Book contents
- Frontmatter
- Dedication
- Contents
- Preface
- PART I GENERAL INFORMATION
- PART II SINGLE EQUATION APPROACH: PRODUCTION, COST, AND PROFIT
- PART III SYSTEM MODELS WITH CROSS-SECTIONAL DATA
- PART IV THE PRIMAL APPROACH
- PART V SINGLE EQUATION APPROACH WITH PANEL DATA
- PART VI LOOKING AHEAD
- APPENDIX
- A Deriving the Likelihood Functions of Single Equation Frontier Models
- B Deriving the Efficiency Estimates
- C Deriving Confidence Intervals
- D Bootstrapping Standard Errors of Marginal Effects on Inefficiency
- E Software and Estimation Commands
- Bibliography
- Index
D - Bootstrapping Standard Errors of Marginal Effects on Inefficiency
Published online by Cambridge University Press: 05 February 2015
- Frontmatter
- Dedication
- Contents
- Preface
- PART I GENERAL INFORMATION
- PART II SINGLE EQUATION APPROACH: PRODUCTION, COST, AND PROFIT
- PART III SYSTEM MODELS WITH CROSS-SECTIONAL DATA
- PART IV THE PRIMAL APPROACH
- PART V SINGLE EQUATION APPROACH WITH PANEL DATA
- PART VI LOOKING AHEAD
- APPENDIX
- A Deriving the Likelihood Functions of Single Equation Frontier Models
- B Deriving the Efficiency Estimates
- C Deriving Confidence Intervals
- D Bootstrapping Standard Errors of Marginal Effects on Inefficiency
- E Software and Estimation Commands
- Bibliography
- Index
Summary
This appendix shows an example of how to bootstrap standard errors of variables' marginal effects on inefficiency. The example follows the model discussed on page 81.
Recall the model we considered is estimated by the following commands.
• use milk
• global xvar llabor lfeed lcattle lland
• sfmodel ly, prod dist(t) frontier($xvar) mu(comp) usigmas(comp) vsigmas()
• sf_srch, n(1) frontier($xvar) mu(comp) usigmas(comp)
• ml max, difficult gtol(1e-5) nrtol(1e-5)
The marginal effects of comp on the inefficiency is calculated here:
• sf_predict, bc(bc_w) marginal
The following is the marginal effect on unconditional E(u) from FOC.
The mean marginal effect of comp on uncond E(u) is -. 03604191 (see comp_M).
The following is the marginal effect on uncond V(u) from FOC.
The mean marginal effect of comp on uncond V(u) is -. 0064839 (see comp_V).
Now, we bootstrap the standard errors of the statistics −. 03604191 and −. 0064839; that is, the mean marginal effect of comp on both E(u)and V(u). This is undertaken using the program below.
Before the illustration, we discuss an important issue. One of the difficulties in bootstrapping statistics from an ML model is what to do with a replication for which the numerical maximization fails. The approach, which we recommend, is to record and examine the problematic bootstrap sample and try to understand and fix the problem. The problem may be solved, for example, by using a different set of initial values. This procedure, however, requires more elaborate codes and user interaction with the program.
The following program, however, takes an easier route for demonstration purposes. It simply discards the samples that fail to converge. In order to make it work, the program has to aim at a number of replications which is larger than the desired (user specified) number in order to make room for the error samples. By default, the program aims at bootstrapping five times as many as the specified samples, but an algorithm is added so that the program stops when the desired (user specified) number of useable (i.e., no estimation error) bootstrap samples is reached.
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- Publisher: Cambridge University PressPrint publication year: 2015