DISCUSSION PAPER ECONOMIES OF SCALE IN AGRICULTURE~ A Stn:vey of the Evidenc~ and Willis Peterson E:con©m.:!cm \~?ob'lcl Bank CJA)e£ 'D,Ot :;hose •:Yf t:he its a~:fiJ ~;~aci.t:slor~s e1re tb:~ ::c~.:Jul ts ,;:;f ::-eseat"ch ~e~e represent 0~~icial of the Banka Uc.e any rna~13 uar3d hi\ for the co~veni~cce do rtoe October, 1986 ECONOMIES OF SCALE IN AGRICULTURE: A Survey of the Evidence Yoav Kislev and Willis Pecerson The authors are, respectively, Associate Professor, Department of Agricultural Economics and Management, Hebrew University, Rehovot, Israel, and Professor, Department of Agricultural and Applied Economics, University of Minnesota. The paper was written when Yoav Kislev was with the Labor Markets Division, Development Research Department, The World Bank. Paul B. Siegel assisted in recalculating the intercountry production function. ABSTRACT Economies of scale have been claimed to characterize agricultural production. If so, they affect farm consolidation and labor exit from the rural to the urban sector. The existence of scale economies was found in many empirical studies. In this paper we study the empirical evidence in American agricult~re. The analysis was conducted for the US farm sector b~~~use of the availability of data 1 but the choice was also motivated by the desire to test the issue in the farm sector which supposedly has exhibited the strongest and the most persistent scale economies. It is shown that, if carefully examined, the data do not support the alleged SLale hypothesis. ECONOMIES OF SCALE IN AGRICULTURE: A Survey of the Evidence MOTIVATION The question of economies of scale often comes up in the discussion of agricultural development. For example, it is sometimes asserted that many cf the farms in the developing countries are to~ small to justify investment in learning and appropriate adoption of new te~hnologies. This means that the larger farms are comparatively more efficient and that there exist economies of scale in agricultural production and farm management. Others suggest that even if there are no economies of scale in the traditional agriculture, they will set in as the farm sector develops. This assertion was made by Hayami and Ruttan (1985), who supported it with econometric estimates of the agricultural production function. Economies of scalB, if they actually exist 1n a competitive industry, are a non-equilibrium phenomenon: farmers with resources--equity capital or credit--will try to acquire large plots of land, the price of land will be higher than the present value of the future stream of income of operators of small farms, they will sell-out and the land will concentrate in the larger farms. For those who sold the land this process means (a) that they enjoyed capital gains if the economies of scale are of recent origin and the acquisition or inheritance of the farm was done before these econom1es affected land prices; and (b) they will move to seek non-farm employment ~arlier or in the larger numbers than otherwise. Thus economies of scale are affecting labor's out-migration fro~1 agriculture over and above the effect of - 2 - urban-rural wage differentials. From the point of view of the economy at large, such out- migration is an effi~ient reallocation process, because with it agriculture enjoys increased productivity as production concentrates on larger farms. For those who move and for the urban centers that have to absorb them the process poses additional adjustment difficulties. For example, the emergence of economies of scale may in principle drive farmers to the non- agricultural sector even if they cause a reduction of non-farm wages. It is therefore of interest and of importance to find out whether the evidence supports the assertion of the e~~istence of economies of scale in .igriculture. This examination of the evidence is not a simple and straight forwat: matter oi counting the number of empirical studies that reported increasing returns in agricu1~'lral production, because most of these studies were and are conducted in the same methodology and may be subject to the same criticism--a criticism we shall detail below. Instead, a careful examination requires the juxtaposition of pieces of evidence accumulated with a large variety of methodological approaches. Data for such an analysis are not available for the developing countries and we turn therefore to American data. The examination of the question of increasing returns to scale in the American farm sector, beside utilizing the wealth of available inform2tion, offers another advantage: American farming was often cited as the most prominent case of economies of scale. If the evidence can be shown not to support the alleged economies of scale in the US, then the case for increasing returns to scale in other economies will also be much weaker. - 3 - PRELIMINARIES Prevented from conducting controlled experiments, the data economists work with are far from ideal. Measurement errors abound, significant variables may be unobservable, not all simultaneity can be accounted for, and we often use state, regional, or national aggregates to estimate firm or household structural parameters. As a result, every measurement and method of estimation can be questioned. Confidence is built when the quantitative a~sessments of ~xplanations and economic magnitudes can be corroborated by obser~~tions 0n independent sets of data and, particularly, by analyses of different aspects of the problem at hand. In this paper we critically ~xamine the widely held vtew that firms 1n American agriculture exhibit economies of scale. We consider three dimensions of the problem: sources of scale economies, measurement of the phenomenon, and the implied consequences. We argue that the exir,tence of economies of scale can be questioned on both conceptual and statistical grounds, and that it is not, in general, consistent with the accumulated evidence. Findings supporting the hypothesis of constant returns to scale in agriculture have been reported several times in the past but they seem to have been disregarded by most of the profession because farm growth was taken as a proof of increasing returns. And indeed, farm size grew substantially over the past half century. Between 1929 and 1982 gross output per farm grew 6.5 times, value added--4.8 times and land--2e8 times. (Table 1). However, unit growth can also be explained by changing factor prices without relying on economies of scale. We elaborated on this elsewhere (Kislev and Peterson 1982) and here we present new evidence that again supports the latter explanation. - 4 - Sources It is a simple truism, that if the world is exactly multiplied, production will also exactly double. But we are not interested in the returns to multiplication of every aspect of production. Rather, changes in scale are changes in the physical dimensions of production assets and in factor flows while the environment, entrepreneurship and often also management stay the same. Then scale effects are mixed. As a pipeline is increased in diameter, the capacity of the line to transport liquids or gases increases more than in proportion to the increase in material and cost of production of the line (Cookeuboo). On the other hand, increasing difficulties of coordination and direction reduce efficiency as scale expands. Scale economies in an indus~ry reflect the sum total of these effects. Most writers attributed economies of sctiie in agriculture to indivisibility of assets; a recent example is Hayami and Ruttan (p. 146}: "The scale economies usually stem from the lumpiness or indivisibility of fixed capital." But it is hard to find indivisible assets on the farm. Returns to scale is a long run concept, and in the long run the size measures of land, structures, irrigation systems, herds and flocks are continuous, not lumpy. Machines are mentioned as indivisible; but tractors and their implements come in a great variety of sizes from the hand driven garden types to the 4-wheel drive behemoths that ply the prairies. Other machines also come in a large variety of sizes; and, in the few cases in which large machines are the most efficient such as combine harvesters and cotton pickers, rental markets develop. Small farmers also have the option of purchasing lower cost, used machines. Considering the wide array of machine sizes and prices along with rental markets, lumpiness and indivisibility of machines - 5 - seem to be more apparent than real. It may be argued that, although machines come in many sizes, the long rua average cost curve is still U-shaped, reaching a minimum at a certain machine capacity and, consequently, a certain farm size. Economies of scale are then a disequilibrium phenomenon (Griliches 1963, p. 232), of a temporary nature. If so, scale economies will be gradually eliminated as farms adjust in size, since at the minimum--average costs are constants In Table 1 (line 14) we present cross-section estimates of returns to scale in American agriculture. In all four estimates for the period 1949-74 the sums of the coefficients in Cobb-Douglas production functions were higher than 1.250. No indication of a reduction of the scale coefficient can be detected. One would expect at least some cloRing of the gap between the actual and the optimum scale over a period in which the average farm doubled in size. An "asset" that is clearly fixed on the farm, particuLarly on the family unit, is entrepreneurial ability and management. This fixity raises important econometric issues which are discussed below. Here we note two considerations: (a) As with machines, adjustment should have eliminated the scale effects. (b) If the existence of a single manager were an importa~t source of economies of scale, part-time farming would have gradually disappeared. However, between 1949 and 1969, the prevalence of part-time farming, as measured by the share of operators working 100 days or more off their farms, nearly doubled (Table 1, line 6). Another possibility is that economies of scale are created by reduced uncertainty due to government intervention in agriculture (Madden and Partenheimer, p. 103). However, the government has been intervening since the 1930s. Adjustment should have been completed by now. - 6 - A dynamic cost hypothesis can be that technological progress results in the production of new and larger machines that are more efficient than the older and smaller ones. Then the U-shaped cost curve shifts to the right over time. Perhaps this is what Bieri, de Janvry, and Schmitz (p. 802) had in mind: "the rate of increase in farm size in the future will be determined, to a large extent, by the rate at which the machine companies manufacture larger and larger equipment." This dynamic hypothesis is indeed consistent both with the observation that farms have grown in size and that measured economies cf scale have not declined. It is not consistent, however, with the continuing prevalence of part-time farming. Nor is this hypothesis consistent with the observed cessation of the growth in farm size which occurred in the mirl-1970s without a corresponding halt to the progression of new technology or the ability to produce still larger machines. Indeed, below we argue that the optimum growth in farm size induced changes in size of machines, rather than the other way around. Measurement Three methods have been employed to test for the existence of scale economies: the survival method, synthetic firm studies, and the sum of the coefficients of Cobb-Douglas production functions. According to the survival method (Stigler, Saving), growth of firms in an industry is an indication that large firms are more etficient than small ones; that is, economies of scale exist. Application to agriculture raises several difficulties. An implicit assumption of the method 1s that economic conditions have not changed. This is not true for American agriculture, where relative prices, labor's alternative income and machine cost have changed - 7 - substantially over the last half century. Also, in this sector, the quality corrected labor input per farm has not grown; it remained between 1.5 and 2.0 workers for more than SO years (Table 1, lines 4 and 5). Thus the large increase 1n size cannot be a regular case of increasing returns to all factors. Moreover, in agriculture, the survival method can be used to prove constant returns. By the logic of the method the existence of part-time farming, and particularly the fact that it increased during the 1950s and 1960s, suggests an absence of economies of scale. Synthetic firm studies are reviewed by Madden and Partenheimer. The difficulty with these studies is that problems of manageutent and coordination and differences in skills and ability of farmers cannot be appropriately accounted for. These problems are considered the major sources of diseconomies of scale. Unless they can be taken account of, the test of scale economies by synthetic cost studies is meaningless. Summing the coefficients of Cobb-Douglas production functions is the most common method of measuring scale economies in agriculture. This measure can, however, be biased. One problem with this approach is that small farms are commonly part-time units. If the labor of the ~perator and the family ia not adjusted correctly for off farm employment, the small units will apr~~~ to use more labor than they actually do, and the larger farms will be measured mistakenly to be more efficient. Such measurement errors will lead to overestimates of returns to scale. A more difficult problem is posed by management. Unlike labor input that can in principle be measured correctly, management 1s unobservable. If management is correlated with size, economies of scale will be overestimated. The same is true for other fixed factors. The following analysis of this issue is due to Mundlak; it was also applied by - 8 - Hoch (for further reference see Hoch). It is recapitulated here in some detail because of its import~nce. Let the firm (farm) production function be (1) Y = F(X, M) where Y ~ output X =a factor of observable inputs M = firm specific factors, management or other fixed factors. In general, M is unobserved and not measured. The estimated production function is then, (2) Y = f(X). With the specification in (2), firms are on different functions--each according to its M value. Better environmental conditions, more productive soil, superior location, as well as better management--are all reflected in higher (unobserved) firm specific factors. Consequently, complementarity prevails between the firm specific factors and most irtputs. As a result, total inputs (observed plus unobserved) will be underestimated on large farms relati~r1 to small farms. In estimating the production function, the OLS regression line will be steeper than it really is, giving the appearance of scale economies. In multivariate cases, overestimates of the regression coefficients yield upward biased sums of the coefficients and overestimates of the returns to scale. Given panel data (combination of time series and cross sections) and assuming that the farm specific effects were constant over the period of observation, the bias can be completely eliminated if, instead of OLS estimates of the pooled function, a covariance analysis is employed; in the - 9 - conventional terminology--if firm dummies are included in the analysis. In a covariance analy~is the regression is estimated not from the original observations, but from deviation& from the firm means; and if, as assumed, M 1s constant, the deviations of this variable are all zeros and all firms are on the same funct1on. The estimated coefficients are then unbiased, "withinu firm estimates. Hoch summarizes 6 previous studies that had reported both OLS and covariance analysis of farm level production functions. In all 6 cases, the sum of the coefficients in the covariance analysis was less than 85 percent of the sum calculated from the OLS estimates and in all cases the sum was smaller than 1. In h:s own analysis of dairy farms, reported in the same paper, Hoch found that covariance analysis reduced the sum of the coefficients to levels smaller than 1 for 10 samples of farms producing milk for the market. He found, however, increasing returns to scale (and higher sums of coefficients) for two samples of dairies producing for manufacturing. To our knowledge this is the only reported evidence of covariance analysis increasing the sum of the coefficients, and the only case in which increasing returns w~re found with covariance analysis. Agricultural production functions are usually estimated for the average farm in a state, a region, or a country. Random aggregation within regions cancels out farm specific effects and eliminates the associated specification biases. However, regions are also characte~ized by regional specific effects, such as soil, climate or economic circumstances, and in samples of individual farms coming from different regions, the regional effects have to be accounted for. Again, one way to do it 1s to include regional dummies in the regressions. Failure to include such dummies, failure - 10 - to account for the regional specific effects 9 results in specification biaseso These specification biases are augmented by regional aggregationo Hence the bias in the estimated sums of the coefficients in Cobb-Douglas functions is likely to be more serious when the obset·vations are regional or country averages than when they ar~ fa~m level data (Kislev), Since soil, climate and other growing conditions differ among the states, the sums of the coefficients calculated from Davis 1 estimates and presented in Table 1~ line 14 are likely to be upward biasedo We do not know of a parallel covariance analysis for the aggregate production function of American agriculture, but we have attempted such an analysis for the intercountry productivity estimates of Hayami and Ruttan. They found increasing returns to scale for the develop,.:;d countries in their sample and constant returns for the developing countries. We recalculated their regressicn for the developed sub-sample (Q21 in their Table 6-2) and added country dummiesc The sum of the coefficients was 1~320 without the dummies and 1.077 with the dummies.. The latter sum was not significantly different from 1 (the standard error of the sum was Ooll9)a Before leaving this section, a caveat should be added about covariance analysis. In general, random errors in the measurement of the observed variables cause underestimations of the regression coefficientsa Griliches (forthcoming) shows that covariance analysis may exacerbate the effect of measurement errorso By giving up 19 betweenn variability we run into 0 the danger of increasing the noise to signalu ratio.. For our discussion of economies of scale, this possibility is particularly worrying--empirical observations are never error freeo The message here is, again, that one cannot rely on a single source of evidenceo Con~inuing with the survey of - 11 - evidence~· we turn now to the examination of the consequences of scale economies .. Consequence2! Returns to scale, if they actually exist in agriculture, affect significantly both the economics of agricultu~e and our understanding of the farm sector, So long as the sources of the phenomenon are'not clearly defined, the term "economies of scale," just like the term "technical change," is 9 in a sense, a name for our ignorance.. To see how ignorant, consider the following, Between 1929 and 1982 gross output per farm in the U.S. increased 6 .. 5-fold (Table 1, line 1). If inputs were all accounted for and perfectly measured, and constant returns to scale prevailed, inputs also would have increased 6.5 times and output per unit of input would have remained constant. If in fact the agricultural production function is homog~~:eous of degree 1.3 (a generally accepted figure, Griliches 1963 9 Davis, Hayami and Ruttan)? then the input growth necessary to achieve a 6oS-fold growth in output would have been 4.2 instead of 6 .. 5 (4.2 103 = 6.5).. In other words, over half of the increase in per farm output would be left unexplained [(6.5 4o2)/4 .. 2 = .SS]o As a degree of homogeneity, 1o3 is a very large number. Economies of scale also affect the distribution of the returns to the factors of production. If, again, the production function is homogeneous of degree lo3? then inputs should receive $1o30 for each dollar of output provided they are paid their VMPs (Euler's Theorem)o If land is a residual claimant and has a production elasticity (factor share) of ol7 (Griliches 1963) then the nonland inputs should receive o83 x $lo30 = $1.08 for each - 12 - dollar of output. This leaves land with a negative return. Such an outcome is contrary to the evidence. In modern times at least, land rents and land prices have been positive, not negative or zero (Table 1, lines 8 and 9). In fact real land prices in the U.S. increased substantially over the 1930-1982 period. To be accurate, one should distinguish between rent and land prices. Dynamic considerations can be used to explain positive land values even if residual returns are negative: If scale economies are a reflection of temporary disequilibrium, then as farms grow to a size in which constant returns prevail, the residual return to land will become positive. Given a sufficiently low rate of interest, the discounted present value of these positive fature returns could also be positive. However, this argument does not explain the positive land rents which prevailed throughout the period for which data are reported in Table 1. Nor does it explain the apparent inability of land buyers to revise their expectations after decades of what should have been negative residual returns to land. A realization that increasing returns were not soon to be eliminated (if they existed) should have led to a decrease in real land pr1ces. Just the opposite occurred. Land pr1ces rose since 1949 and changes in inflationary expectations and terms of trade along with changes in real rates of interest appear to have had a large impact on real land prices during the 1970s and 1980s. It seems that land buyers and sellers did not perce1ve a disequilibrium to exist. There is also no evidence in the land market literature of the existence of such a disequilibrium. - 13 - Farm Growth The major consequence attributed to economies of scale is growth of farm size. And indeed American farma grew significantly up to the mid 1970s (Table 1, lines 1, 2, and 3). However, there can be an alternative explanation to farm growth (Kislev and Peterson 1982). American farms are mostly family units with a relatively constant quality-adjusted labor input; their capital intensity and hence :heir size is determined by the price ratio between labor and machinery. For farming, the price of labor is the alternative earning opportunities outside agriculture (Table 1, line 12). Generally, the cost of machinery is harder to measure. Theoretically it ~~ the rental market price. In agriculture a rental market for machinery services exists in the form of custom work for hire. Cost of machine service is, therefore, measured as the real value of custom rate in combine harvesting of wheat. Between 1929 and 1969 this cost measure declined by 30 percent (Table 1, line 11). Up to 1974, real custom rates declined. The increase in quality of machines and the decrease in the real cost of energy were probably important factors contributing to this decline. At the same time the opportunity cost of farm labor increased; manufacturing wages, for example, grew 2.4-fold in real terms between 1929 and 1969 (Table 1, line 12) causing the wage to rental ratio to increase even more (Table 1, line 13). With these relative pr~ce changes, equilibrium machine-labor ratio in agriculture increased, enabling the family farm to cultivate a l&rger amount of land and in so doing maintain parity income growth with the nonfarm sector. During this time the increase in nonfarm earnings also provided an incentive for many farmers, and particularly their sons and daughters, to leave the land for alternative - 14 - occupations. (The exit of hired labor from agriculture was also affected, to a large extent, by improved urban opportunities. See Peterson and Kislev 1986.) In turn this outmigration freed land for the remaining farmers to expand. Seen from this perspectiv~, as urban wages rise, farmers are induced either to move to town, or--those that remain full-time far~ers--to increase the amount of resources at their command to keep income in parity with alternative earnings. History extended the factor price expriment during the 1970s, and in a new direction, when the trend of wage to rental ratio was reversed and the ratio declined by more than 30 percent (Table 1, line 13). Indeed, from 1974 to 1982, farm size remained essentially constant, whether measur01 by value of product or by land area. The developments in the same period also support the assertion that while wage-rental ratio affects farm size, the demand for land does not. In the 1970s, when farms ceased growing, the demand for land did not decline. On the contrary, it rose dramatically as the prices in line 8 show, but it rose both for those who wanted to expand their farms and as the reservation price of owners of land. On the average, farm size was not affected. As farms are operated by a constant amount of labor, the increased machinery input has taken the form of larger machines. This explains the appearance of the large tractors and implements in agriculture. Technologically, large machines could have been supplied to agriculture much earlier than they were, and indeed large scale machines were built for other industries--earth-moving equipment for example--long before they appeared 1n agriculture. In fact, the first four-wheel-drive tractors were assembled by farmers, so widespread and simple was the technology. Only afterwards did the - 15 - machine compa~ies produce these large tractors. Here, as in many other cases, the companies reacted to economic changes once they were reflected in demand. The decision of the manufacturers to build larger machines is not an exogenous factor determining farm size. It has been argued that the U.S. 1ncome tax law which taxes the earnings from capital at lower rates than earnings from labor through investment credits and accelerated depreciation promoted the growth of large capital intensive farms. This may be true. To the extent that the income tax law reduced the price of capital relative to that of labor, it would, according to our farm size model, have contributed to the increase in farm s1ze. But unless the tax law continued to lower the price of capital, it would have resulted in a once and for all change in equilibrium farm size, not a continued increase. Farm mechanization can be viewed a process of induced innovation. Changing factor prices for agriculture, including the price of energy, induced the machine companies to produce more efficient and larger machines. These and similar changes also induced agricultural research to produce appropriate biological and chemical technologiee. Changes in factor prices induced the suppliers of factors and technology to innovate. An alternative view, that innovations occurred on the farm and in turn increased the demand for machinery even at higher real prices, cannot be supported by any evidence that we know of (Kislev and Peterson 1981). - 16 - Conclusions We conclude that the evidence clearly supports the hypothesis that production in U.S. agriculture is characterized by constant returns to scale, and that the observed increase in farm size from 1930 to the mid 1970s is due to the increase in the wage-rental ratio. Viewed in this light, equilibrium farm size is endogenously determined within the economy by the relative prices of labor and capital, not by some unexplainable phenomena called "economies of scale" or "technical change .. " The discussion also highlighted an old puzzle: what are the economic, technological and institutional factors that support the family unit as the dominant form of organization and maintain it through periods of large economic and technical change? The solution to this puzzle will do much to improve our understanding of the economics ,_,.f agriculture in the United States and elsewhere. Table 1 Agricultural Data - per Farm Output, Inputs and Prices Unit 1929 1949 1959 1969 1974 1978 1982 1. Gross Output $1 ,000 9.5 23.1 31.6 44.3 66.8 69.1 62. i 2. Value Added $1,000 7.0 17.3 21.0 26.5 40.4 39.0 33.7 3. Land Acres 157 216 303 389 440 449 440 4. Fam i I y Labor Labor Years 1.2 1.2 1.3 1 .1 1.0 1.0 1.0 5. Hired Labor Labor Years .4 .3 .5 .4 .4 .5 *.7 -J 6. Part Time Farming Percent 12 23 30 40 36 42 43 7. Machinery $1,000 4.3 9.8 22c2 28.2 33.9 47.8 53.9 8. Land Prices $ Per Acre 271 215 310 445 552 747 794 9. Land Rent $ Per Acre - - 46 69 124 106 86 10. Diesel Fuel $ Per Gallon - .60 .55 .47 .71 .68 1 • 11 11 • Custom Rate $ Per Acre 14.12 11.82 11.52 9.79 15.83 13.39 13.70 12. Manufacturing Wages $ Per Week 140 218 292 334 346 363 330 13. Wage-Rental Index 41 77 105 142 91 113 100 14. Economies of Sca:e Sum of Coefficients - 1.255 1.290 1.289 1.276 * July Note: All dollar values in constant 1982 prices, deflated by the CPl. See appendix for description of data and sources. - 18 - References Bieri, Jurg, Alain de Janvry and Andrew Schmitz. "Agricultural Technology and the Distribution cf Welfare Gains." ~nerican Journal of Agricultural Economics 54(1972):801-8. Burt, Oscar, R. "Econometric Modeling of the Capitalization Formula for Farmland Prices." American Journal of Agricultural Economics 68(1986):10- 26. Cookenboo, L. Jr~ "Costs of Operation of Crude Oil Trunk Lines." Crude Oil Pipelines and Competition in the Oil Industry, pp. 8-32, Cambridge, Mass.: Harvard University Press, 1955. Also in Price Theory. Selected Readings, ed. Harry Townsend, pp. 193-215. Baltimore: Md.: Penguin, 1971. Davis, Jeffrey. "Stability of the Research Production Coefficient for U.S. Agriculture." Unpublished Ph.D Dissertation, Univ. of Minn. 1979. Griliches, Zvi. "The Source of Measured Productivity Growth: United States Agriculture, 1940-60." Journal of Political Economy 71(1963):331-346. Griliches, Zvi. "Data Problems in Econometrics." Handbook of Econometrics, ed. Z. Griliches and M. Intriligator. Amsterdam: North Holland, forthcoming. Hayami, Yujiro and Vernon W. Ruttan. Agricultural Development, An International Perspective. Baltimore and London: Johns Hopkins University Press, 1985, 2nd edition. Hoch, Irving. "Returns to Scale in Farming: Further Evidencea" American Journal of Agricultural Economics 58(1976):745-49. - 19 - Kislev, Yoav. "Overestimation of Returns to Scale in Agriculture: A Case of Synchronized Aggregation." Journal of Farm Economics 48(1966):967-83. Kislev, Yoav and Willis Peterson. "Induced Innovations and Farm Mechanization." American Journal of Agricultural Economics 63(1981):562- 65. Kislev, Yoav and Willis Peterson. "Prices, Technology and Farm Size." Journal of Political Economy 90(1982)•578-595. Madden, Patrick J. and Earl J. Partenheimer. "Evidence of Economies and Diseconomies of Farm Size." Size, Structure, and Future of Farms. Ed. Gordon A. Ball and Earl 0. Heady~ Ames: Iowa University Press, 1972. Mundlak, Yair. "Empirical Production Function Free of Management Bias." Journal of Farm Economics 43(1968):44-56. Peterson, Willis and Yoav Kislev. "The Cotton Harvester in Retrospect: Labor Displacement or Replacement?" Journal of Economic History 46(1986):199- 216. Saving, Thomas R. "Estimation of Optimum Size of Plant by the Survivor Technique." Quarterly Journal of Economics 75(1961):569-607. Stigler, George, J. "The Economies of Scale." Journal of Law and Economics 1(1958):54-71. - 20 - Appendix Data Sources and Definitions Unless otherwise noted, all referertces are published by the Government Printing Office in Washington. In all cases number of farms are from A~ricultural Statistics. 1. Gross Output: Cash receipts from farming plus value of home consumption from Agricultural Statistics, 1957, 1967, and 1984. 2. Value Added: Gross output less feed 1 seed, livestock, fertilizer, and miscellaneous expenses from Agricultural Statistics, 1957, 1967, and 1984. 3. Land:. Acres per farm from the Agricultural Census, 1929, 1949, 1969, 1974, 1978, and 1982. 4. Family Labor: Number of family laborers per farm as reported in Agricultural Statistics 1957, 1967, and 1984, adjusted for quality by the following procedure: Income by years of schooling completed for rural males, ages 25-64, as reported by the 1980 Census of Population, was multiplied by the proportion of rural farm males in each schooling category and summed. The resulting weighted averages for the census years 1940-1980 were then utilized to construct a labor quality index, 1980=100. The labor quality indexes for the other four census years are as follows. 1940: 80, 1950: 82, 1960: 86, 1970: 93. The 1940 quality index is used to adjust the 1929 labor figure while the 1970 index was used to adjust the 1969 and - 21 - 1974 figures. The 1980 index of 100 was applied to the 1978 and 1982 figures. 5. Hired Labor: Data source and quality adjustment procedure are the same as f~z family labor. 6. Part-time Farming: Proportion of farm operators working 100 days or more off the farm as reported by the Censu~ of Agriculture, 1929, 1949, 1959, 1969, 1974, 1978, and 1982. 7. Machinery: Stock of machines on farms obtained by summing the value of shipments over the preceding 15 years each year deflated by the CPI. Data sources: Statistical Abstract, 1928 and Agricultural Statistics, 1957, 1967, and 1984. 8. Land Price: Value of land per acre, excluding buildings, as reported by USDA/ERS, "Farm Real Estate Historical Series Data", Statistical Bulletins 520, 1973 and 738, 1985. 9. Land Rent: Cash rent per acre of cropland, 1969-1982, in the following eight tnidwestern states: Michigan, Wisconsin, Minnesota, Ohio, Indiana Illinois, Iowa and Missouri. Data source: US~~, ERS and ESCS, "Farm Real Estate Market Developments" 1972, 1977, 1981, and 1985. Rental data for these states are not available prior to 1967. The 1959 figure was estimated by the following procedure: Oscar Burt reports a rental figure of $17 per acre for Illinois in 1959 (Burt, p. 26). His 1969 figure for Illinois is $30 per acre. The corresponding figure for 1969 for the eight midwestern states is $25 per acre, or 83 percent of the Illinois rent. We therefore estimated the 1959 rent for the eight states as .83 x $17 = $14 in current year prices, or $46 in constant 1982 prices. - 22 - 10. Diesel Fuel: Data source: Agricultural Statistics, 1953, 1963, 1973, 1977, 1981, and 1984. Figur.e for 1949 is price of distillate. 11. Custom Rate: Charge per acre of custom harvesting of wheat in Kansas. The 1929 figure is from L.A. Reynoldson et al., "The Combined Harvester- Thresher in the Great Plains", USDA Technical Bulletin, no. 70 (February 1928), p. 35. The 1949 rate is from H. J. Friesen et al. ''1952-53 Custom Rates for Farm Operators in Central Kansas", Kansas Agricultural Economic Report, no. 59 (1953) p. 14. The remaining custom rates are from an annual publication, "Kansas Custom Rates'', 1970, 1975, 1980, and 1985, published by the Kansas Crop and Livestock Reporting Service. 12. Manufacturing Wages: Gross weekly earnings in manufacturing as reported in the Economics Report of the President, 1969, and 1985. 13. Line 12 divided by line 11, expressed as an index, 1982=100. 14. Economies 0f Scale: Sum of coefficients from a Cobb-Douglas aggregate agricultural production functions fitted to U.S. data as reported by Davis, p. 64. Some Recent DRD Discussion Papers 188. Evaluating Participation in an African Monetary Union: A Statistical Analysis of the CFA Zone, by Shantayanan Devarajan and Jaime de Melo, October 1986. 189. The Treatment of Foreign Trade in Computable General Equilibrium Models of Small Economies, by Jaime de Melo and Sherman Robinson, June 1986. 190. Problems: Development Theory and Strategies of Latin America, by Vittorio Corbo, September 1986. 191. Criteria for Choice Among Types of Value-Added Tax, by Carl S. Shoup, September 1986. 192. Administrative and Compliance Issues Unique to VAT Lessons from the Two Periods of British ExpGLi,ence, by Cedric Sandford and Michael Godwin, September 1986. 193. Inte£jurisdictional Coordination of Sales Taxes, by Sijbren Cnossen, September 1986. 194. Computarization of VAT in Indonesia, by Malcolm G. Lane and Hamonangan Hutabarat, September 1986. 195. A Simple Model of Seniority and Turnover, by Yoav Kislev, September 1986. 196. Wages, Turnover and Job Security, by Yoav Kislev, September 1986. 197. Import Compression and Export Performance in Developing Countries, by M. Khan and M. Knight, October 1986. 198. Fiscal Deficits, Exchange Rate Crises and Inflation, by S. van Wijnbergen, October 1986. 199. Aid, Export Promotion and the Real Exchange Rate: An African Dilema, by s. van W4.jnbergen, October 1986. 200. Growth, Structural Transformation and Consumption Behavior: Evidence from Asia, by .~.M. Dowling and A.K. Lahi~i, October 1986. 201. Theoretical and Policy Aspects of Dual Exchange Rate Systems, by M. A. Kiguel and Jose Saul Lizondo, October 1986. 202. Fiscal Policies and Real Exchange Rates in the World Economy, by J. Frenkel and A. Razin, October 1986. 203. Economies of Scale in Agriculture: A Survey of the Evidence, by Y. Kislev and W. Peterson, October 1986.