| | In order to measure some of the effects of poor price signals we have used an economic model applied in other regulated farm situations. Brada and King (1993) used this same tool to examine inefficiencies in Polish agriculture. We have estimated the relative technical and economic efficiency across the three Canadian prairie provinces. Aggregating efficiency by years provides information on the average efficiency for each province, indicating which province is most efficient. The technical details of our procedure, data used, estimation technique, and detailed results appear in this appendix.
Data
The data set is aggregated by province and outputs, from 1961 to 1992. The data series for each province consists of seven inputs - land and buildings, labor, machinery, livestock, crop inputs, energy, and miscellaneous inputs. The output is aggregated from observations on five categories - dairy; horticulture; grains, oilseeds, and field crops; red meat; and poultry and eggs.
The data are derived quantities prepared with a divisia price indexing procedure and are equal to nominal values deflated by the divisia price index series. The divisia (Tornqvist) indexing is a chained index which measures changes relative to the previous period rather than to a fixed base, and is approximated to a flexible translog production function (Narayanan, Thomsen, and King, 1994). Approach Technical efficiency is measured using a deterministic production function whose parameters are estimated by linear programming. The specification is a translog production function, which is a second-order Taylor series approximation to an arbitrary production function that is twice differentiable. The parameters are estimated by minimizing the sum of the distances between the estimated production function frontier and the actual observations subject to the constraints that observations lie within or below the frontier and constraints imposed by specific regularity conditions of the translog production function.
The production frontier is estimated from input and output data on 32 years of observations for each of the three provinces, making a total of 96 observations. The output of the pth province in period t, Yp,t, is specified as a function of time, t, and its utilization of I inputs in that period for each province, Xi,p,t, such that
The parameters of equation (1) can be estimated by means of linear programming that minimizes the sum of the distances between the output observations and the frontier function (equation (2)), subject to the constraints that no observations lie within or below the frontier (equation (3)); that the function exhibits constant returns to scale (equation (4)-(6)), concavity (equation (7)), and monotonicity (equations (8) and (9)); and that the parameters are identifiable (equation (10)). The linear program is written as follows:
subject to
for t=1,...,T; and p=1,...,P, 
The estimated parameters are reported in Table B.1. The inefficiency of each province for each year is calculated as the antilog of the slack variable associated with equation (3). For observations on the frontier, the slack variable takes the value zero, with the antilog being one or 100% efficient. For observations below the frontier, the slack variable is less than zero. The antilog of these observations lie between zero and one, reflecting less than 100% efficient. It should be noted that weather, although important in agricultural production, is not accounted for in the production function. Thus, years with poor efficiency could be a result of unfavorable weather conditions.
Table B2 reports the mean level of technical efficiency for each province and the distribution of the annual level of efficiencies . A point on the "best practices" frontier would give a result of 100% efficient. We found the average efficiencies to be 69%, 76%, and 68% for Alberta, Saskatchewan, and Manitoba, respectively. From 1961 to 1992, over 30% of the observations for each province was 90%-100% efficient, and this level is at or near the "best practices" frontier. For Saskatchewan, 43.7% of the observations were at this efficiency level. On average, Saskatchewan exhibited the highest level of technical efficiency and the difference between the Saskatchewan mean level and that for either of the other two provinces is statistically significant. Overall these results suggest prairie farmers are quite efficient from a technical standpoint, but there may be room for improvement if stronger incentives to maximize profits are introduced. The inter-provincial differences in technical efficiency that could be due to a number of factors such as weather, local economic conditions, or other incentives for efficient operation that vary across provinces.
Evidence on economic (allocative) efficiency is reported in Tables B.3 and B.4. Economic efficiency is measured through estimated regional differences between the value of the marginal products of the seven inputs. This is important because economic efficiency across the prairies requires the value of marginal product be equalized across regions on the prairies. Every $1 in additional farm input applied in Alberta should generate the same output return as in either Saskatchewan and Manitoba. If a dollar’s worth of additional fertilizer application in Alberta generates an added $1.20 in farm revenue in Alberta, compared to $1.50 in Saskatchewan, then we would say that Saskatchewan is under-fertilizing and this signals economic inefficiency. Knowledge of the additional value created by the decision to apply more resources is important to the farmer and resources should be added until the value of the marginal output is equal to its cost. Economic inefficiency could arise if a lack of price information means farmers do not have the knowledge of the additional value created by more inputs.
Table B.3 reports the difference between marginal products of inputs of Saskatchewan and Alberta farms, and the corresponding information for Saskatchewan and Manitoba farms is reported in Table B.4. On average, marginal products are greater for Saskatchewan than Manitoba for all inputs. This is essentially the same for Saskatchewan verses Alberta, except for machinery’s marginal product.
These results support the view that resources are not being used in the most efficient way, from an economic standpoint. The regulatory environment likely gives rise to this situation, including CWB pricing and quotas, which are a major source of distortion to producer decision making. With fewer distortions, there would be a reallocation of resources that would tend towards equalization of marginal products of inputs across all three provinces. This would raise the total value of output and prairie agricultural income.
Table B.2. Distribution of Technical Efficiency by Province, 1961-1992 |
Technical
Efficiency | Alberta
(%) | Saskatchewan
(%) | Manitoba
(%) |
1.0-.90 | 37.5 | 43.75 | 31.25 |
| .89-.80 | 9.38 | 9.38 | 9.38 |
| .79-.70 | 9.38 | 12.5 | 12.5 |
| .69-.60 | 6.25 | 6.25 | 3.13 |
| .59-.50 | 3.13 | 9.38 | 12.5 |
| .49-.40 | 6.25 | 6.25 | 6.25 |
| .39-.30 | 18.75 | 6.25 | 12.5 |
| .29-.20 | 3.13 | 6.25 | 9.38 |
| .19-.10 | 3.13 | 0 | 3.13 |
| >.09 | 3.13 | 0 | 0 |
| Total | 100 | 100 | 100 |
| Mean efficiency | 0.688 | 0.76 | 0.677 |
| Standard Deviation | 0.302 | 0.246 | 0.281 |
Table B.3. Differences Between Marginal Products of Inputs of Saskatchewan and Alberta Farms, by Year (MPSaskatchewan-MPAlberta). |
year | LB | LA | MA | LI | CR | EN | MI |
| 1962 | 102.985 | -10.586 | -124.566 | -73.097 | 13.494 | -292.127 | 518.834 |
| 1963 | -214.332 | -4.528 | 16.748 | 38.426 | 5.870 | 55.743 | -259.938 |
| 1964 | -62.418 | 4.238 | -17.648 | -30.821 | 36.794 | -71.520 | -27.534 |
| 1965 | 12.149 | -0.264 | 1.715 | -27.306 | 4.062 | -0.151 | -120.110 |
| 1966 | 206.779 | -1.012 | 4.869 | 372.824 | 25.371 | 18.959 | 8.528 |
| 1967 | -107.664 | 6.445 | -30.081 | 1351.187 | 150.622 | -51.043 | 328.148 |
| 1968 | -153.877 | -0.322 | 1.613 | 19.359 | 57.896 | 19.767 | 414.788 |
| 1969 | -43.722 | 0.614 | 39.693 | 24.529 | -23.167 | 93.872 | -22.073 |
| 1970 | 229.651 | 2.937 | -13.806 | -38.380 | -10.427 | 45.613 | -43.316 |
| 1971 | 91.286 | 21.309 | -16.834 | -50.977 | 46.136 | 117.474 | 13.461 |
| 1972 | -392.714 | 10.755 | -27.614 | 904.007 | -17.834 | -44.776 | -28.799 |
| 1973 | 22.123 | -2.701 | 0.888 | 6.830 | 1.436 | 10.269 | 121.418 |
| 1974 | -42.035 | -1.741 | -0.889 | -2.949 | -7.570 | -62.326 | -22.704 |
| 1975 | 6.506 | 14.077 | 0.023 | -2.645 | -97.464 | -6.431 | -14.607 |
| 1976 | 47.933 | -1.178 | 0.303 | 3.338 | 87.130 | -20.365 | -6.533 |
| 1977 | -10.519 | -0.053 | -15.611 | -2.259 | 2.939 | 9.347 | -2.762 |
| 1978 | 7.465 | 3.352 | -0.998 | -71.459 | -3.231 | -14.653 | -6.840 |
| 1979 | 489.103 | 5.790 | -3.166 | -12.111 | -10.499 | -15.533 | 13.990 |
| 1980 | -2.912 | 245.928 | -0.861 | -0.814 | 11.007 | -21.532 | 464.843 |
| 1981 | 20.547 | 23.718 | 0.838 | 4.290 | 5.390 | 1.842 | 34.602 |
| 1982 | -32.750 | 2.704 | -3.855 | -10.244 | 9.570 | 5.429 | 11.255 |
| 1983 | 26.157 | 2.407 | 1.082 | 3.224 | -4.392 | -28.735 | 52.295 |
| 1984 | 70.447 | 8.036 | -15.340 | -47.215 | -7.209 | -31.665 | 23.529 |
| 1985 | -20.677 | -18.779 | -1.935 | -5.871 | 4.646 | -44.222 | -58.270 |
| 1986 | -268.279 | 8.455 | 24.847 | -58.749 | 4.255 | 498.674 | 877.134 |
| 1987 | 163.163 | 17.647 | -88.973 | 1074.990 | 5.645 | -63.577 | -129.965 |
| 1988 | 1466.579 | 2.140 | 75.700 | -233.168 | 18.357 | 77.531 | -20.463 |
| 1989 | -409.541 | 6.087 | 9.399 | 22.377 | -12.872 | 6.239 | 210.492 |
| 1990 | -713.777 | 3.040 | 7.980 | 35.964 | -63.549 | 133.255 | 190.735 |
| 1991 | -78.613 | 15.759 | 0.464 | 0.675 | 2.732 | 2.741 | -3.198 |
| 1992 | 687.968 | -0.292 | 0.719 | 13.779 | 9.834 | 1.343 | 0.237 |
| average | 35.388 | 11.741 b | -5.655 | 103.475 b | 7.902 | 10.627 | 81.199 a |
| st.dev. | 363.992 | 44.313 | 33.563 | 350.557 | 41.527 | 116.321 | 226.418 |
| t-value. | 0.54 | 1.47 | -0.93 | 1.64 | 1.06 | 0.50 | 2.00 |
The input columns include the following categories: LB=land & buildings, LA=labor, machinery, MA=machinery, LI=livestock, CR=crop input, EN=energy, and MI=miscellaneous inputs such as custom work.
a Hypothesis that efficiency of Saskatchewan farms is greater than Alberta farms is rejected at 5%.
b Hypothesis that efficiency of Saskatchewan farms is greater than Alberta farms is rejected at 10%.
Table B.4. Differences Between Marginal Products of Inputs of Saskatchewan and Manitoba Farms, by Year (MPSaskatchewan-MPManitoba). |
year | LB | LA | MA | LI | CR | EN | MI |
| 1962 | 56.881 | -2.450 | 181.636 | -23.352 | 10.835 | -336.673 | 173.660 |
| 1963 | 65.217 | -11.602 | 41.076 | 59.769 | 16.749 | 138.445 | -184.391 |
| 1964 | -110.222 | 7.116 | -30.179 | -44.381 | 58.030 | -86.312 | -39.844 |
| 1965 | 23.179 | -0.296 | 2.696 | -50.224 | 1.584 | 9.487 | 0.567 |
| 1966 | 266.394 | -1.646 | 13.162 | 473.082 | 17.032 | 39.212 | 5.933 |
| 1967 | -135.866 | -4.405 | -41.480 | 1370.956 | 32.744 | -71.705 | 311.638 |
| 1968 | -224.270 | -0.349 | 2.654 | 16.731 | 35.967 | -63.696 | 191.278 |
| 1969 | -61.526 | 1.217 | 47.313 | 31.370 | -24.864 | 112.176 | -24.828 |
| 1970 | 251.598 | 0.382 | 11.050 | -29.515 | -6.632 | 62.188 | -83.800 |
| 1971 | 187.473 | 1.001 | -8.545 | -35.148 | 39.619 | 78.641 | 2.672 |
| 1972 | -365.433 | 9.218 | 1.273 | 1458.293 | -12.860 | 740.220 | -24.852 |
| 1973 | -5.973 | -0.163 | 0.063 | 3.223 | 1.325 | 3.206 | 137.248 |
| 1974 | -4.472 | -0.847 | 0.824 | 0.692 | 16.382 | -61.241 | 23.490 |
| 1975 | -20.633 | 12.280 | -0.422 | 0.184 | -119.368 | -8.581 | 6.216 |
| 1976 | 30.930 | -0.175 | 0.694 | -7.645 | 88.079 | 26.552 | -1.173 |
| 1977 | 191.159 | -1.321 | 16.328 | 13.837 | -4.918 | -23.004 | -22.645 |
| 1978 | 26.994 | -8.298 | -1.042 | -26.350 | -0.278 | -1.410 | -4.218 |
| 1979 | 287.569 | 7.906 | -1.145 | -5.378 | -8.967 | -8.424 | 201.359 |
| 1980 | 38.346 | -1.208 | 2.983 | 3.695 | -3.077 | -14.284 | -2.165 |
| 1981 | -20.556 | 11.461 | -1.163 | -1.081 | 0.347 | 117.171 | 25.383 |
| 1982 | -11.041 | 4.146 | -0.218 | -5.523 | 15.866 | 43.131 | 19.770 |
| 1983 | 0.056 | -1.033 | -0.692 | -0.272 | -0.083 | 12.230 | 37.378 |
| 1984 | -28.688 | 155.202 | -38.124 | -69.774 | -13.718 | 51.757 | 44.705 |
| 1985 | 768.757 | -20.341 | 3.512 | 5.954 | -18.845 | 19.531 | -72.904 |
| 1986 | -499.034 | 11.440 | -25.506 | -87.820 | 12.731 | 536.581 | 432.261 |
| 1987 | 172.418 | 14.033 | -86.121 | 1158.986 | 3.369 | -38.968 | -10.767 |
| 1988 | 374.933 | -1.702 | 40.044 | -192.471 | 12.908 | 17.586 | -81.326 |
| 1989 | -476.945 | 2.334 | -0.706 | 10.885 | 6.973 | 3.215 | 265.360 |
| 1990 | -504.121 | 17.609 | -133.663 | 16.601 | -80.715 | -118.565 | 203.083 |
| 1991 | -144.357 | 2.426 | -0.951 | -3.628 | 3.475 | -8.849 | 4.245 |
| 1992 | 614.147 | 65.239 | 6.444 | 53.811 | 18.904 | -22.258 | -55.220 |
| average | 23.965 | 8.618 b | 0.058 | 132.113 a | 3.180 | 37.012 | 47.681 a |
| st.dev. | 282.375 | 30.465 | 48.048 | 412.234 | 36.040 | 183.250 | 131.127 |
| t-value | 0.47 | 1.57 | 0.01 | 1.78 | 0.49 | 1.12 | 2.02 |
a Hypothesis that efficiency of Saskatchewan farms is greater than Alberta farms is rejected at 5%.
b Hypothesis that efficiency of Saskatchewan farms is greater than Alberta farms is rejected at 10%. |
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