Tobin s Q and Inequality

Transcription

1 Tobin s Q and Inequality Ignacio González 1 Lídia Brun 2 1 American University 2 Université Libre de Bruxelles Growth, Stagnation and Inequality Bank of England, 2017

2 Introduction The Model Disentangling each mechanism Calibration and Results Conclusions

3 Capital Ratios and Inequality Piketty s two empirical findings: Capital Output Ratio is rising β = K Y Capital s Share of Output is rising: α = rk Y = rβ But strong debate on the value of σ (Chirinko and Mallick 2014, Oberfield and Raval 2014) and the concept of wealth itself (e.g. Bonnet et al. 2014, Rognlie 2015, Stiglitz 2015) Our contribution Fundamental divergence between asset prices and corporate fixed assets. Tobin s Q increases during the period in which inequality explodes. We can t simply assume that F = (W, L) = F (qk, L) Neoclassical growth framework to explain evolution of Tobin s Q, capital ratios, equity returns and inequality Drivers of Tobin s Q are also drivers of inequality. A case for higher capital taxes.

4 Literature On Tobin s Q: McGrattan and Prescott (2005). Secular movements in corporate equity values relative to GDP during due to capital income taxation. They use a complete markets approach where K/Y does not respond to changes in Tobin s Q (No inequality implications). On the desired level of capital in an incomplete markets economy. Davila et al. (2012). Incomplete market model calibrated for the U.S. economy The U.S. economy has too little capital because a large proportion of the population relies mainly on labor income Monopoly power and its implications. Barkai (2016) Philippon and Gutierrez (2016) De Loecker and Eeckhout (2016)

5 Tobin s Q Figure: Equity-Wealth-Output and Corporate-Capital-Output ratios investment real

6 Tobin s Q Figure: Equity Tobin s Q

7 Secular Aggregate Movements: A Hypothesis Figure: Capital Market

8 Equity returns Figure: Equity Returns adjusted for Inflation, Taxes and Portfolio Costs

9 Tobin s Q and Inequality We build a model where changes in asset prices can occur at the expense of corporate investment. Investment is low due to high Tobin s Q, not despite high Tobin s Q (conceptual difference with respect to traditional Q theory and Philippon Gutierrez (2016)) We use an Hugget-Aiyagari framework with monopolistic competition. We use the model to evaluate the aggregate and distribution impact of Tobin s Q drivers. More later on the drivers

10 subject to a Budget Constraint n n p jt c jit + v jt s jit+1 = w tɛ it + j=1 j=1 The Household Problem max U (c i ) = E 0 where c it is a Consumption Bundle t=0 β t u (c it ) n j=1 ( v jt + (1 τ d )d jt τ g (v jt c it = ( n j=1 ) ξ (c jit ) ξ 1 ξ 1 ξ (1 + κ) s ijt are household s i holdings of stocks of firm j at time t v jt is the price of a stock of firm j at time t d jt are the dividends firm j pays to its stockholders κ is a portfolio fee on financial wealth ɛ it is follows a Markov Chain and is iid across households τ d is a tax on dividends and τ g a tax con capital gains ) Pt P t 1 v jt 1 ) s jit

11 The Household Problem The allocation of the consumption bundle across the imperfect substitute goods is done according to the standard Relative Demand Function ( ) ɛ pjt c ijt = c it (1) where P t is a Price Index: P t = ( n j=1 P t p 1 ξ jt ) 1 1 ξ

12 The Household Problem Euler Equation u (c it ) E t[βu (c it+1 )] = v jt+1 + (1 τ d )d jt+1 τ g (v jt+1 v jt P t+1 P t v jt ) P t 1 P t κ Stochastic discount factor (the return on savings has to be equalized for every firm j) 1 + r t+1 = v jt+1 + (1 τ d )d jt+1 τ g (v jt+1 P t+1 P t v jt ) P t 1 P t κ Imposing no bubble condition, the real price of firm s j is: v jt v jt P t = 1 τ d 1 τ g k=1 P t+k l=1 d jt+k k (1 + r t+l ) (2)

13 The Firm s problem Capital is accumulated according to the standard equation: K jt+1 = (1 δ)k jt + i jt (3) Where i jt is an investment bundle: i jt = 1 0 ξ 1 ξ ijht dh ξ ξ 1 (4) We impose that the Elasticity of Substitution between investment goods be the same than for consumption to avoid multiplicity. This yields the standard Relative Investment Demand Function i jht = ( pht P t ) ξ i jt (5)

14 The Firm s problem Total demand for product j is the sum of the consumption demand and the investment demand for that product: y j = = = = 1 1 c ijt dφ t 1 (s, e) ( pjt P t 0 ( pjt P t ( pjt P t 0 i hjt dh ) ξ c itdφ t 1(s, e) + ) ξ 1 0 ) ξ (C t + I t ) = c it dφ t 1 (s, e) + ( pjt P t 1 ( pjt P t ) ξ i htdh i ht dh ) ξ F (K t, L t )

15 The Firm s problem subject to: max V jt = 1 τ d 1 τ g d jt + v jt P t The firm s financing constraint: d jt +P t i jt +w t L jt τ c (p jt F (K jt, L jt ) w t L jt δk jt ) = p jt F (K jt, L jt ) The production function: F (K jt, L jt ) = (φk σ 1 σ ) + (1 φ)l σ 1 σ σ 1 σ

16 The Firm s problem We can express the firm s financing constraint in real terms: ( d jt pjt = (1 τ c ) F (K jt, L jt ) δk jt w ) t L jt (K jt+1 K jt ) P t P t P t Since the firm is a monopolist, it takes into account the demand for its product when deciding the scale of its production: subject to: V (K jt ) = max 1 τ d 1 τ g V (K jt+1 ) 1 + r t+1 F (K jt, L jt ) = ( pjt P t ) ξ F (K t, L t )

17 The Firm s problem First Order Conditions: Capital Demand Function δ + r t+1 = τ c δ + ξ 1 (1 τ c ) p jt+1 F K (K jt+1, L jt+1 ) (6) ξ P t+1 Labor Demand Function w t = ξ 1 p jt F L (K jt, L jt ) (7) P t ξ P t

18 Firm s Capital Demand Using the constant returns to scale assumption after some manipulation K jt+1 = d jt+1 (1 + r t+1 )P t+1 1 ξ F (K, L) = F K (K, L)K + F L (K, L)L ( 1 τc Imposing a no-bubble condition : Then: K jt+1 = k=1 P t+k l=1 1 + r t+1 lim k ) pjt+1 P t+1 F (K jt+1, L jt+1 ) + 1 k (1+ r t+l ) l=1 K jt+1+k = 0 K jt r t+1 d jt+k 1 (1 τ c )p jt+k F (K jt+k, L jt+k ) k ξ k (1 + r t+l ) (1 + r t+l ) P t+k l=1

19 Tobin s Q The Tobin s Q is the ratio between the financial valuation of the firm v jt P t and the value of its capital stock K jt+1 : v jt Q jt = = P t K jt+1 = 1 τ d 1 τ g 1 τ d 1 τ g ξ K jt ξ (1 τ c) 1 τ c K jt+1 K jt+1 p jt+k F (K jt+k,l jt+k ) k k=1 P t+k (1+ r t+l ) l=1 p jt+k F (K jt+k, L jt+k ) k (1 + r t+l ) k=1 P t+k l=1

20 Steady State With symmetric equilibrium: K j = K; p j = P; v j = v; d j = d. The physical capital schedule is: ( K(r) = φ 1 φ + 1 κ+r ξ (1 τ g )(1 τ c ) + δ ) σ 1 1 φ ξ 1 φ σ σ 1 And the financial price schedule is: v(r,k) = (1 τ d)d P (κ + r) P = (1 τ ( d)(1 τ c ) F (K, L) δk w P L) κ + r L

21 Steady State Tobin s Q: Q(r,K) = 1 τ d 1 τ g ( ξ ( 1 τ c F (K, L) τ )) g K r + κ (8) A decrease in τ d increases Q A decrease in τ g decreases Q graph graph A decrease in ξ (increase in markup) increases Q graph If markets are competitive (i.e. ξ = ) neither τ c nor κ affect Q in equilibrium. Under monopolistic competition: A decrease in τ c increases Q graph A decrease in κ increases Q graph

22 Calibration (Baseline) Parameter Value Discount Factor β 0.92 Risk Aversion µ 2 Capital Weight φ 0.32 Capital-Labor Elasticity σ 0.7 Depreciation Rate δ 0.10 Income Process Labor Productivities {ɛ 1, ɛ 2, ɛ 3} {1,5.29,46.55} Transition Matrix Π(ɛ ɛ)

23 Effective Corporate Tax Rate

24 Dividend and Capital Gains Taxes

25 Portfolio Costs

26 Steady States 1980 τ d,τ g markup Equity Return E[a] v(r,k) K(r) Equity Return Equity Return Capital, Assets Capital, Assets Capital, Assets τ c,κ markup+τ c +κ Equity Return Equity Return Equity Return Capital, Assets Capital, Assets Capital, Assets

27 Steady States 1980 τ d, τ g Markup τ c, κ Markup, τ c, κ 2002 ξ Markup ξ Dividend Tax Rate τ d 39.87% 15.55% 39.87% 39.87% 39.87% 15.55% Capital Gains Tax τ g 16.85% 11.41% 16.86% 16.86% 16.86% 11.41% Corporate Tax τ c 35.60% 35.60% 35.60% 19.10% 19.10% 19.10% Portfolio Cost κ 2.26% 2.26% 2.26% 1.14% 1.14% 1.14% Labor Tax τ l 27.26% 28.81% 26.76% 29.99% 29.60% 31.90% Capital-Output Ratio K/Y Physical Capital K(r) Stock Price V (r,k) P Tobin s Q(r, K) Equity Return r 1.76% 3.17% 1.96% 2.62% 2.85% 4.15% Labor Share wl Y Gini Index Average Welfare % -0.31% 2.30% 2.11% 1.49% Aggregate Welfare % 0.58% 2.81% 3.68% 9.42% Distributional Welfare % -0.89% -0.01% -1.51% -7.25%

28 Welfare Analysis The average welfare gain is the % increase in consumption in the no-reform case that gives the same utility as when reform is implemented: X t=0 = X β t u(ct R (ɛ t X 0))µ t (X 0, ɛ t )dψ(x 0) ɛ t E t β t u((1 + )ct NR (ɛ t X 0))µ t (X 0, ɛ t )dψ(x 0) t=0 ɛ t E t We follow? in decomposing the welfare changes into: An aggregate component: welfare changes because reform affects the time series of aggregate variables (1 + a ) = C R C NR A distributional component: welfare changes because reform involves a redistribution of resources (1 + ) = (1 + a )(1 + d )

29 Welfare Analysis τ d, τ g 0.1 markup Welfare Gain Low Productivity Medium Productivity High Productivity Average Productivity Welfare Gain Welfare Gain Asset Holdings Asset Holdings Asset Holdings 0.1 τ c, κ 0.1 markup + τ c + κ Welfare Gain Welfare Gain Welfare Gain Asset Holdings Asset Holdings Asset Holdings

30 Conclusions In this framework, changes Q have a i) direct effect on wealth inequality and an indirect effect on inequality through changes in ii) K wl Y, w and Y Capital income taxation that lowers Q has a positive effect on capital formation and equality. This is the case of dividend income taxation or corporate taxation in interaction with monopoly markups Post-1980 drivers of Q: capital taxation and monopoly rents

31 Dividend Tax Figure: τ d = 20% 1.07 Capital Market 1.07 Stock Market E[s NT (r)] E[a NT (r)] = E[a T (r)] E[s T (r)] Equity Return 1.04 Equity Return v NT (r,k) = K NT (r) = K T (r) 1.02 v T (r,k) Capital, Assets Stock Holdings An increase in τ d reduces the Tobin s Q model

32 Monopoly Power Figure: Markup ξ ξ 1 = Capital Market 1.07 Stock Market E[s M (r)] E[s C (r)] Equity Return 1.04 v M (r,k) Equity Return K M (r) 1.02 v C (r,k) = K C (r) Capital, Assets Stock Holdings An increase in monopoly power increases the Tobin s Q and reduces capital demand model

33 Capital Gains Tax Figure: τ g = 20% 1.07 Competitive Market 1.07 Monopolistic Competition E[a NT (r)] 1.05 V NT (r,k) K NT (r) 1.05 Equity Return 1.04 E[a T (r)] V T (r,k) K T (r) Equity Return Capital, Assets Capital, Assets τ g reduces capital demand and increases the Tobin s Q. model

34 Portolio Costs Figure: κ = 0.5% 1.07 Competitive Market 1.07 Monopolsitic Competition E[a NT (r)] 1.05 V NT (r,k) K NT (r) 1.05 Equity Return 1.04 E[a T (r)] V T (r,k) K T (r) Equity Return Capital, Assets Capital, Assets Under perfect competition, κ reduces capital demand but does not affect the Tobin s Q. Under monopolistic competition, κ reduces capital and the Tobin s Q. model

35 Corporate Tax Figure: τ c = 20% 1.07 Competitive Market 1.07 Monopolsitic Competition Equity Return E[a NT (r)] V NT (r,k) K NT (r) E[a T (r)] V T (r,k) K T (r) Equity Return Capital, Assets Capital, Assets Under perfect competition, τ g reduces capital demand but does not affect the Tobin s Q. Under monopolistic competition, τ g reduces capital and the Tobin s Q. model

36 Figure: Capital - Chained dollars nominal

37 Figure: Corporate Investment stocks