HOMEWORK #3

    Deadline: Friday March 28 (i.e. by 11:59:59PM Friday.)
    Marking scheme:  See syllabus

    Post your assignment on your homepage. Make sure the file on your homepage is called hw3.doc or hw3.pdf in your www/ec360 directory. Students posting a doc file will lose 1 mark out of the report marks. People posting a PDF file get to keep that mark. . The purpose is to encourage you to learn how to make PDF files, a much better way to distribute your work electronically than as a Word Document. Instructions for doing this are given in pdf.html.

    Introduction

    Your goal in this assignment is to explore the joint implications of the job search model and the Canadian employment insurance (EI) system. To carry out the analysis you will modify a spreadsheet program I've created and use HRDC's EI web site (and other sources of your choosing) to gather information on the system.

    A person who becomes unemployed and is eligible for EI gets a weekly benefit level b for a period of T weeks while they remain unemployed. The benefit amount b is a function of previous earnings, and the period of potential benefits T is a function of the past work history and the local unemployment rate.

    In this assignment you will model a person becoming unemployed has having an infinite decision horizon. Once a job is taken it lasts forever. However, EI benefits run out after T periods. Thus, if still searching in period T+1 the problem is the infinite horizon problem studied in class. The updated notes describe the set of equations.

    Tasks

    1. Download the spreadsheet hw3.xls to use as a starting point for your analysis. You have to fill formulas into the spreadsheet to solve for the infinite horizon problem and the finite horizon problem with T periods of EI benefits.
    2. Calibrate your job search model by setting b=0 in the infinite horizon environment (the sheet labelled Inf_Horizon. Experiment with the parameters beta, c, and gamma so that:
      • the probability of a UE spell lasting more than 18 months is close to zero
      • the average duration of a UE spell is approximately 6 months
      • the average accepted wage is approximately 9 (1.5 times the minimum wage).
    3. Starting at the calibrated model, use small changes (say 10%) in the parameter values to verify that the infinite horizon reservation wage w* is positively related to c and beta and negatively related to gamma (which lowers both the mean and variance of job offers at the same time). For c and beta, compute the change in w* divided by the change in the parameter and compare it to the theoretical derivatives given in the notes.
    4. Produce a table of results that describes the calibrated model and your numerical approximations to the theoretical derivatives. Summarize your results.
    5. Analyze the effect on job search under the Canadian EI system.
      • Set the benefit level to 55% of the average accepted wage in your calibrated model
      • Using the HRDC web site, choose two EI regions to study - one with a currently relatively high UE rate, one with a relatively low rate. Use Statistics Canada to get information on these regions or economic regions that are very similar in coverage to them (for example see here, or use CanSim or other sources of your choosing.)
      • Set T equal to the EI benefit duration for each of your two regions and re-solve the job search model. Compare and contrast the outcomes under these policies and relative to the no UI infinite horizon baseline.
      • It's possible that the results for your calibrated model are very extreme when including EI. If so, you might want to re-calibrate in order to get more sensible results. But only one calibrated model should be used for the analysis.
    6. In a 2-3 paragraphs discuss how other aspects of the EI system might affect labour force dynamics (duration of jobs and duration of unemployment).
    7. Write a report that explains your calculations and your analysis of the incentives generated by EI for job search. You can post your spreadsheet file as hw3.xls in www/econ360 to support your report (use binary mode!), but your report must be well formatted as a standalone research report designed for a human to read and understand separate from a spreadsheet.