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We thank Bill Lord for comments.
Galor et al (2006) also make this assumption in their study of how land inequality affects human capital formation.
The link between the farm and the family was surprisingly strong well into the 20th century. At the turn of the century, the farm in the US was still largely operated individually and organized around the family. Most of farm labor was provided within the family. Even by 1930 only 42 percent of all farms reported hiring labor outside the family (Ely and Werwein (1940, p. 162)). As late as 1978, traditional family farms represented 88 percent of all farms accounting for 63 percent of total farm production (Gardner (2002, pp. 56-57)).
Caselli and Coleman use census data on wages and incomes. David measures GDP by sectors.
This is consistent with Margo’s(2000) finding of relatively small gaps in hourly wages in favor of nonfarm workers in the antebellum period. David (2005) goes as far as to argue that farm workers (i) were actually more productive than nonfarm workers, once accounting for unmeasured home production and land improvements, and (ii) received higher annual income, once accounting for entrepreneurial or residual income from farm ownership. It is difficult to say that farmers were more productive per hour since there was certainly unmeasured hours of work that generated the unmeasured home production and land improvements. During the 19th century, Primack (1969) estimates that farmers spent about 20 percent of their annual work hours in activities such as improving land, constructing farm buildings, and fencing property. In addition, if farm incomes were actually higher for the same hours of work, why then was there a steady flow of labor out of agriculture? We assume that land improvements and maintenance are captured in farm TFP. We also assume that such activities did not increase the net flow of income to the current generation, but did increase the quantity of effective land bequeathed to the next generation. Finally, we assume that the entrepreneurial income received by farm owners compensated for much of the gap in real wage income, but did not create a consumption gap in the opposite direction.
Direct quantitative estimates of TFP growth in agriculture and nonagricultural sectors over this periods can be found in Atack, Bateman, and Parker (2000) and Greenwood and Seshadri (2002). Unfortunately these estimates are flawed because Atack et al interpreted Weiss’s (1993) labor productivity estimates as TFP estimates (see also Mundlak (2005, footnote 30)). Greenwood and Seshadri based their calculations on Atack et al’s interpretation, so their estimates suffer from the same problem. Beyond this error, any attempt to calculate TFP growth over this period faces the difficulty of measuring physical and human capital accumulation during the 19th century.
As suggested in the introduction, our approach is consistent with the strong tradition of family farming that persists even today in the US. Intergenerational links to farming seem to be a common feature of many developing countries for a variety of reasons. Hayashi and Prescott (2006) claim that Japan’s development was slowed by a social convention of passing the farm along within the family. The paper includes a passage (p. 40), suggested by Andrew Foster, arguing that the social convention may be strong enough to operate even in the presence of a land market. “First, the heir could sell the inherited farmland and live in the city to collect the higher urban income. However, to prevent this, the father could require the son to remain on the farm until he inherits the land. By the time his son inherits the estate, it may be too late for him to start a career in the city.” Collier, Radwan, and Wange (1986) find that those individuals who indefinitely migrate away from farms in Tanzania tend to lose their land entitlement. In China, explicit migration rules cause migrants to the city to give up ownership claims to land and small businesses in rural areas (Au and Henderson (2006)).
Caselli and Coleman (2001) find little trend in the relative price of farm goods from 1880 to 1980.
One can interpret the loss in consumption as forgone wages from time taken to rear children or the payment for good and services provided to children. In the latter case, the costs of goods and services are interpreted to rise with adult labor costs (e.g. primary schooling) or one can simply assume that young parents offer children a share of their earnings for consumption.
Of course, physical capital also contributes to agricultural production, although less than in industry. For simplicity, we assume no role for physical capital in agriculture, a more dramatic difference between sectors than is present in reality. In our empirical application we do not allow for endogenous changes in physical capital intensity, for reasons that are discussed below. So changes in physical capital intensity, and their differential effect across sectors, are captured in changes in relative TFP across sectors.
Unlike some approaches, we follow Schultz (1964) and assume that human capital is productive on the farm. There is a good deal of evidence supporting this stance (e.g. Jamison and Lau (1982), Lucas (1985), Foster and Rosenzweig (1996), Goldin and Katz (2000), Duflo (2001), and Jenkins and Knight (2005)).
Assuming that the residual income from farm ownership is received in the first period has the advantage of pinning a unique transition path for the farm wage—a primary focus of the paper. However, it comes at the cost of generating too much saving to finance physical capital accumulation in the relatively small industrial sector. The open economy assumption minimizes this problem.
Note that the rental rate on human capital applies to the entire working life. Thus, the rental rate gap across sectors incorporates both differences in hours worked across sectors and differences in productivity per hour worked.
The labor supply of farm households depends on how one interprets the costs of raising children. We considered the costs to be either pure time costs (that reduce parents’ labor supply) or pure goods costs (that reduce parents’ consumption directly). We found that the “goods-costs” interpretation lead to a more plausible calibration of the model. In the pure “time-cost” interpretation, the calibrated values of τ and γ were too high to be consistent with empirical estimates.
This is in contrast to Caselli and Coleman (2001). They explain a large wage gap based solely on differences in schooling across sectors. However, as in our model, schooling differences across sectors have never been very large. Based on the 1915 Iowa census, Goldin and Katz (1999) find the average years of schooling in white collar occupations was 10.8 years, while in blue collar occupations and farming it was 7.8. Using the 1960 US census, Murphy and Welch found the average years of schooling were 13.4 in white collar occupation, 9.8 in blue collar occupations, and 9.1 in farming.
The small open economy assumption does not allow for endogenous changes in physical capital intensity. Historical interest rate data (see Wallis (2000)) suggests an increase in physical capital intensity occurred from 1870 to 1900, as interest rates fell. Increased physical capital intensity over this period increased the relative wage in industry and encouraged migration out of farming, other things constant. Since we do not account for the rise in physical capital intensity on migration, our estimated growth in the relative TFP in agriculture underestimates what is needed to match the data over this period—i.e. in face of a rise in physical capital intensity, the growth in relative TFP in agriculture would have to be higher from 1870 to 1900.
The employment-loss interpretation also has a cleaner interpretation in our model since we do not model the discrimination against migrants that lowers their wage and raises their cost of living, nor do we model any rent that urban employers or landowners may capture from the migrant. Under the employment-loss interpretation, there are no missing “rents” to urban households that go unaccounted for.