The document discusses the differences between recursive and non-recursive models in the context of causal relationships and disturbances. Recursive models have uni-directional effects and uncorrelated disturbances, while non-recursive models involve feedback loops and can face identification challenges. The text also explains the importance of instrumental variables for obtaining consistent estimates in models with endogenous regressors.

1. Recursive and non-recursive
models

2. 2
Recursivity
• All models considered so far are ‘recursive’
• A recursive model is one where all causal
effects are uni-directional and disturbances
are uncorrelated
• A non-recursive model contains one or more
‘feedback loops’ or ‘reciprocal’ effects

3. Recursive Model
3
x2 y1
x3
x1
d11
d2
1
Causal effects uni-directional
Disturbances uncorrelated

4. Non-recursive model
4
x2 y1
x3 x1
d11
d2
1
Reciprocal causal effects
Disturbances correlated

5. Partially recursive 1
5
No direct effects amongst endogenous = recursive
x2 y1
x3 x1
d11
d2
1

6. Partially recursive 2
6
x2 y1
x3 x1
d11
d2
1
Direct effects amongst endogenous = non-recursive

7. Recursivity
• Recursive models always identified, simple to
estimate
• Non-recursive models more flexible
• But can pose problems for identification
• Require additional variables for identification
7

8. Non-recursive models
• Just because a model is identified does not
mean the parameter estimates are correct
• Consistent estimation of reciprocal paths
requires some strict (and often implausible)
assumptions to be met
• E.g. the exogenous variable used to identify of
synchronous parameters must meet be an
‘instrumental variable’
8

9. Endogenous regressor
• OLS assumes error term uncorrelated with predictors
• Correlation can arise from unobserved variables and
from simultaneous causal relationship
• To interpret β as causal effect, we need instrumental
variable for X1
β

10. Instrumental Variables (IV)
• An IV is a variable which introduces exogenous
variability into an endogenous regressor
• The IV, Z, must directly cause the endogenous
regressor but not the outcome
– Cov(Z,u)=0, Cov(xK,Z)≠0
• Random assignment to treatment & control
conditions in RCT is a good instrumental variable
10

11. Instrumental variable
• Z1 causes X1
• Z1 only causes Y1 via effect on X1

12. Instrumental Variables - examples
• Vietnam lottery draft for effect of Vietnam war on later
outcomes (Angrist and Krueger 1991)
• Proximity of nearest college for education on earnings
(Card 1995)
• Variation in amount of compulsory schooling for effects of
education on earnings (Hammon & Walker 1995)
12

13. Non-recursive SEM
Does happiness cause trust or trust cause happiness?
• Direct paths in both directions between happiness and trust
• Model unidentified without exogenous predictors (income and
marital status)
• Are these valid instrumental variables?
Chi2=16; df=10; p<0.098;
RMSEA=.020; CFI=.997
Data: European Social Survey 2004, GB only

14. Non-recursive SEM
Does happiness cause trust or trust cause happiness?
• Direct paths in both directions between happiness and trust
• Model unidentified without exogenous predictors (income and
marital status)
• Are these valid instrumental variables?
Chi2=16; df=10; p<0.098;
RMSEA=.020; CFI=.997
Data: European Social Survey 2004, GB only