The Political Economy of Political Philosophy: Reply
回应Cobb和Hagemann对作者早期模型的批评，指出他们用差分法处理跨州参议员数据存在两个缺陷：差分顺序任意导致估计冲突，且在某些理想情况下无法得到估计。
our earlier article, we developed model which supported the hypothesis that the proportion of the staff budget which each senator from 48 states returned unspent 1978 was significantly influenced by their political philosophy: conservatives, on average, returned higher proportion than liberals. their comment, Steven Cobb and Robert Hagemann emphasize that some state may have been omitted and, as result, the coefficients estimated from our model may be biased. They develop an approach intended to correct this, that is, a regression estimated on differences between state senators will automatically purge the regression of all state effects (p. 524), and find that the relationship between the proportion returned and political philosophy is statistically significant. Although concern about omitted is justified, there are two shortcomings with the approach that Cobb and Hagemann employ that deserve mention. First, differencing is an appropriate technique to use with cross-section data, as Carl Christ observed, because the cross-section has no analogy to the value the time series case (1966, p. 210).1 time-series, the data are uniquely ordered, but this is true cross section. The data which Cobb and Hagemann difference are cross section of two on senators within each of 48 states. The crux of the issue is which senator is subtracted from which within each state, because in economics there is usually no meaningful way to order ... cross-section observations (p. 209).2 As an illustration, consider three states (A, B, C), each with two senators (denoted by subscripts). Several differencing schemes can be proposed which generate for each state: (A,-A2),(Bj-B2), (Cl-C2); (A1-A2), (B1-B2), (C2-C1); and, (A1-A2), (B2-BB), (C2-C1), among others. Each scheme generates different set of values for the dependent variable and for the independent variable measuring political philosophy. The different data sets will produce confficting estimates of the coefficients their model and choosing among them is necessarily arbitrary. When all permutations and combinations among 48 states are considered, Cobb and Hagemann's approach produces hundreds of different data sets that yield hundreds of conflicting estimates for the same parameters. Of course, the within states can be ordered by some rule (political philosophy, proportion returned unspent, tenure office, age, etc.),3 but the choice of rule is itself arbitrary. Second, for purposes of exposition, consider the where senators are either extreme liberals or conservatives; liberals spend all of their staff budgets, whereas conservatives spend none of their funds; also, every state has two senators with the same political philosophy. this ideal case, our model will verify that political philosophy determines spending behavior, but the model presented by Cobb and Hagemann will not, for when differences are taken, the value of the dependent variable (and the independent variable for political philosophy) for every observation is identically zero and no empirical estimates can be obtained whatsoever. One *George Mason University, Fairfax, VA 22030. Research support provided by the Sarah Scaife Foundation and the Earhart Foundation is gratefully acknowledged. 'In strict sense, Cobb and Hagemann are differencing, employing lagged values. However, Christ explicitly points out that ...using first differences as is equivalent to using variables (p. 177). 2Christ adds that In pure cross-section modelthe typically have no natural order, though certain cases we can imagine putting them the order of size, social status, or distance from some focal point, or what not (p. 209, emphasis added). 3If political philosophy is used, the question then becomes which measure of political philosophy. We used three: the American Conservative Union, the AFLCIO, and the Americans for Democratic Action rankings of senators.