The Diffusion of Tractors on the Canadian Prairies: The Threshold Model and the Problem of Uncertainty

Explorations in Economic History 37, 189 –216 (2000) doi:10.1006/exeh.2000.0737, available online at http://www.idealibrary.com on

The Diffusion of Tractors on the Canadian Prairies: The Threshold Model and the Problem of Uncertainty Byron Lew Department of Economics, Trent University, Peterborough, Ontario, Canada The diffusion of tractors during the late 1920s proceeded more slowly than predicted by the threshold model. This lag is reinterpreted as a failure of the threshold model to incorporate farmers’ expectations of future prices. Volatility in wheat prices and falling tractor prices are shown to make delaying a tractor purchase a rational decision for wheat farmers in Saskatchewan in the late 1920s. The pattern of diffusion is better explained by a threshold model modified to include uncertainty. © 2000 Academic Press

INTRODUCTION Agricultural productivity growth more than doubled in Canada over its first century, from less than 1% per annum for the period 1871–1921, to more than 2% per annum for the period 1935–1964. 1 Agricultural growth in general can be attributed to either labor-saving mechanization or yield-increasing biological developments (Hayami and Ruttan, 1985). One of the noted examples of agricultural mechanization in the 20th century is the diffusion of tractors. Significantly, in the period 1926 –1987, technical change in Canadian agriculture was biased toward fertilizer and machinery and away from labor and land. Furthermore, the biases toward machinery and away from labor were greatest on the Prairies (Karagiannis and Furtan, 1990). In other words, the flat, homogenous wheat-growing prairie was ideally suited to tractors. 2 The transition to tractor power, however, was not smooth and seamless. Having been first introduced as a response to labor scarcity and rising grain prices during and immediately following World War I, sales of tractors fell sharply by 1921, then picked up again in earnest by 1925 with continued technical improve1 McInnis (1986, p. 761) reports total productivity growth in Canadian agriculture in the range of 1.08 to 1.34% per annum from 1871 to 1901 and in the range of 0.09 to 0.44% per annum from 1901 to 1921. Furniss (1966) reports growth in farm productivity of 2.2% per annum from 1935 to 1964. 2 The focus of Canadian economic historians on agriculture on the prairies is often on the Wheat Boom and extensive growth, though Dick (1982) and Ward (1994) are two notable exceptions.

189 0014-4983/00 $35.00 Copyright © 2000 by Academic Press All rights of reproduction in any form reserved.

190

BYRON LEW

FIG. 1.

Tractors per 100 farms in Saskatchewan (1921–1961).

ments. 3 Sales collapsed at the onset of the Great Depression, remaining below 10% of the average of the 1920s until the mid-1930s. Still, even with the recovery in the mid 1930s, tractor sales would not surpass their 1928 peak for 20 years. The end of World War II marked the beginning of the great wave of tractor adoption on the Canadian prairies, with horses being almost completely replaced by the middle of the 1950s. The threshold model is a useful tool often used to explain the timing of adoption of a new technology. Its diffusion is a function of the relative prices of inputs and the pace of technical improvements to each technology. The diffusion of a new technology typically follows an S-shaped curve; those few whose scale of production allows for its use adopt first, followed by a period of rapid adoption to saturation. The pattern of diffusion of tractors on the Canadian prairie is illustrated in Figs. 1 and 2. Recently, however, Clarke (1994) has found that tractor adoption on cornbelt farms of the midwestern United States in the late 1920s proceeded more slowly than the threshold model predicts. Apparently, many eligible farmers resisted purchasing a tractor. Significantly, it is shown that this apparent lag in tractor adoption prior to the Great Depression is evident on the Canadian prairie as well. Either farmers were behaving irrationally or their decision process has not been adequately captured by the threshold model. 3

The most widely cited development was the power take-off, incorporated into the Farmall tractor introduced in 1924. The power take-off coupled the implement to the tractor, allowing the transfer of power directly from the engine. Previously, implements were operated by their forward movement turning a wheel to generate motion.

DIFFUSION OF TRACTORS

FIG. 2.

191

Tractor sales in Saskatchewan (1920 –1954).

It is argued that the threshold model’s poor predictive power is, in fact, due to the model’s inability to accommodate the multiperiod nature of the farmer’s problem and the consequent uncertainty this implies. Purchase of a tractor represented the acquisition of service flows into the future and therefore required the farmer to assess future market conditions. However, the period in which the tractor began to gain an advantage over horses, the mid-1920s, was a period of extreme volatility in input and output markets. The weakness of the threshold model lies in the fact that it merely compares two technologies at one point in time. It fails to account for how expectations of price changes— changes that could reverse the relative advantage of each technology—might have influenced the choice. Farmers may have persisted in using horses while forgoing the current benefits of tractor adoption because they expected lower wheat prices or quality improvement in tractors or both. In this article, the farmers’ problem is modeled as an investment choice under uncertainty. By delaying tractor purchase, farmers implicitly held an option to buy a tractor if and when changed conditions might render them more profitable. Thus the farmer’s problem becomes one of choosing when to exercise a call option on tractors. There are many examples in the literature where uncertainty has been incorporated into modeling investment behavior (see Dixit and Pindyck, 1994 for a survey). In economic history, Emery and MacKenzie (1996) evaluate the ex ante value of the subsidy provided to the Canadian Pacific Railway, which some have maintained had been excessive. The model has often been applied to natural resource investment. Brennan and Schwartz (1985) model decisions to

192

BYRON LEW

invest in a mine as well as when to close it down or abandon it. There have also been applications to agriculture. Marcus and Modest (1984) examine crop decisions when output prices and weather behave stochastically. First, the threshold model, its critics, and the consequences of ignoring uncertainty are discussed. Second, the threshold model is estimated for wheat farmers on the Canadian prairies in the 1920s and is shown to overpredict tractor adoption. The central thesis is that farmers were not behaving irrationally. Although many delayed an investment deemed cost saving for the present, this was due to uncertainty over price movements during a time of relatively high volatility. UNCERTAINTY AND THE THRESHOLD MODEL Paul David’s (1975) threshold model has been used in many studies examining the choice between horses and tractors. Ankli, Helsberg, and Thompson (1980) and Sargen (1979) examine wheat farming on the Canadian Prairie and the U.S. Northern Great Plains respectively; whereas Clarke (1994) and Ankli (1980) look at U.S. corn-belt farming, Musoke (1981) and Whatley (1983, 1985) look at cotton, and Ankli and Olmstead (1981) examine California. In these studies, the threshold model is used to explain the diffusion of a new technology by predicting how many farmers should have adopted the technology given the distribution of farm sizes and given input prices. A farmer is faced with choosing between two technologies. In David’s original example, the choice is between reaping by hand or with a mechanical reaper. The mechanized technology, in his example, is fixed-cost using and variable-cost saving relative to the nonmechanized technology. That is, the use of a machine requires a fixed-cost investment, but the cost per unit of use, the variable or marginal cost, is lower. David compared the cost of harvesting by hand with the cost of using a mechanical reaper, showing that there was a threshold farm size beyond which the total cost per acre—fixed cost plus per acre variable cost—was lower for the mechanized technology. In other words, a certain capacity, or farm size, had to be attained in order to cover the fixed-cost investment. The threshold farm size is then a function of the cost of the mechanized technology—itself a function of interest rates, the cash cost of the machine, and the life of the machine—and the cost of using the nonmechanized technology (in David’s example the wage rate). David then compared the number of farms that were larger than the threshold to the number of reaper adopters and showed that the changes in the threshold farm size given changes in wages and reaper prices could account for the pattern of reaper diffusion. However, critics of the threshold model have pointed out how institutional arrangements have been oversimplified and additional explanatory information left out. Some (Olmstead, 1975; Olmstead and Rhode, 1995) have focused on the possibilities of farmers sharing the mechanized technology thereby rendering the individual capacity constraint irrelevant. It seems that because tractors required more care and maintenance than a reaper, they were less suited for sharing than

DIFFUSION OF TRACTORS

193

reapers were (Ankli and Olmstead, 1981). However, custom work—when farmers hire themselves and their equipment out—was common, particularly in the form of postharvest operations (Murchie, Allen, and Booth, 1936, p. 202, Stewart, 1936, p. 298). Others have shown that without incentives to potential adopters, the benefits of cost-saving technology are irrelevant. Whatley (1985) points out that, in the cotton South before the Depression, institutional constraints largely explain why nonmechanized technology persisted despite the advantages of mechanization. Clarke (1994) shows that tractor adoption on the corn belt in the late 1920s proceeded more slowly than predicted by the threshold model until the introduction of particular New Deal government programs. She argues that the apparent lag in tractor adoption is due to the misspecification of farmers’ cost of capital, in turn, a function of the individual farmer’s bankruptcy risk. Farmers’ cost of capital rose with debt load, presumably reflecting a greater bankruptcy risk. Given that debt loads differed across farmers, predictions of the threshold model based on the risk-free rate as the cost of capital will be inaccurate since they fail to account for this heterogeneity. Clarke’s analysis is noteworthy because by incorporating bankruptcy she is arguing that farmers did not simply assess which technology was lowest cost, but rather made decisions predicated on uncertain future outcomes. Bankruptcy risk as a consequence of debt would be irrelevant in a world in which future profits were certain, but uncertainty can alter investment decisions. The threshold model, however, only compares technologies at one point in time under the maintained assumption that purchasers believe the threshold for adoption of the new technology will remain constant or fall. Even though this assumption tends to hold in the long run as continuing improvements increase the advantage of the new technology at all input prices, in the short run particularly acute instability and price volatility can return the advantage to the old technology (Ankli, Helsberg, and Thompson, 1980). Importantly, the period from 1914 to 1945 was particularly volatile for farmers (see Fig. 3). Since tractor adoption began at the end of World War I, this article explores how price changes associated with the interwar period may have made the decision to switch from horses to tractors more difficult. Contemporary observers had noted the problems of price volatility for farmers. Indeed Mackintosh (1935, Ch. 2) discusses in detail how markets on which prairie farmers sold their output and purchased many of their inputs had tended to be volatile and unstable, so that farm income varied substantially from year to year. In response, farmers seem to have tried to insure themselves against such volatility by reducing their exposure to markets and increasing their self-sufficiency at the cost of reducing profits (Stewart, 1936, p. 324). This apparent resistance of farmers to the economic benefits of new markets and new technology has perplexed many contemporary observers and has often been explained as irrational. Economic historians have explained such behavior as rational but risk averse.

194

BYRON LEW

FIG. 3.

Prices (nominal) of inputs on prairies (1914 –1948; 1914 ⫽ 1.00).

Wright and Kunreuther (1975) have argued that cotton farmers may have preferred to maintain self-sufficiency by reducing the amount of land they devoted to cash crops and increased the land devoted to subsistence crops until forced to change. Clarke (1994, pp. 61– 62) argues that farmers may also have tended to reduce reliance on purchased inputs in favor of those they could produce for themselves in order to reduce their cash requirements even though the technology utilizing the purchased inputs was lower cost. A tractor purchase definitely represented a significant investment, whereas the cost of using horses was primarily the cost of feed. The investment in the horse itself was relatively small. A large proportion of the cost of using horses was, thereby, incurred yearly. Furthermore, the actual cost incurred varied with market conditions. As well, feed could be grown on the farm and, therefore, did not represent a cash cost but rather an opportunity cost of revenue foregone by devoting land and labor to its production. As such, it has been argued that farmers valued the cost of feed differently from the cost of purchased inputs regardless of the opportunity cost. If farmers could grow their own feed, they were less likely to need to borrow and, therefore, less exposed to the risk that revenues would not support repayment of loans. Under certain circumstances, including those characteristic of many small prairie farms during the 1920s, the difference between market and farm valuation could be justified. The labor-saving aspect of the tractor is of greater advantage to a farmer with a large farm, as the tractor enables the cultivation of more land within the seasonal constraints. For a farmer with a small farm this benefit was likely of limited value. Small farmers relied on their own labor to a greater degree than did large farmers. Table 1 shows the total weeks of hired labor per family worker by farm size for the year 1930 –1931 in Saskatchewan and for Canada as

DIFFUSION OF TRACTORS

195

TABLE 1 Weeks of Hired Labor per Family Worker Farm size (acres) 1–50 51–100 101–200 201–299 300–479 480–639 640⫹ All

Canada

Saskatchewan

3.53 4.89 5.20 7.29 7.17 11.32 18.79 6.74

2.41 2.44 2.03 4.98 5.82 10.05 17.10 8.42

Source. Census of Canada (1931, Table VI, pp. xxxiii–xxxiv).

a whole. The hired labor requirement clearly increases with farm size, although hired labor is reported for all farm-size categories. For the small farmer, a saving on labor did not represent as large a cash savings. Rather the farmer would have the time available for other pursuits, perhaps for leisure or more likely for the provision of custom work or some other marketable product. Provision of custom work made sense, but only if there were customers nearby. As well, it would make sense for a few farmers in any region to purchase tractors and make up the cash-flow requirements through the provision of custom work, but as more farmers adopt tractors and offer custom work, the value of the farmer’s labor freed up by the tractor declines. In the threshold model, the labor saved by the tractor’s adoption is valued at the market wage. If the labor freed by tractor adoption had a lower value, then the threshold calculation would overstate the case for a tractor. It is not necessary, however, to hypothesize a wedge between market valuation of inputs and the farmer’s own valuation. An important aspect of a farmer’s valuation of inputs was that feed costs tend to be closely correlated with the price of output, since feed production was essentially a substitute for the production of farm output. Consequently, a farmer using horses would have been partially insured against changes in the price of wheat. Because revenues and a large portion of operating costs both rose and fell together, the volatility of net profits was dampened. The only insurance effect provided by a tractor was greater revenues due to its greater capacity. Thus the benefit of a tractor was likely of limited value during periods of low prices. Hence, if wheat prices could have declined in the near future, the cost of using horses would have fallen relative to tractor costs. It may then have been valuable to postpone investment in a tractor at a time when it might be cheaper to operate horses in the future. Essentially, by not purchasing a tractor, farmers were retaining the option to purchase in the future.

196

BYRON LEW

Under the cost-uncertainty approach, the value of postponing investment is determined by potential future cost savings. It is independent of debt levels and bankruptcy risk. However, risk due to debt and bankruptcy is also function of the same uncertainty. Both explanations of the apparently delayed adoption of tractors, cost savings versus revenue shortfalls, reinforce each other. 4 The uncertainty determines the adoption threshold for the risk-free farmer, and differing debt levels might explain the variation of farmers around the predicted threshold. If uncertainty in wheat prices could create value in delaying adoption, so too could uncertainty in tractor prices. Tractor prices initially fell by almost 50% from 1920 to 1925, but then remained absolutely flat through the mid-1930s. 5 Part of the price decline was a demand side effect after wheat prices fell from a post-World War I peak. However, part of this must also have been due to technical change induced by large increases in tractor sales at the beginning of their diffusion. Evidence suggests that while nominal prices did not change dramatically, prices adjusted for quality improvements continued to decline in the mid-1920s and 1930s (White, 1999). A farmer, therefore, by delaying and waiting to purchase a better tractor later on, hoped to obtain greater cost savings in the future. The largest portion of the operating cost of a tractor was the fuel expense and fuel prices, like prices of many other commodities, were volatile during and after World War I. While the threshold model shows that fuel costs were sufficiently low through the mid-1920s for adoption to provide immediate cost-savings, expectations of falling prices or volatility may have been sufficient to encourage farmers to delay a tractor purchase. Gasoline prices almost doubled from 1914 to 1920 but fell back to their prewar price by 1927. The effect of fuel price behavior is, therefore, modeled. Interestingly, Clarke (1994) argues that the gap between the number of tractor adopters predicted by the threshold model and actual adopters evident in 1929 had been closed by 1939. The difference during the interim, and the focus of her study, was the New Deal. Specifically, she cites the establishment of the Farm Credit Administration, which oversaw agricultural financing and reduced the cost of borrowing, and the Commodity Credit Corporation, which set minimum prices for crops and thereby reduced the overall risk of borrowing as key institutional changes. While in Canada farm debt was certainly a political issue, the federal government responded directly to the problem of output price uncertainty

4

Bankruptcy risk might have worked the other way. A farmer already facing high bankruptcy risk might wish to adopt a tractor to increase potential revenue while incurring no additional exposure. 5 Unfortunately, the only data available for tractors in Canada from 1936 to 1943 is expenditure and quantity sold for all tractors undifferentiated by tractor size (Canada, Farm Implement and Equipment Sales), so movements in the resultant price reflect both price changes and shifts to larger tractors.

DIFFUSION OF TRACTORS

197

through the establishment of the Canada Wheat Board in 1933 as an optional marketing channel. 6 Both the Canada Wheat Board and the Commodity Credit Corporation provided farmers long-term price stability thereby reducing their exposure to risk. Both agencies advanced farmers money for delivery at the end of the season. If prices rose, farmers received the difference, though a small spread was retained by the agencies to cover cost of administration. If prices fell, farmers owed nothing. 7 The guaranteed price floor provided by these agencies in both countries would have altered farmers’ exposure to output price risk. In addition, as time passed and the marginal improvements to tractor quality declined, risk associated with falling quality-adjusted prices would have also declined. By the 1940s, the debate had shifted from whether to choose tractors or horses to how soon to switch to tractors (Olmstead and Rhode, 1994). The only problem remaining was the lack of tractors. The analysis proceeds in two stages. First thresholds for tractor adoption will be estimated for the 1920s and early 1930s using the standard threshold model. Next, the farmer’s investment problem will be modeled as a multiperiod analysis incorporating irreversible investment and uncertainty. Ultimately, the results of estimates of this modified model will be compared to those of the simple threshold model to show that inclusion of uncertainty does help to explain the resistance of many farmers to the new technology. THRESHOLD MODEL The method of calculating thresholds used here follows Ankli, Helsberg, and Thompson (1980) with exceptions noted. There are six basic configurations for farm power reported in Hopkins, Armstrong, and Mitchell (1932): four-, six-, or eight-horse teams and two-, three-, or four-plow tractors. Every team of horses included an extra horse. Costs are first divided into a component that varies by acreage farmed and a fixed component. Fixed costs consist of the cost of equipment, including the cost of horses, and a portion of the cost of feed. The equipment used for horses and for tractors and their service lives are listed in Ankli, Helsberg, and Thompson (1980, pp. 24, 29) taken from Hopkins, Armstrong, and Mitchell (1932). 8 Since equipment prices are listed for 1930 only, additional equipment price information for the 1920s and 1930s was drawn from 6

In 1943 the Wheat Board was granted monopsony power and made the sole marketing outlet for grains when agreements between Canada and Britain for grain delivery during the war necessitated circumventing rapidly rising prices. 7 The two agencies differed slightly in that farmers were allowed to reclaim their crop from the CCC anytime by paying off the advance allowing farmers access to a source of cash. The Wheat Board, in contrast, was more rigid, as it retained the crop to sell and offered the farmer a fixed payment schedule. 8 Hopkins, Armstrong, and Mitchell (1932, pp. 35–38, 40, 43) describe a typical setup as including harness, gang plow, drag harrows, cultivator, single disk, grain cleaner, grain drill, binder, mower, rake, wagon, and truck gear. Sizes of each implement differed by number of horses or size of tractor.

198

BYRON LEW

the report of the House of Commons Special Committee on Farm Implement Prices (Canada, 1937) as well as from the Dominion Bureau of Statistics publication Agricultural Implement Industry. The price of horses is from Handbook of Agricultural Statistics: Part VI: Livestock and Animal Products, 1871– 1973, p. 101. All capital costs are converted into a yearly flow or rental rate by R共r, T兲 ⫽

r 1 ⫺ e ⫺rT

,

where r is the interest rate and T is the service life of the equipment (Whatley, 1983, p. 206). While Ankli, Helsberg, and Thompson (1980) considered feed costs to be entirely fixed; Ankli (1980, p. 143) recognized that feed costs are partly variable after Jasny (1935), who estimated that an idle horse will consume about 70% of the feed required by a horse working an average workload of 800 h per year. 9 The extra horse in each team is considered idle, so a four-horse team includes fixed feed costs for five horses but variable feed costs for four. Data on yearly costs of and hours worked by horses are taken from studies of farms in Alberta and Saskatchewan in 1930, reported in Grest (1936). Feed cost as a linear function of hours worked per horse is derived by extrapolation with the intercept representing the fixed component where it is assumed that feed cost for an idle horse is 70% of the feed cost of a horse working 800 h per year. 10 An index of feed prices in western Canada (Canada, 1948) is then applied to feed costs, and an index derived from farm labor wages in Saskatchewan (Leacy, 1983, Series M86) is applied to the cost of care and to miscellaneous costs. Variable cost is calculated as the sum of wages and costs of operation per hour, which includes feed for horses and fuel and lubrication for tractors multiplied by the technical capacity—total time to fully prepare and harvest an acre— of each of the six power configurations. The calculation of technical capacities follows Ankli, Helsberg, and Thompson (1980, p. 26), who in turn rely on Hopkins, Armstrong, and Mitchell (1932, p. 55). Gasoline prices are taken as the price of gasoline in Regina after 1926 and in Toronto before 1926 reported in Prices and Price Indexes. Prices of oil and grease are based on the prices reported in Hopkins, Armstrong, and Mitchell (1932) for 1930, indexed over time by the index of lubricating oil prices, also in Prices and Price Indexes. 11 Only the use of gasoline is considered. Hopkins,

Ankli, Helsberg, and Thompson (1980) and Sargen (1979) assume a 15-year life for horses, whereas Clarke’s (1994) 11-year estimate is used here. 9 Thresholds are not particularly sensitive to the division of feed costs between fixed and variable. 10 It is likely that keeping horses perpetually idle would be much cheaper if they were only pastured. Work horses would be fed a diet richer in concentrates prior to and during the working season. 11 The price for lubricating oil reported in Prices and Price Indexes differs slightly from Hopkins, Armstrong, and Mitchell (1932).

DIFFUSION OF TRACTORS

199

Armstrong, and Mitchell (1932, p. 54) report that by 1929 most prairie farmers were using gasoline. Even those using kerosene consumed the two fuels in equal proportions. While during World War I the ratio of the price of gasoline to the price of kerosene peaked at 2.7, by 1925 the premium on gasoline was only 20%. By 1927 gasoline was selling at virtually the same price as kerosene. Since the technical data used in this study are more reflective of the mid-1920s, and since by the mid-1920s the actual cost difference for a farmer choosing to use both gasoline and kerosene rather than just gasoline was very small, the slight difference is ignored. Undoubtedly kerosene must have been widely used at the beginning of the 1920s because it was so much cheaper. However, by the mid-1920s—the period of the focus of this study—the two fuels are assumed to be perfect substitutes. All preharvest operations are assumed to have taken place in the spring and, further, that there were 30 days in which to prepare the land and complete seeding. In fact, because the growing season is limited by spring and fall frosts, the speed with which the farmer could prepare and seed the land in the spring was the effective constraint on farm size (Grest, 1936, p. 36). 12 The 30-day constraint used here is construed from suggestions in Hopkins, Armstrong, and Mitchell (1932, p. 41). It is also assumed that all plowing of stubble land takes place in the spring rather than in the previous fall. Though this increases the plowing requirement in the spring, moisture trapped in the stubble over the winter raises yields (Spector, 1983, p. 126). There is assumed to be no effective constraint on time spent on operations on summerfallow, although the entire set of operations on all the land for a season would have to be completed within the seasonal limit (Sargen, 1979, pp. 110 –126). A maximum farm size or capacity limit is calculated for each power configuration by determining how much land could be prepared and seeded in 30 days assuming two-thirds of a farm will be under crops and farmers worked 10 h per day everyday (Hopkins, Armstrong, and Mitchell, 1932). 13 Monthly wage rates are converted to hourly rates assuming 10-h days and 6-day work weeks, that is, 260 h per month. The calculation of the threshold is not effected by the calculated capacity limit. The limit is used to determine whether a calculated threshold would be binding; that is, whether it falls into the range of operation of a particular size of horse team or tractor. The results turn out to be rather insensitive to the specification of this limit and are discussed. Information on time taken to perform various operations is presented here in Table 2. These data were collected from a sample of prairie farms in 1929. While these data are assumed to apply for the full period investigated, 1920 –1935, it is 12 According to Bracken (1920, p. 16), wheat yields are maximized if seeding takes place between April 15 and April 30, although seeding can take place over a 6-week period beginning April 7 and finishing by Victoria Day (May 20 actually). 13 Farm size represents improved acreage. The ratio of improved to total acreage in Saskatchewan averaged 60% for each census from 1926 to 1946.

200

BYRON LEW TABLE 2 Acres per Hour by Operation and Maximum Farm Size, circa 1929 Horses

Operation Plowing Discing Cultivating Harrowing Seeding Binding Combine Max farm size (acres)

Tractor (plows)

4

6

8

2

3

0.45 1.37 1.31 3.18 1.92 1.64

0.48 2.03 1.65 4.25 2.54

0.76 3.05 2.01 6.30 3.35

0.81 3.31 3.00 6.65 3.33 2.34 3.25

1.26 6.21 3.50 9.87 4.20 3.16 3.93

2.80 250

309

434

486

671

4 1.57 7.29 3.75 12.30 5.52 3.55 4.36 820

Source. Hopkins, Armstrong, and Mitchell (1932, p. 55).

the latter half of the 1920s that is most closely scrutinized, as it is during this period, it is argued, that predictions and actual behavior diverge. The coefficients agree with Sargen’s (1979, pp. 88 – 89) data for 1920, although at his upper limit, consistent with their timing. The data, however, may be less reflective of performance by the mid-1930s, when pneumatic tires and other developments were widely diffused. The results of the threshold calculations are consistent with Sargen (1979) and Ankli, Helsberg, and Thompson (1980) as horses tended to be fixed-cost using and variable-cost saving. In most years the four-, six-, and eight-horse configurations all had larger fixed costs and lower variable costs than the two-plow tractor. At farm sizes larger than the threshold, the fixed-cost-using, variablecost-saving technology, that is, horses, is the less costly. Therefore the surprising result holds that tractors would have been used on smaller farms and horses on larger farms. However, since tractor capacity greatly exceeded that of horses, for any farm exceeding the capacity of the largest horse team, tractors were the cost-saving technology. 14 So predictions from the threshold model are that both the smaller and the larger farms were suited for tractors while the medium-sized farms should have retained horses. Table 3 shows thresholds between pairs of power sources: between a fourhorse and a two-plow tractor, a six-horse and a two-plow tractor, an eight-horse and a two-plow tractor, and a two-plow and a three-plow tractor. The threshold reported is the threshold at which a horse should be used given that horses were the variable-cost-saving technology. Negative thresholds indicate that the variable-cost-saving technology is also fixed-cost saving and so dominates from the 14 For a farm larger than the acreage limit of the largest tractor available, the additional acreage is treated as if it were a new farm, though in 1926 about 97.5% of farms in Saskatchewan were within the capacity of the four-plow tractor.

201

DIFFUSION OF TRACTORS TABLE 3 Thresholds

Year

4h/2p

6h/2p

8h/2p

2p3p

Number of tractors on farms

1920 1921 1922 1923 1924 1925 1926 1927 1928 1929 1930 1931 1932 1933 1934 1935

166* 46* ⫺10* ⫺7* 98* 279 224* 341 411 380 121* ⫺14* ⫺66* ⫺64* ⫺64* ⫺57*

426 238* 150* 204* 332 560 466 653 749 713 379 194* 94* 95* 119* 141*

510 337* 246* 305* 421* 610 530 680 736 706 453 295* 189* 192* 229* 256*

722 804 632 317* 485* 619 599 622 628 636 721 879 998 1041 948 853

15,431 19,243 20,713 22,291 22,552 23,657 26,674 31,003 38,226 43,104 45,025 43,308 43,074 42,798 42,724 42,819

Limit

250

309

434

486

Note. An asterisk indicates that the threshold occurs below acreage capacity.

smallest farm. However, many thresholds occur beyond the acreage limit of the horse configuration, therefore effective thresholds are marked. For example, in 1924, the threshold between the two-plow tractor and the four-horse team is 98 acres, so farms larger than 98 acres would use the four-horse team up to its capacity of 250 acres. The threshold for the six-horse team with the two-plow tractor, 332 acres, exceeds that team’s capacity of 309 acres, so the two-plow tractor would still be the choice up to the threshold between the eight-horse team and the two-plow tractor, 421 acres. For a farm greater than 421 acres, the choice is an eight-horse team up to its capacity of 434 acres. For farms larger than 434 acres, farmers choose a two-plow, three-plow, and four-plow tractor to their respective acreage limits. At the capacity of the largest tractor, the additional acreage is simply a new farm and the choice procedure is repeated. Some comparisons have not been reported as they can be summarized easily. The four-horse team has lower fixed and variable costs than the six-horse team, which in turn has lower fixed and variable costs than the eight-horse team. Farmers would have chosen the smallest team to use up to that team’s limit: 250, 309, and 434 acres respectively. Beyond the capacity of the eight-horse team, a farmer would merely have chosen the tractor appropriate to farm size. The three-plow tractor also has lower fixed and variable costs than the four-plow tractor and so would be used up to its capacity limit of 671 acres. Comparisons

202

BYRON LEW TABLE 4 Tractors per 100 Farms in Saskatchewan

Size (acres)

Improved* (acres)

1–50 51–100 101–200 201–299 300–479 480–639 604⫹ Total

1–30 30–60 60–120 120–180 180–290 290–385 385⫹

Tractors per 100 farms

Distribution of farms by size

1931

1936

1941

1946

1931

1936

1941

1946

3.2 5.7 9.3 19.1 25.5 44.0 73.6 31.7

4.1 4.3 8.5 18.6 24.8 42.4 70.8 29.5

3.7 6.2 12.9 27.1 34.4 53.0 79.3 39.0

7.2 10.9 23.1 42.5 51.5 71.3 93.8 57.0

0.015 0.010 0.298 0.024 0.322 0.140 0.191 1.000

0.016 0.012 0.323 0.025 0.311 0.131 0.183 1.000

0.017 0.013 0.284 0.027 0.310 0.145 0.204 1.000

0.014 0.011 0.233 0.027 0.314 0.159 0.243 1.000

Note. An asterisk indicates that the number of improved acres is calculated as 60% of the total size. Source. Census of Canada and Census of the Prairie Provinces.

between horses and the three-plow tractor are not reported because in most cases the two-plow tractor dominates the three-plow tractor over the entire range of the two-plow tractor up to its capacity limit, so the horse/two-plow tractor comparison is the critical one. 15 The threshold model’s predictions in Table 3 imply that for the years 1927– 1929, all farmers in Saskatchewan should have purchased a tractor. As well, farms utilizing the larger configurations of six- and eight-horse teams should have adopted tractors by 1925. The threshold between the two-plow tractor and the six-horse team of 560 acres exceeds the 309-acre capacity of the horses by 80%. Adoption of tractors on smaller farms is not as clear until 1927, as the threshold exceeds the horses capacity in 1925 but falls back within its capacity in 1926. These results are not particularly sensitive to the capacity calculation of the horse configurations. The threshold between the four-horse team and the two-plow tractor is calculated to be 341 acres in 1927. For the four-horse team’s capacity to reach 341 acres, farmers would need an extra 110 h over the 300 h already assumed to complete their plowing and seeding operations. By 1928, the threshold increases to 411 acres requiring almost 500 h. The thresholds for the six-horse team over the two-plow tractor exceed the capacity of the six-horse team by even more than this from 1925 on. Yet by 1926 there were just under 27,000 tractors on farms in Saskatchewan, representing less than 25% of farms. Tractor adoption by farm size (Table 4) is reported in the census beginning in 1931. Tractor adoption rates were increasing with farm size, indicating the importance of capacity utilization for tractor ownership on larger farms. By the 1930s, more than 70% of farms 640 acres and larger had tractors, and the proportion was undoubtedly higher for farms larger 15

In 1923 the three-plow tractor is competitive with the two-plow tractor at 317 acres; however, the eight-horse team is cheaper up to its capacity limit.

DIFFUSION OF TRACTORS

203

than the 720 total or 434 improved acres given the trends reported in a more detailed breakdown of farm sizes of the 1936 Census of the Prairie Provinces. However, for the smaller farms, tractor adoption rates are declining, not rising. For farms up to 200 acres, adoption rates were less than 10%. This result is clearly at odds with the predictions of the threshold model. Alternatively, small farms may not have been grain farms and therefore may not have benefited from tractors, but small farms (⬍300 acres) that did not produce wheat account for only 10% of farms in 1931. 16 The fixed-cost savings in the form of the avoidance of the high cost of horse feed available to farmers with smaller farms were apparently forgone. And while the total number of adopters increased after 1926, which is generally consistent with the threshold model, by 1931 there were still only about 43,000 tractors provincewide, representing just under one-third of all farms. TRACTOR INVESTMENT UNDER UNCERTAINTY The farmer’s choice of switching from horse to tractor is treated as an investment problem of the type described in Dixit and Pindyck (1994, Ch. 6). The switch requires an investment of I (the purchase price of the tractor) and at any instant yields a cost savings over using horses, ␲ t , for T years (the life of the tractor). With perfect certainty, a tractor purchase is beneficial if the present value of the cost savings of the tractor exceeds the investment cost. This, however, ignores the value of forgoing the purchase in anticipation of changes in the future altering the relative cost savings ␲ t or the investment cost I of a tractor. Therefore, the value of the option of delaying a tractor purchase is calculated and the results are presented as an investment criterion in the form of a trigger price at which the option is exercised. It may appear unreasonable to assume that farmers had the knowledge to develop such a model and reach the rational conclusion. It is not unreasonable, however, to suppose that farmers had deep though highly specific knowledge regarding their own circumstances. The model to be developed is intended as a model of what a farmer would know intuitively regardless of whether the information was processed identically. Any of the input factors could theoretically impart uncertainty to the investment decision; however, wheat prices and tractor prices are considered as the most important, though the impact of fuel price uncertainty is included. Wheat prices appeared to have been subject to the most volatility. As well, farmers surveyed in the late 1920s held low wheat prices as the key to their delaying purchase of a tractor (Hopkins, Armstrong, and Mitchell, 1932, p. 49). Even if horses did not represent a cash cost for some farmers, horses required feed, which meant less land available for the cash crop. Therefore, wheat prices are reflected 16 This is true of the smallest farms, those less than 50 acres, but for farms between 50 and 100 acres, over 50% reported spring wheat according to the 1931 census. For farms between 100 and 200 acres, over two-thirds reported spring wheat.

204

BYRON LEW

directly in production costs as the opportunity cost of devoting land to feed for horses. When wheat prices were low, the opportunity cost of feed and therefore for the operation of horses was also low. Uncertainty in tractor prices is also modeled. Tractors were the new technology and they continued to undergo substantial technological change throughout the late 1920s and 1930s (Clarke, 1994). While nominal tractor prices appeared very stable after an initial rapid decline in the early 1920s, current research suggests that quality-adjusted prices fell rapidly throughout this period (White, 1999). Farmers may have anticipated better tractors in the future and therefore delayed their purchase. Fuel was the most significant component of tractor operation, so uncertainty in fuel prices may have slowed their adoption. In fact gasoline prices rose substantially during World War I but returned to their prewar price by 1923. However, the behavior of fuel prices may have been smoother. Farmers were able to partially substitute kerosene for gasoline and the price of kerosene actually dipped during the war, cushioning the impact of rising gasoline prices. After the war, as gasoline prices declined, kerosene prices rose until the two prices equalized by 1927. The fuel price series was, therefore, smoother than either of its components. Other inputs may have been subject to some uncertainty. Certainly farm wages fluctuated wildly and high wages during World War I induced the initial wave of tractor adoption. However, farm wages on the prairies were undoubtedly closely correlated with wheat prices, modified by supply-side events such as World War I and changes in immigration policy during the 1920s (Green, 1994). It is therefore unclear how significant wages really were as an independent source of uncertainty. Alternately, it could be argued that wages, like feed, should also be a function of wheat prices. However, the determination of wages on the prairie is as a derived input to grain production, whereas feed is a substitute in production. Both would therefore reflect changes in wheat prices, but for wages this acts indirectly. Also, if most of the labor was supplied by the farm family, the opportunity cost of farm family labor was less likely to be subject to uncertainty. So for farmers able to operate their horses for planting and seeding without the use of hired labor, wage behavior was only an indirect factor. Farmers with larger farms may have been exposed to wage uncertainty. Its inclusion, however, would tilt the results further toward the dominance of the tractor and yet history shows the persistence of the horse. Therefore the focus is on the circumstances of the small farmer and wages, while probably a source of uncertainty, are not examined. Horse prices might also reflect wheat prices, but supply-side factors were also important. The supply of horses was increasing relative to demand over this period as tractor diffusion accelerated, causing horse prices to fall relative to all other inputs after World War I. General farming equipment prices did not appear to move much. As well, the difference in expense of outfitting a horse team and

205

DIFFUSION OF TRACTORS TABLE 5 Correlations among Nominal Input Prices, 1914 –1948

Wheat Feed Machine Wage Gas Horse

Wheat

Feed

Machine

Wage

Gas

0.88 ⫺0.12 0.62 0.63 0.62

0.05 0.74 0.71 0.52

0.48 ⫺0.41 ⫺0.73

0.31 0.07

0.71

Sources. feed, wage, gas, and horse (see text); wheat prices (Leacy, 1983, Series M228); machine price index (Canada, 1948).

outfitting a tractor was small. Correlations among all nominal input prices are reported in Table 5. The other component of the decision considered is the irreversibility of the investment in a tractor. It is assumed that tractors were durable assets subject to lock-in, at least to some degree. Otherwise, a farmer could simply sell off a tractor when prices turned against their use and there would be no risk, other than bankruptcy risk, to their acquisition. To the extent that investment in an asset is irreversible, the uncertainty increases the potential value of waiting. This is important, as a tractor was a farmer’s single largest investment in equipment and one with relatively few alternate uses outside of farming. 17 Tractor investment may have been irreversible given the assumption that their demand was derived solely as an input to wheat production. Tractors particularly would have had limited usefulness within the region except for producing wheat. If feed costs fell as wheat prices fell such that horses became the low-cost technology, demand for tractors would decline and supply would increase. This is exactly what happened at the onset of the Depression. By 1931 there was no farm size at which tractors were cheaper to use than horses according to the threshold model. Unless tractors could be transported to other markets cheaply, their value on the prairies would therefore decline with the decline in output prices. To capture the implications of markets for used tractors, the impact of different degrees of irreversibility are illustrated to capture the possibility of farmers selling their tractors rather than merely losing their investment. Uncertainty in a price series, whether in wheat or in tractor prices, is assumed to evolve as an Ito process, specifically as geometric Brownian motion or random walk, with drift, described by dx ⫽ ␣ xdt ⫹ ␴ xdz,

(1)

where dz ⫽ ⑀ t 公dt, ⑀ t ⬃ N(0, 1), and ␧[ ⑀ t⑀ s] ⫽ 0 for t ⫽ s. The ␣ is the drift parameter and ␴ is the volatility parameter. Two important elements are intro17

A combine was the only other type of equipment as costly as a tractor, but combines were rare during the 1920s and 1930s. In fact, combine ownership was not even reported in the 1926 Census.

206

BYRON LEW

FIG. 4.

Prices of wheat, nominal and real.

duced in this specification: the future path of wheat prices is partly random, and the variance of those random changes increases linearly with time (Dixit and Pindyck, 1994, p. 64). Therefore, while prices in the future can be predicted within bounds, that confidence interval widens the more distant the prediction and the greater the volatility. The price of wheat appears to evolve as a random walk with drift. An augmented Dickey–Fuller test on real wheat prices from 1870 to 1974 cannot reject the null hypothesis that the series contains a unit root. The prices of wheat, both nominal and real, are shown in Fig. 4. The cost savings of operating a tractor over using horses is calculated as the cost of using horses minus the cost of using tractors for a given farm size and is expressed as a function of the variable whose behavior is subject to uncertainty. This cost savings, ␲ t ( p), is made up of two components: c( p) are costs which vary with the price of wheat, and C are all other costs incurred annually but not subject to uncertainty. In the threshold model, costs are variable if they vary by size of farm, vc, and are fixed otherwise, FC. Feed is considered to have a fixed and a variable component with respect to farm size, but feed costs will vary with wheat prices. Therefore FC( p) represents costs fixed with respect to farm size but which vary with wheat prices and vc( p) are costs which vary both with size of farm and with wheat prices. All costs which do not vary with wheat prices but which may be either fixed or variable relative to farm size are represented by FC and vc, respectively. This yields cost savings of tractors at a particular size of farm x:

␲ 共 p兲 ⫽ FC horse共 p兲 ⫹ vc horse共 p兲*x ⫹ FC horse ⫹ vc horse*x ⫺ 关FC tractor ⫹ vc tractor*x兴 ⫽ c共 p兲 ⫹ C.

(2)

DIFFUSION OF TRACTORS

207

The cost-savings equation is estimated using the same data as was used in the threshold calculations above. Costs unaffected by uncertainty are discounted at the risk-free rate, r, while the discount factor for uncertain costs, ␦ ⫽ r ⫺ ␣ , contains a component reflecting the expected growth rate of the uncertain price series. The risk-free rate, r, is taken as 6% per annum as in the threshold calculation above. 18 The expected present value of the cost savings of a tractor with a service life of T years at time of purchase is then V共 p兲 ⫽ ␧

冕

T

e ⫺rt ␲ t 共 p兲

(3)

0

⫽

c共 p兲

␦

共1 ⫺ e ⫺ ␦ T 兲 ⫹

C r

共1 ⫺ e ⫺rT 兲.

In the case of uncertainty in tractor prices, I, the annual cost savings of tractors in use is independent of the behavior of the price of tractors and therefore cost savings is merely ␲, i.e., is fixed relative to the uncertain variable, I. As modeled, it is assumed that by buying a tractor a farmer has purchased a different income path for the life of the tractor. The impact of an option to undo that investment at any time has not been modeled. However, the possibility that a farmer could sell off the tractor at some point before it has been fully depreciated would alter the decision. Therefore, the degree of irreversibility is represented by {␪兩0 ⬍ ␪ ⬍ 1} where ␪ ⫽ 1 for a fully irreversible investment. The irreversible portion of the investment cost of a tractor is ␪ I, and the portion recapturable on sale of a used tractor is (1 ⫺ ␪ )I in present-value terms. A farmer would only be putting the value ␪ I at risk in purchasing a tractor; the portion (1 ⫺ ␪ )I can be recaptured and so is not subject to lock-in. Results are presented for various ␪ representing different degrees of irreversibility. The decision to exercise the option to purchase a tractor is made by comparing the current price with a calculated trigger price, p*. 19 To derive p* the value of the option is expressed as a function of the uncertain price series. The value of the option to purchase a tractor, F( p), must satisfy the differential equation 1 2

␴ 2 p 2 F⬙共 p兲 ⫹ ␣ F⬘共 p兲 ⫺ rF共 p兲 ⫽ 0,

(4)

and is subject to the three boundary conditions F共0兲 ⫽ 0,

(5)

For the results, interpretation is based on different values of ␣ while holding ␳ constant. However, since it is the difference, ␦, which enters into the equation, an alternate interpretation would be adjustment of ␳ holding ␣ constant or even the simultaneous adjustment of both parameters. In this analysis, ␳ is assumed exogenous so that the differences in drift of the price series can be quantified. See Dixit and Pindyck (1994, pp. 120 –124) for discussion. 19 Or I* in the case of uncertainty in the quality-adjusted price of the tractor. 18

208

BYRON LEW

F共 p*兲 ⫽ V共 p*兲 ⫺ I, and

(6)

F⬘共 p*兲 ⫽ V⬘共 p*兲,

(7)

where V( p) is from Eq. (3) and p* is the trigger price. The first boundary condition ensures that the option is worthless if the price ever hits 0, as it is an absorbing barrier. The second and third boundary conditions simply ensure that the solution is nicely behaved (Dixit and Pindyck, 1994, p. 141). In general the trigger price under the assumption of a finitely lived asset is p* ⫽

␤1

␦

共 ␤ 1 ⫺ 1兲 共1 ⫺ e ⫺ ␦ T 兲

I,

(8)

where ␤ 1 is the positive root of either 1 2

␴ 2 ␤ 共 ␤ ⫺ 1兲 ⫹ 共r ⫺ ␦ 兲 ␤ ⫺ r ⫽ 0

(9)

for an option that expires upon exercising or 1 2

␴ 2 ␤ 共 ␤ ⫺ 1兲 ⫹ 共r ⫺ ␦ 兲 ␤ ⫺

r 1 ⫺ e ⫺␦T

⫽0

(10)

for an option that continues to be available. 20 If the price of wheat exceeds p*, a farmer would exercise the option and switch to a tractor, otherwise the option is held. With uncertainty in the price of the asset, I, the trigger level of investment below which it is profitable to invest in the asset, I*, is I* ⫽

␤1

r

共 ␤ 1 ⫺ 1兲 共1 ⫺ e ⫺ ␦ T 兲

␲,

(11)

where ␤ 1 is calculated as the negative root from Eq. (9). 21 When the cost of a tractor falls below a certain trigger price, the farmer would exercise the option to buy and would continue to use horses for tractor prices above the trigger price. Results for uncertainty in wheat prices which are drawn for farms with 250 improved acres are reported in Fig. 5. All estimates are taken for 1927 values because the threshold model predicted that by 1927 all farmers should have adopted tractors. Results for other comparisons are discussed in the text. Each graph illustrates parameter combinations for different levels of invest20 In general, the assumption that the option is perpetual will imply more rapid diffusion if the option is assumed to expire on its exercise (Dixit and Pindyck, p. 204). 21 The negative root is used such that the value of the option F( p) 3 ⬁ as I 3 0, whereas in Eq. (8) the positive root is used such that F( p) 3 0 as p 3 0. In other words, when the price of wheat is the source of uncertainty, if prices fall to 0 the option to buy a tractor becomes worthless. If the source of uncertainty is the investment cost and tractors become very expensive, the value of the option must decline.

DIFFUSION OF TRACTORS

209

FIG. 5. Investment thresholds for uncertainty in wheat prices by degree of irreversibility (four-horse two-plow tractor comparison). The area below each curve represents the parameter combinations for which the trigger price exceeds the threshold price for adopting a tractor.

ment irreversibility, yielding a trigger price equal to $1.46, the price of wheat in 1927. The region below each curve represents parameter combinations for which wheat prices exceed trigger prices and are therefore combinations for which the option to purchase a tractor should be exercised. The region above each curve represents parameter combinations for which wheat prices are less than the trigger price and are therefore combinations for which the option should be retained. Interpreting the results requires assumptions regarding the value of the parameters, and the choice of time period affects the parameter estimates (Fig. 4). Volatility in real wheat prices over the long run, 1870 –1974, is ␴ ⫽ 0.23 (annually), though government price supports from the mid-1930s on would have dampened volatility. For 1870 –1926, ␴ ⫽ 0.16 for real prices. Values are lower still if the war years are eliminated, however, looking only at the period 1913–1927, ␴ ⫽ 0.23. Volatility in wheat prices probably fell in the range 0.10 ⱕ ␴ ⱕ 0.30. Real wheat prices appear to have trended downward modestly, implying a small and negative value for ␣. The results show that in general the more negative the trend in wheat prices, the less likely is tractor investment, as the expectation of lower future opportunity costs for horses more than offsets the short-term cost savings of tractors. Greater volatility in wheat prices also makes tractor investment less desirable. As expected, the less the irreversibility of the investment, the more likely is investment. Starting with the case of fully irreversible investment, trigger prices were probably above the price of wheat for virtually all reasonable values of the parameters. For ␣ ⫽ 0 and ␴ ⫽ 0.16 the trigger price is right at the 1927 price. From this point, the assumption of any additional volatility or any additional

210

BYRON LEW

downward drift in prices raises the trigger price above the price of wheat. These results are quite sensitive to the assumption of irreversibility. For the case of 70% irreversibility, again starting with ␣ ⫽ 0, the investment trigger is at ␴ ⫽ 0.26, and with ␣ ⫽ ⫺0.02, the investment trigger falls below ␴ ⫽ 0.25. Therefore it is probable that given uncertainty in wheat prices, with irreversibility of 70% or greater, tractor investment should have been postponed and farmers with 250 improved acres should have retained their horses. Conditions though were probably not too far from the point where those farmers should have considered adopting. This seems consistent with the perceived uncertainty evident from studies performed to determine the size of farm needed for adoption. While the threshold model predicts that tractors were better suited for the smaller farm, as horses were the fixed-cost-using technology, results for smaller farms show that for the comparison between the two-plow tractor and the four-horse team, the region of adoption in (␣, ␴) space increases monotonically in both parameters as farm size is increased. For farms smaller than 250 acres, the curve in Fig. 5 is essentially shifted down and to the right, albeit modestly. For example, for a 200-acre farm, for full irreversibility, the curve intersects the ␴ axis at ␣ ⫽ 0.15 and approaches ␴ ⫽ 0 at ␣ ⫽ ⫺0.06. The general cost savings of the tractor at smaller farm sizes is outweighed by the greater exposure of horses to the potentially favorable effect of falling wheat prices. This result is consistent with the pattern of adoption by farm size reported in the census. For the two larger sized farm comparisons, the farms of 309 and 434 acres using six- and eight-horse teams respectively, the price of wheat was undoubtedly below the trigger price. Results have not been reported, as there were virtually no reasonable parameter combinations for which the price of wheat was not above the trigger price. For example, for the six-horse team two-plow tractor comparison assuming full irreversibility, trigger prices are below current prices for virtually any value of ␣ for ␴ ⬍ 0.35. With a lesser degree of irreversibility, tractor adoption becomes even more likely. Assuming that tractor investment was 75% irreversible, then farmers would hold onto their horses only if ␴ ⱖ 0.4 for virtually all values of ␣ except positive values. Again, these seem to be unreasonable parameters, suggesting the attractiveness of tractors for the larger farm. The other likely source of uncertainty leading to delayed adoption is the potential for improvements in tractors leading to a quality-adjusted decline in tractor prices. Results of estimates of uncertainty in tractor prices are reported in Fig. 6 and follow very closely the pattern of uncertainty in input prices. The curves illustrated are the ratios of the irreversible portion of the capital cost of the tractor, I, to the calculated trigger price, I*, for combinations of ␣ and ␴. 22 When these ratios fall below 1.0, that is, when the actual cost of a tractor falls below the trigger price, the option is exercised and investment is predicted. Therefore, as above, the area below each curve represents parameter combinations for which adoption is predicted; above is the area of nonadoption. 22

Note that “price” now refers to the price of the tractor, which is the investment cost I.

DIFFUSION OF TRACTORS

211

FIG. 6. Investment thresholds for uncertainty in tractor prices by degree of irreversibility (four-horse two-plow tractor comparison). The area below each curve represents the parameter combinations for which the trigger price exceeds the threshold price for adopting a tractor.

In general, tractor investment is less likely the more negative the trend in tractor prices, the greater the degree of volatility, and the greater the degree of investment irreversibility. For the 250-improved-acre farm, four-horse two-plow tractor comparison, the conclusions are virtually identical to the case of output price uncertainty. The area for which the option is exercised under the assumption that investment is fully irreversible is virtually all in the first quadrant, i.e., for positive ␣. The curve approaches the x axis at ␣ ⫽ ⫺0.03 but crosses the y axis at ␴ ⫽ 0.1, so that the area of adoption for negative values of ␣ is for very low levels of ␴. Unless it can be assumed that tractor prices were not falling, or if falling with very low volatility, then tractor prices must have been above the trigger price for adoption. Unlike the case of wheat price uncertainty, results are much less sensitive to the degree of investment irreversibility. The transition from waiting to adopting is probably near the parameter combinations delineated by the curve representing 50% irreversibility. While not illustrated, the curve shifts significantly for 25% irreversibility such that there are no reasonable parameters for which adoption of a tractor is not predicted. It should be noted in the case of uncertainty in wheat prices that investment irreversibility was a proxy for the impact of falling wheat prices on tractor prices. In the extreme case where assets are fully irreversible, falling wheat prices render tractors valueless, as it is assumed that either their value lies entirely in their use for producing wheat or transport costs are too high to make resale in another region feasible. If tractors were not completely valueless, that is, if they could still be sold on resale markets, then investment is not completely irreversible. On

212

BYRON LEW

FIG. 7. Investment thresholds for uncertainty in fuel prices by degree of irreversibility (fourhorse two-plow tractor comparison). The area below each curve represents the parameter combinations for which the trigger price exceeds the threshold price for adopting a tractor.

the other hand, improvements in new tractors will directly reduce the asset’s resale value because the replacement cost has fallen. What is actually being illustrated by irreversibility in the case of uncertainty in tractor prices is the change in parameters consistent with a given reduction in asset price. The results show that it would take a price reduction of almost 50% to induce farmers to purchase a tractor given expectations of future tractor prices. For the larger farm-size comparisons, again, results are very similar to the case of uncertainty in wheat prices. For 0.1 ⱕ ␴ ⱕ 0.3 and for almost all values of ␣, a tractor would be a better choice than either the six-horse team for the 309 acres or the eight-horse team for the 434 acres, under the assumption of full irreversibility. Decreasing the irreversibility only strengthens the conclusion. It would only be under an assumption of relatively high price volatility or a significant downward trend in tractor prices that a farmer with a farm larger than 250 acres would not exercise the option to buy a tractor. It is also possible that uncertainty over fuel prices could have contributed to delaying the adoption of tractors. Results for the four-horse two-plow tractor comparison are illustrated in Fig. 7. The area below each curve represents parameter combinations for which current prices are below trigger prices. Since the value of tractors rises as fuel prices fall, the option is exercised when fuel prices fall below trigger prices represented by the area under the curve. Note that there are two situations in which delaying tractor purchase is optimal because of the concave shape of the function. If prices are trending up, then tractors are expected to become more expensive to operate in the future and so would not be purchased. On the other hand, if fuel prices are expected to fall, then there may be value in delaying purchase in order to benefit from lower operating costs in the future. The results indicate that investment should be delayed for ␣ ⬎ 0.03 and ␣ ⬍ ⫺0.03 for reasonable values of ␴.

DIFFUSION OF TRACTORS

213

The price of gasoline rose substantially through World War I and then fell back to its pre-World War I price by the mid-1920s. It is unclear for that short a time series if prices were trending down; however, it is unlikely that they were trending up in real terms over the long run. Volatility associated with gasoline prices is as high as ␴ ⫽ 0.05 over this period. Note, however, that farmers could use a mix of gasoline and kerosene to operate their tractors, and kerosene prices were negatively correlated with gasoline prices over this period. The actual volatility of the cost of fuel would therefore be lower than either of its components. Therefore it is probably safe to assume a zero or slightly negative downward trend in prices and volatility less than ␴ ⫽ 0.05. Under these parameters, tractor adoption would have been predicted for the small farm. With full irreversibility of investment, however, it would not take too much upward drift for the model to predict postponement of purchase. With only moderate degrees of irreversibility, postponement becomes extremely unlikely. It is probably safe to conclude that the behavior of fuel prices did not deter tractor adoption. Therefore, that many small farmers chose not to adopt would have to be explained by the behavior of the price of tractors or wheat or possibly both. The analysis has focused on each form of uncertainty entering individually. If more than one form of uncertainty entered, then the covariance among the prices subject to uncertainty would require parameterization. If all three prices, wheat, fuel, and tractor prices, were considered at the time to be volatile and downward trending, then their combined impact would be to reinforce the conclusions drawn from each individually. In this case, tractors would appear even less attractive than indicated by any of the above scenarios taken on their own. The conclusion to be drawn from considering all the results is that the minimum farm size for tractor adoption in the mid- to late 1920s was that which exceeded the capacity of the four-horse team, calculated as approximately 250 improved acres. There are two independent sources which lend support to this conclusion. Farmers surveyed in the late 1920s believed that a minimum of approximately 300 acres of cultivated land was required for tractor adoption (Hopkins, Armstrong, and Mitchell, 1932, p. 52). Also, the census reports that approximately 19% of farms in Saskatchewan in 1926, or 22,000, were larger than 290 improved acres. It reports a total of 23,852 tractors on farms. By 1931 there were 45,000 farms larger than 290 improved acres and the census reports 43,308 tractors on farms. In fact a breakdown of adoption rates by size of farm in Table 4 suggests that this 250-acre cutoff was not quite as biting in practice. There were 44 tractors per 100 farms in the size range of 480 – 640 acres, which is associated with the range of 290 –385 improved acres. That is, less than half of eligible farms in this size range adopted tractors. For farms larger than 640 acres, adoption rates jump to 74 per 100 farms, still falling short of the 100% predicted. The 1936 Census reports an even finer breakdown for farm sizes greater than 640 acres, indicating that adoption rates continue to increase with larger farm sizes. The apparent lack of a strong demarcation by size suggests that while the threshold model and the

214

BYRON LEW

modification developed here are interesting, heterogeneity among farmers due to differences in farmers’ assessment of the parameters due to debt, as shown by Clarke (1994), or due to other possible causes must also be considered. CONCLUSIONS The incorporation of uncertainty into the model of the investment behavior of farmers in the mid-1920s alters the predictions of the threshold model. Farmers with smaller farms, less than 250 improved acres, should have rationally delayed their purchase of a tractor simply due to uncertainty over input prices. Both the falling prices of tractors and the low wheat prices of the period made delaying tractor adoption the rational choice. In contrast, the simple one-period threshold model predicts that all farmers should have adopted a tractor. Since a majority of prairie grain farmers in the 1920s and 1930s had holdings of less than this threshold, tractor diffusion on aggregate appeared to have been delayed. Furthermore, the modified threshold model shows that the transition from horse to tractor could have occurred with merely a modest expansion in farm size. Farmers having recently acquired a second quarter-section and breaking new land may have quite suddenly become eligible to adopt a tractor. Since this was probably not an uncommon scenario, it is not surprising that the relative merits of tractors were debated at the time. In a situation without uncertainty, if the value of tractors was known exactly, the choice would have been straightforward. In contrast to the period of initial diffusion in the 1920s, the period of most rapid diffusion, the post-World War II period, was one of increasing input prices coupled with government-supplied insurance against falling output prices. With governments in both the United States and Canada guaranteeing a minimum price, farmers were provided with long-term price stability. The availability of price floors changed entirely farmers’ exposure to risk, thereby speeding up adoption of a risky technology. The pace of technical change in tractors may have also affected their diffusion in a peculiar way. Until the pace slowed, delaying a purchase and forgoing current benefits in anticipation of greater future benefits may also have been rational and may also explain the reticence of many farmers during the 1920s. ACKNOWLEDGMENTS The author thanks Marvin McInnis, Alan Green, participants at the 1999 Canadian Conference on Economic History, and two anonymous referees.

REFERENCES Ankli, R. E. (1980), “Horses vs. Tractors in the Corn Belt.” Agricultural History 54, 134 –148. Ankli, R. E., Helsberg, H. D., and Thompson, J. H. (1980), “The Adoption of the Gasoline Tractor in Western Canada.” In D. H. Akenson (Ed.), Canadian Papers in Rural History (Vol. 2). Gananoque, Ontario: Langdale. Pp. 9 –39. Ankli, R. E., and Olmstead, A. L. (1981), “The Adoption of the Gasoline Tractor in California.” Agricultural History 55, 213–230.

DIFFUSION OF TRACTORS

215

Bracken, J. (1920), Crop Production in Western Canada. Winnipeg: The Grain Growers’ Guide Limited. Brennan, M. J., and Schwartz, E. S. (1985), “Evaluating Natural Resource Investments.” Journal of Business 58, 35–57. Canada. Dominion Bureau of Statistics. Census of Canada, 1921, 1931, 1941, 1951, 1956, 1961. Ottawa. Canada. Dominion Bureau of Statistics. Census of the Prairie Provinces, 1926, 1936, 1946. Ottawa. Canada. Dominion Bureau of Statistics. (1974), Handbook of Agricultural Statistics: Part VI: Livestock and Animal Products, 1871–1973. Ottawa. Canada. Dominion Bureau of Statistics. (1948), Price Index Numbers of Commodities and Services Used by Farmers, 1913 to 1948. Ottawa. Canada. Parliament. House of Commons Special Committee on Farm-Implement Prices. (1937), Minutes of Proceedings and Evidence and Reports. Ottawa. J. O. Patenaude. Canada. Statistics Canada. Agricultural Implement Industry. Ottawa. Canada. Statistics Canada. Farm Implement and Equipment Sales. Ottawa. Canada. Statistics Canada. Prices and Price Indexes. Clarke, S. H. (1994), Regulation and the Revolution in United States Farm Productivity. Cambridge: Cambridge Univ. Press. David, P. (1975), “The Mechanization of Reaping in the Ante-Bellum Midwest.” In Technical Choice, Innovation and Economic Growth. Cambridge: Cambridge Univ. Press. Pp. 195–232. Dick, T. J. O. (1982), “Mechanization and North American Prairie Farm Costs, 1896 –1930.” Journal of Economic History 32, 199 –206. Dixit, A. K., and Pindyck, R. (1994), Investment Under Uncertainty. Princeton: Princeton Univ. Press. Emery, J. C. H., and McKenzie, K. J. (1996), “Damned If You Do, Damned If You Don’t: An Option Value Approach to Evaluating the Subsidy of the CPR Mainline.” Canadian Journal of Economics 29, 255–270. Furniss, I. F. (1966), “Productivity Trends in Canadian Agriculture, 1935 to 1964.” Canadian Farm Economics 1, 18 –22. Green, A. G. (1994), “International Migration and the Evolution of Prairie Labour Markets in Canada, 1900 –1930.” In T. J. Hatton and J. Williamson (Eds.), Migration and the International Labor Market, 1830 to 1939. London: Routledge. Pp. 156 –174. Grest, E. G. (1936), An Economic Analysis of Farm Power in Alberta and Saskatchewan. Ottawa: Department of Agriculture. Hayami, Y., and Ruttan, V. (1985), Agricultural Development: An International Perspective (revised edition). Baltimore, MD: Johns Hopkins Univ. Press. Hopkins, E. S., Armstrong, J. M., and Mitchell, H. D. (1932), Costs of Producing Farm Crops in the Prairie Provinces. Ottawa: Department of Agriculture. Leacy, F. H. (Ed.) (1983), Historical Statistics of Canada, Second Edition. Ottawa: Statistics Canada. Jasny, N. (1935), “Tractor versus Horse as a Source of Farm Power.” American Economic Review 35, 708 –723. Karagiannis, G., and Furtan, W. H. (1990), “Induced Innovation in Canadian Agriculture: 1926 – 87.” Canadian Journal of Agricultural Economics 38, 1–21. Mackintosh, W. A. (1935), Economic Problems of the Prairie Provinces. Toronto: Macmillan. McInnis, R. M. (1986), “Output and Productivity in Canadian Agriculture, 1870 –71 to 1926 –27.” In S. L. Engerman and R. E. Gallman (Eds.), Long-Term Factors in American Economic Growth. Chicago: Univ. of Chicago Press. Pp. 737–770. Marcus, A. J., and Modest, D. M. (1984), “Futures Markets and Production Decisions.” Journal of Political Economy 92, 409 – 426. Murchie, R. W., Allen, W., and Booth, J. F. (1936), Agricultural Progress on the Prairie Frontier. Toronto: MacMillan.

216

BYRON LEW

Musoke, M. S. (1981), “Mechanizing Cotton Production in the American South: The Tractor, 1915–1960.” Explorations in Economic History 18, 347–375. Olmstead, A. L. (1975), “The Mechanization of Reaping and Mowing in American Agriculture, 1833–1870.” Journal of Economic History 35, 327–352. Olmstead, A. L., and Rhode, P. W. (1994), “The Agricultural Mechanization Controversy of the Interwar Years.” Agricultural History 68, 35–53. Olmstead, A. L., and Rhode, P. W. (1995), “Beyond the Threshold: An Analysis of the Characteristics and Behavior of Early Reaper Adopters.” Journal of Economic History 55, 27–57. Sargen, N. P. (1979), “Tractorization” in the United States and Its Relevance for the Developing Countries. New York/London: Garland. Saskatchewan. Royal Commission on Agriculture and Rural Life. (1955), Mechanization and Farm Costs. Regina: Lawrence Amon. Spector, D. (1983), Agriculture on the Prairies, 1870 –1940. Ottawa: Ministry of the Environment. Stewart, A. (1936), “Trends in Farm Power and Their Influence on Agricultural Development.” In R. W. Murchie, W. Allen, and J. F. Booth (Eds.), Agricultural Progress on the Prairie Frontier. Toronto: MacMillan. Pp. 293–336. Ward, T. (1994), “The Origins of the Canadian Wheat Boom, 1880 –1910.” Canadian Journal of Economics 27, 865– 883. Whatley, W. C. (1983), “Institutional Change and Mechanization in the Cotton South: The Tractorization of Cotton Farming.” Ph.D. Dissertation, Stanford University. Whatley, W. C. (1985), “A History of Mechanization in the Cotton South: The Institutional Hypothesis.” Quarterly Journal of Economics 100, 1191–1215. White, W. J. (1999), “Adjusting for Quality in Historical Time Series: The Farm Tractor,” 1918 – 1955. Department of Economics, The Ohio State University, mimeograph. Wright, G., and Kunreuther, H. (1975), “Cotton, Corn and Risk in the 19th Century.” Journal of Economic History 35, 526 –551.