Human Capital Investments and Expectations About Career and Family - - PowerPoint PPT Presentation

Human Capital Investments and Expectations About Career and Family

Matthew Wiswall & Basit Zafar 11 December 2019

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 2/28

Motivation

➓ Much of the literature on wage inequality trends looks at issue through competitive lens i.e. W=MPL. ➓ Changes to wage inequality can only ever be driven by changes to supply or demand/technology. ➓ When considering rise in graduate wage premium, in a competitive environment it is almost tautological that technology is responsible given increase in supply of graduates. ➓ Introducing search frictions allows for other explanations:

• 1. Transition Rates: Transition out of unemployment,

between jobs, and into unemployment impact average wages.

• 2. Wage Bargain: Institutions affecting the wage bargain

matter e.g. welfare, minimum wages, unions etc.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 3/28

Motivation

➓ Will embed frictions, as per ?, within a classic model of tech change and wage inequality by ?- henceforth KORV ➓ In KORV rising graduate wage premium is driven by capital skill complementarity and falling capital prices. ➓ Adding search frictions to this model serves two aims:

1. Robustness: See whether estimates of capital skill complementarity robust to alternative wage setting environments.

• 2. Decomposition: Decompose growth of wage inequality

into changes to supply, technological, frictional and institutional components.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 4/28

Key Results

➓ Theory Contribution. Develop a framework where wage inequality is driven by changes to labour supply, technology, frictional (and institutional) components. ➓ Quantitative Contribution. I find that allowing for the evolution of search frictions does not significantly change the findings of ?, in the sense that:

• 1. Parameter estimates determining the elasticity of subs.

between capital and skilled/unskilled labour are very similar in competitive and frictional version of model.

• 2. Without capital skill complementarity (CSC), both the

competitive and frictional versions of the model fail to explain growth of wage inequality.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 5/28

Outline

1 Introduction 2 Literature 3 Model 4 Data 5 Estimation 6 Results 7 Conclusion

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 6/28

Related Literature

• 1. Literature explaining wage inequality dynamics.

➓ Skills biased tech change - e.g. Katz and Murphy (1992) - then task biased tech change - Autor and Acemoglu (2011) ➓ Labour Supply: Card & Lemieux (2001) ➓ Institutional explanations: DiNardo et al (1996) ➓ Contribution: Develop model that nests tech, supply and institution explanations, adds transition rates as candidate explanation, and allows counterfactuals.

• 2. Literature explaining cross-sectional inequality.

➓ Postel-Vinay and Robin (2002) decompose residual inequality into worker and firm heterogeneity and frictions. Find frictions account for 45-60% of residual inequality. ➓ Abowd, Kramarz, and Margolis (1999) find much larger worker and firm effects (c.80% of residual wage variance). ➓ Contribution: Applying search literature to explain change in cross-sectional inequality rather than just level.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 7/28

The Model: Workers

➓ Two skill levels - unskilled/skilled- indexed by i P u, s. ➓ Efficiency in production of skill types denoted by Ψi,t (assumed stationary). ➓ Exogenous job destruction δi,t ➓ Flow income in unemployment is bi,t ✝ MPLi,t ➓ Choose to work or not - hours per worker (hi,t ) exogenous (from data) ➓ Job offer arrival in unemployment and in employment denoted by λ0,i,t and λ1,i,t respectively. ➓ Exogenous job offer rates: i.e. vacancy creation not modelled. ➓ Risk neutral

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 8/28

The Model: Firms

➓ I wish to allow for both capital to labour substitution in production, and substitution between skill types. ➓ Not easy in pure search/match framework e.g. potential for complex intra-firm bargaining problems as per ?. ➓ Proposed solution is to have two sectors of production:

• 1. An intermediate goods sector with search frictions
• 2. Competitive final good sector that combines intermediate

goods and capital, with no frictions but with imperfect substitutability of all factors.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 9/28

The Model: Final Goods Firm

➓ Final good produced using capital structures, ks,t, capital equipment, ke,t, and skilled and unskilled labour st & ut:

Yt ✏ Atkα

s,trµuσ t ♣1 ✁ µq♣λkρ e,t ♣1 ✁ λqsρ t q

σ ρ s 1✁α σ

(1)

Without frictions (as per KORV) ➓ Labour input is hours worked in efficiency units e.g ut ✑ Ψu,thu,t, st ✑ Ψs,ths,t ➓ Elas. of subs. between unskilled labour and capital equipment (and skilled labour) is

1 1✁σ. Elas. of subs.

between skilled labour and capital equipment is

1 1✁ρ

➓ Defining πt ✑ ws,t④wu,t, profit max implies: gπt ✔ ♣1 ✁ σq♣ghu,t ✁ ghs,tq σ♣gΨs,t ✁ gΨu,tq (2) ♣σ ✁ ρqλ ke,t st ✟ ♣gke,t ✁ gΨs,t ✁ ghs,tq

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 10/28

The Model: Intermediate Goods Sectors

With Frictions: Intermediate Good Firms ➓ I now interpret ut and st as intermediate goods produced using unskilled and skilled labour. ➓ Labour is hired by heterogeneous intermediate firms with match quality ν, and population cdf Fi,t♣νq. ➓ ℓt,u♣νq is fraction of employees in a match of quality ν. ➓ A worker in a match of quality ν produces exactly ν units

• f intermediate good for every hour they work.

➓ yi,t is the total amount of intermediate goods produced by skill type i for i P u, s. ut ✑ Ψu,tyu,t ✏ Ψu,thu,t ➺ νmax

νinf

νℓt,u♣νqdν (3) st ✑ Ψs,tys,t ✏ Ψs,ths,t ➺ νmax

νinf

νℓt,s♣νqdν (4)

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 11/28

Wage Determination

➓ Final good producers pay a price, pi, for a unit of type i intermediate good given by pi ✏ ❇Y

❇yi Ψi (for i P tu, s✉).

Unemployed Workers ➓ When an unemployed worker of skill type i meets a potential employer of type ν, a Nash type bargaining game ensues and worker is hired at wage contract φ♣pi, νq that solves: V ♣pi, φ♣pi, νq, νq ✏ U♣bipiq βrV ♣pi, piν, νq ✁ U♣bipiqs (5) ➓ β P r0, 1s is the bargaining parameter

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 12/28

Wage Determination

Employed Workers ➓ When an employed worker of skill type i meets a potential alternate employer, a bargaining game involving the worker and both employers of types rν ➙ ν✁s is played, the

• utcome is that the worker:

➓ ends up accepting the more productive type firm’s offer ➓ receives a wage φ♣pi, ν✁, νq that solves

V ♣pi, φ♣pi, ν✁, νq, νq ✏V ♣pi, piν✁, ν✁q (6) βrV ♣pi, piν, νq ✁ V ♣pi, piν✁, ν✁qs

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 13/28

Wage and Employment Distributions

➓ Jumping ahead..the distribution of workers of type i across intermediate firms is (with κ1,i ✑ λ1,i④δi): ℓi♣νq ✏ 1 κ1,i r1 κ1,i ¯ Fi♣νqs2 fi♣νq (7) ➓ And crucially the expected wage for a worker of type i is:

E♣wiq ✏ E♣E♣wi⑤νqq ✏ pi

➺ νmax

ν

✒ ν ✁

• r1 κ1,i ¯

Fi♣νqs2 ✂ (8) ➺ ν

νinf

♣1 ✁ βqr1

δi δiρκ1,i ¯

Fi♣xqs r1

δi δiρκ1,iβ ¯

Fi♣xqsr1 κ1,i ¯ Fi♣xqs2 dx ✟✚ ℓi♣νqdν

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 14/28

Wage Impact of Search Frictions

Figure: Wage Impact of Parameters

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 15/28

Wage and Employment Distributions

➓ Summing up:

➓ Under KORV, with no frictions: gπt ✾ ♣ghu,t④ghs,tq, ♣gΨs,t④gΨu,tq, ♣gke,t④ghs,tq (9) ➓ Under KORV with frictions: gπt ✾ ♣ghu,t④ghs,tq, ♣gΨs,t④gΨu,tq, ♣gke,t④ghs,tq, ♣gβs,t④gβu,tq, ♣gbs,t④gbu,tq, ♣gκ1,s,t④gκ1,u,tq (10)

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 16/28

Data: The KORV story

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 17/28

Data: The KORV story with frictions

➓ Under KORV, with no frictions: gπt ✾ ♣ghu,t④ghs,tq, ♣gΨs,t④gΨu,tq, ♣gke,t④ghs,tq (11) ➓ Under KORV with frictions: gπt ✾ ♣ghu,t④ghs,tq, ♣gΨs,t④gΨu,tq, ♣gke,t④ghs,tq, (12) ♣gβs,t④gβu,tq, ♣gbs,t④gbu,tq, ♣gκ1,s,t④gκ1,u,tq (13) ➓ So question is do trends for transition rates, and for institutional parameters differ much for graduates relative to non-graduates?

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 18/28

Data: The KORV story with frictions

Transition Data: Job Destruction Rates

Source: Current Population Survey, Monthly Files

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 19/28

Data: The KORV story with frictions

Transition Data: Job transition Rates

Source: Current Population Survey, Monthly Files ➓ Used as empirical target for estimating job contact rate, λ1,i,t

Mobility Rate Comparison

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 20/28

Data: The KORV story with frictions

Distribution data: Standard Dev of Resid. Log Wages

Source: Current Population Survey ➓ Used as empirical target for estimating Fi,t

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 21/28

Data: The KORV story with frictions

Distribution data: Lower Bound of Wage Distribution

Source: Current Population Survey ➓ Used as target for estimating reservation match quality νinf,i,t

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 22/28

Data: The KORV story with frictions

Institutions ➓ Not used in estimation (yet)

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 23/28

Estimation Overview

➓ Recall wage equation in model:

E♣wi,tq ✏pi,t

➺ νmax

ν

✒ ν ✁

• r1 κ1,i,t ¯

Fi,t♣νqs2✂ ➺ ν

νinf

♣1 ✁ βqr1

δi,t δi,tρκ1,i,t ¯

Fi,t♣xqs r1

δi,t δi,tρκ1,i,tβ ¯

Fi,t♣xqsr1 κ1,i,t ¯ Fi,t♣xqs2 dx ✟✚ ℓi,t♣νqdν ✏ Eν♣wi,t, pi,t ✏ 1q ❧♦♦♦♦♦♦♦♦♦♦♠♦♦♦♦♦♦♦♦♦♦♥

Stage 1 of Estimation

✂ pi,t ❧♦ ♦♠♦ ♦♥

Stage 2 of Estimation pi,t ✏

❇Yi,t ❇yi,t Ψi,t

➓ Estimation proceeds in two stages:

• 1. Eν♣wi,t, pi,t ✏ 1q. Estimate parameters determining job

market frictions and shape of within skill wage distribution.

➓ Determines shape but not location of wage distribution.

• 2. pi,t. Estimate parameters of KORV production function

➓ Determines location but not shape of wage distribution.

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 24/28

Estimation Approach

➓ Use SMM in two stages:

• 1. Eν♣wi,t, pi,t ✏ 1q. Estimate parameters determining job

market frictions and shape of within skill wage distribution:

➓ Job contact rates for employed, λ1,i,t for i P u, s. Empirical Target: Proportion of continuously employed workers with more than one employer (non concurrent)

• ver year

➓ Sampling distribution of offers, Fi,t♣νq for i P u, s . Assume log normal with lower bound νinf,i,t, mean ζi,t (will normalise this) and variance ηi,t. Empirical Targets:Variance of Log Wages, p2/50 wage percentile ratio

Estimation Detail: Search parameters

• 2. pi,t. Estimate parameters for KORV production function:

➓ Empirical Targets: Time series of Graduate Wage Premium, Labour Share, Output and No arbitrage condition for Capital Structures and Equipment.

Estimation Detail: KORV parameters

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 25/28

Results: Stage 1 (Search Frictions)

E♣wi,tq ✏ Eν♣wi,t, pi,t ✏ 1q ❧♦♦♦♦♦♦♦♦♦♦♠♦♦♦♦♦♦♦♦♦♦♥

Stage 1 of Estimation

✂ pi,t ❧♦ ♦♠♦ ♦♥

Stage 2 of Estimation pi,t ✏

❇Yi,t ❇yi,t Ψi,t

Figure: Eν♣wi,t, pi,t ✏ 1q

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 26/28

Results: Stage 2 (KORV Production Function)

Table: KORV parameter values: the importance of frictions

Parameter With Frictions Without Frictions λ 0.505 0.568 µ 0.833 0.806 α 0.083 0.091 γ

• 0.186
• 0.209

σ 0.329 0.352

• Elas. of Subs. btw S and Keq, εS,Keq (✏ 1④1 ✁ γq)

0.843 0.827

• Elas. of Subs. btw U and Keq, εU,Keq(✏ 1④1 ✁ σq)

1.489 1.544 CSC Strength: εU,Keq ✁ εS,Keq εU,Keq ✁ εS,Keq εU,Keq ✁ εS,Keq 0.646 0.716

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 27/28

Results: Stage 2 (KORV Production Function)

Without some degree of capital skill complementarity (i.e. σ ✏ γ) then both competitive and frictional version of models unable to explain increase in wage premium:

Figure: Model Fit: No Capital Skill Complementarity (CSC)

Introduction

Motivation Key Results

Literature Model

Workers Firms Wages

Data

Story under KORV Story under KORV with frictions

Estimation Results Conclusion 28/28

Conclusions and Next Steps

➓ I have developed a model where relative average wages of skill groups determined by:

• 1. relative labour supply and capital use (?)
• 2. transition probabilities, replacement rates, and bargaining

strength (?)

➓ This approach allows analysis of impact of search frictions

• n wage inequality, and implications for estimates of CSC.

➓ Find that accounting for changes to transition rates and

• utside options does not change estimates of CSC.

➓ Next steps:

• 1. incorporate institutions i.e. minimum wage, estimate

bargaining strength (probably requires MEE data).

• 2. Move away from skilled vs non-skilled split of data.

Thank you! Comments/Questions?

1/7

2/7

Appendix A: Data

Transition Data: Job transition vs Multiple Employer Rates

Source: Current Population Survey, Monthly Files

Return to Presentation

3/7

Appendix B: KORV Estimation With Frictions

1.Estimate Contact Rates ➓ In all cases, note that I target a rolling six year average of the data rather than the actual annual series. ➓ I assume that νmin ➙ b so λ0,i simply equals the empirical unemployment exit rate ➓ λ1,i is chosen to target the proportion of individuals continuously employed in a year who have more than one employer (call this τ).

➓ This is given in model by the following expression (which turns out to be independent of distribution, F):

τi ✏ 1 ✁ ➺ νmax

νmin

♣1 ✁ λ1,i ¯ F♣νqq12ℓi♣νq (14)

4/7

Appendix B: KORV Estimation With Frictions

• 2. Estimate Distribution of Firm Heterogeneity

➓ Per period revenue generated at a match of quality ν, is piν (recall pi ✏ ❇Y

❇yi Ψi)

➓ The distribution of wages for skill type i employees across the quality distribution will be, up to a scale, independent

• f pi.

➓ I can therefore estimate distribution of wages, independently of KORV production parameters (which influenc pi). ➓ Assume distribution is log-normal, and normalize mean, leaving variance and lower bound (ηi,t and νinfi,t) to be estimated. ➓ Empirical Targets:Variance of Log Wages, p2/50 wage percentile ratio

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5/7

Appendix C: KORV Estimation Detail

➓ Estimation is based on three equations coming from firms FOC’s and no-arbitrage condition

wu,thu,t ws,ths,t Yt ✏ lsht♣Xt, Ψt; φq (15) ws,ths,t wu,thu,t ✏ wbrt♣Xt, Ψt; φq (16) ♣1 ✁ δsq At1Gks♣♣Xt, Ψt; φq ✏ Et♣ qt qt1 q♣1 ✁ δeq qtAt1Gke♣♣Xt, Ψt; φq (17) ➓ Here Xt is the set of factor inputs ♣ks,t, ke,t, ut, stq, and φ is the vector of all parameters. ➓ The system of equations above can be summarized in vector form as Zt ✏ f♣Xt, Ψt, ǫt; φq

6/7

Appendix C: KORV Estimation Detail

• 1. Instrument hours worked, so exogenous data is

ˆ Xt ✏ ♣ks,t, ke,t, ˆ hu,t, ˆ hs,tq

• 2. Draw S values of the shocks to labour efficiency,ψi

t for each

period t to get S realizations of Zi

t ✏ f♣ ˆ

Xt, Ψi

t, ǫi t; φq

• 3. Use these S realizations to obtain the following moments:

ms♣ ˆ Xt, φq ✏ 1 S

S

➳

i✏1

f♣ ˆ Xt, Ψi

t, ǫi t; φq

(18) Vs♣ ˆ Xt, φq ✏ 1 S ✁ 1

S

➳

i✏1

♣Zi

t ✁ ms♣ ˆ

Xt, φqq♣Zi

t ✁ ms♣ ˆ

Xt, φqq✶ (19)

• 4. Maximize the following objective function:

ls♣ ˆ Xt, φq ✏ 1 2T

T

➳

t✏1

✧ ♣Zt ✁ ms♣ ˆ Xt, φqq✶Vs♣ ˆ Xt, φq (20) ✂ ♣Zt ✁ ms♣ ˆ Xt, φqq ln♣det♣Vs♣ ˆ Xt, φqqq ✯ (21)

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