Assignment 6

Introduction and Setup

Let’s go back to the simple model of labor supply and program participation from Assignment 2.

Consider the following extension to the model. Suppose that each individual \(n\) belongs to one of \(K\) finite types, \(k(n)\in\{1,2,...,K\}\). Types determine differences in the cost of work and program participation as well as differences in wages:

\[ U_{ntj} = \log(\max\{50,Y_{nt}(W_{nt}H_{j})\}) + \alpha_{l,k}\log(112 - H_{j}) - \alpha_{P,k,1}\mathbf{1}\{P_{j}>0\} - \alpha_{P,k,2}\mathbf{1}\{P_{j}>1\} \]

and \[ \log(W_{nt}) = \gamma_{k,0} + \gamma_{k,1}\text{Age}_{nt} + \gamma_{k,2}\text{Age}_{nt}^2 \]

So the parameters \(\alpha_{l},\alpha_{P},\gamma\) are now heterogeneous by type.

Part 1

Write a routine to classify individuals in the data into one of \(K=3\) types using K-means clustering. You may find the package Clustering.jl useful.

Part 2

Calculate and plot average work and average program participation over time for each of these types. Comment on what you are seeing.

Part 3

Write code to estimate this extended model. You could just make a small extension to the maximum likelihood estimator you used in Assignment 2, or you could try another approach if you prefer.