Mathematical Modeling with Multidisciplinary Applications

CHAPTER 6

BINARY AND ORDINAL DATA ANALYSIS IN ECONOMICS: MODELING AND ESTIMATION

IVAN JELIAZKOV AND MOHAMMAD ARSHAD RAHMAN

Department of Economics, University of California, Irvine

6.1 INTRODUCTION

This chapter is concerned with the analysis of statistical models for binary and ordinal outcomes. Binary data arise when a particular response variable of interest y_i can take only two values, i.e., y_i {0, 1}, where the index i = 1, …, n refers to units in the sample such as individuals, families, firms, and so on. Such dichotomous outcomes are widespread in the social and natural sciences. For example, to understand socio-economic processes, economists often need to analyze individuals’ binary decisions such as whether to make a particular purchase, participate in the labor force, obtain a college degree, see a doctor, migrate to a different country, or vote in an election. By convention, y_i = 1 typically indicates the occurrence of the event of interest, whereas the occurrence of its complement is denoted by y_i = 0.

We also examine modeling and estimation issues related to another type of data, called ordinal data, where y_i can take one of J ordered values, j = 1, …, J. The denning feature of ordinal data is that even though the outcomes are monotone, the scale on which they are measured is not assumed to be cardinal and differences between categories are not directly comparable. For ...