Keisuke Kawata
ISS, UTokyo
Plan
1. DMP model with stochastic production shock 2. Mismatch accounting
1. Explanation
• A role of theory is explanation.
→Improving the explanation power is an important contribution.
e.g.,) By introducing sticky wage into the perfect competitive model, we can explain
• Existence of unemployed,
• Increasing the unemployment rate during recession,
← cannot be explained in the competitive market model.
Note less olatilit of age a e also e plai ed ut o se se.
Explanation
• A paper shows that by incorporating new structure into the model, an unexplained fact is newly explained ← not significant contribution. Multiple unexplained facts are explained ← good!!!
Unexplained facts in the standard model
• In the standard perfect competitive market model,
• Wage a e perfe tl e plai ed orker’s hara teristi s e epti g for the compensation wage model.
Note: Utility is same in the compensation wage model.
Large share of age dispersio a ot e e plai ed orker’s hara teristi s.
← The DMP model cannot be also explained.
1. DMP with Idiosyncratic shock
• Mortencen and Pissarides (MP model 1994) provides an extended DMP model i trodu i g idios rati sho k o fir ’s produ ti it .
DMP: Constant productivity y in DMP
MP: The productivity is statistically changed.
1. Settings
• In each period, the productivity is changed following � supported [ , ത�] by the idiosyncratic shock �.
• Firm can decide whether to fire the worker or not.
• Other structure is same as in the original ← Block recursively also hold.
Note: Perfect competitive model
• We can introduce the stochastics productivity into the standard perfect competitive model.
←With the free-entry condition, only highest productivity firms can attract workers and then survive in the market.
⇒ The productivity distribution is degenerated in the equilibrium.
↔ear h fri tio allo s that a fir a o ti ue to e plo orkers e e if the fir ’s productivity is down.
1. Job destruction condition
The value of a filled job is
� � = � − � + � � ∫ max � � , � + − � � � ,
→ Optimal job destruction can be characterized by the threshold strategy; a match is destructed if and only � < ത� where
� ത� =
1. Value functions
• The value of an employed and unemployed workers are
� = � + � � ത� + � න
ത� �
′ �′ + − � � ,
= + � � + − ,
the value of a filled and unfilled jobs are
� � = � − � + � � ത� + � න
ത� � �
′ �′ + − � � � ,
= −� + � � � + − ,
where � is an initial productivity (given).
1. Market equilibrium
• Additional equilibrium condition is the optimal job destruction, which is given by the firing threshold ത�; a firm fires a worker if and only if ത�.
• Market equilibrium is defined over value functions, wage function � , tightness , and the firing threshold ത�.
← and outside option is the market variables, which are sufficient to characterize the optimal ത� and bargaining result � .
1. Equilibrium condition
• Three equilibrium conditions 1. Wage share rule
� − = � � + � � − − ,
2. Free entry condition
= , 3. Job destruction
� � = .
1. Wage share rule
• The value of an employed worker and filled job, and the standard wage share rule are obtained as
� = �� + − � − � .
← depe di g o the fir ’s produ ti it .
1. Free entry condition
• the value of a filled and unfilled jobs are
� = � � � , Where
� � = − � � − − � + � ∫ത� � �
′ �′
− � + �� where � is an initial productivity (given).
1. Value of firms
• The value of a filled job is
� � = − � � − − � + �� ∫ത� � �
′ �′
− � + �� By integrating in both side,
නത� � �
′ �′ = − � ∫ത� � − − � �′
− � + �� ത�
1. Job destruction
• The wage share rule allows us to rewrite the job destruction condition as
= ത� + � ത� − which can be rewritten as
= ത� − − � + න
ത� � + � � − �
Note that fro the age share rule, i sta ta eous fir ’s profit is ത� − ത� = − � ത� − − �
← Job is not destructed even with negative profit. (Labor hoarding)
1. The value of unemployed
• From the values of unemployed and unfilled job, and the wage share rule and the free entry conditions obtain
− � = + − � � ,�
MP model VS DMP model
• Search friction allows that low productivity firms are survived.
• By introducing idiosyncratic shock, the DM model newly explained
1. Wage dispersion as a result of firm heterogeneity ←Higher productivity firms pay higher wage.
2. Lower productivity firms fire workers. 3. Produ ti it dispersio ?
Walrasian model with entry costs
• MP model can be interpreted as extension of the perfect competitive model with stochastic productivity and the entry costs as Melitz
1. A potential firm entries the market with the entry costs I. 2. Drawing their productivity.
3. Market interactions with monopolistic competitive goods market and perfect competitive labor market.
← lower productivity firms can survive due to the entry costs and monopolistic power in goods market.
← higher productivity firms hire more workers
Worker’s age ust e sa e
Another role for causal inference
• Theory can be used for the causal inference.
Causal inference: Inference for the effects of a treatment. e.g.,
• Effect of minimum wage on employment.
• Effe t of u er of o petitors o fir ’s profits.
• Effect of monetary policy on social welfare.
← a e also used i easure e t .
e.g.,) Global worming due to human activity ← Causal effect of human activity
Potential outcome
• A dominated approach of causal inference is based on potential outcome. Potential outcome: Outcome in different treatment status.
⇒Causal effects is defined as the different of potential outcome. e.g.,
• Employment rate with minimum wage as 800¥ - Employment rate with
minimum wage as 2,000¥ ←Effect of increasing minimum wage from 800¥ to 1,000¥.
Randomized experiment
• For causal inference, we need to observe potential outcome in hypothetical scenario (counterfactual). ←Fundamental problem (Rothemberg) in causal inference.
• We have two approaches; experiment and imagine.
Experiment: Even with heterogeneity, we can observe counterfactual outcomes by the randomized control trial.
e.g.,) Countries are pure-randomly assigned into two groups with minimum wage as 800¥ and 1,000¥.
Limitation of experiment
• In some (many?) cases, the experiment is not relevant.
• The well-designed randomized experiment requires,
Both treatment and outcome can be observed.
No-i tera tio et ee su je ts .
Subjects should be drowning interest population
← Very hard to satisfy those requirements!!!!!.
Imagine
• Imagining-based inference is an alternative
⇒ We i age the ou terfa tual out o e ased o assu ptio s a d side- evidence.
e.g.,) comparative statics
• Definition of causal effect, assumptions (including Lucas critique), and side- evidence should be consistently used ← Theory are useful.
2. Mismatch in frictional labor market
• Safin et., al. (2014 AER) offers an approach to measure the seriousness of employer-employee mismatch.
• The slide shows the simplified version with Japanese data.
• Good example of imaging-based inference with minimum assumptions.
2. Motivation: Job-less recover
• In many developed countries, we can observe the job-less recover after negative economic shock.
Job-less recover: Even if total demand for labor is recovered, wage and employment is not enough recovered.
2. Market tightness and job-finding rate
0.2 0.4 0.6 0.8 1 1.2 1.4
0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09
Job finding rate Tightness
2. Interest counterfactual
• We i age ou terfa tual here the so ial pla er allo ates orkers a ross occupation with zero relocation costs.
• The planner maximizes the number of new employment.
• Causal effect of mismatch: Optimal number of new employment －Real number
←measure of mismatch.
• The model specification of occupation-level-labor market is crucial.
Production sector
0 500,000 1,000,000 1,500,000 2,000,000 2,500,000
2013 2014 2015 2016
Vacancy Seeker hirring
• Matching function-based model is reasonable.
Optimal condition
• The optimal conditions are; (i) the first order condition,
���� ��∗ , ��
� �� =
���′� �′�∗ , �′�
� �′� for a j a d j’, a d ii feasi ilit o strai t
�
�� = �
Optimal condition
• The optimal conditions are; (i) the first order condition,
���� ��∗ , ��
� �� =
���′� �′�∗ , �′�
� �′� for a j a d j’, a d ii feasi ilit o strai t
�
�� = �
Matching function: Empirical specification
• Let specify the matching function as the Cobb-Douglas;
��� = � � ��−� ���
⇒ ���
�� = �� �� = � � �� ��
�
⇒ ln �� �� = ln � + ln � + ln ��
← can be estimated (with error) by the occupation-level panel data including the number of new match, vacancies, and seeker.
←estimated is 0.58.
Estimated efficiency
manager professional office sales service security agriculture, forestry, and fishery production driver construction transport, cleaning, and wrapping
Estimated efficiency
0.1.2.3
0 20 40 60
year_id
manager professional
office sales
service security
agriculture, forestry, and fishery production
driver construction
transport, cleaning, and wrapping
Estimated efficiency
0.1.2.3
0 20 40 60
year_id
manager professional
office sales
service security
agriculture, forestry, and fishery production
Estimated efficiency
1000000 1050000 1100000 1150000 1200000 1250000 1300000 1350000 1400000
2012 2013 2014 2015 2016
Estimated efficiency
0.03 0.04 0.05 0.06 0.07 0.08 0.09
Estimated efficiency 2012
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
manager professional office sales service security agriculture, forestry, and
fishery
production driver construction transport, cleaning, and
wrapping Optimal Real
Estimated efficiency 2012
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Optimal Real
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
Optimal Real
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
0 50000 100000 150000 200000 250000 300000 350000 400000 450000 500000
2013 2014
Reference
Şahi , A., Song, J., Topa, G., & Violante, G. L. (2014). Mismatch unemployment. The American Economic Review, 104(11), 3529-3564.
Mortensen, D. T., & Pissarides, C. A. (1994). Job creation and job destruction in the theory of unemployment. The review of economic studies, 61(3), 397-415.
