An Examination of The Micro Foundations of Aggregate Public Opinion

One of the best-known findings in the public opinion literature is that individual responses to survey questions, by and large, both exhibit little constraint and are highly unstable over time. One response to this bleak finding has been to search for coherence and stability at the aggregate level. Scholars who adopt this approach — most notably Page and Shapiro (1992) — argue that though most individuals are poorly informed about politics and may have unstable attitudes, the “miracle” of aggregation produces rational collective opinions which are remarkably stable over time and respond in predictable ways to external events. But while aggregation may induce cohesion, such stability may come with a price. Specifically, the aggregation of the opinions of individuals may introduce two forms of bias into the aggregate signal. The first relates to an aggregation process which may give greater weight to individuals — and groups — with less variant opinions. This result is potentially problematic from a normative standpoint because opinion variance could be a function of education, political information, and even political attitudes. The second form of bias relates to the preferences of those individuals who abstain from public opinion questions. The same factors that lead individuals to become more variant may also increase the probability that they will abstain from issue placement questions. If those individuals who “go missing” are — like their highly variant brethren — more likely to hold opinions of a particular direction, then the aggregated public opinion signal may again be biased in the direction of those with more stable opinions, a phenomenon I term “exclusion bias.” In this paper, I gauge the degree of inter-group bias introduced through the aggregation process, using data from the 1992 and 1996 National Election Studies (NES) concerning questions of social welfare policy. To assess aggregation bias, I first estimate models of opinion preference using a heteroskedastic probit model. I then use the results of those models to simulate the “errorfree” opinions of both the aggregate sample and among subgroups defined by politically relevant variables. Next, I compare these simulated opinions with aggregate public frequencies predicted by a homoskedastic probit model, to gauge the degree of bias in aggregate public opinion. While the results of these analyses are inconclusive, there are indications that the aggregation process may induce a pro-conservative bias to collective public opinion. To gauge the degree of “exclusion bias,” I estimate models of selection and run simulations to gauge differences between the opinions of those who abstain from the issue position questions and those who answer the seven-point scales. As I demonstrate below, this “exclusion bias” — a phenomenon to this point ignored in the political science literature — is a notable source of bias in aggregate public opinion, as issue “placers” tend to hold more conservative attitudes than those who abstain from the social welfare policy placement scales. THEORY From the early days of opinion polling, survey researchers recognized the potential for polls to give the mass public a voice in the political process. For example, Gallup and Rae (1940) touted the virtues of polls as a means for political elites to assess the “mandate of the people” (see also Brehm 1993). Polls hold special appeal as a form of political participation because, unlike other forms of participation, polls appear to be free of a compositional bias which gives greater voice to those rich in participatory resources, such as education and disposable income (see Verba, Schlozman, and Brady 1995). As Verba (1996) writes, “sample surveys provide the closest approximation to an unbiased representation of the public because participation in a survey requires no resources and because surveys eliminate the selection bias inherent in the fact that participants in politics are self-selected.” 1 This intuition has proven to be valuable because public opinion polls have become a significant source of information for elites about what the “public” thinks about the issues of the day (see Brehm 1993, Herbst 1993; for a more cautionary note, see Ginsberg 1986). Polls are no longer the sole province of academics and journalists. Politicians and interests groups are now both producers and consumers of political polls. Public opinion surveys then are not just a form of participation in theory; the large sums of money politicians are willing to pay to underwrite polls indicates that they are being actively consumed by the political elite. Recent empirical work suggests that not only are polls consumed by elites, but that public opinion appears to play a role in determining policy direction. In particular, defense spending levels (Bartels 1991) and government expenditures more generally (Stimson, MacKuen, and Erikson 1995) both appear to be driven, in part, by the public preferences regarding the proper administration of those policies. But while public opinion polls are, in theory as well as in practice, a potentially consequential form of mass input in the political process, a number of concerns relating to the quality of individual opinion remain. If 30 years of public opinion research has demonstrated one thing, it is that individuals’ opinions, by-and-large exhibit minimal over-time stability and little in the way of coherent grounding principles. Even Lane (1962), often heralded as the patron saint of individual coherence, concedes that people tend to morselize their thinking about politics. While Converse’s (1970) “black-and-white” model — which posits that large segments of the population hold “nonattitudes,” effectively flipping a mental coin when answering survey questions — is no longer universally accepted, even the most sophisticated recent accounts of opinion formation (see, for example, Zaller and Feldman 1992; Zaller 1992; Chong 1993) still present a rather messy view of public opinion at the individual level. At best we can say that people “muddle through” the political cognition process. The question then becomes whether the answers to survey questions are of any value and should be given heed by policy-makers. As Achen (1975) notes, if vast segments of the population do not hold real attitudes concerning the pressing issues of the day, then “democratic theory looses its starting point.” One solution to this normative conundrum has been to change the level of analysis. While individual opinion, taken as a whole, may demonstrate little rationality or coherence, at the macrolevel, things look quite different. Page and Shapiro (1992) demonstrate that collective opinion across a broad range of issues is largely stable and, when it does move, does so in sensible ways, responding to identifiable external events. Thus, while it might be troubling to give currency in the policy-making process to opinions that even Page and Shapiro concede may be “shallow and unstable,” in the aggregate, public opinion may reflect the true collective voice of the American public. In sum, by moving the frame of analysis from the individual to the aggregate level, Page and Shapiro cull macro-level stability and “rationality” from micro-level incoherence.1 But the story, I argue, does not end here. Though Page and Shapiro’s results may paint a more reassuring picture of public opinion, there is a real question regarding how aggregate public opinion is constructed and what information might be lost in the aggregation process that Page and Shapiro largely assume away. 1 Another line of work has developed in response to Converse’s bleak findings, which argues that access to widely available information shortcuts — or “cues and heuristics” — allow poorly-informed individuals to emulate the behavior of well-informed individuals (see Popkin 1993; Lupia 1994). 2 Response Dispersion in Public Opinion Conventional theories of public opinion have treated the survey response as the product of individuals’ attempts to reveal their fixed preference on a given policy issue. Controversies in the literature, therefore, have traditionally centered on how well the survey instrument enables people to translate their preferences into survey responses and whether the over-time attitude instability identified by Converse was due to vague minds (Converse 1964) or vague questions (Achen 1975). Recently, however, a more fluid view of the survey response has emerged, based on theories of preference construction developed in cognitive psychology (see, for example, Slovic 1995). This view, advanced most forcibly by Zaller and Feldman (Zaller and Feldman 1992; Feldman 1989; Zaller 1992; see also Iyengar and Kinder 1987, Chong 1993; 1996), argues that “individuals do not typically possess ‘true attitudes’ on issues, as conventional theorizing assumes, but a series of partially independent and often inconsistent ones.” (Zaller 1992, p. 93). Thus, instead of viewing the survey response as a (potentially imperfect) point estimate of an individual’s fixed preference, Zaller and Feldman argue that answers to survey questions should be viewed as a realization of a stochastic draw from an individual’s underlying response distribution, which itself is an aggregation across one’s potentially diverse feelings — or “considerations” — concerning political issues. When survey responses are viewed in this light, what is important is not merely an individual’s expressed opinion, but also the variance of those expressed opinions. Put another way, to fully understand individual opinion, we must be concerned not only with the mean of opinion, but also the range of individuals’ spread of opinion, or degree of response dispersion. Alvarez and Brehm (1995, 1997a, 1997b) discuss two sources of this response variability; uncertainty and ambivalence. Ambivalence, Alvarez and Brehm assert, is a reflection of the simultaneous existence, within a particular individual, of two or more conflicting “core beliefs,”— those values which are at the root of how individuals come to understand politics. Because such discord is difficult to resolve, core belief friction leads to response instability, as individuals vacillate back and forth along the fault-line of the values called into conflict. For example, Alvarez and Brehm (1995) find that those respondents who can articulate both reasons for and against “hard” abortion questions — such as whether abortions should be allowed as a means of birth control — were more variant in their answers than those individuals who lined up firmly on one side of the controversy. Uncertainty, on the other hand, is driven by deficiencies in an individual’s knowledge about the particular subject area under consideration. “Uncertainty about public polices,” Alvarez and Brehm argue, “is a function of lack of information, either stemming from the respondent’s own personal information costs or in the transmission of information from elites to citizens.” (1997, p. 346). To this I would add that uncertainty could, in its extreme form, arise not only from poor information in a particular area of politics, but from an overall disengagement from the political system as a whole. The distinction between uncertainty and ambivalence drawn by Alvarez and Brehm is clearly important theoretically. As they note, “variation due to ill formed or uncertain responses indicts the respondent or the political process, while variability due to difficult choices and ambivalence identifies the very marrow of politics.” Thus, our understanding of the sources of response dispersion affects how we understand its consequences. In practice, however, it may be difficult to draw as clear a distinction as Alvarez and Brehm would like between the two forms of response variation. Uniformed respondents may be ambivalent and ambivalent respondents — even if highly informed about politics — may be “uncertain” where they stand on particular issues. 3 In fact, ambivalence and uncertainty may interact and reinforce each other. For example, Hochschild’s (1981) in-depth study of the beliefs of 28 residents of New Haven concerning issues of distributional justice found that individuals were able to make distinctions between contradictory beliefs, but reacted to such distinctions with uncertainty. Some respondents even manifested ambivalence as confusion, dissolving into incoherence when attempting to express their thoughts. Ambivalence resulting from conflict among core values, then, may lead to the type of inconsistency in opinion expression found by Alvarez and Brehm, but it can also lead to complete disengagement with those deeply held ideals or utter simply confusions (See Hochschild 1981, Chapter 8). This is not to say that Alvarez and Brehm’s approach is misguided. In fact, I would argue that the two-fold typology represents a rigorous ideal for analysis of response variation. However, in light of the conceptual difficulties in implementing these author’s design, I will, as a first cut at the problem, in this paper jointly consider uncertainty and ambivalence as determinants of response dispersion, without drawing firm distinctions between the two concepts.2 Future work will consider ways to disengage the two concepts and consider the implications for attitude aggregation of variance in individual response due to uncertainty against ambivalence. The Consequences of Uncertainty and Ambivalence While Alvarez and Brehm’s studies of the causes and consequences of uncertainty and ambivalence are interesting in their own right, these manifestations of underlying opinion variance also have implications for how we understand public opinion. Specifically, the phenomena identified above are substantively important because previous work has shown that ambivalence and uncertainty — and the combination of the two — may lead individuals to give unstable question answers or to abstain from “difficult” survey questions altogether. Bartels (1986) posits that respondents’ failure to place presidential candidates on various issue scales results from their extreme uncertainty concerning the true positions of those candidates. Bartels finds empirical support for this proposition in that his “uncertainty” measure — generated from the coefficient estimates of a probit equation predicting item response or nonresponse to the National Elections Study candidate placement scales — relates to vote choice in the way suggested by Enelow and Hinich’s (1981) extension of Shepsle’s (1972) model of spatial voting under uncertainty. Specifically he finds that, consistent with Enelow and Hinich’s model, voters dislike uncertainty and that uncertainty about candidates’ issue positions are important determinants of vote choice Bartels concern was in estimating the effects of uncertainty concerning candidate placement. However, his intuition and empirical findings of a link between item non-response and uncertainty are important and readily transferable to an understanding of how individuals come to answer survey questions about their own political attitudes. Other research has followed a similar vein but has more directly addressed the effects of internal respondent uncertainty and 2 Empirically, the distinction between uncertainty and ambivalence is not critical for the purposes of this paper. As I demonstrate below both uncertainty — as represented by low levels of political engagement — and ambivalence — represented by the existence of conflict between core values — lead individuals to be more variant in their answers to social welfare questions. More importantly for the purposes of this paper, both classes of variant individuals tend to the liberal end of the seven-point scales. Still, the distinction between uncertainty and ambivalence is important from a normative standpoint and will be examined in future work. 4 ambivalence. Hochschild (1981) found that, given the opportunity, people do not make simple definitive statements concerning the government’s proper role in ensuring the well being of the less fortunate. Instead, Hochschild’s respondents “shade, modulate, deny, retract, or just grind to a halt in frustration.” Individuals’ underlying conflict, Hochschild found, was manifest in two ways. First ambivalence or uncertainty led some individuals to equivocate when answering Hochschild’s questions. Second, in extreme instances where respondents’ internal conflict or uncertainty was sufficiently high, individuals abstained from answering the question altogether (see also Feldman and Zaller 1992). Finally, as discussed above, recent work by Alvarez and Brehm, indicates that ambivalence arising from core value conflict and uncertainty arising from differential levels of political information, are a significant source of heteroskedasticity in certain salient issues in politics, such as abortion policy and race policy (Alvarez and Brehm 1995, 1997). In sum, then, uncertainty and ambivalence and — in cases such as that examined by Hochschild, a combination of the two — may lead respondents to express more unstable opinions or, in extreme cases, to abstain from answering such “difficult” questions altogether. Both of these phenomena, which arise from a propensity for response dispersion, have implications for how we understand the political pulse of the nation, as reported in aggregate public opinion measures. Specifically, the aggregation of individual opinion may both (1) give greater weight to individuals and groups with less variant opinions and (2) ensure that the opinions of those variant individuals who do not respond to specific survey questions will “go missing” from the aggregate signal altogether. Below, I discuss the specific nature of these aggregation and exclusion effects and, more importantly, discuss conditions under which these effects may introduce a bias into our understanding of the nature and direction of aggregate public opinion. Aggregation Effects Discussing the formation of aggregate public opinion, Page and Shapiro draw an analogy between the measurement of the opinions of a single individual, with random error, over time and the measurement of the opinions of many individuals at one point in time. They argue that just as the central tendency of the opinion of one individual is revealed by measuring her opinion repeatedly over time, the “central tendency” of collective opinion can be discerned by aggregating the opinions of many individuals at one moment in time. But these two situations discussed by Page and Shapiro are, in fact, very different. In both cases, the aggregation of attitudes measured at several points — in the case of the single individual, across time; in the case of collective opinion, across space — produces a signal which appears more “rational” than the corresponding single-point measures. However, one important difference between the two scenarios laid out by Page and Shapiro remains: whereas the distribution of responses that one individual gives over time exhibit a constant variance, cross sectional data is often plagued by heteroskedasticity, arising from varying levels of ambivalence and uncertainty across the population, as discussed above. If such heteroskedasticity is significantly large, the “signal” measured by aggregate public opinion will not reflect the potential central tendency of public opinion. Instead, aggregate public opinion will be a weighted average of the opinions of individuals in the full population, with those individuals who hold stable attitudes — to use Converse’s (1990) parlance, those with a high “signal” to “noise” ratio — receiving a greater weight than other individuals with more variant opinions — those with a high “noise” to “signal” ratio. 5 Exclusion Effects Collective public opinion measures may also be contaminated by a second type of bias, related to the aggregation bias. As discussed above, the same factors which lead individuals to become more variant may also increase the probability that they will abstain from the issue placement questions. Thus, the opinions of those individuals with variant opinions might not only be washed out as noise in the aggregation process, but might be expunged from the sample altogether. In this way, the underlying preferences of potentially large segments of the population could be removed from the public opinion collectively. The Development of Bias These two processes by which the “variant” respondents are washed out of the aggregate public opinion signal could, under certain circumstances, carry serious normative implications. Specifically, these processes could introduce a compositional tilt into aggregate public opinion favoring those with less variant opinions, as the uncertain and ambivalent are, to use Converse’s (1990) term, “inadvertently disenfranchised.” One might argue that this state of affairs is perfectly acceptable. After all, perhaps the attitudes of those with more stable opinions should count more. For example, if response stability or the propensity to offer answers to survey questions is correlated with levels of political knowledge as they appear to be (Converse 1990; Feldman and Zaller 1992) then maybe it is a good thing that the highly informed speak with a louder voice than those disengaged from the political world. However, levels of political knowledge are not randomly assigned through the population. Instead, those high in political information levels also tend to be those individuals who have accumulated other sauce-economic resources (See Verba, Schlozman, and Brady 1995; Delli Carpini and Keeter 1996) Thus, if one’s level of political knowledge is correlated with opinion stability, then the opinions of those already rich in participatory resources (see Rosenstone and Hansen 1993; Verba, Schlozman, and Brady 1995) will be over-represented relative to society’s disadvantaged in the aggregate public opinion signal. Furthermore, as noted above, knowledge is not the only source of heterogeneity in the levels of uncertainty and ambivalence across the population. Both the probability of offering an opinion to an interviewer and heteroskedasticity in those opinions could also be related to the nature of opinion held by individuals. For example, work by Tetlock (1986) and Feldman and Zaller (1992) has demonstrated that liberals tend to be more conflicted — and therefore more variant — than conservatives in their opinions concerning social welfare policy. These results are again problematic because the process of collecting and aggregating attitudes could give those with certain types of opinions — for example, those with conservative opinions — in addition to certain classes of people, more say than others in determining the types of signals sent to government elites. This overrepresentation may be expressed as a form of bias, similar to that identified by Verba, Schlozman, and Brady (1995) in their discussion of political participation. Specifically, the differential weighting of the opinions of different segments of the population is problematic to the extent that those whose preferences and needs become visible to policy makers — here through public opinion polls — are unrepresentative in significant ways of those who are largely absent from the aggregate signal. 6 The degree of such bias in the aggregate public opinion signal is directly related to the strength of the link between opinion direction and opinion uncertainty and ambivalence. If the determinants of the opinion mean are the same as the determinants of response variance, then the potential for bias is great because the individuals with “noisy” opinions will tend to cluster toward one end of the opinion scale, while those with “clean” opinions will tend toward the other. If the two functions are independent, however, then there should be no systematic relationship between opinion direction and variance and bias should be minimal. Similarly, if the same factors that predispose a respondent to offer an answer to a survey question also push them to one end of the response scale, then the aggregate opinion measure will suffer from the incidental truncation of those individuals who would be otherwise predisposed to give survey answers on that end of the scale. To illustrate this proposition with a concrete example, I turn to a (simplified) scenario in which opinion concerning the capital gains tax is perfectly predicted by one’s income level. If high income respondents both are more likely to oppose a capital gains tax and, simultaneously, are less variant in their opinions regarding that issue, then the potential for an anti-tax bias in the aggregate public opinion signal is great because the supporters of such a tax are likely to get “washed out” of the aggregate signal due to their higher opinion variances and proportionately higher rates of itemnon response. Conversely, if income level affects the direction of opinion on the capital gains issue, but not the level of uncertainty and ambivalence, then the supporters of the capital gain tax are no more likely than the opponents of the tax to be diluted or removed from the sample of respondents who determine the shape of aggregate public opinion. Under these circumstances — where item non-response and opinion variance are unrelated to opinion direction — the threat of bias is eliminated. To assess the validity of my argument, in the next section I examine the nature of compositional bias in public opinion concerning social welfare policy issues, using data from the 1992 and 1996 National Election Studies (NES). I choose to examine two questions of social redistribution — the seven-point Jobs versus Standard of Living” and “Services and Spending” scales3 — because previous work (Hochschild 1981; Tetlock 1986; Feldman and Zaller 1992) suggests that these questions tap an area where response direction and response ambivalence will be driven by similar factors. For example, as noted above, Feldman and Zaller (1992) find that ambivalence and inconsistency in the areas of social welfare policy are not found with equal frequency in all segments of the population. Social welfare conservatives, they find, exhibit less value conflict than liberals because liberals must reconcile their humanitarian impulses with the conservative impulses of individualism and limited government, that are prevalent in American political culture. Thus, if I am to find the patterns of compositional bias which lead to the 3 Specifically the “Jobs and Standard of Living” question reads, “Some people feel the government in Washington should see to it that every person has a job and a good standard of living (Suppose these people are at one end of a scale, at point 1.) Others think the government should just let each person get ahead on their own (Suppose these people are at the other end, at point 7.) And, of course, some other people have opinions somewhere in between, at points 2,3,4,5, or 6. Where would you place yourself on this scale, or haven’t you thought much about it? (List 7-point scale). Similarly, the Services and Spending scale reads, “Some people think the government should provide fewer services even in areas such as health and education in order to reduce spending. (Suppose these people are at one end of a scale, at point 1.) Other people feel it is important for the government to provide many more services even if it means an increase in spending (Suppose these people are at the other end, at point 7.) And, of course, some other people have opinions somewhere in between, at points 2,3,4,5, or 6. Where would you place yourself on this scale, or haven’t you thought much about it? (List 7-point scale).” 7 overrepresentation of certain classes of individuals in the aggregate public opinion signal anywhere, I will surely find them in the realm of opinion concerning social welfare policy. In sum, then, an examination of the NES social welfare items seems an appropriate first cut into an examination of bias in aggregate public opinion. AGGREGATION BIAS To test my intuitions concerning the potential introduction of a pro-conservative compositional bias in aggregate public opinion concerning matters of social welfare policy, I ran a series of simulations using data from the 1992 and 1996 NES. Specifically, I first estimated heteroskedastic ordered probit models to obtain consistent estimates of the determinants of opinion on the seven-point NES issue scales. I then used these coefficients to simulate conditions under which opinion distributions collapse to the mean for all individuals in the sample. In this way, the ratio of “signal” to “noise” in opinion response can be held constant across individuals. Finally, I used these simulations to gauge the degree of bias in aggregate public opinion. Model Derivation As the first step in my simulation, I estimated a heteroskedastic ordered probit model of attitude choice. The heteroskedastic ordered probit is an extension of the ordered probit model, which is generally used when the dependent variable outcomes are (1) discrete and ordered, and (2) the difference between the adjacent points on the dependent variable scale are not necessarily equal (for example, the distance between a “2” and a “3” on the seven-point scale is not necessarily equal to the distance between a “4” and a “5”). (Green 1997, p. 926). The ordered probit model is built around a latent regression in the same manner as the binomial probit model, where the dependent variable y* is unobserved, but the realizations of the variable are observed. Specifically: y * = β ′x + ε and y is observed as follows: (1) y = 0 if y * ≤ 0 = 1 if 0 < y * ≤ µ 1 = 2 if µ 1 < y * ≤ µ 2 M (2) = J if µ J −1 ≤ y * where µj, (j = 1 ,2 , . . . , J) are unknown threshold parameters to be estimated along with β. If we assume that ε is normally distributed across observations, we arrive at the following choice probabilities for the seven-point scale dependent variables used in this paper:4 4 This derivation largely follows Alvarez and Brehm (1996) but draws also on Green (1995; 1997). 8  − Xiβ  P( yi = 0) = Φ   σi   µ − Xiβ  − Xiβ  P( yi = 1) = Φ 1  − Φ   σi   σi   µ − Xiβ   µ1 − Xi β  P( yi = 2) = Φ 2  − Φ  σi    σi  M (3)  µ − Xiβ  P( yi = 6) = 1 − Φ 5   σi  Here yi is the seven-point scale dependent variable, Xi, represents the variables in the choice function, β is the vector of coefficients on the variables in the choice modes, µj are the estimated thresholds between the choice categories and σi2 is the error variance (though the denominator of the probit choice function is the standard deviation, σ, not the variance σi2 i). When estimating this equation, researchers normally assume that σi2 is constant. In addition, to give a scale to the latent dependent variable, σi2 is normalized to unity. Such an approach is, however, clearly inappropriate for my purposes. Specifically, because I believe that individuals vary in their levels of uncertainty and ambivalence concerning social welfare policy, the answers to the NES seven-point scales will exhibit non-constant variance (see Alvarez and Brehm 1995, 1996, 1997). I, therefore, instead parameterize the variance of the outcome equation as a function of Zi, a set of explanatory variables. This parameterization follows the technique described by Greene (1993) and utilized by Alvarez and Brehm (1995, 1996, 1997) 5: var(ε i ) = σ i2 = exp( Z i γ ) 2 This reparameterization yields the following likelihood function: (4)   µ j − Xiβ  µ j −1 − X i β   L = ∏ ∏ Φ  − Φ   exp( Z i γ )   i =1 j =1   exp( Z i γ )  n m yij (5) where y ij =   1 if µ j −1 < yi ≤ µ j  0 otherwise 5 This term must be estimated without a constant to give the latent dependent variable an underlying scale. While the estimated variances can be compared in magnitude to each other, like the normal probit coefficients, the variance term coefficients have been scaled to one and, therefore, have no natural scale. 9 Taking logs, the log-likelihood function estimated below is:6 n m   µ j − Xiβ   µ j −1 − X i β   ln L = ∑ ∑ yij Φ  − Φ   exp( Zi γ )   exp( Zi γ )   i =1 j =1  (6) The heteroskedastic ordered probit model laid out in Equations 1-6 is well suited for my simulation for two reasons. First, it allows me to estimate separate determinants of individual mean and variance parameters. Second, by parameterizing the variance term, I can obtain consistent coefficient estimates for the effects of the variables in the choice equation, because probit estimates — unlike OLS estimates — are not only inefficient, but also inconsistent in the presence of heteroskedasticity. In other words, the heteroskedastic ordered probit model will allow me to obtain reliable estimates of the relationship between various demographic and political variables and attitudes concerning social welfare policy, independent of any effects resulting from unequal levels of response variance across the population. Model Construction For the purposes of estimating the heteroskedastic ordered probit model, I estimated the mean (Xiβ) as a function of measures of general political affiliations, material interests, and political principles (See Kinder 1997). I first included a measure of party identification because, in recent years, debates over social welfare issues have largely broken down along party lines, with Democrats consistently offering greater support than Republicans for programs that aid the economically disadvantaged.7 Next, to assess the effects of “self-interest” I included measures of race and income to gauge the predictive power of membership in those groups who would be aided most by increased government social welfare programs. As an additional self-interest measure, I included a measure of perceived job threat in the “Jobs and Standard of Living” equation to see if those individuals concerned with their own job security would be more supportive of government efforts to help the disadvantaged. To gauge the effect of political principles, I included dummy variables indicating selfidentification with one of three ideological groups, “liberals,” “conservatives,” and “moderates.”8 However, such classifications by no means exhausts the possible predictive power of political principles. While affiliation with these broad ideological categories are almost certainly important determinants of opinion direction, as over thirty years of public opinion research have clearly demonstrated, “the political thinking of much of the public cannot be adequately described as 6 7 For a more complete derivation, see Alvarez and Brehm (1996). For the purposes of these analyses, I have collapsed party identification to a five point scale from the traditional seven point scale. In light of the findings of Keith, et al. (1992) that independent leaners “vote very much like the outright partisans of the parties toward which they incline,” I undertook additional analyses to determine whether independent leaners should be collapsed into the weak partisan categories. Probit analyses in which each of the seven NES partisan identification categories was coded as a dummy variable (with “independent” excluded to avoid perfect multicolinearity) indicated that independent leaners were, in anything, more likely to behave like strong partisans than were weak partisans. 8 The excluded group was those individuals who indicated that they did not know or “hadn’t thought much about” their ideological affiliation. 10 ideological in the sense of deductive reasoning from an overarching set of integrated principles about politics and the social world.” (Feldman 1988, p. 417; see also Kinder 1983). In addition to — or instead of — ideological self-identification, people use more diffuse principles — what Feldman (1988) terms “core beliefs and values” — to understand the political world (see also Feldman and Zaller 1992; Kinder and Sanders 1996; Kinder 1997). Thus, to capture these “subideological” grounding principles, I included measures of support for equality, limited government, and moral conservatism.9 I also included measures of respondents’ levels of religious engagement to disentangle “strong traditional religious conviction” from the “moral conservatism” concept in which I am interested. Finally, I included measures of education and political information, because previous research has suggested that those rich in socio-economic resources are less likely to support social welfare policies.10 Turning to the construction of the variance function, I included many of the same factors which appeared in the choice equation because my theory posits that, from both a normative and an empirical standpoint, the link between the choice and variance equations is the key determinant of the degree of bias in aggregate public opinion. Thus, the variance terms of the equations were modeled as a function of: (1) engagement with the political system, measured by political information and education levels; (2) indicators of membership in groups that would be aided by social welfare programs (namely income and race); (3) politically relevant attitudes, measured through self-identification as a conservative and support for limited government and (4) Following Alvarez and Brehm’s work on ambivalence, measures of conflict in core values that would lead those who are otherwise predisposed to take a liberal position on the seven-point scales — those who score high on the equality scale — to waver in their support for social welfare programs. Specifically, I included measures of the presence of conflict between two sets of political principals: (a) equality and moral conservatism and (b) equality and limited government. INSERT TABLES 1-2 ABOUT HERE Tables 1 and 2 present the parameter estimates of the models estimated using the 1996 NES data. These model results indicate that, as expected, the determinants of the mean and variance term are closely linked. By and large, those individuals who possess characteristics that would incline them toward the liberal positions on the seven-point scales — those with low incomes and low levels of education and political knowledge, for example — also tend to possess higher response variances. This trend holds for both questions, but is stronger on the services and spending scale. Moreover, as predicted by Alvarez and Brehm’s work, those individuals who simultaneously hold values that push them to opposite ends of the seven-point scales are more variant than those individuals who hold a set of consistent values. Specifically, though only the coefficient on the conflict between equality and limited government in the Services and Spending The limited government scale items were not asked in the 1992 NES survey. I therefore included the limited government scale in my analysis of the 1996 items only. 10 It is also important to include these variables in the choice function because education and political information are included in the variance equation and the variance term in the heteroskedastic ordered probit will confound the effects of non-constant variance with variables omitted from the choice equation (Achen 1996). It should also be noted that the variables carried in the variance equation, but not the choice equation — specifically, the value conflict variables — were insignificant predictors of opinion direction, in both a statistical and a substantive sense. The specification concern identified by Achen, therefore, is not a concern in the analyses that follow. 9 11 model is statistically significant, all the conflict measures are in the expected direction across the two equations. Obtaining consistent estimates of the determinants of response direction and stability was, however, only the first step in my analysis. I next used the heteroskedastic ordered probit parameter estimates to simulate how aggregate public opinion might look if all individuals exhibited a constant level of response dispersion. These simulations were then be used to estimate the degree of aggregation bias in collective public opinion. Simulation While it is difficult to say what an individual’s “true opinion” would be in a variance-free world, we can use the information we have about mean individual position— the “signal” — to simulate conditions under which that mean plays a more central role in determining the opinion response.11 Specifically, as individual variance is reduced, the ordered probit probability distribution which describes that individual’s opinion response collapses to a spike over the respondent’s mean opinion position. In turn, the probability that she will place herself in the vicinity of her mean increases. INSERT FIGURE 1 ABOUT HERE Figure 1 illustrates this proposition graphically for the case in which a respondent is placing herself on a 10-point issue scale. The vertical lines on the graph represent the “thresholds” for the response categories. The normal curves are the response probability distributions for a respondent under three conditions which hold constant that respondent’s mean position, but have different variances: (1) a “low variance” condition (2) a “medium variance” condition and (3) a “high variance” condition. While the respondent in the “high variance” condition has the highest probability of answering the response categories closest to her mean, she also has a fairly high probability of answering response options at a significant distance from her mean opinion. In the “low variance” condition, on the other hand, most of her probability mass is centered under her mean and she, therefore, has only a small chance of giving an answer far from her mean. The simulations I employed attempted to “level the playing field” by discerning how aggregate public opinion changed as individual variance is reduced across the board and every individual’s response probability distribution is collapsed to their mean. This process, in turn, will increase the probability that an individual will give an opinion that is close to their pure “signal” response. Specifically: The mean opinion position is a good proxy for an individual’s “signal,” I argue, because it is estimated by utilizing the information we have about the behavior of respondents who are similar in politically relevant ways to that individual. In other words, we can use all the information in our sample to discern what the opinions of particular individuals would look like in the absence of significant response variance. 11 12 (1) One can use the estimates of the βs from the heteroskedastic ordered probit model to generate a predicted value of Xi β for each individual in the sample; (2) Then generate the predicted probabilities of falling into each response category, following equation 3, given (a) the value of Xi β generated in step 1, (b) the thresholds estimated from the heteroskedastic ordered probit model, and (c) a value of σi , which I held constant at some level across all the respondents.12 (3) Using these predicted probabilities, assigned each respondent to the seven-point scale category which had the highest predicted probability of response.13 (4) Finally, I computed mean opinion across these predicted responses. If my theory is correct, as the variance in individual response is reduced across the board (while the Xiβ and thresholds are held constant) and each individual’s expressed opinion approaches their mean, the inequality in the voice of groups with higher response variances should fade. Under such circumstances, collective public opinion should move in the direction of opinion held by the more variant groups, here towards the liberal end of the seven-point scales. To measure the degree of bias in the aggregate public opinion measure, it would be possible to simply compare the aggregate opinion as expressed in the NES survey to the simulated sample with the variance held constant at some minimal level, so that the response probability distributions of all individuals are spiked over their mean. However, in order to see if aggregate opinion moves smoothly toward the opinions held by more variant individuals as variance is reduced across the board, I performed the simulation described above for three conditions: (1) setting all respondents’ variance to the mean in-sample predicted variance14; (2) setting all respondents’ variance to the minimum in-sample predicted variance; and (3) setting all respondents’ variance to a minuscule value near zero.15 To gauge the magnitude of bias in expressed opinion against these simulated opinions, I use as a baseline the aggregate opinion predicted by a homoskedastic ordered probit model.16 By reducing the value of σI, for all respondents across several simulations, while holding constant the values of Xi β and the thresholds across those simulations, I can create response probability distributions which collapse to the mean at the same rate for every individual in the sample (see below). 13 That is, I used the decision rule where:   y = J if p > p ∀j≠k i ij ik 14 The variances were estimated by using the coefficient estimates of the variance model to generate a predicted variance score for each individual in the sample. The mean and minimum in-sample values of this predicted variance were then used in the simulation. 15 To be specific, I used a variance value of .05, which was sufficiently close to zero to produce a highly “spiked” response probability distribution. 16 I use for comparison the predicted values generated by the homoskedastic ordered probit estimates, rather than the actual response frequency distributions, because I wish to control for the fact that my model of opinion formation is imperfect. By using predicted values generated by a model for all four stages of the simulation, I hold constant the predictive power of that model across the estimates of the aggregate public opinion. 12 13 INSERT FIGURE 2 ABOUT HERE The initial results of this simulation using the 1996 estimation results are mixed. In the aggregate, both the “Services and Spending” and the “Jobs and Standard of Living” simulation perform as expected; as response variance is reduced, aggregate opinion moves in the direction of the more variant groups, becoming more liberal across both questions (See Figure 2). However, the movement in the Jobs and Standard of Living Question is larger than for the Services and Spending question, the opposite of what I would expect given the respective strength of the links between the mean and variance functions, estimated above. In an effort to understand this apparent anomaly, I performed a second series of simulations which dropped the focus of analysis down a level of aggregation. Specifically, I examined the movement of the collective opinions of politically relevant subgroups across the three variance conditions. In order to put a sharper edge on the differences among the groups, I based my simulations on a new set of ordered probit results where the variance term was predicted only by the variable used to stratify the sample.17 INSERT FIGURES 3-4 ABOUT HERE These new sets of analyses provide an explanation for the anomalous results presented in Figure 2. As Figure 3, demonstrates, the subgroups in the Services and Spending example largely behave as expected. Those groups predisposed toward the liberal end of the seven-point scale — people with minimal levels of political knowledge and those without a high school education — become more liberal in the aggregate as the variance is reduced, while those who hold more conservative opinions — those with higher education and political knowledge — tend to stay at approximately the same position. The Jobs and Standard of Living simulation on the other hand, shows a general liberalizing trend across all subgroups, regardless of the position they are likely to hold. This pattern of results explains why there is greater aggregate movement in the Jobs and Standard of Living question, even though the Services and Spending probit estimation matched better my theoretical expectations concerning the link between the variance and mean functions. INSERT TABLES 3-4 ABOUT HERE INSET FIGURES 7-10 ABOUT HERE To assess the generalizability of these findings, I replicated my simulation using data from the 1992 NES. The models I estimated were identical except that the limited government scale measures were removed from both the choice and variance equations because the limited government scale was not asked in the 1992 survey. As Tables 3-4 and Figures 7-10 show, the estimates from 1992 largely replicate the findings from 1996. Again, the aggregate opinion movements for the Jobs and Standard of Living question are larger than those for the Services and Spending simulation (see Figure 7). But, once more, these differences are driven by a general liberalizing trend across the “low variance” subgroups in the Jobs and Standard of Living question. On the other hand, the subgroups defined by education and political information levels largely behave as my theory predicts in the Services and Spending simulation. These new estimates differ only in degree from the coefficient estimates of the heteroskedastic ordered probit with the full variance model. While I do not present the estimates here, they are available from the author upon request. 17 14 Summary In sum, the results of my attempts to gauge aggregation bias are mixed. Simulations based on the Services and Spending question work as expected; as opinion variance is reduced across the sample in a consistent manner, the movement of the aggregate public opinion signal toward the liberal end of the scale is driven by those individuals predisposed to take a liberal position on the Services and Spending question, specifically those with low education and the poorly informed. The Jobs and Standard of Living question, on the other hand, shows greater aggregate movement, but this movement is driven by a convergence of opinion to the liberal end of the scale among all subgroups. This finding is puzzling and remains to be explained. INSERT TABLES 5-6 ABOUT HERE EXCLUSION BIAS Examining the causes and consequences of aggregation bias is only the first step in my analysis. My theory also holds expectations regarding the potential overrepresentation of conservative beliefs in aggregate measures of public opinion concerning social welfare policy resulting from uneven patterns of item non-response. To test this intuition, I estimated models of selection bias and used these models to gauge the differences in the preferences of seven-point scale “placers” against those individuals who abstain from the social welfare items. Differences As hypothesized, response instability may lead individuals not only to give more variant answers, but also may increase their propensity to abstain from answering questions altogether. Specifically, the same factors which increase individual variance also increase one’s propensity to abstain from issue placement questions (see Table 5). There is reason to expect that this of nonresponse, resulting from uncertainty and ambivalence, may affect how we understand the “signal” represented by aggregate public opinion. Item non-response across the two social welfare questions is reasonable high in 1996 (15 percent for the Services and Spending Question; nine percent for the Jobs and Standard of Living Question) and are even higher in 1992 (19 percent for the Services and Spending Question; 13 percent for the Jobs and Standard of Living Question). More importantly, issue placers and nonplacers show consistent differences across the two surveys on a number of politically relevant characteristics which have been shown to affect position on the two issue placement scales under examination (see Table 6). Thus, there is reason to believe that the — fairly substantial — population of respondents who abstain from the issue placement questions, because of high levels of uncertainty and ambivalence, differ in their political preferences concerning social welfare policy from the population of respondents. Given such circumstances, to fully account for any bias in aggregate public opinion, we need to somehow account for the preferences of those individuals who choose to abstain from the issue placement questions. 15 Selection Bias? Given the observed differences between the population of issue placers and non-placers, it is possible that the choice equations estimated above, though corrected for the effects of non-constant variance, are still contaminated by the residual effects of uncertainty and ambivalence because of selection effects. Achen (1986) argues that the effects of selection bias can be avoided in regression analysis if and only if the unobserved factors influencing selection are uncorrelated with the unobserved factors influencing outcomes. Such a state of affairs may arise if (1) the selection and outcome processes are independent events or (2) if every variable influencing selection is controlled in the outcome equation.18 Given that the analyses so far indicate that the determinants of attitude variance and item non-response overlap with the determinants of opinion direction, the first condition identified by Achen clearly does not hold. The next step in my analysis, therefore, was to make certain that the second condition described by Achen does not hold. Ideally, to correct for possible selection effects, I would construct a model that would account for both selection bias and heteroskedasticity in the context of the ordered probit model. While models of selection bias for binary probit outcome equations are widely used (see Dubin and Rivers 1990) extending such a model to the ordered probit case would be extraordinarily complicated. Thus, as a preliminary attempt to get a sense of whether my models were contaminated by selection bias, I estimated a Heckman selection model for my dependent variables of interest.19 The Heckman is a model intended to analyze data which have been censored; that is data for which we do not have information about the dependent variable of interest for some respondents, but we do have some information about the attributes of the non-respondents (Heckman 1979; Achen 1986; Brehm 1993; Breen 1996; Green 1997) .20 Specifically Heckman’s model assumes that the relationship of interest can be specified as a simple linear model of the form: y i = β ′xi + ε i (7) We also assume that Y is observed if and only if a second, unobserved latent variable, Z*, exceeds a particular threshold (here set to 0): 21 Achen (1986) notes that if the error terms in the selection and outcome equations — u1i and u2i respectively — are correlated in the censored sample, the disturbance term of the outcome equation u2i has neither mean zero nor zero correlation with the outcome independent variables, even though it has both properties in the full sample. Thus, when the sample selection process is related to the error of the outcome equations, separate estimation of the selection and outcome equation will lead to faulty inferences concerning the effect of the variables of interest in the outcome equation. 19 While the models used in previous simulations assumed that regression was an inappropriate technique for analyzing issue placement data, as a first cut to gauge the presence of selection bias in my outcome equations, the Heckman appears to be a adequate compromise between theoretic concerns and computation feasibility. 20 This state of affairs contrasts to a truncated sample, in which we have no information about nonrespondents, because observations are missing for both endogenous and exogenous variables (Brehm 1993; Breen 1996; Greene 1997). 21 This selection equation is an integral part of the model because Heckman’s model is a model of incidental selection, in that selection into the sample of respondents depends on a selection mechanism which is based on the observed exogenous factors. This contrasts to models of explicit selection, such as 18 16 zi* = α ′wi + ui ;  1 if zi* > 0; zi =   0 otherwise This selection mechanism may be modeled as a probit: (8) Pr (zi = 1) = Φ(α ′wi ) (9) Finally, the Heckman model assumes that the errors ui and εi are distributed bivariate normal22:  0  σ 2 εi    ~ N   ,   ui    0  ρσ ρσ    1   (10) These assumptions lead to the following model: E ( yi | yi observed ) = E (β ′xi + ε i |α ′wi + ui > 0) = β ′x i + ρσλ Where λ is known as the “inverse Mills ratio,” or the “hazard rate” and: (11) λ= Φ(α ′wi ) φ (α ′wi ) (12) Equation 11 implies that ignoring the sample selection mechanism in effect omits a variable — the expected value of the error term of the outcome equation under censoring — from the outcome equation. Thus, the OLS coefficient estimates of any independent variable, βk will be unbiased if and only if (1) ρ=0, so that the second term drops out of the equation or (2) if the correlation between the hazard rate and Xk is zero, such that the “omitted” hazard rate does not bias our estimate of βk. In practice, any possible selection effects are avoided in the analysis of the equations of interest by including the omitted “variable” — the hazard rate — in those equations. Specifically, the Heckman is performed by (1) running a probit on the selection equation to obtain predicted values of the hazard rate (2) including the hazard rate as an additional regressor in the outcome equation, and (3) correcting the standard errors in the outcome equation by a procedure that also allows the researcher to recover the estimate of ρ. Alternatively, the Heckman can be estimated using maximum likelihood techniques.23 the Tobit (Greene 1997), where appearance in the sample depends on values of the endogenous variables only. 22 σε is normalized to one because α and σε are not separately identifiable in the probit. 23 Assuming the same selection as outcome equations as above, the log-likelihood (Breen 1996, p. 40) is: 17 INSERT TABLES 7-10 To gauge the presence of selection bias in my model, I ran a Heckman selection model for both the Jobs and Standard of Living and the Services and Spending questions.24 The results of this estimation are clear; the outcome equations are not contaminated by selection bias. Not only do the coefficients not move in any meaningful sense once the Heckman correction for sample selection is estimated, but ρ is insignificant in both a statistical and substantive sense (see Tables 7-10) Exclusion Bias But just because incorporating information about those who select themselves out of the sample does not affect estimates of the determinants of the mean does not necessarily indicate that excluding the non-responders is inconsequential for the purposes of estimating the aggregate sample mean. Removing the non-respondents from the sample, I argue, affects the direction of the mean, even if the estimates of the determinants of the mean are unchanged, a phenomena I call “exclusion bias.” This exclusion bias is critical for the purposes of understanding aggregate public opinion — in both an empirical and a normative sense — because, after all, when assessing what the public thinks about a particular issue, we care about the actual distribution of opinion as much, if not more, than the determinants of those opinions. The fact that the Heckman does not indicate the presence of selection bias means that there is no correlation between the error terms in the selection equation and the outcome equation. This result indicates that there is nothing about the process of selecting into the sample of respondents that affects the structure of that respondent’s opinion. Thus, the relationship between the independent and dependent variables are not different for the people who select into the sample against those who are excluded from the sample. In other words, the β for the sample under analysis (that is, the sample which excludes the non-scale placers) is the full sample β.  1   + ∑ 1 y − x′β 2 Ln L = ∑ Ln 1 - Φ(wi α ) + ∑ Ln  2πσ 2  1 2σ 2 ( i i ) 0 1 u  u ( )   y − x ′β    wi α + ρ i i    σu   + ∑ LnΦ   1 (1 − ρ)2     It is possible to identify the Heckman model through the nonlinearity of the selection equation. In practice, however, identifying the equation system in this manner is problematic because of high levels of colinearity between the hazard rate instrument and the variables in the outcome equation (Breen 1996). Identification of the system of equations should, then, proceed from exclusion restrictions. That is, it is important that some variable(s) be included in the selection equation, but not the outcome equation. This in mind, I included measures indicating how difficult it was to contact the respondents (Brehm 1993), on the assumption that those who are difficult to reach would also be reluctant to answer specific survey questions, but would differ in their opinions concerning social welfare policy, independent of the other factors controlled In the equation.. 24 18 However, the fact that the factors that lead someone to enter into the sample — such as high education, high political information, and high income — also lead them to take more conservative positions on the social welfare scales, means that there is a conservative bias to the estimated sample mean. In particular, the population of non-respondents are disproportionately composed of individuals who, by dint of their exogenous variables, would tend to support social welfare policies at higher rates than those individuals who answer the issue placement questions. Thus, when estimating aggregate public opinion on social welfare issues, we are excluding from the sample those respondents who would be inclined to take a liberal position on the issue scales. Because this "exclusion bias" works through the independent variables, and we know that the β estimated using the self-selected sub-sample of respondents is the same as the full-sample β, I argue that we can predict the issue positions of the non-issue placers and compare this constructed mean against the true mean to gauge the degree of "exclusion bias" in the sample mean. INSERT TABLE 11 ABOUT HERE As Table 11 indicates, these differences are significant across both issue placement scales in the two years under examination. Looking at simulated issue position, issue placers are almost one-half a point more conservative on the seven-point scales then our best estimate of the mean position of those who abstain from the issue placement questions in 1996. Though the differences in 1992 are of a smaller magnitude, the same basic pattern holds Given that these differences were assessed using opinion placements constructed, in part, by imputing interests to individuals who opted out of answering survey questions, a healthy degree of skepticism is understandable. However, the finding of a pro-conservative tilt among the population of “issue placers” extends from the world of imputed interests to that of expressed opinions. Specifically, the difference in the simulated opinions of the two groups is replicated in the differences between Service and Spending issue placers and non-placers on the Jobs and Standard of Living scale and the differences between the Jobs and Standard of Living issue placers and non-placers on the service and spending scale. In both cases, non-placers take significantly more liberal positions than issue-placers on the scales (see Table 11). Thus, the analysis of both simulated and expressed opinions of the NES survey respondents lead to the same answer: Those individuals who — due to extreme uncertainty and ambivalence surrounding the social welfare issues examined here — choose not to answer the Jobs and Standard of Living and the Services and Spending scales are more favorable to policies which support the welfare state than those individual who respond to the NES issue placement questions. Summary In sum, then, exclusion bias works in the same direction as aggregation bias. In both cases, factors relating to selection and non-constant variance work to construct a measure of collective public opinion on social service policy questions that is more conservative than the underlying preferences of the population at large. More generally, these analyses point to the need to account for “exclusion bias” when analyzing aggregate opinion distributions. Even if the outcome equation of interest does not exhibit selection bias — and, by association, the determinants of opinion direction do not differ from selfselected sample to full sample — it is important to attend to compositional differences between the 19 in-sample and out-of-sample populations. As shown here, significant differences between respondents and non-respondents may affect how we understand aggregate public opinion, even in the absence of selection effects. CONCLUSION The analyses presented in this paper have significant implication for how we understand aggregate public opinion and, more importantly, how we understand the links between individual opinion and aggregate opinion. While the “miracle of aggregation” may provide a happy solution to the disturbing picture of the instability and apparent “irrationality” of individual opinion, that solution comes with a price; specifically the measurement and aggregation of the, sometimes noisy, opinions of individuals introduces a bias into aggregate public opinion which inadvertently disenfranchises those individuals predisposed to support the policies of the welfare state. The key to understanding this bias is to recognize that the same factors which lead an individual to take a liberal position on the social welfare questions also lead them to be more variant in their opinions on those questions and, in some cases, to abstain from the issue placement questions altogether. Simulations based on the Services and Spending questions in the 1992 and, especially, the 1996 NES indicate that the cross-sectional aggregation of individual opinion may introduce a proconservative bias into collective opinion. Consistent with my theory, as the ratio of “signal” to “noise” in individual opinion is increased across the board, the movement of the aggregate public opinion signal to the liberal end of the scale is driven by those individuals already predisposed to take a liberal position on the Services and Spending question. These findings do not, however, neatly extend to the Jobs and Standard of Living question. Thus, while the aggregation bias results are suggestive, they are by no means definitive. Conceivably, the mixed results of the aggregation bias analysis are due to the fact that it is difficult to parse out from cross-sectional studies the types of data needed to test my theory. The simulations presented above use similarities among individuals in cross-sectional data to leverage individual-specific response variances. Perhaps, however, this strategy is not ideal for my purposes. Future work will, therefore, assess alternative strategies — such as the use of panel data or other longitudinal measures of opinion — to measure the shape of individual opinion distributions Though the results of the aggregation bias analysis may not speak as loudly as I would like, the exclusion bias results are clear and striking. In line with previous empirical work by Hochschild (1981) and Bartels (1986) I find that those individuals who are more likely to give variant opinion responses are also more likely to abstain from issue placement questions altogether. Given that these “non-placers” are more likely to support social welfare policies than the issue placers, the patterns of non-response in the NES dataset introduces into our estimate of aggregate public opinion a potentially serious pro-conservative exclusion bias. The portability of the bias identified in this paper outside of the realm of social welfare policy remains to demonstrated in future work. Still, the analyses in this paper suggest that the presence of aggregation bias and, especially, exclusion bias work against the rosy picture painted by Page and Shapiro. More generally, then, this paper points to the need to pay closer attention to the micro-foundations of aggregate public opinion. As Converse argues, the reason that aggregate public opinion appears “rational” is that “aggregation drives out noise, and noise is what most vividly roars to attention with the total disaggregation of the sample survey” (1990, p. 378). Similarly, as demonstrated above, the very process of deciding to answer survey questions drives 20 out those individuals with variant opinions. Thus, we may buy “rationality” by moving from the individual to the aggregate level, but we do so because we expunge those individuals whose opinions are “noisy.” This mechanism has potentially serious normative consequences because differences in levels of response variance are rooted in politically consequential variables. The process of collecting and aggregating opinions may, therefore, result in opinion measurements which are unrepresentative of the preferences of the full population. Put another way, the aggregate public may be “rational” but it is a public which seems to speak with a biased voice. Future public opinion research should, then, not just focus on rejuvenating our view of the “rationality” of the American public. In addition, researchers should seek to identify the causes of heterogeneity in uncertainty and ambivalence in individual preferences and the consequences of this heterogeneity for opinion aggregation. By acknowledging the vast differences in the stability of opinions across individuals — instead of looking for ways to rehabilitate our picture of the mass public — we will be forced to turn to the less pleasant, but equally critical, task of redressing the inequalities in the voice of different segments of the mass public. 21 TABLE 1: ORDERED PROBIT ESTIMATES: 1996 JOBS AND STANDARD OF LIVING Variable Model 1: Homoskedastic Coefficient (SE) OUTCOME EQUATION 1.025 (0.177)** 0.199 (0.079)** 0.128 (0.089) -0.168 (0.136) 0.042 (0.125) -0.242 (0.097)** -0.318 (0.086)** -0.078 (0.085) 0.263 (0.052)** 1.500 (0.176)** -0.545 (0.088)** -0.205 (0.168)** 0.220 (0.086)** -0.128 (0.068)* 0.139 (0.092) VARIANCE FUNCTION — — — — — — — — THRESHOLD PARAMETERS 0.824 (0.044) 1.474 (0.051) 2.202 (0.058) 2.657 (0.064) 3.124 (0.074) 1355/-2283.655 Model 2: Heteroskedastic Coefficient (SE) 0.622 (0.122)** 0.132 (0.055)** 0.122 (0.084) -0.077 (0.078) 0.033 (0.073) -0.167 (0.065)** -0.200 (0.059)** -0.096 (0.059) 0.144 (0.033)** 0.872 (0.122)** -0.337 (0.060)** -0.115 (0.094)** 0.123 (0.050)** -0.078 (0.041)* 0.086 (0.055) -0.002 (0.072) 0.261 (0.094)** -0.068 (0.052) -0.362 (0.097)** -0.349 (0.105)** -0.083 (0.072) 0.176 (0.130) 0.156 (0.103) 0.464 (0.047) 0.842 (0.076) 1.285 (0.109) 1.578 (0.130) 1.907 (0.154) 1355/-2237.187 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Limited Government Moral Conservatism Religious Importance Born Again Job Threat Level Low Income Black Education Political Information Conservative Limited Government Conflict: EQ/MC Conflict: EQ/LG µ1 µ2 µ3 µ4 µ5 N/Log Likelihood * = p < .10; ** = p < .05 22 TABLE 2: ORDERED PROBIT ESTIMATES: 1996 SERVICES AND SPENDING Variable Model 1: Homoskedastic Coefficient (SE) OUTCOME EQUATION 2.240 (0.175)** 0.155 (0.074)** 0.218 (0.095)** -0.261 (0.141)* -0.223 (0.125)* -0.049 (0.095) -0.118 (0.090) -0.133 (0.090) 0.314 (0.054)** 1.009 (0.173)** -0.772 (0.087)** -0.565 (0.087)** 0.176 (0.087)** -0.108 (0.070) VARIANCE FUNCTION — — — — — — — — THRESHOLD PARAMETERS 0.752 (0.053) 1.502 (0.060) 2.556 (0.067) 3.235 (0.073) 3.829 (0.084) 1297/-2283.655 Model 2: Heteroskedastic Coefficient (SE) 1.352 (0.162)** 0.131 (0.063)** 0.120 (0.086) -0.143 (0.083) -0.138 (0.074)* -0.001 (0.065) -0.109 (0.061)* -0.122 (0.064)* 0.188 (0.038)** 0.596 (0.111)** -0.490 (0.067)** -0.355 (0.102)** 0.130 (0.052)** -0.061 (0.043) 0.165 (0.063)** 0.176 (0.087)** -0.358 (0.106)** -0.311 (0.087)** -0.043 (0.050) -0.169 (0.067) 0.088 (0.131) 0.170 (0.100)* 0.415 (0.052) 0.844 (0.088) 1.500 (0.137) 1.945 (0.173) 2.369 (0.208) 1297/-2045.578 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Limited Government Moral Conservatism Religious Importance Born Again Low Income Black Education Political Information Conservative Limited Government Conflict: EQ/MC Conflict: EQ/LG µ1 µ2 µ3 µ4 µ5 N/Log Likelihood * = p < .10; ** = p < .05 23 TABLE 3: ORDERED PROBIT ESTIMATES: 1992 JOBS AND STANDARD OF LIVING Variable Model 1: Homoskedastic Coefficient (SE) OUTCOME EQUATION 0.882 (0.159)** 0.241 (0.090)** 0.404 (0.090)** -0.118 (0.136) -0.281 (0.134)** 0.057 (0.093) -0.270 (0.087)** -0.036 (0.083) 0.234 (0.049)** 0.949 (0.156)** -0.060 (0.145) -0.128 (0.086) -0.005 (0.068) 0.171 (0.090)* VARIANCE FUNCTION — — — — — — THRESHOLD PARAMETERS 0.584 (0.037) 1.211 (0.046) 1.845 (0.052) 2.316 (0.057) 2.800 (0.065) 1364/-2436.566 Model 2: Heteroskedastic Coefficient (SE) 0.618 (0.127)** 0.194 (0.094)** 0.261 (0.083)** -0.111 (0.096) -0.121 (0.090) 0.049 (0.071) -0.202 (0.068)** -0.035 (0.066) 0.182 (0.037)** 0.646 (0.118)** -0.046 (0.104) -0.052 (0.060) -0.008 (0.049) 0.133 (0.067)** -0.133 (0.091) 0.094 (0.074) -0.306 (0.104)** -0.502 (0.104)** -0.002 (0.050) 0.176 (0.130) 0.416 (0.037) 0.857 (0.064) 1.314 (0.091) 1.660 (0.114) 2.038 (0.139) 1364/-2406.818 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Moral Conservatism Religious Importance Born Again Job Threat Level Low Income Black Education Political Information Conservative Conflict: EQ/MC µ1 µ2 µ3 µ4 µ5 N/Log Likelihood * = p < .10; ** = p < .05 24 TABLE 4: ORDERED PROBIT ESTIMATES: 1992 SERVICES AND SPENDING Variable Model 1: Homoskedastic Coefficient (SE) OUTCOME EQUATION 1.802 (0.157)** 0.200 (0.076)** 0.330 (0.082)** -0.182 (0.120) -0.669 (0.124)** -0.072 (0.087) -0.234 (0.080)** -0.013 (0.080) 0.321 (0.045)** 0.850 (0.147)** -0.278 (0.136)** 0.065 (0.082) -0.040 (0.124) VARIANCE FUNCTION — — — — — — THRESHOLD PARAMETERS 0.618 (0.044) 1.230 (0.052) 2.200 (0.057) 2.841 (0.061) 3.328 (0.066) 1645/-2750.133 Model 2: Heteroskedastic Coefficient (SE) 1.333 (0.136)** 0.119 (0.072)** 0.236 (0.081)** -0.161 (0.088)* -0.508 (0.088)** 0.049 (0.068) -0.198 (0.066)** -0.005 (0.064) 0.248 (0.035)** 0.638 (0.109)** -0.209 (0.094)** -0.038 (0.057)** -0.020 (0.045) 0.074 (0.062) 0.128 (0.070)** -0.338 (0.086)** -0.421 (0.088)** -0.035 (0.042) 0.049 (0.096) 0.449 (0.041) 0.884 (0.062) 1.590 (0.095) 2.075 (0.119) 2.459 (0.139) 1645/-2712.719 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Moral Conservatism Religious Importance Born Again Low Income Black Education Political Information Conservative Conflict: EQ/MC µ1 µ2 µ3 µ4 µ5 N/Log Likelihood * = p < .10; ** = p < .05 25 TABLE 5: VARIANCE/ITEM NON-RESPONSE DETERMINANTS 1996 SERVICES AND SPENDING Variable Constant Low Income Black Conservative Political Information Education Limited Government Conflict: EQ/MC Conflict: EQ/LG Variance Function Coefficient (SE) — 0.165 (0.063)** 0.176 (0.087)** -0.043 (0.050) -0.311 (0.087)** -0.358 (0.106)** -0.169 (0.067)** 0.088 (0.131) 0.170 (0.100)* JOBS AND STANDARD OF LIVING Variable Constant Low Income Black Conservative Political Information Education Limited Government Conflict: EQ/MC Conflict: EQ/LG * = p < .10; ** = p < .05 Variance Function Coefficient (SE) — -0.002 (0.072) 0.261 (0.094)** -0.068 (0.052) -0.362 (0.097)** -0.349 (0.105)** -0.083 (0.072) 0.176 (0.130) 0.156 (0.103) 7-Point Placer? Coefficient (SE) | 0.558 (0.168)** -0.120 (0.121) 0.037 (0.144) 0.360 (0.119)** 0.445 (0.207)** 0.698 (0.223)** -0.010 (0.144) -0.516 (0.288)* -0.135 (0.211) 7-Point Placer? Coefficient (SE) -0.013 (0.156) 0.074 (0.114) -0.135 (0.128) 0.538 (0.112)** 0.466 (0.189)** 1.163 (0.208)** 0.225 (0.134)* -0.361 (0.260) -0.084 (0.203) 26 TABLE 5 (CONTINUED): VARIANCE/ITEM NON-RESPONSE DETERMINANTS 1992 SERVICES AND SPENDING Variable Constant Low Income Black Conservative Political Information Education Conflict: EQ/MC Variance Function Coefficient (SE) — 0.074 (0.062) 0.128 (0.070)** -0.338 (0.086)** -0.421 (0.088)** -0.035 (0.042) 0.049 (0.096) JOBS AND STANDARD OF LIVING Variable Constant Low Income Black Conservative Political Information Education Conflict: EQ/MC * = p < .10; ** = p < .05 Variance Function Coefficient (SE) — -0.133 (0.091) 0.094 (0.074) -0.306 (0.104)** -0.502 (0.104)** -0.002 (0.050) 0.176 (0.130) 7-Point Placer? Coefficient (SE) | 0.217 (0.099)** 0.007 (0.096) -0.031 (0.104) 0.307 (0.092)** 0.920 (0.187)** 0.731 (0.175)** -0.977 (0.221)** 7-Point Placer? Coefficient (SE) -0.243 (0.093)** 0.059 (0.089) -0.145 (0.094) 0.513 (0.088)** 1.328 (0.177)** 1.044 (0.208)** -0.565 (0.195)** 27 TABLE 6: DEMOGRAPHIC DIFFERENCES 1996 SERVICES AND SPENDING 7-Point Placers Mean (SE Mean) 0.573 (0.006) 0.460 (0.008) 0.085 (0.018) 0.157 (0.010) Non Placers Mean (SE Mean) 0.398 (0.014) 0.288 (0.017) 0.235 (0.039) 0.253 (0.028) Difference (2-Tailed T-Test) 0.175** 0.173** 0.150** 0.096** Education Political Information Party Identification Low Income JOBS AND STANDARD OF LIVING 7-Point Placers Mean (SE Mean) 0.561 (0.006) 0.449 (0.008) 0.092 (0.017) 0.158 (0.009) Non Placers Mean (SE Mean) 0.413 (0.019) 0.302 (0.022) 0.240 (0.050) 0.294 (0.036) Difference (2-Tailed T-Test) 0.149** 0.147** 0.148** 0.136** Education Political Information Party Identification Low Income ______________________________________________________________________________ 1992 SERVICES AND SPENDING 7-Point Placers Mean (SE Mean) 0.539 (0.006) 0.393 (0.006) 0.079 (0.015) 0.145 (0.008) Non Placers Mean (SE Mean) 0.346 (0.011) 0.205 (0.010) 0.177 (0.029) 0.245 (0.020) Difference (2-Tailed T-Test) 0.193** 0.188** 0.098** 0.103** Education Political Information Party Identification Low Income JOBS AND STANDARD OF LIVING 7-Point Placers Mean (SE Mean) 0.524 (0.006) 0.378 (0.006) 0.081 (0.014) 0.152 (0.009) Non Placers Mean (SE Mean) 0.359 (0.014) 0.222 (0.013) 0.208 (0.036) 0.248 (0.025) Difference (2-Tailed T-Test) 0.165** 0.156** 0.128** 0.095** Education Political Information Party Identification Low Income * = p < .10; ** = p < .05 28 TABLE 7: SELECTION BIAS TEST: 1996 JOBS AND STANDARD OF LIVING Variable Model 1: Separate Equation Coefficient (SE) OUTCOME EQUATION (REGRESSION) 2.087 (0.250)** 0.283 (0.115)** 0.220 (0.139) -0.247 (0.181) -0.337 (0.141)** -0.449 (0.130)** -0.126 (0.127) 0.371 (0.077)** 1.975 (0.232)** -0.748 (0.118)** -0.293 (0.236) 0.300 (0.119)** -0.155 (0.096)* 0.200 (0.138) SELECTION EQUATION (PROBIT) — — — — — — — — — — — — CORRELATION PARAMETERS — Model 2: Heckman Coefficient (SE) 2.103 (0.265)** 0.283 (0.115)** 0.226 (0.139) -0.251 (0.182) -0.343 (0.149)** -0.455 (0.139)** -0.129 (0.133) 0.371 (0.076)** 1.968 (0.231)** -0.749 (.118)** -0.292 (0.236) 0.301 (0.119)** -0.158 (0.096)* 0.197 (0.137) 0.314 (0.187)* -0.110 (0.124) -0.004 (0.149) 0.376 (0.237) 0.264 (0.217) 0.711 (0.166)** 0.766 (0.142)** 0.584 (0.133)** 0.021 (0.148) -0.491 (0.298)* -0.138 (0.230) 0.016 (0.011) -0.017 Constant Low Income Black Education Liberal Conservative Moderate Party Identification Equality Limited Government Moral Conservatism Religious Importance Born Again Job Threat Level Constant Low Income Black Education Political Information Liberal Conservative Moderate Limited Government Conflict: EQ/MC Conflict: EQ/LG Number of Calls ρ * = p < .10; ** = p < .05 29 TABLE 8: SELECTION BIAS TEST: 1996 SERVICES AND SPENDING Variable Model 1: Separate Equation Coefficient (SE) OUTCOME EQUATION (REGRESSION) 3.302 (0.221)** 0.183 (0.101)* 0.281 (0.128)** -0.328 (0.163)** -0.252 (0.151)* -0.001 (0.128) -0.149 (0.118) -0.169 (0.115) 0.370 (0.066)** 1.176 (0.202)** -0.902 (0.104)** -0.669 (0.206)** 0.211 (0.103)** -0.131 (0.085) SELECTION EQUATION (PROBIT) — — — — — — — — — — — — CORRELATION PARAMETERS — Model 2: Heckman Coefficient (SE) Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Limited Government Moral Conservatism Religious Importance Born Again Constant Low Income Black Education Political Information Liberal Conservative Moderate Limited Government Conflict: EQ/MC Conflict: EQ/LG Number of Calls ρ * = p < .10; ** = p < .05 3.301 (0.249)** 0.180 (0.101)* 0.292 (0.128)** -0.328 (0.167)** -0.257 (0.152)* -0.001 (0.128) -0.138 (0.133) -0.157 (0.125) 0.368 (0.066)** 1.173 (0.201)** -0.905 (0.104)** -0.675 (0.205)** 0.207 (0.103)** -0.135 (0.084) -0.330 (0.172)* 0.108 (0.118) -0.128 (0.132) 0.834 (0.220)** 0.260 (0.199) 0.836 (0.147)** 1.020 (0.130)** 0.725 (0.142)** 0.247 (0.139)* -0.241 (0.265) -0.128 (0.209) -0.017 (0.010)* 0.017 30 TABLE 9: SELECTION BIAS TEST: 1992 JOBS AND STANDARD OF LIVING Variable Model 1: Separate Equation Coefficient (SE) OUTCOME EQUATION (REGRESSION) 2.059 (0.254)** 0.415 (0.143)** 0.626 (0.152)** -0.173 (0.215)** -0.452 (0.205)** 0.102 (0.145) -0.424 (0.138)** -0.059 (0.135) 0.351 (0.079)** 1.471 (0.242)** -0.071 (0.231) -0.207 (0.134) 0.004 (0.106) 0.264 (0.143)* SELECTION EQUATION (PROBIT) — — — — — — — — — — CORRELATION PARAMETERS — Model 2: Heckman Coefficient (SE) 2.060 (0.301)** 0.415 (0.143)** 0.626 (0.152)** -0.173 (0.255)** -0.452 (0.207)** 0.102 (0.159) -0.425 (0.151)** -0.059 (0.145) 0.351 (0.079)** 1.471 (0.245)** -0.071 (0.231) -0.207 (0.134) 0.004 (0.106) 0.264 (0.142)* -0.255 (0.112) -0.175 (0.111) -0.069 (0.118) 1.019 (0.208)** 0.531 (0.211)** 0.681 (0.134)** 0.631 (0.115)** 0.517 (0.111)** -0.884 (0.246)** 0.355 (0.112)** -0.001 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Moral Conservatism Religious Importance Born Again Job Threat Level Constant Low Income Black Education Political Information Liberal Conservative Moderate Conflict: EQ/MC Refusal Conversion ρ * = p < .10; ** = p < .05 31 TABLE 10: SELECTION BIAS TEST: 1992 SERVICES AND SPENDING Variable Model 1: Separate Equation Coefficient (SE) OUTCOME EQUATION (REGRESSION) 3.156 (0.206)** 0.185 (0.103)** 0.444 (0.121)** -0.260 (0.159)** -0.916 (0.159)** 0.106 (0.117) -0.309 (0.110)** 0.005 (0.109) 0.421 (0.061)** 1.108 (0.196)** -0.372 (0.184)** -0.083 (0.106) -0.045 (0.084) SELECTION EQUATION (PROBIT) — — — — — — — — — — — CORRELATION PARAMETERS — Model 2: Heckman Coefficient (SE) 3.222 (0.256)** 0.173 (0.104)** 0.451 (0.121)** -0.282 (0.164)** -0.924 (0.168)** 0.084 (0.139) -0.339 (0.133)** -0.021 (0.127) 0.415 (0.061)** 1.084 (0.197)** -0.382 (0.184)** -0.072 (0.106) -0.045 (0.084) -0.502 (0.100)** 0.054 (0.093) -0.123 (0.100) 0.771 (0.176)** 1.132 (0.188)** 0.986 (0.117)** 0.991 (0.102)** 0.761 (0.097)** -0.322 (0.213) -0.552 (0.260)** 0.215 (0.160) -0.033 Constant Low Income Black Education Political Information Liberal Conservative Moderate Party Identification Equality Moral Conservatism Religious Importance Born Again Constant Low Income Black Education Political Information Liberal Conservative Moderate Conflict: EQ/MC Refusal Conversion Persuasion Letter ρ * = p < .10; ** = p < .05 32 TABLE 11: ISSUE PLACEMENT POSITIONS 1996 SERVICES AND SPENDING 7-Point Placers Mean (SE Mean) 2.855 (0.024) n=1297 2.492 (0.046) n=1389 Non Placers Mean (SE Mean) 3.336 (0.051) n=190 2.938 (0.148) n=161 Difference (1-Tailed T-Test) 0.481** 0.446** Predicted Services and Spending Actual Jobs and Standard of Living JOBS AND STANDARD OF LIVING 7-Point Placers Mean (SE Mean) 2.503 (0.026) n=1361 2.874 (0.040) n=1389 Non Placers Mean (SE Mean) 2.921 (0.069) n=127 3.197 (0.202) n=76 Difference (1-Tailed T-Test) 0.418** 0.323* Predicted Jobs and Standard of Living Actual Services and Spending ______________________________________________________________________________ 1992 SERVICES AND SPENDING 7-Point Placers Mean (SE Mean) 3.097 (0.017) n=1656 2.627 (0.040) n=1870 Non Placers Mean (SE Mean) 3.520 (0.031) n=349 3.146 (0.115) n=293 Difference (1-Tailed T-Test) 0.424** 0.499** Predicted Services and Spending Actual Jobs and Standard of Living JOBS AND STANDARD OF LIVING 7-Point Placers Mean (SE Mean) 2.593 (0.019) n=1378 3.086 (0.036) n=1870 Non Placers Mean (SE Mean) 2.771 (0.047) n=146 3.455 (0.127) n=143 Difference (1-Tailed T-Test) 0.178** 0.368** Predicted Jobs and Standard of Living Actual Services and Spending * = p < .10; ** = p < .05 33 APPENDIX: CODING PROTOCOL Race Dummy indicating the race of the respondent (0=nonblack; 1=black) 7 category NES education variable measuring highest level of education (0=grade school; 1=advanced degree). Dummy indicating whether the respondent is in the lower 15 percent of the sample income range (0= not in the lower 15 percent; 1= in the lower 15 percent) 9 category NES variable measuring knowledge of politics. (0=low; 1=high). Dummy indicating self-identification as “extremely liberal,” “liberal,” or “slightly liberal” on the NES sevenpoint ideology scale. (0=not liberal; 1=liberal) Dummy indicating self-identification as “extremely conservative,” “conservative,” or “slightly conservative” on the NES seven-point ideology scale. (0=not conservative; 1=conservative) Dummy indicating self-identification as “moderate; middle of the road” on the NES seven-point ideology scale. (0=Not moderate; 1=moderate) 5 category partisanship variable. This variable is simply the NES 7-Category partisanship variable with the independent leaners collapsed with the weak partisans (-1=Strong Republican; 1=Strong Democrat). 6 category NES Equality scale. Respondents are assigned their mean score across all the individual equality items as long as they answer half or more of those items. (0=Low support for equality; 1=high support for equality) 4 category NES Limited Government scale. Respondents are assigned their mean score across all the individual limited government items as long as they answer half or more of those items. (0=Low support for limited government; 1=high support for limited government) Education Low Income Political Information Liberal Conservative Moderate Party Identification Equality Limited Government 34 APPENDIX: CODING PROTOCOL (CONTINUED) Moral Conservatism 4 category NES Moral Conservatism scale. Respondents are assigned their mean score across all the individual moral conservatism items as long as they answer half or more of those items. (0=Low support for moral conservatism; 1=high support for moral conservatism) 4 category variable which gauges the degree of guidance religion provides in the respondent’s everyday life. (0=Not important; 1=provides a great deal of guidance) Dummy indicating self-identification as a “born again Christian.” (0=no; 1=yes) 3 category variable indicating respondents level of fear about loosing their job. Homemakers and students without current outside employment are coded as having “not much at all” fear about loosing their job. (0=Not much at all; 1=a lot) Level of conflict between the “equality” and “moral conservatism” scales. Computed by taking the negative of the absolute value of the difference between the two scales. (-1=Low conflict; 0=high conflict) Level of conflict between the “equality” and “limited government” scales. Computed by taking the negative of the absolute value of the difference between the two scales. (-1=Low conflict; 0=high conflict) The number of face-to-face and telephone calls made to the respondents home in order to obtain the interview. Dummy variable indicating whether the interviewer attempted to convert a respondent who initially refused to participate in the NES. (0=no; 1=yes) Religious Importance Born Again Job Threat Level Conflict EQ/MC Conflict EQ/LG Number of Calls Persuasion Letter Refusal Conversion Dummy variable indicating whether a persuasion letter was sent to the respondent. (0=no; 1=yes) 35 REFERENCES Achen, Christopher H. 1986. The Statistical Analysis of Quasi-Experiments. Berkeley: University of California Press. ————. 1996. Discussant Remarks at the 1996 Annual Meeting of the Midwest Political Science Association, April, 1996, Chicago, IL. R. Michael Alvarez and Brehm, John. 1995. “American Ambivalence Towards Abortion Policy: A Heteroskedastic Probit Method for Assessing Conflicting Values.” American Journal of Political Science, 39:1055-82. ————. 1996. “Uncertainty and Ambivalence in the Ecology of Race.” Paper presented at the 1996 Annual Conference of the American Political Science Association, San Francisco, CA. ————. 1997. “Are Americans Ambivalent Toward Racial Policies?” American Journal of Political Science, 41:345-75. Bartels, Larry M. 1986. “Issue Voting Under Uncertainty: An Empirical Test.” American Journal of Political Science, 30:709-28. ————. 1991. "Constituency Opinion and Congressional Policy Making: The Reagan Defense Build-Up." American Political Science Review 85: 457-474. Breen, Richard. 1996. Regression Models: Censored, Sample Selected, or Truncated Data. Sage University Paper series on Quantitative Applications in the Social Sciences, 07-111. Thousand Oaks, CA: Sage. Brehm, John. 1993. The Phantom Respondents: Opinion Surveys and Political Representation. Ann Arbor: University of Michigan Press. Chong, Dennis. 1993. “How People Think, Reason, and Feel about Rights and Liberties,” American Journal of Political Science, 37:867-99. Converse, Philip E. 1964. “The Nature of Belief Systems in The Mass Publics,” in David Apter (ed.) Ideology and Discontent. New York: Free Press. ————. 1970. “Attitudes and Non-Attitudes: Continuation of a Dialog,” in Edward R. Tufte (ed.) The Quantitative Analysis of Social Problems. Reading, MA: Addison-Wesley Publishing Company. ————. 1990. "Popular Representation and the Distribution of Information." in John Ferejohn and James Kuklinski (eds) Information and Democratic Processes, Urbana and Chicago: University of Illinois. 36 Delli Carpini, Michael X. And Scott Keeter. 1996. What Americans Know About Politics and Why It Matters. New Haven: Yale University Press. Dubin, Jeffrey A. and Douglas Rivers. 1990. “Statistical Bias in Linear Regression, Logit and Probit Models.” Sociological Methods and Research, 18:360-90. Enelow, James and Melvin J. Hinich. 1981. “A New Approach to Voter Uncertainty in the Downsian Spatial Model.” American Journal of Political Science, 25:483-93. Feldman, Stanley. 1988. "Structure and Consistency in Public Opinion: The Role of Core Beliefs and Values." American Journal of Political Science 32: 416-440. Feldman, Stanley and John Zaller. 1992. "The Political Culture of Ambivalence." American Journal of Political Science 36: 268-307. Greene, William H. 1995. LIMDEP Version 7.0 User’s Manual. New York: Econometric Software, Inc. ————. 1997. Econometric Analysis, Third Edition. New York: MacMillian Publishing Company. Heckman, James J. 1979. “Sample Selection Bias as a Specification Error.” Econometrica. 47:153-161. Herbst, Susan. 1993. Numbered Voices: How Opinion Polling Has Shaped American Politics. Chicago: University of Chicago Press. Hochschild, Jennifer L. 1981. What’s Fair? American Beliefs about Distributive Justice. Cambridge: Harvard University Press. Iyengar, Shanto and Donald Kinder. 1987. News that Matters. Chicago: University of Chicago Press. Kinder, Donald R. 1983. "Diversity and Complexity in American Public Opinion." in Ada Finifter, ed., Political Science: The State of the Discipline. ————. 1997. “Opinion and Action in the Realm of Politics.” in Daniel Gilbert, Susan Fiske, and Gardner Lindsey (eds.) Handbook of Social Psychology, fourth edition. Boston: McGraw Hill. Kinder, Donald R. and Lynn M. Sanders. 1996. Divided by Color: Racial Politics and Democratic Ideals. Chicago: Chicago University Press. Lane, Robert E. 1962. Political Ideology: Why the Common Man Believes What He Does. New York: Free Press. Lupia, Arthur. 1994. "Shortcuts Versus Encyclopedias: Information and Voting Behavior in California Insurance Reform Elections." American Political Science Review 88: 63-76. 37 Page, Benjamin I. and Robert Y. Shapiro. 1992. The Rational Public: Fifty Years of Trends in American Policy Preferences. Chicago: University of Chicago Press. Popkin, Samuel L. 1991. The Reasoning Voter. Chicago: University of Chicago Press. Rosenstone, Steven J. and John Mark Hansen. 1993. Mobilization, Participation, and Democracy in America. New York: MacMillian Publishing Company. Shepsle, Kenneth A. 1972. “The Strategy of Ambiguity: Uncertainty and Electoral Competition.” American Political Science Review. 66:555-68. Slovic, Paul. 1995. “The Construction of Preference.” American Psychologist. 50:364-371. Stimson, James A., Michael B. MacKuen, and Robert S. Erikson. 1995. “Dynamic Representation.” American Political Science Review. 89:543-565. Tetlock, Philip E. 1986. “Value Pluralism Model of Ideological Reasoning,” Journal of Personality and Social Psychology, 50: 819-827. Verba, Sidney, Kay Lehman Schlozman and Henry E. Brady. 1995. Voice and Equality: Civic Voluntarism in American Politics. Cambridge, MA: Harvard University Press. Zaller, John. 1992. The Nature and Origins of Mass Opinion. Cambridge: Cambridge University Press. Zaller, John and Stanley Feldman. 1992. "A Simple Theory of the Survey Response." American Journal of Political Science 36: 579-616. 38 THE “MIRACLE” REVISITED: AN EXAMINATION OF THE MICRO-FOUNDATIONS OF 1 AGGREGATE PUBLIC OPINION Adam J. Berinsky University of Michigan Department of Political Science e mail: berinsky@umich.edu August 1997 1 Paper presented at the Annual Meeting of the American Political Science Association, August 28-31, 1997, Washington, DC. For many helpful discussions regarding this project and comments on earlier drafts of this paper, I would like to thank Nancy Burns, Donald Kinder, Scott Allard, Fred Cutler, Paul Freedman, Marc Hetherington, and Nick Winter. I, of course, am responsible for any errors that remain. The data used in this paper were made available by the Inter-University Consortium of Political and Social Research. Neither the collector of the original data nor the consortium bears any responsibility for the analyses or interpretations presented here. This material is based upon work supported under a National Science Foundation Graduate Fellowship. Any opinions, findings, conclusions, or recommendations expressed in this paper are those of the author and do not necessarily reflect the views of the National Science Foundation.