Keep it simple: estimation strategies for ordered response models with fixed effects

Abstract

By running Monte Carlo simulations, we compare different estimation strategies of ordered response models in the presence of non-random unobserved heterogeneity. We find that very simple binary recoding schemes deliver parameter estimates with very low bias and high efficiency. Furthermore, if the researcher is interested in the relative size of parameters the simple linear fixed effects model is the method of choice.

Keywords:

• fixed effects ordered logit
• ordered responses
• finite sample properties
• Monte Carlo simulation
• happiness

JEL Classifications:

• C230
• C250
• I310

Acknowledgements

The authors are grateful to Stefan Sperlich, Paul Frijters, Gregori Baetschmann and two anonymous referees for valuable comments and Martin Breßlein for programming support.

Notes

1. For example, a data setup of 3000 individuals with 15 observations over time can take about half an hour computation time.

2. First difference transformation of the model yields equivalent results.

3. We use the statistical software STATA to run our simulations. The corresponding STATA ado-file for the FCF estimator can be downloaded from: http://hdl.handle.net/11022/0000-0000-1F7A-6.

4. Adding a random component would merely alter the size of α_i which, however, does not matter after we condition on all time constant characteristics, i.e. apply the conditional logit estimator or the fixed effects linear estimator.

5. We also perform simple t-tests to compare the means of the respective estimators’ coefficients when I and T increase. The differences of the means are statistically significant when starting from small T and small I and become insignificant when both dimension sizes are large.

6. For our data set with we did the following binary recoding: , if y_it>2.

7. Furthermore, our simulations for increasing samples sizes (not reported) indicate that the FE and POLS deliver in fact consistent estimates of parameter ratios.

8. We distinguish between three different settings of frequencies denoted in % (K=1: 10%, K=2: 80%, K=3: 10%); (K=1: 10%, K=2: 20%, K=3: 70%); (K=1: 5%, K=2: 47.5%, K=3: 47.5%).

9. Our result cannot be generalized for other potential misspecifications of the model. That is, misspecifications due to wrong choice of e.g. other probability functions, missing covariates, measurement error, failure to control for non-linearities and neglect of overdispersion could severely alter coefficient estimates and standard errors as well as coefficient ratios. In our view, simulation studies never can systematically deal with all kinds of potential misspecification to yield generalizable results. It is the responsibility of the researcher to come up with the most appropriate model specification which we consider independent of his choice of a particular binary recoding scheme.

10. To accommodate higher K it is necessary to have more observations per individual. We therefore increase the number of time periods from T=6 in Table 3 to T=12.