Problem Set 1: Female labor market participation
Guideline • Please submit your report (MS word or PDF) and programs. I will make a submission form. • The due date is February 3, 2023. • This problem set requires your original data and model exercise. To get credit, you must try all questions. • For Question 1 and 2, please use Matlab for practice. For Question 3, you can use any computer language. MS Excel is also fine. • If you use proprietary or heavy data in Question 3, please tell me and submit only programs.
In this problem set, you will study female labor market participation using a simple extension of our lecture’s static labor supply model. Table 1 shows the average work hours and wages of Japanese married couples in 2001 and 2021. Table 1: Raw Data
Weekly hours of work are calculated as the hours of employed workers multiplied by the employment rate. These are interpreted as macro-level labor supply by gender. As you see, husbands’ hours declined while wives’ hours increased. In particular, the hours of mothers significantly increased. The wage data is also included. The unit is a thousand of Japanese Yen. It is the annual income of full-time workers between 25 and 50 years old. Therefore, the gender wage difference is not made by a larger share of female part-time jobs. Both male and female annual income increased, and the growth rate of female wage is higher than male.
Given these observations, you can imagine that the increase in female hours (and decline in male hours) of work may be caused by the relatively faster wage growth of women. Let’s study this hypothesis using a simple model. Suppose that the macro-level married couple solves the following optimization problem.
max ln(c) + α ln(100 − hm ) + β ln(100 − hf ) s.t. c = wm hm + wf hf
The subscripts m and f stand for male (or husband) and female (or wife), respectively. 100 is the total weekly hours men and women have. It means, 68 hours in 168 = 24 × 7 is a necessary time for, let’s say, sleep and eating. People divide 100 hours to work, hm and hf , and leisure, 100 − hm and 100 − hf . The household consumption is c. It is not divided into husband and wife because there are some shared expenditures, for example, housing. The wages are wm and wf . There are also two preference parameters: α for utility caused by the husband’s leisure and β for that by the wife’s leisure.
To compare the model and data, we can directly use hours in Table 1 for hm and hf , because those are weekly both in the model and data. For wm and wf , let’s normalize the 2001 male annual wage as 1. Then, after the CPI adjustment for the price level, we get the following wage data.
Question 1 Using the 2001 hours of work data in Table 1, and 2001 wage data in Table 2, calculate α and β, separately for couples with and without children. Due to data limitation, assume that wm and wf are the same for the two types of couples. Discuss the interpretation of the parameter differences in child status.
Question 2 Using the calibrated α and β using 2001 data in Question 1, make model predictions of hours of work in 2021. It is a simulation of hours of husband/wife and with/without children by changing wages from 2001 to 2021 data. It is the result of our hypothesis: hours of work reallocated by wage changes between 2001 and 2021. Given your results, discuss how much the model succeeds in capturing the data.
Question 3 You have found that, in Question 2, this model is still imperfect in explaining data. Extend this exercise both in theory and data to conduct your original research.
• Theory – Introduce at least one new factor to the model. Those may be parameters and/or variables. – Examples: full-time/part-time job differences, child care service availability, tax and social security policies, etc. • Data – Obtain new data corresponding to your theory extension. It must be used for calibration. – Examples: full-time/part-time number of workers and wage data, the number of children in subsidized child care centers, tax and social security rules, etc. • Goals – One goal is to improve the model’s prediction about Japanese 2021 data. – But you can also have another research goal. For example, if you incorporate full-time/part-time difference in the model, the change in this ratio between 2001 and 2021 can be your target. • Do you need to exactly follow this exercise and study Japanese data? – No – You can study your home country or favorite country. If so, please redo Question 1 and 2 using your county’s data. You can also change years. After that, try an extension. – You can also analyze two or more countries and conduct cross-country comparisons as Prescott (2004). – If you are familiar with microdata, I recommend to choose the United States and use the IPUMS USA or CPS. You can easily calculate average hours and income as in Table 1 from individual-level data. Moreover, the detailed data, for example, difference in educational level, is available. https://www.ipums.org/
