¹ Richard Neustadt, Presidential Power and the Modern Presidents (New York: The Free Press, 1990); Samuel Kernell, Going Public: New Strategies of Presidential Leadership (Washington, D.C.: Congressional Quarterly Press, 1997).

² For legislative success, see George Edwards, Presidential Influence in Congress (San Francisco: Freeman, 1980); Douglas Rivers and Nancy Rose, ‘Passing the President’s Program: Public Opinion and Presidential Influence in Congress’, American Journal of Political Science, 29 (1985), 183–96; Brandice Canes-Wrone and Scott de Marchi, ‘Presidential Approval and Legislative Success’, Journal of Politics, 64 (2002), 491–509. For conflicting perspectives on approval’s effect on legislative influence, see Kenneth Collier and Terry Sullivan, ‘New Evidence Undercutting the Linkage of Approval with Presidential Support and Influence’, Journal of Politics, 57 (1995), 197–209; and Jeffrey Cohen, Jon Bond, Richard Fleisher and John Hamman, ‘State Level Presidential Approval and Senatorial Support’, Legislative Studies Quarterly, 15 (2000), 577–90. For electoral outcomes, see James Campbell and Joe Sumners, ‘Presidential Coattails in Senate Elections’, American Political Science Review, 84 (1990), 513–24; James Campbell, ‘Presidential Coattails and Midterm Losses in State Legislative Elections’, American Political Science Review, 80 (1986), 45–63; Robert Erikson and Chris Wlezien, ‘Of Time and Presidential Election Forecasts’, PS: Political Science and Politics, 29 (1996), 37–9. On the frequency of military action, see Charles Ostrom and Bryan Job, ‘The President and the Political Use of Force’, American Political Science Review, 80 (1986), 541–66; Patrick James and John Oneal, ‘The Influence of Domestic and International Politics on the President’s Use of Force’, Journal of Conflict Resolution, 35 (1991), 307–32. For a contrasting view, see James Meernik, ‘Presidential Decision-making and the Political Use of Force’, International Studies Quarterly, 38 (1994), 121–38; William Howell and Jon Pevehouse, ‘Presidents, Congress and the Use of Force’, International Organization, 59 (2005), 209–32.

³ Such a strategy may have made sense in 2004 when Bush’s approval hovered in the low 50s. By contrast, in January 2007, with his approval mired in the low 30s, Bush shifted strategies. In his 2007 ‘State of the Union Address’, the president proposed a number of policies designed not to minimize the variance in his support, but to appeal to moderates in the hopes of increasing it, even if some of his initiatives, such as comprehensive immigration reform, may raise approval volatility among his core supporters.

⁴ See, for example, Robert Erikson and Christopher Wlezien, ‘Post-Election Reflections on Our Pre-Election Predictions’, PS: Political Science and Politics, 38 (2005), 25–6; Alan Abramowitz, ‘The Time for Change Model and the 2004 Presidential Election: A Post-Mortem and a Look Ahead’, PS: Political Science and Politics, 38 (2005), 31; Thomas Holbrooke, ‘A Post-Mortem and Update of the Economic News and Personal Finances Forecasting Model’, PS: Political Science and Politics, 38 (2005), 35–6.

⁵ Of course, if the mean level of support for the president was exactly 50 per cent and the other 50 per cent unanimously supported his opponent, reducing the variance would only affect the likely margin of victory or defeat, not its probability. However, if the mean level of support was in the low 50s, or if support for the president’s chief rival was less than 50 per cent, then reducing the variance in support, absent any change in the mean, could greatly increase the president’s probability of receiving more support than his opponent. To some extent, these dynamics mirror an important strand of literature on congressional elections. For example, Thomas Mann argues that the growing personal incumbency advantage of Members of Congress has not resulted in significantly lower turnover rates in Congress in recent decades because, while the mean margin of victory has increased, so, too, has the variance in congressional vote swings (Thomas Mann, Unsafe at Any Margin: Interpreting Congressional Elections (Washington, D.C.: American Enterprise Institute, 1978)). Even as the average margin of victory grows, because the variance is also increasing, the electoral risks incumbents face also rise. See also Gary Jacobson, ‘The Marginals Never Vanished: Incumbency and Competition in Elections to the U.S. House of Representatives’, American Journal of Political Science, 31 (1987), 126–41; Gary Jacobson, Politics of Congressional Elections (New York: Pearson Longman, 2004). For a more sceptical analysis of whether this dynamic continues to hold true in recent decades, see Stephen Ansolabehere and James M. Snyder, ‘The Incumbency Advantage in U.S. Elections: An Analysis of State and Federal Offices, 1942–2000’, Election Law Journal, 1 (2002), 315–38.

⁶ R. Michael Alvarez and Charles Franklin, ‘Uncertainty and Political Perceptions’, Journal of Politics, 56 (1994), 671–88; R. Michael Alvarez and John Brehm, Hard Choices, Easy Answers: Values, Information and American Public Opinion (Princeton, N.J.: Princeton University Press, 2002); Bear Braumoeller, ‘Explaining Variance; Or, Stuck in a Moment We Can’t Get Out Of’, Political Analysis, 14 (2006), 268–90; Luke Keele and Jennifer Wolak, ‘Value Conflict and Volatility in Party Identification’, British Journal of Political Science, 36 (2006), 671–90; Dean Lacy, ‘A Theory of Nonseparable Preferences in Survey Responses’, American Journal of Political Science, 45 (2001), 239–58. For studies of variance specifically focusing on presidential approval, see Paul Gronke, ‘Policies, Prototypes, and Presidential Approval’ (paper presented at the Annual Meeting of the American Political Science Association Atlanta, 1999); Paul Gronke and John Brehm, ‘History, Heterogeneity, and Presidential Approval: A Modified ARCH Approach’, Electoral Studies, 21 (2002), 425–52; Douglas Kriner, ‘Examining Variance in Presidential Approval: The Case of FDR in World War II’, Public Opinion Quarterly, 70 (2006), 23–47.

⁷ John Mueller, ‘Presidential Popularity from Truman to Johnson’, American Political Science Review, 64 (1970), 18–34; Richard A. Brody and Catherine Shapiro, ‘A Reconsideration of the Rally Phenomenon in Public Opinion’, in Samuel Long, ed., Political Behavior Annual (Boulder, Colo.: Westview, 1989), pp. 77–102; Bradley Lian and John R. Oneal, ‘Presidents, the Use of Military Force, and Public Opinion’, Journal of Conflict Resolution, 37 (1993), 277–300; Paul Brace and Barbara Hinckley, ‘The Structure of Presidential Approval’, Journal of Politics, 53 (1991), 993–1017.

⁸ John Mueller, War, Presidents, and Public Opinion (New York: John Wiley and Sons, 1973); Adam Berinksy, ‘Assuming the Costs of War: Events, Elites, and American Public Support for Military Conflict’, Journal of Politics, 69 (2007), 975–97; Christopher Gelpi, Peter Feaver and Jason Reifler. ‘Success Matters: Casualty Sensitivity and the War in Iraq’, International Security, 30 (2005/2006), 7–46; Eric Larson, Casualties and Consensus: The Historical Role of Casualties in Domestic Support for U.S. Military Operations (Santa Monica, Calif.: RAND, 1996); Bruce Jentleson and Rebecca Britton, ‘Still Pretty Prudent: Post-Cold War American Public Opinion on the Use of Military Force’, Journal of Conflict Resolution, 42 (1998), 395–417; Bruce Jentleson, ‘The Pretty Prudent Public: Post Post-Vietnam American Opinion on the Use of Military Force’, International Studies Quarterly, 36 (1992), 49–74.

⁹ Phillip Converse, ‘The Nature of Belief Systems in Mass Publics’, in David Apter, ed., Ideology and Discontent (New York: Free Press, 1964), pp. 206–61.

¹⁰ Converse, ‘Nature of Belief Systems’; Phillip Converse and Gregory Markus, ‘Plus ça Change …: The New CPS Panel Study’, American Political Science Review, 73 (1979), 32–49.

¹¹ Christopher Achen, ‘Mass Political Attitudes and the Survey Response’, American Political Science Review, 69 (1975), 1218–31; Gillian Dean and Thomas Moran, ‘Measuring Mass Political Attitudes: Change and Unreliability’, Political Methodology, 4 (1977), 383–401; Robert Erikson, ‘The SRC Panel Data and Mass Political Attitudes’, British Journal of Political Science, 9 (1979), 16–49; Stanley Feldman, ‘Measuring Issue Preferences: The Problem of Response Instability’, Political Analysis, 1 (1989), 25–60.

¹² Timothy Wilson and Sarah Hodges, ‘Attitudes as Temporary Constructs’, in Abraham Tesser and L. Martin, eds, The Construction of Social Judgment (Hillsdale, N.J.: Erlbaum, 1991), pp. 37–65; Jennifer Hochschild, What’s Fair? Americans’ Attitudes Toward Distributive Justice (Cambridge, Mass.: Harvard University Press, 1981); Robert Wyer and Jon Hartwick, ‘The Recall and Use of Belief Statements as Bases for Judgments’, Journal of Experimental Social Psychology, 20 (1984), 65–85.

¹³ Shelly Taylor and Susan Fiske, ‘Salience, Attention and Attribution: Top of the Head Phenomena’, in Leonard Berkowitz, ed., Advances in Experimental Social Psychology (New York: Academic Press, 1978), pp. 249–88; Amos Tversky and Daniel Kahneman, ‘The Framing of Decisions and the Psychology of Choice’, in Robin Hogarth, ed., Question Framing and Response Consistency (San Francisco: Jossey-Bass, 1982), pp. 3–20.

¹⁴ Angus Campbell, Philip Converse, Warren Miller and Donald Stokes, The American Voter (New York: Wiley, 1960); Stanley Kelley, Interpreting Elections (Princeton, N.J.: Princeton University Press, 1983); John Zaller, The Nature and Origin of Mass Opinion (Cambridge: Cambridge University Press, 1992).

¹⁵ A third school of thought embraces an on-line processing or running tally model, suggesting that individuals process additional information as it arises and use it to update their prior opinions on a given topic. See Milton Lodge, Kathleen McGraw and Patrick Stroh, ‘An Impression-Driven Model of Candidate Evaluation’, American Political Science Review, 83 (1989), 399–420; Reid Hastie and Bernadette Park, ‘The Relationship Between Memory and Judgment Depends on Whether the Judgment Task Is On-line or Memory Based’, Psychological Review, 93 (1986), 258–68; Kathleen McGraw, Milton Lodge and Patrick Stroh, ‘On-Line Processing in Candidate Evaluation: The Effects of Issue Order, Issue Importance, and Sophistication’, Political Behavior, 12 (1990), 41–58; Milton Lodge, Marco Steenbergen and Shawn Brau, ‘The Responsive Voter: Campaign Information and the Dynamics of Candidate Evaluation’, American Political Science Review, 89 (1995), 309–26. In this model, conflicting considerations should not affect the variance in individuals’ responses, but only the mean level of individuals’ responses.

¹⁶ John Zaller and Stanley Feldman, ‘A Simple Theory of the Survey Response: Answering Questions Versus Revealing Preferences’, American Journal of Political Science, 36 (1992), 579–616, at p. 598. Others have stressed the importance of uncertainty, in addition to and distinct from ambivalence, in driving response variance (see Alvarez and Franklin, ‘Uncertainty and Political Perceptions’; R. Michael Alvarez and John Brehm, ‘Are Americans Ambivalent Towards Racial Policies?’ American Journal of Political Science, 41 (1997), 345–74). Indeed, an uncertainty perspective may explain the high base level of variance (relative to the average approval variance for members of the president’s party) observed for independents’ support of the president, as they lack strong predispositions to guide their approval responses and hence may be less certain in their evaluations than partisan identifiers. We discuss uncertainty as a possible source of approval variance further when we discuss our reasons for adding a ‘month of term’ variable to track changes in variance over the course of a presidential administration. However, because our theory emphasizes the way in which various positive and negative events reinforce or conflict with partisan predispositions, we focus here on conflicting considerations and ambivalence.

¹⁷ Partisan attachments, reinforced by self-selection of media sources, may also dramatically shape how individuals view the same events (see Larry Bartels, ‘Beyond the Running Tally: Partisan Bias in Political Perceptions’, Political Behavior, 24 (2002), 117–50). However, we contend that while there is some room for differences in interpretation of high combat casualties and positive or negative rally events, there is enough of an objective basis on which most can agree that these developments either reflect positively or negatively upon the president and his administration.

¹⁸ In a similar vein, Paul Sniderman and Edward Carmines explore whether liberals who hold negative stereotypes of blacks are more ambivalent when asked their support for government assistance to ‘blacks and minorities’ than when asked their support for assistance to ‘new immigrants from Europe’. Measuring ambivalence as the time it takes to respond to the survey question, Sniderman and Carmines demonstrate that this group was more ambivalent when the question triggered their conflicting liberalism and racial stereotypes than when the question queried support for aiding white immigrants and therefore did not trigger an underlying value conflict (Paul Sniderman and Edward Carmines, Reaching Beyond Race (Cambridge, Mass.: Harvard University Press, 1997), pp. 84–9).

¹⁹ Before proceeding to the empirical work, a caveat regarding ecological inference is in order. Our hypotheses for positive and negative developments’ effects on approval volatility are based on assumptions about how these developments will affect cognitive processes at the individual level. However, any inferences drawn from patterns in volatility at the aggregate level about micro-foundations are potentially suspect. That is, even if we observe approval volatility at the aggregate level responding in the predicted ways, we cannot claim this is evidence for the hypothesized cognitive processes at the individual level. As a result, after discussing the aggregate level results we shift to an analysis of individual level panel data in the next section. Moreover, previous studies of variance in approval at the individual level have confirmed the importance of conflicting considerations and ambivalence emphasized here (Gronke, ‘Policies, Prototypes, and Presidential Approval’; Kriner, ‘Examining Variance’); as has recent work on the sources of volatility in partisan identification (Keele and Wolak, ‘Value Conflict and Volatility in Party Identification’).

²⁰ Converse, ‘The Nature of Belief Systems in Mass Publics’.

²¹ Charles Franklin, ‘Eschewing Obfuscation? Campaigns and Perceptions of U.S. Senate Incumbents’, American Political Science Review, 85 (1991), 1193–214.

²² R. Michael Alvarez and John Brehm, ‘American Ambivalence Towards Abortion Policy: Development of a Heteroscedastic Probit Model of Competing Values’, American Journal of Political Science, 39 (1995), 1055–82; Alvarez and Brehm, ‘Are Americans Ambivalent Towards Racial Policies?’ Alvarez and Brehm, Hard Choices, Easy Answers; Keele and Wolak, ‘Value Conflict and Volatility in Party Identification’.

²³ For advances in the presidential approval literature, see Nathaniel Beck, ‘Comparing Dynamic Specifications: The Case of Presidential Approval’, Political Analysis, 3 (1991), 51–88; Matthew Lebo, ed., ‘Advances in the Analysis of Political Time Series’, Special Volume of Electoral Studies, 19 (2000), 1–110, p. 1; B. Dan Wood, ‘Weak Theories and Parameter Instability: Using Flexible Least Squares to Take Time Varying Relationships Seriously’, American Journal of Political Science, 44 (2000), 603–18; Barry Burden and Anthony Mughan, ‘International Economy and Presidential Approval’, Public Opinion Quarterly, 67 (2003), 555–78. For a review, see Paul Gronke and Brian Newman, ‘From FDR to Clinton, From Mueller to ?: A Field Essay on Presidential Approval’, Political Research Quarterly, 56 (2003), 501–12. On heteroscedasticity-consistent standard errors, see Halbert White, ‘A Heteroscedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroscedasticity’, Econometrica, 48 (1980), 817–38.

²⁴ Gronke and Brehm, ‘History, Heterogeneity, and Presidential Approval’; Kriner, ‘Examining Variance’.

²⁵ Gronke and Brehm, ‘History, Heterogeneity, and Presidential Approval’; for example, Gronke and Brehm find no influence for two broad categories of positive and negative effects on approval variance, but a positive relationship between the percentage of the electorate identifying as independents at a given time and approval volatility. When disaggregating the event categories into eight categories, they find significant negative effects for adverse economic events and domestic accomplishments, but the coefficient for independent identifiers is no longer statistically significant.

²⁶ Because the sample sizes are considerably smaller, a handful of one-day polls conducted by Gallup, primarily from the Clinton era, were dropped. Re-estimating the models with these polls in the sample yields very similar results. As a robustness check, all models were also re-estimated using Kalman filtered approval data (Donald Green, Alan Gerber, and Suzanna De Boef, ‘Tracking Opinion over Time: A Method for Reducing Sample Error’, Public Opinion Quarterly, 63 (1999), 178–92) with very similar results across specifications.

²⁷ For rally events, see Brace and Hinckley, ‘The Structure of Presidential Approval’; Gronke and Brehm, ‘History, Heterogeneity, and Presidential Approval’. Although all of the sources originally used by Brace and Hinckley were not available for the current period, the event series was updated using both the World Almanac and Time Almanac annual chronologies (Time Almanac only after October 2005) following identical coding rules. In examining only Vietnam casualties during the Johnson administration, we follow, inter alia, Gronke and Brehm, ‘History, Heterogeneity, and Presidential Approval’; Michael MacKuen, Robert Erikson and James Stimson, ‘Peasants or Bankers? The American Electorate and the US Economy’, American Political Science Review, 86 (1992), 597–611. Vietnam casualty information was compiled from the National Archives and Record Administration’s Coffelt Database [Records with Unit Information on Military Personnel Who Died During the Vietnam Conflict] and Iraq casualty information obtained from Department of Defense records [http://siadapp.dior.whs.mil/personnel/CASUALTY/castop.htm]. Alternatively, we also replicated our models using a simple dummy variable for each war with virtually identical results. Specifically, both the Vietnam and Iraq dummies were negative and statistically significant in the mean specification for all three partisan series. For the president’s co-partisans, the coefficient for both war dummies in the variance equation was positive and statistically significant. For the president’s partisan opponents, both war coefficients were negative, though the Vietnam coefficient narrowly failed to meet conventional levels of statistical significance. And neither coefficient was significant in the variance equation for independents. Quarterly Index of Consumer Sentiment data was taken from the University of Michigan’s Survey of Consumers.

²⁸ Mueller, War, Presidents, and Public Opinion; Eugene Wittkopf, Faces of Internationalism: Public Opinion and American Foreign Policy (Durham, N.C.: Duke University Press, 1990); Samuel Kernell, ‘Explaining Presidential Popularity. How Ad Hoc Theorizing, Misplaced Emphasis, and Insufficient Care in Measuring One’s Variables Refuted Common Sense and Led Conventional Wisdom Down the Path of Anomalies’, American Political Science Review, 72 (1978), 506–22; Scott Sigmund Gartner and Gary M. Segura, ‘War, Casualties, and Public Opinion’, Journal of Conflict Resolution, 42 (1998), 278–300; Benjamin Schwarz, Casualties, Public Opinion and U.S. Military Intervention: Implications for U.S. Regional Deterrence Strategies (Santa Monica, Calif.: RAND, 1994); Matthew Baum and Samuel Kernell, ‘Economic Class and Popular Support for Franklin Roosevelt in War and Peace’, Public Opinion Quarterly, 65 (2001), 198–229. But see Eric Larson, Casualties and Consensus: The Historical Role of Casualties in Domestic Support for U.S. Wars and Military Operations (Santa Monica, Calif.: RAND, 1996); and James Burk, ‘Public Support for Peacekeeping in Lebanon and Somalia: Assessing the Casualties Hypothesis’, Political Science Quarterly, 114 (1999), 53–78.

²⁹ Christopher Gelpi, Peter Feaver and Jason Reifler, ‘Casualty Sensitivity and the War in Iraq’, International Security, 30 (2005), 7–46; Richard Eichenberg, Richard Stoll and Matthew Lebo, ‘War President: The Approval Ratings of George W. Bush’, Journal of Conflict Resolution, 50 (2006), 783–808; Erik Voeten and Paul Brewer, ‘Public Opinion, the War in Iraq, and Presidential Accountability’, Journal of Conflict Resolution, 50 (2006), 809–30.

³⁰ Inter alia, Robert Shapiro and Bruce Conforto, ‘Presidential Performance, the Economy and the Public’s Evaluation of Economic Conditions’, Journal of Politics, 42 (1980), 49–67. Indeed, MacKuen, Erikson and Stimson have shown that after controlling for public perceptions of economic health, traditional objective measures such as unemployment and inflation are no longer significant predictors of approval (MacKuen, Erikson and Stimson, ‘Peasants or Bankers?’). In the past twenty years a growing debate has arisen over whether prospective (MacKuen, Erikson and Stimson, ‘Peasants or Bankers?’ Robert Erikson, Michael MacKuen and James Stimson, ‘Bankers or Peasants Revisited: Economic Expectations and Presidential Approval’, Electoral Studies, 19 (2000), 295–312) or a mix of prospective and retrospective (Harold Clarke and Marianne Stewart, ‘Prospections, Retrospections and Rationality: The ‘Bankers’ Model of Presidential Approval Reconsidered’, 38 (1994), 1104–23) evaluations of the economy best account for movement in the approval series. While these scholars have decomposed the Index of Consumer Sentiment into its constituent parts to examine the relative influence of its prospective and retrospective components, we follow the lead of Burden and Mughan and others and simply include the undifferentiated index as a control (e.g. Burden and Mughan, ‘The International Economy and Presidential Approval’; Eichenberg, Stoll and Lebo, ‘War President’). However, to insure that our results are not sensitive to the operationalization of the economic measures, we re-estimated all of our models in Table 1 first by disaggregating the ICS into its constituent parts and in a second robustness check by also adding the objective measures of unemployment and inflation. When using these disaggregated measures, consistent with MacKuen, Erikson and Stimson, we find that prospective evaluations of expected future economic performance are strong predictors of support for the president. And most importantly, in both alternative specifications all of our substantive findings in the variance equation remain virtually identical to those reported in Table 1.

³¹ Mueller, ‘Presidential Popularity from Truman to Johnson’; Charles Ostrom and Dennis Simon, ‘Promise and Performance: A Dynamic Model of Presidential Popularity’, American Political Science Review, 79 (1985), 334–58; Brace and Hinckley, ‘The Structure of Presidential Approval’; Brody and Shapiro, ‘A Reconsideration of the Rally Phenomenon in Public Opinion’; George C. Edwards and Tami Swenson, ‘Who Rallies? The Anatomy of a Rally Event’, Journal of Politics, 59 (1997), 200–12. But see Lian and Oneal, ‘Presidents, the Use of Military Force, and Public Opinion’; Matthew Baum, ‘The Constituent Foundations of the Rally-Round-the-Flag Phenomenon’, International Studies Quarterly, 46 (2002), 263–98.

³² There is considerable debate within the literature as to whether presidential approval is a stationary series. Augmented Dickey–Fuller Tests (ADF), GLS Dickey–Fuller tests (DFGLS) and Phillips–Perron (PP) tests all reject the null hypothesis of a unit root, p < 0.01, for each of our three partisan approval series. However, KPSS tests suggest that we can reject the null hypothesis that the series is stationary. Thus, all three of our approval series may be near-integrated (Suzanna DeBoef and Jim Granato, ‘Near-Integrated Data and the Analysis of Political Relationships’, American Journal of Political Science, 41 (1997), 619–40) or fractionally-integrated (Matthew Lebo and Harold Clarke, ‘You Must Remember This: Dealing with Long Memory in Political Analyses’, Electoral Studies, 19 (2000), 31–48). While such series are asymptotically stationary, in finite samples they may mimic integrated series and be susceptible to spurious regression results. One solution for analysing near-integrated data is to transform the approval series into first differences (DeBoef and Granato, ‘Near-Integrated Data and the Analysis of Political Relationships’; Harold Clarke, Marianne Stewart, Mike Ault and Euel Elliot, ‘Men, Women, and the Dynamics of Presidential Approval’, British Journal of Political Science, 35 (2004), 31–51). Therefore, as a robustness check we reanalysed all three of our models using the change in presidential approval from the preceding to the current observation as the dependent variable. ADF, DFGLS and PP tests on all three first-differenced series reject a unit root, and KPSS tests cannot reject the null hypothesis that the resulting series are stationary. All results remain virtually identical to those presented in the text. Specifically, for members of the president’s party, combat casualties in Vietnam and Iraq increased the variance in change in approval. Negative events were also positively correlated with increasing variance, though the coefficient failed to meet conventional levels of statistical significance. Among opposition party identifiers, positive rally events increased approval variance, while combat casualties in both wars decreased it. Variance also decreased considerably over the course of each presidency. And among independents, neither rally events nor casualties had any statistically significant effect on variance, and the coefficient for the month of term variable, while negative as expected, narrowly misses conventional levels of statistical significance. Because of this robustness check on the differenced approval series, we are confident that the results presented in the text and Table 1 are not spurious.

³³ As Nathaniel Beck notes, it is empirically difficult to distinguish MA from AR error processes (Nathaniel Beck, ‘Comparing Dynamic Specifications: The Case of Presidential Approval’, Political Analysis, 3 (1991), 51–88). All models were also re-estimated with an AR(1) error specification with virtually identical results. Most importantly, the signs and significance levels for all of our variables of interest in the variance equation remain unchanged.

³⁴ Gary King, Unifying Political Methodology: The Likelihood Theory of Statistical Inference (Ann Arbor: The University of Michigan Press, 1998); M. Davidian and R.J. Carroll, ‘Variance Function Estimation’, Journal of the American Statistical Association, 82 (1987), 1079–91.

³⁵ The Lagrange multiplier test statistics for all three series are as follows. For president’s co-partisans, the statistic was 33.42; for partisan opponents it was 20.07; and for independents it was 15.79. All of these are higher than the chi-squared p < 0.01 critical value with one degree of freedom (6.64), leading us to reject the null hypothesis of no first order ARCH effects. Regression analysis of the squared residuals on multiple lags showed no evidence of higher order ARCH effects.

³⁶ Scholars have demonstrated that a variety of factors – from an omitted variable in the mean equation to residual autocorrelation – can cause an erroneous rejection of the null of conditional homoscedasticity. See Dick van Dijk, Philip Hans Franses and Andre Lucas, ‘Testing for Arch in the Presence of Additive Outliers’, Journal of Applied Econometrics, 14 (1999), 539–62; Robin Lumsdaine and Serena Ng, ‘Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean’, Journal of Econometrics, 93 (1999), 257–79. Consequently, we also re-estimated all three models using only a multiplicative heteroscedastic parameterization of the variance, with no ARCH term. For each partisan series, the results are virtually identical to those reported in Table 1, greatly strengthening confidence in the robustness of our results.

³⁷ See Alvarez and Franklin, ‘Uncertainty and Political Perceptions’; Alvarez and Brehm, ‘Are Americans Ambivalent Towards Racial Policies?’

³⁸ Moreover, the significant, positive relationships for both Vietnam and Iraq casualties are robust across specifications and operationalizations of casualties (e.g. last month, quarterly, cumulative).

³⁹ Gary C. Jacobson, A Divider, Not a Uniter: George W. Bush and the American People (New York: Pearson Longman, 2006).

⁴⁰ All first differences in Table 2 are estimated for the George W. Bush presidency, except for the Vietnam casualties effects, which were estimated for the Johnson presidency. The positive and negative event first differences were estimated for the pre-Iraq period in the twenty-fourth month of the Bush presidency. The month of presidency first difference was also estimated with Iraq casualties set equal to zero.

⁴¹ Baum, ‘The Constituent Foundations of the Rally-Round-the-Flag Phenomenon’.

⁴² Brody and Shapiro, ‘A Reconsideration of the Rally Phenomenon’; Richard A. Brody, Assessing the President: The Media, Elite Opinion, and Public Support (Stanford, Calif.: Stanford University Press, 1991).

⁴³ Fred Greenstein, The Hidden Hand Presidency: Eisenhower as Leader (New York: Basic Books, 1982).

⁴⁴ Indeed, there are other potential explanations for why aggregate-level approval variance increases or decreases in the manner observed. For example, the effect of combat casualties on presidential support among members of his party may be conditional. In some cases, his co-partisans may rally behind the ‘Commander in Chief’; in others, they may remain steadfast in their previous levels of support; and in still other conditions, as we are now beginning to witness with the war in Iraq, some co-partisans may begin to drift away from their party leader. On average, we observe a modest decline, as captured in the model of mean approval; however, because the effect of casualties is conditional on other factors not captured in the model, we observe greater levels of uncertainty and variance around that mean estimate. If this alternative dynamic is driving aggregate level variance, then the observed variance is a result of model misspecification, not increased volatility in individual level support for the president. New theory would be needed to illuminate our understanding of how the impact of traditional explanatory variables, such as casualties and positive and negative events, on approval is contingent and varies across environmental and political conditions. We thank an anonymous reviewer for suggesting this alternative to us.

⁴⁵ These overall levels of volatility are consistent with other studies of approval instability across repeated panel surveys; see Kent Tedin, ‘Change and Stability in Presidential Popularity at the Individual Level’, Public Opinion Quarterly, 40 (1986), 555–62; Charles Ostrom and Dennis Simon, ‘The President’s Public’, American Journal of Political Science, 32 (1988), 1096–119.

⁴⁶ These respondents’ attitudes on the economy and Iran were constant across all three surveys.

⁴⁷ In the reported analysis, we define a switch as any change in approval response – including for example a shift from no opinion to support, or from disapproval to no opinion (less than 2 per cent of all switches were of this type). Although the number of approval switches is essentially a count variable, not an ordinal one, it has an upper bound of two, which raises concerns about whether a Poisson model is appropriate. However, replicating the analyses in Table 4 with a Poisson event count model yields virtually identical results in both specifications. Moreover, the predicted values from this model for all observations are within the bounds of 0 and 2. As a further robustness check, we also created a binary variant of the dependent variable (switchers v. non-switchers) and estimated the same specifications with a logit model. These models, too, yielded virtually identical results.