**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 (LFSCan.zip, which contains excel file, text file and .dta file for each database) in the folder “TA Conf”.

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.

*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.

*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).

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

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).

- 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.

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

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.

- 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?

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.

**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)?

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.

- 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.

“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.

- 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%).

- Fraction of workers who are members of union members or covered by collective aggreement.

- Fraction of workers who are members of union members by province.

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

- Plot and interpret the following statistics using bar chart. If there is a difference of unionization, discuss why? (Less than 3 sentences).

- Fraction of Canadian (union_mem) by gender (sex)

```
##
## Female Male
## Non-Union member 65.34273 69.90245
## Union Member 34.65727 30.09755
```

- Distribution of union members(union_mem) by age group (age_12)

- Regress hourly wage on union membership (union_mem). Do union members earn higher wages than non-union member?

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 |

**Answer**

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.

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.*