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The causal interpretation of estimated associations in regression models

  • Luke Keele (a1), Randolph T. Stevenson (a2) and Felix Elwert (a3)


A common causal identification strategy in political science is selection on observables. This strategy assumes one observes a set of covariates that is, after statistical adjustment, sufficient to make treatment status as-if random. Under adjustment methods such as matching or inverse probability weighting, coefficients for control variables are treated as nuisance parameters and are not directly estimated. This is in direct contrast to regression approaches where estimated parameters are obtained for all covariates. Analysts often find it tempting to give a causal interpretation to all the parameters in such regression models—indeed, such interpretations are often central to the proposed research design. In this paper, we ask when we can justify interpreting two or more coefficients in a regression model as causal parameters. We demonstrate that analysts must appeal to causal identification assumptions to give estimates causal interpretations. Under selection on observables, this task is complicated by the fact that more than one causal effect might be identified. We show how causal graphs provide a framework for clearly delineating which effects are presumed to be identified and thus merit a causal interpretation, and which are not. We conclude with a set of recommendations for how researchers should interpret estimates from regression models when causal inference is the goal.


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Acharya, A, Blackwell, M and Sen, M (2016) Explaining causal findings without bias: detecting and assessing direct effects. American Political Science Review 110, 512529.
Campbell, A, Converse, PE, Miller, WE and Donald, E (1966) Stokes. 1960. The American Voter. New York: Wiley.
Carsey, TM and Layman, GC (2006) Changing sides or changing minds? Party identification and policy preferences in the American electorate. American Journal of Political Science 50, 464477.
Cox, GW (1997) Making Votes Count: Strategic Coordination in the World's Electoral Systems. Cambridge, UK: Cambridge University Press.
Duverger, M (1959) Political Parties: Their Organization and Activity in the Modern State. New York, NY: Methuen.
Elwert, F (2013) Graphical causal models. In Stephen, L. Morgan (ed). Handbook of Causal Analysis for Social Research. Amsterdam: Springer, pp. 245273.
Fiorina, MP (1981) Retrospective voting in American national elections.
Gibler, DM (2017) State development, parity, and international conflict. American Political Science Review 111, 2138.
Glynn, AN and Quinn, KM (2010) An introduction to the augmented inverse propensity weighted estimator. Political Analysis 18, 3656.
Goren, P and Chapp, C (2017) Moral power: how public opinion on culture war issues shapes partisan predispositions and religious orientations. American Political Science Review 111, 159177.
Green, DP and Palmquist, B (1994) How stable is party identification? Political Behavior 16, 437466.
Green, DP, Palmquist, B and Schickler, E (2004) Partisan Hearts and Minds: political Parties and the Social Identities of Voters. New Haven, Conn: Yale University Press.
Gulzar, S and Pasquale, BJ (2017) Politicians, bureaucrats, and development: evidence from India. American Political Science Review 111, 162183.
Hainmueller, J and Hazlett, C (2013) Kernel regularized least squares: reducing Misspecification bias with a flexible and interpretable machine learning approach. Political Analysis 22, 143168.
Highton, B and Kam, CD (2011) The long-term dynamics of partisanship and issue orientations. The Journal of Politics 73, 202215.
Ho, DE, Imai, K, King, G and Stuart, EA (2007) Matching as nonparametric preprocessing for reducing model dependence in parametric causal inference. Political analysis 15, 199236.
Imai, K, Keele, L, Tingley, D and Yamamoto, T (2011) Unpacking the black box of causality: learning about causal mechanisms from experimental and observational studies. American Political Science Review 105, 765789.
Keele, LJ (2015) The statistics of causal inference: a view from political methodology. Political Analysis 23, 313335.
Kim, IS (2017) Political cleavages within industry: firm-level lobbying for trade liberalization. American Political Science Review 111, 120.
Klasnja, M and Titiunik, R (2017) The incumbency curse: weak parties, term limits, and unfulfilled accountability. American Political Science Review 111, 129148.
MacKuen, MB, Erikson, RS and Stimson, JA (1989) Macropartisanship. American Political Science Review 83, 11251142.
Miller, WE and Shanks, JM (1996) The New American Voter. Cambridge, MA: Harvard University Press.
Morgan, SL and Winship, C (2014) Counterfactuals and Causal Inference: Methods and Principles for Social Research. 2nd Edn. New York, NY: Cambridge University Press.
Ordeshook, PC and Shvetsova, OV (1994) Ethnic heterogeneity, district magnitude, and the number of parties. American Journal of Political Science 38, 100123.
Page, BI and Jones, CC (1979) Reciprocal effects of policy preferences, party loyalties and the vote. American Political Science Review 73, 10711089.
Pearl, J (2009 a) Causal inference in statistics: an overview. Statistics Surveys 3, 96146.
Pearl, J (2009 b) Causality: Models, Reasoning, and Inference. 2nd Edn. New York: Cambridge University Press.
Powell, GB (1982) Contemporary Democracies. Cambridge, MA: Harvard University Press.
Przeworski, A and Sprague, J (1986) Paper Stones: A History of Electoral Socialism. Chicago, IL: University of Chicago Press.
Taagepera, R and Shugart, MS (1989) Seats and Votes: The Effects and Determinants of Electoral Systems. New Haven, CT: Yale University Press.
Touchton, M, Sugiyama, NB and Wampler, B (2017) Democracy at work: moving beyond elections to improve well-being. American Political Science Review 111, 6882.
Van der Weele, TJ (2009) On the distinction between interaction and effect modification. Epidemiology 20, 863871.
Van der Weele, TJ (2015) Explanation in Causal Inference: Methods for Mediation and Interaction. Oxford, UK: Oxford University Press.
Van der Weele, TJ, Hernán, MA and Robins, JM (2008) Causal directed acyclic graphs and the direction of unmeasured confounding bias. Epidemiology (Cambridge, Mass.) 19, 720.



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