Macroeconomics of Labor Market - Fudan...

Macroeconomics of Labor Market

Jinfeng Ge

4 19th, 2013

Jinfeng Ge () Macroeconomics of Labor Market 4 19th, 2013 1 / 43

Introduction

In this lecture, we discuss the empirics and theories of labor market.

This lecture focuses on the macroeconomics aspect of labormarket. Iwill abstract from the interest issues covered in micro laboreconomics.

Two lines of research are emphasized: long-run and short-rundetermination of unemployment and labor supply.

At first, groups of evidences are reviewed.

Later on, several theories are discussed including search matchingtheory and efficiency wage. The theory of union are disregarded.

Jinfeng Ge (Fudan University) Macroeconomics of Labor Market 4 19th, 2013 2 / 43

Stylized Facts

666 Richard Rogerson and Robert Shimer

Une

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1965 1970 1975 1980 1985 1990 1995 2000 2005

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Germany

France

UKUS

Figure 17 The four lines show trend unemployment in Germany, France, the United States, and theUnited Kingdom.

Une

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1965 1970 1975 1980 1985 1990 1995 2000 2005

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SpainBelgiumItaly

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Figure 18 The four lines show trend unemployment in Spain, Belgium, Italy, and Switzerland.


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Figure 17 The four lines show trend unemployment in Germany, France, the United States, and theUnited Kingdom.

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SpainBelgiumItaly

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Figure 18 The four lines show trend unemployment in Spain, Belgium, Italy, and Switzerland.


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Search in Macroeconomic Models of the Labor Market 667

12

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Finland

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Figure 19 The four lines show trend unemployment in Finland, Sweden, Denmark, and Norway.

1965 1970 1975 1980 1985 1990 1995 2000 2005

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Ireland

CanadaAustralia

Portugal

Japan

Figure 20 The five lines show trend unemployment in Ireland, Canada, Australia, Portugal, andJapan.

difficult to say at this point whether these differences will continue to change in thefuture. For example, in countries such as the United States and Ireland, unemploymentis basically the same at the beginning and the end of the period. In contrast, in countriessuch as France and Germany, unemployment is substantially higher at the end of the


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Finland

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4

Figure 19 The four lines show trend unemployment in Finland, Sweden, Denmark, and Norway.

1965 1970 1975 1980 1985 1990 1995 2000 2005

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Ireland

CanadaAustralia

Portugal

Japan

Figure 20 The five lines show trend unemployment in Ireland, Canada, Australia, Portugal, andJapan.

difficult to say at this point whether these differences will continue to change in thefuture. For example, in countries such as the United States and Ireland, unemploymentis basically the same at the beginning and the end of the period. In contrast, in countriessuch as France and Germany, unemployment is substantially higher at the end of the


Stylized FactsSearch in Macroeconomic Models of the Labor Market 669

1965 1970

1400

1100

1150

1200

1250

1300

1350

1975 1980 1985 1990 1995 2000 2005

Year

Tot

al h

ours

Figure 21 The line shows the OECD average of country trends in total hours.

some important differences. For example, whereas the decrease in total hours was almostcomplete as of 1985, the unemployment rate continued to increase sharply after 1985.

A simple decomposition allows a more quantitative assessment of the importance ofunemployment rate changes. Our measure of total hours (H ) is the product of hoursper worker (h) and the employment-population ratio (E/P). And the employment-population ratio can itself be expressed as the product of the participation rate (PR) andone minus the unemployment rate (1 − UR). To see this note that if we let the stock ofemployed, unemployed and total population be denoted by E , U , and P respectively,then PR = (E +U )/P and 1− UR = E/(E +U ). Total hours can then be expressedas the product of three terms:

H = h · PR · (1− UR).

The contribution of changes in unemployment to changes in total hours is accounted forby the third term. Figure 22 plots the time series for the trend components of the cross-country averages for each of these three series, with each value expressed relative to its1965 value in order to facilitate comparisons. By examining the relative change in eachof these three terms over time we can assess the relative importance of each component.

The figure shows that over the entire period, the increase in the unemployment ratereduced total hours by about four percent. At its peak, in the mid 1990s, the contribu-tion was around seven percent. While this is large relative to changes at business cyclefrequencies, it is much smaller than any of the other trend changes that took place inthe labor market over this same time period. For example, the increase in labor force


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1.2

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0.8 h

1 – UR

PR

Figure22 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h. Each is the OECD average of country trends.

participation raised total hours by almost 15 percent, while the decrease in hours peremployed worker lowered total hours by 20 percent.

The large trend changes in participation and hours per worker are probably not asso-ciated with search frictions. The increase in participation is due entirely to the increasedparticipation of women, and it seems unlikely that search is a key factor in understandingthe widespread increase in female participation.44 And the decrease in hours per workeris accounted for by increases in vacation days and statutory holidays, decreases in thelength of the full-time work week, and increases in part-time work. Once again, searchfrictions do not seem to be a key element in explaining these trends. We conclude thatsearch is probably not a key element of the explanation for the dramatic decline in hoursworked over the entire period since 1965.45

To pursue this a bit further, we focus on four individual countries—France, Germany,the United Kingdom and the United States. We begin in Fig. 23 by displaying the seriesfor total hours. All three European countries experienced a very significant drop in totalhours over this period, ranging between 25 and 35 percent. In contrast, the change intotal hours for the United States between 1965 and 2007 was relatively modest.

There are again some qualitative similarities between the evolution of total hours andunemployment rates for these four economies. The United States had relatively littlechange in both its unemployment rate and total hours from 1965 to 2007, though in

44 For example, prominent papers in this literature include Galor and Weil (1996), Goldin and Katz (2002), Jones et al.(2003), Greenwood et al. (2005), Olivetti (2006), and Attanasio et al. (2008), and none even mentions search as animportant element to consider.

45 See Pissarides (2007) for an analysis that jointly considers evolutions in unemployment and total hours.


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1965 1970 1975 1980

1800

1600

1400

1200

1000

8001985 1990 1995 2000 2005

Year

Tot

al h

ours

UK

US

Germany France

Figure 23 The four lines show trend total hours inGermany, France, theUnited States, and theUnitedKingdom.

each case there are some low frequency movements between the two endpoints. And foreach of the three other countries, there was a net increase in the unemployment rate anda net decrease in total hours over the period.

Once again, these qualitative comparisons at the individual country level might leadone to suspect that changes in total hours were dominated by changes in unemployment.Figures 24–27 decompose low frequency movements in total hours for each of these fourcountries. While the exact numbers vary a little across countries, these figures confirmthe earlier conclusion reached on the basis of cross-country averages—the participationand hours per worker margins were collectively much more important than the unem-ployment margin in accounting for changes in total hours. In particular, whereas totalhours fell between 25 and 35 percent for the three European economies, the decreaseaccounted for by changes in the unemployment rate was only between four and ninepercent.

A related but distinct calculation is to ask how important cross-sectional differencesin unemployment are in accounting for cross-sectional differences in total hours. Moreprecisely, we ask what would total hours be in a country relative to the United States ifwe were to move individuals between employment and unemployment so as to give allcountries the same unemployment rate as the United States, but leave hours per workerand labor force participation unchanged. Figure 28 reports the results of such an exercisebased on the 2005 cross-section. Consistent with the earlier calculations, we see thatdifferences in unemployment account for differences in total hours on the order of fivepercent or less. While differences of this magnitude are quantitatively important from a


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h

1 – UR

PR

1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Val

ue r

elat

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to 1

965

1.1

1.0

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0.8

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Figure24 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in France.

h

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PR

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965

1.1

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0.8

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Figure25 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in Germany.

business cycle perspective, they are relatively small in the context of understanding thecross-sectional dispersion in total hours across countries.

2.1.3. Unemployment inflows and outflowsOne key feature of search models is that they make predictions about flows into and outof unemployment. In our earlier analysis of business cycle fluctuations, we argued that


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1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Val

ue r

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to 1

965

0.7

1.1

1.0

0.9

0.8

h

1 – UR

PR

Figure26 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in the United Kingdom.

1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Val

ue r

elat

ive

to 1

965

1.1

1.2

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1.0

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h

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PR

Figure27 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in the United States.

recessions are characterized by a short, sharp spike in the inflow rate into unemploymentand a persistent decline in the outflow rate. We are interested in knowing whetherpersistent changes in the unemployment outflow rate also accounted for the substantialincrease in the unemployment rate from 1965 to 1995 and the subsequent reversal.Unfortunately, data availability limits the extent to which one can readily carry out such


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1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Val

ue r

elat

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to 1

965

0.7

1.1

1.0

0.9

0.8

h

1 – UR

PR

Figure26 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in the United Kingdom.

1965 1970 1975 1980 1985 1990 1995 2000 2005

Year

Val

ue r

elat

ive

to 1

965

1.1

1.2

1.3

1.0

0.9

0.8

h

1 – UR

PR

Figure27 Thethree lines showthe labor forceparticipationratePR, theemployment-labor force ratio1− UR, and hours per worker h in the United States.

recessions are characterized by a short, sharp spike in the inflow rate into unemploymentand a persistent decline in the outflow rate. We are interested in knowing whetherpersistent changes in the unemployment outflow rate also accounted for the substantialincrease in the unemployment rate from 1965 to 1995 and the subsequent reversal.Unfortunately, data availability limits the extent to which one can readily carry out suchJinfeng Ge (Fudan University) Macroeconomics of Labor Market 4 19th, 2013 13 / 43

Stylized Facts674 Richard Rogerson and Robert Shimer

1.2

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Actual

Adj

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DEFRBE

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NZJP

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Figure 28 Total hours relative to the United States 2005, actual and adjusted for unemployment.

an analysis for a large set of countries over a long time period. Nonetheless, there aredata that can shed some light on this issue, and recent work has made some headway inproducing estimates for several countries. In this section we summarize this evidence.

The evidence that we present here supports the following three conclusions. First,there are large differences in unemployment inflow and outflow probabilities acrosscountries that are not related to differences in unemployment rates. Second, in termsof accounting for low frequency changes in unemployment, changes in both inflowand outflow probabilities played a significant role. Third, there does not appear to bea systematic pattern regarding the importance of changes in inflows and outflows thatholds across countries. Moreover, for some countries the relative importance of thesetwo flows changes over time.

Our main source of worker flow data is the OECD, which publishes the distributionof unemployment duration for the current stock of unemployed workers. The coverageis incomplete, starting at 1976 in some countries but not until 1983 for many other coun-tries. For the most part, therefore, these results apply to the post 1980 period. We empha-size that many factors can influence unemployment duration distributions, including theprevalence of switches between unemployment and inactivity, the role of temporary lay-offs and temporary jobs, the demographic and industrial composition of the workforce,


Stylized Facts


Dev

iatio

n fr

om tr

end

Year

–4

–2

0

2

4

1975 1980 1985 1990 1995 2000 2005

Figure 1 Solid line shows total hours. Dashed line shows the fraction of people at work. Dotted lineshows the fraction of people in the labor force. Gray bands indicate NBER recession dates.

parameter 1600. Cociuba et al. (2009) extend these series back to 1959 using data thatare not available online. Since the rest of our data series are not available before 1976, werestrict attention to this shorter time period here.

The solid and dashed lines in Fig. 1 show the strong comovement between detrendedhours and employment. The standard deviation of detrended total hours is 1.5 percent,while the standard deviation of the fraction of people at work is 1.0 percent and thecorrelation between the two series is 0.96. We thus conclude that, as was the case in theearlier period, “the biggest component of the variation in hours is fluctuations in thelevel of employment.” (Lilien and Hall, 1986, p. 1006).

On the other hand, there is little change in the size of the labor force at businesscycle frequencies, as shown by the dotted line in Fig. 1.5 The standard deviation of thedetrended labor force participation rate is 0.3 percent and the correlation with total hoursis 0.67. For example, during the worst year of the 2008-2009 recession, from August2008 until August 2009, total hours fell by 7.5 log points, the fraction of the populationat work fell by 4.9 log points, while the size of the labor force fell by only 0.9 log points.6

Most of the decline in total hours thus came from a decrease in employment, which wasassociated with a roughly equal increase in the unemployment rate. In contrast to the

5 We measure the labor force participation rate as the number of employed people (LNU02000000) plus unemployedpeople (LNU03000000) divided by the population aged 16-64. We seasonally adjust and detrend the data in the sameway.

6 Recall from footnote 4 that hours data from September 2009 are low because of the timing of the Labor Day holiday.From September 2008 to September 2009, measured total hours fell by 13.2 log points, employment fell by 5.5 logpoints, and labor force participation by 1.2 log points.


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Search in Macroeconomic Models of the Labor Market 631Jo

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Job finding probability Ft

UE transition probability ΛtUE

EU transition probability ΛzEU

Employment exit probability Xt

Figure 6 The top panel shows the job finding probability and the UE transition probability. Thebottom panel shows the employment exit probability and the EU transition probability. Gray bandsindicate NBER recession dates.

that the employment exit probability is contemporaneous with the unemployment rate,while the job finding probability lags the cycle slightly.

1.1.3. Three-statemodelThere are interesting patterns in the flow of workers in and out of the labor force as well.During recessions, unemployed workers are not only less likely to find a job, but alsoless likely to drop out of the labor force. Employed workers are not only more likely tobecome unemployed, they are also less likely to drop out of the labor force. Similarly,inactive workers are more likely to become unemployed and less likely to find a job.


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Job finding probability Ft

UE transition probability ΛtUE

EU transition probability ΛzEU

Employment exit probability Xt

Figure 6 The top panel shows the job finding probability and the UE transition probability. Thebottom panel shows the employment exit probability and the EU transition probability. Gray bandsindicate NBER recession dates.

that the employment exit probability is contemporaneous with the unemployment rate,while the job finding probability lags the cycle slightly.

1.1.3. Three-statemodelThere are interesting patterns in the flow of workers in and out of the labor force as well.During recessions, unemployed workers are not only less likely to find a job, but alsoless likely to drop out of the labor force. Employed workers are not only more likely tobecome unemployed, they are also less likely to drop out of the labor force. Similarly,inactive workers are more likely to become unemployed and less likely to find a job.


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10

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02001 2002 2003 2004 2005 2006 2007 2008 2009

Per

cent

Year

Unemployment rate

Vacancy rate

Figure 9 The solid line shows the unemployment rate. The dashed line shows the vacancy rate. Graybands indicate NBER recession dates.

At one level, we know the matching function is an incomplete description of the jobfinding probability because unemployed workers are not the only ones who find jobs.We have already shown that some inactive workers move directly into employment andthat some employed workers switch jobs without an intervening unemployment spell. Itis therefore remarkable that this simple theoretical structure describes the comovementof the job finding probability and market tightness so well.

To show this, we use data on job vacancies from the Job Openings and Labor TurnoverSurvey (JOLTS), a monthly survey of 16,000 business establishments.16 According tothe survey form, a job opening must satisfy three conditions: “A specific position exists;work could start within 30 days; and [the employer is] actively seeking workers fromoutside this location to fill the position.” The survey started in December 2000, at thepeak of a business cycle, and has since followed a modest expansion and strong recession.Figure 9 shows the strong negative correlation between the unemployment rate and thevacancy rate, defined as vacancies divided by vacancies plus employment.17 This stablerelationship is called the Beveridge curve.

Since unemployment is strongly negatively correlated with vacancies and withmeasures of the job finding probability, market tightness is strongly positively correlatedwith the job finding probability. Figure 10 shows the close link between a three month

16 We use BLS series JTS00000000JOL, total non-farm job openings.17 Davis et al. (2008) argue that there are significant measurement problems in the JOLTS. These mostly show up in labor

turnover statistics, but they find that job openings are unreported by about eight percent, with little cyclical variationin measurement error. The BLS has since modified the reported JOLTS data to address these concerns, but in any case,

this type of error would not substantially change our conclusions.


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Labor Markets and Macroeconomics - p. 35

Vacancies

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Labor Markets and Macroeconomics - p. 38

Reduced-Form Matching Function

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Stylized Facts2176

Table 6 Average hourly earnings by industry and sex (by firm size, May 1983 CPSy ~

W. Y. Oi and T. L. ldson

Industry and sex In firms with an employment of Ratio h

Total 1-24 1000 +

A. Males, 1983 1. Agriculture 4.677 4.388 6.436 1.467 2. Mining 12.369 8.316 13.487 1.622 3. Construction 9.380 7.995 13.679 1.711 4. Manufacturing 10.300 7.344 11.705 1.594 5. Trans/Comlnunication 11.541 7.761 13.096 1.687 6. Trade 7.433 6.253 8.438 1.349 7. Finance 11.696 8.437 12.588 1.492 8. Services 8.677 7.526 10.020 1.331

B. Femalea, 1983 1. Agriculture 4.696 4.556 5.013 1.100 2. Mining 9.606 9.917 9.706 .979 3. Construction 6.687 6.344 8.262 1.302 4. Manufacturing 6.880 6.032 7.714 1.279 5. Trans/Communication 8.697 5.722 9.787 1.710 6. Trade 4.858 4.403 5.269 1.197 7. Finance 6.902 6.193 7.538 1.217 8. Services 6.656 5.955 7.759 1.303

'~ Source: Tabulated from the May 1983 Current Population Survey. b Ratio = wages in firm size 1000 +/firm size 1-24.

provide more specific training. Employees in larger firms are slightly older and have more years of schooling. The fraction on part-time schedules is inversely related to size falling from 39.9 to 23.7% for females.

Table 5(A,B) describes the wage-size profiles based on the May CPS data for 1983 and 1979. The shape of the wage-size profile obviously differs by gender and has shifted over time. The wage ratio for males in the largest and smallest size categories {F5 over F1 } was 1.627 in 1983 and 1.497 in 1979. The corresponding figures for females were 1.384 and 1.292. The wage-size premium is clearly larger for males. To the extent that small employers employ less skilled workers and the dispersion of wages expands in a downturn, it is not surprising to find a larger size-wage gap in 1983, a recession year. The last column presents the gender wage ratio, G = ( W f / W m ) for each size group. Notice that the gender wage gap G declines with firm size; the relative wages of females are higher in small firms.

In the last four panels of Table 5, workers are divided into two size groups, <500 versus 500+ employees. In small firms with <500 workers, the gender wage ratio climbed from 0.675 in 1979 to 0.761 in 1993; the corresponding rise in large firms, panel E, was 0.615 to 0.721. Panel F presents the size-wage ratio, S = (W~.5/WF1). For both sexes, this ratio fell from 1.329 in 1979 to 1.244 in 1993.


Stylized FactsCh. 33: Firm Size and Wages

Table 9 Wage equations for full-time employees by sex, 1983 a'b

2181

Variable Male employees Female employees

Mean B t Mean B

A. Firm~plant size dummies c F2SP 0.030 0.110 3,96 0.032 F3SP 0.025 0.092 3,04 0.027 F4SP 0.008 0.147 2,76 0.007 F5SP 0.051 0.117 5.17 0.040 F2LP 0.115 0.087 5.32 0.116 F3LP 0.109 0.142 8.38 0.124 F4LP 0.043 0.134 5.53 0.055 F5LP 0.353 0.245 17.90 0.316

0.088 0.127 0.048 0.131 0.075 0.127 0.160 0.232

3.06 4.06 0.83 4.96 4.41 7.50 7.00

17.00

B. Worker~job characteristics Education 12,915 0,063 33.45 12.684 0.064 26.77 Ten 8.205 0.020 12.09 5,537 0.028 14.17 Ten-2 145.516 - 0 . 0 4 0 e - 2 -8 .01 72,606 - 0 . 0 5 8 e - 2 -8 .05 Exp 18.452 0.025 16.02 17,772 0.012 8.22 Exp-2 496.391 - 0 . 0 4 3 e - 2 -13 .10 473.881 - 0 . 0 2 7 e - 2 -8 .35 Married 0.744 0.122 10.52 0,629 0,003 0.30 Black 0.055 0.170 -8 .14 0,078 -0 .100 -5 .33 SMSA 0.374 0.122 11.48 0,390 0.134 13.16 South 0.280 -0 .048 -4 .64 0,292 -0 .047 4.29

C. Industrial affiliation Agriculture 0.025 -0 .351 - 11.28 0,005 Mining 0.024 0.193 6.31 0.005 Construction 0.084 0.186 9.91 0.012 TCU (Utilities) 0.094 O. 103 6.08 0.055 Trade 0.216 -0 .129 9.53 0.240 Finance 0.055 0.031 1.43 0.119 Service 0.162 -0 .112 -7 .49 0.350

0.170 0.326 0.079 0.161

-0 .190 -0 .006

0,026

-2 .40 4.69 1 . 7 0

6.86 - 12.44

0.35 - 1.84

Summary statistics In AHE 2.155 1.777 R-square 0.4064 0.3352 N 7833 5973

a Source: May 1983 CPS. b Dependent variable is in(average hourly earnings). c F2-F5 correspond to firm size categories 25-99, 100499, 500-999, 1000+; SP, LP correspond to small

plants (1-24) and larger plants (25+), respectively.

ees . F o r m o s t o f t h e o c c u p a t i o n s i d e n t i f i e d i n t h e i r T a b l e 1 (p. 24 ) , w a g e s a re f a i r l y s t a b l e

f o r f i r m s w i t h l e s s t h a n 1 0 , 0 0 0 e m p l o y e e s b u t r i s e s h a r p l y t h e r e a f t e r . C o m p u t e r o p e r a t o r s 3

i n f i r m s w i t h 5 0 t h o u s a n d e m p l o y e e s o r m o r e e a r n e d 2 4 % m o r e t h a n t h o s e in t h e s m a l l e s t


Search Matching Theory

Dale Mortensen, Peter A. Diamond and Christopher A. Pissarides gotNobel Prize because of search matching theory.

Search matching theory are widely applied in housing market, assetmarket especially in labor market.

There are different versions of search matching theories, we will focuson the most popular version, we refer it as DMP framework.

Basic idea of this model in the labor market is very intuitive, there aretwo sides in labor market: supply and demand. But search frictionmaking matching with supply and demand imperfect. Existence ofBeveridge curve demonstrate this market friction.


Matching Function

One key component of the theory is matching function.

ut unemployed workers are looking for jobs in period t, and thereexist vt vacancy. The successful matching between unemployed andvacancies are

mt = M (ut , vt) .

If there is no friction in this process, the matching is determined bythe short side of the market

M (ut , vt) = min (ut , vt) .

Usually we assume the matching function is a constant return function

M (λut , λvt) = λM (ut , vt) .

The Cobb-Douglas Matching function is consistent with the empiricalfacts

M (ut , vt) = uαt v

1−αt .


Matching Function

Define the market tightness as

θt =vtut

.

The probability of filling a vacancy is

mt

vt=

M (ut , vt)

vt= M

(1

θt, 1

)= f (θt) .

The probability of finding a job is

mt

ut=

M (ut , vt)

ut= θtM

(1

θt, 1

)= θt f (θt) .


Inflow and Outflow in Labor Market

Assume that jobs disappear at a constant rate

lt+1 = (1− q) lt +mt ,

and

lt =LtNt

.

In the steady state, outflow equals to inflow of unemployment

q (1− u∗) = θ∗f (θ∗) u∗,

oru∗ =

q

q + θ∗f (θ∗)


Value Functions

Assume that a filled job can generate benefit y . It costs c to sustaina vacancy and recruit. Each period, worker find a job with probabilityf (θ).Denote Jo as discounted profit of a filled job and Jv as discountedprofit of a vacancy. Then

Jvt = −c + β {f (θt) Jvt+1 + [1− f (θt)] Jvt+1} ,

Jot = y − w + β {qJvt+1 + (1− q) Jot+1} .

We only focus on the stationary equilibrium

Jv = −c + β {f (θ) Jv + [1− f (θ)] Jv} ,

Jo = y − w + β {qJv + (1− q) Jo} .

With free entry conditionJv = 0.

we obtain

Jo =c

βf (θ)=

y − w

1− β + βq.


Value Functions

Workers get wage w when they are employed and get unemploymentbenefit b when they are unemployed. in the stationary equilibrium, weobtain

vu = b+ β {θf (θ) v e + [1− θf (θ)] vu} ,

v e = w − e + β [qvu + (1− q) v e ] .

It is easy to solve

v e − vu =w − e − b

1− β + βq + βθf (θ).


Wage Determination

Another key component of search matching model is how todetermine wage rate. When search friction are presented traditionalcompetitive market assumption could not hold. Two sides of marketwhen they are matched are both monopolist. Different search modelsrely on different ways to solve the problem of wage determination.Here we introduce a very common assumption: Nash Bargaining.

Nash bargaining demands

max (v e − vu)γ (Jo − Jv )1−γ

It leads to the rent sharing rule

(1− γ) (v e − vu) = γ (Jo − Jv )

Combine the previous conditions, we obtain

w = (1− γ) (b+ e) + γ (y + θc) .


Equilibrium

The stationary equilibrium can be characterized by two equations

u =q

q + θf (θ).

y − (1− γ) (b+ e) + γ (y + θc) =(1− β + βq) c

βf (θ).

You can think these two equations as supply and demand functions inthe labor market.


equilibrium I

Ch 39." New Developments in Models of Search in the Labor Market 2581

V = 0 (23)

holds. A steady state search equilibrium for this simple economy is vector (u,w,O,V,U) that

satisfies Eqs. (14), (20), (23), (22), and (21). Substitution from Eqs. (16) and (23) into (22) yields the alternative form for the job creation condition

c p - w - - ( 2 4 )

~7(0) r + 6 '

Note that Eq. (24) is a dynamic demand for labor condition. The expected duration of the vacancy is 1/~7(0), so with a flow recruiting cost c, the expected hiring cost for this job is c~ ~7(0). Thus, the condition requires that the expected hiring cost equal the present discounted value of the difference between the future flows of marginal product and wage payments where the discount rate is the sum of the interest and job destruction rates. Because Eqs. (22), (21), (19) and (23) imply

(1 - f l ) ( r U - b) r V = - c + = 0 ,

~0

substitution into Eq. (20) for rU gives the equilibrium wage equation

w = (1 - fl)b + ~(p + cO). (25)

The wage increases with the unemployment benefit, job productivity, and market tight-

N Wage Curvet

Fig. 1. Equilibrium market tightness and wage rate.


equilibrium II

2582 D. T. Mortensen and C. A, Pissarides

ness. Finally, the equilibrium is fully described by the wage and market tightness pair (w ,O) that satisfies Eqs. (24) and (25).

The two equilibrium conditions have useful descriptive properties shown in Fig. 1. They intersect only once, hence equilibrium is unique. An increase in the worker's unemployment income b shifts the wage curve up and so increases wages and reduces m~ket tightness. An increase in the worker's share parameter/3 has similar effects. In contrast, an increase in match product p shifts the job creation condition up, increasing both wages and market tightness. More turbulence in the labor market in the sense of an increase in the arrival rate of negative reallocation shocks, 3, shifts the job creation condition down reducing both wages and tightness.

Given the solution for tightness obtained from Fig. 1, we can now draw the Beveridge diagram to derive equilibrium unemployment and vacancies as illustrated in Fig. 2. With fixed productivity, the solution for 0 is independent of unemployment, so equilibrium 0 in the Beveridge diagram is shown as a straight line through the origin. Call it the job creation condition. Equilibrium unemployment is at the point where the job creation condition intersects the Beveridge curve,

Following on from our previous analysis, an increase in either the worker's share parameter or unemployment income rotates the job creation line down in Fig. 2 and so increases equilibrium unemployment. A higher job productivity rotates it up and reduces unemployment. Higher arrival rate of idiosyncratic shocks shifts the Beveridge curve out and rotates the job creation line down, so it increases unemployment but has ambiguous effects on vacancies.

riot2

j 0 u

Fig. 2. Equilibrium vacancies and unemployment. Jinfeng Ge (Fudan University) Macroeconomics of Labor Market 4 19th, 2013 32 / 43

Comparative Statics

Use the above equation, we can derive the following comparativestatics

∂θ

∂γ< 0

∂θ

∂b< 0.

Combined with Beveridge curve, we obtain

∂u

∂γ> 0

∂u

∂b> 0,

∂v

∂γ< 0

∂v

∂b< 0.

What is the intuition behind these results?


Concluding Remarks

We only focus on the stationary equilibrium, we can use thisframework to answer the questions such as why the same workerreceive different wage in different firms or industries, why Europe hashigher unemployment rate than US?

This framework can be used to interpret unemployment volatilityalong business cycle. But Shimer (2005) AER find that the model cannot generate enough volatility of unemployment along business cycle.


Efficiency Wage Model

Idea of Efficiency wage can trace back to Karl Marx. There aredifferent version of the efficiency wage model. Shapiro and Stiglitz(1984) is the most popular.

In the following, I will describe this model.

When a worker is employed, the employer face a moral hazardproblem: employee can shirk. If worker shirks in period t he get utilityU (w), and if not he get utility U (w)− e. e is the disutility comesfrom working effort.

If worker shirks he is found by probability d and fired immediately.

Exogenous constant seperation rate q.


Basic Setting

v et , v st and vut denote the discounted utility of no-shirking employee,shirking employee and unemployed respectively.

Dynamic value function can be written as

v et = U (wt)− e + β [qtvut+1 + (1− qt)max (v et+1, v st+1)] ,

vut = U (b) + β [(1− ht) vut+1 + ht max (v et+1, v st+1)] .

The expected utility of shirking worker can be decomposed into twoparts: U (wt) if he is not found and U (b) if he is found

v st = (1− d) {U (wt) + β [qtvut+1 + (1− qt)max (v et+1, v st+1)]}

+ d {U (b) + β [(1− ht) vut+1 + ht max (v et+1, v st+1)]} .


Basic Setting

Only consider stationary equilibrium

v et = v e , v st = v s , vut = vu.

Then

v e = U (w)− e + β [qvu + (1− q)max (v e , v s)] ,

vu = U (b) + β [(1− h) vu + hmax (v e , v s)] .

v s = (1− d) {U (w) + β [qvu + (1− q)max (v e , v s)]}+ d {U (b) + β [(1− h) vu + hmax (v e , v s)]} .


Equilibrium

Combine the above three equations, we obtain

v s = (1− d) v e + dvu + (1− d) e

Firm dislike shirking, therefore they set no shirking condition satisfied

v e ≥ v s .

Then

v e − vu ≥ (1− d) e

d.

when d is smaller, the difference is larger. It means that when moralhazard is severe firm will deliver higher wage to deter shirking.


Equilibrium

If v e = v s , we obtain

v e = U (w)− e + β [qvu + (1− q) v e ] ,

vu = U (b) + β [(1− h) vu + hv e ] .

Then

v e − vu =U (w)− e − U (b)

1− β + β (q + h).

Since in steady state(1− u) q = uh,

we have

v e − vu =U (w)− e − U (b)

1− β + βq/u.


Equilibrium

In the end, we derive the key equation in efficiency wage model

U (w)− e − U (b)

1− β + βq/u=

(1− d) e

d.

This equation characterize a negative relation between wage rate andunemployment rate.

On the other hand, labor demand can be derived from the condition:wage equals to marginal product of labor

w = F ′ (L) = F ′ ((1− u)N) .

Then the equilibrium is featured with high employment rate becauseof moral hazard problem.


Supporting Evidences

There are two types of evidence offered in the literature in support ofefficiency wages.

The first type of evidence shows the presence of substantialinter-industry wage differences (e.g., Krueger and Summers). Suchwage differentials are consistent with efficiency wage theories sincethe monitoring problem (d in terms of the model above) is naturallymore serious in some industries than others.

Nevertheless, this evidence does not establish that efficiency wageconsiderations are important, since there are at least two otherexplanations for the inter-industry wage differentials. Therefore, theinter-industry wage differentials are consistent with efficiency wages,but do not prove that efficiency wage considerations are important.



The second line of attack looks for direct evidence for efficiency wageconsiderations. A number of studies find support for efficiency wages.

Krueger compares wages and tenure premia in franchised andcompany owned fast food restaurants. Krueger makes the naturalassumption that there is less monitoring of workers in a franchisedrestaurant. He finds higher wages and steeper wage-tenure profiles inthe franchised restaurants, which he interprets as evidence forefficiency wages.



Cappelli and Chauvin provide more convincing evidence. They look atthe number of disciplinary dismissals, which they interpret as ameasure of shirking, in the different plants located in different areas,but all by the same automobile manufacturer (and covered by thesame union). The firm pays the same nominal wage everywhere(because of union legislation). This nominal wage translates intogreater wage premia in some areas because outside wages differ. Theyfind that when wage premia are greater, there are fewer disciplinarydismissals. This appears to provide strong support to the basicimplication of the shirking model.

Campbell and Kamlani survey 184 firms and find that firms are oftenunwilling to cut wages because this will reduce worker effort andincrease shirking.


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