Legislative Context , Legislator Quality and CampaignContributionsbyWalter

Legislative Context, Legislator Quality and Campaign Contributions We introduce a simple theoretical model of the relationship between the campaign contributions a legislator receives from a PAC and the amount of \service" the legislator provides to the PAC, a key assumption being that the marginal cost of service decreases as the quality of the legislator increases. Optimal solution of the constrained optimization problem that each PAC faces in allocating its campaign contributions among legislators implies a conditional two-limit tobit model for the relationship between contributions and aspects of the quality of each legislator. The constraints arise because PAC contributions must be positive but no greater than a legally limiting value and because each PAC's budget for contributions is nite. We extend the tobit model to support pooling data from several similar PACs. We estimate the empirical model using data from the U.S. House of Representatives. The fact that optimal PAC behavior implies censoring suggests that it is usually inappropriate to aggregate contributions from di erent PACs; but pooling can work well. We introduce a model of PACs' portfolio choices that explains how PACs allocate their campaign nance resources among House members. The key formal innovation in our approach is that we derive an empirical model of PAC campaign contributions directly from an explicit model of optimizing behavior subject to price and budget constraints, given each PAC's judgment of the quality of each legislator. The result is a particular form of a two-limit tobit model. We propose a method by which data from di erent PACs that are assumed to be similar in their appraisals of legislators' quality may be pooled to estimate the e ects that observed attributes of quality have on contributions. The pooling method is compatible with our model of optimizing behavior by each PAC, in a way that a method based on aggregating contributions data from the PACs would not be. We use our pooling method to analyze contributions to House incumbents during the 1991{92 House campaign period by a collection of telecommunications company PACs. In representing contributions as conditional on institutional attributes of each legislator (such as committee memberships) and on selected aspects of the election in each legislator's district, our approach to measuring each legislator's quality is similar to models used in numerous other studies (e.g., Gopoian, Smith and Smith 1984; Grier and Munger 1991, 1993; McCarty and Rothenberg 1996, 2000; Milyo 1997; Poole and Romer 1985; Stratmann 1998). An innovation in our data speci cations is that we use information about legislators' subcommittee memberships and chairmanships in a systematic way to augment the usual collection of simple dummy variables that represent committee memberships. Our model is based on the idea that each PAC uses its campaign contributions to purchase some amount of what we call \service" from each legislator. The PAC maximizes the total amount of service it receives from all legislators, subject to a budget constraint and to a legally determined upper bound on the size of each contribution (necessarily nonnegative) given to each legislator. The PAC may pay nothing to a legislator and hence receive no service. We intend the concept of service that we have in mind to be at once comprehensive and elemental. It is intended to be a composite of expectations a PAC has for actions a legislator may take to do such things as vote in a way the PAC would like, provide access, perform district service, intervene with an executive agency or state-level government or political actors, and so forth. We do not intend to suggest that the relationship between PACs and legislators is based on a strict|or even a weak|quid pro quo. A contribution increases the PAC's expectation that something good for the PAC will be forthcoming from the legislator who receives the contribution. The increased expectation may re ect an increase in the probability with which the PAC believes a favorable discrete action will occur, an increase in the value of some event the probability of which does not change, or a continuous increase in the value or amount of some continuous process. We do not distinguish among these or other possible interpretations of the service the PAC's contribution is buying.1 We do not model strategic interaction between PACs and legislators, nor among PACs. We treat each PAC as acting independently of every other PAC, while legislators are reduced to reaction functions. We recognize that such an approach may be subject to numerous and serious limitations. Our justi cation is the thought that the very general optimizing model we use may apply as a kind of nal constraint on a PAC's contributions in a wide array of strategic contexts. We do not know yet whether that idea will ultimately be supportable. We also say nothing about the timing of a PAC's contributions. All of a PAC's contributions to House members are considered to be decided simultaneously and paid at once. With service being conceived in such a broad way, we do not expect it to be observable. But one of our primary goals is to obtain an empirical model that it is feasible to estimate and test. 1This implies that we are implicitly assuming risk neutrality for all interpretations that involve a PAC's buying bundles of uncertain events. 1 A constraint on our model is therefore that the model must imply relationships that are de ned directly between contributions and the quality that each PAC attributes to each legislator. According to a de nition of quality that we stipulate, we can observe attributes of quality su cient to support useful statistical analysis. Quality and Optimal Contributing Members of Congress do not have equal abilities to secure service on behalf of PACs. For example, the legislator most able to in uence a regulatory agency may be the chairman of the committee that oversees that agency. An arbitrary member of Congress may attempt to provide such service, but the expected probability of a successful outcome would be lower|perhaps vastly lower. Institutional positions that a ect or signal a legislator's ability include committee assignments, seniority, leadership positions and membership in the majority party. Electoral conditions or constituency constraints, legislator ideology, the political environment or other considerations may also be pertinent. Some legislators are not able to provide certain kinds of service at all. We may think of such limitations as de ning an upper bound on the amount of service each member is able to supply any particular PAC. The bound for each legislator with respect to each PAC is jointly determined by the legislator's resources and the speci c bundle of service demanded by the PAC. Among legislators who are able to supply a given amount of service, some are able to do so at lower cost (Denzau and Munger 1986). If the marginal cost of providing service determines the price of a contribution from a PAC, then for any amount of service the PAC would prefer to purchase the service from the low-cost legislator. We de ne the concept of a legislator's quality to encompass both the upper bound on the total amount of service the legislator can supply to a PAC and the cost at which the legislator can supply any amount of service up to that maximum. To say that one legislator has higher quality than another is to say both that the former legislator can supply more service than the latter can do and that the former can supply any positive amount of service at a lower cost than the latter can do. Given a legislature composed of members of heterogenous quality, a PAC that has a limited budget for service has to decide how to allocate its resources among them. Should the PAC buy only from high quality legislators, perhaps only the highest one? Or would the PAC do better to buy from several legislators of low quality? Using standard methods for constrained nonlinear optimization, we show that a PAC that allocates its budget optimally in order to maximize the amount of service it obtains makes purchases from all legislators who have quality above a certain threshold value. The PAC buys service from each legislator in amounts that equate the marginal costs of service from the legislators. The exceptions to the equal-marginals rule are legislators for whom the price implied by that rule is greater than the maximum contribution allowed by law. To such legislators the PAC pays that maximum amount. General Form of the Theoretical Model Let pi denote the price (i.e., contribution) paid by a PAC to legislator i, i = 1; : : : ; m, for service si, where si 0 and 0 pi hip, with p > 0 being the upper bound on any PAC's total contributions to any one legislator in a single election and hi being the number of elections for i.2 Each legislator 2Notice that our \price" pi corresponds to the total amount paid for service si, not the amount paid for a unit of service. Below we derive the marginal cost of service given optimal behavior by the PAC (for unconstrained contributions the marginal cost of service from legislator i is ~ i). Regarding the construction hip, U.S. federal election law has for many years allowed most PACs to contribute up to $5000 per election to each candidate. The primary, general election and any runo each counts as a separate election. 2 has a quality value qi > 0 such that si < qi. We assume the relationship according to which each legislator supplies service as a function of the legislator's quality and of the price the PAC pays to have the following properties. Assumption 1 (A1) Bijective Mapping: For each qi > 0, every price pi 0 buys a unique amount of service si = s(pi; qi), and every service value, 0 si < qi, may be bought for a unique price pi = p(si; qi). Assumption 2 (A2) Increasingness: si is strictly increasing in pi. Together with the stipulation that pi and si have lower