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Locational Choice in the Antebellum South
Published online by Cambridge University Press: 03 March 2009
Abstract
This article examines the economic and noneconomic factors that influenced the migration decisions of antebellum Southern households. It appears that nonslaveowners were neither pushed to inferior locations nor did they move independently of the economic consequences. For slaveowners, the observed links between locational choice and the economic characteristics of locations are weaker. The proportion of whites in a location's population was positively associated with the choice of a location for the nonslaveowners. This association was not found for any other group.
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References
Earlier versions of this article were presented at the economic history seminar at the University of California, Berkeley, and disseminated by the Agricultural History Center, University of California, Davis. Jeremy Atack, Peter Lindert, Robert McGuire, Richard Steckel, David Weiman, and Thomas Weiss kindly read and provided comments on earlier versions. Two anonymous referees also provided useful insights. The data were gathered under a grant from the National Science Foundation.
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9 If the conditions at a location worsen, a farmer can choose to leave; if the conditions worsen at a location and the farmer must leave (for example, the land is lost due to foreclosure), then the farmer is coerced into leaving. Both are instances of pushes.
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16 It is empirically convenient to assume and additive stochastic term for the utility function. That is: Uij = Uij (Zij + εij) where Zij represents both deterministic components of the utility function. Daniel McFadden has proven that utility maximizing behavior produces selection probabilities (that is, probabilities of selecting a given location) consistent with those produced by the multinomial (or conditional) logit model if, and only if, the errors across locations are independently distributed according to the Weibull distribution. The selection probabilities become:Pik = efit/j + efijj=1 where Pik is the ex ante probability of individual i choosing location k, and f is a specific function of the deterministic portion of the utility function (Zij) for individual i. McFadden, “Conditional Logit Analysis.”
17 The independence of errors across locations implies that the selection probabilities would not vary if an additional choice were added or if any of the existing choices were removed from the set of alternative locations. This independence from irrelevant alternatives depends on the members in the alternative set (in this case the set off possible j locations) being sufficiently distinct from each other. A counterexample given by McFadden, , “Conditional Logit Analysis,” p. 113, can illustrate the meaning of this assumption. Suppose the transportation alternatives facing individuals are automobile and bus service. If a second bus service, identical in all essential ways to the first, was introduced, the probability of taking a specific bus service would be halved. In this case the independence assumption is violated. In the present research the alternatives are counties which differed markedly along a number of dimensions, so the assumption seems secure.Google Scholar
18 Individual behavior will also vary since the arguments of unobserved personal attributes (collected in the stochastic part of the utility function) will vary across individuals.
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20 The role of uncertainty for the most part has been neglected in empirical studies using the conditional logit model. For example, transportation studies have rarely considered that the user may have imperfect knowledge of transportation modes other than the one currently being used.
21 Mueller, , The Economics of Labor Migration, pp. 81–83.Google Scholar Kenneth Arrow has shown that quadratic utility functions imply increasing absolute risk aversion as wealth increases–a result he finds dubious. Arrow, Kenneth, Essays in the Theory of Risk-Bearing (New York, 1974), pp. 96–97.Google ScholarRothschild, Michael and Stiglitz, Joseph, “Increasing Risk: I. A Definition,” Journal of Economic Theory, 2 (09 1970), pp. 225–43;CrossRefGoogle Scholar and Rothschild, Michael and Stiglitz, Joseph, “Increasing Risk: II. Its Economic Consequences,” Journal of Economic Theory, 3 (03 1971), pp. 66–84, also provide an argument against the use of a quadratic utility function by showing that the usual results for that type of function are dependent upon the unknown values of the Pratt-Arrow measure of risk aversion.CrossRefGoogle Scholar
22 Lerman, Steven and Louviere, J., in “Using Functional Measurement to Identify the Form of the Utility Functions in Travel Demand Models,” Transportation Research Record, 673 (1979), pp. 78–86, found that a behaviorally derived utility function was statistically superior to other functional forms, such as linear, exponential, reciprocal, and quadratic. Their paper emphasizes overall goodness of fit and prediction, and does not provide any information on the signs and significance of the coefficients for individual variables.Google Scholar
23 The sample was derived from those households in the Parker-Gallman sample that met certain empirical standards, such as the enumeration of land, labor, and capital measures. Schaefer, “A Statistical Profile”; and Schaefer, Donald, “A Model of Migration and Wealth Accumulation: Farmers at the Antebellum Southern Frontier,” Explorations in Economic History, 24 (04 1987), pp. 130–57,CrossRefGoogle Scholar contain further information on the sample. Steckel, Richard, “Census Matching and Migration: A Research Strategy,” Historical Methods, 21 (Spring 1988), pp. 52–60, contains information on the general problem of developing matched samples.CrossRefGoogle Scholar
24 Most of the unmatched portion were either too young to be heads of household in 1850 (they were under 30 in 1860) or were not heads of household in 1850. This last group included sons and (presumably) widows, located in the census, who became heads of household between 1850 and 1860. Roughly 15 percent of the sample was not accounted for in any of the above categories and included households who appeared to be both migrants and nonmigrants.
25 In a practical sense the sampling could not have been done any other way since the matching was accomplished by using computerized census indexes for the 1850 Census of Population. The 1860 indexes had not yet been published.
26 Manski, Charles and Lerman, Steven, “The Estimation of Choice Probabilities From Choice Based Samples,” Econometrica, 45 (11 1977), pp. 1977–88. If the empirical work refers only to the sample or to a hypothetical population with the same 1850 characteristics as the sample then the issue of bias and inconsistency does not arise.CrossRefGoogle Scholar
27 These states are Alabama, Louisiana, Mississippi, and Tennessee. Migration from the old South and the frontier was less frequent.
28 This implied rate of approximately 22 percent migration over the decade is substantially lower than the 32 percent rate estimated in Richard Steckel, “Household Migration and Rural Settlement in the United States, 1850–1860,” Explorations in Economic History (forthcoming). One possible explanation for this difference is that the present study matched 1860 farm households back to 1850 while Steckel matched households from the general population. Farmers had a lower propensity to migrate.
29 When estimating a multinomial logit model it is desirable to ascertain whether this assumption is warranted. In some simple applications tests appropriateness of the assumption is testable. Hausman, J. and McFadden, Daniel, “Specification Tests for the Multinomial Logit Model,” Econometrica, 52 (09 1984), pp. 1219–40. In the present application these tests are not possible.CrossRefGoogle Scholar
30 Train, Kenneth, Qualitative Choice Analysis (Cambridge, MA, 1986), pp. 47–48.Google Scholar
31 The Appendix contains information on the specific definitions and sources for these variables.
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34 Steckel, “Household Migration and Rural Settlement.” This does not preclude the possibility that some households were at their optimal locations. Since there were hundreds of counties in the cotton South, the more likely case is that more information, ceteris paribus, made a household more likely to migrate.
35 Development, the ratio of improved to unimproved farm acres, is a proxy for pressures on land prices. The association between degree of improvement, agricultural development, and land prices in antebellum Ohio has been noted by Winkle, Kenneth, The Politics of Community (New York, 1988), p. 32.CrossRefGoogle Scholar Similarly, evidence from the Bateman-Foust sample of northern families shows that the quantity of improved acres was positively associated with length of settlement and farm value. Easterlin, Richard, Alter, George, and Condran, Gretchen, “Farms and Farm Families in Old and New Areas: The Northern States in 1860,” in Hareven, Tamara and vinovskis, Mans, eds., Family and Population in Nineteenth-Century America (Princeton, 1978), p. 50.Google Scholar
36 Given the form of the likelihood function for the multinomial logit model, this variable enters the model as the natural logarithm of the square miles contained in a county and should take on a value between 0 and I.Lerman, Steven, “A Disaggregate Behavioral Model of Urban Mobility Decisions” (Ph.D. diss., Massachusetts Institute of Technology, 1975),Google Scholar cited in Mueller, , The Economics of Labor Migration, pp. 132–33.Google Scholar
37 Maximum-likelihood estimates of the parameters in the conditional logit model were obtained from QUAIL, a mainframe software package produced by Daniel McFadden and his students. The highly nonlinear likelihood function is solved by iterative techniques (such as Newton-Raphson or steepest ascent) to estimate the parameters and their standard errors.
38 Approximately 170 heads of household were enumerated as illiterate. Thus the literacy coefficient is not a small sample artifact.
39 The likelihood ratio statistic used to test the hypothesis that all the coefficients of the two subsets are equal is 34.6, which with 15 degrees of freedom is significant at the 0.01 level.
40 The variable, previous move, is not significant for the slaveholding subset while it is positive and significant for the other subsets and the entire sample. As formulated above, the noneconomic pull hypothesis implies a negative coefficient.
41 The likelihood ratio statistic is 20.8. The 0.05 chi-square rejection region with 15 degrees of freedom starts at 25.
42 These regressions were also estimated using the levels of temperature and rainfall. The coefficients for rainfall were negative and significant while those for temperature were positive and significant. In the case of cotton, an oversupply of water creates conditions favoring excessive vegetative growth and yield reduction. Jordan, Wayne, “Cotton,” in Teare, I.and Peet, M., eds., Crop-Water Relations (New York, 1983), p. 237.Google Scholar
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44 Due to the nature of the multinomial logit model and the way they were defined, personal characteristics were not included in the model specification. It would be possible to include these characteristics by interacting them with the place variables. However, the sample size is very small and it is difficult to get a fully interacted model to converge.
45 The origin is one choice in a simple model to move or stay.
46 The use of an elasticity measure with zero-one dummy variables is conceptually inappropriate. Some of these dummy variables might also have had major substantive effects on locational choice.
47 In data sets with a small number of alternatives it is usual to calculate the elasticities with respect to each alternative. With 129 possible locations this is not feasible. Here, the elasticities are calculated with respect to choice, and the choice taken in the first four groups includes both to stay and to move. Thus the elasticities are averaged across two very different types of choices. However, in these four groups, the alternative to stay at the origin was selected in the vast majority of cases and the elasticities with respect to the origin are very similar to those reported (except for distance and north-south distance). By concentrating on migrants the dominating effect of the stayers is eliminated and conceptually, the interpretation is sharpened. See Inaba, Fred S. and Wallace, Nancy E., “Spatial Price Competition and the Demand for Freight Transportation” (Washington State University, mimeo, 1988).Google Scholar
48 Schaefer, “A Model of Migration and Wealth Accumulation.”
49 An alternative approach to distinguish between migrants and nonmigrants is to compare the direct aggregate elasticities with respect to the origin versus those with respect to a composite alternative “not the origin” rather than computing the elasticities with respect to the actual choice. These elasticities are similar to those reported for the first four groups in Table 3. Systematic differences between the alternatives include larger elasticities with respect to age and race for the alternative “not the origin.”
50 More precisely, the marginal rate of substitution is the negative value of this ratio of the coefficients times a scaling factor of 100. Ben-Akiva, and Lerman, , Discrete Choice Analysis, pp. 157, 160;Google Scholar and Train, , Qualitative Choice Analysis, pp. 153–54, 239–40.Google Scholar
51 A cost of $1 per mile seems generous given that the average rural household contained 10 to 15 persons, including slaves, and that railroads cost approximately 5 cents per person mile.
52 Schaefer, , “A Model of Migration and Wealth Accumulation,” p. 138.Google Scholar
53 For example, all migrants would accept a drop in the proportion of whites in a county from 0.70 to 0.65 while nonslaveowners would accept a decline to only 0.67.
54 All the place variables except the soil and vegetation difference dummies were made quadratic by the addition of square terms. This was done to represent the uncertain nature of the potential migrants' knowledge about the alternative locations. There are serious theoretical objections to this functional form.
55 However, many of the quadratic terms were significant as well. Thus the coefficient for the distance variable remained negative and significant while the coefficient for the distance quadratic term was positive and significant. The major exception was the productivity variable whose coefficient became negative with addition of the quadratic term, possibly indicating the presence of collinearity. Another exception occurred for slaveowners where the sign of the coefficient for the race variable was reversed. The race variable in general showed large increases in the standard errors, making this variable statistically not significant and suggesting that collinearity may also have been a problem in this case.
56 Steckel, “Household Migration,” implicitly makes a similar assumption since the regressions explaining rural to rural migration only allow for different regional intercepts while holding the slope parameters fixed across regions.
57 Berwanger, Eugene, in The Frontier Against Slavery (Urbana, 1967), pp. 23, 32, 43, documents a wide range of actions toward free Negroes that apparently stemmed from racial antipathy.Google Scholar
58 Steckel, “Household Migration.”
59 For the twentieth century, the factors causing farmers to be forced from the land are well known. Donald Schaefer, “Agricultural Displacement at the Southern Frontier: A Test of the Phillips Hypothesis,” presented at the 1987 Cliometrics Conference.
60 See, for example, Adams, John and Kasakoff, Alice, “Wealth and Migration in Massachusetts and Maine: 1771–1798,” this JOURNAL, 45 (06 1985), pp. 363–68.Google Scholar
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