Abstract This paper outlines a classical–Marxian model of the antebellum US economy. The model assumes that the mobility of capital tended to equalize the rate of profit between North and South, whilst land rents were minimized by an expanding frontier. Under these conditions slave prices are the capitalized present value of the excess surplus value produced by slaves. This excess surplus value arose because slaves could be forced to work harder at a lower standard of subsistence than wage laborers, who were free to move between individual employers and also between sectors by farming frontier lands. If the growth of the slave population saturated the land available for slave production, land rents would rise to capture the excess surplus value produced by slaves, and slave prices would collapse. We find the model predicts historical movements of slave prices, and is compatible with contemporaneous views of the impact of territorial restriction on the viability of slavery. The price paid for a slave is nothing but the anticipated and capitalized surplus-value or profit to be wrung out of the slave. —Marx, Capital, vol. 3 1. Introduction In the 1970s several economic historians concluded that Southern slaveowners had no economic motive to support the Westward expansion of slavery (Passell and Wright, 1972; Kotlikoff and Pinera, 1977; Lee, 1978). Their models showed that Lincoln’s electoral promise to cut off slavery from the Western territories would have raised slave prices, benefitting existing slaveowners, rather than reducing them, as Lincoln had assumed. On this basis they rejected the notion—common among Northerners of Lincoln’s generation—that slavery had to ‘expand or die.’ More recently, however, historians have rediscovered the economic motives that Southern slaveowners themselves often gave for territorial expansion. For instance, we now know that the secession conventions in 1860 and 1861 were dominated by fears that Lincoln’s ban on slavery in the Western territories would undermine slave prices (Dew, 2001). In addition, Walter Johnson (2013) has recently shown that many slaveowners in the Southwest believed that the future of American slavery depended on access to land farther south, in Cuba and Central America. In this paper, we present an alternative model of antebellum slavery which suggests an economic rationale for Southern expansionism. In our model, land and slave prices represent competing claims to the excess surplus value generated by slave labor. Ongoing slave population growth in a restricted territory would ultimately lead to a surplus population of slaves, and in our model slave prices would fall in anticipation of that outcome, undermining the economic viability of slavery long before the saturation of available land. The model thus suggests that slavery did indeed need to ‘expand or die.’ However, it differs from the traditional view of Southern expansionism, since the relevant factor is not technological stagnation or soil erosion, but rather the peculiarity of an economic system in which labor itself is capitalized, such that a fall in the price of labor threatens the wealth and power of existing capitalists.1 The paper is organized as follows. In the following, we define our terms and clarify a key assumption of the model. In Section 2, we describe the model and derive a formula for the price of slaves. In Section 3, we explore the predicted interaction between slave prices, wages and land rents, and test these predictions with antebellum data. In Section 4, we look more closely at the territorial question in the run-up to the Civil War, comparing our predictions to those of other economic historians. We conclude that our model is not only consistent with available data, but also better fitted to the explanations that slaveowners themselves gave for secession and civil war. 1.1. A classical approach to slave prices The classical political economists identified the net product of labor—gross output minus depreciation and wages—as a surplus whose division among asset-owners would be regulated by competition. Thus, for Ricardo a market in land allowed landowners to capture the non-reproducible advantages of certain lands—their capacity to generate a larger net product (due to natural fertility or location) than the marginal land. If capitalist farmers can make a normal profit by farming marginal land, then competition dictates they will accept the same profit as tenants on surpramarginal land, allowing landowners to pocket the difference as rent. Marx defined the net product of labor as ‘surplus value’, and referred to this rental component as ‘differential rent.’ We define the net product of slave labor as gross output minus depreciation and slave maintenance costs (food, clothing, shelter, medical and supervisory expenses).2 Where slave and wage labor coexist, as in the antebellum USA, the difference between their net products (or surplus value) will regulate capital flows. When slaves produce more surplus value than wage laborers—because slaves may be worked harder or ‘paid’ less—then slaveowners will be in a position to capture this excess surplus value in the form of rent.3 Just as land rents are capitalized in land prices, we view slave prices as the present value of the expected stream of slave rents.4 In our model, differences in the rate of surplus value between wage and slave labor—that is, the ratio of surplus value to the cost of labor power, or what Marx called the ‘exploitation rate’—determine the returns to slaveownership and the long-term viability of slavery. However, this does not imply that slaves and wage laborers coexisted in a single labor market.5 Rather, we assume that competition between slave and wage labor took place primarily via capital markets, such that slave prices adjusted to arbitrage differences in the rate of exploitation. Capital mobility is thus a key assumption of our model, just as it was for the classical political economists (Foley, 2011). This assumption might seem controversial, as some economic historians have questioned whether capital was free to move in the nineteenth-century USA.6 However, Bodenhorn and Rockoff (1992) have shown that regional interest rates were closely correlated in the antebellum period, suggesting the presence of an integrated capital market capable of arbitraging profit rate differentials between regions. Figure 1a presents the short-term lending rate in the Northeast and the South, while Figure 1b displays the average profit rate of banks in each region.7 As one would expect, the period of adjustment is longer for profit rates than interest rates, but both series exhibit a tendency to fluctuate around the mean, suggesting that profit rates had a tendency to equalize in the medium term. Fig. 1. View largeDownload slide Profit rates (above) and interest rates (below) in banking, North and South 1825–1859. Fig. 1. View largeDownload slide Profit rates (above) and interest rates (below) in banking, North and South 1825–1859. The presence of capital mobility in the nineteenth-century USA suggests a simple answer to a long-standing debate among historians about whether or not antebellum slavery was “capitalist” (Smith, 1998). This debate has tended to focus on questions of culture and individual psychology, such as whether slaveowners valued status or tradition over profits (Genovese, 1965). However, the integration of antebellum capital markets makes this a moot point, for competition over mobile capital would have compelled slaveowners to maximize profits, whatever their “mentality”. After all, slaves were often bought on credit, and were commonly mortgaged to purchase land and other slaves (Kilbourne, 1995; Martin, 2010). Failure to maintain interest payments on these debts raised the threat of foreclosure (Clegg, 2017). In this context, slaveowners who were not interested in maximizing profit could easily lose their slaves to those who were. 2. Presentation of the model We base our model on the conventional wage model with land of Foley and Michl (1999, ch. 11), adapting it to the mixed slave/wage labor capitalist economy of the antebellum USA. This is a one-sector model. In the context of the antebellum USA, this amounts to the assumption that the relative prices of cotton and manufactured goods can be taken as exogenously determined by the world market (or political factors like the tariff), though not necessarily constant over time. We take dollars as the numéraire and measure outputs in terms of the value of the commodities produced in dollars. Changes in world market prices of produced commodities can be incorporated in the model as changes in productivity, though we will, for simplicity, assume that technology is constant over time in working out the model. The key actors in the Foley-Michl model are entrepreneurs who undertake production by hiring wage labor and renting slaves, capital and land from capitalists, who collect rents and optimize their portfolios with regard to their present and future consumption. The theoretical distinction between entrepreneurs and capitalists is somewhat artificial, since in the real world these functions tended to be combined, but helps clarify the various political economic forces at work. 2.1. Production with wage labor and capital Entrepreneurs in the North organize production by hiring wage laborers at a wage w, renting capital at the rent vkt, and producing according to the technique: 1 wage laborer +k capital→x value of output In this model, one wage laborer equipped with k units of capital can produce output worth x dollars at the end of a period. We suppose that wage labor is available at the wage w. For purposes of exposition of the model, we assume w is constant over time, although it varied historically, for example, in response to the availability of land on the frontier and economic conditions in Europe. We denote the rental cost of capital in period t by vkt, which is the amount of dollars the entrepreneur has to pay for the use of capital for one period. We assume that Northern manufacturing production uses negligible amounts of land, and that agriculture in the North is organized by independent family farmers.8 The profit an entrepreneur makes in production with wage labor in period t is thus x−w−vktk. As Foley and Michl explain, in this type of model competition forces entrepreneurial profit to zero (capitalist owners of land and capital appropriate all of the surplus value). Thus, we have: vktk=x−w or: vk=x−wk (1) Because we treat x, k and w as constant in the presentation of the model, we may write vk for the rental on capital. This is the ratio of surplus value to capital tied up in production, or the gross rate of profit. 2.2. Production with slave labor, capital and land Entrepreneurs (plantation operators) in the South organize production by renting slaves from their owners at the rental rate vst, capital from its owners at a rent vk, land from its owners at the rent vut, and producing according to the technique: 1 slave + k capital + u land→y value of output In this model, one slave equipped with k units of capital and working on u area of land can produce output worth y dollars at the end of a period.9 Entrepreneurs must maintain slaves at a conventional standard of living that costs (net of slave subsistence production) m dollars. The profit an entrepreneur makes in production with slave labor in period t is thus y−m−vst−vkk−vutu. As in wage labor production, capitalist owners appropriate all of the surplus value due to competition among entrepreneurs. Thus we have, using equation 1: vst+vkk+vutu=y−m or:vst=(y−m)−(x−w)−vutu (2) This states that the rent of a slave for a period is equal to the difference between the surplus value appropriated in slave and wage labor production, less whatever part of this excess surplus value is absorbed by land rent.10 The difference in surplus value between the two labor regimes may be decomposed into a higher-value production of slaves due to greater compulsion in the labor process ( y>x), or a lower cost due to their weaker bargaining power ( m<w). As we shall see in the discussion below (Section 3.1), at least one of these inequalities must hold in order for slave prices and rents to be positive. 2.3. The capitalist’s consumption and investment problem We assume there are a large number of identical capitalist wealth-holders each of whom own the same share of land, Ut, capital, Kt, and slaves, St. (Of course historically the same individuals often combined entrepreneurship and ownership of slaves, capital and land as plantation operators or entrepreneurship and capital ownership as factory operators.) For simplicity we assume, following Foley and Michl (1999), that these capitalists choose consumption, investment and portfolio plans in order to maximize the sum of the logarithm of their consumption of output (measured in dollars) discounted at a discount factor β between 0 and 1. The capitalist receives rent vk on capital, vut on land holdings, and vst on slaves. The price of capital is 1 in a one-sector model of this type, and we denote the price of land and slaves as put and pst, respectively. While capital depreciates at the rate δ, we assume that land does not depreciate. As we explain in Section 2.4 below, we assume that slaves exhibit negative depreciation, or a positive natural rate of increase, due to an excess of fertility over mortality, which we denote by σ. Thus from the point of view of the capitalist, production takes the following form: 1 slave for one period slaves→ vst+(1+σ) slaves 1 unit of capital for one period→vk+(1−δ) capital 1 unit of land for one period → vut+1 unit of land The typical capitalist’s budget constraint is thus: Ct+Kt+1+put+1Ut+1+pst+1St+1=(1−δ+vk)Kt+(put+1+vut)Ut+((1+σ)pst+1+vst)St (3) This states that at the end of a period, the capitalists can dispose of: the depreciated value of their capital together with the rent on the capital; the value at next period’s price of their land holdings, together with any rental income from those holdings; and the value of their slaves, augmented by natural increase, at the next period’s slave prices, together with the rental income from slave production. These resources are available for consumption, and purchases of capital, land and slaves in the next period. We assume the capitalist knows the paths of the prices of land and slaves, and the profit rate. Under these conditions the typical capitalist will consume a fraction 1−β of their end-of-period wealth, composed of capital, land and slaves valued at their end-of-period prices. As we explain in more detail in Section 2.5, arbitrage requires slaves and land to have the same rate of return as capital, so the growth of capitalist wealth, Jt=Kt+pstSt+putUt, follows the law: Jt+1=β(1+r)Jt (4) In this expression, r=vk−δ=xf−wk−δ is the net return on wealth, which is equal to and determined by the net rate of profit on capital in wage based production. Note that investment in slaves tends to reduce the rate of accumulation of capital, because growing slave wealth tends to raise the consumption of capitalists, and on paths where the total capitalized market value of slaves is rising, this absorbs some of the capitalist saving that otherwise would take the form of capital accumulation.11 2.4. The supply of slaves Following the ban on the international slave trade (in 1808), there was effectively no channel through which capitalist investment in slaves could influence the supply of slaves. In this respect, slave labor as an input to production is analytically similar to land. This is not to say that the slave population was fixed over time, but rather that the slave population grew according to its own ‘natural’ rate of increase, not in response to price incentives: St+1=(1+σ)St (5) This process is in sharp contrast to the accumulation of capital, which depends on capitalist consumption and investment, and as a result is responsive to political economic factors such as land and slave prices. Slave population growth, at this level of abstraction, is a factor external to the political economy of slave pricing, since there is no feedback to stabilize the size or growth rate of the slave population relative to the size or growth rate of the free labor capitalist economy.12 This will have important consequences for expected profits under different assumptions about the supply of land (see Section 3.2 below). 2.5. The arbitrage principle Following Foley and Michl, we abstract from risk in considering the typical capitalist’s consumption, investment and portfolio decisions. The capitalist can hold three assets: capital, land or slaves, and the typical capitalist has to wind up holding these in the proportions in which they are available. In this situation the arbitrage principle implies that the anticipated rate of return on the various available assets must be equal in each period. A capitalist who holds slaves during period t at the price pst will have (1+σ)pst+1+vst at the end of the period, from the rental of the slave, the effects of natural increase and the change in slave prices. The capitalist could, alternatively, have invested pst in capital instead and received (1+r)pst=(1−δ+vk)pst at the end of the period. The arbitrage principle requires that these returns be equalized through competition. Writing gpst=pst+1pst−1 for the rate of change of slave prices, the mathematical expression of the arbitrage principle applied to capital and slaves is: 1+r=1−δ+vk=(1+σ)pst+1+vstpst=(1+σ)(1+gpst)+vstpst (6) Taking gpst as given for the moment, using Equation (2), and neglecting the small term σgpst, we can solve this arbitrage condition for pst: pst=vstr−σ−gpst=(y−m)−(x−w)−vutur−σ−gpst (7) Equation (7) states that the price of a slave is the present value of the excess of surplus value appropriated in slave production over surplus value appropriated in wage labor production, less the rent on land required to employ a slave.13 The formula for the present value is simplified by the inclusion of the slave reproduction rate, σ, in the discount term, which extends the stream of slave rents across future generations. The presence of gpst means that Equation (7) has no determinate solution (we will provide this in Section 3.2), but it points to the influence of expected capital gains on slave pricing. 3. Discussion Our model captures two essential intuitions about a political economy—like that of the antebellum USA—in which slave and wage labor coexist. First, in such an economy, capital mobility will tend to arbitrage the two labor systems, such that any excess surplus value produced by slave labor may be captured as rent. Second, as long as slave production requires land, this rent will be divided between the owners of land and slaves according to their relative scarcity. In this section, we explore these dynamics by focusing on the impact of changes in wages (w) and land rent ( vut) on slave prices. 3.1. Slave prices and wages One implication of Equation (7) is that in order for slave prices to be positive, the net output of slaves must be higher than that of wage laborers: Condition 1.if ps>0 then (y−m)>(x−w). This is the inverse of Domar’s formula for the conditions under which emancipation would take place. Domar (1970, p. 22), following Nieboer (1900), wrote that slaveowners would only be willing to free their slaves if the difference between the productivity of free workers and slaves were greater than the difference between wages and maintenance costs: (x−y)>(w−m). The connection between our formula and Domar’s is evidently that a positive slave price reflects the economic viability of slave-based production.14 In Marxian terms, condition 1 implies that slaves are exploited at a higher rate than wage laborers. This is a proposition that we may test with historical data. Since the Marxian concept of a rate of exploitation is often poorly understood,15 we will focus on the more intuitive comparison of the wage share ( wx) with the share of slave maintenance costs in the output of slave labor ( my). Condition 1 may thus be rewritten as: wx>my Table 1 presents our estimates of these labor shares for 1850 to 1870. Depending on the estimate of m, the proportion of net output received by slaves ranges from 12 (Foust and Swan, 1970) to 25% (Ransom and Sutch, 1977). This is consistently lower than both the wage share in manufacturing and the share of output received by freedmen in the form of wages.16 These numbers are consistent with the predictions of our model in so far as they indicate that slaveowners used the additional power they wielded over their slaves to maximize exploitation. Table 1. Comparative labor shares 1850–1870 Manufacturing wage sharea Slave shareb Freedman’s wage sharec 1850 52% 12 to 20% 1860 42% 15 to 25% 1870 43% 25 to 31% Manufacturing wage sharea Slave shareb Freedman’s wage sharec 1850 52% 12 to 20% 1860 42% 15 to 25% 1870 43% 25 to 31% aAuthors’ calculations from the Census of Manufacturers (Atack and Bateman, 1999), assuming a 3% depreciation rate on capital stock. bHere the denominator, y, is derived by taking the value of slave-produced staples (cotton, molasses, rice, sugar and tobacco) per slave in agriculture (Towne and Rasmussen, 1960; Weiss, 1992), subtracting depreciation (Ransom and Sutch, 1977, p. 211) and adding estimates of m, consumption per slave, from Conrad and Meyer (1958, p. 104), Foust and Swan (1970, p. 50) and Ransom and Sutch (1977, p. 211). These micro-level estimates of the slave share (which assume a high degree of plantation self-sufficiency) are consistent with more macro estimates. Data collected by Lindert and Williamson (2016) (kindly shared with the authors) indicate that slave consumption as a share of Southern property incomes in 1860 was 23%. cAverage share of wage laborers on cotton plantations from 10 southern states in 1867 and 1868 (USDA, 1868). View Large Table 1. Comparative labor shares 1850–1870 Manufacturing wage sharea Slave shareb Freedman’s wage sharec 1850 52% 12 to 20% 1860 42% 15 to 25% 1870 43% 25 to 31% Manufacturing wage sharea Slave shareb Freedman’s wage sharec 1850 52% 12 to 20% 1860 42% 15 to 25% 1870 43% 25 to 31% aAuthors’ calculations from the Census of Manufacturers (Atack and Bateman, 1999), assuming a 3% depreciation rate on capital stock. bHere the denominator, y, is derived by taking the value of slave-produced staples (cotton, molasses, rice, sugar and tobacco) per slave in agriculture (Towne and Rasmussen, 1960; Weiss, 1992), subtracting depreciation (Ransom and Sutch, 1977, p. 211) and adding estimates of m, consumption per slave, from Conrad and Meyer (1958, p. 104), Foust and Swan (1970, p. 50) and Ransom and Sutch (1977, p. 211). These micro-level estimates of the slave share (which assume a high degree of plantation self-sufficiency) are consistent with more macro estimates. Data collected by Lindert and Williamson (2016) (kindly shared with the authors) indicate that slave consumption as a share of Southern property incomes in 1860 was 23%. cAverage share of wage laborers on cotton plantations from 10 southern states in 1867 and 1868 (USDA, 1868). View Large However, Equation (7) not only implies condition 1, it also suggests that, all else being equal, the slave price will be proportional to the difference in exploitation rates. A second implication of our model is therefore that, controlling for other factors influencing the slave price (i.e. assuming maintenance costs, land rent and relative productivity remain unchanged), one should expect to find a positive correlation between slave prices and wages.17 Condition 2.Cov (ps,w)>0∣m¯,y¯x We can test this second implication by looking at the correlation between average wages and slave prices over time. Figure 2 plots slave prices against wages and consumer price level for the nineteenth century.18 One can see from this figure that apart from during the British trade embargo of 1808–1815 (which drove up manufacturing wages and drove down cotton prices), slave prices and wages appear to move in the same direction. Figure 3 displays log–log scatter plots and lists the correlation coefficient with the slave price for nine wage series. As can be seen, the correlation is high and robust across all of them. Fig. 2. View largeDownload slide Slave prices, wages and consumer price level 1804–1860.Sources: Slave price: Engerman’s prime male field hands age 18–30 (Carter et al., 2006, Table Bb210). Common wages: Officer and Williamson (2012) based on daily and monthly payroll records for common or unskilled labor, 1800–1824 data from David and Solar (1977), 1824–1860 from Margo (2000). CPI: David and Solar 1977, Table 1. Fig. 2. View largeDownload slide Slave prices, wages and consumer price level 1804–1860.Sources: Slave price: Engerman’s prime male field hands age 18–30 (Carter et al., 2006, Table Bb210). Common wages: Officer and Williamson (2012) based on daily and monthly payroll records for common or unskilled labor, 1800–1824 data from David and Solar (1977), 1824–1860 from Margo (2000). CPI: David and Solar 1977, Table 1. Fig. 3. View largeDownload slide Log-log plots of slave prices against different wage series (with correlation coefficients in parentheses). Fig. 3. View largeDownload slide Log-log plots of slave prices against different wage series (with correlation coefficients in parentheses). In Table 2, we analyze the impact of changes in the wage level on changes in the slave price, controlling for the value of cotton output per slave and industrial output per wage worker.19 The coefficients can be interpreted as elasticities, such that a 1% increase in either variable corresponds to a roughly 0.28% increase in slave prices. Cointegration tests further reveal that slave prices are cointegrated with wages (with a long-run multiplier of 1.26), but not with value of output per slave or raw cotton prices.20 Table 2. Regression of the growth rate of slave prices on the growth rates of real wages and other variables 1804–1861 (all prices in 1860 dollars) EXPLANATORY VARIABLES Slave prices ( Δlnpst) Wages of common labor ( Δlnwt) 0.279* 0.306** (0.150) (0.139) Value of cotton output per slave ( Δlnyt−1) 0.275*** 0.242*** (0.0831) (0.0819) Industrial output per wage worker ( Δlnxpx) 0.426 (0.268) Constant 0.0146 0.0124 0.00441 (0.0186) (0.0175) (0.0173) Observations 57 57 57 R-squared 0.059 0.166 0.253 EXPLANATORY VARIABLES Slave prices ( Δlnpst) Wages of common labor ( Δlnwt) 0.279* 0.306** (0.150) (0.139) Value of cotton output per slave ( Δlnyt−1) 0.275*** 0.242*** (0.0831) (0.0819) Industrial output per wage worker ( Δlnxpx) 0.426 (0.268) Constant 0.0146 0.0124 0.00441 (0.0186) (0.0175) (0.0173) Observations 57 57 57 R-squared 0.059 0.166 0.253 Standard errors in parentheses. *p<0.1, **p<0.05, ***p<0.01. Sources and methods: See note 19 and Table B.1. View Large Table 2. Regression of the growth rate of slave prices on the growth rates of real wages and other variables 1804–1861 (all prices in 1860 dollars) EXPLANATORY VARIABLES Slave prices ( Δlnpst) Wages of common labor ( Δlnwt) 0.279* 0.306** (0.150) (0.139) Value of cotton output per slave ( Δlnyt−1) 0.275*** 0.242*** (0.0831) (0.0819) Industrial output per wage worker ( Δlnxpx) 0.426 (0.268) Constant 0.0146 0.0124 0.00441 (0.0186) (0.0175) (0.0173) Observations 57 57 57 R-squared 0.059 0.166 0.253 EXPLANATORY VARIABLES Slave prices ( Δlnpst) Wages of common labor ( Δlnwt) 0.279* 0.306** (0.150) (0.139) Value of cotton output per slave ( Δlnyt−1) 0.275*** 0.242*** (0.0831) (0.0819) Industrial output per wage worker ( Δlnxpx) 0.426 (0.268) Constant 0.0146 0.0124 0.00441 (0.0186) (0.0175) (0.0173) Observations 57 57 57 R-squared 0.059 0.166 0.253 Standard errors in parentheses. *p<0.1, **p<0.05, ***p<0.01. Sources and methods: See note 19 and Table B.1. View Large 3.2. The territorial question Different assumptions about the supply of land to slave-based agriculture can provide a closure to equation (7) and determine the long-run path of slave prices in our model. We will explore the dynamics of the model, as well as its predictions about the long-term viability of slavery, by playing out two scenarios envisaged by Lincoln in his famous ‘house divided’ speech of 1858. In that speech Lincoln set out two possibilities for the future of the USA: one in which slavery had unimpeded access to Western (and potentially Northern) lands, and would therefore continue to expand, and one in which it would be cut off from those lands, and therefore be left ‘in the course of ultimate extinction’. We call the former vision the ‘Dred Scott scenario’, after the 1857 Supreme Court decision Lincoln feared would allow slavery to spread without limit, and the latter the ‘Free Soil scenario’, after Lincoln’s own plan to surround the South with a ‘cordon of freedom’. For Lincoln in 1858 these were the only options on the horizon: he couldn’t envisage civil war, but he was sure that the USA could not remain ‘half slave and half free’; it would have to ‘become all one thing or all the other’.21 3.2.1. Dred Scott scenario Lincoln reasoned that had the USA ‘opened all the national territory to slavery’ (not to speak of territory in Central America and the Caribbean that was then being eyed by slaveowners), then the viability of slavery would be assured, at least for the foreseeable future. Our model agrees with this prediction, since in this case the frontier would remain open and there would be little danger of land rents rising to absorb the surplus value generated by slaves. Yet a Dred Scott future would be one in which the allocation of resources between slavery and free labor would still have to be settled. Such a world might still ‘have to become all one thing or all the other’, not due to the decisions of courts and legislatures, but due to the competitive advantages of one or the other form of labor. The predicted path of slave prices in such a scenario depends crucially on whether the natural rate of increase of the slave population exceeds or falls short of the rate of accumulation of capital, that is, whether 1+σ is greater than or smaller than β(1+r). If the slave population grew faster than capital could accumulate in the wage labor sector, then slave production would eventually absorb the whole available capital stock, squeezing out wage labor production altogether. In a closed economy, the rental on capital would rise to r* where β(1+r*)=1+σ or r*=1−β+σβ (8) At this higher profit rate, which depends only on β and σ, the exploitation of wage labor would not be profitable, but capital would grow rapidly enough to support continually growing slave production. In this long-run steady state, vut=0, vk=r*+δ, and the rental of slaves would satisfy: vst+vkk=y−m or vst=(y−m)−(r*+δ)k (9) Under the arbitrage principle, in order for the typical capitalist to hold both slaves and capital, their rates of return would have to be equalized, requiring: (1+σ)ps*+vst=(1+r*)ps* or ps*=vstr*−σ=(y−m)−(r*+δ)kr*−σ (10) Such a nightmare scenario, in which slavery comes to dominate the entire continental USA, was just the vision Lincoln wanted to instill in his Illinois audience in 1858. Yet the premise underlying this outcome, 1+σ>β(1+r), is not particularly consistent with either Lincoln’s own beliefs about the economic advantages of free labor, or the observed growth rates of these variables over the nineteenth century.22 With the more realistic assumption, 1+σ≤β(1+r), the rental of slaves will continue to satisfy equation (2) and the price of slaves will be stable at the level: ps*=vsr−σ=(y−m)−(x−w)r−σ (11) This equation states that in the presence of a competitive system of wage labor (and the absence of a land constraint) the slave price is simply the capitalized excess surplus value produced by slaves. As long as capital accumulates at a higher rate than the growth of the slave population, equation (11) suggests a long run in which ps*SK will tend to zero.23 In this scenario a small and relatively shrinking slave economy would theoretically survive as a niche of a very large wage labor economy, although it might be difficult for a relatively shrinking class of slaveowners to defend their ‘peculiar institution’ against abolitionist sentiment.24 How long could these Dred Scott scenarios have survived had they not been interrupted by civil war? Using post-war land-use data and projected population trends, we find that slave-based production would have used up all the cultivated land in the USA by 1940.25 However, we expect that slavery would have begun to decline even before this point, for as it approached the limit of territorial expansion it would begin to approximate the ‘Free Soil scenario’. 3.2.2. Free Soil scenario For Lincoln the primary alternative to the Dred Scott scenario was one in which free-soilers in the North would cut off slavery from the Western territories. According to Lincoln, this would ‘arrest [slavery’s] further spread and place it where the public mind shall rest in the belief that it is in the course of ultimate extinction’. Here our model agrees with both Lincoln and the ‘public mind’. This is because as long as land rents are a residual claim on the excess surplus value produced by slaves, there is a trade-off in our model between land and slave rents. If land on which slave production can be carried out becomes scarce land rent will appropriate all of the excess surplus value generated in slave production. This will occur when the slave population satisfies uST=u(1+σ)TS0=U, where S0 is the slave population in some base period.26 As a result slave rents and prices will fall to zero at period T. We can determine the slave price in any intervening period by working backward from psT=0 using equation (6) and assuming that vst=vs=(y−m)−(x−w) is a constant for all t<T, such that the price of slaves declines steadily towards zero: psT = vsT=0,vuT = (y − m) − (x −w)where t<T: vst=(y−m)−(x−w), vut=0pst−1=(1+σ)pst+vst−11+r=(1+σ)pst+(y−m)−(x−w)1+r (12) The reason the slave price falls to zero in period T is that in and after period T there is a surplus of slaves, so their owners will be unable to appropriate a slave rent from entrepreneurs. After period T in this scenario, the scarce input is land, so the surplus value available from slave production will be appropriated as rent on land, not on slaves.27 We can estimate T in 1860 based on the expected growth rate of the 1860 slave population ( S0), a maximum of improved southern acreage ( Umax) and the average land per slave (u): S0(1+σ)T=Umaxu, (13) Solving this equation for T, we find that slave agriculture would have saturated existing Southern land somewhere between 1884 and 1895.28 The model thus predicts that in a land-constrained South, slavery would not have survived much longer than the 25 years estimated by Thaddeus Stevens.29 4. Slave prices and the Civil War Our model explains why antebellum Americans, in both North and South, believed that slavery needed to ‘expand or die’.30 For most of the antebellum nineteenth century, slavery was free to expand westward. In this case, with a virtually endless source of cheap land, slave rents would only reflect changes in slave productivity and wages, as in equation (11). However, if the expansion of slavery were to be restricted by federal legislation, as Lincoln promised to do in 1859, then the continued growth of the slave population would sooner or later lead land rents to rise and slave rents to fall. Given the dependence of current slave prices on future rents, this eventuality need not have been imminent (i.e. not all existing Southern lands need have already been used up) for slave prices to begin to fall in anticipation. Falling slave prices would both damage the immediate interests of slaveowners and erode their collective interest in preserving slavery. A collapse of slaveowner unity would threaten the legal defense of slave property at the local and national level, giving rise to a deterioration in the security of slave assets and further price falls. Yet even setting aside these political considerations, after a certain point a fall in slave prices would have undermined the institution of slavery itself, for at low prices it becomes easier for slaves to buy their freedom, and at very low prices they would fail to cover their costs of upbringing, leading to a breakdown of the slave economy. 4.1. Comparison with other models In his analysis of the causes of the Civil War, Gavin Wright points out that a unique feature of slavery, one that distinguishes it from all other labor regimes, is that it generates a property-owning elite with a common interest in maintaining a high price for labor. Wright gives the examples of the resistance of slaveowners to the reopening of the slave trade (1978, pp. 150–54), and their opposition to free immigration to the region (2006, p. 74). In both cases Wright suggests that slaveowners were acting rationally to prevent slave imports or immigrant labor from undermining the value of their existing slave property. Our model suggests another example of slaveowners colluding to prop up the price of labor: their decision to secede from the union in 1860–61. Many secessionists argued that Lincoln’s electoral promise to restrict slavery from the territories would lead to falling slave prices.31 This would seem to be in keeping with Wright’s argument that slaveowners were driven by a rational incentive to protect the value of their assets. Yet here Wright’s own models (Passell and Wright, 1972; Wright, 1978) suggest that Southern fears were irrational, that territorial restriction would raise slave prices rather than reduce them. Wright is not alone in drawing this conclusion. Passell (1971), Kotlikoff and Pinera (1977) and Lee (1978) all put forward models with similar results. They argue that a less-than-perfectly elastic demand for cotton would mean that any limitation in output due to a land restriction would boost cotton prices and thus slave prices.32 Part of the reason our model differs from those of the above authors is that we make different assumptions about the degree of factor substitutability. Passell and Wright (1972) follow Fogel and Engerman (1975, vol. 2, p. 54) in assuming a Cobb-Douglas slave production function with an elasticity of substitution between slaves and land equal to one. This rules out by assumption any limits to the viability of slavery arising from a limited supply of land, for it implies that slaves would command a positive price even as the amount of land on which they could be employed became infinitely small.33 Our model, by contrast, assumes a Leontief production function, with an elasticity of substitution of zero. But as we show in Appendix A.2, even if we were to allow for a variety of production techniques, involving varying amounts of land per slave, our conclusions regarding the viability of slavery would still hold as long as we assume that the elasticity of substitution was less than one.34 In this case there will still be a maximum land-labor ratio above which the marginal product of slaves consists of the entire value of output less the capital costs and maintenance (i.e. the excess surplus value produced by slaves), and land rents are zero. There will symmetrically be a minimum land-labor ratio beneath which the marginal product of slaves falls to zero, and land rents appropriate all the excess surplus value in the slave sector. Thus in our Free Soil scenario, slave prices will eventually fall whatever the elasticity of demand for cotton, and whatever the relative productivity of Southwestern plantations. For the significance of the land constraint does not lie in the impact of more fertile land on slave productivity (as in the models of Wright et al.), but rather in the competing claims of land and labor on the same net product. When land rather than labor becomes the scarce factor, it will be ownership of land rather than labor that will command the relative advantages of slave labor.35 4.2. Evidence from contemporary sources Note that our version of the ‘expand or die’ thesis is not premised on any claims about slave-based agriculture’s inherent propensity to exhaust the soil,36 that Southern slavery had become ‘unprofitable’, or that the South had run out of fertile land on its existing territories in 1859. In rejecting these implausible claims, some historians (Fogel, 1989; Ashworth, 2011) have drawn the unwarranted conclusion that the ‘expand or die’ thesis was merely the fear-mongering of Northern free-soilers, based either on ignorance or willful distortion of Southern conditions. However, this fails to account for the widespread acceptance of the ‘expand or die’ thesis among pro-slavery Southerners. The conundrum is resolved when we note that Southern arguments for the necessity of expansion were not typically based on the idea that slavery was inherently unprofitable or destructive of the soil, and that in many cases they cited the very mechanism suggested by our model: slave population growth and falling land-labor ratios. The Southern political economist George Tucker put forward this argument as early as 1820: As soon as our population has overspread the whole habitable parts of our territory, and brought our waste lands into cultivation, human labor will begin to decline in value. . . . In the same proportion that the price of labor diminishes, must the value of slaves decline, until at length the cost of bringing up a slave will be more than he is worth.37 In Tucker’s Malthusian model, slavery would eventually collapse because the cost of feeding the slave population would exceed the revenue that could be generated with their labor. By comparing Southern land-labor ratios to those in Europe at the end of serfdom, Tucker (1847, p. 117) predicted that slave agriculture could survive in its current territory for another 80 years.38 Our model predicts an earlier demise because it depends on rent dynamics rather than food prices.39 Nevertheless, Tucker’s causal mechanism—falling land-labor ratios—is the same as ours. Tucker’s argument proved highly influential among slavery’s critics. Henry Clay himself reiterated Tucker’s thesis in the Missouri Crisis debates of 1820–21, and it seems that it was from Clay, his idol, that Lincoln took the reference to a territorially restricted slavery’s ‘ultimate extinction’ (Hodgson, 2009). The Southern abolitionist Daniel Goodloe (1846, p. 27) concluded his influential economic indictment of slavery with a version of Tucker’s thesis. However, perhaps because it counseled patience, the argument also found support among a number of pro-slavery writers.40 Indeed, it may have reached the height of its influence in the secession debates of 1860, in which concerns over the future of slave prices played a prominent role. For example, a South Carolina editorial in 1860 declaimed that by ‘surrounding the slave states with free territory, and building us in with an impassable wall, you will eventually force the abolition of slavery. Our population would become so dense, and our slaves so numerous, that we could not live; their value would depreciate to nothing; and we would not be able to keep them.’41 4.3. Territory and security As this editorial makes clear, Southerners rarely discussed their fears of territorial restriction without mentioning its impact on the security of slave property rights. Many imagined that territorial restriction would lead to what historian David Blight (2008) has called ‘the shrinking South.’ In this scenario, the greater risk of fugitives in the border states would lead slaveowners there to sell their slaves into the deep South, leading ultimately to the abolition of slavery in the border states, such that the border would move inwards, concentrating the slave population in the deep South states, where slave prices would correspondingly fall.42 In this regard they echoed the popular metaphor of the Republicans, who argued that territorial restriction would lead slavery to destroy itself ‘like the scorpion surrounded by fire’ who will ‘sting itself to death’ (Oakes, 2014). In our model we have so far ignored the security of slave property rights. However, we may incorporate the risk of fugitives into equation (6) as a decrease in slave population growth σ or a compensatory increase in out-of-pocket expenses (m) on security (e.g. the wages of overseers and the fees of slave catchers). In both cases increased risk will lower slave prices. However, slaveowners could also offload the cost of security onto non-slaveowners, by funding slave patrols and slave catchers from local, state and federal taxation. There is evidence that the Fugitive Slave Act of 1850 reduced the overall number of fugitives, and Figure 4 suggests that it may have also reduced the discount on border-state slave prices.43 Lincoln’s determination to overturn this act, as well as the Dred Scott ruling which extended it, thus threatened to further undermine the price of slaves. Fig. 4. View largeDownload slide Percentage discount on slave prices in border states, 1840s and 1850s Fig. 4. View largeDownload slide Percentage discount on slave prices in border states, 1840s and 1850s The question of land and security interacted in a number of ways. First, they were linked by the division of senatorial seats between free and slave states, such that territorial questions directly impacted the votes necessary to secure slave property rights. Second, without access to the West, the South not only risked being outnumbered by anti-slavery Northerners in the Senate, but also becoming politically divided against itself. On the one hand, a fall in slave prices would diminish the stake of all slaveowners in the institution.44 On the other hand, since land is a less liquid asset than slaves, the benefits of rising land prices would be spread unequally among Southern subregions, and threatened to pit the interests of slaveowners against yeomen landowners.45 Such a collapse of Southern unity would further threaten the legal defense of slavery at both the local and national level.46 None other than Jefferson Davis, in his justification of secession, placed the link between territorial restriction, slave security and falling slave prices at the centre of his argument: [The Republican party has] the avowed object of using its power for the total exclusion of the slave States from all participation in the benefits of the public domain acquired by all the States in common, whether by conquest or purchase; of surrounding them entirely by States in which slavery should be prohibited; of thus rendering the property in slaves so insecure as to be comparatively worthless, and thereby annihilating in effect property worth thousands of millions of dollars. This party, thus organized, succeeded in the month of November last in the election of its candidate for the Presidency of the United States . . . With interests of such overwhelming magnitude imperiled, the people of the Southern States were driven by the conduct of the North to the adoption of some course of action to avert the danger with which they were openly menaced.47 5. Conclusion One year prior to Jefferson Davis’s declaration before the Confederate Congress, Abraham Lincoln gave a speech in Hartford, Connecticut, in which he both echoed and explained Davis’s reasoning: The entire value of the slave population of the United States is, at a moderate estimate, not less then $2,000,000,000. This amount of property has a vast influence upon the minds of those who own it. The same amount of property owned by Northern men has the same influence on their minds. … Public opinion is formed relative to a property basis. Therefore the slaveholders battle any policy that depreciates their slaves as property. What increases the value of this property, they favor.48 The policy that Lincoln here refers to was his own: to ban slavery from the territories. Lincoln appears to have believed this would ‘depreciate’ slave property for the same reason as Tucker: falling land-labor ratios would eventually crowd out the returns to slaveownership, and slave prices would fall in anticipation.49 Our model provides the rationale for the arguments of both Davis and Lincoln: slavery did indeed have to ‘expand or die’. It suggests that this commonly held view was neither abolitionist propaganda nor ‘fire breathing’ paranoia, and that slaveowners therefore had every reason to battle Lincoln’s policy, even if it meant breaking from the Union.50 The threat to the slave system posed by rising land rents could not be mitigated by raising the rate of exploitation of slaves. If land is the limiting resource, higher rates of exploitation of slaves would raise land, not slave prices. As we have remarked above in Section 3, slaveowners had strong incentives and actively sought to maximize the rate of exploitation of slaves regardless of the relative scarcity of land and slave labor. Of course, to point to an economically rational motive for Southern secession is not to provide an adequate explanation of the Civil War. Other motives for secession no doubt existed, not all of them rational, and any explanation for war must also account for the North’s refusal to allow the South to secede. Nor does our argument provide any support for the traditional view of slavery as economically moribund in the 1850s. The fact that Southerners in 1860 valued their slave property in the billions of dollars attests to just the opposite: that the Southern economy was booming, and slaveowners expected the good times to continue. Our model suggests their expectations were well founded—as long as labor looked likely to remain the scarce factor. Yet Lincoln’s election reversed these expectations, making rational exuberance irrational. His electoral promise to restrict slavery from the territories threatened to turn a virtuous spiral of capital gains into a downward spiral of capital losses. It was not an unprofitable past or present, but rather the prospect of an unprofitable future, which set the slaveowners on the path to war.51 The authors would like to thank Robin Blackburn, Alf Coles, Stanley Engerman, Suresh Naidu, Gavin Wright and two anonymous reviewers at CJE for comments on earlier drafts of this paper. Thanks also to Warren Weber, Howard Bodenhorn, Peter Lindert and Jeffrey Williamson for kindly making their data available. An earlier version of this paper was presented to the conference Slavery, Emancipation and the New Left: The Work of Robin Blackburn at The New School for Social Research, NY in 2011 Footnotes 1 On the capitalist nature of antebellum slavery, see Clegg (2015, 2017). 2 Some scholars, apparently conflating fixed and constant capital, have suggested that, according to Marx’s definition, slaves (like machinery and other constant capital) are not productive of either value or surplus value (Harvey, 2010, p. 90; Linden and Roth, 2013, p. 470; Murray, 2016, pp. 187–88). However, since slave labor is indeed labor, and the purchaser buys not actual labor but potential labor, or labor-power, the money that exchanges for the latter is, according to Marx’s definition, variable capital, which may in this case take either a fixed or circulating form. When slaves are rented, all of the variable capital circulates like wages. But even when purchased outright, the actual cost of slave labor power is not entirely fixed, for maintenance costs form part of the circulating capital (Anderson and Gallman, 1977). 3 Slaves may generate a higher net product either because of the greater means of physical coercion available to their owners, or because the maintenance costs of slaves were lower than the going wage. 4 Our use of the term ‘slave rent’ is analytical, for such rents are implicit even in the absence of a rental market. Nonetheless, the existence of rental markets in the antebellum South, as well as the fact that slave prices capitalized slave rents at average discount rates (Evans, 1962), bolsters our analytical approach. 5 For various reasons (e.g. harsh work conditions in certain crops, the aversion of wage laborers to such competition, racist ideology), there are few historical examples of slaves and wage laborers working in the same line of production, let alone at the same tasks. 6 Davis (1963) points to divergent regional interest rates, whilst Ransom and Sutch (1988, p. 137) conclude that ‘there is no reason to believe that there were significant capital flows between the North and South’ in the postbellum period. However, Bodenhorn (2000, p. 164) finds that ‘regional interest rate differentials were generally smaller before 1860 than after 1900’, suggesting that sustained interest rate differentials were peculiar to postbellum agrarian finance. 7 Bank profit rates (return on equity) were constructed by multiplying state-level interest rates from Bodenhorn (2000) by weighted averages of capital ratios from Warren Weber’s (2011) balance sheets of antebellum banks. This method of estimation was kindly suggested by Howard Bodenhorn in personal correspondence with the authors. 8 In their calculations of the relative efficiency of slave labor, Fogel and Engerman (1975) compare slaves not (as here) to wage laborers, but to Northern family farmers. Family farming in the antebellum USA was often subsistence orientated and insulated from competitive markets, with farmers marketing only their surplus. Attempts to calculate rates of return to such activity not only confront limited data, but also the incalculable non-pecuniary benefits of security and independence (insulation from the market may itself be a non-pecuniary benefit in this sense). Unlike wage and slave labor, capitalists could not invest directly in family farm production, but only indirectly through extending credit to farmers, so the principal arbitrage mechanism we outline in this paper did not apply. 9 The assumption that slave production requires the same amount of capital per worker as wage production is arbitrary, but greatly simplifies the mathematics of the model. We relax this assumption in a more general version of the model in Appendix A.1. 10 In discussions of the economics of slavery based on neoclassical production functions, what we call the rent of slave labor is often referred to as the ‘marginal product of slave labor’. The model we analyze here is of the Leontief type, with only one technique of production that requires fixed proportions between the labor, capital and land inputs, in which marginal products of the inputs are not well defined. If we assume that the entrepreneurs organizing production with slave labor face a set of techniques described by a constant returns to scale differentiable neoclassical-type production function yS=Sf[1,k,u], profit maximization will lead them to adjust the input proportions so that the marginal value product of each input is equal to its price, fs=vs,fk=vk,fu=vu, which, given vk=r+δ and vu=0, will determine a unique cost-minimizing technique like that described above. The neoclassical product exhaustion theorem will then reproduce (2). See Appendix A.2 for a fuller discussion of factor substitution under slavery. 11 Moes (1961) and Ransom and Sutch (1988) make this point with regard to slave population growth, but neglect similar ‘wealth effects’ due to an increase in slave prices (which in our model could be driven by, e.g., an increase in Northern wages). Note, however, that any resulting growth deficit would not have been confined to the slave states, due to the aforementioned mobility of capital. For a discussion of similar dynamics with regard to land, see Foley and Michl (1999, pp. 212–14). 12 Note that this does not amount to a denial of ‘slave breeding’, but to a denial that such activities successfully altered slave fertility in response to changes in demand. Much of the controversy over ‘slave breeding’ is definitional. Sutch (1986, 1972) defines it as interference in the sexual life of slaves designed to increase fertility, whereas Fogel and Engerman (1975) define it as the specialization of Eastern plantations in the production of slaves for sale. The evidence of either form of ‘breeding’ is mixed, but note that neither definition implies that actual fertility rates be responsive to market signals (although Fogel and Engerman make this assumption in their pricing model [Fogel and Engerman, 1974, p. 60]). Evidence for the exogeneity of slave population growth ( σ) with respect to slave pricing can be found in the fact that it tended to be lower when prices were higher (Goldin, 1975, Table 7.1). 13 A version of Equation (7) is implicit in several cliometric formulas. For instance, Foust and Swan (1970, p. 49) define the present value of the total capital invested in a slave as y−mr−σ, which may be derived from (2) above. Yet by collapsing together slaves, capital and land, such formulas misleadingly suggest that slavery will be viable as long as slaves produce a positive surplus value. By contrast, in specifying the surplus produced by wage labor as the opportunity cost of slave exploitation, and in separating out the residual claimants to the surplus value produced by slaves, our formula shows that slavery could be non-viable given y>m, if either 1) the surplus value generated by wage laborers were equal or greater than that generated by slaves: (y−m)≤(x−w); or 2) land rents were to rise to absorb all the excess surplus value in slave production: vuu≥(y−m)−(x−w). For a comparison of our model with neoclassical approaches, see note 10 above. 14 The link between competition from wage labor, economic viability and slave prices was also recognized by Hicks (1969), and by Douglass North (1965) in an early critical comment on the cliometric debate: Only if the wages of free labor fell to the subsistence level, so that in fact the prices of slaves fell to below their reproduction cost, would the institution become non-viable. As Sutch (1965) points out, North here implicitly assumes that slaves and wage laborers were equally productive. Condition 1 implies that if wage laborers were more productive than slaves, slavery could become non-viable at above-subsistence wages. 15 The Marxian rate of exploitation (e) is sv, where s is surplus value, and v is variable capital, or the wages of labor. Given that s+v is equal to value added, the wage share can be written as ω=vs+v, and e=1−ωω. The discussion of exploitation in the economic literature on slavery has been dominated by the neoclassical view of exploitation as the difference between factor compensation and marginal productivity, and has been unnecessarily complicated by the question of whether to discount returns over a slave’s lifetime. For instance, Fogel and Engerman define the ‘Marxian rate of exploitation’ of a slave as: e=∑t=0nλt(MPt−mt)∑t=0nλtMPt where MPt is the marginal product of slave labor, and λt is the probability that a slave will die in year t. But this is neither ‘Marxian’, nor a rate of exploitation. It is more accurately described as the slaveowner’s quasi-rent-share of the undiscounted value of a slave’s expected lifetime marginal product. Vedder (1975) and Ransom and Sutch (1977) use simpler annual estimates, but also rely on questionable assumptions about the ‘marginal product’ of slave labor (see note 10 and Appendix A.2). 16 The fact that freed slaves received a lower wage share than predominantly Northern manufacturing workers is presumably explained by the relative bargaining power of each group. However, Ransom and Sutch’s data for 1879 reveal that the average sharecropper received 53% of the value of their output (Ransom and Sutch, 1977, pp. 215–16, 240–41), although that is prior to interest payments to merchants or landlord-creditors. 17 The cliometric literature has generally ignored the correlation between slave prices and wages, but Gerald Gunderson (1974, p. 918, n. 6) identified the relevant mechanism when he wrote that: the opportunity cost of using slaves tended to rise to the level of free labor because, when it was less, potential employers had reason to purchase slaves to capture those extra profits, thereby bidding up the price of the slaves. 18 Figure 2 displays an index of the Officer and Williamson (2012) series for common and unskilled wages, the David and Solar (1977, Table 1) consumer price index and Stanley Engerman’s series of slave prices, based on a large New Orleans sample of ‘males ages 18 to 30, without skills, fully guaranteed as without physical or other infirmity’ (Carter et al., 2006, Table Bb210). Studies show that prices in different slave markets closely tracked one another (Kotlikoff, 1979). 19 We first differenced all our variables because several were flagged in tests as unit roots. We report the effect on levels in Appendix B, where we also attempt to identify causal effects by instrumenting for the wage using the productivity of farms on the frontier. We constructed our variable for the value of output per slave by multiplying Hammond’s wholesale cotton prices (deflated to 1860 dollars) by a smoothed interpolation of Olmstead and Rhode’s 2008 decennial estimates of average bales per slave. Only the one-year lag of this variable was significant in our regressions. Conrad and Meyer’s 1958 annual estimate of the value of output per slave was not a significant predictor of slave prices at any lag. We constructed our estimate of industrial output per worker by dividing Davis’s 2004 index of industrial production by a smoothed interpolation of Weiss’s non-farm labor force (Carter et al., 2006, Table Ba829–830). Unfortunately, we could find no aggregate price series for manufactured goods prior to 1840, so we were only able to record physical changes in output per worker. 20 This may be explained by the fact that cotton prices tended to be volatile, such that annual changes had little effect on investment (and secular trends may have been capitalized by the value of land suited to cotton; see below), whereas expectations of the rate of profit in wage sectors directly affected the opportunity cost of purchasing a slave. 21 For the text of Lincoln’s speech see Lincoln (1989). For references to the ‘cordon of freedom’ by many abolitionists—including Sumner, Stevens, Greeley and Chase—see Oakes (2012). For Lincoln’s reasoning, see the discussion in Section 4.2 below. 22 Piketty and Zucman (2014, Table 9, Table US.3) report a saving-induced annual growth rate of 2.9% in the USA from 1870 to 1910 and a real annual growth rate of private wealth 4.7% from 1810 to 1910. The average annual slave population growth from 1800 to 1860 was 2.5%. 23 Note, though, that any rise in wages would counteract such a tendency, by both slowing accumulation and increasing ps* 24 If, by a ‘fluke’, the natural rate of increase of the slave population were exactly equal to the rate of accumulation of capital, a slave sector of arbitrary size would coexist indefinitely with a wage labor economy. But a tiny variation of the parameters of the model would destabilize this mixed-economy steady state. 25 This estimate is based on a comparison of actual land use data (Carter et al., 2006, Table Cf103) to the projected growth of the slave population, holding land per slave constant (see Equation (13) and note 28 below). This assumes that all the cultivated land in the post–Civil War USA could have potentially been farmed by slaves, that aggregate cultivation would not have grown faster if slavery had persisted and that the optimal amount of land per slave would not have fallen as a result of technical change. All of these assumptions make our estimate an upper bound of slavery’s potential longevity. For the implicit assumption that slavery could not have competed with wage labor in industry, see Appendix A.2 below. 26 This assumes that slavery cannot compete with wage labor in industry over the long run. For a justification of this assumption, see Appendix A.2 below. 27 The political economic logic is parallel to the reasoning behind the version of the Ricardian steady state explained in Foley and Michl (1999, ch. 11). 28 S0 = 3.95 million, u = 17 acres, σ = 2.5%. Using T=logUmax−logu−logS0log(1+σ), we derive a lower bound estimate of T=23 and an upper bound of T=35 These bounds are set by uncertainty in Umax. We interpret this as the maximum cultivatable land given existing technologies and crops, and take improved Southern land in the agricultural census of 1890 (119 million acres) and 1910 (151 million) as our lower- and upper-bound estimates. Note that our measure of u improved acreage per slave in 1860, includes land in non-slave farms, and is thus itself an upper bound. 29 Another abolitionist, Owen Lovejoy, gave it 25–50 years, while Lincoln, in an offhand remark, was prepared to think it could last 100 (Engerman, 2013; Oakes, 2014). 30 On the prevalence of the ‘expand or die’ thesis, in both North and South, see Foner (1995, pp. 115–16), Oakes (2014) and Rainwater (1935). 31 See, e.g., Mississippi’s declaration of secession: ‘[we] must either submit to degradation and the loss of property worth four billions of dollars, or we must secede from the Union’ (Dew, 2001), as well as Jefferson Davis’s speech before the Confederate Congress quoted below. 32 For a critique of the specifications of these models see Schmitz and Schaefer (1981). 33 Passell and Wright (1972, p. 1199) admit their results are ‘sensitive to variation in the elasticity of substitution’, and that ‘one can still believe consistently that land expansion was desirable to preserve the peculiar institution if one also believes that slavery could not adapt to labor-intensive methods of cultivation.’ They base their assumption of unit elasticity on census data which indicate a positive correlation between land-labor ratios and labor productivity (ibid., p. 1192), however Wright elsewhere argues that the productivity advantage on large plantations was due to land quality rather than quantity, and that most such plantations typically held surpluses of uncultivated land (Wright, 1978, p. 62). 34 Under the assumptions of our model, substitutability between labor and other inputs makes no difference to the short-run equilibrium conditions describing rents and price dynamics. See note 10 above. 35 All the above authors assume that Western expansion was the main driver of observed slave labor productivity growth, but this view has recently been challenged by Olmstead and Rhode (2008), who show that the amount of cotton picked per slave increased rapidly in both the Old and New South. If cotton price effects were dominant, as the above authors assume, such productivity growth would make territorial expansion even less attractive. By contrast, in our model, if, as Olmstead and Rhode argue, increased productivity in cotton picking led to an increase in the amount of land that could be cultivated per slave u then it may increase the demand for land, and hasten the decline of slavery in a territorially restricted South. 36 Defenders of the soil exhaustion thesis include Stoll (2003), Trimble (1985) and Genovese (1965, ch. 4). Critics include Fogel and Engerman (1975, vol. 1, pp. 196–97; vol. 2, pp. 149–51), Earle (1988) and Passell (1971). While it is clear that slaveowners did little to preserve soil fertility, this appears to be consistent with agricultural practices in the North and land-abundant agricultural regimes more generally. 37 George Tucker’s 1820 speech to Congress, cited in Hodgson (2009). 38 Tucker revised this estimate upwards after the annexation of Texas (Engerman, 2013). 39 Malthusian models like Tucker’s also tend to predict that wages would follow a similar downward path as slave prices. By contrast, our assumption that wage labor was more suited to industry (see Appendix A.2) generates divergent paths for the two labor systems in our model. 40 See Edward Brown (1826, p. 31), Edward B. Bryan (1850, p. 101), J. H. Hammond (1853, p. 122), John H. Van Evrie (1853, pp. 8–9), Edmund Ruffin (1857, p. 7) and Samuel Seabury (1861, p. 312). 41 Congressional Globe South Carolina, 14 March 1860, cited in Bensel (1991, p. 42). 42 ‘While the conditions of things in the [Border] States will force their slaves on the markets of the Cotton States, the timid of the Cotton States, will also sell their slaves. The general distrust, must affect purchasers. The consequences must be, slave property must be greatly depreciated’ (Charleston Mercury, 11 October 1860, cited in Wright [1978, p. 149]). 43 Census records indicate that the number of fugitives fell between 1850 and 1860, in spite of a 20% increase in the slave population (Hummel and Weingast, 2006). Dittmar and Naidu (2012) find that the mean number of advertisements for runaway slaves also fell from 1849. 44 ‘Would you be willing to shoulder your musket in defense of slaveholding rights, if your slaves were only worth five dollars apiece? Every man sees this is an absurdity. Therefore the permanence of the system depends on keeping prices high’ (H. S. Foote, Debow’s Review, vol. 27, August 1859, cited in Wright [1978, p. 152]). 45 Schmitz and Schaefer (1981, n. 17) note that falling land values and rising slave prices due to westward expansion ‘redistributed wealth from yeomen landowners to slaveowners’. Oakes (1983) claims that future supplies of cheap fertile land also promised yeomen farmers access to slaveownership. Territorial restriction could thus be expected to both increase the influence of yeomen farmers and decrease their loyalty to slavery. That loyalty was already in doubt in 1860, when upland farm areas tended to vote against secession (Wooster, 1962). 46 Territorial restriction may also have directly affected the risk of fugitives. Continued slave population growth in a restricted South threatened to bring more slaves closer to the border and thus closer to freedom. It should thus be no surprise that the compromise of 1850 exchanged free soil in the West (California and potentially New Mexico) for a beefed-up Fugitive Slave Act. For, if the South were cut off from Western lands, it would become all the more important to neutralize the escape route to the North. For concerns about fugitive risk among border state slaveowners, see Oakes (2012). 47 Jefferson Davis, ‘Message to the Confederate Congress’, 29 April 1861 (Richardson, 1905, pp. 67–68). Emphasis added. 48 Abraham Lincoln, speech at Hartford, Connecticut, 5 March 1860. Lincoln’s estimate was indeed moderate. Contemporary scholarship puts the total value of slave property in 1860 at around three billion dollars—that is, significantly more than the total capital invested, at the time, in manufacturing and railroads combined (Huston, 2003, p. 28, Table 2.3). 49 For the Malthusian assumptions behind Lincoln’s argument, see Engerman (2013, p. 83). Despite our differences with Tucker (mentioned above), the causal mechanism in our model is the same. 50 It might be objected that, according to our argument, secession would still be irrational in that it would confine the South to the very territory to which Lincoln had threatened to restrict it. But this would be to ignore the Confederacy’s expansionist aspirations. Much antebellum westward expansion had been driven by slaveowners (e.g. the annexation of Texas), and by the 1840s many of them were looking South (perhaps in part due to security costs associated with proximity to the North). A proslavery Southerner, William Walker, attempted a takeover of Nicaragua in 1857, hoping that US president Franklin Pierce would annex Nicaragua as Polk had annexed Texas in 1844. The plan backfired, however, when several other Latin American countries sent troops to depose Walker, and Pierce failed to intervene. Pierce, a pro-Southern Democrat, nonetheless threatened to invade Cuba in 1854, and the annexation of Cuba was included in the Southern Democrats’ electoral platform of 1860. Southerners had also long had their eyes on Mexico, and during the Civil War attempted to persuade Northern Mexico to join the Confederacy (Genovese, 1965, p. 258). Such neocolonial ambitions are difficult to explain if we assume (with Wright, Passel and Lee) that Southern expansion would lead to falling slave prices, but are consistent with our model. 51 With slave prices as high as they were in 1860, there were few options for a peaceful transition away from slavery, for slaveowners could not have liquidated their slave assets without suffering huge losses, and compensation was both fiscally and politically unfeasible. 1 It would also be possible to consider a model in which wage-labor production requires a significant land input, but as we discuss in Section 1.1 above, this case seems to have minimal relevance to the political economy of the antebellum USA. 2 Starobin (1970) estimates that 5% of the slave population worked in industry in 1860, but this includes industrial pursuits on plantations (e.g. cotton ginning and sugar milling). Moreover, Southern industry lagged far behind the North, and it is hard to find any industry in which wage laborers and slaves worked at similar tasks. There seem to be no examples of a successful industrial use of chattel slaves in any other country. 3 Adam Smith ( 1976, vol. 1, 8.40; vol. 4, 9.47) famously argued that slaves were less productive because they lacked the ability to share in the rewards of labor. David Hume ( 1985) came to the same conclusion after observing that slaves couldn’t be fired (i.e. they lacked negative rather than positive incentives). Marx (1973, p. 1071) also seems to support this argument, stressing elsewhere the reluctance of slaves to learn skills and handle expensive machinery. 4 Slave rental markets in the South were a byproduct of the plantation system. There are no examples of slaveowners who specialized in renting. It thus seems doubtful whether rental markets could be sufficiently deep to give slave labor short-run flexibility. Moreover, slave rental contracts, unlike wage contracts, often involved clauses requiring lessees to pay insurance, to offset the risk of injury or death, and allowed lessors to sue for damages, generating additional costs and inflexibility. 5 For historical evidence of nominal wage rigidity, see Hanes (2000) and James (1998). For contemporary evidence, see Bewley (1999). 6 Yet even if it were not the case that wage labor, due its greater flexibility, could out-compete slaves in all industries, this would be insufficient to guarantee an economic future for slavery in a land-constrained South. All it would take would be for wage labor to be more competitive in some industries. For, in this case, industrialization would inevitably attract more wage laborers to the region, whose animosity to working alongside slaves tended to be expressed in both workplace action and the ballot box (Wade, 1964). One needn’t appeal to any pre-modern ideology to explain slaveowners’ deep-seated suspicions of urban and industrial development. One can simply point to the fact that wage laborers have historically been unreliable defenders of the institution of slavery. Their growing presence therefore threatened the security of slave property rights in both the short and long run. Appendix A. General model The model worked out above makes two convenient, but not crucial, assumptions: that slave and wage labor production use the same capital per worker, and that there is no alternative slave production technique that requires no land.1 In this appendix we relax both assumptions and show that in most historically realistic scenarios our key conclusions continue to hold. Appendix A.1. Varying capital-labor ratios We can relax the first of these assumptions by assuming the technologies: 1 wage laborer + kw capital →x value of output 1 slave + ks capital+ u land →y value of output In this model the zero-profit condition for entrepreneurs operating the wage labor technique are unchanged from (1): vktkw=(x−w) or vkt=x−wkw (A.1) The corresponding zero-profit condition for entrepreneurs operating the slave labor technique are: vst+vktks+vutu=y−m orvst=(y−m)−(x−w)kskw−vutu (A.2) The ratio of the capital per worker required in wage labor and slave labor production appears as a coefficient multiplying surplus value in wage labor production. It is straightforward to modify the analysis above to accommodate this small change. For example, Equation (7) becomes: pst=vstr−σ−gpst=(y−m)−(x−w)kskw−vutur−σ−gpst (A.3) The qualitative conclusions of the model above remain unaltered by the introduction of different capital requirements per worker for wage and slave production. Appendix A.2. Slaves in industry A production function in which the elasticity of substitution between slave labor and land is less than unity implies an asymptotic minimum land-slave labor ratio, which would have the same implications for the eventual absorption of the excess surplus value of slave labor by land rents with limited land as the fixed land-slave labor ratio assumed in this paper (see note 10 above). To approximate and evaluate scenarios in which the elasticity of substitution is greater than or equal to one, we here modify the model to include an alternative ‘backstop’ slave technology that requires a much smaller amount of land, and which therefore could absorb a slave workforce that had outgrown the land constraint. The simplest case would be an alternative slave technology that required no land at all: 1 slave+ ks capital →yi value of output where yi<y, that is, the value of output per slave is lower in the backstop technology that does not require land than in the primary technology that does require land. This backstop technology will support a positive slave rental and slave price only if (yi−mi)>(x−w). If this condition is met, at period T when the slave population saturates the available land for the primary technology, slave rentals will fall to those supported by the backstop technology, and slave prices to the corresponding level, psi, rather than to zero. The price dynamics (12) will govern the path of slave prices, with psT=psi. The central question posed by the possibility of such a backstop technology for the antebellum USA is whether there was a realistic prospect of profitable employment of slaves in industry. The absence of a significant industrial slave sector of the Southern economy suggests yi<y, but it is difficult to estimate the relation of yi−mi and x−w on the basis of observed historical production experience.2 Many scholars have tried to explain the relative absence of industrial slavery by claiming that wage laborers are more productive than slaves ( x>yi) due to the unique positive and negative incentives available to their employers (e.g. rewards for increased productivity and the threat of involuntary unemployment).3 However, we know from the high rate of productivity growth in Southern agriculture that slaves were capable of working hard and adapting to new, more productive, techniques (Olmstead and Rhode, 2008). We also know that slaves were often rewarded for performance (Fogel and Engerman, 1975). And while they lacked the credible threat of imposing involuntary unemployment on their slaves, slaveowners were plentifully supplied with other threats, including physical and psychological torture by overseers (Stampp, 1956; Baptist, 2014), and the capacity to break up families through sales (Tadman, 1996, ch. 6). But whilst wage labor may not be more productive, it still may be cheaper ( w<mi), in so far as it shifts a significant part of the costs of reproduction of the labor force away from the capitalist employer. Individual employers are free to pay wages beneath reproduction costs, but slaveowners who do this risk losing valuable assets. Maintenance costs are also typically more fixed than wage costs. In the absence of thick slave rental markets, transaction costs associated with buying and selling slaves would make it exorbitant for slaveowners to adjust their labor supply according to short-term fluctuations in demand. As a result, slaves tend to be employed by a given firm for longer than an average wage labor contract. Even slave rental contracts tended to be for six months or a year, whilst wage laborers were often hired by the day or week.4 This short-run illiquidity means that temporary restrictions to the productive use of slaves—due, e.g., to harvest failure, negative demand shocks, or illness—are necessarily borne by slaveowners as sunk costs, just like the cost of idle plant and equipment. But whereas machinery can be switched off, slaves must be fed, clothed and medically treated, as much during downtimes as during productive periods. Moreover, to the extent that these costs take the form of purchases of goods and services (as they must do in industrial slavery), they are directly vulnerable to fluctuations in the market price of these goods and services, whereas wage costs tend to lag behind movements in the price of wage goods.5 This fact may be particularly significant in agriculture, where subsistence crops could be grown in slack seasons of the export crop, allowing slaveowners to substitute the purchase of food and clothing with self-production on the plantation (Anderson and Gallman, 1977). Industrial slaveowners were clearly unable to reduce their maintenance costs in this way, and this may help to explain the under-development of Southern industry.6 Thus, even if we were to assume that the value of output per slave could be the same in industrial and agricultural use of slaves ( y=yi), the inability of industrial slaveowners to set seasonally redundant slave labor to work cheapening its own maintenance would still have reduced the rate of exploitation of slaves in industry ymi>ym In this case the prospect of the slave population exceeding the size employable in agriculture would still have a qualitatively depressing effect on slave prices. Arguments invoking a high elasticity of substitution between slave labor and land or the existence of a backstop technology that could absorb an indefinitely growing slave population boil down to the question of whether it would be possible to employ slaves profitably enough in industry to maintain slave prices near the levels based on cotton production. Neither contemporary proponents nor opponents of slavery seem to have taken this seriously, and the considerations we have brought forth here make us doubt the relevance of this branch of the Free Soil scenario. Appendix B. An IV regression of wages on slave prices Our model predicts that wages and slave prices should be correlated with one another, controlling for other relevant variables (see condition 2 above). In the article we show that annual wage and slave prices series are cointegrated, and that their first differences are significantly correlated. In this appendix we explore causal effects by using free farmer productivity to identify wages. However, since most of these variables are non-stationary, and since none have significant coefficients when first differenced, we report the results here with the important caveat that they are liable to be spurious. In Tables B.2 and B.3, we use free farmer productivity as an instrument for the wage, and regress real slave prices on the predicted real wage and a bevy of controls. The results suggest that much of the movement of slave prices can be explained by independent movements in the wage level. However, the fact that both wages and slave prices have unit roots renders these results potentially spurious, so we report them only in this appendix. We derived our annual estimates of the productivity of free farmers by dividing the total value of farm output (excluding slave-produced goods) from Towne and Rasmussen (1960) by the total free farm labor force (Weiss, 1986). The intuition behind using free farmer productivity as an instrument for the real wage is that free farmers occupying cheap frontier lands constituted a reserve army of labor whose living standards functioned as a reservation wage. It is possible that shared agricultural technologies drive both free farmer productivity and slave productivity, and thus also slave prices, thus violating the exclusion restriction. However, the lack of a significant effect for slave productivity (columns 2–3) casts doubt on this hypothesis. In column 2 of Tables B.2 and B.3, we add two controls: slave population growth (based on decennial census records) and acres of federal land sold. In column 3 of Table B.2, we provide a ‘false experiment’ specification, controlling for future values of the instrument. The lack of significance supports our causal hypothesis. We also control for the effect of immigration, which excludes a possible confounder. The positive coefficient for immigration suggests that it is itself a function of the wage level, which is why we didn’t use this variable as an instrument for the wage. Table B.1. Descriptive statistics Mean SD N Min Max Average slave price 1804–1861*a 832.24 264.39 58 504 1564 Wage index for common labor 1800–1861b 80.45 12.96 61 57 111 Value productivity of slaves (cotton) 1800–1861*c 119.75 41.57 61 55.26 223.1 Value productivity of free farmers 1800–1861*d 236.77 28.53 61 197.66 289.75 Index of physical productivity of industrial labor 1800–1861e .021 .006 61 .013 .036 Slave population 1804–1861 (millions)f 2.25 0.9 58 1 4.04 Net free immigration 1800–1860 (thousands)g 108.99 88.93 60 2.5 420.29 Consumer price index 1800–1861h 28.28 122.74 61 89 211 Mean SD N Min Max Average slave price 1804–1861*a 832.24 264.39 58 504 1564 Wage index for common labor 1800–1861b 80.45 12.96 61 57 111 Value productivity of slaves (cotton) 1800–1861*c 119.75 41.57 61 55.26 223.1 Value productivity of free farmers 1800–1861*d 236.77 28.53 61 197.66 289.75 Index of physical productivity of industrial labor 1800–1861e .021 .006 61 .013 .036 Slave population 1804–1861 (millions)f 2.25 0.9 58 1 4.04 Net free immigration 1800–1860 (thousands)g 108.99 88.93 60 2.5 420.29 Consumer price index 1800–1861h 28.28 122.74 61 89 211 *Yearly averages in current dollars. aEngerman’s annual price for prime male field hands age 18–30 (Carter et al., 2006, Table Bb210). bOfficer and Williamson (2012) annual index (1860 = 100) based on daily and monthly payroll records for common or unskilled labor, 1800–1824 data from David and Solar (1977), 1824–1860 from Margo (2000). cDecennial estimates of cotton output per slave (Olmstead and Rhode, 2005) interpolated annually and multiplied by annual wholesale cotton prices (Carter et al., 2006, Table Cc222). dDecennial estimates of total sales and consumption of farm gross product minus slave produced crops (Towne and Rasmussen, 1960) divided by total farm labor force (Weiss, 1992) minus slaves in agriculture (Weiss, 1986), interpolated annually. eAnnual index of industrial production (Davis, 2004) divided by interpolated non-farm labor force (Carter et al., 2006, Table Ba829–830). fFrom manuscript census (Carter et al., 2006, Table Bb214). gMcClelland and Zeckhauser’s estimate (ibid., Table Ad17). hDavid and Solar (1977, Table 1, 1860 = 100). View Large Table B.1. Descriptive statistics Mean SD N Min Max Average slave price 1804–1861*a 832.24 264.39 58 504 1564 Wage index for common labor 1800–1861b 80.45 12.96 61 57 111 Value productivity of slaves (cotton) 1800–1861*c 119.75 41.57 61 55.26 223.1 Value productivity of free farmers 1800–1861*d 236.77 28.53 61 197.66 289.75 Index of physical productivity of industrial labor 1800–1861e .021 .006 61 .013 .036 Slave population 1804–1861 (millions)f 2.25 0.9 58 1 4.04 Net free immigration 1800–1860 (thousands)g 108.99 88.93 60 2.5 420.29 Consumer price index 1800–1861h 28.28 122.74 61 89 211 Mean SD N Min Max Average slave price 1804–1861*a 832.24 264.39 58 504 1564 Wage index for common labor 1800–1861b 80.45 12.96 61 57 111 Value productivity of slaves (cotton) 1800–1861*c 119.75 41.57 61 55.26 223.1 Value productivity of free farmers 1800–1861*d 236.77 28.53 61 197.66 289.75 Index of physical productivity of industrial labor 1800–1861e .021 .006 61 .013 .036 Slave population 1804–1861 (millions)f 2.25 0.9 58 1 4.04 Net free immigration 1800–1860 (thousands)g 108.99 88.93 60 2.5 420.29 Consumer price index 1800–1861h 28.28 122.74 61 89 211 *Yearly averages in current dollars. aEngerman’s annual price for prime male field hands age 18–30 (Carter et al., 2006, Table Bb210). bOfficer and Williamson (2012) annual index (1860 = 100) based on daily and monthly payroll records for common or unskilled labor, 1800–1824 data from David and Solar (1977), 1824–1860 from Margo (2000). cDecennial estimates of cotton output per slave (Olmstead and Rhode, 2005) interpolated annually and multiplied by annual wholesale cotton prices (Carter et al., 2006, Table Cc222). dDecennial estimates of total sales and consumption of farm gross product minus slave produced crops (Towne and Rasmussen, 1960) divided by total farm labor force (Weiss, 1992) minus slaves in agriculture (Weiss, 1986), interpolated annually. eAnnual index of industrial production (Davis, 2004) divided by interpolated non-farm labor force (Carter et al., 2006, Table Ba829–830). fFrom manuscript census (Carter et al., 2006, Table Bb214). gMcClelland and Zeckhauser’s estimate (ibid., Table Ad17). hDavid and Solar (1977, Table 1, 1860 = 100). View Large Table B.2. First-stage regression of real wages on productivity of free farmers (1860 dollars) OLS EXPLANATORY VARIABLES (1) (2) (3) Instrument: Productivity of free farmersa 0.330*** 0.299*** 0.186*** (0.022) (0.025) (0.067) Net immigrationb 0.032*** (0.010) Productivity of free farmersa t+1 0.066 (0.050) Productivity of slaves (cotton)a 0.037 0.028 (0.025) (0.027) Acres of federal land soldb -.0001 -.00006 (.0002) (.0001) Growth of the slave population -10.78 -7.483 (6.964) (6.064) Constant 2.54 30.61 30.11 (4.764) (23.40) (20.74) Observations 57 56 55 Centered R-squared 0.811 0.850 0.863 OLS EXPLANATORY VARIABLES (1) (2) (3) Instrument: Productivity of free farmersa 0.330*** 0.299*** 0.186*** (0.022) (0.025) (0.067) Net immigrationb 0.032*** (0.010) Productivity of free farmersa t+1 0.066 (0.050) Productivity of slaves (cotton)a 0.037 0.028 (0.025) (0.027) Acres of federal land soldb -.0001 -.00006 (.0002) (.0001) Growth of the slave population -10.78 -7.483 (6.964) (6.064) Constant 2.54 30.61 30.11 (4.764) (23.40) (20.74) Observations 57 56 55 Centered R-squared 0.811 0.850 0.863 Autocorrelation robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 aValue of output in 1860 dollars. bThousands. View Large Table B.2. First-stage regression of real wages on productivity of free farmers (1860 dollars) OLS EXPLANATORY VARIABLES (1) (2) (3) Instrument: Productivity of free farmersa 0.330*** 0.299*** 0.186*** (0.022) (0.025) (0.067) Net immigrationb 0.032*** (0.010) Productivity of free farmersa t+1 0.066 (0.050) Productivity of slaves (cotton)a 0.037 0.028 (0.025) (0.027) Acres of federal land soldb -.0001 -.00006 (.0002) (.0001) Growth of the slave population -10.78 -7.483 (6.964) (6.064) Constant 2.54 30.61 30.11 (4.764) (23.40) (20.74) Observations 57 56 55 Centered R-squared 0.811 0.850 0.863 OLS EXPLANATORY VARIABLES (1) (2) (3) Instrument: Productivity of free farmersa 0.330*** 0.299*** 0.186*** (0.022) (0.025) (0.067) Net immigrationb 0.032*** (0.010) Productivity of free farmersa t+1 0.066 (0.050) Productivity of slaves (cotton)a 0.037 0.028 (0.025) (0.027) Acres of federal land soldb -.0001 -.00006 (.0002) (.0001) Growth of the slave population -10.78 -7.483 (6.964) (6.064) Constant 2.54 30.61 30.11 (4.764) (23.40) (20.74) Observations 57 56 55 Centered R-squared 0.811 0.850 0.863 Autocorrelation robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 aValue of output in 1860 dollars. bThousands. View Large Table B.3. Instrumental variable regression of slave price on predicted wages (1860 dollars) IV-2SLS EXPLANATORY VARIABLES (1) (2) Predicted real wage 15.71*** 13.12*** (2.372) (2.334) Productivity of slaves (cotton)a 1.160 (0.725) Acres of federal land soldb 0.0053 (0.0047) Growth of the slave population -268.4** (101.2) Constant -364.2** 302 (156.5) (380) Observations 57 56 Centered R-squared 0.697 0.824 IV-2SLS EXPLANATORY VARIABLES (1) (2) Predicted real wage 15.71*** 13.12*** (2.372) (2.334) Productivity of slaves (cotton)a 1.160 (0.725) Acres of federal land soldb 0.0053 (0.0047) Growth of the slave population -268.4** (101.2) Constant -364.2** 302 (156.5) (380) Observations 57 56 Centered R-squared 0.697 0.824 Autocorrelation robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 aValue of output in 1860 dollars. bThousands. View Large Table B.3. Instrumental variable regression of slave price on predicted wages (1860 dollars) IV-2SLS EXPLANATORY VARIABLES (1) (2) Predicted real wage 15.71*** 13.12*** (2.372) (2.334) Productivity of slaves (cotton)a 1.160 (0.725) Acres of federal land soldb 0.0053 (0.0047) Growth of the slave population -268.4** (101.2) Constant -364.2** 302 (156.5) (380) Observations 57 56 Centered R-squared 0.697 0.824 IV-2SLS EXPLANATORY VARIABLES (1) (2) Predicted real wage 15.71*** 13.12*** (2.372) (2.334) Productivity of slaves (cotton)a 1.160 (0.725) Acres of federal land soldb 0.0053 (0.0047) Growth of the slave population -268.4** (101.2) Constant -364.2** 302 (156.5) (380) Observations 57 56 Centered R-squared 0.697 0.824 Autocorrelation robust standard errors in parentheses. *** p<0.01, ** p<0.05, * p<0.1 aValue of output in 1860 dollars. bThousands. View Large Bibliography Anderson , R. and Gallman , R . 1977 . 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Cambridge Journal of Economics – Oxford University Press
Published: Feb 17, 2018
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