For their helpful comments, he thanks P. David, M. Percy, T. MaCurdy, and R. M. Mclnnis. He also thanks M. C. Urquhart both for his comments and for making available to him unpublished data from the “National Accounts Project” at Queen's University. The many useful suggestions of two anonymous referees are gratefully acknowledged, as is the support of the Social Sciences and Humanities Research Council of Canada. A version of this paper was presented to the Tenth Conference on Quantitative Research in Canadian Economic History at Halifax in October, 1979.Google Scholar

¹ Norrie, K. H., “The Rate of Settlement of the Canadian Prairies, 1870–1911,” this JOURNAL, 25 (06 1975), 410–27;Google ScholarMarr, W. and Percy, M., “The Government and the Rate of Prairie Settlement,” Canadian Journal of Economics, 11 (11 1978), 757–67; andCrossRefGoogle ScholarGrant, K. G., “The Rate of Settlement of the Canadian Prairies, 1870–1911: A Comment,” this JOURNAL, 38 (06 1978), 471–73.Google ScholarFor a discussion of late nineteenth century settlement in the U.S. Midwest using the same model, see Harley, C. K., “Western Settlement and the Price of Wheat, 1872–1913,” this JOURNAL, 38 (12 1978), 865–78.Google Scholar

² Nerlove, M., The Dynamics of Supply: Estimation of Farmers' Response to Price (Baltimore, 1958).Google Scholar

³ There are only two significant differences in the methods employed by Grant, “The Rate of Settlement,” and Marr and Percy, “The Government and the Rate.” Marr and Percy include railroad mileage as a determinant of desired settlement, whereas Grant does not, and Marr and Percy treat the adjustment coefficient as a function of the level of government expenditures directed at promoting immigration. Grant correctly redefined Norrie's settlement variable as the stock of homesteads in each year rather than the increase in the number of homesteads; but otherwise their estimation procedures are identical.Google Scholar

⁴ This assumption may seem a bit extreme given the incomplete knowledge of new settlers about soil and climatic conditions. It should be pointed out, however, that settlers were not bound to their original farm site. Indeed, the large number of homestead cancellations during the period of rapid net expansion attests to the attempts by farmers to settle permanently on the best available land. As Mackintosh pointed out: “Settlers are neither more nor less rational than other humans. With such knowledge as they have, they select good land. Their knowledge is often scanty and much of it hear say …. Individual preferences and prejudices, quite irrational, frequently account for an early bias in the pattern …. Over longer periods, however, the pattern of population yields to the persistent pressure of the physical world, if, in the meantime, there have not already been discovered methods of turning handicaps to advantage.” Mackintosh, W. A., Prairie Settlement: The Geographical Setting, Canadian Frontiers of Settlement, vol. 1 (Toronto, 1934; reprinted, New York, 1974), pp. 58, 59.Google Scholar

⁵ Letting s be one half the distance between rail shipping points, letting d be the distance to a rail line, and remembering that each township is 6 × 6 miles, we have from Figure 3 that the amount of land at distance x from a loading platform in each rectangle isGoogle Scholar

where n=0, 1, 2, ….

The density function, ρ(x), is derived by dividing each ρ_i′(x) by the area of a rectangle (2s × 6) and then multiplying by the proportion of land in the corresponding distance interval, given in Table 1. For example, suppose we wish to determine the proportion of the land in Crop District 1 that was within 3 miles of a loading platform in 1898. The proportion of the land within 3 miles of a rail line that was also within 3 miles of a loading platform equalled 9π/45.6 or.62 (from equation (a), we have

— in 1898 the average distance between loading platforms [2s] was 7.6 miles). Since 11.7 percent of the land in Crop District I was within 3 miles of a rail line (see Table 1), it follows that 7.3 percent was within 3 miles of a loading platform.

⁶ The following note accompanied the schedule of enquiry: “ Kindly let estimates be for your own or hired, should be estimated upon the basis of the prevailing rate of wages paid, whether the actual work is done by owner or hired labour.” The information requested included: “(1) Preparing the ground for seed [$2.93]. (2) Seed [$1.38]. (3) Planting or Seeding [$.54]. (4) Cultivation [$.56]. (5) Harvesting [$1.04]. (6) Threshing or preparing the grain for market [$1.96]. (7) Wear and tear on implements [$.45]. (8) Other items of cost [$.49]. (9) Total cost per acre [$9.35].” Values in brackets are the cost estimates for Crop District 1. The Statistics Bureau of the U.S. Department of Agriculture estimated the cost of growing weat in 1909, and arrived at a similar value for total cost per acre, $9.74, in the U.S. Midwest. Province of Saskatchewan, Department of Agriculture, Seventh Annual Report, 1911 (Regina, 1912), pp. 53, 54.Google Scholar

⁷ lnterest on implements is put at 36 cents. This value is based on the assumption that the ratio of wear and tear (which was 45 cents) to interest was equal to the ratio of the depreciation rate (10 percent) to the interest rate (7.95 percent). See Lewis, F. D., “The Canadian Wheat Boom and Per Capita Income: New Estimates,” Journal of Political Economy, 83 (12 1975), 1257.CrossRefGoogle Scholar

⁸ The average wheat yield in Crop District I was 17.2 bushels per acre. My estimate of postharvest costs per acre is slightly higher than component (6), “threshing or preparing the grain for market” (see footnote 6) because I allocated part of the cost of implements to postharvest costs.

⁹ Trevor Dick has made preliminary estimates of productivity change in wheat farming. Although he finds significant improvement in efficiency from 1900 to 1910, his results are too tentative to be applied here. Dick, T. J. O., “Productivity Change and Grain Farming Practice on the Canadian Prairie, 1900–1930,” this JOURNAL, 40 (03 1980), 105–10.Google Scholar

¹⁰ A weight of. 825 is applied to the wage index, and. 175 is applied to the implements price index. Lewis, F. D., “The Canadian Wheat Boom,” p. 1257; andGoogle ScholarUrquhart, M. C. and Buckley, K. A. H., eds., Historical Statistics of Canada (Toronto, 1965), pp. 84, 292.Google Scholar

¹¹ This is the assumption made by Harley (“Western Settlement,” p. 874). Man and Percy apply a weighted sum of prices in the three previous years; see Marr and Percy, “The Government and the Rate,” p. 761.Google Scholar

¹² Equation (7) is derived from

where numbers in parentheses are the t-statistics.

¹³ The implied increase in the trend price of wheat is from 66.7 cents per bushel in 1898 to 69.3 cents in 1911. The wholesale price index used as a deflator is the Department of Labour index by commodity group. Deflating by any of the commonly-used alternate price indexes would not affect the finding that the (deflated) price of wheat exhibited almost no upward trend. Urquhart, M. C. and Buckley, K. A. H., Historical Statistics, pp. 283–85, 291–96.Google Scholar

¹⁴ The average cost per bushel of shipping wheat by rail from Saskatchewan to Fort William declined from 12.67 (current) cents between 1898 to 1901 to 11.4 cents between 1902 and 1911. These values are reduced to 11.41 cents and 10.26 cents, respectively, because of the location of Crop District 1, and then are deflated to 1890/99 prices. Additional freight costs (commissions and handling) are put at 3 (1890/99) cents per bushel over the entire period. Urquhart, M. C., director, “National Accounts Project” (Queen's University), p. W52.Google Scholar

¹⁵ This is derived from his estimate of the cost of hauling wheat a distance of 9 miles, which was 7.83 cents per 100 lbs. A bushel of wheat weighed about 60 lbs. Andrews, F., Cost of Hauling Crops from Farms to Shipping Points, U.S. Department of Agriculture, Bureau of Statistics, Bulletin No. 49 (Washington, D. C., 1907), p. 33.Google Scholar

¹⁶ Saskatchewan, Department of Agriculture, Annual Report 1911, p. 54.Google Scholar

¹⁷ His figure is an average estimate for the United States. Fogel, R. W., Railroads and American Economic Growth (Baltimore, 1964), p. 67.Google Scholar

¹⁸ This can be derived from the portion of a unit circle subtended by an angle of 45°. For any θ ≦ 45°, the distance from the boundary to the center of the circle, along two sides of a right angle triangle, is sin θ + cos θ. The average distance isGoogle Scholar

.

¹⁹ The corresponding regression equation isGoogle Scholar

where numbers in parentheses are the t-statistics. I explored the possibility that the trend in wheat yields was biased upward because of generally higher yields on virgin land. Accordingly, I estimated another equation in which I reduced by 20 percent yields on land that was cultivated for the first time. Yields on land in the second year of cultivation were reduced by 10 percent. The trend was not affected significantly by these changes. (In deriving my result, I assume that, in 1898, land under wheat had been cultivated for at least two years.)

²⁰ If 1900 is excluded, the data exhibit a downward trend in yields.Google Scholar

²¹ The Department of Agriculture report for 1900 included the following account: “A large acreage was successfully sown, but the early part of the season was very dry and hot with high winds, and the crop presented a very poor appearance before the rains in August and September. These rains brought on a second growth of grain and weeds, and several hail storms did a large amount of damage in some districts. Gophers were also somewhat destructive…. Much grain was damaged also by bad weather at harvesting.… Northwest Territories, Department of Agriculture, Annual Report 1900 (Regina, 1901), p. 18.Google Scholar

²² The estimated equation is

.

²³ Annual wheat yields by rural municipality were made available by the Statistics Division, Saskatchewan Department of Agriculture. Throughout the analysis wheat yields are assumed to be independent of distance to a rail line. The correlation coefficient between average wheat yield from 1918 to 1958 and distance to a rail line in 1898, both by rural municipality, is –.02.Google Scholar

²⁴ This variance estimate is likely to be biased downward because it is derived using aggregated data from rural municipalities (RMs). It does not include, therefore, variations in yield within RMs. (If all RMs had the same number of acres under wheat, then the true variance would be the sum of the variance between RMs [6.32] and the average variance within RMs.) In deriving the feasible region of cultivation, I assume that yields on land at each distance from a rail shipping point had the same variance (see equation 6), and that this variance equalled the estimate for all land in Crop District I. If land at the same distance to a rail shipping point was more homogeneous, then the downward bias would be offset however, it appears that land quality was independent of distance to a rail line (see footnote 23). I should note that using a higher variance estimate would tend to strengthen my results.Google Scholar

²⁵ The “ceiling” of 1.7 million was not passed until 1915 when 1.78 million acres were cultivated in wheat. From 1916 to the 1950s it appears that there was almost no further increase in wheat acreage in the area of Crop District 1.Google Scholar

²⁶ The rising mean yield can also be interpreted in the following way. From 1898 to 1911, less and less fertile land was brought under cultivation. If there had been no improvement in land productivity, observed wheat yield would have fallen sharply. Instead, there was only a small reduction in observed yields. This suggests that an overall increase in land productivity must have offset the decline in yields that resulted from the introduction of poorer land.Google Scholar

²⁷ The problem with treating settlement as a short-run adjustment can be illustrated by analyzing the results of cases 1 and 2 in a Nerlovian framework. I have estimated equation (2):Google Scholar

where A_t* = my estimate of the feasible region of wheat cultivation, and A_t = actual area of wheat cultivation. The estimate of β is very sensitive to the assumption on price expectations. For Case 1, β =. 353 (.098), indicating rapid adjustment; whereas for Case 2, β =. 132 (.065), indicating that adjustment was slow (terms in parentheses are the standard errors).

²⁸ Southey argues that, with increasing rents over time, land would have a positive discounted present value before it entered the feasible region. Since homesteads were offered at close to a zero price, rational farmers would settle prematurely. Southey's analysis applies in a world where there is perfect mobility of labor and information in the short run, but these assumptions may not be appropriate in explaining settlement on the Canadian prairies. Southey, Clive, “The Staples Thesis, Common Property, and Homesteading,” Canadian Journal of Economics, 11 (08 1978), 547–59.CrossRefGoogle Scholar

²⁹ Turner, F. J., The Frontier in American History (New York, 1920);Google ScholarInnis, H. A., “Significant Factors in Canadian Economic Development,” Canadian Historical Review, 18 (12 1936), 374–84; andCrossRefGoogle ScholarMackintosh, W. A., “Economic Factors in Canadian History,” Canadian Historical Review, 4 (03 1923), 12–25.CrossRefGoogle Scholar

³⁰ Norrie offers several hypotheses for the delay in settlement. He suggests that Canada had to await both the settlement of superior land in the U.S. Midwest and improvements in the application of dry-farming techniques. He also argues that there was a significant lag in farmers' response to the extension of the feasible region. Norrie, “The Rate of Settlement,” 417–27.Google Scholar

³¹ The finding that mean yield increased by 12 percent is weakened by the lack of direct observations on that variable. The increase can only be inferred from data on actual yields, and is based on the assumption that farmers cultivated more profitable land first.Google Scholar

³² Equation (3A) shows the relationship between the mean, μ, of the entire distribution, and the mean, y(x), of the conditional distribution where yields are restricted to be greater than or equal to y_min′(x). For a general formulation see Mood, A. M. and Graybill, F. A., Introduction to the Theory of Statistics (New York, 1963), p. 138.Google Scholar

³³ For example, the November closing prices in 1911 ranged between 61 cents per bushel for “feed” and 98 cents per bushel for No. 1 Northern.Google Scholar

³⁴ The average price of Saskatchewan wheat over this period was 71.8 cents per bushel as compared to 74.0 cents per bushel for all wheat sold at Fort William (see Appendix Table 1).Google Scholar