Flow Approach to the Labor Market Toshihiko Mukoyama University of Virginia
July 2017 Keio Lecture 1
Flows and stocks
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Traditional (pre-1980s) approach to the aggregate labor market · · · emphasize the determination of stocks: employment, unemployment, labor force participation, etc.
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New (post-1980s) approach to the aggregate labor market · · · emphasize the determination of gross flows: worker flows, job flows.
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The emphasis of gross flows is also related to the recognition of the general importance of reallocation of productive factors, such as capital and labor.
Flows and stocks
Three labor market states we will look at today
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Employment (E)
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Unemployment (U )
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Not in the labor force (N )
We can also look at the flows across locations, industries, occupations, firms, and establishments. But not today.
Three labor market states we will look at
Three labor market states we will look at
Three labor market states we will look at
Earlier approaches looked at these stocks.
Earlier approaches looked only at these stocks.
Stocks and business cycles
12
68
lfpr 10
8
66
unemployment rate
64
6
62
4
60
2 1940
1950
1960
1970
1980
1990
2000
2010
58 2020
Worker flows (monthly transition probabilities)
Worker flows (monthly transition probabilities)
Comparison
Theoretical framework
The three state model: Krusell et al. (2011)
The three state model: Krusell et al. (2011) ◮
Flows between (E and U ) and N is mainly driven by the choice of the workers (labor supply).
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Flows between E and U is driven by the frictions (labor demand).
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The model evolved into the business cycle analysis in Krusell et al. (2017).
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For the rest of today, we will focus on the flows between E and U and ignore N . “How to ignore N ” is different across studies: some bunch E and N together and analyze “inflow into U ” and “outflow from U ”. Here, I will take a more direct approach of focusing on EU and U E flows. Somewhat surprisingly, a model with only these two flows (assuming there are no flows in and out of labor force) can reproduce the unemployment rate dynamics similar to the data.
EU and U E flows
0.03
0.4
0.025
0.35
EU 0.02
0.3
0.015
0.25
0.01
0.005 1965
0.2
UE
1970
1975
1980
1985
1990
1995
2000
2005
2010
0.15 2015
The theory of U E flows: the matching function approach ◮
Firms and unemployed workers meet through a matching function (a “black box”): ◮ ◮ ◮
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Firms post vacancies Vt ≥ 0. Unemployed workers Ut ≥ 0. → Then, M (Vt , Ut ) ≥ 0 numbers of matches are created at time t + 1. M (Vt , Ut ) is increasing in Vt and Ut .
We assume that the matching function has the following properties: M (Vt , Ut ) ≤ Vt , M (Vt , Ut ) ≤ Ut , and M (µVt , µUt ) = µM (Vt , Ut ) for any µ > 0.
The theory of U E flows: the matching function approach ◮
Then, the stock of employment follows Et+1 = M (Vt , Ut ) + (1 − σ)Et .
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In terms of the unemployment rate, this can be rewritten as vt ut+1 = 1 − λ ut + σ(1 − ut ), ut where λ(vt /ut ) ≡ M (vt /ut , 1).
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When vt is constant, this converges to a steady state. The steady-state unemployment rate satisfies u= u is decreasing in v.
σ . λ(v/u) + σ
The steady state relationship between v and u
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Over the business cycle, v moves around (v is high in booms and low in recessions) and u changes following this relationship. Off-the-steady-state behavior turns out to be not too important in the U.S. context (except for a large recession like the Great Recession).
Beveridge curves in the United States United States, January 2001 − June 2011 4 Data from BLS Beveridge Curve
Vacancy Rate (%)
3.5
3
2.5
2
1.5
4
5
6
7 8 Unemployment Rate (%)
9
10
11
Beveridge curves in the United States
Jan. 1961 - Dec. 1970
4.5
5.5
4 3.5 3 2.5 2
4 6 Unemployment Rate (%)
5 4.5 4 3.5 3 2.5 2
8
Jan. 1981 - Dec. 1990 Job Vacancy Rate (%)
Job Vacancy Rate (%)
5 4.5 4 3.5 3
8
4
4.5 4 3.5 3
12
10
4
4
3.5
3
2.5 2
6 8 Unemployment Rate (%) Jan. 2001 - Dec. 2011
4.5
6 8 10 Unemployment Rate (%)
5.5
Jan. 1991 - Dec. 2000
5
2.5 4
4 6 Unemployment Rate (%)
Job Vacancy Rate (%)
2
Jan. 1971 - Dec. 1980 6 Job Vacancy Rate (%)
6 Job Vacancy Rate (%)
Job Vacancy Rate (%)
Jan. 1951 - Dec. 1960 5
4 6 Unemployment Rate (%)
8
3.5 3 2.5 2 1.5
4
6 8 10 Unemployment Rate (%)
12
Theory vs. Data
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The theory fits the data very well.
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Why does v move around over the business cycle?
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This is what the Diamond-Mortensen-Pissarides model (Pissarides, 2000) explicitly consider.
References
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Krusell, Per, Toshihiko Mukoyama, Richard Rogerson, and Ay¸seg¨ ul S ¸ ahin (2011). “A Three State Model of Worker Flows in General Equilibrium” Journal of Economic Theory 146, 1107–1133.
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Krusell, Per, Toshihiko Mukoyama, Richard Rogerson, and Ay¸seg¨ ul S ¸ ahin (2012). “Is Labor Supply Important for Business Cycles?” NBER Working Paper 17779.
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Krusell, Per, Toshihiko Mukoyama, Richard Rogerson, and Ay¸seg¨ ul S ¸ ahin (2017). “Gross Worker Flows over the Business Cycle” American Economic Review, forthcoming.
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Lin, Ching-Yang and Hiroaki Miyamoto (2012). “Gross Worker Flows and Unemployment Dynamics in Japan,” Journal of the Japanese and International Economies.
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Pissarides, Christopher A. (2000) Equilibrium Unemployment Theory 2nd ed. Cambridge: MIT Press.
