Please work in Groups of 4 - Due Oct. 9, 2019 at the Beginning of the Lecture (submit one version of this homework per group to the assignment 2 folder created on mycourses).

For exercise 1 and 2, consider the data extract Canjuly18.txt based on the July 2018 wave of the Canadian Labor Force Survey collected by StatCan. For exercise 3, consider the time series database TsCanada. The data are available in a zip file (, which contains excel file, text file and .dta file for each database) in the folder “TA Conf”.

Exercise 1 : Estimation of labor supply.

The propose of this exercise is to estimate the elasticity of labor supply with respect to hourly wage using Canadian Data from Labor Force Survey (LFS,Statistic Canada, July 2018). We will consider the Usual hours per week at their main job (uhrsmain) as the labor supplied by an individual at given hourly wage (hrlyearn).

Each group should choose one Census Metropolitan Area (CMA) as well as the province in which the CMA lies (see Table 1). The codes are useful for those using Stata.

  1. Plot the distribution of categorical hours per week at main job (hours_categ, created from uhrsmain) of Canadian workers. Do the same by gender. Briefly describe what you observe. Are Canadians usually working full-time at their main job? Do women work longer hours than men at their main job? (Please, max. 150 words).

Possible answer

The majority of canadians are working more than 35 hours per week i.e full time at their main job. However, other are working partial time at their main job (less than 30 hours). This result suggest that not all canadians are workin full time. By gender, we observe a left-skewed distribution for men and a right-skewed distribution for women. This result suggest that the fraction of women working partial time at their main job is much higher the fraction of men.

  1. Regress the usual hours per week at the main job (uhrsmain) on the hourly wage. What would the labor supply model predict for this regression? Are your regression results consistent with the theoretical predictions of the labor supply model? Interpret the results (max. 5 sentences).

\[ h_i = \beta_0 +\beta_1 \omega_i +\varepsilon_i \]

Table 1: Estimation of labor supply (The question was only to estimate for Canada but if you estimated for a given province)
Estimate Std. Error t value Pr(>|t|)
Country Canada
constant 32.64402 0.0955 341.80445 0
log wage 0.13837 0.00322 42.93507 0
Province Alberta
constant 32.56817 0.30414 107.08257 0
log wage 0.15366 0.00884 17.3766 0
Province British Columbia
constant 30.70814 0.28917 106.19427 0
log wage 0.18742 0.00973 19.26642 0
Province Manitoba
constant 32.32418 0.31692 101.99595 0
log wage 0.1614 0.01176 13.72249 0
Province NewBrunswick
constant 35.47828 0.45526 77.93004 0
log wage 0.0993 0.01796 5.52978 0
Province Newfoundland_Labrador
constant 34.86002 0.60824 57.31334 0
log wage 0.13154 0.02154 6.10552 0
Province NovaScotia
constant 33.27812 0.40739 81.68675 0
log wage 0.15362 0.01555 9.88155 0
Province Ontario
constant 32.34865 0.18691 173.0739 0
log wage 0.1299 0.00602 21.56292 0
Province PrinceEdIsland
constant 34.39774 0.59296 58.00996 0
log wage 0.10996 0.02465 4.46066 1e-05
Province Quebec
constant 32.80834 0.20417 160.68961 0
log wage 0.10985 0.00723 15.20258 0
Province Saskatchewan
constant 31.73455 0.36177 87.72001 0
log wage 0.16875 0.01192 14.15272 0

Possible answer

The theorical model predict a backward bending labor supply, which is the result of substitution and income effects. In this empirical result, as wage increase the labor supplied by a worker increases. This result suggest that the substitution effect is much higher than the income effect (Of course the linear model is an assumption).

  1. Regress the log usual hours per week at the main job (uhrsmain) on the logarithm hourly wage. How would you interpret ? Use this parameter in a sentence.

\[ \log(h_i) = \beta_0 + \beta_1 \log(\omega_i) +\varepsilon_i\]

Table 1: Estimation of the elasticity of labor supply
Estimate Std. Error t value Pr(>|t|)
Country Canada
constant 2.90608 0.01127 257.75559 0
log wage 0.1998 0.00353 56.56082 0
Province Alberta
constant 2.78867 0.03581 77.87064 0
log wage 0.23301 0.01073 21.70615 0
Province BritishColumbia
constant 2.7279 0.03432 79.48506 0
log wage 0.24847 0.0107 23.22013 0
Province Manitoba
constant 2.86586 0.03753 76.37157 0
log wage 0.21687 0.0121 17.93018 0
Province NewBrunswick
constant 3.02274 0.05208 58.041 0
log wage 0.18401 0.01704 10.79777 0
Province Newfoundland_Labrador
constant 3.01096 0.05883 51.17888 0
log wage 0.1842 0.01884 9.77941 0
Province NovaScotia
constant 2.99769 0.0417 71.88127 0
log wage 0.18615 0.0136 13.687 0
Province Ontario
constant 2.83663 0.02365 119.95811 0
log wage 0.21409 0.0073 29.32981 0
Province PrinceEdIsland
constant 3.0752 0.06747 45.5767 0
log wage 0.16051 0.02238 7.17315 0
Province Quebec
constant 3.02924 0.02362 128.2522 0
log wage 0.16078 0.00747 21.51592 0
Province Saskatchewan
constant 2.79446 0.04312 64.80858 0
log wage 0.23137 0.01338 17.28653 0

Possible answer

The elasticity of labor supply is positive. If the wage rate increases, the worker will supply more labor.

  1. Now, we want to compare the labor supply of women versus men. Estimate the elasticity of supply for both both genders. According to your regressions, is the labor supplied by men or women more elastic?
Table 2: Elasticity of labor supply by gender
Men Women
(Intercept) 3.0784885 2.8544354
log(hrlyearn) 0.1658351 0.1959058

Possible answer:

The empirical result suggest that the elasticity of labor supply is more elastic for women than for men.

  1. Urban economics: Compare the elasticity of labor supply in the CMA that you chose with that of rest of the corresponding province. Is labor supply in the CMA more elastic than in the rest of the province (excluding the CMA)?
Table 3: Elasticity by geographical area
Census Metropolitan Area Rest of the province
Edmonton Alberta
Intercept 2.78263 2.7906
log(wage) 0.23254 0.23323
Hamilton Ontario
Intercept 2.69865 2.84583
log(wage) 0.24922 0.2117
Montréal Quebec
Intercept 3.09289 3.00952
log(wage) 0.1413 0.16685
Ottawa Ontario
Intercept 2.8803 2.82549
log(wage) 0.18723 0.21851
Québec Quebec
Intercept 3.03295 3.02731
log(wage) 0.15596 0.16182
Toronto Ontario
Intercept 2.98219 2.79527
log(wage) 0.17089 0.22644
Vancouver BritishColumbia
Intercept 2.95642 2.60448
log(wage) 0.18197 0.28472
Winnipeg Manitoba
Intercept 2.93138 2.72242
log(wage) 0.19496 0.26472

Answer Both elasticities are are positive. The conclusion between CMA and the rest of the province depend on your province.

  1. Do you believe that estimates of this type (as in exercise 1 a-d) provide unbiased estimates of labor supply elasticities? Discuss.

Answer The main concerns are the problems of cofounding and omitted variables. Also, the linear model is a strong assumption. Thus, these estimates are probably biased.

Exercise 2 : Unions impact on wage.

“Unions are collective organizations whose primary objective is to improve the well-being of their members. In Canada, this objective is met primarily through collective bargaining with the employer. The outcome of this process is a collective agreement specifying wages and non-wage benefits”.

To test whether unions have impact on wage in Canada (this is an exercise, in reality, we need more to test this assumption), consider the database Canjuly18.txt based on the July 2018 wave of the Canadian Labor Force Survey collected by StatCan.

  1. What fraction of Canadian workers are members of unions and what fraction are not members of unions? Please, find the same fractions for each province? Why there is a difference between provinces? (Hint: you can use tables or bar chart to displays your result the fraction of union members by province. Fraction of members + fraction of non-members = 100%).

** Answer** This result is similar what yoi have in the lecture notes. We observed some disersion acrross province.

  1. Plot and interpret the following statistics using bar chart. If there is a difference of unionization, discuss why? (Less than 3 sentences).
##                      Female     Male
##   Non-Union member 65.34273 69.90245
##   Union Member     34.65727 30.09755

  1. Regress hourly wage on union membership (union_mem). Do union members earn higher wages than non-union member?
Table 4: Unions-nonUnions wage gap
Estimate Std. Error t value Pr(>|t|)
(Intercept) 24.44570 0.07232 338.01954 0
union_memUnion Member 5.90609 0.12713 46.45843 0


Many empirical work in the union literature aims at estimating the wage effect of unions, i.e. the union-nonunion wage gap. This exercise confirmed the Union wage premia. Both right-to-manage or efficient bargaining model could explain this result.

Exercise 3: employment and earnings.

Consider the database of Labour Force Survey from 2009 to 2017, TsCanada.txt. This is a yearly data. Use all provinces. An unit of observation is a province-year.

Plot the employment rate against the average hourly earnings. Put the employment rate on the y-axis and the average wave (hrlyearn) on the x-axis.

Discuss: is this Demand, Supply, or something else. (Less than 200 words)

Possible answer

This graph illustrates only a set of equilibria.