Micro Data for Macro Models Topic 4: Firm Lifecycle

Micro Data for Macro Models Topic 4: Firm Lifecycle Thomas Winberry November 20th, 2017 1

Stylized Facts About Firm Dynamics 1. New entrants smaller than the average firm 2. Young firms more likely to exit than average firm 3. Conditional on survival: Young firms grow faster than average Small firms grow faster than average, conditional on age 4. Distribution of firm size has fat tail 2

Benchmark Model of Firm (Non) Dynamics Consider firms i with production function y it = e z it k θ it nν it, where θ + ν < 1 Productivity shocks feature mean reversion z it+1 = ρz it + ε it+1 Suppose firms enter with average productivity z i0 and low capital k i0 < E [k it ] Investment satisfies 1 = E [MP K it+1 + (1 δ)] = All growth occurs in first period 3

Mechanisms Generating Firm Dynamics 1. Selection upon entry and exit (Hopenhayn 1992) Surviving firms have higher productivity than entrants Mean reversion + selection = growth patterns 2. Capital adjustment costs (Clementi and Palazzo 2015) Keeps investment from all happening in first period 3. Financial frictions (Ottonello and Winberry 2017) Costly to finance investment 4. Demand accumulation (Foster, Haltiwanger, and Syverson 2016) Another form of investment 4

Clementi and Palazzo (2015) Adds capital adjustment costs to Hopenhayn (1992) model Model matches key stylized facts about firm dynamics 1. New entrants smaller than average 2. Young firms more likely to exit 3. Conditional on survival, young/small firms grow faster Generates persistence in response to aggregate shocks 5

Model Overview Incumbent Firms Idiosyncratic + aggregate productivity shocks Fixed operating cost + exit Fixed + quadratic adjustment costs Potential Entrants Fixed mass Signal of productivity if enter Fixed entry cost Partial equilibrium Fixed discount factor 1/R Labor supply function L(w) = w γ 6

Incumbent Firms Production function y it = e Zt e z it k θ it nν it Aggregate shock Z t+1 = ρ Z Z t + ε Z t+1 Idiosyncratic shock z it+1 = ρ z z it + ε z it+1 Capital accumulation follows k it+1 = (1 δ)k it + i it Fixed cost c 0 k it if i it 0 Quadratic adjustment cost c 1 2 ( iit k it ) 2 kit To continue into next period, must pay fixed operating cost c f log N(µ cf, σ cf ) 7

Timing and Decision Problem v 1 (z, k; s) = max e Z e z k θ n ν [ w(s)n + E cf max{v 0 (k), v 2 (z, k; s) c f } ] n v 2 (z, k; s) = max (k (1 δ)k) AC(k, k) + 1 k R E [ z,z z,z v 1 (z, k ; s ) ] 8

Potential Entrants Fixed mass M of potential entrants Draw signal of future productivity q Pareto(q) z = ρ s q + η, η N(0, σ s ) To become an incumbent, pay fixed entry cost c e 9

Potential Entrants Fixed mass M of potential entrants Draw signal of future productivity q Pareto(q) z = ρ s q + η, η N(0, σ s ) To become an incumbent, pay fixed entry cost c e 9

Potential Entrants Fixed mass M of potential entrants Draw signal of future productivity q Pareto(q) z = ρ s q + η, η N(0, σ s ) To become an incumbent, pay fixed entry cost c e v(q; s) = k + 1 R E [ z,z z,q v 1 (z, k ; s ) ] 9

Calibration 10

Survival Probability by Age Survival probability decreases with age Productivity increases with age 11

Growth by Age and Size Growth rate decreasing in size Mean reversion in productivity Growth rate decreasing in age Young firms have lower capital 12

Calibrating Aggregate TFP Shocks Parameters Targets 13

Calibrating Aggregate TFP Shocks Parameters Targets Entry and Exit Over the Cycle 13

Aggregate Impulse Respones 14

Aggregate Impulse Respones 14

Propagation 15

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α L α t Nt 1 α ( [ A t = Z t (E t z 1/(1 α), where ] [ E t k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 16

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α ( [ A t = Z t (E t L α t N 1 α t, where ] [ E t z 1/(1 α) k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 17

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α L α t Nt 1 α ( [ A t = Z t (E t z 1/(1 α), where ] [ E t k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 1. External propagation: exogenous component of TFP z t = ρz t 1 + ε t 17

Three New Propagation Mechanisms in This Model Y t = A t K 1 α t L α t Nt 1 α ( [ A t = Z t (E t s 1/(1 α), where ] [ E t k θ/(1 α) ] + Cov t (s 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 1. External propagation: exogenous component of TFP z t = ρz t 1 + ε t 2. Internal propagation: Capital accumulation 17

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α ( [ A t = Z t (E t L α t N 1 α t, where ] [ E t z 1/(1 α) k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 1. External propagation: exogenous component of TFP z t = ρz t 1 + ε t 2. Internal propagation: Capital accumulation Firm accumulation 17

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α L α t Nt 1 α ( [ A t = Z t (E t z 1/(1 α), where [ ]E t k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 1. External propagation: exogenous component of TFP z t = ρz t 1 + ε t 2. Internal propagation: Capital accumulation Firm accumulation Selection 17

Three New Propagation Mechanisms in This Model Y t = A t Kt 1 α L α t Nt 1 α ( [ A t = z t (E t z 1/(1 α), where ] [ E t k θ/(1 α) ] + Cov t (z 1/(1 α) ) 1 α, k θ/(1 α) ))/K t 1. External propagation: exogenous component of TFP z t = ρz t 1 + ε t 2. Internal propagation: Capital accumulation Firm accumulation Selection Allocation 17