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

Motivation Introduction Motivation ➓ Much of the literature on wage inequality trends looks at Key Results Literature issue through competitive lens i.e. W=MPL. Model Workers ➓ Changes to wage inequality can only ever be driven by Firms changes to supply or demand/technology. Wages Data ➓ When considering rise in graduate wage premium, in a Story under KORV Story under competitive environment it is almost tautological that KORV with frictions technology is responsible given increase in supply of Estimation graduates. Results ➓ Introducing search frictions allows for other explanations: Conclusion 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. 2/28

Motivation Introduction Motivation Key Results Literature ➓ Will embed frictions, as per ? , within a classic model of Model tech change and wage inequality by ? - henceforth KORV Workers Firms Wages ➓ In KORV rising graduate wage premium is driven by Data capital skill complementarity and falling capital prices. Story under KORV Story under ➓ Adding search frictions to this model serves two aims: KORV with frictions 1. Robustness : See whether estimates of capital skill Estimation complementarity robust to alternative wage setting Results environments. Conclusion 2. Decomposition : Decompose growth of wage inequality into changes to supply, technological, frictional and institutional components. 3/28

Key Results Introduction Motivation Key Results Literature ➓ Theory Contribution . Develop a framework where wage Model inequality is driven by changes to labour supply, Workers technology, frictional (and institutional) components. Firms Wages Data ➓ Quantitative Contribution . I find that allowing for the Story under evolution of search frictions does not significantly change KORV Story under the findings of ? , in the sense that: KORV with frictions 1. Parameter estimates determining the elasticity of subs. Estimation between capital and skilled/unskilled labour are very Results similar in competitive and frictional version of model. Conclusion 2. Without capital skill complementarity (CSC), both the competitive and frictional versions of the model fail to explain growth of wage inequality. 4/28

Outline Introduction Motivation Key Results 1 Introduction Literature Model Workers 2 Literature Firms Wages Data 3 Model Story under KORV Story under KORV with 4 Data frictions Estimation Results 5 Estimation Conclusion 6 Results 7 Conclusion 5/28

Related Literature Introduction 1. Literature explaining wage inequality dynamics. Motivation ➓ Skills biased tech change - e.g. Katz and Murphy (1992) - Key Results then task biased tech change - Autor and Acemoglu (2011) Literature Model ➓ Labour Supply: Card & Lemieux (2001) Workers Firms ➓ Institutional explanations: DiNardo et al (1996) Wages Data ➓ Contribution: Develop model that nests tech, supply and Story under KORV institution explanations, adds transition rates as candidate Story under KORV with explanation, and allows counterfactuals. frictions Estimation 2. Literature explaining cross-sectional inequality. Results ➓ Postel-Vinay and Robin (2002) decompose residual Conclusion 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. 6/28

The Model: Workers Introduction Motivation ➓ Two skill levels - unskilled/skilled- indexed by i P u, s . Key Results Literature ➓ Efficiency in production of skill types denoted by Ψ i,t Model (assumed stationary). Workers Firms Wages ➓ Exogenous job destruction δ i,t Data Story under ➓ Flow income in unemployment is b i,t ✝ MPL i,t KORV Story under KORV with ➓ Choose to work or not - hours per worker ( h i,t ) exogenous frictions Estimation (from data) Results ➓ Job offer arrival in unemployment and in employment Conclusion denoted by λ 0 ,i,t and λ 1 ,i,t respectively. ➓ Exogenous job offer rates: i.e. vacancy creation not modelled. ➓ Risk neutral 7/28

The Model: Firms Introduction Motivation Key Results Literature Model ➓ I wish to allow for both capital to labour substitution in Workers production, and substitution between skill types. Firms Wages Data ➓ Not easy in pure search/match framework e.g. potential for Story under complex intra-firm bargaining problems as per ? . KORV Story under KORV with ➓ Proposed solution is to have two sectors of production: frictions Estimation 1. An intermediate goods sector with search frictions Results 2. Competitive final good sector that combines intermediate Conclusion goods and capital, with no frictions but with imperfect substitutability of all factors. 8/28

The Model: Final Goods Firm Introduction ➓ Final good produced using capital structures, k s,t , capital Motivation equipment, k e,t , and skilled and unskilled labour s t & u t : Key Results Literature σ 1 ✁ α t � ♣ 1 ✁ µ q♣ λk ρ e,t � ♣ 1 ✁ λ q s ρ ρ s Y t ✏ A t k α s,t r µu σ t q (1) Model σ Workers Firms Without frictions (as per KORV) Wages Data ➓ Labour input is hours worked in efficiency units e.g Story under u t ✑ Ψ u,t h u,t , s t ✑ Ψ s,t h s,t KORV Story under KORV with frictions ➓ Elas. of subs. between unskilled labour and capital Estimation 1 equipment (and skilled labour) is 1 ✁ σ . Elas. of subs. Results 1 between skilled labour and capital equipment is Conclusion 1 ✁ ρ ➓ Defining π t ✑ w s,t ④ w u,t , profit max implies: g π t ✔ ♣ 1 ✁ σ q♣ g h u,t ✁ g h s,t q � σ ♣ g Ψ s,t ✁ g Ψ u,t q� (2) � k e,t ✟ ♣ σ ✁ ρ q λ ♣ g k e,t ✁ g Ψ s,t ✁ g h s,t q s t 9/28

The Model: Intermediate Goods Sectors Introduction With Frictions: Intermediate Good Firms Motivation Key Results ➓ I now interpret u t and s t as intermediate goods produced Literature using unskilled and skilled labour. Model Workers ➓ Labour is hired by heterogeneous intermediate firms with Firms match quality ν , and population cdf F i,t ♣ ν q . Wages Data ➓ ℓ t,u ♣ ν q is fraction of employees in a match of quality ν . Story under KORV Story under KORV with ➓ A worker in a match of quality ν produces exactly ν units frictions of intermediate good for every hour they work. Estimation Results ➓ y i,t is the total amount of intermediate goods produced by Conclusion skill type i for i P u, s . ➺ ν max u t ✑ Ψ u,t y u,t ✏ Ψ u,t h u,t νℓ t,u ♣ ν q dν (3) ν inf ➺ ν max s t ✑ Ψ s,t y s,t ✏ Ψ s,t h s,t νℓ t,s ♣ ν q dν (4) ν inf 10/28

Wage Determination Introduction Motivation Key Results Literature ➓ Final good producers pay a price, p i , for a unit of type i Model intermediate good given by p i ✏ ❇ Y ❇ y i Ψ i (for i P t u, s ✉ ). Workers Firms Wages Unemployed Workers Data ➓ When an unemployed worker of skill type i meets a Story under KORV potential employer of type ν , a Nash type bargaining game Story under KORV with frictions ensues and worker is hired at wage contract φ ♣ p i , ν q that Estimation solves: Results Conclusion V ♣ p i , φ ♣ p i , ν q , ν q ✏ U ♣ b i p i q � β r V ♣ p i , p i ν, ν q ✁ U ♣ b i p i qs (5) ➓ β P r 0 , 1 s is the bargaining parameter 11/28

Wage Determination Introduction Motivation Key Results Literature Employed Workers Model ➓ When an employed worker of skill type i meets a potential Workers alternate employer, a bargaining game involving the worker Firms and both employers of types r ν � ➙ ν ✁ s is played, the Wages Data outcome is that the worker: Story under KORV ➓ ends up accepting the more productive type firm’s offer Story under KORV with frictions ➓ receives a wage φ ♣ p i , ν ✁ , ν � q that solves Estimation Results Conclusion V ♣ p i , φ ♣ p i , ν ✁ , ν � q , ν � q ✏ V ♣ p i , p i ν ✁ , ν ✁ q � (6) β r V ♣ p i , p i ν � , ν � q ✁ V ♣ p i , p i ν ✁ , ν ✁ qs 12/28

Wage and Employment Distributions Introduction Motivation Key Results ➓ Jumping ahead..the distribution of workers of type i across Literature intermediate firms is (with κ 1 ,i ✑ λ 1 ,i ④ δ i ): Model Workers 1 � κ 1 ,i Firms Wages ℓ i ♣ ν q ✏ F i ♣ ν qs 2 f i ♣ ν q (7) r 1 � κ 1 ,i ¯ Data Story under KORV ➓ And crucially the expected wage for a worker of type i is: Story under KORV with frictions Estimation E ♣ w i q ✏ E ♣ E ♣ w i ⑤ ν qq Results ➺ ν max ✒ F i ♣ ν qs 2 ✂ Conclusion r 1 � κ 1 ,i ¯ � ✏ p i ν ✁ (8) ν ➺ ν δ i � ρ κ 1 ,i ¯ δ i ♣ 1 ✁ β qr 1 � F i ♣ x qs ✟✚ F i ♣ x qs 2 dx ℓ i ♣ ν q dν δ i � ρ κ 1 ,i β ¯ δ i F i ♣ x qsr 1 � κ 1 ,i ¯ r 1 � ν inf 13/28

Wage Impact of Search Frictions Introduction Motivation Key Results Figure: Wage Impact of Parameters Literature Model Workers Firms Wages Data Story under KORV Story under KORV with frictions Estimation Results Conclusion 14/28