Patrick Sturgis, Department of Sociology, University of Surrey

1. Using repeated measures data to analyse reciprocal effects:the case of Economic Perceptions and Economic Values Patrick Sturgis, Department of Sociology, University of Surrey Peter Smith, Ann Berrington, Yongjian Hu, Department of Social Statistics, University of Southampton

2. Reciprocal Causality • Often viewed as a ‘nuisance’ to be removed (simultaneity bias). • But can be of substantive and policy interest. • Achievement/self-esteem • Anti-social behaviour/depression • Problematic to estimate with observational data.

3. Overview • Approaches to estimating reciprocal effects. • General Linear Model • Instrumental variable approaches • Cross-lagged panel models • Errors of Measurement • Unobserved variables and error covariance • Example: economic values and perceptions • Conclusions

4. ‘True’ Model a X Y b

5. e e Standard Approach X-Sectional Data (Ignore the problem) c Y Y X X c = f(a + b)

6. d1 d2 Instrumental Variables Approach Instruments Instruments X Y

7. cross-lagged panel model • cross-lagged panel model (Campbell 1960; Campbell and Kenny 1999; Finkel 1995; Marsh and Yeung 1997). • Particularly useful for examining questions of reciprocal causality. • Each Y variable is regressed onto its lagged measure and the lagged measure of the other Y variable(s) of interest. • Can the history of X predict Y, net of the history of Y (Granger causality)? • Problematic for correlational designs (Rogossa 1995). • But with SEM it is much more powerful (Marsh 1993; 1997).

8. d11 d21 Cross-lagged Panel Model Yt1 Yt0 Xt1 Xt0

9. Problems with this model • 2 waves = limited information about causal relationship. • Concepts are assumed to be measured with zero error. • No account taken of correlations between disturbances of endogenous variables.

10. Consequences of Measurement Error • All measurements of abstract concepts will contain error. • Error can be stochastic ( ) or systematic • ( ) . • Systematic error biases descriptive and causal inferences. • Stochastic error in dependents leaves estimates unbiased but less efficient. • Stochastic error in independents attenuates effect sizes. • Both problematic for hypothesis testing and causal inference.

11. e1 e4 e2 e5 e3 e6 item1t1 item1t2 item2t2 item2t1 item3t1 item3t2 Xt1 Xt2 Correction for Measurement Error Specify each concept of interest as a latent variable with multiple indicators: Specify error covariance structure: d1

12. Correlated Disturbances 1 • The disturbance terms for the same endogenous variable over time are likely to be correlated. • Similarly, the disturbance term for the 2 endogenous variables are likely to be correlated at the same time point. • Caused by unobserved variable bias; a third variable, Z, may be causing both Y variables simultaneously. • Failing to consider these parameters can bias stability and cross-lagged estimates (Williams & Posakoff 1989; Anderson & Williams 1992).

13. d11 d21 Y11 Y12 Y10 Y21 Y22 Y20 d21 d22 Correlated Disturbances 2

14. Example: Economic Perceptions & Values • Left-right economic value posited as fundamental explanatory variable for political preferences & vote (Feldman 1989; Bartle 2000). • Similarly, perceptions of economic performance are seen as crucial determinants of electoral outcomes (Lewis-Beck & Stagmaier 2000). • What is the relationship between them? • Different macro-economic conditions require different approaches to economic policy. • People’s left-right leanings are likely to influence their perceptions of economic performance (Evans and Andersen 1997).

15. Data and Measures • Data come from the 1992-1997 British Election Panel Study. • Analytical sample = those interviews at all five waves (n=1640). • Left-right value measured by 6 item scale (Heath et al 1993). • Economic perceptions measured by 3 items tapping retrospective (past year) perceptions of: • Level of unemployment • Rate of inflation • Standard of living

16. Cross-sectional Model

17. IV Model .17 -.31 .12 .67 .50

18. Cross-lagged Observed Score Model .04 .26 .26 .68

19. e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 x11 x21 x31 x41 x51 x61 x12 x22 x32 x42 x52 x62 d2 lr92 lr94 econ92 econ94 d1 y11 y31 y21 y12 y32 y22 e1 e2 e3 e16 e17 e18 Cross-lagged latent 2 wave 1.01 .97 .48 .53 -.10 .12 .58 .27

20. e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 x11 x21 x31 x41 x51 x61 x12 x22 x32 x42 x52 x62 d2 lr92 lr94 econ92 econ94 d1 y11 y31 y21 y12 y32 y22 e1 e2 e3 e16 e17 e18 e20 e21 e22 e23 e24 e25 x13 x23 x33 x43 x53 x63 d4 lr95 econ95 d3 y13 y33 y23 e26 e27 e28 Cross-lagged latent 5 wave a a c c etc. d d b b

21. Cross-lagged latent Pooled Effect(zero disturbance covariances) Chi Square = 2671 df=1024 p<0.001 IFI = .938; RMSEA = .031

22. e4 e5 e6 e7 e8 e9 e10 e11 e12 e13 e14 e15 x11 x21 x31 x41 x51 x61 x12 x22 x32 x42 x52 x62 d2 lr92 lr94 econ92 econ94 d1 y11 y31 y21 y12 y32 y22 e1 e2 e3 e16 e17 e18 e20 e21 e22 e23 e24 e25 x13 x23 x33 x43 x53 x63 d4 lr95 econ95 d3 y13 y33 y23 e26 e27 e28 Cross-lagged latent 5 wave(correlated disturbances)

23. Cross-lagged latent Pooled Effect(disturbance covariances estimated) Chi Square = 2537 df=1050 p<0.001 IFI = .943; RMSEA = .029

24. Summary of Cross Lagged Effect Estimates

25. Conclusions • Reciprocal relationships can be seen as either a nuisance or of substantive interest. • Either way, they are hard to model with observational data. • Repeated measures data offers significant leverage relative to x-sectional. • Problems of error variance and covariance much greater with panel data. • Need to correct for errors in the measurement of abstract concepts. • And estimate relationships between measurement errors over time.

26. Conclusions • Unobserved variable bias likely to manifest through covariance between residuals. • Failure to model these errors and their covariance structures can lead to seriously biased causal inference. • Naïve analyses showed strong non-recursive relationship between economic values and perceptions. • More appropriate treatment of error structures altered causal inference substantially.