Working Paper: NBER ID: w29519
Authors: Sergei Bazylik; Magne Mogstad; Joseph P. Romano; Azeem Shaikh; Daniel Wilhelm
Abstract: It is common to rank different categories by means of preferences that are revealed through data on choices. A prominent example is the ranking of political candidates or parties using the estimated share of support each one receives in surveys or polls about political attitudes. Since these rankings are computed using estimates of the share of support rather than the true share of support, there may be considerable uncertainty concerning the true ranking of the political candidates or parties. In this paper, we consider the problem of accounting for such uncertainty by constructing confidence sets for the rank of each category. We consider both the problem of constructing marginal confidence sets for the rank of a particular category as well as simultaneous confidence sets for the ranks of all categories. A distinguishing feature of our analysis is that we exploit the multinomial structure of the data to develop confidence sets that are valid in finite samples. We additionally develop confidence sets using the bootstrap that are valid only approximately in large samples. We use our methodology to rank political parties in Australia using data from the 2019 Australian Election Survey. We find that our finite-sample confidence sets are informative across the entire ranking of political parties, even in Australian territories with few survey respondents and/or with parties that are chosen by only a small share of the survey respondents. In contrast, the bootstrap-based confidence sets may sometimes be considerably less informative. These findings motivate us to compare these methods in an empirically-driven simulation study, in which we conclude that our finite-sample confidence sets often perform better than their large-sample, bootstrap-based counterparts, especially in settings that resemble our empirical application.
Keywords: confidence sets; ranking; political parties; multinomial data
JEL Codes: C12; C14; D31; I20; J62
Edges that are evidenced by causal inference methods are in orange, and the rest are in light blue.
| Cause | Effect |
|---|---|
| constructed finite-sample confidence sets for the ranks of political parties (D79) | are informative across the entire ranking (A14) |
| constructed finite-sample confidence sets (C46) | maintain coverage probability at or above the desired nominal level (C41) |
| constructed finite-sample confidence sets (C46) | are more informative than bootstrap-based confidence sets (C11) |
| constructed finite-sample confidence sets (C46) | produce shorter intervals compared to bootstrap sets (C59) |
| bootstrap methods (C51) | can yield shorter confidence sets (C51) |
| finite-sample methods (C51) | are generally superior to bootstrap methods (C52) |