unemployment - lecture 18, econ 4310€¦ · tord krogh econ 4310 november 15, 2012 13 / 52. e...

UnemploymentLecture 18, ECON 4310

Tord Krogh

November 15, 2012

Tord Krogh () ECON 4310 November 15, 2012 1 / 52

Intro

General question: Why do we have involuntary unemployment?


Intro II

Answer provided by search theory:

Search frictions are preventing workers and firms from meeting

Gives an equillibrium with unemployment

The unemployed are indeed involuntary unemployed, since they are willing to work at thegoing wage rate


Intro III

Benefits of search theory:

Provides micro-foundations for analyzing search frictions

Can use the model for policy analysis to evaluate the effect of changes in e.g. productivityand benefits

(Matchting function is debated)


Intro IV

Today: More on unemployment (based on Romer, chapter 10 and Blanchard’s paper onunemployment in Europe). Will focus at

Efficiency wages

Blanchard’s main points


Efficency wages: Shapiro-Stiglitz model

To discuss efficiency wages, we look at the Shapiro-Stiglitz model. It was very imporant in theearly 1980s. Search models are different, but the way the models are constructed can be viewedas inspired by Shapiro-Stiglitz.

Firms’ production depends on employment, L and the workers’ effort e (taking into accountthe distinct difference between labor and e.g. capital)

The term ‘efficiency wages’ is natural since we have a model where the workers are moreefficient when they recieve a higher wage (they induce more effort)

We can therefore have an equilibrium where the wage rate is higher than the market clearingwage because firms need to induce effort

Here we will motivate the link between wages and effort with firms’ limited monitoringabilities

Setup will be slightly different from Romer’s (allowing us to utilitze the what we used in thesearch and matching lectures).


Efficency wages: Shapiro-Stiglitz model II

There are L workers. Each is assumed to have a lifetime utility funciton

U =∞∑

t=0

βt yt

where yt = wt − et is employed and yt = 0 if unemployed. et measures effort and we assume that

et =

{0e

This means that a worker can be in three different states:

1 Employed, exerting effort

2 Employed, not exerting effort

3 Unemployed


Efficency wages: Shapiro-Stiglitz model III

There are N firms. Each firm has a production function as just discussed. Profits areF (eLe )− w(Le + Ls ), where Le is the number of workers with effort and Ls is the number ofshirkers. We see that what matters for production is eLe , the ‘efficient’ labor stock.


Efficency wages: Shapiro-Stiglitz model IV

If there is perfect observability of effort (and no other frictions), workers will accept any job witha wage exceeding e.


Efficency wages: Shapiro-Stiglitz model V

Further, if there is perfect observability of effort, the firm can choose to not hire shirkers. Theirdemand function is found by differentiating profits with respect to Le :

F ′(eLe ) = w

This defines the labor demand function for each firm. Must hold for all N firms (they areidentical). We assume that

F ′(eL

N) > e

This means that the marginal product of each firm at full employment exceeds e.


Efficency wages: Shapiro-Stiglitz model VI

Equilibrium when there are no frictions:

No unemployment if effort is perfectly observable. Equilibrium wage is wo .


Efficency wages: Shapiro-Stiglitz model VII

Then we introduce imperfect monitoring. What happens? We need to impose some structure toanalyze the model:

Firms hire workers at the market wage w

Job separation happens at the exogenous rate δ

Shirking will be unobservable, but firms will discover that a shirking worker is actuallyshirking with probability q

Unemployed workers are hired by firms at a rate a


Efficency wages: Shapiro-Stiglitz model VIII

We therefore have

P(Fired|Employed;et = e) = δ

P(Fired|Employed;et = 0) = δ + (1− δ)q

P(Hired|Unemployed) = a

To ease notation, let q∗ = (1− δ)q be the probability of shirk detection conditional on noseparation.


Efficency wages: Shapiro-Stiglitz model IX

The rates δ and q∗ are taken to be exogenous. The job finding rate is taken as given by workers,but in equilbirium it will follow from the flows in and out of unemployment. Remember, there areL workers. We let there be N firms, and each firm is assumed to hire L workers. The law ofmotion for the unemployed, Ut = L− Nt Lt , in an equilibrium where no agents shirk (ourequilibrium will have that property) will be:

Ut+1 = (1− at )Ut + δNt Lt

Steady state requires Ut = Ut+1, implying

a =δNL

U=

δNL

L− NL(1)


Efficency wages: Shapiro-Stiglitz model X

As in search models, we need to introduce value functions. Let Ve be the value function for anunemployed worker who is exerting effort. Vs is the value function for a shirking worker, while Vu

is the value function for an unemployed. We define them as end-of-period value functions.


Efficency wages: Shapiro-Stiglitz model XI

The Bellman equation defining Ve is straightforward. Next period, you get w − e in period utilityfor sure. Then there is a probability δ you loose your job, and probability 1− δ you get to keep it.Hence:

Ve = β [w − e + δVu + (1− δ)Ve ]

or, after re-writing in our usual way:

ρVe = w − e + δ(Vu − Ve ) (2)

where ρ = 1/β − 1 is the discount rate.


Efficency wages: Shapiro-Stiglitz model XII

For a shirker, the setting is almost the same as for an employed worker with effort. The onlydifference is that they don’t face the effort cost today, but at the same time they face a higherprobability of loosing the job, namely δ + q∗.

Vs = β [w + (δ + q∗)Vu + (1− δ − q∗)Vs ]

or, after re-writing:ρVs = w + [δ + q∗](Vu − Vs ) (3)


Efficency wages: Shapiro-Stiglitz model XIII

For the unemployed, we assume that they will choose to exert effort if employed (i.e., the wage ishigh enough). We therefore need

Vu = β [b + aVe + (1− a)Vu ]

orρVu = a(Ve − Vu) (4)

Here b continues to be the unemployment benefit.


Efficency wages: Shapiro-Stiglitz model XIV

Let us now derive a ‘labor supply’ relationship, which shows the wage rate needed to makeworkers exert effort.

This requires Ve ≥ Vs

At the same time, firms will not pay more than necessary. Let us therefore look at the wagethat gives Ve = Vs .

Using equations (2) and (3), Ve = Vs gives us

w − e + δ(Vu − Ve ) = w + [δ + q∗](Vu − Ve )

or

Ve − Vu =e

q∗

Immediately we see that Ve > Vu , so workers strictly prefer employment to unemployment. Inthis sense, all unemployment in this model is indeed involuntary.


Efficency wages: Shapiro-Stiglitz model XV

To find out what the required wage rate is, we use (2) and (4), since this gives

ρ(Ve − Vu) = w − e − b − (a + δ)(Ve − Vu)

Inserting for Ve − Vu = e/q∗, we get

w = e + b + (a + δ + ρ)e

q∗

The required wage therefore compensates not only for the cost of effort (e), but for e at a factor> 1. The factor increases in the discount rate, job finding rate, and separation rate. It is falling inq∗, the conditional probability of shirk detection. Intuition?


Efficency wages: Shapiro-Stiglitz model XVI

Finally we insert for the steady state value of a from equation (1):

a =δNL

U=

δNL

L− NL

since we then get

w = b + e + (δNL

L− NL+ δ + ρ)

e

q∗

= b + e + (δNL + δ(L− NL)

L− NL+ ρ)

e

q∗

= b + e + (δL

L− NL+ ρ)

e

q∗(5)

We refer to (5) as the no-shirking condition. It gives the wage rate required to make the workersexert effort once employed.


Efficency wages: Shapiro-Stiglitz model XVII

This condition gives the wage rate as an increasing function in employment. Why? Since lowerunemployment makes the threat of being fired less relevant. In the limit, as L→ L, the wage rategoes to infinity! This is because all workers get a job nevertheless, so why bother to exert anyeffort?


Efficency wages: Shapiro-Stiglitz model XVIII

What about demand for labor? Is strictly speaking different from the frictionless case, but not inequilibrium, since no workers shirk in equilibrium. Can therefore use same labor demand curve asbefore:

eF ′(eL) = w (6)


Efficency wages: Shapiro-Stiglitz model XIX

Drawing equations (5) and (6) together shows what the equilibrium wage and level ofemployment is:


Efficency wages: Shapiro-Stiglitz model XX

Observations:

There is involuntary unemployment since Ve > Vu

Firms are not willing to hire unemployed workers at a wage rate w < w eq , since they knowthat a worker with this wage will shirk for sure

A higher value of q∗ shifts the no-shirk curve down, and hence lowers unemployment,bringing us closer to the competitive equilibrium

More generous unemployment benefits (b) will increase unemployment since it shifts theno-shirk condition up. Workers are more inclined to shirk than before

We can improve the outcome by subsidizing firms that hire workers. This will improvewelfare if the cost of taxation (to finance the subsidy) is not too great.


Efficency wages: Shapiro-Stiglitz model XXI

Can the model help us understand why wages appear to be rigid?

If the no-shirk condition is flat, shifts in demand for labor will only change employment andnot the real wage

Hence, may be that observed wage rigidity is due to efficiency wages?


Efficency wages: Shapiro-Stiglitz model XXII

As we see, this will not hold in the model when unemployment is ‘low’.

As Romer points out, calibrated versions of the model indicate that the no-shirk condition shouldbe steep along the relevant interval – hard to use it to explain wage rigidity then.


Efficency wages: Shapiro-Stiglitz model XXIII

Romer discusses four extensions. Let us look at the first three:

Can we explain why firms more often use layoffs rather than lowering overall hours?Under work-sharing, you make it more likely that workers shirk (since their surplus is lowered).Layoffs does not change surplus of work for remaining workers

What happens when there are more sectors?Add extra sector with perfect monitoring. May give segregated labor markets (if there isheterogeneity in δ’s that signal quality)

Let workers caught shirking get a lower wage for a period instead of firing themMakes the no-shirk condition horizontal in the short run. Will give more employment volatility


Efficency wages: Shapiro-Stiglitz model XXIV

Fine. You should think of the Shapiro-Stiglitz model as another possible (and elegant) way towrite down a microfounded model to explain involuntary unemployment. Less important thansearch and matching models today.

But both models have a natural place in your toolkit for how to think about the labor market

Both imperfect monitoring and search frictions are probably important frictions

Useful starting points if you want to build models for policy analysis


Unemployment in Europe

Next, let us move on to Blanchard’s magnificent paper on unemployment in Europe. This is amust-read, and extremely efficient introduction to macroeconomic theories for unemployment.Style of the paper: Go chronologically through movements in unemployment and theories used toexplain it, from the 1970s until today.


Unemployment in Europe: The increase in the 1970s

Unemployment in most European countries went from low to high levels during the 1970s. Thiseconomic stagnation occured at the same time as inflation remained high → stagflation.Blanchard attributes the rise in unemployment to adverse supply shocks. Both due to slowertechnological growth and oil price shocks. Blanchard builds his argument on a simple bargainingmodel. (You have seen such models in introductory macroeconomics.)


Unemployment in Europe: Bargain models

Firms are assumed to act as price-setting monopolists. Will under standard assumptions lead toprices being set as a constant mark-up over nominal unit labor costs

P = µW

A

where A is labor productivity. In logs:

pt = log µ+ wt − at

where lowercase letters indicate logs. Ignoring the constant term, we define the warranted wageas wt − pt = at .


Unemployment in Europe: Bargain models II

Wages are assumed to be determined through bargaining between workers and firms. Could forinstance assume that the outcome is the solution to a Nash bargaining problem as we looked atfor search models. Assume that the real wage resulting from the bargaining is given by (in logs):

wt − pt = ωat − βut + γzt

Here ut is the unemployment rate while z measures ‘other factors’. Blanchard refers to this realwage as the bargained wage.


Unemployment in Europe: Bargain models III

The level of unemployment that makes the wage and price curves intersect is labeled the naturalrate or the NAIRU (these terms are often used interchangeably).

Analytically it is easy to verify that

uNAIRUt =

(ω − 1)at + γzt

β


Unemployment in Europe: Bargain models IV

How to think about the ‘natural rate’?

At the natural rate, we have a constant real wage

The bargained wage coincides with the warranted wage.

Implies a constant rate of inflation (and wage inflation)

Unemployment below the natural rate will lead to higher inflation (and lower inflation whenit is above)

NAIRU shifts when a and z changes. But for ω = 1, a will only affect the real wage.


Unemployment in Europe: Bargain models V

In this static model, it is only for ut = uNAIRUt we can have stable inflation in equilbrium.

Therefore widely held that monetary and fiscal policy cannot maintain unemployment levelsbelow NAIRU

(But this conclusion may change in dynamic models)


Unemployment in Europe: The increase in the 1970s II

This model forms the basis for Blanchard’s thinking about unemployment changes in the 1970s.We interpret the oil shocks and slower technological growth as a reduction in a.

But in the model put up here, it should for the most part only change the real wage. Ifω = 1 (or is close to 1) the unemployment rate is determined solely by z.

⇒ Must add some sort of frictions to the model to explain the slow adjustment

Blanchard argues that we need to look at two sources of frictions: Real and nominal wagerigidities.


Unemployment in Europe: Bargain models with real rigidities

First we consider real rigidities. We do that by changing the wage bargaining equation into:

wt − pt = ωaet − βut + γzt

aet is the ‘expected’ value of at , or rather the labor unions perception of the true level of at .

Assume that aet is updated as

aet = λae

t−1 + (1− λ)at

while the actual process for at is a random walk:

at = at−1 + εt


Unemployment in Europe: Bargain models with real rigidities II

What is now the equillibrium level of employment? Assuming ω = 1 and zt = z, it isstraightforward to verify that

ut = −1

β(at − ae

t ) +γ

βz

or, after inserting for how aet is updated:

ut = −1

β

(at − λae

t−1 − (1− λ)at)

+γ

βz

= −λ

β

(at − λae

t−1

)+γ

βz

= −λ

β

(at−1 + εt − λae

t−1

)+γ

βz

= λ

(ut−1 −

γ

βz

)−λ

βεt +

γ

βz

= λut−1 −λ

βεt + (1− λ)

γ

βz


Unemployment in Europe: The increase in the 1970s III

Consider now an adverse supply shock, ∆a = ε < 0, and no more shocks after that. What effectdo we get?

In the model where at = aet , we get an immediate shift the real wage, but no change in the

unemployment rate/NAIRU (ω = 1)

But when the unions are slow in recognizing the fall in the ‘warranted wage’, they keep onbargaining for a higher wage. The initial shock has persistent effects. Will have a period ofhigher unemployment until the real wage is finally reduced to the necessary level.

⇒ This type of ‘real’ rigidity can explain why adverse supply shocks in the 70s had effects onunemployment for a long period

Real wage rigidites are frictions that prevent the real wage from adjusting to its ‘long-run’equilbrium value.


Unemployment in Europe: Bargain models with nominal rigidities II

What about nominal rigidities? Refers to situations where nominal prices are slowly adjusted.One way to introduce that in our model is to change the bargaining equation into

wt = pet + ae

t − βut + γzt

So, it is not just productivity that the workers have to form expectations over, but also the pricelevel. This gives us nominal wage stickiness. Equilibrium level of unemployment is now:

ut = −1

β((at − ae

t ) + (pt − pet )) +

γ

βzt

Shows that monetary policy can counteract real wage rigidities using monetary policy to changethe rate of inflation! If ae

t > at , they need to make sure that pt > pet .


Unemployment in Europe: The increase in the 1970s IV

This means that differences in real and nominal rigidities across Europe may explain why fairlysimilar adverse technology shocks led to very different outcomes.

Unemployment is expected to increase more when there are greater real rigidities, or smallernominal rigidities

It is argued that countries with either very centralized collective bargaining or very littlecollective bargaining have smaller real wage rigidities

The presence of wage indexation in many central and southern European countries willcontribute to less nominal rigidities


Unemployment in Europe: 1980s

But unemployment continued to rise during the 1980s. Hard to argue that this was the effect ofshocks more than 10 years ago. Furthermore, inflation seemed to have stabilized, even thoughunemployment was high. Shouldn’t this imply that NAIRU had actually increased? New elementsin theory to explain this:

Respones of capital accumulation

Hysteresis


Unemployment in Europe: Bargaining model with capital accumulation

The role of capital accumulation is straightforward to include in our bargaining model. Earlier, weassumed that the ‘warranted wage’ was given by w − p = a. But this was based on a modelwhere labor was the only input factor, as well as constant returns. What if we instead assumeCobb-Douglas production? In logs:

yt = (1− α)kt + α(nt + at )

(note that this is labor-augmenting technology). The marginal product of labor will now give areal (warranted) wage

wt − pt = (α− 1)(nt + at − kt ) + at

This shows that changes in the capital stock affects the warranted wage. If the capital stock falls,this lowers the warranted wage!


Unemployment in Europe: Bargaining model with capital accumulation II

If n is log of the labor stock, we can use the approximation u = n − n. The unemployment ratethat equalizes the bargained and warranted wage is now

pet + ae

t − βut = pt + (α− 1)([n − ut ]− kt + at ) + at

or after re-arranging:

ut = −1

1− α+ β[(pt − pe

t ) + (at − aet ) + (α− 1)(n − k + a)]

As before, unemployment depends on pt − pet and at − ae

t (nominal and real rigidities). But wealso get an effect from changes in the capital intensity!


Unemployment in Europe: 1980s II

It is natural to think that the adverse shocks to a, together with the slow adjustment in realwages (and thus too high levels of employment, lowering profits), led to lower investmentand thus a smaller capital stock. This adds persistence to the effect of the shocks, possiblyexplaining why unemployment remained high in the 1980s.

Expansionary monetary policy should have made the reduction in investment less severe (dueto the low real interest rates). But many countries had a monetary contraction (in responseto the high inflation rates).


Unemployment in Europe: 1980s III

Another source of persistence could be hysteresis.

Alternative number one (Nickell): Periods of unemployment leads to loss of human capital

Alternative number two: Insider/outsider model where unions in the wage bargain only careabout keep those employed still in work. Will also lead to hysteresis, since in the extremeform unemployment follows a random walk (hence no force that pulls it back to the‘NAIRU’-level). Intuition: The bargained wage is set to keep employment constant. Anyshock to productivity or prices will be fully absorbed by unemployment.


Unemployment in Europe: Bargaining model with hysteresis

The last model is easy to include in our setting. Keep the warranted wage the same as in thecapital accumulation case, but assume that kt is constant. Then, instead of the normal wagebargaining equation, assume that unions will bargain for a wage such that their expected value ofemployment next period, ne

t , is equal to the number of members in its union, mt . Theunion-member process is given by

mt = nt−1 + θ(n − nt−1) ≈ nt−1 + θut−1

Hence, θ is a measure of how much the union ‘cares’ about unemployed (outsiders) relative to theemployed (insiders).


Unemployment in Europe: Bargaining model with hysteresis II

The wage that makes net = mt can be found using the warranted wage equation in expectations:

wt = pet + (α− 1) [ne

t + aet − kt ] + ae

t

Impose net = mt , and insert for mt :

wt = pet + (α− 1) [nt−1 + θut−1 + ae

t − kt ] + aet

Then subtract the expression for the actual warranted wage:

0 = [pet − pt ] + (α− 1) [nt−1 + θut−1 − nt + [ae

t − at ]] + [aet − at ]


Unemployment in Europe: Bargaining model with hysteresis III

Next trick: Use that nt−1 − nt = (nt−1 − n)− (nt − n) ≈ ut − ut−1. Therefore:

[pt − pet ] + α[at − ae

t ] = (α− 1) [ut − (1− θ)ut−1]

Or, finally:

ut = (1− θ)ut−1 −1

1− α([pt − pe

t ] + α[at − aet ])

We still have real and nominal rigidities. In addition, we now get the persistence effect dependingon θ. If we set θ = 0, we get unemployment as a random walk! Hyper-persistent.

This model attempted to describe how collective bargain would disrupt the entire adjustmentprocess that should bring unemployment back to its NAIRU level. But seems very extreme toassume θ = 0.


Unemployment in Europe: 1990s

Finally: What is the situation in the 1990s? Still very high unemployment on average, but evengreater heterogeneity now. Focus shifted over to institutions. Especially search frictions. As allof us know, this is possible to model using search and matching models.

Focus on institutions led to a large literature

Seems like differences in institutions are helpful to explain differences across countries

But not that easy to show how it matters across time within a single country (too littlevariation? delayed effects?)

Policy advise from search literature: Must motivate search effort


Unemployment in Europe

Other issues (in general):

In what ways can the tax system and other institutions be changed to reduce e.g. searchfrictions?

Still not a concencus on why strong unions seems to be effective in e.g. Scandinavia, butnot, say, France

How much can fiscal and monteary policy affect the equilibrium unemployment rate in thelong run?

All of you must read Blanchard’s paper!


unemployment - lecture 18, econ 4310€¦ · tord krogh econ 4310 november 15, 2012 13 / 52. e...

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