Discrete Hours Labour Supply Modelling: Specification, Estimation and Simulation

New Zealand Treasury Working Paper 03/20

Published: September 2003

Authors: John Creedy and Guyonne Kalb

Abstract

The assumption behind discrete hours labour supply modelling is that utility-maximising individuals choose from a relatively small number of hours levels, rather than being able to vary hours worked continuously. Such models are becoming widely used in view of their substantial advantages, compared with a continuous hours approach, when estimating and their role in tax policy microsimulation. This paper provides an introduction to the basic analytics of discrete hours labour supply modelling. Special attention is given to model specification, maximum likelihood estimation and microsimulation of tax reforms. The analysis is at each stage illustrated by the use of numerical examples.

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Abstract Table of Contents List of Tables List of Figures 1 Introduction 2 The basic model 2.1 Utility maximisation 2.2 Probability distributions 2.3 A more formal statement 2.4 Labour supply elasticities 3 A numerical example of hours probabilities 4 Specification of the error distribution 4.1 A special case: The extreme value distribution 5 Parameter estimation 5.1 The likelihood function 5.2 Maximum likelihood estimation 6 A numerical example of estimation 7 Alternative specifications 7.1 Utility functions 7.2 Welfare participation 7.3 Personal characteristics 7.4 Characteristics of hours points 7.5 Alternative error distributions 8 Tax reforms and simulations 8.1 Individual calibration 8.2 A numerical example 9 Conclusions Appendix: An iterative solution procedure References	twp03-20.pdf (416 KB) pp. 38
List of Tables Table 1 – Hypothetical discrete distribution of the error term Table 2 – Conditional probabilities for hours level 3 Table 3 – Three individuals and three hours levels Table 4 – Utility pre- and post-reform Table 5 – Utility pre-reform and post-reform for ten sets of accepted draws from the extreme value distribution Table 6 – Labour supply transition matrix Table 7 – Expected hours and wage elasticities of labour supply: simulated approach List of figures Figure 1 – Three Hours Levels and Utility Distributions Figure 2 – Extreme value probability density function Figure 3 – Extreme value cumulative distribution function and the discrete distribution from Table 1 Figure 4 – Newton’s method

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Abstract

List of Tables

List of Figures

1 Introduction

2 The basic model

3 A numerical example of hours probabilities

4 Specification of the error distribution

4.1 A special case: The extreme value distribution

5 Parameter estimation

6 A numerical example of estimation

7 Alternative specifications

8 Tax reforms and simulations

9 Conclusions

Appendix: An iterative solution procedure

References

twp03-20.pdf (416 KB) pp. 38

List of Tables

List of figures

Acknowledgements

We should like to thank Nathan McClellan and Jenny Williams for comments on an earlier draft of this paper

Disclaimer

The views expressed in this Working Paper are those of the author(s) and do not necessarily reflect the views of the New Zealand Treasury. The paper is presented not as policy, but with a view to inform and stimulate wider debate.

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Publication Details

Discrete Hours Labour Supply Modelling: Specification, Estimation and Simulation

Abstract

Table of Contents

Abstract

Table of Contents

List of Tables

List of Figures

1 Introduction

2 The basic model

3 A numerical example of hours probabilities

4 Specification of the error distribution

5 Parameter estimation

6 A numerical example of estimation

7 Alternative specifications

8 Tax reforms and simulations

9 Conclusions

Appendix: An iterative solution procedure

References

List of Tables

List of figures

Acknowledgements

Disclaimer