Master 2 - Paris School of Economics

Master 2 - Paris School of Economics

François Fontaine & Francois Langot 2014-2015

Sujet 1 : MORTENSEN [1977]

Unemployment benefits and job search

Dale T. Mortensen, 1977. "Unemployment insurance and job search decisions," Industrial and Labor Relations Review, vol.

30(4), pages 505-517, July.

In the model of job search, it is assumed that unemployment benefits b(t) depends on the time spent unemployed t. The utility job is the salary w, and the unemployed is b − ψ(t) with ψ > 0. ψ(t) represents the disutility of search effort a(t) after t periods of unemployment. The suppliers of labor have a probability π(a(t)) = 1 − exp(−φ(t)) to draw an offer. They then have access to a unique wage w. Each job is destroyed with probability s. We denote β the discount factor.

– Write the agent program, assuming that we have b(t) = b for t = 1, ..., n and b(t) = b/2 for t > n.

– Write the agent program, assuming that we have b(t) = b ∗ (t

).

– Write program for this model (numerical analysis with Matlab or ano- ther tools) with b(t) = b ∗ (t

) and for the following calibration pa- rameters : Determine the value of φ to obtain an average duration of

Table 1 – Parameters

ψ s β w b µ

1 0.2/12 0.995 100 75 0.25

unemployment of 13 months when b is constant ∀t, with b = 50.

– From this calibration, analyze the impact of a change of b and µ on the results. Explain.

Sujet 2 : MORTENSEN [1990]

Minimum wage, heterogenous productivity and inequali- ties

D. Mortensen, “Equilibrium Wage Distributions : A Synthe- sis” in J. Hartog, G. Ridder, and J. Theeuwes, eds, Panel Data and Labor Market Studies. Amsterdam : North Holland, 1990.

We present an equilibrium on the labor market where there are two types of firms i = 1, 2, characterized by their levels of productivity : y

< y

. The exogenous fraction of firms with low productivity level is denoted σ. λ is the probability of obtaining a wage offer.

The profits of each type of firms is :

π = sλ

(s + λ[1 − F (w)])

(y

− w) (1) We define the distribution function offers pay F (.) as the weighted average salary offer made by the two types of company :

F (w) = σF

(w) + (1 − σ)F

(w)

where F

(.) is the distribution function of wage offers posted by the firm-type i.

– Determine the conditions defining the equilibrium, ie the distributions of wage offers and firm profits for each level of productivity, (F

, F

, π

, π

).

– For what value of the minimum wage, firms of type 1 are excluded from the market ?

– Write the code file (for Matlab or another tools) of this model for the following parameters :

Table 2 – Parameters

mw s λ y

y

σ

0.8 0.287 0.142 2 2.5 0.25

– Explain the impact of a wage increase in wage inequality that is mea- sured by the difference between the average wage and the mw.

To do this, you compare the impact of this policy in two economies, one where σ = 0.25 and the other where σ = 0.75, then two other economies, where a{y

, y

} = {2, 2.25}, the other where {y

, y

} = {2, 3}. Comment on your results.

Sujet 3 : MORTENSEN [1990]

Minimum wage, heterogenous outside opportunity and inequalities

D. Mortensen, “Equilibrium Wage Distributions : A Synthe- sis” in J. Hartog, G. Ridder, and J. Theeuwes, eds, Panel Data and Labor Market Studies. Amsterdam : North Holland, 1990.

Let b

for i = 1.2, the monetary value received by an individual i if it does not work (outside opportunities). Assume that b

< b

. We denote m

(m

) the number of supplier working with external opportunities equal to b

(b

).

The total population is then m = m

+ m

and the aggregate unemployment rate u = u

+ u

. λ is the probability of obtaining a wage offer.

– Determine the reservation wage R

and R

of the two types of agent.

– Determine the equilibrium between the Ins and Outs of unemployment for the suppliers of labor of type i.

– Determine the equilibrium flow for a given wage level wage (w).

– Determine the distribution function of wages G(w).

– Show that the number of employees per firm is

for w ≥ R

, l(w|R

, R

, F ) = λ sm

(s + λ[1 − F (w)])

for w < R

, l(w|R

, R

, F ) = λ sm

(s + λ[1 − F (w)])

– The optimal strategy for fixing wages is a solution of : π = max

w

(y − w)l(w|R

, R

, F )

Show that the introduction of heterogeneity of suppliers of labor can lead to a wage offer distribution with discontinuous support. Explain.

– Write the code file (for Matlab or another tools) of this model for the

Table 3 – Parameters y s λ b

b

m

/m

2 0.287 0.142 .6 .8 1

– How the introduction of a minimum wage can reduce inefficiencies in the labor market. What is the threshold level of the minimum wage to reduce unemployment. Explain.

Sujet 4 : CAHUC, POSTEL-VINAY & ROBIN [2006]

Job-to-Job Mobility and Wage Dispersion

Cahuc, Postel-Vinay and Robin, “Wage Bargaining with On- the-Job Search : Theory and Evidence”, Econometrica , 2006.

– Assume that β = 0 and that all workers are identical with ε = 0.

Explain what happens when an offer from a firm p

reaches a worker already employed in a firm p. Consider different cases depending on p vs p

. Derive the wage equation.

– Under the same assumptions, derive the steady state within-firm dis- tribution of wages. Start by right the flow equation for the type (w, p) jobs. Interpret the result.

– Explain what changes occur, in term of mechanism, when β 6= 0. Is it likely to create, in the model, more wage dispersion ?

– Propose what could be an alternative estimation method using a simu- lated method of moments (e.g. indirect inference).

– Interpret the results of the paper in the light of the wage dispersion

literature.

Sujet 5 : CHETTY [2008]

Unemployment Insurance

Chetty, “Moral Hazard versus Liquidity and Optimal Unem- ployment Insurance”, Journal of Political Economy , 2008.

– Using equations (1), (2) and (3), derive the link between i) the level of the unemployment benefits and the search effort s

, ii) the wealth of the individual, A

, and their search behaviors, iii) there expected wage and their search behaviors. Interpret the results.

– Show that the effect of unemployment benefits on assets can be de- compose between a moral hazard effect and a liquidity effect (that is equation (9)). Interpret this result in the light of the results of the op- timal insurance literature when there is no saving choices and no credit market imperfections.

– In the static case, present the program of the social planner. Explain the arbitrage he faces when choosing the level of the unemployment benefits. Derive carefully the equation (11). Interpret the result.

– Explain the methodology used by Chetty to bring the model to the data (what he calls the exact identification approach ). What are the advantages with respect to the usual methods ?

Sujet 6 : GAUTIER et alii [2014]

Equilibrium Effects of Job Search Assistance

Gautier, Muller, van der Klaauw, Rosholm and Svarer, “Es- timating the Equilibrium effects of Job Search Assistance”, Working paper , August 2014

– Explain how and why equilibrium effects can biased the results drawn usually from randomized experiments. From that perspective, discuss the results found in Section 4 of the paper.

– Discuss the framework used in Section 5 from that perspective (i.e. the

matching technology and more generally the main hypotheses).

– Derive carefully the wage equation (equation (12)). Discuss the result.

– Present and discuss the welfare measure (equation (15)).

– Using the same calibration, reproduce the results presented in section

6.2 and sum up in Figure 5 (nb : Please provide a code file that can be

understand easily !). Interpret the results.