A model of migration and wealth accumulation: Farmers at the antebellum southern frontier

EXPLORATIONS

IN ECONOMIC

24, 130-157 (1987)

HISTORY

A Model of Migration and Wealth Accumulation: Farmers at the Antebellum Southern Frontier* DONALD F. SCHAEFER Department of Economics, Washington State University Studies for portions of the 19th-century United States have shown that earlier arrivals have greater wealth than do later migrants. This paper finds that the same was true for the frontier states Texas and Arkansas in 1860 using real wealth. Within the context of a specific model it is shown that the relatively high price appreciation for improved land at the frontier, the larger initial (1850) wealth endowments of the earlier arrivals, and the cost of migration largely account for this. 0 1987 Academic Press, Inc.

I. INTRODUCTION

Many studies of the frontier in the antebellum United States have found evidence suggesting that earlier arrivals had greater wealth than did later arrivals. Lathrop (1949, p. 69), in his study of East Texas, noted that length of residence and wealth were positively related. The 1850 median real estate holdings for recent arrivals was $100; for residents of 4 to 6 years the ,median was $400, while those Texans with 13 to 15 years of residency had a median of $1000. Similarly, Kearl et al. (1980, pp. 487, 489) found for Utah heads of household in 1870 that earlier migrants (as indicated by enumeration in the 1850 or 1860 manuscript censuses) held higher levels of total estate than did later migrants. What is less certain is the source of the observed differences in wealth holding among persons with differing duration at the frontier. Lathrop (1949, p. 73) went no further than to note that the data suggest “the bulk of migrants did in time better themselves economically.” Easterlin et al. (1978, p. 50), in an analysis of the farm families in the BatemanFoust sample of northern families, concluded that the quantity of improved *The author thanks Philip Coelho, William Hallagan, Larry Neal, Joseph Reid, Mark Schmitz, and the referees for helpful comments. The data collection was facilitated by grants from the National Science Foundation (SES-8006419), the Office of Grant Research and Development at Washington State University, and the College of Business and Economics at Washington State University. 130 0014-4983187 $3.00 Copyright All rights

0 1987 by Academic Press, Inc. of reproduction in any form reserved.

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acreage (along with proximity to markets) was an important determinant of farm value. Further, they noted that length of settlement and the quantity of improved acres were positively related. In the Utah study, which did control for age, sex, occupation, Utah location, and place of birth, Kearl et al. (1980, p. 480) hypothesized that time of entry (independent of age) affects the level of wealth holding in two ways. First, a Ricardian economy at work allows initial settlers to acquire land that generates high rents (capital gains) though time as the stock of labor increases and as less productive land is settled and brought into production. Second, in time an economy allows one to collect information that increases income. . .

In this paper I provide an analysis of the land wealth holdings of a distinct group of migrant and nonmigrant families living in the cotton region of Arkansas and Texas in 1860. In doing so I make some very specific behavioral assumptions which allow me to identify specific sources of the differences in wealth holding by time of migration. Three tasks are undertaken here. First, I show that time of migration and level of wealth are positively associated for farm families living in the cotton region of Arkansas and Texas in 1860. In other words, families migrating to Arkansas and Texas during the decade of the 1850s had less wealth than did those who already were living in these states before 1850. This result is consistent with the previously mentioned studies. Second, I provide evidence on land price appreciation, land improvement and acquisition, and farm value appreciation for frontier and new South nonmigrants. Third, I present a behavioral model describing wealth accumulation that is consistent with the historical literature on migration and the empirical record. Finally, using the information derived from nonmigrants in the second section as well as other data, I estimate the parameters of this model and provide numerical estimates of the factors responsible for the difference in wealth holdings of migrants and nonmigrants at the frontier in 1860. The data employed in this paper are based on a matched sample (derived from the Parker-Gallman sample) of households enumerated as operating farms in cotton South in both the 1850and the 1860manuscript censuses of the free population and agriculture.’ More specifically, the households and the farms were located in the cotton counties of Arkansas and Texas (the frontier) and of Alabama, Louisiana, Mississippi, and Tennessee (the new South) in 1860. The sample includes both migrants and nonmigrants. The migrants in 1850 were located in these six states and other southern states. The specific wealth measure used in this paper ’ For a further discussion of the Parker-Gallman sample, see Foust (1973, Foust and Swan (1970), Wright (1970), and Schmitz and Schaefer (1986).

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is farm value (the value of agricultural land and improvements). Thus personal wealth, including the value of slaves, is excluded from consideration. Further information on the data is contained in the Appendix and in Schaefer (1985). II. DIFFERENCES

IN WEALTH

HOLDING

Did migrants to the southern frontier states (Arkansas and Texas) during the decade of the 1850s have less wealth in 1860 than individuals who lived in the frontier states for the entire decade (nonmigrants)?’ And if so, can any wealth differences be explained by differences in the personal characterstics or 1850 wealth holdings of the migrants and nonmigrants? The 1860 wealth holdings of migrants to the frontier were palpably less than those of frontier nonmigrants (persons living in the frontier states in 1860 whose county of residence was the same in both the 1850 and 1860 censuses). The mean real wealth and cash value of farm (farm value) of individuals in the sample grouped by personal characteristics (mostly of the head of household) are shown in Table ls3 Certainly the mean real wealth and farm value of nonmigrants were greater than those of the 1850s migrants to the frontier (the ratio is approximately 1.5:1). However, other groups present even stronger contrasts. For example, households headed by individuals age 40 years and older on average had twice the wealth of those headed by younger individuals; slaveowners had more than eight times the real wealth of non-slaveowners. Thus the question remains whether migrants, ceterus paribus, had less wealth than did nonmigrants or whether the observed difference can be accounted for by the varying personal characteristics or the initial (1850) wealth holdings of the two groups. Using OLS regression with wealth as the dependent variable and personal characteristics and nonmigrants as the independent variables it is possible to isolate the effect of migration on the 1860 level of real wealth. Further, by including 1850 real wealth as a right-hand-side variable the effect of pre-1850 real wealth accumulation can be removed. In Table 2 the real wealth (RW) regressions for all families and for non-slaveowners are presented. The latter provide comparability with the studies of Easterlin * Throughout this paper the terms “frontier” and “West” are used interchangeably as are “nonfrontier” and “East.” 3 The variable real wealth, while of broad interest, has some shortcomings. Most prominently, it is unclear how it is divided between agricultural and nonagricultural holdings. A more clearly defined agricultural land-holding variable is dollar value of farm. But farm value as enumerated in the census did not necessarily imply ownership. Thus these two variables could relate to migration differently. However, it is known that they were very highly correlated in the South (Schaefer and Schmitz, 1985, p. 222).

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TABLE 1860 Wealth and Personal Characteristics Group Total sample Age (years) Under 40 40 to 50 50 to 60 60 and older Sex Male Female 1850 occupation Farm operator Not in agriculture Farm worker Other Land Landowner Nonlandowner Slaves Slaveowners Non-slaveowners Migration Interstate migrants Intrastate migrants Nonmigrants State Texas Arkansas

Percentage of sample 100

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ACCUMULATION 1 of Frontier Households (n = 279) Mean real wealth 69

Mean farm value cl3

5,415

4,888

28.7 33 25.1 13.3

3,561 6,185 5,685 6,995

3,368 5,393 5,067 6,583

98.2 1.8

5.441 6,995

4,910 3,684

78.9 5.4 10.4 5.4

5,562 8,825 929 8,512

5,252 6,203 1,121 5,523

90.7 9.3

5,971 0

5,222 1,640”

44.6 55.6

10,589 1,276

9,201 1,438

43.7 11.1 45.2

4,086 4,829 6,840

3,628 5,180 6,037

86.4 13.6

5,384 5,609

4,947 4,512

Source. See Appendix. ’ Some farmers were tenants. Most of these have been removed in the estimation of the models presented below.

et aE. (1978) and Kearl et al. (1980) since they are for non-slaveowners only.4 For the RW regressions the usual nonlinear life cycle pattern is present with the maximum occurring at age 48 years for non-slaveowners and age 40 years for all heads of household, ceterus paribus. The results for the migration variables mirror those of Kearl et al. and Lathrop. The estimated coefficients for intrastate and interstate migrants (relative to those for the base group of nonmigrants) all are negative. The coefficients 4 In addition there is a large historical literature that assigns different roles to planter and yeoman farmer migration in the South. Foust (1975, Chap. 1) provides a summary of this literature.

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TABLE 2 1860 Wealth and Household Characteristics RW Independent variable Intercept

All -3,987

(8,150)

Age Age* Migration Intrastate Interstate 1850 Occupation Not in agriculture Farm worker Other

408 (358) -5.07 (3.60) - 1084 (1,345) - 1,597*

(983 5,297* (2,744) - 1,493** (619) 1,473

(2,267) Arkansas 1850 real wealth

- 399

(843) 1.77** (0.338)

Non-slaveowners 363 (1,632) $8) - 0.429 (0.667) -571* (325) - 735** (310)

10,989 (7,305) -417 (304) 3.19 (3.03) 2,012 (1,414) - 2,263**

(822)

-601*

(320) - 87.6

(269 -96.6 (236) 121

(247) 1.29% (0.665)

1850 farm value

1.68** (0.457) 1,067**

Labor n Adjusted R2

FVb All

(211) 279 0.472

155 0.122

202 0.707

Source. See text and Appendix. * Significant at the 0.05 level against a one-tailed test. ** Significant at the 0.01 level against a one tailed test. 0 Real wealth-value of real estate owned. ’ Farm value-dollar value of farm operated. ’ Includes only farm operators whose farms have a positive dollar value and a positive number of acres, and who have available a positive amount of labor in both 1850 and 1860.

for the latter group are larger in absolute value and are more highly significant.5 Finally, the estimated regression coefficient for 1850 real wealth is highly significant in all the equations. Thus equations that omit ’ The data exhibit a good deal of heteroskedasticity. This is to be expected in wealth studies where the range of the data is large. Instead of attempting to correct for this problem, the standard errors are calculated using the heteroskedastic robust estimator proposed by White (1980). This estimator is easily calculated with any statistical package such as SAS that allows matrix manipulation.

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this variable must either contain quite detailed information concerning that history, including items such as parent’s wealth, inheritance rules, and number of siblings, or risk being highly misspecified.6 The regression for farm value (FV) in Table 2 illustrates the extent to which the same (or similar) independent variables affect the two wealth measures.7 For interstate migrants the relationship between wealth and migration is similar to that found using real wealth; migrants had significantly less farm value in 1860 than did nonmigrants holding constant personal characteristics and 1850 farm value. However, intrastate migrants had more wealth than did nonmigrants. Curiously, the relationship between age and farm value is strikingly different from that between age and real wealth. This difference could be explained by postulating that the head of household over time allowed his children to operate part of the farm (thus enabling them to be enumerated in the census of agriculture with a positive farm value) while remaining the farm operator of record. However, we have no evidence to test this hypothesis. Finally, the labor variable (the arithmetic mean of the 1850 and 1860 standardized units of available labor) is included in the FV equation to capture the ability of the household to transform unimproved land into improved land, thereby increasing farm value. It is positive and highly significant. The magnitudes of the coefficients in the FV equation are also informative. The observed difference in the average farm value of nonmigrants and interstate migrants was approximately $3150 in 1860.’ The coefficient for interstate migration ($2263) thus implies that roughly 72% of the difference in FV is not explained by the initial (i.e., 18.50) levels of farm value, labor, or life cycle. That 72% should include differential rates of land price appreciation, differences in the changes in the quantity of land, and out of pocket costs of migration, among other things. We refer to this result below in the discussion of the sources of real wealth differences. 6 Wealth regressions were run with 1860 real wealth, personal wealth, and total wealth as the dependent variable while omitting the appropriate 1850 wealth variable. The conclusion that non-slaveowning migrants had less real wealth than did nonmigrants was unaffected by this omission. The estimated coefficients of the migration variables for the personal wealth equation were small, positive, and insignificant. For other variables in the real wealth equation, the signs of coefficients were generally unchanged but the magnitudes and signilicance varied greatly. ’ The FV equation was fit to data only for farm operators since by definition they were the only group having enumerated farm value. In addition, to minimize the role of tenants only observations with positive enumerated values of labor and acres (improved or unimproved) and farm value were included (Bode and Ginter, 1981, 1984). These constraints were relevant to only the 1850 data since the 1860 sample was chosen to be consistent with the rules set out by Fogel and Engerman. a The underlying data used in the model presented below, including FV, are contained in Appendix Table A-l. These differ from the data in Table 1 because of the restrictions placed on the observations used in the FV regression and the models that follow.

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In the remainder of this paper the focus is on FV for nonmigrants and interstate migrants to the frontier. Intrastate migrants are dropped from the sample. In addition, the data are restricted to farms enumerated with a positive number of acres, a positive cash value of farm in both 1850 and 1860, and a labor force (measured in standardized units) that is positive. These choices are dictated by two considerations. First, the sources of FV are more easily determined and modeled than are those of RW.9 Second, the relationship between migration status and FV is similar to that found for migration status and RW-at least for nonmigrants and interstate migrants. Thus the benefits of the chosen approach are similar to those that could be achieved using RW while the costs are considerably less. III. CHANGES IN THE WEALTH OF NONMIGRANTS:

1850-1860

Since the difference in the average farm value of migrants and nonmigrants is not explained fully by the personal characteristics of the two groups or by their 1850 farm values, it seems reasonable to search for the residual sources of that difference in the process of migration and for the migrants’ reactions to the origin and destination locations. Unfortunately, our direct knowledge of migration and its effects on wealth accumulation is limited. The 1850 and 1860 farm values and land quantities for migrants and nonmigrants were enumerated in the census. Missing is information on land prices, land improvement and acquisition, costs of migration, and time of migration. For the migrant these gaps in our knowledge are especially troublesome since we must determine not only the role of economic forces on wealth accumulation at the origin and destination locations but also the effects of making the transition across regions. Initially the most tractable empirical problem is the estimation of the change in farm value and its components over the decade for eastern and western nonmigrants. These provide information about the environments in which the migrant lived over the decade. The annual percentage increase in the farm value of the average western nonmigrant (w) was approximately 15.5% over the decade of the 1850s while for the average eastern nonmigrant the annual percentage increase (w*) was not quite 13%. (The data are contained in Table 4 while a list of the symbols used throughout the paper is contained in Table 3.) These increases arose from increases in the quantities of improved and unimproved land held by the nonmigrant households in each region and from improved and unimproved land price appreciation. These differed across regions. Eastern unimproved land prices Cj*) rose faster than those held by the average 9 The one major ambiguity, farm operation ownership, farms with no land or labor or farm value.

has been minimized by omitting

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TABLE 3 Symbols Used in the Text wF,w,---Wealth of western migrants and nonmigrants at time t. A.,--w, - w;“. WE-Wealth of migrants at time of migration (before incurring migration costs). pY,p?,p,---Migrant, eastern, and western prices for improved land at time 0. pr&,p,---Migrant, eastern, and western prices for unimproved land at time 0. #,&-Prices paid by migrants for improved and unimproved land at time kr. pF’,p?t,pf--Prices of migrant, eastern, and western improved land at time t. pl”‘,p,*t,p:-Prices of migrant, eastern, and western unimproved land at time. t. $,qi*,qi--Migrant, eastern, and western quantities of improved land at time 0. qF,qZ,qp-Migrant, eastern, and western quantities of unimproved land at time 0. q?,q,ht,qj---Migrant, eastern, and western quantities of improved land at time t. q?,qU*t,q:---Migrant, eastern, and western quantities of unimproved land at time t. Qi*,Qi---Eastern and western annual number of acres improved per unit of labor. Q:,Qn--Eastern and western annual number of unimproved acres acquired. .i*,j-Eastern and western annual percentage increase in unimproved land prices. l*,l--Eastern and western annual percentage increase in improved land prices. w*,w-Eastern and western annual percentage increase in farm value. c-Out of pocket costs of migration. n”,n-Average labor force (measured in standard units) over the time interval (0,t) for western migrants and nonmigrants. $,+---Average labor force for migrants and western nonmigrants over the time interval Wt). rz;“,n,-Average labor force for migrants and western nonmigrants over the time interval S&t). cY--Proportion of proceeds from the sale of the eastern farm (minus out of pocket costs) used by migrants to purchase unimproved land in the West. t-Endpoint in the time interval over which wealth is accumulated. In this model t is 10 (years). k-Time of migration expressed as a proportion of t. m--Used as a superscript to denote a value calculated from migrant data. *-Used as a superscript to denote a value derived from eastern nonmigrant data. Note. Details of the calculations to obtain these variables are contained in Appendix.

western nonagrant (~1 while the opposite was true for improved land. In the West and in the East the average annual rate of land improvement per (standard) Ilaborer (Qi and QT, respectively) were roughly identical while the average annual increase in unimproved acres in the West (QU) was nearly double that in the East (Qz). Are these results statistically robust and historically plausible? The land prices in 1850 and 1860 are open to question since they were estimated from census data using regression techniques rather than enumerated in the census. To test the sensitivity of the land price results in Table 4, I assumed the improved land prices were estimated subject to normally distributed errors with mean zero and standard deviations equal to the standard errors of the regression parameter estimates. Given a price for improved land drawn from this distribution, the quantities of

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TABLE 4 Growth Rates for Farm Value and Its Components in the East and the West Parameter

Estimate

j J‘* 1 I*

4.4% 10.5% 11.9% 6.9% 1.05 1.oo 31.6 17.7 15.5% 12.9%

;; 2 W W*

per year per year per year per year acres per acres per acres per acres per per year per year

year year year year

Source. See Appendix.

land, and the assumption that the errors did not affect the farm value, the price of unimproved land is determined.” Using random number generators, I then produced 100 observations with different average improved and unimproved land prices for eastern and western nonmigrants in both 1850 and 1860. These observations were used to determine the robustness of the ordering of the annual percentage increases in land price by region and land type. For improved land, the empirical probability that 1 is no less than I* is 0.99 while for unimproved land the probability thatj* is no less thanj is 0.91. For the East and the West, the probabilities that the observed intraregional orderings hold are 0.86 and 0.97, respectively. Thus the orderings of the annual percentage increases in land prices are very robust against the assumed uncertainty in land prices. The historical record on land prices suggests that unimproved land prices were rising throughout the decade in many part of the United States (Bogue and Bogue, 1957; Silver, 1944; Russell, 1942; Chapman, 1940). While there clearly was wide variation in the rate of return, most estimates fall between 2 and 10% per annum. For farm land and buildings (that is, for improved and unimproved land), Gray (1933, p. 643) used data from the published 1850 and 1860 censuses and found that the average annual rate of price increase for the southern states varied from about 3 to 10%. On the basis of this evidence, the absolute levels of the average annual percentage increases of land prices appear reasonable.” lo For example if a farm has 10 improved acres valued at $10 per acre and 100 unimproved acres valued at $1 per acre, then the farm value is $200. If the price of improved land is changed to $15 per acre, then the 100 unimproved acres are worth $50 or $0.50 per acre. ” Are different rates of land price increases consistent with economic theory? Confining our attention for the present to the difference in inter-regional changes in land prices, there is no reason to question the presence of different rates, These are quite consistent with

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I assume that. the pattern of price appreciation for eastern and western improved and unimproved land represents the outcome of economic behavior rather than the underlying economic causal structure but even with this assumption, the pattern is subject to numerous interpretations. The interpretation seemingly most consistent with the historical record is that in each region there were outward shifts in the demand curves for land along stable supply curves for land. The shifts in the demand curves were caused in part by the increase in population over time. These increases were not uniform across the frontier and the new South. Over the decade the white population in the two frontier states increased by around 135% while the increase for Alabama, Louisiana, Mississippi, and Tennessee (the new South states) was approximately 19%; in absolute terms the frontier states also experienced the greater increase in population (U.S. Dept. of Commerce, 1975, pp. 24-35). One other factor was also responsible for shifting the demand curve for land at the frontier, especially in Texas. Over the course of the decade railroads were introduced to the frontier states.” The effect was to raise the demand for land in response to actual and anticipated decreases in transportation costs. While railroads were also being built in the new South states, their major impact on land prices had probably occurred in the 1840~.‘~ The historical record seemsto support the notion that the supply curve for unimproved land was more elastic in the frontier states than in the new South. There were two main types of land: land owned by farm operators (agricultural land) consisting of improved and unimproved acreage, and land owned privately and pubicly by nonfarm operators (nonagricultural land). In the West there was less agricultural land per square mile than in the East.14From 1850to 1860the number of unimproved the notion of economic equilibrium as a “state of rest” given imperfect information, transactions costs, different land quality, etc. A second meaning of equilibrium is the equality of supply and demand within a market. It is possible to attain equilibrium in the first sense simultaneously with disequilibrium in the second sense (Benassy, 1982, p. 3; Machlup, 1958). Similarly it is possible to imagine intraregional land markets for different types of land in which the rates of price appreciation differ, especially if land is conceived. of as an input to agriculture rather than just a speculative investment. ” In 1850 there were no railroads in Texas. By 1860, 272 miles had been built running inward from the two major points of entry, Galveston on the Gulf of Mexico and the Red River near Shreveport, LA (Meyer, 1917, plate 5, p. 654; Texas Almanac, 1860, Vol. 4, p. 220). I3 For example, the Nashville and Chatanooga Railroad, organized in 1848, planned to construct 123 miles of track between these two cities. From 1848 to 1849 the value of and in the four counties through which the railroad ran-Davidson, Rutherford, Bedford, and Franklin-rose by $2.5 million. The road was eventually opened to the public in 18.54 (Meyer, 1917, p. 471). Overall, the four new South states (plus Kentucky) had built 195 miles of railroad by 18.51 (Meyer, 1917, p. 480). I4 For example, in Anderson county, TX, in 1850 the census enumerated 103,264 acres of unimproved land or less than 100 acres per square mile; in Arkansas county, AK, the

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acres in the frontier states increased by 141% while in the new South the published census data show only a 37% increase. Of equal importance was the ownership of the nonagricultural land. In Texas much of that land was held by the state. From 1845 through 1856 land was available on a homesteading or a preemption basis for no more than 50 cents per acre payable in par funds (Miller, 1972, pp. 35-36). In the remainder of the states nonagricultural land was held by both the federal government and private speculators. The laws of 1841 and 1854 (Graduation Act), designed in part to encourage the transfer of land from the public domain to the .private sector, damped the rise of unimproved land prices. In Arkansas, given the lack of agricultural land and the smallness of the white population, it seems likely that much of the remainder was still in public hands in 1850. On the other hand, there is reason to argue that labor shortages at the frontier made the supply curve for improved land relatively inelastic. Contemporary observers often commented on the labor shortage and the scarcity of improved lands (Adamson, 1839, pp. 7, 10-11; An Emigrant, 1840, pp. 268-69; Fisher, 1841, p. 50).” In addition, the relative shortage of slaves in the lower South (including the frontier states) is shown by the sale and hire prices in the upper and lower South (Fogel and Engerman, 1974, Vol. 2, p. 73)? The annual rates of land improvement per unit of labor for nonmigrants and migrants (Q and Q*, respectively) are consistent with those found by Primack (1962, p. 484), who noted that five acres of land clearing in addition to raising crops was the limit for a family farm assuming the land cleared was initially forested. This generally appears to be the case although some of the cotton counties in Texas were combinations of forests and grasslands (U.S. Dept. of the Interior, 1970, pp. 89-90). The information in Table 4 relating to eastern and western nonmigrants is relevant to the question of why migrants to the West had less wealth than did nonmigrants in the West. However, it clearly is not sufficient to explain that difference. Some of the missing information includes the initial wealth holdings of the migrants and the cost and timing of migration. These can be reconstructed from available data sources. What cannot be reconstructed is the pattern of wealth accumulation of the migrant figure was less than 40 unimproved acres per square mile. For new South or eastern counties the ratio of unimproved acres to square miles was substantially greater. For example, in Autauga county, AL, the ratio was approximately 290 acres per square mile. Taking into account the number of improved acres only increases the disparity between the East and the West. I5 However, this view was not universally held (Smith, 1849, pp. 38,100). I6 An entirely different explanation has been put forward (Reid, 1976). Reid argues that differing rate-life cycles along with risk aversion are sufficient to produce higher rates of return at the frontier.

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from 1850 to the time of migration, the composition of wealth purchased in the West, and the pattern of wealth accumulation in the West (although the resultant 1860 wealth, land prices, and land quantities are known). No systematic data are available to provide clues for these migrant wealth accumulation paths. Without this information, it is impossible to determine quantitatively the various sources of the observed difference in the average wealth of nonmigrants in the West and of migrants to the West unless one is willing to make behavioral assumptions about the migrants and wealth accumulation. IV. MODELS

OF MIGRATION

AND WEALTH

ACCUMULATION

In what follows a scenario describing migration and real wealth accumulation is presented. This scenario, the product of empirical constraints, economic reasoning, and historical knowledge, then becomes the basis for a model (or statistical reconstruction) of wealth accumulation that is sufficient (but clearly not necessary) to reproduce the observed values for farm value and land holdings in 1860. A series of restricted models (counterfactuals) is then presented as a vehicle to isolate the sources of differences in FV for migrants and nonmigrants. The General Scenario

There are two regions, East and West, i.e., the nonfrontier and the frontier portions, respectively, of the cotton South. These regions are observed over a time interval [0, t] where t is a positive number (e.g., t = 10 years). At time 0 there are three separate groups. First are the farm operators living in the western region (nonmigrants). The farm operators living in the eastern region at time 0 comprise two groups: migrants who move to the western region at time kt where k is some number between zero and one, and eastern nonmigrants who do not move at all. The farmers all operate farms that have a positive cash value and a positive number of acres. Migrants sell their farms (that is, their improved and unimproved land) at the going market rate in the East just prior to moving. On arriving in the West the migrants use the proceeds from the sale of their eastern farms, less out of pocket costs of migration, to purchase farms at the going market rate in the West. Farm value grows in two ways; through the increase in land prices over time and through changes in the quantities of land. Each of these mechanisms operates for two types of land: improved and unimproved. Thus changing quantitites of land implies two different processes: the transformation of unimproved to improved land and the acquisition of land. Except for the case of migrants purchasing western land, all land acquisitions are assumed to be unimproved acreage and the source of the funds is external to the farm value (that is, a farmer does not sell

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existing land to purchase different land). Migrants do not face these restrictions since they sell existing land prior to migration and use the proceeds from this sale (less out of pocket costs of migration) to purchase unimproved or improved land in the West. Within each region the rate of land price appreciation by land type (improved or unimproved) was equal for migrants and for nonmigrants; both were price takers. Further, the annual quantity of land improved per unit of labor did not vary by migration status. In slack periods both migrants and nonmigrants used their internal labor forces equally efficiently to improve land. Finally, the annual quantity of unimproved land acquired within each region was identical for migrants and for nonmigrants. This last assumption is born from empirical necessity since the behavior of migrants is not observed.” The model that follows was constructed to match the general scenario. One other constraint was imposed. The model had to be capable of reproducing our limited empirical knowledge. For example, any assumed rates of land improvements had to be capable of reproducing the enumerated quantities of improved acres in 1860. And most certainly it had to reproduce, at least approximately, the observed difference in farm value for nonmigrants and migrants. Historically and analytically it is apparent that at least four forces could have been responsible for the observed difference in farm value: different rates of land price appreciation due to different regional locations, different rates of change in the quantity of land, different initial resource endowments, and the out of pocket costs of migration. Each of these forces is modeled below by restricting the general model to make these factors equal for migrants and for nonmigrants. To the extent that these restrictions cause the observed difference in farm value to diminish, it is argued that they “explain” this difference. A General Model

of Wealth Accumulation

In this general model wealth is directly affected by four factors: land price appreciation, changes in the quantity of land, initial resource en” It would be justified if the utility function and its arguments were identical for migrants and for nonmigrants. The assumption of identical utility functions is not novel. The literature for multinomial logit models provides numerous examples (McFadden, 1973, p. 106; Mueller, 1982, Chap. 3). The arguments of the utility function include both place and personal characteristics. The average migrant and nonmigrant within each region faced the same agricultural environment. However, Steckel (1983) makes the point that migrants who followed an isolatitude migration path were more productive than those who deviated from such a path. Migrants to the frontier did not follow an isolatitude migration path (Schaefer, 198.5, p. 569). Thus it is possible that the different incomes earned by migrants and by nonmigrants (who had a chance to adapt) facing-the same environment led to different rates of unimproved land acquisition. Nonetheless, many of the personal characteristics of the migrants and nomnigrants were comparable. In any event the empirical results presented below are not greatly affected by different rates of unimproved land acquisition in the two regions.

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ACCUMULATION

dowments, and out of pocket costs. For the nonmigrant,. t can be written as W, = puej’(q,

wealth at time

- ntQi + tQJ + pfelt(qi + ntQJ

(1)

where p and q are land prices and quantities at time 0, the subscripts i and u refer to improved and unimproved land, err and ej* are the factors by which land prices grow from time 0 to time t assuming continuous compounding (Chiang, 1984, pp. 276-280), 1 andj are the nominal rates of growth, Qi is the average annual amount of land improvement per standardized unit of labor, Qll is the average annual quantity of unimproved land purchased, and IZ is the average labor force. (All symbols are defined in Table 3.) Thus the first term in parentheses describes the change in the unimproved acres over time while the second does the same for improved acres. The analytical restrictions on the parameters of this model are YI, p, q > 0, 1, j 2 0 and qu > tQi. This last restriction says that the quantity of unimproved acres available in the time interval 0,t is not a constraint on land improvement. In addition the estimates ofj, I, Qi, and QU are constrained to be consistent with the available empirical information for farm acreage and value in 1850 and 1860. The wealth accumulation model for migrants is most easily interpreted in two parts: pre- and postmigration. The premigration model is quite similar to that for nonmigrants: W; = pFe’*k’(qF

- n”,krQT

+ ktQ,*) + pre’*k”(qy

+ r$ktQt)

(2)

where kt is the time of migration (0 < k < 1). Analogous to Eq. (l), the terms in parentheses represent the quantities of unimproved and improved land over time, respectively. For the sake of simplicity migration is assumed to be instantaneous although not costless. The migrant is assumed to sell his eastern land at the market rate. The proceeds from this sale, rnz, less out of pocket costs of migration, c, are used to purchase improved and unimproved land in the West at the market rate. The migrant then improves land at the same rate as the nonmigrant and obtains the same rate of appreciation on land. The wealth accumulation model for migrants at time t becomes

a(wE - cl - nY(l - k)tQj i (1 - k)tQ, PF

(l - a)(wk7 - ‘) + n”Z(l _ t P$

As before, the two major bracketed terms unimproved and improved land over time, of the two major bracketed expressions, the land purchased given the western prices and

k)tQ-

I

(3)

I I

represent the quantities of respectively. Within each first term is the quantity of (31represents the proportion

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of the proceeds from the sale of eastern land going into the purchase of unimproved land. The remaining terms represent land improvement and unimproved land acquistion, (Y,pp, pf, and c are not directly observed but are inferred from the available data for time t.‘* The observed difference in farm value, A,,,, then is defined as w, w;“. This is the fixed reference point against which all of the restricted models are evaluated. Restricted Models of Wealth Accumulation

The restricted models presented here are counterfactuals designed to show the effect of a specific difference between migrants and nonmigrants on the observed difference in wealth at time t. The explanatory power of the restricted model is the proportionate reduction in A,,, that comes about as a result of the given restriction. (i) Equal land price appreciation. This restricted model assumes that land price appreciation in the East is equal to that in the West, i.e., that j* = j and 1* = 1. These conditions can be imposed separately as well. The effect of this restriction (and of the two that follow) is to modify Eq. (2). Here premigration wealth becomes wz = pTejk* (qr - n?ktQT + ktQz) + pyelk* (qr + n?ktQf).

(2a)

(ii) Equal rates of change in the quantity of land. In this restricted model equal rates of land improvement and of unimproved land acquisition are assumed to hold across regions. Symbolically, QT = Qi and Qz = Q,, . The economic interpretation is that the relative investment opportunities are identical across regions and within regions. Equation (2) of the general model is modified in an analogous fashion to Eq. (2a). (iii) Equal initial resources. In this restriction, migrants and nonmigrants are assumed to have the same farm value and labor at time 0. The former is achieved by adjusting the quantity of unimproved acres held by migrants at time 0.” That is, 41: =

P&u + PiQi - PT4T PI:

at time 0. Labor also enters this model since it is the determinant of the annual rate of change in the stock of improved acreage. Thus np = nk and $” = n, in Eqs. (2) and (3) of the general model. (iv) Out of pocket costs of migration. Finally, we restrict migration costs to be zero for migrants as they are for nonmigrants. I8 Estimation procedures are discussed in the Appendix and in the following section containing the empirical results. ” The equality of initial farm value could also have been achieved by augmenting improved acres as well as by some mixture of these two. Since the composition of migrant FV was already more heavily weighted toward improved acres, the present approach was adopted. The effect of this restriction is thus both quantitative and qualitative.

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in Farm Value

Beyond the restrictions applied above there are two other sources for the observed difference in the farm value of migrants and of nonmigrants. The first source is the interactions among the four models presented above. Imposing all restrictions simultaneously produces an overall level of explanation that is less than the sum of the explanatory power of all the restrictions applied separately. The second source, the residual (100 minus the explanatory power of all restrictions applied simultaneously), takes into account the effects of other factors not included in the model as well as measurement error. V. EMPIRICAL Estimation

RESULTS

Technique

Estimation of the general and restricted models occurs in two phases. In the first phase the general model is estimated. The goals when estimating the general model are simultanously to reproduce the observed difference in farm value at time t for migrants and western nonmigrants and the observed mean values for land prices and quantities and farm value at time t. The approach taken to ensure that these goals are met is to let c, the out of pocket costs of migration, take on a value that allows the model to reproduce the observed mean farm value for migrants at time t. This is accomplished by a trial and error procedure, Given c and the assumptions of the model, the available wealth immediately after migration, the allocation of wealth between improved and unimproved land (a~), and the land prices facing migrants at the time of migration are determinate. Land prices at kt are determined given the land prices at time t and the regional rate of land price appreciation; (Y is determined given the land prices at time kt, the regional rate of land improvement, and the observed quantity of improved land at time t. In the second phase of the estimation process, the parameter estimates are varied in accordance with the restricted models. A new estimate of migrant farm value at time t is generated and a new difference between the farm value of migrants and western nonmigrants at time t is calculated. Model

Validity

Since the general model is estimated so that it reproduces the observed average wealth levels for migrants and nonmigrants, other methods are required to test the validity of the model. In this section I examine three indicators of validity. First, since the model is a simplification of reality, how important are omitted variables? Second, because the model is estimated using means rather than individual data, it is useful to ask how well the model describes the diverse behavior of the individuals within the sample. Third, how plausible are the intermediate parameter estimates

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generated by the model? These three indicators are examined in this section. This examination, while not comprehensive, is supportive of the model’s validity. One variable that is missing from the general model but which was included in the regression models is age of the head of household. Since it is generally conceded that there is some life cycle pattern of wealth accumulation, it is possible that some portion of the difference in the farm value is due to the average migrant and the average nonmigrant operating at different points along the (nonlinear) life cycle. This would occur if the average ages of the migrant and the nonmigrant heads of household were very different. Such is not the case. The average age of the nonmigrant head of household in the sample of families at the frontier was enumerated in 1860 as 49.4 years while for the migrant it was 48.0 years. This hardly seems to be of substantive importance. On the issue of individual behavior vs group means, one test is to determine the extent to which individuals increased the acreage of their farms over the decade as the model postulates. (From Table 4 it can be seen that the model is clearly appropriate for the average nonmigrant.) For individual frontier nonmigrants this information can be ascertained directly from the sample. Of this group, 80% increased their improved acreage over the decade while 68% acquired additional unimproved acreage over the decade (assuming all increased improved acreage was transformed from unimproved acres). Thus it seems appropriate to characterize nonmigrants as increasing their improved acreage and unimproved acreage over the decade, while at the same time to recognize that this behavior did not hold universally. The third indicator, parameter plausibility, relates to the values of a! (the proportion of net wealth used by migrants to purchase unimproved land in the West) and c (the out of pocket cost of migration), both of which are generated by the general model rather than by outside information. The estimate for a, 0.543, appears to coincide with the historical pattern at the frontier. Certainly there was an active market for farms in the mid-19th century (Lebergott, 1985, pp. 196-197; Smith, 1849, p. 100). Alternatively, 1 - (Ycan be interpreted as the proportion of wealth spent on improvements either by purchase of a farm or by purchase of labor to improve virgin land. From either vantage the value of (Y is quite plausible. Chosen to make the results of the general model conform to the enumerated average farm value for migrants, c deserves close attention and at first glance its value of $775 seems too high. However, when the components of this cost are considered, it does not appear too unreasonable. First, from the sample we know that the average household incurred transportation costs for 13 persons (including slaves) traveling a straight-

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line distance of approximately 470 miles plus the costs of transporting household effects and farm equipment. In addition, any search costs would be included in this category.2o Second, the costs associated with the sale and the purchase of real estate would be included. What is less certain is whether these costs would have been covered from the proceeds of the sale of real estate or from outside sources such as personal wealth or bank loans. The model assumes that all costs were paid from the proceeds of the sale of real estate. If this assumption is grossly incorrect, then the value for c may be too high. Sources of Real Wealth Diflerences

Table 5 (middle column) contains the estimates of the contributions of the various forces in explaining the difference in wealth accumulation. In interpreting Table 5, some factors should be borne in mind. First, the explicit counterfactuals being examined are those contained in the restricted models of wealth accumulation presented above. For example, land price appreciation in Table 5 is derived from restricted model (i) and provides an empirical answer to the question “By what percentage would the observed difference in 1860 farm value between migrants and western nonmigrants have been decreased if the annual rate of price land appreciation had been the same in the East as it was in the West?” Here 25.9% of the difference is explained by differing rates of land priGe appreciation. The remaining entries in Table 5 correspond exactly to the discussion of the restricted models and other sources of differences presented above. Second, the explanatory power of each potential source is highly dependent on the time of migration. To continue the example, 2o To test the plausibility of c a rough estimate of transportation calculating for each family c = (pop, + pop,)(0.50)(1.5dist)(0.05)

costs was obtained by -~

+ (l.Sdist)(O.O7)

where the tirst term is the cost of transporting by railroad the average number of persons in the household in 1850 and 1860 (5 cents per passenger mile) with the distance increased by 50% to reflect the indirectness of the actual route taken. The second term is the cost of transporting goods over that same distance by rail where the rate per ton mile is 7 cents and it is assumed that each family had 1 ton of household goods. The rail rates roughly coincide with those for southern states (Meyer, 1917, p. 576). This calculation yields an average cost of approximately $560. This estimate is based on one of many possible scenarios. Given the paucity of rail services within Texas for most of the 1850s it seems likely that some wagon or stage travel would have been necessary. Within Texas, stage lines charged 10 cents/person/mile while oxen wagons charged 2 cents/mile/l00 pounds (Richardson, 1870, p. 31). Also, water transport to Texas seems to have been a popular option. Steamboat fares from New Orleans to Galveston or Shreveport varied from $10 to $35 per person (Smith, 1849, p, 98; Richardson, 1870, p. 45; Stiff, 1840, p. 150). If other routes or transportation modes were used, then the transportation costs might have been substantially different. In addition, there were costs associated with the sale and purchase of land at the origin and destination as well as search costs (Ankli, 1974, p. 56, note 36).

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TABLE 5 Sources of Real Wealth Differences between Migrants and Nonmigrants

Source Land price appreciation Unimproved land Improved land Change in land quantity Land improvement Land purchase Unequal initial endowments Farm value Labor Cost of migration Sum of sources Interactions Residual

Percentage explained (c = 775) 25.9 -2.8 28.7 3.7 1.0 2.7 32.5 28.9 3.6 39.5 101.6 6.6 5.0

at the Frontier Interquartile range WI -5.8-0.1 19.8-40.6 0.9-1.1 0.5-5.1 27.8-34.2 3.1-4.0 30.4-39.8

Source. See text and Appendix.

if the eastern rate of land price appreciation was not equal to the western rate but the migrant moved at the very beginning of the decade, then the wealth difference generated by restricted model (i) would be little different from the enumerated difference. In other words, land price appreciation would have less explanatory value than was estimated when time of migration was near the midpoint of the decade. Conversely, if the migrant moved toward the end of the decade, then restricted model (3 would explain more than the 25.9% estimated for migration occurring near the midpoint of the decade. For other specific counterfactuals, an opposite pattern might be expected. Finally, it must be emphasized that the model that generates these results is an example. It is consistent with the known empirical data, conforms to historical reality, and does not violate the assumptions of economic theory. Still for all that, it is one specific scenario. Others could certainly be devised. Table 5 contains the results produced by the model for the sources of the differences in the farm value of nonmigrants and of migrants. More than 70% of the difference in wealth is explained by the unequal initial endowments of the migrants and the nonmigrants and the cost of migration. The remaining 30%, which has been the focus of the historical literature, is apportioned to land price appreciation and change in land quantity. These results imply that to a certain extent the regression results in Table 2 were superficially misleading. While the farm value regression equation implied that roughly 70% of the difference in farm value ($2263 of $3150) was explained by factors other than unequal initial endowments, it can now be seen that most of this unexplained portion is accounted for by

MIGRATION

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the cost of migration (39.5%) with the remainder apportioned to land price appreciation and change in land quantity (29.6%). Looking at the difference in farm value not explained by initial endowments or cost of migration, the model results show that land price appreciation, especially for improved land, was the major determinant of the difference in farm value while changes in the quantity, of land were substantively unimportant. The explanatory power of unimproved land acquisition is smaller than might have been expected given the difference in the acquisition rates for unimproved land. However, since this difference applies only to the premigration period when the additional unimproved land was very cheap, the rate differential is of little substantive importance.*l Some of the data underlying the results presented in Table 5 are open to question. Certainly c which was chosen to replicate the wealth of migrants in 1860 falls in this category. To test the sensitivity of the results in Table 5 to the more uncertain portions of the data, I introduced uncertainty into all the land prices (following the same procedures that were described previously) and c.** The interquartile ranges for the sources of differences in migrant and nonmigrant wealth (shown in the last column of Table 5) were in some instances substantial. For example, the range for improved land price appreciation shows the explanatory value falling between 19.8 and 40.6%. Nonetheless, the broad pattern of results is intact. VI. CONCLUSIONS Migrants to the frontier in the decade of the 1850s had less real wealth (as measured by farm value) in 1860 than did the population already living at the frontier in the 1850s. This result, which holds even when the initial (1850) real wealth and personal characteristics are held constant, is consistent with other studies for different regions of the United States over roughly the same time period. Within the context of a specific model it has been shown that the greater price appreciation of improved land at the frontier (relative to the new South), differences in initial (1850) *I An interesting side issue is whether the costs of migration were offset by the higher rate of price appreciation for improved land at the frontier. If the migrants had not moved, then c would have been 0 and the migrants’ land prices would have appreciated at eastern rates, as the quantities of land would have. The model produces an average 1860 farm value of $4375 now. This value is larger than the $3627 enumerated for the migrants but is less than the $5641 average for the eastern nonmigrants. 22 I assumed that c was subject to triangularly distributed errors with a minimum value of $200 and a maximum value of $1000, and with the mode of the distribution occurring at $775. The maximum and minimum values represent my subjective estimates of the bounds for average out of pocket costs while the mode is the value used previously in the model estimation.

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wealth holdings, and out of pocket migration costs account for a good deal of the observed difference in the wealth of migrants and nonmigrants at the frontier states. These results imply a somewhat different interpretation of the relationship between wealth and migration ‘from that found in other studies. Unlike the Utah case where labor pressures were hypothesized to have caused capital gains on land to accrue to earlier migrants at the southern frontier, the shortage of labor is hypothesized to have caused the price of improved land to appreciate at a relatively high rate (Kearl et al., p. 480). And unlike in the northern U.S. example where the quantity of improved land was associated with farm value, at the southern frontier the association is between the price of improved land and farm value (Easterlin et al., p. 50). Certainly there is great scope for further research on the relationship between wealth and migration. In general our knowledge on the institutional aspects of migration including the travel patterns and the associated financial transactions could be stronger. This knowledge would allow a more sophisticated modeling process to bear fruit. Also, the scope of our knowledge could be expanded usefully. We need more information on broader wealth measures and empirical studies for different times and places. APPENDIX:

DATA

The Sample The data used here are based on the Parker-Gallman sample of farm families living in the frontier states of Arkansas and Texas or in the nonfrontier states (Alabama, Louisiana, Mississippi, and Tennessee). This sample was refined by dropping those observations that did not meet the criteria proposed by Fogel and Engerman. An attempt was then made to locate the remaining families in the 1850 manuscript census of population. The set of farms so located constitutes the data source for this paper. Using a variable in the Parker-Gallman sample identifying the page and line of each sample farm in the 1860 manuscript census of agriculture, I determined the name of the head of household. Next, the 1860 free population manuscript census for the county containing the farm was searched to obtain the age and place of birth of the head of household and the names, ages, and places of birth of other family members. Then temporal matching began. I used the Accelerated Indexing Systems census *’ The following were excluded: (1) farms with more than three slaves with no male slaves, (2) farms with no labor, (3) farms with no improved acreage, (4) farms with no farm value, (5) farms that produced no corn, (6) farms with zero value of farm machinery, and (7) farms with a grain supply insufficient to feed the working stock.

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indexes for each state to locate the county and page where the head of household was listed in the 1850free population manuscript census. Two major problems were encountered at this stage. First, there were multiple listings for the same name and variant spelling of surnames, These required muhiple searches for households with the correct match being determined by family member names, ages, and places of birth. For common surnames there were cases of 20 or more searches before the correct match was achieved. The second problem was that many families made interstate moves. To find the likely 1850 location of families, the ages and states of birth of the household children were examined. Other information considered were the states of birth of the heads of household and their spouses. These and all intervening states were searched using the census indexes. Thus searching for interstate movers was not appreciably more difficult than searching for families that did not migrate across state lines. Once a family was located in the free population census, attempts were made to find that family in the agricultural and slave censuses. Nonfarm operators were not located in the former and non-slave holders were not located in the latter. The plausibility of no farm or slaves was checked by examining ancillary informtion from the 1850 census such as real wealth and occupation. A family was considered matched if it had the same head of household in 1850 and 1860. Certain conditions occurred from time to time to prevent matching. First, since heads of household were generally at least 20 years old, families headed by an individual who was under 30 years old in 1860were rarely matched. Second, there were instances when the female spousebecame the head of household sometime during the decade. Given the women’s ages, it is probable that these were usually widows. Third, there were cases where the family had migrated internationally. The most important example of this is the German migration to Texas. Finally, there were some illegible and incomplete manuscripts.24 Variables

Used in the Regressions

The two migration variables are zero-one dummies. The first takes on a value of one if a family was matched in different counties in the same statein the 1850and 1860censuses(intrastate movers) and is zero otherwise. The second dummy is one if the family was located in different states in the 1850and 1860 censuses (interstate movers) and is zero otherwise. A second group of variables, “1850 occupation,” is defined by a series of zero-one dummy variables. “Farm operator” is one if the farm of the head of household was located in the 1850 census of agriculture. 24 The effect of these restrictions has been examined. The preliminary results suggest that the 1860 portion of the matched sample is representative of a truncated version of the Parker-GaIlman sample containing only heads of household at least 33 years old.

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“Not in agriculture,” is one if no farm for the head of household was located in the 1850 census of agriculture and the occupation of the head of household was clearly nonagricultural. “Farm worker” is one if no farm was located in the 1850 census of agriculture and the head of household had an agricultural occupation such as farm laborer or more rarely overseer. Typically families in this group had no real wealth. The final category, “other,” was not located in the 1850 census of agriculture, had an occupation such as farmer or planter, and generally had large real wealth holdings and many slaves. I suspect that these were individuals who lived in locations separate from their farms or plantations.25 One final variable, “labor,” was constructed from census data. This is the number of male prime field-hand equivalents adjusted for participation rate. Fogel and Engerman (n.d.) contains the computational details. Underlying Data and Parameters Used in the Models

The basic data used either as parameter estimates or to construct parameter estimates are contained in Table A-l. There are two types of data in this table: those items enumerated directly from the census and those constructed from enumerated data. The former include the land quantities and farm values, while land prices and labor are examples of the latter. All of the data in Table A-l pertain to a very specific subset of the sample. (1) Those families whose head was a farm operator in 1850. (2) Those farms for which the labor supply was positive in 1850 and 1860. (3) Those farms which had a positive number of acres enumerated in the census in both 1850 and 1860. The criteria for deciding whether a family should be included in a specific group were (1) Western nonmigrants lived in either Arkansas or Texas in 1860 and were enumerated by the census in the same county in 1850 and 1860. (2) Eastern nonmigrants lived in either Alabama, Louisiana, Mississippi, or Tennessee in 1860 and were enumerated by the census in the same county in 1850 and 1860. (3) Migrants were those families who lived in Arkansas or Texas in 1860 and in a different state in 1850. These other states for the most part were the same as those in the previous group but also included the southern Atlantic seaboard states as well. 2X This category also includes a small number of families from Georgia for whom the 1850 census of agriculture was missing and who appeared to be farm operators. In the sample these groups are coded separately, but the small number of families affected by the missing agricultural manuscript census did not make it worthwhile to create a separate class here.

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TABLE A-l Underlying Data Data Land prices” 1850 unimproved 1850 improved 1860 unimproved 1860 improved Land quantitie@ 1850 unimproved 1850 improved 1860 unimproved 1860 improved Labor’ 1850 1860 Farm value” 1850 1860 Time of migratio& n

Western nonmigrant 2.82 9.37 4.40 30.91 356.02 73.32 616.70 128.26 4.462 5.986 1599.26 6779.23 102

Eastern nonmigrant 1.034 13.85 2.94 27.55 199.88 108.23 316.03 168.84 5.060 7.003 1677.41 5641.24 624

Eastern migrant 0.505 15.314 4.677 18.22 210.64 80.68 377.74 102.87 4.144 5.235 1335.35 3627.05 4.63 77

Source. See Appendix text. a Measured in current dollars. b Measured in acres. ’ Measured in units standardized for age and sex. d Years after 1850.

In the following paragraphs the procedures used to construct variables are explained in detail. Land prices. Using the technique employed by Fogel and Engerman (1977, pp. 283-285), the following type of equation was estimated: fu = p,i + p2u

wherefu is the dollar value of a farm, i and u are the numbers of improved and unimproved acres, and p, and pz are the prices of improved and unimproved acres. This estimating procedure led to two major econometric problems. First, the data were highly heteroskedastic. In this particular application the standard errors produced by ordinary least squares tended to be a good deal larger than those correctly estimated using a heteroskedastic robust method (White, 1980). More important, certain portions of the data exhibited collinearity. Many of the classic symptoms were present including large simple correlations between the two independent variables and correlations between the independent variables that exceeded those between the dependent variable and independent variables. This was

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most frequently the case with the correlation between farm value and unimproved acres. But the most disturbing feature of this problem was the instability of the estimated regression parameters for small changes in the sample. The most extreme case of collinearity occurred in the estimation of the 1860 land prices for eastern nonmigrants. Four of the largest farms were dropped from the sample to combat the effects of this problem.26 The adjusted R2 rose by more than 0.25 and the root mean square error was reduced to one-fourth of its previous size. More important, the price estimates produced by this trimming of the sample became generally consistent with the observed farm value and land quantity data. As might be expected, the largest impact was on the calculated price for unimproved land. While casting out observations is not generally a desirable procedure, in this instance it was without a doubt the lesser of two evils. To use the price data in the model, they have to be consistent with the observed data, that is, with the land quantity data they must be able to reproduce the observed farm value. The 1850 prices did this almost exactly. The 1860 land prices were 10 to 15% too high (because of the restriction that the intercept was zero). While these percentages are not out of line with those experienced by Fogel and Engerman (1977, p. 284), I considered them too large for the purposes of this study. Therefore I reduced the 1860 land prices for western and eastern nonmigrants by 15.1 and 10.4% while the reduction for price of migrants’ land was 11.5%. These reductions allowed me to reproduce the observed 1860 farm values. Since all three groups’ land prices were reduced by roughly the same percentage, this data adjustment has little effect on the empirical results of the study. Land price appreciation. The model uses four rates of return for four different sets of land: eastern unimproved land (j*), eastern improved land (I*), western unimproved land (~3, and western improved land (I). They all are calculated in a similar fashion. For example:

[ I1

j* = In p$

(0.10)

where pf” is the 1860 price of improved land held by eastern nonmigrants, etc. Migrants receive the eastern rates of return before moving and the western rates after moving. Annual accumulation of improved acres per unit of labor. There are eastern and western rates (Qf and QJ. These are estimated by the difference between the 1860 and 1850 quantities of improved land divided by the 26 These farms have values averaging $287,125 in 1860 while the mean for the remaining farms is less than $6000.

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average labor force times 10. For the West this is ~~ = (4: - 4i)

1012 * Since the assumption is that these rates are determined by regional characteristics, migrants accumulate at the rate QT before migration and Q afterward. Annual accumulation of unimproved acres. Unlike accumulation of improved acres which is simply a transfer between types of existing land, the accumulation of unimproved acres is a net addition to the stock of land that is financed from sources external to this model. The total accumulation is the 1860 quantity of unimproved acres minus the 1850 stock of unimproved acres plus the accumulation of improved acres over the decade. The annual accumulation is the total accumulation divided by 10. Annual accumulation is assumed to be a function of the characteristics of the two regions. Thus there is an eastern rate and a western rate. Migrants’ accumulation is a function of their regional location. The price of land obtained by migrants in the west. Once the prices of land held by migrants in 1860 and the rates of return for land are estimated, the price of land obtained at the time of migration is determinate. For improved land the price at migration is

The price of unimproved land at migration is determined in an analogous manner. Time of migration. Using the census information on the ages and states of birth for children in the household (or lacking these, the age and place of birth of the head of household), the earliest and latest dates a famiIy could have arrived at their 1860 state of residence were estimated. For known migrants the time range is no greater than 0 to 10 years before 1860or conversely 0 to 10years after 1850. The time of migration variable (kt) was then calculated as the midpoint of the migration time range relative to 1850. Lacking any information, this variable would take on a value of 5, the midpoint of the interval (0,lO). Lathrop (1949) and Easterlin et aZ. (1978, pp. 44-48) used similar apnroaches. The result in Table A-l implies that the average household moved approximately 4.6 years after the census date (June 1850). Alpha (a). In this model (Y, the proportion of the proceeds from the sale of real wealth that is reinvested in unimproved land after migrating, is a function of the time of migration and the observed quantity of improved acres held by migrants in 1860. The earlier the migration’and the smaller the number of improved acres, the higher the value of CY.

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The value of (Y is chosen to ensure that the migrant has the observed 1860 quantity of improved acres. The explicit formula thus becomes a=l-

(~’

- n~(l - k)tQi)P~ wg - c

REFERENCES Adamson, J. (1839) An Account of Texas; with Instructions for Emigrants. London: Eames (Western Americana No. 35). An Emigrant (1840), Texas in 1840: Or the Emigrant’s Guide to the New Republic: Being the Result of Observations, Enquiry and Travel in That Beautiful Country. New York: Allen (Western Americana No. 5341). Ankli, R. F. (1974), “Farm-Making Costs in the 18.50s.” Agricultural History, 48, 51-70. Benassy, J. (1982), The Economics of Market Disequilibrium. New York: Academic Press. Bode, F. A., and Ginter, D. E. (1981), “Farm Tenancy and the Census in Antebellum Georgia.” Unpublished manuscript. Bode, F. A., and Ginter, D. E. (1984), “A Critique of Landholding Variables in the 1860 Census and the Parker-Gallman Sample.” Journal of Interdisciplinary History 15,277295:

Bogue, A. G., and Bogue, M. B. (1957), “Profits and the Frontier Land Speculator.” Journal of Economic History 17, 1-24. Chapman, E. W. (1940), Land Speculation in Tate County 1836-1861. Unpublished master’s thesis, University of Mississippi. Chiang, A. C. (1984), Fundamental Methods of Mathematical Economics, 3rd ed. New York: McGraw-Hill. Easterlin, R. A., Alter, G. A., and Condran, G. A. (1978), “Farms and Farm Families in Old and New Areas: The Northern States in 1860.” In T. K. Hareven and M. A. Vinovskis (Eds.), Family and Population in Nineteenth-Century America, pp. 22-84. Princeton, NJ: Princeton Univ. Press. Fisher, 0. (1841), Sketches of Texas in 1840; Designed to Answer, in a Brief Way, the Numerous Enquiries Respecting the New Republic. . . Springfield, IL: Walters & Weber (Western Americana No. 1968). Fopl, R. W., and Engerman, S. L. (1977), “Explaining the Relative Efficiency of Slave Agriculture in the Antebellum South.” American Economic Review 67, 275-296. Fogel, R. W., and Engerman, S. L., “Instructions for Computing Output and Input Data from the ParkerGalIman Sample for 1860 to Be Used in Production Function Estimation. Mimeo. Fogel, R. W., and Engerman, S. L., (1974), Time on the Cross, Vol. 2. Boston: Little, Brown, Foust, J. D. (1975), The Yeoman Farmer and WestwardExpansion of U.S. Cotton Production. New York: Arno Press. Foust, J. D., and Swan, D. E. (1970), “Productivity and Profitability of Antebellum Slave Labor: A Micro-Approach.” Agricultural History 44, 39-62. Gray, L. C. (1933), History of Agriculture in the Southern United States to 1860, Vol. 2. Washington, DC: Carnegie Institution. Kearl, J. R., Pope, C. L., and Wimmer, L. T. (1980), “Household Wealth in a Settlement Economy: Utah 1850-1870.” Journal of Economic History 40, 477-496. Lathrop, B. F. (1949), Migration into East Texas, 1835-1860. Austin, TX: Texas State Historical Assoc. Lebergott, S. (1985), “The Demand for Land: The United States, 1820-1860.” Journal of Economic History 45, 181-212.

MIGRATION

AND WEALTH

ACCUMULATION

157

Machlup, F. (1958), “Equilibrium and Disequilibrium: Misplaced Concreteness and Disguised Politics.” Economic Journal 68, l-24. McFadden, D. (1973), “Conditional Logit Analysis of Quantitative Choice Behavior.” In P. Zarembka (Ed.), Frontiers in Econometrics, pp. 10.5-142. New York: Academic Press. Meyer, B. H. (1917) History of Transportation in the United States before 1860. Washington, DC: Carnegie Institution. Miller, T. L. (1972) The Public Lands of Texas 1519-1970. Norman, OK: Univ. of Oklahoma Press. Mueller, C. F. (1981), The Economics of Labor Migration: A Behavioral Analysis. New York: Academic Press. Primack, M. L. (1962), “Land Clearing under Nineteenth-Century Techniques: Some Preliminary Calculations.” Journal of Economic History 22, 484-497. Reid, .I. D., Jr. (1976), “Progress on Credit: Comment.” Agricultural History SO, 117-124. Richardson, D. (1870), Texas as Seen in 1870, Giving Reliable Information on All Subjects Thought to Be of Interest to Emigrants. Elysian Fields, TX: Richardson’s Correspondence and Immigration Agency (Western Americana No. 4517). Richardson, W. (1857-1873), Texas Almanac and Emigrant’s Guide. Galveston, TX: W. Richardson & Co. (Western Americana No. 5.536). Russell, M. (1942), Land Speculation in Tippah County 1836-1861. Unpublished master’s thesis, University of Mississippi. Schaefer, D. F. (1985), “A Statistical Profile of Frontier and New South Migration: l@O-1860.” Agricultural History 59, 463-578. Schaefer, D. F., and Schmitz, M. D. (1985), “The Parker-Gallman Sample and Wealth Distributions for the Antebellum South: A Comment.” Explorations in Economic History 22, 220-226. Schmitz, M. D., and Schaefer, D. F., “Interpreting Antebellum Southern Agriculture Using Manuscript Census Samples: Procedures, Purposes, and Critiques.” Journal of Znterdisciplinary History 17, 399-414. Silver, J. W. (1944), “Land Speculation Profits in the Chicasaw Cession.” Journal of Southern History 10, 84-92. Smith, E. (@349), Account of a Journey through North-Eastern Texas Undertaken in 1849 for the Purposes of Emigration. London: Hamilton, Adams & Co. (Western Americana No. 4981). Steckel, R. H. (1983), “The Economic Foundations of East-West Migration during the 19th Century.” Explorations in Economic History 20, 14-36. Stiff, E. (1840), The Texan Emigrant: Being a Narration of the Adventures of the Author in Texas and a Description of the Soil, Climate, Productions, and Minerals. Cincinnati: Con&n (Western Americana No. 5166). U.S. Department of Commerce (1975), Historical Statistics of the United States Colonial Times to Z970, Part 1. Washington, DC: U.S. Govt. Priming Office. White, H. (1980) “A Heteroskedasticity-Consistent Govariance Matrix and a Direct Test for Heteroskedasticity.” Econometrica 48, 817-837. Wright, G. (1970). “Note on the Manuscript Census Samples.” Agricultural History 44, 95-100.