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Context and Economic Expectations: When Do Voters Get It Right?

Published online by Cambridge University Press:  28 September 2010

Raymond M. Duch  and
Randolph T. Stevenson
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Abstract

This article discusses the accuracy and sources of economic assessments in three ways. First, following the rational expectations literature in economics, a large sample of countries over a long time period permits tests of the unbiasedness implication of the rational expectations hypotheses (REH), revealing much variation in the accuracy of expectations and the nature of the biases in expectations. Secondly, a theory of expectation formation encompassing the unbiasedness prediction of the REH and setting out the conditions under which economic expectations should be too optimistic or too pessimistic is elucidated. Zaller’s theory of political attitude formation allows the identification of variables conditioning the accuracy of expectations across contexts, drawing a link between the thinking of political scientists and economists about expectation formation. Finally, the theoretical argument that political context impacts the accuracy of average expectations is tested.

Type
Research Article
Information
British Journal of Political Science , Volume 41 , Issue 1 , January 2011 , pp. 1 - 31
Copyright
Copyright © Cambridge University Press 2010

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References

1 We use the term economic ‘perceptions’ exclusively to refer to subjective perceptions of the past or current economy and economic ‘expectations’ to refer to expectations of the future economy. When we mean to refer to both perceptions and expectations, we use the term ‘assessments’ or ‘evaluations’.

2 Zaller, John, The Nature and Origins of Mass Opinion (New York: Cambridge University Press, 1992)CrossRefGoogle Scholar.

3 Our empirical work adheres, more closely than is usual in political science, to the lessons learned in the well-developed econometric literature on testing rational expectations (or, more generally, using expectations data to examine questions about accuracy). While this may distract some political scientists unfamiliar with the somewhat technical econometric debates that animate much of this literature, we think this approach is essential if our contextual analysis of economic expectations is to have more impact in the economics literature than has previous work on economic expectations in political science.

4 Johnston Conover, Pamela, Feldman, Stanley and Knight, Kathleen, ‘Judging Inflation and Unemployment: The Origins of Retrospective Evaluations’, Journal of Politics, 48 (1986), 565–588CrossRefGoogle Scholar.

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8 Duch, Palmer and Anderson, ‘Heterogeneity in Perceptions of National Economic Conditions’; Hetherington, Marc J., ‘The Media’s Role in Forming Voters’ National Economic Evaluations in 1992’, American Journal of Political Science, 40 (1996), 372–395CrossRefGoogle Scholar; Bartels, Larry, ‘Uninformed Votes: Information Effects in Presidential Elections’, American Journal of Political Science, 40 (1996), 194–230CrossRefGoogle Scholar. It should be pointed out that an important difference between the measurement of subjective economic evaluations in political science versus economic research is the content of the survey instruments. One of the major factors contributing to endogeneity of economic perceptions in the political science realm is the fact that questions regarding economic evaluations are typically asked in survey instruments that include a battery of political partisanship and preference questions which might principally cause the bias ( Palmer, Harvey D. and Duch, Raymond M., ‘Do Surveys Provide Representative or Whimsical Assessments of the Economy?’ Political Analysis, 9 (2001), 58–77CrossRefGoogle Scholar; Erikson, ‘Macro vs. Micro-Level Perspectives on Economic Voting’.). Instruments designed by economists to measure subject economic assessments are not likely to include these political items.

9 Erikson, Robert S., Mackuen, Michael B. and Stimson, James A., The Macro Polity (Cambridge: Cambridge University Press, 2002), p. 85Google Scholar.

10 MacKuen, Michael B., Erikson, Robert S. and Stimson, James A., ‘Peasants or Bankers? The American Electorate and the U.S. Economy’, American Political Science Review, 86 (1992), 597–611CrossRefGoogle Scholar.

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14 De Boef and Kellstedt, ‘The Political (and Economic) Origins of Consumer Confidence’.

15 Though certainly not our main focus, our empirical strategy in this article reflects our argument that insights into the relationship between economic evaluations and actual economic outcomes must be grounded on evaluations of specific economic outcomes. Very few of the existing studies in political science (which usually question the accuracy of average economic evaluations) examine respondents’ evaluations of specific indicators of the economy like inflation or unemployment. They focus instead on the correspondence between these kinds of economic indicators and evaluations of the economy in general (Durr, ‘What Moves Policy Sentiment?’; Freeman, John, Hauser, Daniel, Kellstedt, Paul and Williams, John, ‘Long Memoried Processes, Unit Roots, and Causal Inference in Political Science’, American Journal of Political Science, 42 (1998), 1289–1327CrossRefGoogle Scholar; De Boef and Kellstedt, ‘The Political (and Economic) Origins of Consumer Confidence’; Suzuki, Motoshi, ‘Political Business Cycles in the Public Mind’, American Political Science Review, 86 (1992), 989–996CrossRefGoogle Scholar; Nadeau, Richard, Niemi, Richard, Fan, David and Amato, Timothy, ‘Elite Economic Forecasts, Economic News, Mass Economic Judgements and Presidential Approval, Journal of Politics, 61 (1999), 109–135CrossRefGoogle Scholar; MacKuen, Erikson and Stimson, ‘Peasants or Bankers’; Haller and Norpoth, ‘Let the Good Times Roll’; Goidel, R. K. and Langley, R. E., ‘Media Coverage of the Economy and Aggregate Economic Evaluations: Uncovering Evidence of Indirect Media Effects’, Political Research Quarterly, 48 (1995), 313–328CrossRefGoogle Scholar; Krause, George, ‘Voters, Information Heterogeneity, and the Dynamics of Aggregate Economic Expectations’, American Journal of Political Science, 41 (1997), 1170–1200CrossRefGoogle Scholar; Sanders, David and Gavin, Neil, ‘Television News, Economic Perceptions and Political Preferences in Britain, 1997–2001’, Journal of Politics, 66 (2004), 1245–1266CrossRefGoogle Scholar). Most commonly, scholars have measured general economic evaluations using the University of Michigan’s Index of Consumer Sentiment in the United States. This measure is an aggregation of responses to questions about current family finances, current business conditions, current buying conditions, next year’s family finances, short-term business expectations and long-term business expectations. The problem with using this measure to investigate a respondent’s knowledge about the state of the macro economy is that it confounds knowledge with the voter’s unknown process of aggregating various kinds of information in making a general assessment. As such, it is unclear exactly what correspondence one would expect between this summary measure and specific economic indicators. Since the respondent’s answer to any one of the questions that make up the index will be likely to combine his knowledge of various economic indicators (among other things) in potentially complicated ways, deviations between measures of the realized economy (e.g., an unemployment or inflation time series) and consumer sentiment may not be indicative of a lack of knowledge on the part of the voter. Rather, such deviations may simply reflect the weight the average voter places on that indicator in her overall assessment of the economy. The same critique applies to other common measures of general economic evaluations, as pointed out by Clark and Stewart (Harold Clark and Marianne Stewart, ‘Prospections, Retrospections, and Rationality’, American Journal of Political Science, 38 (1994), 104–23). There are exceptions, though. In the 1980s, Conover, Feldman and Knight examined unemployment expectations per se. And more recently, examples of modelling efforts that focus on specific indicators include Haller and Norpoth, ‘Let the Good Times Roll’;per se. And more recently, examples of modelling efforts that focus on specific indicators include Haller and Norpoth, ‘Let the Good Times Roll’; Granato, Jim and Krause, George A., ‘Information Diffusion within the Electorate: The Asymmetric Transmission of Political-Economic Information’, Electoral Studies, 19 (2000), 519–537CrossRefGoogle Scholar; Krause, George A. and Granato, Jim, ‘Fooling Some of the Public Some of the Time? A Test for Weak Rationality with Heterogeneous Information Levels’, Public Opinion Quarterly, 62 (1998), 135–151CrossRefGoogle Scholar; and Krause, George A., ‘Testing for the Strong Form of Rational Expectations with Heterogeneously Informed Agents’, Political Analysis, 8 (2000), 285–305CrossRefGoogle Scholar.

16 For a somewhat similar approach to estimating the REH on European data, see Ricardo Mestre, ‘Are Survey-Based Inflation Expectations in the Euro Area Informative’ (European Central Bank Working Paper Series no. 721, 2007), although these estimates of REH are based on the aggregated EU consumer inflation expectation series for the Euro area and hence are not concerned with specific country estimates and cross-county variations.

17 Pesaran, M. H., The Limits to Rational Expectations, reprinted with corrections (Oxford: Basil Blackwell, 1989)Google Scholar.

18 This is important to the interpretation of the results. In our view, the ‘expectations’ data thus generated (and used by almost all economic studies of REH) are really a combination of perceptions and expectations and so the most accurate way to think about these data is as measures of both expectations of the future and perceptions of the past. However, since most of the arguments that have been made concerning REH and the arguments we will make about political and economic differences in context can be applied to both perceptions and expectations with little adjustment (the formal conditions for rational economic perceptions would be very similar to those provided below, with the exception that the only relevant piece of information in the citizens information set would be the real value of the economy itself), we will focus on, and use the language of, expectations (as all other analyses in economics do).

19 One could reverse the process – using the expectations data in the transformation of the scale of the perceptions data, but then using that series as if it were somehow different from the one transformed in the other direction strikes us as illegitimate. Finally, there are other methods of transformation that do not rely on having both kinds of series, but these both require the evaluations data to be disaggregated at a level that is not available to us, and have been shown to be less accurate for expectations than the method we use.

20 As it turns out, our intuition, that there would be large differences between the reported series and the updated series, and that these would be consequential for the analysis, was wrong. The use of reported data here is not substantively important. One result of this is that we use it for both the prospective and retrospective analyses, despite the argument that rational expectations about the true economy, if they come from a correct ‘model’ that citizens use to forecast the economy, should be compared to the real economy, not the reported one.

21 Madsen, Jakob, ‘Formation of Inflation Expectations: From the Simple to the Rational Expectations Hypothesis’, Applied Economics, 28 (1996), 1331–1337CrossRefGoogle Scholar.

22 Carroll, Christopher D., ‘Macro-economic Expectations of Households and Professional Forecasters’, Quarterly Journal of Economics, 118 (2003), 269–298CrossRefGoogle Scholar; Thomas, Lloyd B. Jr, ‘Survey Measures of Expected U.S. Inflation’, Journal of Economic Perspectives, 13 (1999), 125–144CrossRefGoogle Scholar; Forsells, M. and Kenny, G., ‘The Rationality of Consumers’ Inflation Expectations: Survey-Based Evidence for the Euro-Area’ (Working Paper No. 163, European Central Bank Work Paper Series, 2002) http://www.ecb.int/pub/pdf/scpwps/ecbwp163.pdfGoogle Scholar; Lamla, Michael J. and Lein, Sarah M., ‘The Role of Media for Consumer’s Inflation Expectations Formation’ (Zurich: KOF Working Papers, KOF Swiss Economic Institute, 2008)Google Scholar.

23 Sargent, Thomas and Wallace, Neil, ‘Rational Expectations and the Theory of Economic Policy’, Journal of Monetary Economics, (1976), 169–183CrossRefGoogle Scholar; Lucas, Robert E. Jr, Studies in Business Cycle Theory (Cambridge, Mass.: MIT Press, 1981)Google Scholar.

24 Alt, James E. and Alec Chrystal, K., Political Economics (Berkeley: University of California Press, 1983)Google Scholar; Krause and Granato, ‘Fooling Some of the Public Some of the Time?’; Granato, Jim and Sunny Wong, M. C., The Role of Policymakers in Business Cycle Fluctuations (Cambridge: Cambridge University Press, 2006)CrossRefGoogle Scholar.

25 Lopes, A., ‘On the “Restricted Cointegration Test” as a Test of the Rational Expectations Hypothesis’, Applied Economics, 30 (1998), 269–278CrossRefGoogle Scholar.

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28 Krause and Granato, ‘Fooling Some of the Public Some of the Time?’

29 Maddala, G. and Kim, I., Unit Roots, Cointegration, and Structural Change (Cambridge: Cambridge University Press, 1998), pp. 183–184Google Scholar.

30 More specifically, this structure implies an eleven-period moving average process in the errors in Equation 1 (see Krause and Granato, ‘Fooling Some of the Public Some of the Time?’ and Hansen, Lars Peter and Hodrick, Robert J., ‘Forward Exchange Rates as Optimal Predictors of Future Spot Rates: An Econometric Analysis’, Journal of Political Economy, 88 (1980), 829–853CrossRefGoogle Scholar).

31 Phillip, P. and Hansen, B., ‘Statistical Inference in Instrumental Variables Regression with I(1) Processes’, Review of Economic Studies, 57 (1990), 99–125CrossRefGoogle Scholar.

32 Hendry, David, ‘Econometric Modeling with Cointegrated Variables: An Overview’, Oxford Bulletin of Economics and Statistics, 48 (1986), 201–239CrossRefGoogle Scholar; Saikkonen, P., ‘Asymptotically Efficient Estimation of Cointegrating Regressions’, Econometric Theory, 7 (1992), 1–21CrossRefGoogle Scholar; Stock, J. and Watson, M., ‘A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems’, Econometrica, 61 (1993), 783–820CrossRefGoogle Scholar; Phillips, P. and Loretan, M., ‘Estimating Long-Run Economic Equilibria’, Review of Economic Studies, 58 (1991), 407–436CrossRefGoogle Scholar. Hakkio, Craig S. and Rush, Mark, ‘Market Efficiency and Cointegration: An Application to the Sterling and Deutschemark Exchange Markets’, Journal of International Money and Finance, 8 (1989), 75–88CrossRefGoogle Scholar, and others (e.g. Engsted, ‘A Note on the Rationality of Inflation Expectations in the United Kingdom’) have explored the possibility of using the integration (and cointegration) properties of expectation and outcome series to produce tests of REH. In general, such tests will come down in favour of REH if outcomes and expectations are both integrated and also cointegrated. If this is true, then the series is in a long-run equilibrium and they can never wander too far apart. However, one problem with such tests (as pointed out by Lopes in ‘On the “Restricted Cointegration Test” as a Test of the Rational Expectations Hypothesis’ – especially with respect to the popular restricted cointegration test) is that two variables can be cointegrated and yet still take an extremely long time to get back into equilibrium after a shock. However, any persistence of out-of-equilibrium shocks violates the usual requirements of REH. Our own review of this literature reveals a great deal of controversy and disagreement (see, for example, Lopes, ‘On the “Restricted Cointegration Test” as a Test of the Rational Expectations Hypothesis’ and the review of studies in Maddala and Kim, Unit Roots, Cointegration, and Structural Change). This leads us to be more sceptical of the use of the integration tests for the purposes of testing REH (which, incidentally, seems to accentuate the ‘knife-edge’ quality of integration tests in general) than those which try to directly estimate the parameters of Equation 1 (or Equation 2), while allowing for the possibility that the variables are integrated and/or cointegrated. Further, since our principal interest is not in tracing out the long-term dynamics in expectations, but rather in testing some comparative hypotheses about how political and economic institutions accentuate biases in expectations, we find that equations like Equations 1 and 2 are adequate for our substantive purposes. That said, we did perform a whole set of integration based tests of REH, which are available from the authors, www.raymondduch.com\economicvoting. In general, these tests showed that both the inflation and expectations series were integrated in each country and that they were also cointegrated. However, different ECM (or, equivalently, lagged-DV) specifications, estimated in different ways, told different stories about the dynamics of the processes and were not stable to relatively minor changes in estimation strategy and specification. Thus, we could come to no firm conclusions about the nature of the biases (if any) revealed in these kinds of estimates. Thus, we chose to stick with the well-understood and often-used methods reported in the text.

33 For a review, see Maddala and Kim, Unit Roots, Cointegration, and Structural Change.

34 Stock and Watson, ‘A Simple Estimator of Cointegrating Vectors in Higher Order Integrated Systems’. Estimating dynamic regressions requires a choice of lag length for the lags and leads of differences that are included in the model. Following Ng and Perron’s review (S. Ng and P. Perron, ‘The Exact Error in Estimating the Special Density at the Origin’ (Centre interuniversitaire de recherche en économie quantitative, 1995)) of the relevant literature, we adopt Hall’s general to specific strategy ( Hall, A., ‘Testing for a Unit Root in Time Series with Pretest Data-based Model Selection’, Journal of Business and Economic Statistics, 12 (1994), pp. 461–470Google Scholar). Specifically, we start out with a large lag length (we chose 11, given the overlapping data problem discussed above), and then estimate models sequentially for decreasing lag lengths, stopping when the longest lag in a given specification is significant. This approach was applied country by country.

35 Stock and Watson estimate Saikkonen’s DOLS model and then clean up any remaining serial correlation by using the residuals from this estimation to produce a generalized least squares (GLS) estimate. Similarly, we estimate DOLS but rather than using GLS to clean up remaining serial correlation, we simply replace OLS standard errors with Newey–West standard errors (with an 11th order lag structure).

36 Since presenting the estimates of three estimation methods (and several sets of standard errors) for ten countries takes up considerable space, we relegate the detailed results to Table 1 of the Appendix.

37 We would be concerned, for example, if we ever estimated a negative relationship between expectations and realized inflation.

38 Zaller, The Nature and Origins of Mass Opinion.

39 Lazarsfeld, P. F., Berelson, B. and Gaudet, H., The People’s Choice (New York: Duell, Sloan, and Pearce, 1944)Google Scholar; Jim Granato and Krause, George A., ‘Information Diffusion within the Electorate: The Asymmetric Transmission of Political-Economic Information’, Electoral Studies, 19 (2000), 519–537Google Scholar.

40 Granato and Krause, ‘Information Diffusion within the Electorate’.

41 In Zaller’s model, all messages are ultimately conveyed to individuals from the media and thus originate from elite sources of some kind (whether commentators, politicians, bureaucrats or economic forecasters). Even messages communicated interpersonally ultimately derive from some mediated source. This is almost certainly reasonable for information about national economic aggregates, for which individuals are likely to have little independent information.

42 Zaller is much concerned with the impact of levels of political awareness on differences in individual rates of message reception and a centrepiece of his theory is that people at middle levels of political awareness are the ones most likely to receive and accept any particular message (so most likely to change opinions). Since we lack individual-level data, however, our focus is on aspects of the theory that should manifest themselves in differences in average opinion across contexts, not only in differences between individuals in the same context. Since aggregate distributions of political awareness across the Western democracies are quite similar and slow to change, we are less concerned with differences in the distribution of political awareness than with differences across contexts in the distribution of partisanship (as explained below).

43 Zaller, The Nature and Origins of Mass Opinion. In another version of the theory, messages are rejected if the individual knows the partisanship of the source of the message and this does not match his or her own ( Zaller, John, ‘The Myth of Massive Media Impact Revived: New Support for a Discredited Idea’, in Diana Carole Mutz, Paul M. Sniderman and Richard A. Brody, eds, Political Persuasion and Attitude Change (Ann Arbor: University of Michigan Press, 1996), pp. 17–67Google Scholar).

44 The US case is the only one for which we have the necessary data to examine this directly.

45 Zarnowitz, Victor and Braun, Phillip, ‘Twenty-Two Years of the NBER ASA Quarterly Economic Outlook Surveys: Aspects and Comparisons of Forecasting Performance’, Working Paper No. 3965, (Cambridge, Mass.: National Bureau of Economic Research), pp. 45–46Google Scholar. Published under the same name (though not including the quote cited here) in Stock, James H. and Watson, Mark W., eds, Business Cycles, Indicators, and Forecasting (Chicago: University of Chicago Press, 1993)CrossRefGoogle Scholar.

46 Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’.

47 An interesting illustration is the reporting of inflation results for Britain on 20 May 2009. The headline in the Financial Times’s story read: ‘Inflation falls but price rises exceed other big nations’; the Wall Street Journal headline read: ‘UK inflation slows as retail prices decline’.

48 Mankiw, Gregory N. and Reis, Ricardo, ‘Sticky Information versus Sticky Prices: A Proposal to Replace the New Keynesian Phillips Curve’, Quarterly Journal of Economics, 117 (2002), 1295–1328CrossRefGoogle Scholar.

49 Carroll, ‘Macro-economic Expectations of Households and Professional Forecasters’.

50 Doepke, J., Dovern, J., Fritsche, U. and Slacalek, J., ‘The Dynamics of European Inflation Expectations’, B.E. Journal of Macroeconomics, 8 (2008), 1–21CrossRefGoogle Scholar; Doepke, , Dovern, , Fritsche, and Slacalek, , ‘Sticky Information Philips Curves: European Evidence’, Journal of Money, Credit, and Banking, 40 (2008), 1513–1520CrossRefGoogle Scholar; Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’; Berger, Helge, Ehrmann, Michael and Fratzscher, Marcel, ‘Monetary Policy and the Media’ (European Central Bank Working Paper Series, No. 679, 2006)Google Scholar.

51 Granato and Krause, ‘Information Diffusion within the Electorate’.

52 Carroll, ‘Macro-economic Expectations of Households and Professional Forecasters’; Doepke et al., ‘The Dynamics of European Inflation Expectations’; Doepke et al., ‘Sticky Information Philips Curves’; Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’; Berger et al., ‘Monetary Policy and the Media’.

53 Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’.

54 Duch, Palmer and Anderson, ‘Heterogeneity in Perceptions of National Economic Conditions’; Erikson, ‘Macro vs. Micro-Level Perspectives on Economic Voting’.

55 The data are from the 1999 and 2004 European Election Studies.

56 Mankiw and Reis, ‘Sticky Information versus Sticky Prices’.

57 Carroll, ‘Macro-economic Expectations of Households and Professional Forecasters’.

58 Croushore, Dean, ‘An Evaluation of Inflation Forecasts From Surveys Using Real-Time Data’ (Working Paper No. 06-19, Federal Reserve Bank of Philadelphia, 2006)Google Scholar; Croushore, , ‘Evaluating Inflation Forecasts’ (Working Paper No. 98-14, Federal Reserve Bank of Philadelphia, 1998)Google Scholar.

59 We recognize that many economists are critical of the rationality of professional forecasts. While we find Croushore’s critiques of those criticisms persuasive, we hope that this assumption will be relaxed in future work. We maintain it here so that we can focus on the other parts of the model that are, at least for now, more interesting in terms of their contextual implications.

60 Doms and Morin, ‘Consumer Sentiment, the Economy, and the News Media’; Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’; Berger et al., ‘Monetary Policy and the Media’.

61 We explored the idea that the extent of media negativity might vary across contexts depending on the extent to which the media is owned by the government or is in private hands. However, in our sample of countries (over our time period), there is simply not enough variation in this contextual variable. All newspapers in our sample are held privately and variation in the ownership of television stations has also become quite limited.

62 Croushore, ‘An Evaluation of Inflation Forecasts From Surveys Using Real-Time Data’.

63 Norris, Pippa, ‘Comparative Political Communications: Common Frameworks or Babelian Confusion?’ Government and Opposition, 44 (2009), 321–340CrossRefGoogle Scholar.

64 We estimate these models using STATA’s (version 10) ‘xtmixed’ command. We allow random coefficients on expectations and a random intercept and make no assumption about the correlation between the random effects for these two coefficients (which we estimate).

65 Our time period runs from 1986 to 2001. Since levels of partisanship (at least when restricted to the relatively strong identifiers we have used) change relatively slowly, the use of surveys at four time points spanning our time period should provide a reasonable approximation to the underlying levels of partisanship as it changed over time.

66 Mueller, W. and Strom, K., Coalition Governments in Western Europe (Oxford: Oxford University Press, 2000)Google Scholar.

67 Doms and Morin, ‘Consumer Sentiment, the Economy, and the News Media’; Haller and Norpoth, ‘Let the Good Times Roll’; Lamla and Lein, ‘The Role of Media for Consumer’s Inflation Expectations Formation’; Berger et al., ‘Monetary Policy and the Media’.

68 More specifically, in order to estimate these changes in the extent of pessimism or optimism in expectations across different contexts, and in order to get standard errors around these changes, we first estimated the statistical models that appear in the tables and then, setting our contextual variable to a desired value, used these estimates to approximate (using the composite trapezoidal rule with 9,000 sub-intervals) two areas – any area above the 45° line and below our estimated expectations line (over the range of the expectation data), and any area below the 45° line and our estimated expectations line. With these two areas, we could calculate the net pessimism reflected in our estimates (at the given level of a contextual variable) by subtracting the first area from the second. We could then repeat this for a second level of the contextual variable and then calculate the difference in the two net pessimism scores. This difference is what our empirical model is telling us about the impact of the difference in the level of the contextual variable on the changes in net pessimism in expectations. Finally, if instead of using our original coefficients in this process, we use a draw from an appropriate multivariate normal distribution in which our estimated coefficients are the mean vector (and the estimated variance covariance matrix of the coefficients is the variance covariance matrix of the target multivariate normal), then we can repeat the process (with different draws) 500 times, simulating the variation in the calculated areas and, ultimately, the change in net pessimism. This simulation method for calculating standard errors and confidence intervals around quantities of interest is now common in political science (see King, Gary, Tomz, Michael and Wittenberg, Jason, ‘Making the Most of Statistical Analyses: Improving Interpretation and Presentation’, American Journal of Political Science, 44 (2000), 347–361CrossRefGoogle Scholar), though our application of it in this setting is new.

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