Runaway slaves constituted another major problem, about which Southerners complained constantly. John Hope Franklin and Loren Schweninger (1999, p. 282) have estimated that total runaways exceeded 50,000 annually. This large number, however, includes short-term absences and unsuccessful attempts, as well as successful escapes to the free states or beyond. Franklin and Schweninger acknowledge that "most runaways remained out only a few weeks or months." The U.S. Censuses for 1850 and 1860, therefore, provide probably the most accurate glimpse at the problem of permanent runaways and--as several authors indicate (Hummel 2001, pp. 268-71; Gara 1961, p. 38, and 1964, p. 230, n. 4)--a lower bound on its magnitude. This source ([U.S. Census Office, 1860 Census], p. 338) indicates a minimum of about a thousand slaves fled per year: or more precisely, **1,011 in 1850 and 803 in 1860**.

At first glance, these numbers seem small. The total U.S. slave population in 1850 was 3.2 million, meaning only 0.03 percent permanently escaped, while in 1860 slaves numbered nearly 4 million, with only 0.02 percent fleeing north. Slaveholders would tend to discount the value of any slave by a premium proportionate to the probability of losing their property. The higher the probability, the lower the price of the slave, other things equal. As a rough approximation (Hummel, 2001, pp. 406-11), if the annual risk of permanent escape remained constant at p, and the annual interest rate was 10 percent, then a slave's price will fall from PV0, its value with no risk of running away, to PVp, as in formula (1):

(1) PVp = (1 - p) PV0 (.10)/(.10 + p).

Table 1 illustrates how changes in this probability affect the price of a prime male hand whose value was $1,200 without any risk of permanent flight (p = 0). If only one out of every ten thousand prime hands ran away permanently (p = 0.0001, or 0.01 percent), the impact on average price would have been negligible. PVp would have fallen by merely $1. Raise the probability to one out of thousand (p = 0.001), and now average price will fall by $13, or a little over 1 percent. Assuming that one out of every hundred hands permanently ran off each year (p = 0.01), the effect becomes quite significant. PVp falls to $1,080, or by 10 percent. When the annual probability went up to one out of twenty (p = 0.05), the price would have dropped to $760, or by 37 percent. And if the probability ever reached one of ten (p = 0.10), the value of all remaining male hands would have plummeted by over half to $540.