Lecture 2: Firms, Jobs and Policy

Transcription

1 Lecture 2: Firms, Jobs and Policy Economics 522 Esteban Rossi-Hansberg Princeton University Spring 2014 ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

2 Restuccia and Rogerson (2009) Assess the quantitative role of resource allocation across productive uses in development Consider a version of neoclassical growth model with heterogeneous producers Consider distortions to the prices faced by different producers (idiosyncratic distortions) Credit market imperfections and non-competitive banking systems Public enterprises Trade restrictions Labor market regulations Corruption and selective government industrial policy Resource misallocation can decrease aggregate output and TFP in the range of 30 to 50 percent A theory of measured TFP ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

3 The Model Infinitely-lived representative household: β t u(c t ), 0 < β < 1 t=0 Endowments: One unit of productive time each period, K 0 > 0 units of the capital stock, and equal shares of all plants Budget constraint: p t (C t + K t+1 (1 δ)k t ) = p t (r t K t + w t N t + π t T t ) t=0 t=0 ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

4 Technology Production unit a plant: f (s, k, n) = sk α n γ, 0 < γ + α < 1 Idiosyncratic productivity s constant over time Exogenous probability of exit λ Fixed cost of operation c f every period Entry cost c e and productivity of entrants from cdf H(s) ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

5 Policy Distortions They focus on policies that create idiosyncratic distortions to plant-level decisions Each plant faces its own output tax/subsidy denoted by τ ( 1, 1) Entering plants face draws of s and τ Given cdf H(s), policy distortions induce a joint distribution cdf G (s, τ) ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

6 Incumbent and Entrant s Problem Incumbent: Per-period profit function π(s, τ) = max n,k {(1 τ)sk α n γ wn rk c f } Let k(s, τ), n(s, τ) denote the optimal decisions With constant (s, τ), present value of incumbent plant: W (s, τ) = π(s, τ) 1 ρ, ρ = 1 λ = (1 λ) β 1 + R Entrant: The expected value of a potential entrant: W e = max [W (s, τ), 0] dg (s, τ) c e (s,τ) Let x(s, τ) be its optimal entry decision ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

7 Invariant Distribution of Plants Denote µ(s, τ) the distribution of producing plants this period and E the mass of entrants Next period s distribution: µ (s, τ) = (1 λ)µ(s, τ) + x(s, τ)dg (s, τ)e Let ˆµ be the invariant distribution associated with E = 1: ˆµ(s, τ) = x(s, τ) dg (s, τ) λ ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

8 Labor Market Clearing Aggregate labor demand: N(r, w) = E n(s, τ)d ˆµ(s, τ) (s,τ) Labor supply inelastic equal to one, entry E satisfies: E = 1 (s,τ) n(s, τ)d ˆµ(s, τ) ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

9 Equilibrium A steady state competitive equilibrium with entry is w, r, T, µ(s, τ), E, W (s, τ), π(s, τ), W e, x(s, τ), k(s, τ), n(s, τ), C, and K such that: Consumer optimization r = 1/β (1 δ) Plant optimization Free-entry W e = 0 Market clearing: labor, capital, output Government budget balance T + τf (s, k, n)dµ(s, τ) = 0 s,τ Invariant µ µ(s, τ) = E x(s, τ) dg (s, τ) λ ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

10 Calibration Calibrate undistorted benchmark economy to U.S. data Model period equal to a year Parameter Value Target α 0.3 Capital income share γ 0.6 Labor income share β 0.96 Real rate of return δ 0.08 Investment to output ratio c e 1.0 Normalization c f 0.0 Benchmark case λ 0.1 Annual exit rate ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

11 Calibration Key elements: range of s and H(s) Use mapping from s to n and from H(s) to µ(s) implied by the model ( ) 1 n i si 1 γ α = n j s j µ(s) = x(s) λ dh(s) Number of workers per plant in U.S. Census of Manufactures implies s [1, 2.43] (given α = 0.3, γ = 0.6, and normalizing lowest s to one) Micro evidence of TFP suggest range of 1 to 3 across plants within narrowly defined manufacturing industries ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

12 Distribution of Plants by Employment U.S. Data ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

13 Distribution of Plants by Employment Model vs. Data ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

14 Share of Valued Added and Employment ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

15 Distribution Statistics of Benchmark Economy Plant Size by Employment < to or more Share of plants Share of output Share of labor Share of capital Average employment ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

16 Aggregate Distortions An output tax of 0.5 implies relative steady state output (distorted/undistorted) of 0.63 In standard growth model (capital share half the labor share), same tax policy implies relative steady state output of = 0.7 Output effect 10 percent larger in model with plant heterogeneity than in standard growth model: accounted for by a fall in measured aggregate TFP Plant heterogeneity allows another form of aggregate distortions that is empirically relevant: entry cost An increase in the cost of entry ce due to government regulation of 50 percent implies a drop in aggregate measured TFP of 10 percent Distortion to the entry cost leave the capital to output ratio unaltered ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

17 Idiosyncratic Distortions: Tax/Subsidy Policies Assume a fraction of plants are taxed and the rest are subsidized Output tax/subsidy combinations: Tax packages of 0.1, 0.2, 0.3, 0.4, with subsidies so that the net effect on steady state capital accumulation is zero Lump-sum redistribution to consumers to balance the government budget ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

18 Ind. Idiosyncratic Distortions: Tax/Subsidy Policies τ t Relative Y Relative TFP Relative E Y s /Y S/Y τ s ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

19 Corr. Idiosyncratic Distortions: Tax/Subsidy Policies τ t Relative Y Relative TFP Relative E Y s /Y S/Y τ s ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

20 Sensitivity Sensitivity of results: Decreasing returns at the plant level (1 α γ) Fixed cost of operation (cf > 0): potential selection of entering plants Plant dynamics: potential selection of exiting plants Capital and human accumulation can amplify these differences ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

21 Hopenhayn and Rogerson (1993) Examine the qualitative and quantitative impact of government policies that make it costly for firms to adjust their employment levels Large volume of job creation and destruction at the level of the individual firm Important to understand the effects of labor market regulation Extend Hopenhayn (1992) to a general equilibrium setting Finding: A tax equal to 1 year s wages reduces utility by over 2 percent measured in terms of consumption Important reduction in average labor productivity ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

22 The Model Labor is the only input Profits are given by p t f (n t, s t ) n t p t c f g(n t, n t 1 ) where n t denotes employment, wages are normalize to one s t is a firm specific productivity shock, that evolves according to transition probabilities F (s, s ) F (s, ) is the distribution function for next period s value of the shock Shock is independent across firms c f is a fixed operating cost g captures the presence of adjustment costs Policy experiments can be represented as changes in g Firing cost of τ would imply g (n t, n t 1 ) = τ max(0, n t 1 n t ) ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

23 Timing ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

24 Entry and Preferences Entry cost c e Initial draw s from distribution ν, iid Continuum of agents uniformly distributed in unit interval with preferences β t [u (c t ) v (n t )] t=1 where c t > 0 and n t {0, 1} denote consumption and labor supply As in Rogerson (1988) individuals use lotteries and diversify idiosyncratic risk so economy behaves as β t [u (c t ) an t ] t=1 where N t is the fraction of individuals who are employed in period t ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

25 Equilibrium Look at stationary equilibrium so assume constant p Bellman equation is W (s, n; p) = max n 0 {pf (n, s) n pc f g(n, n) +β max[e s W (s, n ; p), g(0, n )]} Optimal decisions N(s, n; p) and X (s, n; p) with X = 1 corresponding to exit and X = 0 stay Value of entering is W e (p) = W (s, 0; p)dv(s). µ(s, n) denotes the mass of firms with s and n, and M the mass of entrants ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

26 Aggregates Total output is given by Y (µ, M; p) = [f (N(s, n; p), s) c f ]dµ(s, n) + M f (N(s, 0; p), s)dv(s) Individual adjustment costs r(s, n; p) = [1 X (s, n; p)] g(n(s, n ; p), n )df (s, s ) + X (s, n; p)g(0, n ) integrate to get R(µ, M, p) the aggregate adjustment costs Labor demand L d (µ, M; p) = N(s, n; p)dµ(s, n) + M N(s, 0; p)dv(s) Profits Π(µ, M; p) = py (µ, M; p) L d (µ, M; p) R(µ, M; p) Mpc e All homogenous of degree one in µ and M ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

27 Aggregates In SS with 1/(1 + r) = β consumer problem is This implies N = L S (p, Π + R) max u(c) an s.t. pc N + Π + R A stationary equilibrium consists of an output price p 0, a mass of entrants M 0, and a measure of incumbents,µ, such that L d (µ, M, p ) = L S (Π(µ, M, p ) + R(µ, M, p )) T (µ, M, p ) = µ W e (p ) p c e with equality if M > 0 Need strict concavity and INADA on f, L S 2 < 0, F is continuous F 1 < 0 and ν has a continuous cdf ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

28 Quantitative specification Benchmark model: f (n, s) = sn θ, 0 θ 1 g(n t, n t 1 ) = 0 log(s t ) = a + ρlog(s t 1 ) + ε t, where ε t N(0, σ 2 ε ) u (c) = ln (c) and v(n) = An Persistence ρ < 1 important since it determines how much firms care about firing costs s exhibits mean reversion ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

29 Optimal Rules For this case n not a state variable so log n t = 1 1 θ (log θ + log p + log s t ) X (s t, n t, p) = 1 if s t s for some s So employment of surviving firm evolves according to log n t+1 = 1 ρ a (log θ + log p + 1 θ 1 ρ ) + ρ log n t θ ε t (1) ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

30 Calibration Length of period is set to 5 years Let β =.8 and θ,labor s share of total revenue, is set to.64 Use (1) to estimate ρ and σ ε Fix price p = 1 Choose cf and a to match average of log employment and exit rate Choose ν to match size distribution in data Choose cε so that p = 1 ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

31 Calibration ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

32 Distortions Introduce distortions such that g(n t, n t 1 ) = τ max(0, n t 1 n t ) If τ =.2 tax of 1 year of wages ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

33 s-s Policy Bands ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34

34 Deviations from MPL = 1/p ERH (Princeton University ) Lecture 2: Firms, Jobs and Policy Spring / 34