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Do Corrections for Selectivity Bias Improve Forecasts of Navy Officer Retention?

Do Corrections for Selectivity Bias Improve Forecasts of Navy Officer Retention? Principal Investigator: Walter Mayer Research Assistant: Yang Li. General Forecasting Problem. Forecast Stay/Leave Decisions of Navy Officers Conditional on:

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Do Corrections for Selectivity Bias Improve Forecasts of Navy Officer Retention?

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  1. Do Corrections for Selectivity Bias Improve Forecasts of Navy Officer Retention? Principal Investigator: Walter Mayer Research Assistant: Yang Li

  2. General Forecasting Problem Forecast Stay/Leave Decisions of Navy Officers Conditional on: • Index of military-civilian earnings differential • Conditions in civilian Economy • Individual attributes • Chose to stay in previous periods (Selectivity Bias)

  3. Issue: Do “Corrections” for Selectivity Bias Improve Forecasts? • Estimate more parameters or restrict sample • “Corrections” decrease bias but increase variance: • Mean squared errors?

  4. Important Factors? • Sample size • Ratio of “stays” and “leaves” in sample • Economic conditions

  5. Previous Studies • Not been previously investigated for our model • Type 2 Tobit Model Zuelke and Zeman (1991, RevStat) Leung and Yu (1996, Journal of Econometrics) • Evidence favors “uncorrected” techniques for certain sample sizes and model configurations • Did not consider semiparametric techniques

  6. Econometric Model Specification Sequence of Stay/Leave Decisions • Linear Random Effects yit* = xitb + ci + uit, yit* = net benefit of the decision to stay for the ith officer at decision point t (latent variable) xit = observable explanatory variables ci = unobserved individual effect uit = unobserved transitory error term i = 1,…N individuals; t =1,…,Ti decision points.

  7. Sampling Process • Observed Variables: (yit, xit), where yit = 1 if yit* >0 (stay in Navy) = 0 if otherwise (leave Navy) • Sample Selection for t>1: (yit,xit) is observed only if zit = 1 zit = 1 if yit-1 = …= yi1 =1 = 0 if otherwise.

  8. Forecasting Retention Model and Estimate it(xit, () ) =P(yit=1| yit-1=1,…yi1=1, xit) Predict “stay” iff. it(xit, () ) 0.50  Probit parametric model depends on , () Assumes normal errors • MSCORE semiparametric model depends on ; () is unrestricted Assumes conditional symmetry Use kernel regression to estimate it(xit, () )

  9. Corrections for Selectivity Bias • “Uncorrected” Methods restrict: it(xit, () ) = P(yit=1| xit) =git(xit) Pooled Probit assumes: () diagonal Pooled MSCORE: apply standard MSCORE to pooled cross-sections

  10. Corrections for Selectivity Bias (b) “Corrected” Methods allow: it(xit, () )  P(yit=1| xit)  Pooled Probit with () not diagonal Cost: Estimate more parameters  Pooled MSCORE: “Restrict Sample to set A” Ait = {xit: xit ≥ 0 or E(Yit| zit=1, xit)<0, t>1} Cost: Use fewer observations

  11. Overview of Findings Simulated data “leaves” 125 (24%), “stays” 397 (76%) • For “leaves” uncorrected methods best: MSCORE, Probit • For “stays” corrected methods best: MSCORE, Probit • Does not depend on distribution of errors Normal distribution, T-distribution DF=3 • Probit versus MSCORE: MSCORE does slightly better with Non-normal errors; otherwise, neither method dominates

  12. Overview of Findings Navy Officers (Nuclear) data “leaves” 659 (44%), “stays” 847 (56%) • MSCORE: best method: For “leaves” uncorrected method For “stays” corrected method • Probit: best method: For “leaves” corrected method For “stays” uncorrected method • Probit versus MSCORE: neither method dominates

  13. Description of Data Nuclear Officers Data • Source: Navy’s Officer Master File • Data extracted and organized by ONR • Sample Characteristics: 4317 nuclear officers DP1 DP2 DP3 Y 4317 2075 1506 Stay(%) 2075(48%) 1506(73%) 847(56%)  7 independent variables: ACOL, UE, NONWHT,LOS, ACAD, ROTC, DEP

  14. Description of Data Simulated Data DP1 DP2 DP3 Y 1000 707 522 Stay(%) 707(71%) 522(74%) 397(76%)  Random number generators LIMDEP • 3 Decision Points • 2 independent variables • Errors: Normal, Non-normal (t-dist. df=3)

  15. Out-sample Prediction Simulation Result: Normal Error, Decision Point Three • Probit without Correction • Probit with Correction

  16. Out-sample Prediction Simulation Result: Normal Error, Decision Point Three • Mscore without Correction • Mscore with Correction

  17. Out-sample Prediction Simulation Result: Non-normal Error, Decision Point Three • Probit without Correction • Probit with Correction

  18. Out-sample Prediction Simulation Result: Non-normal Error, Decision Point Three • Mscore without Correction • Mscore with Correction

  19. Out-sample Prediction Nuclear Officers Data Result: Decision Point Three • Probit without Correction • Probit with Correction

  20. Out-sample Prediction Nuclear Officers Data Data Result: Decision Point Three • Mscore without Correction • Mscore with Correction

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