Why Has CEO Pay Increased So Much? QJE 2008

Transcription

1 Why Has CEO Pay Increased So Much? QJE 2008 Xavier Gabaix and Augustin Landier

2 Motivation p p p p Large popular and academic focus on the increase of CEO pay in the US since the 80s. This paper provides an equilibrium model to think about this Changes in firm sizes appear to explain much of the variations in CEO pay, across time (since 1970s at least), industries, countries Calibratable corporate finance

3 Short Literature Review: Reminder of 2 facts and 3 theories p Fact 1: CEO pay has been multiplied by 5 to 7 since 1980 Average Executive C ompensation of Top Firms normalized to 1 in Year Murphy_index Frydman_index

4 Empirical Evidence: USA Time-series Executive Com pensation and Market Cap of T op 500 Firm s normalized to 1 in Year Murphy_index Mean_mktcap_500 Frydman_index

5 Short Literature Review: Reminder of 2 facts and 3 theories p Fact 2: US top CEOs are paid more than their foreign counterparts. (Kaplan (1994), Abowd and D.Kaplan (1998)) C EO compensation across countries 1996 USA CAN GBR FR A ITA ESP JPN DEU NLD CHE BEL SWE mean of compensation Source: Abowd&al. 1995,1999

6 Short Literature Review: Reminder of 2 facts and 3 theories p Theory 1: Higher Incentives à Rents n Murphy (1985), Jensen-Murphy (1990): importance of market-based incentives n Holmstrom Kaplan (2001,2003): discovery of high-powered incentives in the 80s? Need strong limited liability & risk-aversion frictions to explain such higher rents. (calibration: e.g. Gayle & Miller 2005)

7 Short Literature Review: Reminder of 2 facts and 3 theories p Theory 2: Skimming View n Bertrand and Mullainathan (2001), Kuhnen and Zwiebel (2006) n Bebchuk & al. (2002, ) p Increased entrenchment & camouflage techniques n Hall&Murphy (2003), Jensen, Murphy & Wruck (2004) p Boards underestimate the cost of stock-options

8 Short Literature Review: Reminder of 2 facts and 3 theories p Theory 3: Changes in CEO job/labor market n Murphy and Zabojnik (2004), Frydman (2005) p Higher importance of general (vs. specific) skills à higher CEO outside options, more external hires n Garicano and Rossi-Hansberg (2006) p Technological change and hierarchies in equilibrium n See also Bloom et al. (2006), Daines, Nair, Kornhauser (2005), Malmendier and Tate (2005), Shleifer (2004)

9 Short Literature Review: Inequalities at the top and superstars p Changes in inequality, at the top n Katz and Murphy (1992), Autor, Katz and Krueger (1998), Goldin and Katz (1999), Piketty and Saez (2004, 2006), Lemieux (2006), Guvenen and Kuruscu (2006), Huggett, Ventura and Yaron (2006) p Economics of superstars n Rosen (1982), Krueger (2006), Andersson et al. (2006), DeVany (2004), Garicano and Hubbard (2006), Malmendier and Tate (2005), Tervio (2008)

10 Short Literature Review: Scaling and and detail-independent economic laws p Schumpeter ( 49) on the Pareto law: Few if any economists seem to have realized the possibilities that such invariants hold for the future of our science. In particular, nobody seems to have realized that the hunt for, and the interpretation of, invariants of this type might lay the foundations for an entirely novel type of theory. p Wealth distribution (Champernowne 53, Wold and Whittle, Benhabib and Bisin 06) p Cities (Simon 55, Gabaix 99, Rossi-Hansberg and Wright 06) p Firms (Luttmer 06, Gabaix 06) p Firms and GDP or trade balance fluctuations (Gabaix 06, Canals p et al. 06) Stock market returns and volume (Mandelbrot 55, Gabaix et al. 03, 06, Ibragimov and Walden 06) p Networks (Simon 55, Barabasi and Albert 99, Jackson 06) p Money demand (Allais-Baumol-Tobin, Mulligan 97) p Regulation (Mulligan and Shleifer 04) p Ideas (Kortum 1998, Jones 2004)

11 Our Approach: the Size of Stakes View p p p p Focus on one important source of variation: n firm size Assortative matching of firms and managers n Lucas (1978), Sattinger (1979),Rosen (1981,82), Himmelberg and Hubbard (2000),Tervio (2003) CEO pay = price of talent n Depends on: p Asset distribution p Production function p Talent distribution (unobservable!) General results using Extreme Value Theory

12 An Apparent Difficulty p p Empirically, link between the CEO pay and firm size, follows Roberts law (1957) in the cross-section: w = cs k with k» 1/ 3 n n It is tempting to extrapolate that, in the time-series, if the size of all firms is multiplied by 6, then CEO wages should be multiplied by 6 k» 2 p But CEO wages have increased by a factor of 6. p We know from Sattinger (1993) that extrapolating from cross-section to time-series is not valid, but can we go further?

13 CEO Pay in Equilibrium p p N firms to match with N managers n Firms have size S(m) (descending order) n Managers talent T(n), paid w(n) in equilibrium. Firm s Program: Hiring the CEO increases earnings by: max C T( n) S n g - w( n) CEO impact Price of talent #n p p Relevant size measure? n Permanent CEO impact à S=market value (D+E) n Temporary CEO impact à S=earnings Benchmark case: constant returns of talent n g=1, empirically validated

14 Equilibrium: An equilibrium consists of: p (i) a compensation function W(T), which specifies the wage of a CEO of talent T p (ii) an assignment function M(m), which specifies the index n=m(m) of the CEO heading firm m in equilibrium,such that p (iii) each firm chooses its CEO optimally: g Mm ( ) Î argmax C Sm ( ) Tn ( )-WTn ( ( )) n p (iv) the CEO market clears, i.e. each firms gets a CEO.

15 Equilibrium: p First order condition: g C S( m) T'( n) = w'( n) p Assortative matching: n Firm #n is matched with manager #n n N ( ) ( ) ( ) g Þ wn = wn - ò C Sm T '( m ) dm < 0 p Equilibrium wages depend on n n Productivity Scarcity of talent p How do we go further?

16 Distributions p Firms: observable S ( n) = n Useful for calibration: Zipf s law ( a» n Simon (1955, 1958), Gabaix (1999, 2006), Axtell (2001), Luttmer (2005), Rossi-Hansberg and Wright (2005) A a n 1)

17 Power Law for Market Value ln(rank-1/2) Ln(Asset Market Value) plargest 500 firms in the US in 2004 lnrank Fitted values pln(rank-1/2) = a ln Size, R 2 =0.99 p(rank-1/2:gabaix Ibragimov 2011)

18 Distributions g wn ( ) = wn ( )- ò C Sm ( ) T'( m) dm n N Talent: unobservable à use Extreme Value Theory T'( n) =-Bn b - n Valid approximation for a all regular distributions p Gaussian, log-normal, Weibull, log-gamma, etc. n Exact for uniform, exponential, Pareto 1

19 Universal functional form for spacings

20 T (n), continued

21 Main Proposition -a b-1 Sm ( ) = Am,- T'( m) = Bm g ABC N wn ( ) = g wn ( ) = wn ( )- ò C Sm ( ) T'( mdm ) n ag - b p Using def. of A and B, get: n 1 ag -b w( n) = D S b / a S ( g -b / a ) n * n Reference ) 1/3 2/3 fim, e.g. the 250 th fim * w ( n = D S S - n* T' ( n* ) D = C ag - b Own Firm Size Reference Size Can be country specific

22 Main Predictions w( n) = D S b / a S ( g -b / a ) n * n p Cross-sectional: (change n) w( n) = ( cste) Sn p Cross-time: (change A in constant) ( g -b / a ) Sn ( ) = An / a w(*) n = ( cste) S g n*, keep n p Cross-country: (keep S(n) & Pop. Size constant) w S = cste S b / a ( ) ( ) n*

23 Main Predictions 2/3 1/3 * wn ( ) = D S S n n Wage of CEO of firm n Median CEO wage Size of firm n: S Cross-section: Wage is a concave function of size: w n = k S n 1/3 Median firm size: S n* Time series: Wage is a linear function of size: w n* = k S n* The relationship between size and pay is very different in the cross section and the time-series

24 Empirical Evidence: USA Time-series Executive Com pensation and Market Cap of T op 500 Firm s normalized to 1 in 1980 Remark: This is where we identify g=1, in : C T( n) S g m Year Murphy_index Mean_mktcap_500 Frydman_index

25 Update (G, L, Sauvagnat EJ 2014)

26 Remark: Earnings vs. Price-Earnings Ratios Between 1980 and 2003, increase by:

27 Estimating g with change on change regression D t ( W _ index) = ˆ g D t ( Mkt) + b W _ index( t -1) + c Mkt( t -1) Δ(Murphy_index) Δ(Frydman_index) Δ(mkt) (4.12)***, s.e (3.14)*** W_index(-1) (3.70)*** (5.27)*** mkt(-1) (3.52)*** (4.89)*** Constant (1.75)* Observations R-squared

28 Panel Evidence: USA, w = D S S ( - b / ) b / n n n*

29 Pay levels across industries (48 Fama-French) lo g(comp ensatio n) Compensation and Industry Firm Size medium log size (top 20) (p 50) medlcomp Fitted values

30 Empirical Evidence: cross-country lo g(comp ensatio n) THA MEX CAN ITA AUS FR A BRA ZAF SW E KOR CH N NLD DEU CHE JPN GBR USA log(firm size) lcomp Fitte d value s Source: Towers-Perrin (2001) for CEO compensation Compustat Global (2000) for firm size

31 Empirical Evidence: cross-country Social Norm= mean agreement to We need large income differences as incentives for individual effort in World Value Survey, S.e. of Social Norm is 10.

32 Calibration, I p a=1 (Zipf s law: Gabaix 99; Axtell 01; Luttmer 05) p g =1 from time-series p Distribution of talent: w~s 1/3 1 3 b = g - b=2/3 a p It would be interesting to compare to: movie stars, lawyers, pianists, sport stars f( T) = k( T - T) = k( T -T) max 1/ b -1 1/2 max

33 Calibration, II p Take year=2004. Look at median of top 500 firms and top CEOs. A la Tervio ( 03) n n*=250: W(n*)=$8.3 Mil, S*=$25 Bil -b w* n* -6 Þ BC = ( a - b ) = S* p Interpretation: #1 CEO, compared to #250 CEO n increases market value by: n Gets paid more by: BC b CT ( (1)- T(250)) = (250-1) = 0.02% b w w 1/3 æ S ö - = ç -» -» ès ø 1/ % * *

34 Extensions p If C random, independent from S: S( n) = A n a Þ ( C S)( n) = ( EC n p Exploiting this nice aggregation property to study: 1/ a p Whole top executives market equilibrium Division manager at GE could be CEO of smaller company p Contagion effects: can a few firms trigger pay inflation? a ) a A p What happens if we include incentive problem?

35 Extension 1: Contagion Effects, I p f% of firms want to pay their manager l (e.g., twice) as much as the market (as similarly-sized firms) n E.g. misperception of stock-option cost, or Star CEO effect. p Then CEO wages are multiplied by L: p p p If 10% of firms want to pay their CEO half as much as the market, total CEO pay decreases by 9% If 10% of firms want to pay their CEO twice as much as the market, total CEO pay increases by 100% Similarly, can consider diffusion of sector shock (e.g. fund management) to other sectors. The impact is linear, then.

36 Contagion Effects, II p f% of firms think that pay costs w/l rather than the true cost, w n E.g. misperception of stock-option cost. p Then CEO wages are multiplied by L=1+f(l-1) p If f=10% of firms underestimate the pay by a factor of l=2, total CEO pay increases by 10%

37 Extension 2: Top H executives p p Assume human cap increases firm value by factor: H H H æ ö 1+ å C T maxs ç 1+ C T - w T è å ø å Think of firm S i as H C i -scaled assets each looking for manager : ( ) h h h h h ( C S,..., C S ) 1 i H i p In equilibrium, executive #h at firm i earns: p Steepness of wage ratio and firm organization: w w 1 æ C = ç è 1 h C h ö ø 1-b /a

38 Extension 3: Supply of CEOs p p p p p How does compensation scale with the country size? If population is P, call N e the effective number of potential executives p=1: the whole population contends p=0: The top K CEOs need to have served in the top LK firms before, then receive a productivity shock. CEO pay is: w( n) D Ne = = ap p b / a ( g -b / a ) = D S n * Sn kp -bp p Empirically, p=0.24 (s.e. 0.14)

39 Extension: Beyond CEOs p Extend the model to lawyers, movie stars, 1 athletes, singers, using max C T ( n) S n p Extend to real estate prices T'( n) =-Bn b - w( n) p When the equity premium goes down, the human-capital rich benefit more. Perhaps that makes equity extra risky? g -

40 Conclusion: 1. Large part of CEO pay variation across time, countries, industries explained by variation in sizes. To study: Contagion effects 2. Calibratable Corporate Finance 3. Extreme Value Theory is the right tool for the economics of superstars T'( n) =-Bn b - 4. Reference size matters in compensation regressions 1/3 w ( n) = D S S 1 2/3 * Governance, Misperception of stock-options etc. Own Firm Size Reference Size Can be industry/country specific

41 Extension 4: with Stock-Options p p Add standard moral-hazard pb n Maintain risk-neutrality n Look for minimum amount of options to avoid shirking Result: n sensitivity of compensation to firm value is not scale-free n Elasticity of comp to firm value is scale-free: d(ln w) b = / D d(ln S) =L Cost of effort for manager Cost of shirking for firm n With b=1/3, D=30%, we get L<10%

42 (Edmans, Gabaix, Landier RFS 2009)

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46 Conclusion 1. Simple CEO pay model. Under general assumptions: p w ( n) = D S k S 1-k n * n Reference firm size, S*, matters 2. Empirical implications: CEO compensation across time, countries, industries 3. Calibratable Corporate Finance

47 The Dynamics of Inequality Xavier Gabaix Jean-Michel Lasry Pierre-Louis Lions Benjamin Moll Econometrica 2016

48 Question 20 Top 1% Income Share (excl. Capital Gains) Year In U.S. past 40 years have seen rapid rise in top income inequality Why? 1

49 Question Main fact about top inequality (since Pareto, 1896): upper tails of income (and wealth) distribution follow power laws Equivalently, top inequality is fractal top 0.01% are X times richer than top 0.1%,... are X times richer than top 1%,... are X times richer than top 10%, top 0.01% share is fraction Y of 0.1% share,... is fraction Y of 1% share,... is fraction Y of 10% share,... 2

50 Evolution of Fractal Inequality Relative Income Share S(0.1)/S(1) S(1)/S(10) Year S(0.1) S(1) = fraction of top 1% share going to top 0.1% S(1) S(10) = analogous 3

51 This Paper Starting point: existing theories that explain top inequality at point in time differ in terms of underlying economics but share basic mechanism for generating power laws: random growth Our ultimate question: which specific economic theories can also explain observed dynamics of top income inequality? e.g. falling income taxes? superstar effects? 4

52 This Paper Starting point: existing theories that explain top inequality at point in time differ in terms of underlying economics but share basic mechanism for generating power laws: random growth Our ultimate question: which specific economic theories can also explain observed dynamics of top income inequality? e.g. falling income taxes? superstar effects? What we do: study transition dynamics of cross-sectional income distribution in theories with random growth mechanism contrast with data, rule out some theories, rule in others Today: income inequality. Paper: also wealth inequality. 4

53 Main Results Transition dynamics of standard random growth models too slow relative to those observed in the data analytic formula for speed of convergence transitions particularly slow in upper tail of distribution jumps cannot generate fast transitions either Two parsimonious deviations that generate fast transitions 1. heterogeneity in mean growth rates 2. superstar shocks to skill prices Both only consistent with particular economic theories 5

54 Main Results Transition dynamics of standard random growth models too slow relative to those observed in the data analytic formula for speed of convergence transitions particularly slow in upper tail of distribution jumps cannot generate fast transitions either Two parsimonious deviations that generate fast transitions 1. heterogeneity in mean growth rates 2. superstar shocks to skill prices Both only consistent with particular economic theories Rise in top income inequality due to simple tax stories, stories about Var(permanent earnings) rise of superstar entrepreneurs or managers 5

55 A Random Growth Theory of Income Dynamics Continuum of workers, heterogeneous in human capital h it die/retire at rate δ, replaced by young worker with h i0 Wage is w it = ωh it Human capital accumulation involves investment luck 6

56 A Random Growth Theory of Income Dynamics Continuum of workers, heterogeneous in human capital h it die/retire at rate δ, replaced by young worker with h i0 Wage is w it = ωh it Human capital accumulation involves investment luck Right assumptions wages evolve as d log w it = µdt + σdz it growth rate of wage w it is stochastic µ, σ depend on model parameters 6

57 Stationary Income Distribution Result: The stationary income distribution has a Pareto tail Pr( w > w) Cw ζ Density, f(w) Log Density, log p(x) p(x)= ζ e -ζ x slope = -ζ Income, w Log Income, x... with tail exponent ζ = µ+ µ 2 +2σ 2 δ σ 2 Convenient to work with log income x t = log w t Tail inequality 1/ζ increasing in µ, σ, decreasing in δ 7

58 Transitions: The Thought Experiment Suppose economy is in Pareto steady state Log Density, log p(x) p(x)= ζ e -ζ x slope = -ζ Log Income, x 8

59 Transitions: The Thought Experiment Suppose economy is in Pareto steady state At t = 0, σ. Know: in long-run higher top inequality Log Density, log p(x) Old steady state New steady state Log Income, x What can we say about the speed at which this happens? Which part of the distribution moves first? 8

60 Average Speed of Convergence Proposition: p(x, t) converges to stationary distrib. p (x) rate of convergence without reflecting barrier with reflecting barrier 1 λ := lim t t log p(x, t) p (x) λ = δ λ = 1 µ 2 2 σ 2 1 {µ<0} + δ Half life is t 1/2 = ln(2)/λ precise quantitative predictions Note: L 1 -norm p(x, t) p (x) := p(x, t) p (x) dx 9

61 Transition in Upper Tail Similarly, can characterize tail-weighted norm p(x, t) p (x) ξ := Proposition: rate of convergence is p(x, t) p (x) e ξx dx, ξ < 0 λ(ξ) = µξ σ2 2 ξ2 + δ 10

62 Transition in Upper Tail Similarly, can characterize tail-weighted norm p(x, t) p (x) ξ := Proposition: rate of convergence is p(x, t) p (x) e ξx dx, ξ < 0 λ(ξ) = µξ σ2 2 ξ2 + δ Strategy: closed-form solution for Laplace transform of p p (ξ, t) := e ξx p (x, t) dx = E [ e ξx] Natural interpretation: ξth moment of dist Closed-form solution for all moments of cross-sectional dist for all t 10

63 Instructive Special Case: σ = 0 ( Steindl Model ) In special case σ = 0, can solve full transition dynamics x t grows at rate µ, gets reset to x 0 = 0 at rate δ stationary distribution p(x) = ζe ζx, ζ = δ/µ Result: the time path of the income distribution is p(x, t) = ζe ζx 1 {x µt} + αe αx+(α ζ)t 1 {x>µt} where 1 { } = indicator function and old steady state distribution: p 0 (x) = αe αx new steady state distribution: p (x) = ζe ζx 11

64 Transition in Steindl Model Log Density, log p(x,t) t=0 t= Log Income, x 12

65 Transition in Steindl Model Log Density, log p(x,t) t=0 t=10 t= Log Income, x 12

66 Transition in Steindl Model Log Density, log p(x,t) t=0 t=10 t=20 t= Log Income, x Transition is slower in upper tail Initially parallel shift, tail parameter unaffected 12

67 Can the model explain the fast rise in inequality? Recall process for log wages d log w it = µdt + σdz it + death at rate δ σ 2 = Var(permanent earnings) Literature: σ has increased over last forty years Kopczuk, Saez and Song (2010), DeBacker et al. (2013), Heathcote, Perri and Violante (2010) using PSID but Guvenen, Ozkan and Song (2014): σ flat/decreasing in SSA data Can increase in σ explain increase in top income inequality? experiment: σ 2 from 0.01 in 1973 to in 2014 (Heathcote-Perri-Violante) 13

68 Putting the Theory to Work Recall formula λ(ξ) = µξ σ2 2 ξ2 + δ Compute half-life t 1/2 (ξ) = log 2/λ(ξ) σ 2 =0.025 σ 2 =0.02 σ 2 =0.03 Half Life t 1/2 (ξ) in Years Moment under Consideration (equiv. Weight on Tail), -ξ 14

69 Transition following Increase in σ 2 from 0.01 to Top 1% Labor Income Share Data (Piketty and Saez) Model Transition Model Steady State Year 15

70 OK, so what drives top inequality then? Two candidates: 1. heterogeneity in mean growth rates 2. superstar shocks to skill prices 16

71 OK, so what drives top inequality then? Two candidates: 1. heterogeneity in mean growth rates 2. superstar shocks to skill prices 16

72 Heterogeneity in Mean Growth Rates Casual evidence: very rapid income growth rates since 1980s (Bill Gates, Mark Zuckerberg) Two regimes: H and L with µ H > µ L Assumptions drop from H to L at rate ψ retire at rate δ dx it = µ H dt + σ H dz it dx it = µ L dt + σ L dz it See Luttmer (2011) for similar model of firm dynamics Proposition: Speed of transition determined by λ H (ξ) := ξµ H ξ 2 σ2 H 2 + ψ + δ λ L(ξ) 17

73 Revisiting the Rise in Income Inequality Jones and Kim (2015): in IRS/SSA data, µ H since 1970s Experiment: in 1973 µ H by 8% 30 Top 1% Labor Income Share Data (Piketty and Saez) Model w High Growth Regime Model Steady State Year 18

74 Superstar shocks to skill prices Second candidate for fast transitions: x it = log w it satisfies x it = χ t y it dy it = µdt + σdz it ( ) i.e. w it = (e y it ) χt and χ t = stochastic process 1 Note: implies deviations from Gibrat s law dx it = µdt + x it ds t + σdz it, S t := log χ t 0 Some empirical support: Parker and Vissing- Jorgensen (2010), Guvenen et al. (2017) Call χ t (equiv. S t ) superstar shocks 19

75 Superstar shocks to skill prices Second candidate for fast transitions: x it = log w it satisfies x it = χ t y it dy it = µdt + σdz it ( ) i.e. w it = (e y it ) χt and χ t = stochastic process 1 Note: implies deviations from Gibrat s law dx it = µdt + x it ds t + σdz it, S t := log χ t 0 Some empirical support: Parker and Vissing- Jorgensen (2010), Guvenen et al. (2017) Call χ t (equiv. S t ) superstar shocks Proposition: The process ( ) has an infinitely fast speed of adjustment: λ =. Indeed ζ x t = ζ y /χ t or η x t = χ t η y where ζ x t, ζ y are the PL exponents of incomes x it and y it. 19

76 A Microfoundation for Superstar Shocks χ t term can be microfounded with changing skill prices in assignment models (Sattinger, 1979; Rosen, 1981) Here adopt Gabaix and Landier (2008) continuum of firms of different size S Pareto(1/α t ). continuum of managers with different talent T, distribution T (n) = T max B β nβt where n:= rank/quantile of manager talent Match generates firm value: constant T S γt 20

77 A Microfoundation for Superstar Shocks χ t term can be microfounded with changing skill prices in assignment models (Sattinger, 1979; Rosen, 1981) Here adopt Gabaix and Landier (2008) continuum of firms of different size S Pareto(1/α t ). continuum of managers with different talent T, distribution T (n) = T max B β nβt where n:= rank/quantile of manager talent Match generates firm value: constant T S γt Can show: w(n) = e at n χt (= e at+χty it, y it = log n it ) Increase in χ t due to χ t = α t γ t β t β t, γ t : (perceived) importance of talent in production, e.g. due to ICT (Garicano & Rossi-Hansberg, 2006) Other assignment models (e.g. with rent-seeking, inefficiencies) 20

78 Conclusion Transition dynamics of standard random growth models too slow relative to those observed in the data Two parsimonious deviations that generate fast transitions 1. heterogeneity in mean growth rates 2. superstar shocks to skill prices Rise in top income inequality due to simple tax stories, stories about Var(permanent earnings) rise in superstar growth (and churn) in two-regime world superstar shocks to skill prices See paper for wealth inequality results 21