef animals can be imported either for feeding or for slaughter purposes; dressed beef products can also be imported into Canada. Poultry and dairy production are constrained by quotas established by provincial marketing boards. Production of poultry and dairy commodities are used to satisfy only domestic demands. The crop sector of the Canadian agricultural industry is represented in the model with production occurring in 29 separate regions, each having different soil and climatic condition: seven in the province of Alberta, nine in the province of Saskatchewan, six in the province of Manitoba and one in each of the other seven provinces. Crops in the model include four grades of wheat, as well as barley, oats, flax, canola, corn (for grain and silage), soybeans, tame hay, pasture and other crops. The category of other crops differs by region and represents historic production levels of minor crops such as pulses, sunflowers, potatoes, buckwheat and canary seed. The model selects the most profitable crops to be grown in each region with provision for both summer fallow and stubble planting in the prairie provinces of Alberta and Saskatchewan. CRAM selects the optimal amount of summer fallow (land left idle for a single year in a rotation) in each region of the prairie provinces on the basis of the relative profitabilities of available crops planted on summer fallow and stubble (land planted and harvested in the preceding year), with the constraint that the area of summer allow must equal the total area of crops planted on summer fallow in each region. Crops produced in each region can be used to satisfy demands for livestock feed, domestic consumption, or export. Domestic consumption of crops is fixed at historic levels. Excess supplies of each crop are transported to terminal locations (Thunder Bay or west coast) for export, with appropriate freight costs included. The prices for farm products are dependent on the quantity produced and offered for sale, as well as on demand for the product. These effects are represented in C R A M through a series of stepped demand functions established for the major categories of final agricultural products.
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
Since Canada trades all categories or grains and oilseeds, as well as beef and hogs, Canadian producers face import and export prices for these commodities. The small country assumption is used in CRAM; that is, changes in Canadian production will have no effect on world price levels. Thus, domestic prices must be between an export price floor and an import price ceiling The downward-sloping demand functions in CRAM for wheat, barley, canola, high quality beef, low quality beef, and primal cuts of pork represent price levels between the floors and ceilings. The objective of the model is to maximize consumers' plus producers' surplus. Consumers' surplus is increased when the price of food falls due to greater production. Producers' surplus is measured as the difference between gross agricultural income and costs of production plus transportation. Commodities traded internationally are valued on an export basis. Farm-level grain prices are derived by subtracting handling and transportation costs from the in-store prices at the export position.
PROCEDURES The study by Fox et al. (1987a) used economic data from the Canadian beef industry over the period 1968-84. Consumers' and producers' surpluses were estimated as a function of research expenditures for each year from 1972 to 1986, then projected to the year 2000 under the assumption that no further research was done after 1986. The present value of this 29-year stream of benefits was then compared to the present value of the 17-year stream of research expenditures by the federal government, the provincial government and industry. The present values of benefits and costs were derived for discount rates of 2%, 5% and 10%o. In this study, the mathematical programming approach allowed an evaluation of returns to beef research with and without concomitant changes in technology of feed grain crops production. Including changes in the technology of feed grain processing allows for the effects of changing crop technology on the profitability of the beef industry to be determined. For example, a change in crop technology may lower the price of feed grains and thus alter the optimal ratios of forage and grain used to feed cattle. The increases in cattle gain through the use of diets that are higher in grain might be interpreted as being due to beef research rather than due to crop research. To account for this possibility, two separate evaluations of net benefits were made using CRAM: one where changes occurred in beef technology only, and a second where changes occurred in both beef and crop technology.
451
Returns to beef research in Canada
The model was solved for production coefficients that were set to mid1960s conditions. The estimated benefits were then compared to those where production, cost and price conditions were set to levels of the mid1980s. After accounting for the costs of research, the differences in estimated net benefits between the two situations could then be calculated. Each of the situations modelled is described briefly as follows. (1) Change in beef productivity only In this situation, total beef productivity in the mid-1960s run was adjusted to be 79% of the level of that existing in the 1980s run. This was the ratio of change in heavy steer equivalents (1967 over 1984) estimated by Fox et al. (1987a). Although the mathematical programming approach makes it relatively easy to insert different productivity indices for such individual factors as conception rates, calving rates, birth weights of calves, average daily gains, slaughter rates, dressing percentage, etc., this simple gross approach was used so that changes in beef production were exactly the same as those reported in the econometric study by Fox et al. (1987a). (2) Change in beef and crop productivity Yields of crops increased considerably over the 1960-80 period (Table 2). It is possible that these changes in yields could affect returns to research in beef. Thus, for the second comparison, the change in total beef production, as in (1) above, as well as the change in grain yields were combined and the results compared for the two time periods. All other technical coefficients and prices were held constant. In the study by Fox et al. (1987a), estimates were developed for the lags in adoption of new technology by beef producers as well as the residual effects of the technology after the expiration of the accounting TABLE 2
Percentage Changes in Crop Yields from 1966-68 to 1983-85 Crop
High quality wheat Barley Forage Grain corn Flaxseed Canola Pasture
Western Canada
Eastern Canada
13.0 13.0 7.0 0-0 44-0 26-0 7.0
45.0 21.0 13.0 20.0
Source: Canada Grains Council (1976, 1987).
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
period. Costs of research from 1968 to 1984 were counted and a fouryear lag in adoption was assumed so benefits from research began to accumulate in 1972. After 1988 (four years after these authors stopped counting the costs of the research), residual benefits from the research were assumed to decrease in a linear manner, ending in the year 2000. The annual flow of net benefits from 1972 to 2000 was then discounted at three interest rates and reported in 1981 Canadian dollars. In this study, the calculated changes in net benefits represent a single year's improvement since C R A M is a single-year model. A separate calculation could be made for each year of the analysis, then a present value could be determined for the stream of benefits. For this study, however, a simpler approach as chosen. In each situation, it was assumed that benefits to beef research started in 1972, four years after research costs began, a used by Fox et al. (1987a). The calculated net benefits were linearly interpolated between zero in 1971 and their full calculated values (from the C R A M results), in 1986, then linearly extrapolated to the year 2000 in the same manner as used by Fox et al. (1987a). Following this approach, present values of each of the streams of net benefits were calculated for discount rates of 2%, 5%, and 10% (as done by Fox et al., 1987a).
RESULTS AND DISCUSSION Overall benefits The estimate of overall net benefits of research to the Canadian beef sector was $682m when only beef technology was considered, and $553m when both beef and crop technology were considered (Table 3). The value of the objective function was $677m lower with the 1960s beef technology, but $2645m lower with the 1960s beef and crop technology. TABLE 3 Estimate of Overall Net Benefits ($ Millions) to Canadian Beef Sector from Research on Beef and Crops
Change in beef technology
Change in beef and crop technology
Change in objective function Less change in government payments Less change in crop exports
677.23 2.14 -7.31
2 645.09 424.72 1 667.02
Estimated net benefits to beef sector
682.40
553.35
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Returns to beef research in Canada
However, two important adjustments were made to these changes in value of the objective function in order to obtain a more accurate estimate of the benefits from research that actually accrue to the beef sector. Government payments are modelled in CRAM as a direct injection from government with no offsetting cost to the agricultural industry. They are based on levels of output produced as well as costs and quantities of inputs used. Any change in government payments directly affects the change in the objective function and, without a corresponding adjustment, would bias the estimate of return to beef research. Since production and inputs are different for the different technologies, government payments are also different. The changes in government payments in the two modelled situations are shown in Table 4. Government payments were $2m lower under 1960s beef technology but nearly $425m lower under 1960s beef and crop technology. These changes in government payments (which can easily be handled in a mathematical programming model) provide a reminder that this important variable is often overlooked in econometric models. The objective function was also adjusted to account for the change in crop exports (Table 5). The first situation where only beef technology was changed, resulted in an extra 52 000 tonnes of barley and corn being available for export in the 1960s compared with the 1980s. This additional grain for export came from changes in the beef diets in some provinces to economize on the relatively higher opportunity costs for feedgrains. However, when both beef and crop technology of the 1960s TABLE 4
Estimated Changes in Government Payments ($ Millions) by Province and National Totals Province
British Columbia Alberta Saskatchewan Manitoba Ontario Quebec New Brunswick Prince Edward Island Nova Scotia Newfoundland Total
Change in beef technology
0-000 0-355 - 0.325 0.586 0.579 0.000 0.263 0-002 0.670 0.015 2.14
Change in beef and crop technology
1-112 95.869 181.040 74.416 37.157 32.440 0-729 0.989 0.949 0.015 424.72
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox TABLE 5
Estimated Changes in Exports of Grains and Oilseeds (Thousand Tonnes) Crop
Change in beef technology
Change in beef and crop technology
Wheat Barley Flaxseed Canola Corn
0.00 - 6.60 0.00 0.00 -46.05
3 618.39 264.43 194.87 1212.56 2 927.49
Total
- 52.65
8 217.74
were simulated, nearly 3 000 000 fewer tonnes of grains and oilseeds were exported. Since these changes in exports of grains and oilseeds should not be credited (or debited) to the beef sector when estimating the returns to beef research, the value of the changes in exports were deducted from the changes in objective function values (Table 3). Benefit-cost ratios
The annual (and total) net benefits to beef research were calculated and reported in Table 6. The estimated present value of the stream of net benefits for changes in beef technology alone varied from $5500m (discounted at 2%) to $2000m (discounted at 10%) in 1981 dollars. The net benefits to beef research when both beef and crop technology were considered varied between $4500m $1600m in 1981 dollars. Figure 1 displays the present value of benefits for both the change in beef technology and changes in beef and crop technology scenarios for the 5% dis250
r-
-
20O
2~ °
~ Z
~
1so
50 0
,
1972
,
1978
1984
1990
I
1996
!
2002
Year
Fig. 1. Present value of benefits from changes in beef technology and changes in beef
and crop technologyscenarios at a 5% discount rate.
455
Returns to beef research in Canada
TABLE 6 Comparison of Net Returns to Beef Research Using Mathematical Programming Approach versus Econometrics Approach as Used by Fox et al. (Millions of 1981 Dollars) Real discount rate 2%
5%
10%
8 555.0 65.4
4 921.2 48.3
2 177.6 30.3
(i) Change in beef technology Net present value Ratio to benefits to costs Ratio of net present value to Fox et al. (1987a)
5 519.9 42.6 0.65
3 666.9 37.0 0.75
2 025.5 29.1 0.93
(ii) Change in beef and crop technology Net present value Ratio of benefits to costs Ratio of net present value to Fox et al. (1987a)
4476. I 34.9 0.52
2 973.5 30.4 0.60
1 642.5 24.0 0.75
(a) Fox et al. (1987a), Table 4.18, p. 86 Net present value Ratio of benefits to costs (b) Mathematical programming approach
count rate. Benefits rise from almost zero in 1972 to a maximum in 1988 and fall to the year 2000. The pattern reflects the lagged returns to agricultural research until 1988. Thereafter, it reflects the residual returns to that same research assuming it has stopped in 1984. The lower estimated present value of net benefits when both beef and crops technology were allowed to change illustrate the risk of misinterpretation when conducting this type of analysis in a partial equilibrium framework. A standard practice in the econometric approach is to hold variables in all other agricultural sectors constant. This is similar to what was done in the first situation in this study where only beef technology was permitted to change. By allowing for changes in crop as well as beef technology, the net benefits to beef research were estimated to be at a lower level than when crop technology was held constant. The estimates in this study are generally lower than those reported by Fox et al. (1987a) (Table 6). At a real discount rate of 5%, the benefit-cost ratios estimated in this study were 37.0 to 1 for changes in beef technology only, and 30.4 to 1 for changes in beef and crop technology. Though these are very high benefit-cost ratios and demonstrate the very large payoff from investments in beef research, they are only 75% and 60%, respectively, of the estimates of Fox et al. (1987a). Although the estimates in this study are lower than those reported by
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
Fox et al. (1987a), they still may err on the high side due to the assumption in CRAM of optimizing behaviour. It is well known that many producers do not maximize expected net returns due to considerations such as risk and other factors that may not be adequately modelled in a linear programming framework. Other considerations
In the model solution, a number of other minor changes occurred in production and marketing of agricultural commodities when the beef and crop technologies were changed. Although no adjustments were made to the estimated benefits in this study, they are discussed because they illustrate conditions that are typically ignored in econometric studies In Alberta, Saskatchewan and Quebec, changes in opportunity costs of feed resulted in a change in diets fed to cows. Feedlots in British Columbia and Alberta switched from feeding slower-growing longyearlings (18-month-old cattle) to faster-growing yearlings (12-monthold cattle). When the model incorporated only changes in beef technology, an increase occurred in unimproved pasture (a relatively cheaper feed source) and a decrease occurred in tame hay production. When 1960s cropping technology was added to the 1960s beef technology, the production of most grains and oilseeds except soybeans was reduced, and production of tame hay increased. Such changes in production patterns demonstrate an advantage of the mathematical programming approach for estimating research benefits. In an econometric analysis, these would be implicitly assumed to be constant and, consequently, ignored.
CONCLUSIONS Although the mathematical programming approach affords greater flexibility than the econometric approach in accounting for changes in variables such as conception rates, calving rates, feed conversion ratios pest infestation levels and dressing percentages, this capability was not exploited in the present study. Instead, a simple approach was followed in which input levels were kept constant and only output was changed. This provided a better comparison with the econometric results of Fox et al. (1987a). However, full utilization of the capabilities of the mathematical programming model would permit a more accurate assessment of the returns to investment in agricultural research activities.
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The mathematical programming approach requires judgement in the definition of the objective function to account for interaction effects. In this study, adjustments were made to the objective function to account for changes in government payments and exports of grains and oilseeds. While this may first appear to be a disadvantage of the mathematical programming approach, it actually provides two advantages. First, it directs the analyst's attention to the effects of new technologies on other variables such as government expenditures and international trade, which are easily overlooked and seldom incorporated in econometric studies. Second, it provides an opportunity to conduct sensitivity analyses on the relative importance of demand and price level in other sectors. The mathematical programming approach causes the analyst to be much more cognizant to the general equilibrium effects of changes in technology in a single sector. A change in production or marketing technology in one sector changes the opportunity costs of production not only in that sector, but in all related sectors. Judgement is required to determine whether or not to attribute all positive and negative impacts in other sectors to the change in technology in the sector being studied. The CRAM estimated rates of return to beef research investments, while still very high, were significantly lower than those reported by Fox e t al. (1987a). The lower estimates were caused by inclusion of the (sometimes negative) impacts of changes in other sectors of the Canadian agricultural industry However, the estimates from this study may still be biased upwards due to the assumption in CRAM of strictly profit-maximizing behaviour. The mathematical programming approach is very flexible and can be used to easily estimate the economic impacts of new technological coefficients. This approach provides a real opportunity for conducting meaningful e x a n t e analyses. Anticipated changes in production technology can be analyzed prior to conducting the research. Research managers can use this type of information to help allocate research resources. The flexibility of the mathematical approach also allows analysis of various types of agricultural research. Payoffs from funding of applied projects by commodity organizations, provincial governments or private corporations can be readily quantified and determined or each sector, province or region. The combined effects of changes in agricultural technology and agricultural programs can be estimated. For example, the release of a more drought-resistant cultivar of wheat may permit some changes in a crop insurance program. The impacts on environmental variables of changes in production technologies could be investigated. These types of analyses greatly extend the usefulness of assessment of the benefits from agricultural research activities.
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox REFERENCES
Brown-Andison, N. & Brinkman, G. (1986). Cost:benefit assessment of selected agricultural research, University of Guelph. Highlights of Agricultural Research in Ontario, 9(1), 8-11. Canada Grains Council (1976). Statistical Handbook, Canadian Grains Industry. Canada Grains Council, Winnipeg. Canada Grains Council (1987). Statistical Handbook, Canadian Grains Industry. Canada Grains Council, Winnipeg. Chang, C., Eddleman, B. R. & McCarl, B. A. (1991). Potential benefits of rice variety and water management improvements in the Texas Gulf Coast. West. J. Agr. Econ., 16(2), 185-93. Farrell, C., Funk, T. & Brinkman, G. (1984). An Evaluation of the Economic Potential of Biotechnology in the Process of Crop Improvement. Publication AEEE/84/10, School of Agricultural Economics and Extension Education, University of Guelph, Guelph, Ontario, October 1984. Fox, G., Brinkman, G. & Brown-Andison, N. (1987a). An Economic Analysis of the Returns to the Animal Productivity Research Program of Agriculture Canada from 1968 to 1984. Program Evaluation Branch, Agriculture Canada, Ottawa. Fox G., Brinkman G. & Brown-Andison, N. (1987b). Returns to the Animal Productivity Research Program of Agriculture Canada from 1968 to 1984. Program Evaluation Branch, Agriculture Canada, Ottawa. Funk, T. & Farrell, C. (1985). The determination of ex ante returns to agricultural research and the case of plant biotechnology research in Canada. Can. J. Agr. Econ., 33, 67-82. Haque, A., Fox, G. & Brinkman, G. (1989). Product market distortions and the returns to federal laying-hen research in Canada. Can. J. Agr. Econ., 37, 2946. Horbasz, C. N., Fox, G. & Brinkman, G. (1988). A comparison of ex ante and ex post measures of producer's surplus in estimating the returns to research: The case of sheep research in Canada. Can. J. Agr. Econ., 36, 489-500. Huot, M., Fox, G. & Brinkman, G. (1989). Returns to swine research in Canada. North Central J. Agr. Econ., 111, 189-202. Nagy, J. G. & Furtan, W. H. (1978). Economic costs and returns from crop development research: The case of rapeseed breeding in Canada. Can. J. Agr. Econ., 26, 1-14. Ruttan, V. W. (1980). Agricultural Research and the Future of American Agriculture. Staff Paper, Dept. of Agr. & Applied Econ., University of Minnesota, St Paul, Minnesota, July 1900. Ruttan, V. W. (1982). Agricultural Research Policy. University of Minnesota Press, Minneapolis, MN. Schultz, T. W. (1953). The Economic Organization of Agriculture. McGraw-Hill, New York. Ulrich, A. & Furtan, W. H. (1985). An Investigation in the Rates of Return from the Canadian Crop Breeding Program. Program Evaluation Division, Agriculture Canada, January 1985. Ulrich, A., Furtan, W. H. & Downey, K. (1984). Biotechnology and Rapeseed Breeding: Some Economic Considerations. Science Council of Canada, Ottawa.
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Ulrich, A., Furtan, W. H. & Schmitz, A. (1985). Public and private returns from joint venture research in agriculture: The case of malting barley. In Economics of agricultural Research in Canada, ed. K. K. Klein & W. H. Furtan. University of Calgary Press, Calgary, Alberta, pp. 143-67. Webber, C. A., Graham, J. D. & Klein, K. K. (1986). The Structure of CRAM." A Canadian Regional Agricultural Model Marketing and Economics Branch, Agriculture Canada, Ottawa. Widmer, L. Fox, G. & Brinkman, G. L. (1988). The rate of return to agricultural research in a small country: The case of beef cattle research in Canada. Can. J. Agr. Econ., 36, 23-35. Zachariah, O. E. R., Fox, G. & Brinkman, G. (1989). Product market distortions and the returns to broiler research in Canada. J. Agr. Econ., 40, 40-1. Zentner, R. P. & Peterson, W. L. (1984). An economic evaluation of public wheat research and extension expenditures in Canada. Can. J. Agr. Econ., 32, 327-53.
Returns to Beef Research in Canada: A Comparison of Time Series and Mathematical Programming Approaches K. K. Klein The University of Lethbridge, Lethbridge, Alberta, Canada, T1K 3M4
B. Freeze* Agriculture Canada Research Station, PO Box 3000, Main, Lethbridge, Alberta, Canada, T1J 4B1
J. Stephen Clark Nova Scotia Agricultural College, Truro, Nova Scotia, Canada
& G. Fox Department of Agricultural Economics and Business, University of Guelph, Guelph, Ontario, Canada, N1G 2Wl (Received 5 March 1993; revised version received 10 November 1993, accepted 25 November 1993)
ABSTRA CT A general equilibrium sectoral model of Canadian agriculture was used to determine whether economic payoffs from investment in beef research might be more completely estimated with mathematical programming than with traditional time series analyses Using this approach, estimated rates of return to beef research were significantly lower than those estimated in earlier studies that used an econometric approach. At a 5% discount rate, benefit-to-cost ratios generated were 37 to I for unadjusted beef research and 30.4 to I for beef research adjusted for concomitant effects of crop research. These compare with a benefit-to-cost ratio of about 48 to 1 in * To whom correspondence should be addressed. This paper is Lethbridge Research Station Contribution no. 3879296. 443
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox earlier econometric studies. Flexibility of the mathematical programming approach provides an opportunity to estimate various secondary impacts of specific agricultural research programs, including regional payoffs, environmental externalities, and interactions with agricultural policies and programs.
BACKGROUND
AND OBJECTIVES
Estimation of the returns to public investments in agricultural research began with the work o f Schultz (1953). Griliches' w o r k on hybrid corn in 1958 followed in this tradition . Since these early studies, an enormous literature has evolved (Ruttan, 1982). F o r the most part, rates of return on agricultural research have been found to be high, much higher than those determined for many other public investment opportunities. R u t t a n 1980) argued that public investments in agricultural research in the United States have generated exceptionally high returns and that these returns contrast with the perception o f public sector inefficiencies. As an example, estimates o f the returns to Canadian public sector agricultural research have been made since the late 1970s. Estimates o f rates of return for Canadian public agricultural research have been found to be high but variable (Table 1). TABLE 1 Summary of Canadian Return to Research Studies Study Nagy & Furtan, 1978 Farrell, Funk & Brinkman, 1984
Commodity
Period
Ulrich, Furtan & Schmitz, 1985
Rapeseed Corn Wheat Barley Canola Rapeseed Wheat Wheat Rapeseed Barley Alfalfa Malt barley
1951-1981
Brown-Andison & Brinkman, 1986 Haque, Fox & Brinkman, 1989 Widmer, Fox & Brinkman, 1988 Horbasz, Fox & Brinkman, 1988 Zachariah, Fox & Brinkman, 1989 Huot, Fox & Brinkman, 1989
Dairy cattle Laying hens Beef cattle Sheep Broilers Swine
1968-1984 1968-1984 1968-1984 1968-1984 1968-1984 1968-1984
Ulrich, Furtan & Downey, 1984 Zentner & Peterson, 1984 Ulrich & Furtan, 1985
1960-1975 1984-2003
1951-1981 1946-1979 1950-1983
Rate of return 101% 20-22% 41% 1540% 17-21% 51% 34-39% 29% 51% 22% 14% Public 50% Private 74% 115% 81-98% 66% 25% 61% 50%
Returns to beef research in Canada
445
Previous studies on the social benefits of agricultural research have used an econometric approach based on time series data on outputs and inputs, including research expenditures (Nagy & Furtan, 1978; Zentner & Peterson, 1984; Funk & Farrell, 1985; Horbasz et al., 1988; Widmer et al., 1988; Haque et al., 1989). This approach has several well-known limitations, including the usual need to specify variables in an aggregate manner to preserve degrees of freedom for statistical testing. An alternate approach to estimation of benefits from agricultural research is the use of a general equilibrium industry-wide mathematical programming model. A mathematical programming approach provides virtually limitless opportunities for output and input disaggregation and permits a more thorough analysis of indirect, as well as direct, impacts of agricultural research activities. Chang et al., (1991) used this approach to analyze the potential benefits of rice research, with and without government programs. The overall objective of this study was to assess the usefulness of mathematical programming in estimating returns to investment in agricultural research, using beef research in Canada as an example. Data used in a previously published econometric analysis of returns to investments in beef research in Canada (Fox et al., 1987a) were inserted in a regional linear programming systems model of Canadian agriculture. This permitted a direct comparison between the two approaches. In addition, the process involved in transforming the time series data into input-output coefficients suitable for use in the linear programming model focused attention on the assumptions inherent in both approaches.
The econometric approach Measurement of yearly changes in consumers' and producers' surpluses forms the basis of the econometric approach. A supply function for the commodity is estimated with quantity supplied as a function of several independent variables including lagged research expenditures. Supply is estimated for each time period, with and without research expenditures, to establish a sequence of annual benefits and costs from research. Various net benefit measures, such as net present value, internal rate of return and benefit-cost ratio, can then be calculated. Net present value is the discounted value of the benefit stream minus the discounted value of the cost stream based to the earliest time period in which research expenditures occurred in the data series. Regression analysis is used to estimate parameters of the supply function. The supply function is generally represented as QS = f ( p , G, E, R,_k, T)
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
where Q~ is the level of output in a particular time period, P is a vector of relevant product and input prices, G consists of variables reflecting the impact of government policies, E represents environmental variables such as weather, Rt_k is research expenditures in past time periods, and T consists of other technology-related variables such as levels of education or information. Time series data are used to estimate parameter values for each of the above types of variables once a specific algebraic representation of the supply function is chosen. Many studies have compared the results of variations in the algebraic representation of supply (Fox et al., 1987a,b; Haque et al., 1989). The purpose of the regression analysis is to separate effects of research expenditures on industry output from many other factors that can influence supply. Because the econometric approach uses historical data, estimates are based on what has actually occurred in the industry. The lag structure associated with the development, adoption and obsolescence of new technology is estimated directly, without the use of subjective interview data. Results can be readily compared with the international literature, since this has been the most frequently employed approach. Estimates of returns at the industry level are usually interpreted as average effects from all research activities, including unsuccessful projects. The main limitation of the econometric approach relates to the problem of aggregation. Most studies have focused on single commodities for large regions or whole countries. It is well known that technological change can create ripple effects across markets and within regions. For example, improvements in feed efficiency of beef cattle shift the demand for forages and feed grains. Variations in the supply and price of beef could influence demand and prices in hog markets. Regional patterns of adoption of a new technology can influence the distribution of gains from research. It is difficult to incorporate these interactions into the analysis when using the econometric approach. A second limitation of the econometric approach is that it is difficult to correctly account for all factors that can shift the supply function for a given commodity. Since the inception of empirical analyses of research investments, researchers have attempted to ensure that effects of supplyshifters, such as improvements in the level of education and experience of farm operators, are not falsely attributed to research and technological change. A third limitation of the econometric approach is in the interpretation of results. Not only are results dependent on assumptions employed, they are usually not easily understood by research administrators and research funding agencies Moreover, due to the aggregate nature of variables,
Returns to beef research in Canada
447
econometric analysis usually give no clear prescription of what to do next. For example a high estimated return to beef research gives no indication of what kinds of beef research should be conducted, or even if more expenditures should be devoted to beef research. As a consequence, many econometric studies of returns to agricultural research have largely been seen by research administrators and budget committees as interesting but of little practical use.
The mathematical programming approach Sectoral mathematical programming models select combinations of inputs and levels of outputs to maximize the sum of producers' and consumers' surpluses for a set of interrelated markets, subject to a set of technical input/output relationships and constraints. The outcomes of agricultural research may be inserted directly as changes in input/output coefficients, as changes in product or input prices, or as changes in quality of inputs or outputs. The sector model is solved first with production costs and yields corresponding to the 'old' or 'bench-mark' technology. The costs of production and yields are then adjusted to reflect the 'new' or proposed technology and the model solved a second time. Since the objective function of the model represents the sum of consumers' and producers' surpluses in all agricultural sectors, the difference between model solutions provides an estimate of the annual net benefits to society from development of the new technology. In addition, the model may summarize net earnings of each agricultural sector so that gainers and losers among various groups of producers and consumers can be identified. The mathematical programming approach differs from the econometric approach in the way consumers' and producers' surpluses are calculated. In the econometric approach, only one market is normally considered, while in the mathematical programming approach, markets for all major agricultural products are considered simultaneously. Since these markets are closely linked, a change in one market may affect conditions in other markets. By considering all major agricultural products simultaneously, the mathematical programming approach calculates the change in consumers' and producers' surpluses in the agricultural industry as a whole, thus providing a more complete analysis of the effects of research. Finally, additional output from the mathematical programming approach allows evaluation of the distribution of the benefits in terms of commodities and regions. The assumptions inherent in linear programming also make for some disadvantages to its use in estimating returns to research Optimizing
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
behaviour is assumed and linear programming activities depend on linear, continuous functions which may not always represent production conditions in agriculture. However, the inherent problems in linear programming models may be overcome by using more complex mathematical programming procedures, such as goal programming, stochastic programming or quadratic programming. For example, the quadratic programming approach provides a way to accommodate risk in production. The flow of benefits from new research are uncertain, depending on rate of adoption, time lag and elasticities of demand. Probability distributions of net present values of benefits could be constructed by Monte Carlo simulations performed by repeated solving of the mathematical programming model. Mathematical programming also lacks statistical tests for the estimates. Unlike the econometric approach which provides the analyst with many alternatives for testing hypotheses against known probability distributions, mathematical programming estimates are merely point estimates. No information is available on their distribution. However, sensitivity analyses may be employed to provide some information on the reliability of the estimates.
CANADIAN REGIONAL A G R I C U L T U R A L MODEL (CRAM) To accomplish the study objectives, the Canadian Regional Agricultural Model (CRAM) (Webber et al., 1986) was used to estimate the total return and the rate of return to beef research in Canada over the period 1968-84. These estimates were then compared with results from an econometric study of returns to beef research in Canada conducted over the same time period, as reported by Fox et al. (1987a). CRAM is a regional linear programming model that simulates production, marketing and transportation of the major agricultural commodities produced in Canada. It optimizes production of these commodities within the constraints of available agricultural resources and final demands for products. It is a single-year model based, in its current configuration, on the calendar year 1989. Beef, hogs, dairy and poultry production in Canada is modelled in CRAM for each of the ten provinces. Low and high quality beef are produced, with low quality beef coming from the slaughter of mature dairy and beef cows and bulls. Pork primal cuts are produced in the hog sector of the model. Fluid and industrial milk products are produced in the dairy sector of the model. Eggs, broiler meat, and turkey meat are produced in the poultry sector of the model.
Returns to beef research in Canada
449
Animals are fed grains grown in the crops sector of the model: stored forage, pasture, barley and corn for beef and dairy animals, barley for hogs, and wheat for poultry. Protein supplements are treated as a cash cost. Based on relative prices and nutritional characteristics of feedstuffs, feeder animals and the beef breeding herd can be fed different ratios of feed grains and forages. The model also chooses the optimal rate of growth of feeder animals, within specified constraints. Domestic level demand is specified for low and high quality beef, pork, final dairy products, eggs, broilers and turkeys. Excess supplies can be exported. Both meat and livestock animals can be transported to other provinces and to export locations. Live beef animals can be imported either for feeding or for slaughter purposes; dressed beef products can also be imported into Canada. Poultry and dairy production are constrained by quotas established by provincial marketing boards. Production of poultry and dairy commodities are used to satisfy only domestic demands. The crop sector of the Canadian agricultural industry is represented in the model with production occurring in 29 separate regions, each having different soil and climatic condition: seven in the province of Alberta, nine in the province of Saskatchewan, six in the province of Manitoba and one in each of the other seven provinces. Crops in the model include four grades of wheat, as well as barley, oats, flax, canola, corn (for grain and silage), soybeans, tame hay, pasture and other crops. The category of other crops differs by region and represents historic production levels of minor crops such as pulses, sunflowers, potatoes, buckwheat and canary seed. The model selects the most profitable crops to be grown in each region with provision for both summer fallow and stubble planting in the prairie provinces of Alberta and Saskatchewan. CRAM selects the optimal amount of summer fallow (land left idle for a single year in a rotation) in each region of the prairie provinces on the basis of the relative profitabilities of available crops planted on summer fallow and stubble (land planted and harvested in the preceding year), with the constraint that the area of summer allow must equal the total area of crops planted on summer fallow in each region. Crops produced in each region can be used to satisfy demands for livestock feed, domestic consumption, or export. Domestic consumption of crops is fixed at historic levels. Excess supplies of each crop are transported to terminal locations (Thunder Bay or west coast) for export, with appropriate freight costs included. The prices for farm products are dependent on the quantity produced and offered for sale, as well as on demand for the product. These effects are represented in C R A M through a series of stepped demand functions established for the major categories of final agricultural products.
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
Since Canada trades all categories or grains and oilseeds, as well as beef and hogs, Canadian producers face import and export prices for these commodities. The small country assumption is used in CRAM; that is, changes in Canadian production will have no effect on world price levels. Thus, domestic prices must be between an export price floor and an import price ceiling The downward-sloping demand functions in CRAM for wheat, barley, canola, high quality beef, low quality beef, and primal cuts of pork represent price levels between the floors and ceilings. The objective of the model is to maximize consumers' plus producers' surplus. Consumers' surplus is increased when the price of food falls due to greater production. Producers' surplus is measured as the difference between gross agricultural income and costs of production plus transportation. Commodities traded internationally are valued on an export basis. Farm-level grain prices are derived by subtracting handling and transportation costs from the in-store prices at the export position.
PROCEDURES The study by Fox et al. (1987a) used economic data from the Canadian beef industry over the period 1968-84. Consumers' and producers' surpluses were estimated as a function of research expenditures for each year from 1972 to 1986, then projected to the year 2000 under the assumption that no further research was done after 1986. The present value of this 29-year stream of benefits was then compared to the present value of the 17-year stream of research expenditures by the federal government, the provincial government and industry. The present values of benefits and costs were derived for discount rates of 2%, 5% and 10%o. In this study, the mathematical programming approach allowed an evaluation of returns to beef research with and without concomitant changes in technology of feed grain crops production. Including changes in the technology of feed grain processing allows for the effects of changing crop technology on the profitability of the beef industry to be determined. For example, a change in crop technology may lower the price of feed grains and thus alter the optimal ratios of forage and grain used to feed cattle. The increases in cattle gain through the use of diets that are higher in grain might be interpreted as being due to beef research rather than due to crop research. To account for this possibility, two separate evaluations of net benefits were made using CRAM: one where changes occurred in beef technology only, and a second where changes occurred in both beef and crop technology.
451
Returns to beef research in Canada
The model was solved for production coefficients that were set to mid1960s conditions. The estimated benefits were then compared to those where production, cost and price conditions were set to levels of the mid1980s. After accounting for the costs of research, the differences in estimated net benefits between the two situations could then be calculated. Each of the situations modelled is described briefly as follows. (1) Change in beef productivity only In this situation, total beef productivity in the mid-1960s run was adjusted to be 79% of the level of that existing in the 1980s run. This was the ratio of change in heavy steer equivalents (1967 over 1984) estimated by Fox et al. (1987a). Although the mathematical programming approach makes it relatively easy to insert different productivity indices for such individual factors as conception rates, calving rates, birth weights of calves, average daily gains, slaughter rates, dressing percentage, etc., this simple gross approach was used so that changes in beef production were exactly the same as those reported in the econometric study by Fox et al. (1987a). (2) Change in beef and crop productivity Yields of crops increased considerably over the 1960-80 period (Table 2). It is possible that these changes in yields could affect returns to research in beef. Thus, for the second comparison, the change in total beef production, as in (1) above, as well as the change in grain yields were combined and the results compared for the two time periods. All other technical coefficients and prices were held constant. In the study by Fox et al. (1987a), estimates were developed for the lags in adoption of new technology by beef producers as well as the residual effects of the technology after the expiration of the accounting TABLE 2
Percentage Changes in Crop Yields from 1966-68 to 1983-85 Crop
High quality wheat Barley Forage Grain corn Flaxseed Canola Pasture
Western Canada
Eastern Canada
13.0 13.0 7.0 0-0 44-0 26-0 7.0
45.0 21.0 13.0 20.0
Source: Canada Grains Council (1976, 1987).
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox
period. Costs of research from 1968 to 1984 were counted and a fouryear lag in adoption was assumed so benefits from research began to accumulate in 1972. After 1988 (four years after these authors stopped counting the costs of the research), residual benefits from the research were assumed to decrease in a linear manner, ending in the year 2000. The annual flow of net benefits from 1972 to 2000 was then discounted at three interest rates and reported in 1981 Canadian dollars. In this study, the calculated changes in net benefits represent a single year's improvement since C R A M is a single-year model. A separate calculation could be made for each year of the analysis, then a present value could be determined for the stream of benefits. For this study, however, a simpler approach as chosen. In each situation, it was assumed that benefits to beef research started in 1972, four years after research costs began, a used by Fox et al. (1987a). The calculated net benefits were linearly interpolated between zero in 1971 and their full calculated values (from the C R A M results), in 1986, then linearly extrapolated to the year 2000 in the same manner as used by Fox et al. (1987a). Following this approach, present values of each of the streams of net benefits were calculated for discount rates of 2%, 5%, and 10% (as done by Fox et al., 1987a).
RESULTS AND DISCUSSION Overall benefits The estimate of overall net benefits of research to the Canadian beef sector was $682m when only beef technology was considered, and $553m when both beef and crop technology were considered (Table 3). The value of the objective function was $677m lower with the 1960s beef technology, but $2645m lower with the 1960s beef and crop technology. TABLE 3 Estimate of Overall Net Benefits ($ Millions) to Canadian Beef Sector from Research on Beef and Crops
Change in beef technology
Change in beef and crop technology
Change in objective function Less change in government payments Less change in crop exports
677.23 2.14 -7.31
2 645.09 424.72 1 667.02
Estimated net benefits to beef sector
682.40
553.35
453
Returns to beef research in Canada
However, two important adjustments were made to these changes in value of the objective function in order to obtain a more accurate estimate of the benefits from research that actually accrue to the beef sector. Government payments are modelled in CRAM as a direct injection from government with no offsetting cost to the agricultural industry. They are based on levels of output produced as well as costs and quantities of inputs used. Any change in government payments directly affects the change in the objective function and, without a corresponding adjustment, would bias the estimate of return to beef research. Since production and inputs are different for the different technologies, government payments are also different. The changes in government payments in the two modelled situations are shown in Table 4. Government payments were $2m lower under 1960s beef technology but nearly $425m lower under 1960s beef and crop technology. These changes in government payments (which can easily be handled in a mathematical programming model) provide a reminder that this important variable is often overlooked in econometric models. The objective function was also adjusted to account for the change in crop exports (Table 5). The first situation where only beef technology was changed, resulted in an extra 52 000 tonnes of barley and corn being available for export in the 1960s compared with the 1980s. This additional grain for export came from changes in the beef diets in some provinces to economize on the relatively higher opportunity costs for feedgrains. However, when both beef and crop technology of the 1960s TABLE 4
Estimated Changes in Government Payments ($ Millions) by Province and National Totals Province
British Columbia Alberta Saskatchewan Manitoba Ontario Quebec New Brunswick Prince Edward Island Nova Scotia Newfoundland Total
Change in beef technology
0-000 0-355 - 0.325 0.586 0.579 0.000 0.263 0-002 0.670 0.015 2.14
Change in beef and crop technology
1-112 95.869 181.040 74.416 37.157 32.440 0-729 0.989 0.949 0.015 424.72
454
K. K. Klein, B. Freeze, J. S. Clark, G. Fox TABLE 5
Estimated Changes in Exports of Grains and Oilseeds (Thousand Tonnes) Crop
Change in beef technology
Change in beef and crop technology
Wheat Barley Flaxseed Canola Corn
0.00 - 6.60 0.00 0.00 -46.05
3 618.39 264.43 194.87 1212.56 2 927.49
Total
- 52.65
8 217.74
were simulated, nearly 3 000 000 fewer tonnes of grains and oilseeds were exported. Since these changes in exports of grains and oilseeds should not be credited (or debited) to the beef sector when estimating the returns to beef research, the value of the changes in exports were deducted from the changes in objective function values (Table 3). Benefit-cost ratios
The annual (and total) net benefits to beef research were calculated and reported in Table 6. The estimated present value of the stream of net benefits for changes in beef technology alone varied from $5500m (discounted at 2%) to $2000m (discounted at 10%) in 1981 dollars. The net benefits to beef research when both beef and crop technology were considered varied between $4500m $1600m in 1981 dollars. Figure 1 displays the present value of benefits for both the change in beef technology and changes in beef and crop technology scenarios for the 5% dis250
r-
-
20O
2~ °
~ Z
~
1so
50 0
,
1972
,
1978
1984
1990
I
1996
!
2002
Year
Fig. 1. Present value of benefits from changes in beef technology and changes in beef
and crop technologyscenarios at a 5% discount rate.
455
Returns to beef research in Canada
TABLE 6 Comparison of Net Returns to Beef Research Using Mathematical Programming Approach versus Econometrics Approach as Used by Fox et al. (Millions of 1981 Dollars) Real discount rate 2%
5%
10%
8 555.0 65.4
4 921.2 48.3
2 177.6 30.3
(i) Change in beef technology Net present value Ratio to benefits to costs Ratio of net present value to Fox et al. (1987a)
5 519.9 42.6 0.65
3 666.9 37.0 0.75
2 025.5 29.1 0.93
(ii) Change in beef and crop technology Net present value Ratio of benefits to costs Ratio of net present value to Fox et al. (1987a)
4476. I 34.9 0.52
2 973.5 30.4 0.60
1 642.5 24.0 0.75
(a) Fox et al. (1987a), Table 4.18, p. 86 Net present value Ratio of benefits to costs (b) Mathematical programming approach
count rate. Benefits rise from almost zero in 1972 to a maximum in 1988 and fall to the year 2000. The pattern reflects the lagged returns to agricultural research until 1988. Thereafter, it reflects the residual returns to that same research assuming it has stopped in 1984. The lower estimated present value of net benefits when both beef and crops technology were allowed to change illustrate the risk of misinterpretation when conducting this type of analysis in a partial equilibrium framework. A standard practice in the econometric approach is to hold variables in all other agricultural sectors constant. This is similar to what was done in the first situation in this study where only beef technology was permitted to change. By allowing for changes in crop as well as beef technology, the net benefits to beef research were estimated to be at a lower level than when crop technology was held constant. The estimates in this study are generally lower than those reported by Fox et al. (1987a) (Table 6). At a real discount rate of 5%, the benefit-cost ratios estimated in this study were 37.0 to 1 for changes in beef technology only, and 30.4 to 1 for changes in beef and crop technology. Though these are very high benefit-cost ratios and demonstrate the very large payoff from investments in beef research, they are only 75% and 60%, respectively, of the estimates of Fox et al. (1987a). Although the estimates in this study are lower than those reported by
456
K. K. Klein, B. Freeze, J. S. Clark, G. Fox
Fox et al. (1987a), they still may err on the high side due to the assumption in CRAM of optimizing behaviour. It is well known that many producers do not maximize expected net returns due to considerations such as risk and other factors that may not be adequately modelled in a linear programming framework. Other considerations
In the model solution, a number of other minor changes occurred in production and marketing of agricultural commodities when the beef and crop technologies were changed. Although no adjustments were made to the estimated benefits in this study, they are discussed because they illustrate conditions that are typically ignored in econometric studies In Alberta, Saskatchewan and Quebec, changes in opportunity costs of feed resulted in a change in diets fed to cows. Feedlots in British Columbia and Alberta switched from feeding slower-growing longyearlings (18-month-old cattle) to faster-growing yearlings (12-monthold cattle). When the model incorporated only changes in beef technology, an increase occurred in unimproved pasture (a relatively cheaper feed source) and a decrease occurred in tame hay production. When 1960s cropping technology was added to the 1960s beef technology, the production of most grains and oilseeds except soybeans was reduced, and production of tame hay increased. Such changes in production patterns demonstrate an advantage of the mathematical programming approach for estimating research benefits. In an econometric analysis, these would be implicitly assumed to be constant and, consequently, ignored.
CONCLUSIONS Although the mathematical programming approach affords greater flexibility than the econometric approach in accounting for changes in variables such as conception rates, calving rates, feed conversion ratios pest infestation levels and dressing percentages, this capability was not exploited in the present study. Instead, a simple approach was followed in which input levels were kept constant and only output was changed. This provided a better comparison with the econometric results of Fox et al. (1987a). However, full utilization of the capabilities of the mathematical programming model would permit a more accurate assessment of the returns to investment in agricultural research activities.
Returns to beef research in Canada
457
The mathematical programming approach requires judgement in the definition of the objective function to account for interaction effects. In this study, adjustments were made to the objective function to account for changes in government payments and exports of grains and oilseeds. While this may first appear to be a disadvantage of the mathematical programming approach, it actually provides two advantages. First, it directs the analyst's attention to the effects of new technologies on other variables such as government expenditures and international trade, which are easily overlooked and seldom incorporated in econometric studies. Second, it provides an opportunity to conduct sensitivity analyses on the relative importance of demand and price level in other sectors. The mathematical programming approach causes the analyst to be much more cognizant to the general equilibrium effects of changes in technology in a single sector. A change in production or marketing technology in one sector changes the opportunity costs of production not only in that sector, but in all related sectors. Judgement is required to determine whether or not to attribute all positive and negative impacts in other sectors to the change in technology in the sector being studied. The CRAM estimated rates of return to beef research investments, while still very high, were significantly lower than those reported by Fox e t al. (1987a). The lower estimates were caused by inclusion of the (sometimes negative) impacts of changes in other sectors of the Canadian agricultural industry However, the estimates from this study may still be biased upwards due to the assumption in CRAM of strictly profit-maximizing behaviour. The mathematical programming approach is very flexible and can be used to easily estimate the economic impacts of new technological coefficients. This approach provides a real opportunity for conducting meaningful e x a n t e analyses. Anticipated changes in production technology can be analyzed prior to conducting the research. Research managers can use this type of information to help allocate research resources. The flexibility of the mathematical approach also allows analysis of various types of agricultural research. Payoffs from funding of applied projects by commodity organizations, provincial governments or private corporations can be readily quantified and determined or each sector, province or region. The combined effects of changes in agricultural technology and agricultural programs can be estimated. For example, the release of a more drought-resistant cultivar of wheat may permit some changes in a crop insurance program. The impacts on environmental variables of changes in production technologies could be investigated. These types of analyses greatly extend the usefulness of assessment of the benefits from agricultural research activities.
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K. K. Klein, B. Freeze, J. S. Clark, G. Fox REFERENCES
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