Model Misspecification in LQRE & Logit Models

1. Model Misspecification in LQRE & Logit Models James E. Monogan III

2. Quantal Response Models • Generate a stochastic formal model • Agent error • Private information • Regressor error • Directly derive an MLE estimator

3. “All models are wrong but some are useful.” --George Box, 1979 • QRE holds up when it perfectly captures the data-generating process. • Robustness: How does QRE perform with parsimonious models? • How would a correctly-specified logit do by comparison? • A good way to do EITM in practice?

4. Method: Monte Carlo Analysis • Create a data-generating process based on Signorino’s strategic deterrence model. • Misspecify one utility function in analysis. • Test for estimate properties in two cases: • Measurement error • Endogeneity • LQRE v. Sequential Logit Model

5. 1 U1(A)+α1A U1(~A)+α1~A 2 0 U2(~R)+α2~R U2(R)+α2R X2B2 X3B3+X4B4 X1B1 0 Strategic Deterrence Model

6. Likelihood Functions LQRE=ΠP(sq)sq P(cap)capP(war)war LSL=ΠP(war)war (1-P(war))1-war

7. 1 U1(A)+α1A U1(~A)+α1~A 2 0 U2(~R)+α2~R U2(R)+α2R X2B2 X3B3+X4B4 X1B1 0 Strategic Deterrence Model

8. Bias in β3 by Level of Measurement Error

9. Bias in β1 by Level of Measurement Error

10. 1 U1(A)+α1A U1(~A)+α1~A 2 0 U2(~R)+α2~R U2(R)+α2R X2B2 X3B3+X4B4 X1B1 0 Strategic Deterrence Model

11. Bias in β3 by Level of Endogeneity

12. Bias in β1 by Level of Endogeneity

13. Root Mean Squared Error by Endogeneity Level

14. Discussion • QRE performs marginally better for a misspecified utility function. • QRE performs much better for correctly specified utility functions. • Is there a more interesting alternative than sequential logit? • At an absolute level, is QRE useful with these properties?

15. Model Misspecification in LQRE & Logit Models James E. Monogan III