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John H. Kagel, Raymond C. Battalio, Howard Rachlin, and Leonard Green, "Demand Curves for Animal Consumers," Quarterly Journal of Economics 96 (Feb. 1981): 1—16; John H. Kagel, Raymond C. Battalio, Howard Rachlin, and Leonard Green, "Experimental Studies of Consumer Demand Behavior Using Laboratory Animals," Economic Inquiry 13

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(Jan. 1975): 22^-38; Raymond C. Battalio, John H. Kagel, and Owen R. Phillips, "Optimal Prices and Animal Consumers in Congested Markets," Economic Inquiry 24 (Apr. 1986): 181-93; Todd Sandler, "Optimal Prices and Animal Consumers in Congested Markets: A Comment," Economic Inquiry 25 (Oct. 1987): 715-20; Raymond C. Battalio, John H. Kagel, and Owen R. Phillips, "Optimal Prices and Animal Consumers in Congested Markets: A Reply," Economic Inquiry 25 (Oct. 1987): 721-22; and Raymond C. Battalio, John H. Kagel, Howard Rachlin, and Leonard Green, "Commodity Choice Behavior with Pigeons as Subjects," Journal of Political Economy 84 (Feb. 1981): 116-51.

94. William M. Landes, "An Economic Study of U.S. Aircraft Hijacking, 1961-1976," Journal of Law and Economics 21 (Apr. 1978): 1—29.

95. Alfred Blumstein and Daniel Nagin, "The Deterrent Effect of Legal Sanctions on Draft Evasion," Stanford University Law Review 28 (1977): 241—76.

96. For a particularly well-done piece that uses data from another country, see Kenneth Wolpin, "An Economic Analysis of Crime and Punishment in England and Wales, 1894-1967," Journal of Political Economy 86 (1978): 815-40. For a recent survey of papers in this area, see Isaac Ehrlich, "Crime, Punishment, and the Market for Offenses," Journal of Economic Perspectives 10 (Winter 1996): 43-67.

97. Alfred Blumstein, Jacqueline Cohen, and Daniel Nagin, eds., Deterrence and Incapacitation: Estimating the Effects of Criminal Sanctions on Crime Rates (Washington, DC: National Academy of Sciences, 1978), pp. 4, 7. Economists have responded to this report; see Isaac Ehrlich and Randall Mark, "Fear of Deterrence: A Critical Evaluation of the 'Report of the Panel on Research on Deterrent and Incapacitation Effects,'" Journal of Legal Studies 6 (June 1977): 293-316.

98. Wallace P. Mullin, "Will Gun Buyback Programs Increase the Quantity of Guns?" Michigan State University working paper (Mar. 1997), and Martha R. Plotkin, ed., Under Fire: Gun Buy-Backs, Exchanges, and Amnesty Programs (Washington, DC: Police Executive Research Forum, 1996).

CHAPTER TWO

1. The Supreme Court Justices would not uphold broad protections for gun ownership "if they thought blood would flow in the streets." This point was made by Professor Daniel Polsby in a talk given at the University of Chicago, February 20,1997. As he points out, the Supreme Court would not have allowed the publication of the Pentagon Papers, despite the arguments about the freedom of the press, if it had posed a severe military risk to the United States. It is not the role of this book to debate the purpose of the Second Amendment. However, the argument that the Second Amendment implies broad protection of gun ownership seems quite strong. William Van Alstyne argues that the reference to a "well-regulated Militia" refers to the "ordinary citizen" and that it was emphatically not an allusion to "regular armed soldiers." It was ordinary citizens who were to bring their own arms to form an army when the Republic was in danger. The amendment was viewed as the ultimate limit on a government's turning against the will of the people. See William Van Alstyne, "The Second Amendment Right to Arms," Duke Law Review 43 (Apr. 1994): 1236-55.

2. The opposite of endogenous is exogenous. An exogenous change in something is an independent change, not a response to something else. In reality, almost everything is to some extent related to something else, so the distinction between exogenous and endogenous is a matter of degree. Since models and statistical methods must put a limit on how much to include, some variables will always be treated as "exogenously given" rather than dependent on other variables. For the social sciences, this is a constant headache. Virtually any study is open to the criticism that "if variable X depends upon variable

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Y, your results are not necessarily valid." In general, larger studies that rely on more data have better chances of reliably incorporating more relationships. Part of the process of doing research is determining which relationships may raise important concerns for readers and then attempting to test for those concerns.

3. With purely cross-sectional data, if one recognizes that differences may exist in crime rates even after all the demographic and criminal-punishment variables are accounted for, there are simply not enough observations to take these regional differences into account. One cannot control for more variables than one has observations to explain.

The problem with time-series data is the same. Time-series studies typically assume that crime follows a particular type of time trend (for example, they may simply assume that crime rises at a constant rate over time, or they may assume more complicated growth rates involving squared or cubic relationships). Yet almost any crime pattern over time is possible, and, as with cross-sectional data, unexplained differences over time will persist even after all the demographic and criminal-punishment variables are accounted for. Ideally, one could allow each year to have a different effect, but with time-series data we would again find that we had more variables with which to explain changes than we had observations to explain.

4. Gary Kleck and E. Britt Patterson, "The Impact of Gun Control and Gun-Ownership Levels on Violence Rates," Journal ofQuantitative Criminology 9 (1993): 249—87.

5. David McDowall, Colin Loftin, and Brian Wiersema, "Easing Concealed Firearm Laws: Effects on Homicide in Three States," Journal of Criminal Law and Criminology 86 (Fall 1995): 193-206.

6. Arthur L. Kellermann, et al., "Gun Ownership as a Risk

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