Growth in the Shadow of Expropriation
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1 Growth in the Shadow of Expropriation Mark Aguiar and Manuel Amador Rochester and Stanford 1/55
2 motivation low growth linked to poor economic policies weak institutions and property rights barriers to investment and technology adoption 2/55
3 develop a model with endogenous barriers to investment government policy induces transition dynamics tax rates vary along the path link growth rates to political economy frictions 3/55
4 overview of environment small open economy foreign direct investment contracting friction lack of commitment political economy frictions love of incumbency political turnover 4/55
5 overview of results political economy frictions induce transition dynamics in an environment which otherwise would have none taxes on capital income start out high and decline over time first best investment may be achieved in long run despite governmental impatience a greater love of incumbency slows growth higher political turnover may speed growth 5/55
6 outline of talk environment linear utility numerical simulations 6/55
7 environment small open economy world interest rate: R =(1+r) > 1 domestic government and workers foreign capitalists 7/55
8 firms owned by foreigners operate a deterministic, neoclassical production function f (k, l) capital sunk within a period hire workers in competitive labor market profits: π = f (k, l) wl face tax on profits τ Objective: max k t,l t (1 + r) t[ (1 τ t )π t k t+1 +(1 d)k t ]. t=0 8/55
9 firms foc standard first order conditions: (1 τ t )f k (k t, l t )=r + d f l (k t, l t )=w t. denote first best capital k : f k (k, 1) = r + d. 9/55
10 domestic agents measure one (everything in per capita terms) domestic workers supply labor inelastically have preferences: β t u(c t ). t=0 consumption decisions controlled by government: c t = w t + T t 10 / 55
11 government government taxes capital and makes transfers to workers government receives endowment income y government s budget constraint: y + τ t π t + b t+1 = Rb t + T t non-contingent debt aggregate resource constraint: c t +(1+r)b t = b t+1 + τπ t + w t + y 11 / 55
12 political environment political economy frictions along two dimensions incumbent government prefers consumption while in power incumbent enjoys disproportionate share of consumption incumbent may lose power 12 / 55
13 love of incumbency for given per capita consumption c, incumbents flow utility is: θu(c) while in power u(c) while out of power θ = 1: benevolent government θ : zero weight on private utility 13 / 55
14 political turnover incumbent faces probability γ of losing office at end of period let p t be probability incumbent is in power t periods ahead starting from π 0 = 1, assume p t+1 =(1 γ)p t =(1 γ) t γ = 0: never lose power γ =1: losepowerforsure 14 / 55
15 incumbent preferences incumbent preferences are: W t = β s t (1 γ) s t θu(c s )+ β s t (1 (1 γ) s t )u(c t ) s=t s=t 15 / 55
16 more general political process allow government to lose and regain office γ 0 probability of losing office p t+1 = γ 1 +(γ 0 γ 1 )p t γ 1 probability of regaining office can map into same preferences with appropriate choice of θ and γ 16 / 55
17 limited commitment contracting frictions: government cannot commit to pay debt or to abide by promised tax rate consider self-enforcing equilibria that are supported by punishment equilibria U t is payoff if deviate at time t self-enforcing policies require: W t U t for all t 17 / 55
18 equilibrium concept A self-enforcing equilibrium is a sequence of allocations {c t, k t, b t },taxratesτ t,andwagesw t, such that (i) firms maximize profits given taxes and wages; (ii) the labor market clears; (iii) the sequence of taxes and debt maximizes the period-0 government s a objective function subject to the resource constraint given some initial debt b 0 and a No Ponzi condition; and (iv) the participation constraint holds: W t U t, t. Alternative: (iii) the sequence of taxes and debt maximizes the representative private agent s objective function subject to the resource constraint and a No Ponzi condition 18 / 55
19 deviation payoffs capital requires foreign expertise capital can only be operated by foreigners alternative: domestic agents cannot create new capital, but can operate existing capital consume all output during deviation period consume endowment thereafter U(k) θu(f (k)+y)+βw aut ( W aut u(y) θ 1 1 (1 β)(1 γ) β ). 19 / 55
20 punishment equilibrium deviation triggers worst equilibrium (if utility is bounded below) allocation on pareto frontier foreign banks confiscate existing and future assets government taxes all foreign income and defaults on all new debt no foreign investment no net financial assets 20 / 55
21 no renegotiation no renegotiation after deviation more to this assumption than usual: allocation on pareto frontier for period-0 government not on pareto frontier for future governments rule out pareto improving renegotiation deviation speaks to credibility atomistic investors raise negotiation costs 21 / 55
22 from firms foc and crs: simplify resource constraint (1 τ)f k k =(r + d)k (1 τ)f l l =(1 τ)wl (1 τ)f =(r + d)k +(1 τ)wl government revenues are τπ = τ(f wl) aggregate resources: wl + τπ + y = f (r + d)k + y can remove τ from constraint set 22 / 55
23 government s problem W (b 0 )= max c t,k t,b t t=0 β t (1 γ) t θu(c t )+ t β t (1 (1 γ) t )u(c t ) subject to b 0 (1 + r) t (f (k t ) (r + d)k t + y c t ) t=0 W t U(k t ), t, 23 / 55
24 W b 24 / 55
25 dual approach W (b 0 ) is strictly decreasing in debt define B(w) tobetheinverseofw : B(W (b 0 )) = b 0. B(w) solves: B(w 0 )= max c t,k t,b t subject to (1 + r) t (f (k t ) (r + d)k t + y c t ) b 0 t=0 w 0 β t (1 γ) t θu(c t )+ t=0 t where w 0 = W (b 0 ). β t (1 (1 γ) t )u(c t )W t U(k t ), t 25 / 55
26 B w 26 / 55
27 expanding the state space problem can be solved recursively with expanded state space W t = β s t (1 γ) s t θu(c s )+ β s t (1 (1 γ) s t )u(c t ) s=t s=t = θu(c t )+β(1 γ)w t+1 + βγv t+1, where V t = β s t u(c s ) s=t = u(c)+βv t+1. special case: γ = 1 corresponds to hyperbolic preferences 27 / 55
28 choice variables choice variables: u, w, v and h = f (k) (r + d)k + y let c(u) beinverseofu let K(h) beinverseofh 28 / 55
29 recursive problem subject to B(w, v) = max h c(u)+ 1 {u,w,v,h} Ω 1+r B(w, v ) w θu +(1 γ)βw + γβv v u + βv U(K(h)) θu +(1 γ)βw + γβv 29 / 55
30 first order conditions c (u) =θ(λ + η)+μ B 1 (w, v )= βr(1 γ)(λ + η) B 2 (w, v )= βr(γ(λ + η)+μ) f k (r + d) =ηu (k) envelope: B 1 = λ and B 2 = μ period zero: μ 0 =0orλ 0 =0 dynamics after period zero independent of who makes decisions, conditional on w and v 30 / 55
31 immediate results if participation binds (η >0) then capital is taxed and investment is distorted down higher w implies lower tax: w U(k) 31 / 55
32 linear utility linear utility provides an interesting benchmark u(c) =c drop constraint c 0 absent political economy frictions (θ = 1), jump immediately to steady state from foc: λ t = β(1 + r), t η t =1 β(1 + r), t 32 / 55
33 tax rate tax rate linked to η recall: (1 τ)f k = r + d in linear case: solving: τ = θη η = f k r d θf k if θ =1,wehaveτ =1 β(1 + r) forallt 33 / 55
34 introducing political economy now let γ>0and1<θ< from foc s, we can solve for dynamics for t 1: η t+1 = for t =1: (1 βr)(1 βr(1 γ)) θ ( + βr 1 γ ) η t. θ θ βrγ θβr(1 γ) η 1 = θ 2 note: η 1 independent of initial conditions 34 / 55
35 dynamics of tax rates Initial Capital: Given an initial promised utility w 0, the initial capital stock satisfies: k 0 = k if w 0 U(k ) k 0 solves U(k 0 )=w 0 otherwise. Dynamics: The tax on capital at t =1is: ( γ ) τ 1 =1 βr θ +1 γ, For t > 1, we have: τ t+1 =(1 βr)(1 βr(1 γ)) + βr For all t we have 1 βr τ t 1. ( 1 γ ) τ t. θ 35 / 55
36 steady state The steady state level of τ ss and capital k ss solve: τ ss =1 r + d f k (k ss ) (1 βr)(1 βr(1 γ)) = ( ). 1 βr 1 γ θ The steady state consumption and debt solve: w ss = U(k ss ) c ss = θ(1 β)(1 β(1 γ))f (k ) + y θ(1 β)+βγ ( ) 1+r B ss = (f (k ss ) (r + d)k ss c ss ) r 36 / 55
37 τ t+1 τ ss τ 1 τ t 37 / 55
38 τ t+1 τ ss τ 1 τ t 38 / 55
39 βr =1 if βr =1,thenτ ss =0andk ss = k for all γ and θ< discount rate of government: β t ((θ 1)(1 γ) t +1). as t,termswithθ and γ disappear and discount factor β as long as the government cares a non-zero amount about private utility, the first best is achieved in the long run if consumers are patient 39 / 55
40 βr =1 political economy frictions determine level of debt in steady state greater political economy friction whether θ or γ reduces debt levels in the steady state political economy frictions determine speed of convergence: ( τ t+1 = 1 γ ) τ t. θ 40 / 55
41 τ t+1 slope: 1 γ θ τ ss τ t 41 / 55
42 τ t+1 increase in γ θ τ ss τ t 42 / 55
43 why are there dynamics? two competing forces determining optimal allocation: want to deliver consumption early due to impatience want to delay consumption to sustain investment suppose τ were constant over time lower period 1 consumption, which lowers capital (raises taxes) in period 1 raise period 2 consumption, which raises period 2 capital (lowers taxes) and mitigates decline in period 1 capital at equal marginal products, this raises output more than the change in present value of consumption flat taxes cannot be optimal as we approach the steady state, the value of increasing k falls relative to the value of shifting consumption, and tax rates flatten out 43 / 55
44 comparative statics an increase in θ generates slower convergence higher θ generates more impatience on the part of the government, making it harder to lower taxes credibly an increase in γ generates faster convergence note that an increase in γ makes the government more impatient, but also twists the relative value of future periods if γ = 1: any two future periods have a relative discount factor of β an increase in γ generates a higher initial tax, but a faster speed of convergence if γ = 0, growth is zero as we jump immediately to the steady state 44 / 55
45 βr < 1 if βr < 1, then steady state tax rate is not zero long run tax rate depends on political economy frictions an increase in either θ or γ raises the steady state tax rate 45 / 55
46 increase in θ τ t+1 τ ss τ ss τ t 46 / 55
47 increase in γ τ t+1 τ ss τ ss τ t 47 / 55
48 summing up linear case political economy frictions induce dynamics will approach first best if βr =1 love of incumbency slows growth political turnover may speed growth 48 / 55
49 general utility relax assumption regarding linear utility suppose γ =1: w = θu(c)+βv v is the only state variable c (u) =θη + μ μ = βr(η + μ) f k (r + d) =ηu (k) 49 / 55
50 βr =1 if βr =1: μ = η + μ μ trends up v trends up over time and taxes decline at some point v = v and τ =0 converge to first best steady state debt is negatively related to θ 50 / 55
51 nonlinear dynamics solve dynamics numerically log utility (robust to power utility) set γ =1 compare θ =1withθ =2 convergence rate close to 1/θ, as in linear case 51 / 55
52 nonlinear u dynamics: βr = 1 Dynamics of tax rates 52 / 55
53 nonlinear u dynamics: βr < 1 Dynamics of tax rates 53 / 55
54 still to do comparative statics with respect to γ quantitative results 54 / 55
55 conclusion endogenize path of taxation induced transition dynamics political economy frictions lead to high but declining tax rates love of incumbency leads to slower growth increased political turnover may increase speed of convergence first best still attainable in limit if private sector patient enough steady state debt may decline as government becomes more impatient 55 / 55
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