Assignment 2: Labour Force Participation
Due: October 16, 2010
1. Suppose that a person has the following utility function defined over income(Y) and leisure (l):
U = aY + 2 l0.5
Where ‘a’ is a positive constant. The person faces a time constraint: T=H+l where T= total amount of time available, H is hours worked and l is leisure time. The person earns two types of income: non-labour income (I) and labour income (wH) where w is the wage rate paid per unit of time worked. So Y is defined as: Y =wH+I.
(a) Give an economic interpretation to the parameter ‘a’.
(b) Combine the time constraint and the definition of income to give the expression for the budget
constraint with Y as a function of l. Graph the budget constraint in Y, l space. Be sure to
show its slope and intercepts.
(c) (i) Derive the expression for the Marginal rate of substitution (MRS) between income and
leisure for this person. What does the MRS tell you?
(ii) What is a “reservation wage”? Use your result in (c)(i) to give the expression for the
reservation wage for the person in this problem. Under what conditions will this person
be a participant if their wage rate (w) is $20/hour and T=24 hours? Explain. Sketch
this situation using indifference curves and a budget line.
(d) Set up this person’s maximization problem and derive the first order condition(s) for a
participant (assume that the wage is ‘w’ again rather than $20). Show your work.
Sketch the outcome in a diagram.
(e) (i) Use your result in (d) to derive the leisure demand function. Next state the labour supply
function associated with your leisure demand function.
(ii) In this case what exogenous variables or exogenous parameters determine labour supply?
Derive the comparative statics effects of changes in these parameters on labour supply.
(iii) Sketch the labour supply curve for this person.
(iv) Is there anything unusual about the labour supply function derived from this utility
function? What exactly is different? How does this difference affect the slope of the labour supply curve?
2. Using Statistics Canada’s CANSIM Database
(a) Collect the data below for the assigned province. For the period 1976-2013 retrieve the annual Labour Force participation rate for men in age groups 15-24, 25-54 and 55 years and over. Also retrieve the labour force participation rate data for women for each of the three same age groups. Present your data in a table and plot the six series in graphs.
(b) Describe and compare the trends in labour force participation you observe in the data.
Assigned province:
Dou, Tong / British ColumbiaFu, Xiaoyu / Alberta
Guo, Jian / Saskatchewan
Lei, Yang / Manitoba
Li, Yueheng / Ontario
Liao, Yangyang / Quebec
Liu, Shuang / Nova Scotia
Luo, Yanxuan / New Brunswick
Instructions on Using CANSIM:
CANSIM is Statistics Canada’s publicly available time series database. You can find it by searching for CANSIM in your browser or at : CANSIM contains Canadian data on a wide variety of economic variables including prices, national accounts, financial data and labour data. The data is presented in table format and there are options to customize the tables. You can save the data in worksheet format.
Finding and saving the data:
- Once you are on the CANSIM site you will see that there are a couple of search options:
(1) you can type a name in the search box and see if you can locate the data (this
sometimes works but is often unreliable) – there is also an option to use the relevant table number should you happen to know it ; or
(2) you can browse by subject or source dataset.
Let’s say you have chosen the second method and choose subject. Click the subject that seems most closely related to the type of data you are looking for e.g. “Labour” when looking for the employment or the Labour Force Participation rate data you need below. Go through the resulting list of folders under the subject category and click on what seems to be the most appropriate option e.g. “Employment and Unemployment” for the series you need. Look through the resulting Table titles in the list of search results. Then click on the table number that seems most likely to have what you are looking for and then look at what it contains. You need the annual Labour Force Participation Rate for men and women by age group for the years 1976-2013. So you need a table with Labour Force Estimates by sex and age that reports the data annually. Find the appropriate table.
- After clicking the table name you are given the default version of the relevant CANSIM data table. This is typically not what quite you want! To customize the table click the "Add/Remove data" tab. This will give you a set of options that allows you to specify the precise data series you want to retrieve.
- In the table you are looking for you need to specify Geography (your assigned province), Sex (you want data for men and women separately), age (15-24, 25-54 and 55 and older) and years (1976 to 2013). Once you have indicated exactly what you want you can click "Apply" and an "html" version of the results table will be displayed. You can cut and paste the data from this table or click "Download" which will give you a page that allows you to save the table in spreadsheet format (CSV).
3. Estimation of a labour force participation equation for women age 20 and over
This question uses the Labour Force Survey June 2014 data from assignment 1 (see file: LFS_June_2014_data.csv and the command you used to read it in assignment 1). Variables definitions are included in the same codebook used in Assignment 1.
Variables used:
LFSSTAT - Labour Force Status
SEX – Sex
PROV - Province
AGE_12 - age category variable
MARSTAT – marital status
EDUC90 – highest educational attainment
SCHOOLN – student status
SP_LFSST – spouse’s labour force status
AGYOWNKN – age of youngest own child
FWEIGHT – sample weight.
Step 1: Define the sample
- The sample is women age 20 or older. So you need to use the keep and/or drop
commands to omit both people under age 20 and men.
Step 2: Define key variables
Define dummy variables:
- Labour Force Participant (any labour force status other than not-in-labour force,
use LFSSTAT)
- Highest Level of Education dummies: (use EDUC90)
- define a dummy variable for each of the seven categories.
- Province dummies: one for each of the ten provinces.
- Age dummies: 20-24, 25-34, 35-44, 45-54, 55-64 and 65 and over.
- Marital status: a dummy equal 1 if Married or common law.
- A dummy equal to one if the person’s spouse was employed.
- Youngest child dummies: Child under age 3, Child age 3-5, Child age 6-12,
Child age older than age 12.
- Student status dummy (=1 if a student)
Use “summarize” to report the means of your new dummy variables (hand in the resulting output). Make sure that you weight the results using FWEIGHT. What is the labour force participation rate on your sample?
Step 3: Estimate the linear probability model (OLS regression with a dummy dependent
variable)
Dependent variable: labour force participation dummy.
Explanatory variables: Age dummies, married or common law, age of youngest child
dummies, education dummies, region dummies, student status dummy, and a
spouse employed dummy.
Don’t fall into the “dummy variable trap”! (see handout) If you include all dummies that describe some characteristic that set of dummies will be perfectly collinear with the intercept. To avoid this choose one category as a default group and omit the default group dummies from the list of explanatory variables included in the regression. This issue arises in this regression for the age, province and education sets of dummies. Choose as your default groups15-19 for age, Newfoundland for province and 0-8 years of education for education.
Be sure to turn the weight option on when running the regression and use FWEIGHT as the weight and the ‘pweight’ option for weighting in the regression.
Step 4: Estimate a probit version of the model in step 3 (weight this as well) -- use the "probit" command in STATA.
Drawing on your results answer the following.
(a) Interpret the estimates of the linear probability model from Step 3, i.e. explain what each coefficient estimate tells us (check the third set of notes and the reading from Wooldridge on the linear probability model). Remember to interpret coefficients from a set of dummies (e.g. all dummies describing age) relative to the default group.
(b) Are the signs of the probit model coefficients the same as those obtained from the linear probability model? How do the relative sizes of the coefficients compare between the two models?
(c) The coefficients in the probit model show the effect of an explanatory variable on the ordinate of the probability distribution and so has no straightforward interpretation. To measure the size of the effect of a characteristic on the probability of being a participant you can fix the size of the “index” (I*) (i.e. the value of the ordinate of the probit model). Equivalently, you can specify a starting value of the probability of being a participant (e.g., a probability of 0.5 implies a value of the ordinate of 0) and then evaluate the effect of changing a characteristic on this probability.
(i) Assume an initial probability of participation of 0.5. Calculate the change in the probability of being a participant associated with:
- being age 25-34 rather than age 20-24,
- having a university bachelor’s degree rather than being a high school graduate,
- having a child under age 3 vs. not having no children (i.e. all of the child
dummies equal to 0).
(To do the above calculation you will need to use some source linking the values of the ordinate to the value of the cumulative standard normal distribution: EXCEL has such as function, as does STATA (norm), some statistics texts supply a table).
(ii) How do the figures in (i) change when the initial probability is assumed to be 0.75 ?
Explain why – provide a diagram.
(iii) Now calculate these effects at the mean values of the explanatory variables (STATA can do this using the “margins” command – see STATA help). Discuss how the resulting effects compare to those of the linear probability model.
(d) There is no wage variable in the participation models estimated above yet knowing the size of wage effects on participation is often of key interest.
(i) say that we assume that the main reason that educational attainment affects
participation is through its effect on wages (the earnings literature suggests a
strong positive relationship between wages and education). Are the probit
education coefficient estimates consistent with what the theoretical model of
labour supply suggests is the effect of wages on participation? Explain.
(ii) how might the coefficients on the age of youngest child variables, the marital status and the age variables be interpreted from the perspective of the simple labour supply model? i.e. might they reflect wage, non-labour income or value of time in non-work uses? Explain.
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