Labor Economics Take Home 2019 PDF

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Warning: TT: undefined function: 32 Warning: TT: undefined function: 32Labor EconomicsTake-Home assignment2019Hand-out: November 18, 2019Hand-in: December 2, 2019 by 12:00pmExam no:Question 1 (20 points)In 1999, 4,860 recipients of a welfare program called “Temporary Assistance for Needy Families” (...

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Exam no:

Labor Economics

Labor Economics Take-Ho me assign ment Hom gnm 2019 Hand-out: November 18, 2019 Hand-in: December 2, 2019 by 12:00pm

Exam no:

Side 1 af 11

Dec 2, 2019

Exam no:

Labor Economics

Dec 2, 2019

Question 1

(20 points) In 1999, 4,860 recipients of a welfare program called “Temporary Assistance for Needy Families” (TANF) were asked how many hours they worked in the previous week. In 2000, 4,392 of these recipients were again subject to the same TANF rules and were again asked their hours of work during the previous week. The remaining 468 individuals were randomly assigned to a “Negative Income Tax” (NIT) experiment which gave out financial incentives for welfare recipients to work and were subject to its rules. Like the other group, they were asked about their hours of work during the previous week. The data from the experiment are contained in the table below. Number of Recipients TANF NIT Total

4.392 468 4.860

Number of Recipients Who Worked at Some Time in the Survey Week

1999 1.217 131 1.348

Total Hours of Work by all Recipients in the Survey Week

2000 1.568 213 1.781

1999 15.578 1.638 17.216

2000 20.698 2.535 23.233

a) What effect did the NIT experiment have on the employment rate of recipients? Develop a standard difference-in-differences table to support your answer. (10 points) The calculations can be seen in the table below: 1999 2000 TANF NIT Diff-in-diff

1217 ) · 100 ( 4392 131 ) · 100 ( 4392

Calculating the diff-in-diff:

1568 ) · 100 ( 4392 213 ) · 100 ( 468

Difference 1217 1217 ) · 100) − (( (( ) · 100) 4392 4392 131 213 ) · 100) − (( (( ) · 100) 468 4392 𝐷𝑖𝑓𝑓𝑇𝐴𝑁𝐹 − 𝐷𝑖𝑓𝑓𝑁𝐼𝑇

17,52% − 7,99% = 9,53%

An overview of the results from the calculations above: 1999 2000 TANF 27,71% 35,70% NIT 27,99% 45,51% Diff-in-diff

(1.1)

Difference 7,99% 17,52% 9,53%

So, NIT has increased the number of employments with 9.53 ≈ 9,5%. b) What effect did the NIT experiment have on the weekly hours worked of recipients who worked positive hours during the survey week? Develop a standard difference-in-differences table to support your answer. (10 points) To find the effect it is needed to find the average of weekly hour worked for each worker for both year 1999 and 2000.

Side 2 af 11

Exam no:

Labor Economics

1999 1.217 131 2000 1,568 213

1999

Dec 2, 2019

Ave. hour worked per recipients 15,578 15,578/1217=12.80 1,638 1,638/131=12.50 2000 Ave. hour worked per recipients 20,698 20,698/1,568=13.20 2,535 2,535/2,13=11.90

The differences-in-differences (or diff-in-diff) estimate is calculated below. The difference for TANF:

The difference for NIT:

Diff-in-diff:

13.20 − 12.80 = 0.40

(1.2)

11.90 − 12.50 = −0.60

(1.3)

∆ = −0.60 − 0.40 = −1

(1.4)

An overview of the results for both years: 1999 2000 12.80 13.20 TANF 12.50 11.90 NIT Diff-in-diff

Difference 0.40 -0.60 -1.00

The value of differences in difference (diff-in-diff) is -1. This mean that NIT decrease the weekly hours worked with 1 hour.

Question 2

(25 points) Consider a person who can work up to 80 hours each week at a pre-tax wage of $20 per hour but faces a constant 20% payroll tax. Under these conditions, the worker maximizes her utility by choosing to work 50 hours each week. The government proposes a negative income tax whereby everyone is given $300 each week and anyone can supplement her income further by working. To pay for the negative income tax, the payroll tax rate will be increased to 50%. a) On a single graph, draw the worker’s original budget line and her budget line under the negative income tax. (Hint: Ignore any non-labor market income, given that it is irrelevant for this setup. Calculate the net wage without and with the negative income tax.) (10 points) - There are mentioned two situations, an initial situation and a situation where there is negative income tax. The answer will be set up in these two situations in the below. - The initial situation: o If 𝐼 is the total income per week, H is the hour worked and L is the hour of leisure then it is possible to calculate the rate of wage after the tax: o Computing the employee’s rate of wage after tax each hour: o 80%=0.8 0.8 · $20 = $16 (2.1) Side 3 af 11

Exam no:

Labor Economics

o

So, the worker will earn $16 each hour worked

o

But if the employee decide to work 80 hours (which is the maximal hours they can work) in a week then the earned amount would be: 80 · $16 = $1280 (2.2)

o

Using the results founded above the budget line will be: 𝐼 = 1280 − 16𝐿

o

-

Dec 2, 2019

(2.3)

So, if the leisure is 80, then the worker actually doesn’t earn anything, i.e. if L=80 then C=$0. This is can be illustrated by graphing the budget line. (see figure 1)

The negative income tax situation: o In this situation a person will earn $300 per week and the after-tax is now changed to 50% of $20. Finding this for each hour: o 50%=0.5 0.5 · $20 = $10 (2.4) o

Now it will be determined how much an employee will earn when working in this situation when working for all 80 hours: $300 + $10 · 80 = $1,100 (2.5)

o

The workers budget line in this situation is now: 𝐼 = 1,100 − 10𝐿

o o

(2.6)

From the graph below we can see that at a leisure of 80 a worker will get $300, which is the same as 50 · $10 + $300 = $800 Both the situations are illustrated in the figure below:

Figure 1: This figure show the initial budget line, which show that at a leisure 0 a worker will earn $0. The blue budget line is after the negative income tax, which show that at a leisure of 80 a worker will earn $300. In other words it is the endownment point (E), which means that when the worker is not working and has a leisure of 80 hours there can still be purchased for $300

Side 4 af 11

Exam no:

Labor Economics

Dec 2, 2019

b) Show that this worker will choose to work fewer hours if the negative income tax is adopted. (Hint: Determine the point where the two budget lines intersect and plot the indifference curves corresponding to the optimal choice of the worker under both scenarios.) (10 points) - Setting the two budget lines equal to each other and isolating L: 1280 − 16 · 𝐿 = 1100 − 10 · 𝐿 (2.7) ⇓ 1280 − 16𝐿 − 10𝐿 = 1100 (2.8) ⇓ 1280 − 6𝐿 = 1100 (2.9) ⇓ −6𝐿 = −1280 − 1100 (2.10) ⇓ − 6𝐿 ⁄−6 = − 180⁄ −6 (2.11) ⇓ 𝐿 = 30 (2.12) -

-

The utility/indifference curve is tangent to the initial budget line when L = 30 but it is not tangent to the budget line from the situation of negative income tax, since when L = 30 was the optimal choice (the optimum) when there was not negative income tax. So, from the equation solved above and from figure 1 we can see that at a lower value of leisure a worker will work, so it is actually fewer hours worked when there is negative income tax.

c) Will the worker’s utility be greater under the negative income tax? (5 points) - In the situation of the negative income tax the utility for the worker will be greater, since the person could keep to have a leisure of 30 hours per week and still earn $800 (i.e. the same in the initial situation). Instead it is preferred from the employee’s side to leisure more which will cause to consume less. This means that the situation of the negative tax will increase the workers utility.

Question 3

(15 points) Suppose there are two inputs in the production function, labor and capital, and these two inputs are perfect substitutes. The existing technology permits 1 machine to do the work of 3 workers. The firm wants to produce 100 units of output. Suppose the price of capital is $750 per machine per week. a) What combination of inputs will the firm use if the weekly salary of each worker is $300? (5 points) - We are informed about following: o The output that will be produced is Q=100 units o The price of capital is r=$750 per machine o The wage rate is w=$300 per worker - It is also given that the capital and labor are perfect substitutes, therefore the isoquant of producing 100 units will be linear. Here the firm would either choose only capital or only labor. This choice is depending on whether which one is cheaper of producing 100 elements of output, i.e. the firm will choose the one which lead to lowest cost. - The slope of the isocost line is: (3.1) − 𝑤 ⁄𝑟 = − 300⁄750 = − 2⁄5 = −0.4

Side 5 af 11

Exam no:

-

-

Labor Economics

Dec 2, 2019

The marginal rate of technical substitution, MRTS is the absolute value of the slope of the isoquant. This is formally: MRTS = MPE ⁄MPK = 1 ⁄3 ≈ 0.333 ≈ 0.3 (3.2)

MPE = 1 since there is 1 machince and 𝑀𝑃𝐾 = 3 since the work is for 3 workers Since the firm substitutes more labor for capital the isoquant will be more decreased, because of convexity.

Figure 2

-

-

The isocost line is the light blue with a slope of 1/3=0.3 and the isoquant line is the dark blue with a slope of 2/5=-0.4. From the illustration shows that the isocost line has a more steep gradient/incline compared to the isoquant line. This could also be seen from the calculations above since: (3.3) 2⁄ 5 = 0.4 > 1 ⁄3 = 0.3 So it can be concluded that it will at least cost the firm to hire only capital at point marked with red so there can be produced 100 elements.

b) What combination of inputs will the firm use if the weekly salary of each worker is $225? (5 point) - To determine which combination of inputs the firm will make use of the slope of the isocost and the isoquant will be determined: - Isocost: − 𝑤 ⁄𝑟 = − 225⁄750 = − 3⁄10 (3.4) -

-

Isoquant, is exactly the same from part a): MRTS = MPE⁄MPK = 1⁄3 ≈ 0.333 An illustration of the situation:

Side 6 af 11

(3.5)

Exam no:

Labor Economics

Dec 2, 2019

Figure 3

-

In this illustration the isoquant line is the same one as in part a) - the blue with a slope of 1/3 and the new isocost line is the green with a slope of 3/10. 1⁄ 3 = 0.333 > 3 ⁄10 = 0.3 (3.6)

-

In this situation the least cost for the firm to hire only labor is the point marked with a pink circle, so the firm can produce 100 elements.

c) What is the elasticity of labor demand as the wage falls from $300 to $225? - To determine the elasticity of labor demand the following formula can be used: δLR = -

∆%ELR ∆%w

=

∆ELR/ELR ∆w/w

(5 points) (3.7)

It is actually not possible to use a formula to find an exact value, since the labor demand from the beginning goes to a positive size as the wage fall to $225 the elasticity of labor demand will therefore not has an exact value, i.e. it is infinity.

Question 4

(10 points) There are two types of farming tractors on the market, the FT250 and the FT500. The only difference between the two is that the FT250 is more prone to accidents than the FT500. Over their lifetime, one in one-thousand FT250s is expected to result in a fatal accident (so a probability of 1/1000 = 0.1%), as compared to only one in five-thousand FT500s (corresponding to a probability of 1/5000 = 0.02%). The FT250 sells for $125,000 while the FT500 sells for $137,000. At these prices, 2,000 of each model are purchased each year. What is the statistical value of a life of a farmer? - If the farmer has Model FT500 then the person also need to expense with a supplementary cost of an amount on $12,000 because 137,000-125,000=12,000. This model has only a risk to imply an accident of 4%. - As a first thing lets determine the probability of that the accident increasing from model FT500 to model FT250: 1

1

( 1000 · 100) − (5000 · 100) = 0.1% − 0.02% = 0.08%

-

Now let’s determine the quantity of tractors that can accident in a year: 0.08 · 2,000 = 160 Side 7 af 11

(4.1)

(4.2)

Exam no:

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Labor Economics

It is now possible to find out what the farmers value for a tractor accident: 12,000 · 2,000 = 150,000 160

-

-

(4.3)

It will now be determined for the farmer’s life value - The calculation method is actually the same as above: % 𝑜𝑓 𝑓𝑎𝑡𝑎𝑙 𝑖𝑛𝑗𝑢𝑟𝑦 =

-

Dec 2, 2019

1

1,000

Calculating the value of fatal injury:

−

1 = 0.0008 = 0.08% 5,000

0.0008 · 2,000 = 1.6

(4.4)

(4.5)

Now, determining the statistical value of a life of a farmer:

2,000·12,000 = 15,000,000 1.6

(4.6)

So, the statistical value of the farmer’s life is $15,000,000.

Question 5

(10 points) Peter lives for three periods. He is currently considering three alternative education-work options. He can start working immediately, earning $100,000 in period 1, $110,000 in period 2 (as his work experience leads to higher productivity), and $90,000 in period 3 (as his skills become obsolete and physical abilities deteriorate). Alternatively, he can spend $50,000 to attend college in period 1 and then earn $180,000 in each of periods 2 and 3. Finally, he can receive a doctorate degree in period 2 after completing his college education in period 1. This last option will cost him nothing in period 2, when he is attending graduate school in the second period, because his expenses on tuition and books will be covered by a research assistantship (he would still need to pay for college in period 1). After receiving his doctorate, he will become a professor in a business school and earn $400,000 in period 3. Peter’s discount rate is 20 percent per period. What education path maximizes Peter’s net present value of his lifetime earnings? - The calculations for this problem are based on the following formula: 𝑃𝑉 = 𝑐𝑜𝑠𝑡 + -

-

110,000

Present value for college: 𝑃𝑉𝐶𝑂𝐿 = −50,000 +

-

+

𝑤

(1+𝑟 )𝑡

(5.1)

where: o r is the interest of rate, w is the wage earned next year and t is the period. Finding the present values of each the three choices Peter has: Present value for high school: 𝑃𝑉𝐻𝑆 = 100,000 +

-

𝑤

(1+𝑟)

1+0.2

+

180,000

Present value for doctorate: 𝑃𝑉𝑃ℎ.𝐷 = −50,000 +

1+0.2 0

1+0.2

+

+

Side 8 af 11

90,000 ≈ 254,166.667 (1+0.2)2

180,000 ≈ 225,000 (1+0.2)2

400,000 ≈ 227,777.778 (1+0.2)2

(5.2)

(5.3)

(5.4)

Exam no:

Labor Economics

𝑃𝑉𝐻𝑆 > 𝑃𝑉𝑃ℎ𝐷 > 𝑃𝑉𝐶𝑂𝐿 -

Dec 2, 2019

(5.5)

So, it would be best for Peter if he choose to start with high school, since the present value for high school is higher than the other two alternatives.

Question 6

(20 points) The file TWINS.CSV includes the following variables describing 298 observations on 149 pairs of identical twins: - famid = twin-pair ID number (from 1 to 298) - twinid = person number within twin-pair (1 or 2) - age = age in years - agesq = age squared - lhrwage = log hourly wage - white = indicator for race of the individual (1 = white, 0 = other) - male = indicator for gender (1 = male, 0 = female) - educ = number of years of education a) Estimate a Mincer earnings function using all the variables above (except for the twin-pair and person identifiers). (5 points) - This problem is solved in R (RStudio)

-

From the function summary() we can get the coefficients:

Side 9 af 11

Exam no:

Labor Economics

Dec 2, 2019

b) Interpret the coefficient of the variable educ. What does its magnitude mean according to the human capital model? (5 points) - From the overview of coefficient above we can see that the variable educ (or education) is approximately 8,39%. This means that every schoolyear is related with 8,39% of a higher wage. - If we think of the human capital model it means that going to school or taking an education actually increases the wage with 8,39%. - Based on the signalling model schooling work as an indication of productivity, which means that the estimate is a sign of that people who learn more (i.e. take a longer years of education/schooling and therefore have a higher level of knowledge/academic knowledge) will be more productive and therefore these persons will earn more. c) Suppose the human capital model is correct. Can you interpret the coefficient of the variable educ as causal? Explain. (5 points) - With the purpose of interpreting the coefficient for the variable educ as causal it is necessary to know whether there are omitted variables which have a correlation with wage and age, years of education. In theory people who have a high ability would earn more and would also have a lower cost when getting continued educated. d) One way to eliminate the potential bias identified in part c) is to use identical twins to eliminate unobserved individual characteristics. From the original dataset, construct a new dataset with 149 observations and two variables: deduc and dlhrwage, calculated for each of the 149 twin-pairs as the difference between the values of educ (and lhrwage) for twin 1 and twin 2, respectively. Note that the differences between the twins for all the other variables should be equal to zero because the twins are identical. Then estimate an OLS regression with dlhrwage as the dependent variable and deduc as the independent variable, making sure that your specification does not include a constant. The coefficient of deduc is the estimated return to a year of schooling. How does it compare to your answer in part b)? (5 points) - In the following the data set for twins will be divided among twin 1 and twin 2. - Using the subset function to create a new dataset for twin 1 and twin 2.

-

Line 42: Computing the difference among twin 1 and twin 2 for deduc by using the definitions in line 36 and 37. Line 44: Computing the difference among twin 1 and twin 2 for dlhrwage Line 46: Estimating the OLS-regression by the lm function The result from the OLS-regression is:

Side 10 af 11

Exam no:

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Labor Economics

Dec 2, 2019

Compared the coefficient for deduc with the coefficient of educ from part b) the new coefficient deduc is higher.

Side 11 af 11...