Using%20repeated%20measures%20data%20to%20analyse%20reciprocal%20effects:%20the%20case%20of%20Economic%20Perceptions%20and%20Economic%20Values

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

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True Model
a
X
Y
b
5
Standard Approach X-Sectional Data
(Ignore the problem)
c
Y
X
Y
X
c f(a b)
6
Instrumental Variables Approach
Instruments
Instruments
X
Y
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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).

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Cross-lagged Panel Model
Yt1
Yt0
Xt1
Xt0
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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.

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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.

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Correction for Measurement Error
Specify each concept of interest as a latent
variable with multiple indicators
Specify error covariance structure
d1
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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).

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Correlated Disturbances 2
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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.
• Peoples left-right leanings are likely to
  influence their perceptions of economic
  performance (Evans and Andersen 1997).

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Data and Measures

• Data come from the 1992-1997 British Election
  Panel Study.
• Analytical sample those interviews at all five
  waves (n1640).
• 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

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Cross-sectional Model
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IV Model
.17
-.31
.12
.67
.50
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Cross-lagged Observed Score Model
.04
.26
.26
.68
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Cross-lagged latent 2 wave
1.01
.97
.53
.48
.12
-.10
.58
.27
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Cross-lagged latent 5 wave
a
a
c
c
etc.
d
d
b
b
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Cross-lagged latent Pooled Effect(zero
disturbance covariances)
Chi Square 2671 df1024 plt0.001 IFI .938
RMSEA .031
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Cross-lagged latent 5 wave(correlated
disturbances)
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Cross-lagged latent Pooled Effect(disturbance
covariances estimated)
Chi Square 2537 df1050 plt0.001 IFI .943
RMSEA .029
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Summary of Cross Lagged Effect Estimates
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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.

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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.