Survey
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
* Your assessment is very important for improving the workof artificial intelligence, which forms the content of this project
Ragnar Nurkse's balanced growth theory wikipedia , lookup
Steady-state economy wikipedia , lookup
Fei–Ranis model of economic growth wikipedia , lookup
Rostow's stages of growth wikipedia , lookup
Circular economy wikipedia , lookup
Refusal of work wikipedia , lookup
Wage Risk and the Skill Premium Ctirad Slavı́k, CERGE-EI, Prague (with Hakki Yazici, Sabanci University, Istanbul) January 9, 2017 Swiss Macro Workshop 1 / 58 Motivation Recent decades in the United States: Dramatic rise in relative wages of college vs. non-college graduates (skill premium). Residual wage volatility has also gone up (Gottschalk and Moffitt 1994; 2012, Heathcote et al. 2010, Hong et al. 2015). 2 / 58 This Project 1 Propose a mechanism through which rise in residual wage risk increases skill premium. Possible interpretation: provide a novel link from within-group inequality to between-group inequality. 2 Assess significance of mechanism by measuring how much of skill premium increase it can account for. 3 / 58 Framework and Mechanism Key ingredients of the framework: 1 Uninsured individual labor income risk. 2 Capital-skill complementarity. Mechanism: ↑ labor income risk → ↑ (precautionary) savings → ↑ capital stock → ↑ skill premium, due to capital-skill complementarity. 4 / 58 The Exercise Build an incomplete markets (Aiyagari 1994) model with capital-skill complementarity. Focus on steady state comparisons. Calibrate the model to 1967 U.S. economy. Feed in changes in wage risk and other factors (technology, skill supply, and policies) and compute skill premium in 2010. Measure the effect of increase in wage risk on skill premium alone by changing risk only. 5 / 58 Benchmark Results Benchmark model matches total rise in skill premium between 1967 and 2010 quite well: 1.51 → 1.9 in the data vs. 1.51 → 1.87 in the model. Rise in wage risk alone increases skill premium by 13 pp. or by 1/3 of the overall change observed between 1967 and 2010. 6 / 58 Extensions 1 Open Economy: Rise in savings implied by rise in risk translates into a rise in capital in benchmark closed economy. In an open economy, fraction of the rise in savings may be absorbed by foreign countries. In a calibrated open economy exercise, skill premium increases by 8 pp. in return to the rise in risk. 7 / 58 Extensions 1 Open Economy: Rise in savings implied by rise in risk translates into a rise in capital in benchmark closed economy. In an open economy, fraction of the rise in savings may be absorbed by foreign countries. In a calibrated open economy exercise, skill premium increases by 8 pp. in return to the rise in risk. 2 Endogenous Skill Supply: Fraction of skilled workers exogenous in baseline analysis. This is because in counterfactual we are interested in isolating effect of rise in wage risk on skill premium. Alternative exercise: Rise in risk increases skill premium by 9 pp. taking into account people’s education choice responses. 8 / 58 Rest of the Talk Environment. Quantitative results. Extensions. Conclusion. 9 / 58 Environment 10 / 58 Environment Aiyagari (1994) model with capital-skill complementarity. Incomplete markets model with: Government, measure 1 of agents and a firm. 2 types of capital: equipments and structures. 2 types of labor: skilled and unskilled. 11 / 58 Production Production Function: F (Ks , Ke , Ls , Lu ) As in KORV (2000), equipment capital-skill complementarity: MPLs MPLu increasing in Ke (independent of Ks ). 12 / 58 Firm Problem Representative firm solves: max Ks ,Ke ,Ls ,Lu F (Ks , Ke , Ls , Lu ) − rs Ks − re Ke − ws Ls − wu Lu 13 / 58 Skill-Biased Technological Change (SBTC) Following KORV (2000), model SBTC as a decline in cost of equipment capital in terms of consumption good. Aggregate feasibility: C +G +Ks0 +qKe0 = F (Ks , Ke , Ls , Lu )+(1−δs )Ks +(1−δe )qKe . SBTC is a decline in q over time. 14 / 58 Government Spends G , has debt D. Raises revenue with: linear capital income taxes τs , τe , linear consumption tax τc , non-linear labor income taxes T (y ), implies partial insurance. Government budget constraint: RD + G = D + τc C + τe (re − qδe )Ke + τs (rs − δs )Ks + Tagg , where Tagg is aggregate labor tax revenue. 15 / 58 Demographics Each period a fraction (1 − δ) of agents born with no assets. Agents survive from one age to another with prob δ. No accidental bequests: assets of dead distributed among the survivors (actuarially fair life insurance). Agents are born skilled or unskilled (exogenous). πi denotes the total fraction of skill type i. 16 / 58 Individual Wage Risk Each period agent of skill type i draws idiosyncratic productivity shock zi . Agent of skill type i and productivity zi receives a wage rate w̄i = wi · zi per unit time, with wi = MPLi . The process for zi is skill specific. log (zi ) is the sum of a persistent and a transitory component. zi is the only source of residual wage inequality. 17 / 58 Preferences Preferences over stochastic (ci,t , li,t )∞ t=0 is given by Ei ∞ hX i (βδ)t u(ci,t , li,t ) . t=0 Endogeneous labor supply allows for partial insurance. 18 / 58 Agent’s Problem vi (zi , ai ) = max (ci ,li ,ai0 )≥0 u(ci , li ) + βδEi [vi (zi0 , ai0 )] s.t. (1 + τc )ci + δai0 ≤ wi zi li − T (wi zi li ) + Rai , where R = 1 + (rs − δs )(1 − τs ) = 1 + (re − qδe )(1 − τe )/q is the after-tax asset return. 19 / 58 Stationary Recursive Competitive Equilibrium Definition: SRCE are value functions vu , vs , policy functions cu , cs , lu , ls , au0 , as0 , firm’s decision rules Ks , Ke , Lu , Ls , government policies, distribution of types λu (z, a), λs (z, a) and prices wu , ws , rs , re , R s.t. 1 The value and policy functions solve consumers’ problem given prices and government policies for all i ∈ {u, s}. 2 The firm maximizes profits. 3 The distribution over productivities and assets is stationary. 4 Markets clear. 5 Government BC is satisfied. 20 / 58 The Mechanism 1 ↑ labor income risk → ↑ (precautionary) savings, because of incomplete insurance markets. 2 ↑ savings → ↑ stock of equipment capital. 3 ↑ stock of equipment capital → ↑ skill premium, due to equipment capital-skill complementarity. 21 / 58 Quantitative Analysis 22 / 58 Quantitative Analysis Overview: Calibrate model economy to 1967 U.S. economy. Model fit: Feed in observed changes in all factors between 1967 and 2010 and compute skill premium in 2010. Counterfactual: Feed in the change in wage risk only and compute skill premium. 23 / 58 Production Function Production function: KORV (2000) 1−α η η Y = Ksα ν [ωKeρ + (1 − ω)Lρs ] ρ + (1 − ν)Lηu Use α, η, ρ, δs , δe from KORV and GHK. Calibrate ω and ν. Parameter α η ρ δs δe Value 0.117 0.401 -0.495 5.6% 12.4% Source KORV (2000) KORV (2000) KORV (2000) Greenwood, Hercowitz, Krusell (1997) Greenwood, Hercowitz, Krusell (1997) q normalized to one in 1967. 24 / 58 Agents Cobb-Douglas utility function: u(c, l) = φ 1−σ c (1 − l)(1−φ) φ − 1 1−σ φ . Balanced growth path compatible. In benchmark, use σ = 2, and calibrate β and φ. Survival probability δ = 0.978 to match average working life of 40 years as in Castañeda, Dı́az-Giménez, Rı́os-Rull (2003). πs = 13.56% (CPS 1967, males aged 25-60, with earnings). 25 / 58 Productivity Shocks: 1967 Hong, Seok, You (2015) estimate skill specific wage processes: log zi,t = θi,t + εi,t , θi,t = ξi θi,t−1 + κi,t . Identification: ξ and Var (θ) of entrants remains constant, Var (ε) and Var (κ) change over time. Variable Variance of ε Variance of κ ξ Var of θ for entrants Skilled 0.0116 0.0037 0.9834 0.1172 Unskilled 0.0177 0.0052 0.9859 0.1488 26 / 58 Government Policy: 1967 Consumption taxes τc = 5%; Mendoza, Razin, Tesar (1994). As in HSV (AER, 2014) approximate progressive labor taxes by T (y ) = y − χ · y 1−τl , τl = 0.185, let χ clear the budget. Govt. expenditure G /Y = 0.16 on average. These policy parameters (except for χ) remain constant between 1967 and 2010 in the quantitative exercise. 27 / 58 Government Policy: 1967 Capital income taxes 15% at consumer level, differential taxes at corporate level (Auerbach, 1983): τs = 0.57, τe = 0.50. Govt. debt D/Y = 0.36 in 1967 (St. Louis FED). These change between 1967 and 2010 in our exercise. 28 / 58 Internal Calibration Parameter ω ν φ β·δ χ Value 0.8333 0.4122 0.3985 0.9908 0.8708 Target Labor share Skill premium in 1967 Labor supply Capital-to-output ratio Gvt. budget balance Data & SRCE 2/3 1.51 1/3 2.9 Source NIPA HPV NIPA, FAT Skill premium from CPS 1967, males aged 25-60, working at least 260 hours a year. 29 / 58 Changes in Factors Between 1967 and 2010 30 / 58 Changes in Wage Risk between 1967 and 2010 Hong et al. (2015): Variable Variance of εs Variance of εu Variance of κs Variance of κu 1967 0.0116 0.0177 0.0037 0.0052 2010 0.0673 0.0627 0.0304 0.0157 Wage risk. Has gone up for both groups. Risk has increased more for skilled (see also Lee et al. 2015). 31 / 58 Changes in Other Factors between 1967 and 2010 Skill biased technical change: Technology: Relative price of equipments decreases from 1 in 1967 to 0.1577 in 2010 (St. Louis FRED data base). Change in relative skill supply: Fraction of skilled workers increase from 13.56% in 1967 to 31.36% in 2010. 32 / 58 Changes in Other Factors between 1967 and 2010 Government policy: Capital taxes. Have decreased from τs = 0.57, τe = 0.50 (Auerbach, 1983) to τs = 0.42 and τe = 0.37 (Gravelle, 2011). Gvt debt. Increased from 36% in 1967 to 89% in 2010. 33 / 58 Main Quantitative Results 34 / 58 Change in Skill Premium from 1967 to 2010 Model matches the change in skill premium quite well. Skill premium 1967 1.51 Data 2010 1.9 Change 0.39 1967 1.51 Model 2010 1.87 Change 0.36 35 / 58 Counterfactual: Change Wage Risk Only Skill premium Change 1967 1.51 Risk 1.64 0.13 2010 (model) 1.87 0.36 2010 (data) 1.9 0.39 Increase in residual wage risk increases skill premium by 13 pp. That is 34% of the total increase between 1967 and 2010 Mechanism: Risk ↑ → 21% increase in equipment capital, which ↑ skill premium due to capital-skill complementarity. 36 / 58 Alternative Counterfactual Feed in changes in other factors first, and then change in risk. Skill premium Change 1967 1.51 All but Risk 1.79 0.28 2010 (model) 1.87 0.36 2010 (data) 1.9 0.39 Increase in wage risk increases skill premium by 8 pp. That is 20% of overall increase between 1967 and 2010. Magnitude of mechanism depends on order of decomposition due to non-linearities. 37 / 58 Sensitivity to Risk Aversion Results sensitive to degree of risk aversion, σ. σ 1 2 4 1967 1.51 1.51 1.51 Risk 1.57 1.64 1.80 2010 1.83 1.87 1.94 Mechanism quantitatively important for range of σ. Rise in risk creates up to 29 pp. rise in skill premium for values of σ within plausible range. 38 / 58 Extensions 39 / 58 Open Economy 40 / 58 Closed vs. Open Economy Risk changes matter because they affect capital accumulation. In a closed economy: risk → savings = investment. In an open economy: risk → savings 6= investment. How strong is the mechanism in an open economy? Answer depends on the extent to which foreign countries can absorb the rise in domestic savings. 41 / 58 Open Economy Two-country model: U.S. vs. rest of the world (ROW). ROW modelled as a similar incomplete market economy. International dimension: Intertemporal trade in (single) good. Perfect international capital mobility: IIPUS + IIPROW = 0, where IIP is international investment position. No labor mobility. 42 / 58 Open Economy During this time, ”global imbalances” in world financial markets: decline in IIPUS and global real interest rate. Follow Bernanke (2005)’s ”savings glut” hypothesis: global imbalances caused by rise in ROW saving. 43 / 58 Open Economy We want to: 1 Quantify role of rise in U.S. wage risk on U.S. skill premium in open economy. 2 Investigate effect of savings glut on skill premium (secondary). 44 / 58 Open Economy Quantitative exercise: ROW consists of top 20 trading partners of U.S. Calibrate the parameters of the two economies together in 1967 to match in particular IIPUS and IIPROW . Feed in changes in U.S. economy and calibrate change in ROW saving behavior to match IIPUS and IIPROW in 2010. Change only U.S. wage risk and measure quantitative significance of mechanism in open economy. Add savings glut, measure its contribution to skill premium. Open Economy Details 45 / 58 Open Economy Results Skill premium Contribution (pp.) 1967 1.51 2010 1.88 Risk 1.59 8 Risk + Savings glut 1.65 14 Effect of rise in wage risk on skill premium significant: 8 pp. Mechanism weaker than in closed economy since part of the rise in savings absorbed by ROW. Savings glut contributed to rise of U.S. skill premium by 6 pp. 46 / 58 Endogenous Skill Supply 47 / 58 Exogenous vs. Endogenous Skill Supply In baseline environment, fraction of skilled exogenous. Reason: In counterfactual, interested in understanding effect of rise in risk on skill premium given observed supply of skilled. Alternative: How much does rise in risk increase skill premium when people can alter their education decisions in response? 48 / 58 Environment Environment same as before except people choose skill level: Newborns draw utility cost ψ ≥ 0, distributed acc. to F (ψ). Reduced form way of capturing cross sectional variation in psychological and pecuniary costs of acquiring a degree. Get educated iff Es,0 [vs (z, 0)] − Eu,0 [vu (z, 0)] ≥ ψ. 49 / 58 Cost of Education Assume ψ is distributed according to exponential distribution with parameter n > 0. Calibrate n to match fraction of skilled in 1967: πs = 13.56%. Note: One dimensional distribution because only one target. Results almost identical if F is uniform instead. 50 / 58 Significance of Mechanism with Endogenous Skills Rise in wage risk increases skill premium by 9 pp. Less than in case with exogenous skills: 9 pp. vs. 13 pp. Fraction of skilled rises if skill premium ↑: from 13.56% to 13.92%, which prevents skill premium from further ↑. Fraction of skilled does not rise too much because risk rises more for skilled. Change in risk has first order effect on skill premium. 51 / 58 Conclusion Novel mechanism through which inequality leads to inequality: ↑ wage risk → ↑ skill premium. Mechanism is quantitatively important: 1/3 of the overall change in skill premium in the U.S. between 1967 and 2010. Mechanism also significant under open economy and endogenous labor supply extensions. 52 / 58 ROW Basics An Aiyagari economy with: Measure m̂ of agents. Inelastic labor supply: u(c) = c 1−σ̂ −1 1−σ . Cobb-Douglas production function: F (K , L) = ÂK α̂ L1−α̂ . Wage process: log ẑt = θ̂t + ε̂t , θ̂t = ξˆθ̂t−1 + κ̂t , No government. 53 / 58 ROW Savings Behavior From being a net saver in 1960’s, U.S. has become a net borrower in 2000’s. Surge in the rest of the world savings, “savings glut”. Following Kehoe et al. (2016), we use an exogenous saving wedge ψ̂ to account for the change in ROW saving behavior: E ∞ hX i (ψ̂ β̂)t u(ct ) . t=0 We change ψ̂ exogenously to match the international investment positions of the U.S. in 1967 and 2010. 54 / 58 Calibrating the Two-Country Model to 1967 Since we know IIP’s of the 2 countries, we calibrate them separately. U.S. calibration as before except: New target, US IIP / US GDP in 1967, and new parameter to choose, R 67 (world interest rate in 1967). Parameter R 67 Value 1.13% Target US IIP / US GDP Data & SRCE 10% Source NIPA 55 / 58 Calibrating the Two-Country Model to 1967 ROW calibration: Set σ̂ = 2, β̂ = βδ, α̂ = 1/3, and δ̂ = 0.08. Set m̂67 = 9.3 (Angus Maddison dataset). Set parameters of wage process to a weighted average of values for Germany, U.K., France, and Italy, as estimated by Le Blanc and Georgarakos (2013). ξˆ 0.9335 σκ̂ 0.0158 σε̂ 0.0399 56 / 58 Calibrating the Two-Country Model to 1967 Choose Â67 and ψ̂ 67 to match ROW IIP and GDP in 1967. Parameter Value Target Value Source Â67 ψ̂ 67 0.1910 0.9474 ROW GDP / US GDP ROW IIP / US GDP 1.76 -10% Maddison Maddison 57 / 58 Calibrating the Two-Country Model to 2010 U.S. calibration: Choose R 10 that matches U.S. IIP in 2010. Parameter R 00s Value 0.47% Target US IIP / US GDP Data & SRCE -17.5% Source NIPA ROW calibration (savings glut): Set m̂10 = 11 (Angus Maddison dataset). Choose Â10 and ψ̂ 10 to match ROW IIP and GDP in 2010. Parameter Value Target Data & SRCE Source Â10 ψ̂ 10 0.3270 0.9575 ROW GDP / US GDP ROW IIP / US GDP 2.25 17.5% Maddison Maddison Back 58 / 58