Labour Economics PS1 Solutions PDF

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Warning: TT: undefined function: 32LABOUR ECONOMICSProblem set 1Question 1. There’s a tiny island where 10 people live. We go visit the island and observe that 7 people are working for the only company in the island, while 1 person is applying for a job at the firm but has not been hired yet, and 2 ...

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LABOUR ECONOMICS Problem set 1

Question 1. There’s a tiny island where 10 people live. We go visit the island and observe that 7 people are working for the only company in the island, while 1 person is applying for a job at the firm but has not been hired yet, and 2 are sick and cannot work. The people who are working make 12 euros an hour, and they work 40 hours a week. The company provides no benefits, and there is no other way of making money in the island. a) Calculate the labour force participation rate and the unemployment rate in the island. LFPR = Labour Force / Population = (Employed+Unemployed)/Population = (7+1)/10 = 80% UR = Unemployed / Labour Force = 1/(7+1) = 12,5% b) Calculate the monthly earnings of the workers. What’s their total (monthly) income? Income = 12€/h * 40h/week * 4week/month = 1920€/month

We come back to the island after 2 years and first of all notice that the population has increased by a recent birth of twins. We also find out that now 8 people are working and 2 applying for a job at the company, and that the workers are now making 13 euros an hour. We go to the local market and notice that prices are 10% higher than 2 years ago. c) Describe the change in the labour force participation rate and in the unemployment rate from the first visit to the second. LFPR = Labour Force / Population = (Employed+Unemployed)/Population = (8+2)/10 = 100% The population is still 10 because we only account the adult (+16) population and the Labour Force increased because there are more people working and looking for a job, so the LFPR increased. UR = Unemployed / Labour Force = 2/(8+2) = 20% The Unemployment rate increased because previously there were people seek and not able to work and now they are looking for one. d) Calculate real wages for the workers, at the prices of the year when we first visited the island. Did real wages increase or decrease? By how much? Real wages = Old wages * New CPI / Old CPI = 1920€/month * 110% / 100% = 2112€/month (CPI = Consumer Price Index) Income = 13€/h * 40h/week * 4week/month = 2080€/month Income - Real wages = 2080€/month - 2112€/month= - 32€/month → The real wages decreased in 32€/month.

Question 2. In France, women raising their children on their own are eligible for the Allocation de Parent Isolé (API, or single parent benefit), as long as the youngest child is under 3 years of age. In 1998, a single mother with 2 children (one of them under 3) is eligible for 900 euros a month from the government if she has no other income. The benefit actually received equals the difference between the 900 euros guarantee and her income from other sources. → 900€ guarantee

a) Assuming the only sources of income in the household are benefits and earnings, draw the budget constraint for a single mother with 2 children, one of them younger than 3. Draw the indifference curve for a woman who would choose not to work under these conditions, and the indifference curve for another woman who would choose to work. (Use a month as the reference period. Assume there are 25 workdays per month and 16 hours a day available for either work or leisure. Assume also that the woman can find a job at the minimum wage, which is 8 euros an hour.) → 8€/h * 16h/day * 25day/month =3200 €/month (maximum with 400h/month)

b) How many hours does the woman need to work a month for her income to be higher than 900 euros a month? How many hours would she need to work per day? 113h/month (and she wins 904€/month) 5h/day (and she wins 1000€/month)

c) Explain the incentives created by this program (talk about the income and substitution effects). Does it make single mothers more or less likely to participate in the labour market? Are all types of single mothers affected by the program? This program generates and income effect (the individual has a higher income now) and a substitution effect (the salary goes down to 0 unless the individual works a lot). It makes single mothers less likely to participate in the labour market, it discourages work and usually the optimal is not to work. Nonetheless, not all types of single mothers are affected by the program: it can depend if they have someone who helps carrying the under 3 years of age child and maybe the others, and the salary they are used to, if it is much more than 900€/month the women will not benefit from the program because she will prefer to work.

Question 3. The API was reformed in 1999 in order to modify the incentives to work. After the reform, a woman on API who started working could keep the full API guarantee during the first 6 months. After that, and during the following 9 months, 50% of the woman’s earnings had to be subtracted from the API guarantee. After that period, 100% of earnings had to be subtracted, just like before the reform. a) Draw the budget set under the new rules for a woman on API who is considering whether to start working. (Assume the API guarantee is still 900 euros. Note that there is one budget constraint for the first 6 months, a different one for the following 9 months, and a third one after those initial 15 months.)

b) Explain how the reform alters the incentives to work for single mothers with young children (argue relative to the initial design of the program as described in Question 2 and use the concepts of income and substitution effects). After 1999, should we expect more single mothers to work or fewer? This program generates and income effect (the individual has a higher income now) even higher than the previous one for the first 15 months. While the substitution effect (the salary goes down to 0 unless the individual works a lot) was pretty heavy on the first program, on this one during the first 6 months it is non existent and on the following 9 months although 50% of the woman’s earnings had to be subtracted from the API guarantee, women still won a salary working so there is not substitution effect for the first 15 months. All this makes single mothers more likely to participate in the labour market,because they have a lot of incentives (having the API guarantee plus salary or a part of it). They win more than not working in any case. Question 4. The table at the end of this problem set contains information about 40 French single mothers (in Aula Global you can find this data set in Stata format). We know how many hours they work a week, and we know whether this information was collected before or after the 1999 reform (the variable “After the reform” takes value 1 if the information was collected after the reform). We also know how many children each woman had, and the age of the youngest child. We want to estimate the effect of the reform on hours of work for single mothers. a) Run a regression for hours of work including only the indicator for after the reform as an explanatory variable. Does it seem like the reform may have increased or decreased hours of work? Is the effect significant?

Weekly hours = 18,7 + 7,9*AfterReform p-value = 0,06 > 0,05 = significant value → Although it seems like the reform may have increased the hours of work by 7,9, a large p-value suggests that changes in the predictor are not associated with changes in the response, so it is insignificant for us. We cannot be sure if the effects are caused by the “after the reform” variable. b) Number of children and age of the youngest child are probably also related to hours of work. Run another regression including these two additional variables. Interpret the results.

Weekly hours = 24,77 + 6,25*AfterReform - 5,19*NumberChildren + 1,08*AgeYoungestChildren Now, adding new dependent variables to the regression, we can see how the “After the reform” variable is significant. With this regression we can see that the reform adds 6,25 hours of work, the number of children subtracts 5,19 hours of work per children and the age of the children adds 1,08 hours per year of age. c) The reform affected only single mothers with children younger than 3. Create a dummy variable that takes value 1 if a single mother has a child under the age of 3, and 0 otherwise. Also, create a dummy that takes value 1 if a single mother has a child under the age of 3 AND the information was collected after the reform. Run a regression adding these two explanatory variables. Interpret the results.

Weekly hours = 27,56 + 1,13*AfterReform - 5,26*NumberChildren + 1,08*AgeYoungestChildren 5,35*DummyAge +10,73*DummyAgeReform Finally, taking all the variables into account, with the p-value we can see that “After the reform” and “Dummy age” are insignificant (0,67>0,05 and 0,16>0,05 respectively). This makes sense because we have another dummy variable called Dummy age+form which explains both of them. So, having a look at the significant variables, the number of children decreases 5,26 hours of work per children and the age of the children adds 1,08 hours per year of age. But what concerns us is the effects the reform had, and we can see that the mothers who could take advantage of reform actually worked more after it, the regression shows that it adds 10,73 hours of work if the youngest child is less than 3 years old and we are after the reform. d) Explain what you think we can conclude from the data regarding the effects of the reform. Do you think we can claim we have estimated the causal effect correctly? Why? As said in the previous question, we can conclude from the data regarding the effects of the reform that it actually worked because the regression shows that it adds 10,73 hours of work if the youngest child is less than 3 years old and we are after the reform. The causal effect is correct because we took into account the p-value and in the last regression all the variables were taken into account. Question 5. An individual has a utility function given by U(L,Y)=Y2L where Y is earned income (assume the individual has no non-labour income) and L is hours of leisure per day. The individual divides the 24 hour day between leisure and market work. The wage rate is 6 euros per hour. a) How many hours does this individual work per day? Y = w*H + V T=H+L→L=T-H Y = Total income W = salary/hours V = wealth = non-labour income H = Hours worked Y = w*H + V = 6*H L = T - H = 24 - H We have to max the utility U(L,Y)=Y2L → U(H) = (6*H)*2*(24-H) → U’(H) = 288 - 24H = 0 → H = 12 h/day

b) What is his/her utility? U(H) = (6*H)*2*(24-H) = (6*12)*2*(24-12)= 1728 c) If there were a law preventing individuals working more than 8 hours per day what would be the utility of the individual with the above utility function. Comment on the desirability of such a law. U(H) = (6*H)*2*(24-H) = (6*8)*2*(24-8) = 1536 The individual wouldn’t like that kind of law because his utility is under the optimal (1536 < 1728). Question 6. The data set “incpanel”, available in Aula Global both in Stata and Excel format, includes administrative data on 32,901 individuals working in the German labour market. a) Compute average wages for each specific age and plot these averages against age. What is the general relationship? How does this relationship vary across education groups (where 1=“lower secondary education”, 2=“higher secondary education”, 3=“tertiary education”)?

Until the age of 46 the older you have the greater that your wage is, but then it seems to decrease.

There is not a crear relationship between education groups and log wage. b) Run a least squares regression of log daily wages on age and age squared as well as a set of education group dummies. Interpret your estimates.

This regression tells us that we cannot take into account the years (because its p-value = 0,15 > 0,05 = significant value). That said, the education level increases a bit the log wage but what most increases it is the age squared....