Estimating Production Functions - Faculty of Artsfaculty.arts.ubc.ca/pschrimpf/565/02-production.pdf · 2019-01-15 · Estimating Production Functions PaulSchrimpf Introduction Setup

EstimatingProductionFunctions

Paul Schrimpf

Estimating Production Functions

Paul Schrimpf

UBCEconomics 565

January 10, 2019


Paul Schrimpf

Introduction

Setup

SimultaneityInstrumentalvariables

Panel data

Fixed effects

Dynamic panel

Control functions

Applications

SelectionOP and selection

1 Introduction

2 Setup

3 SimultaneityInstrumental variablesPanel data

Fixed effectsDynamic panel

Control functionsApplications

4 SelectionOP and selection


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Section 1

Introduction


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Why estimate productionfunctions?

• Primitive component of economic model• Gives estimate of firm productivity — useful forunderstanding economic growth

• Stylized facts to inform theory, e.g. Foster, Haltiwanger,and Krizan (2001)

• Effect of deregulation, e.g. Olley and Pakes (1996)• Growth within old firms vs from entry of new firms, e.g.

Foster, Haltiwanger, and Krizan (2006)• Effect of trade liberalization, e.g. Amiti and Konings

(2007)• Effect of FDI Javorcik (2004)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


General references:

• Aguirregabiria (2017) chapter 2• Ackerberg et al. (2007) section 2• Van Beveren (2012)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Section 2

Setup


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Setup

• Cobb Douglas production

Yit = AitKβkit L

βlit

• In logs,yit = βkkit + βllit + ωit + εit

with log Ait = ωit + εit, ωit known to firm, εit not• Problems:

1 Simultaneity: if firm has information about log Ait whenchoosing inputs, then inputs correlated with log Ait, e.g.price p, wage w, perfect information

Lit =( pwβlAitKβkit

) 11−βl

2 Selection: firms with low productivity will exit sooner3 Others: measurement error, specification


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Section 3

Simultaneity


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Simultaneity solutions

1 IV

2 Panel data

3 Control functions


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Instrumental variables

• Instrument must be• Correlated with k and l• Uncorrelated with ω + ε

• Possible instrument: input prices• Correlated with k, l through first-order condition• Uncorrelated with ω if input market competitive

• Other possible instruments: output prices (more oftenendogenous), input supply or output demand shifter(hard to find)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Problems with input prices as IV

• Not available in many data sets• Average input price of firm could reflect quality as wellas price differences

• Need variation across observations• If firms use homogeneous inputs, and operate in the

same output and input markets, we should not expectto find any significant cross-sectional variation in inputprices

• If firms have different input markets, maybe variationin input prices, but different prices could be due todifferent average productivity across input markets

• Variation across time is potentially endogenous becausecould be driven by time series variation in averageproductivity


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Fixed effects

• Have panel data, so should consider fixed effects• FE consistent if:

1 ωit = ηi + δt + ω∗it

2 ω∗it uncorrelated with lit and kit, e.g. ω∗

it only known tofirm after choosing inputs

3 ω∗it not serially correlated and is strictly exogenous

• Problems:• Fixed productivity a strong assumption• Estimates often small in practice• Worsens measurement error problems

Bias(βFEk ) ≈ − βkVar(∆ε)

Var(∆k) + Var(∆ε)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel: motivation 1

• General idea: relax fixed effects assumption, but stillexploit panel

• Collinearity problem: Cobb-Douglas production, flexiblelabor and capital implies log labor and log capital arelinear functions of prices and productivity (Bond andSöderbom (2005))

• If observed labor and capital are not collinear thenthere must be something unobserved that varies acrossfirms (e.g. prices), but that could invalidatemonotonicity assumption of control function


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel: momentconditions

• See Blundell and Bond (2000)• Assume ωit = γt + ηi + νit with νit = ρνi,t−1 + eit, so

yit = βllit + βkkit + γt + ηi + νit + εit

subtract ρyi,t−1 and rearrange to get

yit =ρyi,t−1 + βl(lit − ρli,t−1) + βk(kit − ρki,t−1)++ γt − ργt−1 + ηi(1 − ρ)︸︷︷︸

=η∗i

+ eit + εit − ρεi,t−1︸︷︷︸=wit

• Moment conditions:• Difference: E[xi,t−s∆wit] = 0 where x = (l, k, y)• Level: E [∆xi,t−s(η∗

i + wit)] = 0


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel: economicmodel 1

• Adjustment costs

V(Kt−1, Lt−1) = maxIt,Kt,Ht,Lt

PtFt(Kt, Lt) − PKt (It + Gt(It,Kt−1)) −

− Wt (Lt + Ct(Ht, Lt−1)) +ψE [V(Kt, Lt)|It]

s.t. Kt = (1 − δk)Kt−1 + ItLt = (1 − δl)Lt−1 + Ht

Implies

Pt∂Ft∂Lt

− Wt∂Ct

∂Lt=Wt + λLt

(1 − (1 − δl)ψE

[λLt+1

λLt|It

])

Pt∂Ft∂Kt

− PKt∂Gt

∂Kt=λKt

(1 − (1 − δk)ψE

[λKt+1

λKt|It

])


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel: economicmodel 2

• Current productivity shifts ∂Ft∂Lt and (if correlated with

future) the shadow value of future labor E[λLt+1

λLt|It

]

• Past labor correlated with current because ofadjustment costs


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel data: problems

• Problems:• Sometimes imprecise (especially if only use difference

moment conditions)• Differencing worsens measurement error• Weak instrument issues if only use difference moment

conditions but levels stronger (see Blundell and Bond(2000))

• Level moments require stronger stationarity assumption- ηi uncorrelated with ∆xit


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Control functions

• From Olley and Pakes (1996) (OP)• Control function: function of data conditional onwhich endogeneity problem solved

• E.g. usual 2SLS y = xβ + ε, x = zπ + v, control functionis to estimate residual of reduced form, v and thenregress y on x and v. v is the control function

• Main idea: model choice of inputs to find a controlfunction


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


OP assumptions

yit = βkkit + βllit + ωit + εit

1 ωit follows exogenous first order Markov process,

p(ωit+1|Iit) = p(ωit+1|ωit)

2 Capital at t determined by investment at time t − 1,

kt = (1 − δ)kit−1 + iit−1

3 Investment is a function of ω and other observedvariables

iit = It(kit, ωit),

and is strictly increasing in ωit

4 Labor variable and non-dynamic, i.e. chosen each t,current choice has no effect on future (can be relaxed)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


OP estimation of βl

• Invertible investment implies ωit = I−1t (kit, iit)

yit =βkkit + βllit + I−1t (kit, Iit) + εit

=βllit + ft(kit, iit) + εit

• Partially linear model• Estimate by e.g. regress yit on lit and series functions of

t, kit, iit• Gives βl, fit = ft(kit, iit)


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


OP estimation of βk

• Note: ft(kit, iit) = ωit + βkkit• By assumptions, ωit = E[ωit|ωit−1] + ξit = g(ωit−1) + ξitwith E[ξit|kit] = 0

• Use E[ξit|kit] = 0 as moment to estimate βk.• OP: write production function as

yit − βllit =βkkit + g(ωit−1) + ξit + εit=βkkit + g (fit−1 − βkkit−1) +

+ ξit + εit

Use βl and fit in equation above and estimate βk by e.g.semi-parametric nonlinear least squares

• Ackerberg, Caves, and Frazer (2015): use

E[ξit(βk)kit

]= 0


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Dynamic panel vs controlfunction

• Both derive moment conditions from assumptionsabout timing and information set of firm

• Dealing with ω• Dynamic panel: AR(1) assumption allows

quasi-differencing• Control function: makes ω estimable function of

observables

• Dynamic panel allows fixed effects, does not makeassumptions about input demand

• Control function allows more flexible process for ωit


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Applications

• Olley and Pakes (1996): productivity in telecom afterderegulation

• Söderbom, Teal, and Harding (2006): productivity andexit of African manufacturing firms, uses IV

• Levinsohn and Petrin (2003): compare estimationmethods using Chilean data

• Javorcik (2004): FDI and productivity, uses OP• Amiti and Konings (2007): trade liberalization inIndonesia, uses OP

• Aw, Chen, and Roberts (2001): productivity differentialsand firm turnover in Taiwan

• Kortum and Lerner (2000): venture capital andinnovation


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Section 4

Selection


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Selection

• Let dit = 1 if firm in sample.• Standard conditions imply d = 1{ω ≥ ω∗(k)}

• Messes up moment conditions• All estimators based on E[ωitSomething] = 0, observed

data really use E[ωitSomething|dit = 1]• E.g. OLS okay if E[ωit|lit, kit] = 0, but even then,

E[ωit|lit, kit, dit = 1] =E[ωit|lit, kit, ωit ≥ ω∗(kit)]=λ(kit) = 0

• Selection bias negative, larger for capital than labor


Paul Schrimpf

Introduction

Setup


Panel data

Fixed effects

Dynamic panel

Control functions

Applications


Selection in OP model

• Estimate βl as above• Writedit = 1{ξit ≤ ω∗(kit)−ρ(fi,t−1−βkkit−1) = h(kit, fit−1, kit−1)}

• Propensity score Pit ≡ E[dit|kit, fit−1, kit−1]• Similar to before estimate βk, from

yit − βllit =βkkit + g (fit−1 − βkkit−1, Pit) ++ ξit + εit


Paul Schrimpf

Ackerberg,Caves, andFrazer (2015)Collinearity in OP

ACF estimator

Relation to dynamicpanel

Empirical example

Gandhi,Navarro, andRivers (2013)Identificationproblem

Identification fromfirst order conditions

Value added vs grossproduction

Empirical results

Critiques and extensions

• Levinsohn and Petrin (2003): investment often zero, souse other inputs instead of investment to form controlfunction

• Ackerberg, Caves, and Frazer (2015): control functionoften collinear with lit — for it not to be must be firmspecific unobervables affecting lit (but not investment /other input or else demand not invertible and cannotform control function)

• Gandhi, Navarro, and Rivers (2013): relax scalarunobservable in investment / other input demand

• Wooldridge (2009): more efficient joint estimation• Maican (2006) and Doraszelski and Jaumandreu (2013):endogenous productivity


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Section 5

Ackerberg, Caves, and Frazer (2015)


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Ackerberg, Caves, and Frazer(2015): contributions

• Document collinearity problem in OP and Levinsohnand Petrin (2003)

• Need lit, fit(kit, iit) not collinear, i.e. something causesvariation in l, but not k

• Propose alternative estimator• Relates estimator to dynamic panel (Blundell and Bond,2000) approach

• Illustrates estimator using Chilean data

0∗These slides are based on the working paper version Ackerberg,Caves, and Frazer (2006).


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Collinearity in OP 1

• OP assume iit = It(kit, ωit)• Symmetry, parsimony suggest lit = Lt(kit, ωit)• Then lit = Lt(kit, I−1

t (kit, iit)) = gt(kit, iit)

yit = βllit + ft(kit, iit) + εit

lit collinear with ft(kit, iit)• Worse in Levinsohn and Petrin (2003)

• Uses other input mit to form control function

yit =βllit + βkkit + βmmit + ωit + εitmit =Mt(kit, ωit)

• Even less reason to treat labor demand differently thanother input demand


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Collinearity in OP 2• Collinearity still problem with parametric inputdemand

• Plausible models that do not solve collinearity• Input price data

• Must include in control function to preserve scalarunobservable

• Same logic above implies m and l are functions of bothprices, so still collinear

• Adjustmest costs in labor• Need to add lit−1 to control function

• Change in timing assumptions• Measurement error in l (but not m)

• Solves collinearity, but makes βl inconsistent

• Potential model change that removes collinearity• Optimization error in l (but not m)• m chosen, l specific shock revealed, l chosen• OP only: lit chosen at t − 1/2, lit = Lt(ωit−1/2, kit), iit

chosen at t


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

ACF estimator• Idea: like capital, labor is harder to adjust than otherinputs

• Model: lit chosen at time t − 1/2, mit at time t• Implies mt = Mt(kit, lit, ωit)

• Estimation:1 yit = βkkit + βllit + ft(mit, kit, lit)︸︷︷︸

≡Φt(mit,kit,lit)

+εit gives

ωit(βk, βl) = Φit − βkkit − βllit

2 Moments from timing and Markov process for ωit

assumptions:

ωit = E[ωit|ωit−1] + ξit

• E[ξit|kit] = 0 as in OP• E[ξit|lit−1] = 0 from new timing assumption• ξit(βk, βl) as residual from nonparametric regression ofωit on ωit−1

• Can add moments based on E[εit|Iit] = 0


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Relation to dynamic panelestimators

• Both derive moment conditions from assumptionsabout timing and information set of firm

• Dealing with ω• Dynamic panel: AR(1) assumption allows

quasi-differencing• Control function: makes ω estimable function of

observables

• Dynamic panel allows fixed effects, does not makeassumptions about input demand

• Control function allows more flexible process for ωit


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Empirical example

• Chilean plant level data• Compare OLS, FE, LP, ACF, and dynamic panel estimators• LP and ACF using three different inputs (materials,electricity, fuel) for control function

• Results:• 311=food, 321=textiles, 331=wood, 381=metal• Expected biases in OLS and FE• ACF and LP significantly different• ACF less sensitive to which input used for control

function• Dynamic panel closer to ACF than LP, but still significant

differences

TABLE 1Industry 311

Capital Labor Returns to ScaleEstimate SE Estimate SE Estimate SE

OLS 0.336 0.025 1.080 0.042 1.416 0.026FE 0.081 0.038 0.719 0.055 0.800 0.066ACF – M 0.371 0.037 0.842 0.048 1.212 0.034ACF – E 0.379 0.031 0.865 0.047 1.244 0.032ACF – F 0.395 0.033 0.884 0.046 1.279 0.028LP – M 0.455 0.038 0.676 0.037 1.131 0.035LP – E 0.446 0.032 0.764 0.040 1.210 0.034LP – F 0.410 0.032 0.942 0.040 1.352 0.036DP 0.391 0.026 0.987 0.043 1.378 0.028

Industry 321Capital Labor Returns to Scale

Estimate SE Estimate SE Estimate SEOLS 0.256 0.035 0.953 0.056 1.210 0.034FE 0.204 0.068 0.724 0.087 0.927 0.108ACF – M 0.242 0.041 0.893 0.063 1.135 0.040ACF – E 0.272 0.037 0.832 0.060 1.104 0.039ACF – F 0.272 0.038 0.873 0.061 1.145 0.040LP – M 0.320 0.037 0.775 0.059 1.094 0.049LP – E 0.241 0.037 0.978 0.065 1.219 0.047LP – F 0.254 0.039 1.008 0.062 1.262 0.048DP 0.320 0.042 0.837 0.064 1.157 0.041


Estimate SE Estimate SE Estimate SEOLS 0.236 0.047 1.038 0.074 1.274 0.052FE -0.028 0.103 0.897 0.095 0.869 0.136ACF – M 0.196 0.064 0.923 0.085 1.119 0.076ACF – E 0.195 0.065 0.897 0.088 1.092 0.073ACF – F 0.212 0.062 0.915 0.086 1.127 0.075LP – M 0.352 0.056 0.678 0.077 1.030 0.072LP – E 0.305 0.059 0.786 0.086 1.090 0.075LP – F 0.241 0.052 0.993 0.079 1.234 0.071DP 0.252 0.054 0.998 0.073 1.249 0.061


Estimate SE Estimate SE Estimate SEOLS 0.223 0.025 1.160 0.045 1.383 0.033FE 0.036 0.056 0.783 0.077 0.819 0.098ACF – M 0.262 0.033 1.010 0.053 1.273 0.040ACF – E 0.250 0.030 1.002 0.053 1.252 0.040ACF – F 0.259 0.028 1.022 0.051 1.280 0.039LP – M 0.342 0.038 0.803 0.053 1.145 0.056LP – E 0.306 0.033 0.944 0.047 1.251 0.044LP – F 0.265 0.031 1.090 0.049 1.355 0.041DP 0.275 0.034 1.056 0.053 1.331 0.037

TABLE 2Industry 311 Industry 321

M E F M E FACF vs OLS ACF vs OLS

K 0.111 0.040 0.010 K 0.585 0.192 0.192L 1.000 1.000 1.000 L 0.970 1.000 0.996

RTS 1.000 1.000 1.000 RTS 0.998 1.000 0.998

ACF vs LP ACF vs LPK 1.000 1.000 0.707 K 0.982 0.052 0.070L 0.000 0.000 0.899 L 0.048 0.998 1.000

RTS 0.000 0.061 0.990 RTS 0.198 1.000 1.000

ACF vs DP ACF vs DPK 0.737 0.788 0.505 K 1.000 0.992 0.992L 1.000 1.000 1.000 L 0.052 0.511 0.084

RTS 1.000 1.000 1.000 RTS 0.820 0.996 0.669

Industry 331 Industry 381M E F M E F

ACF vs OLS ACF vs OLSK 0.892 0.840 0.830 K 0.060 0.058 0.054L 0.974 0.990 0.984 L 1.000 1.000 1.000

RTS 1.000 1.000 1.000 RTS 1.000 1.000 1.000

ACF vs LP LP vs ACFK 1.000 1.000 0.860 K 0.996 0.980 0.683L 0.000 0.024 0.876 L 0.000 0.072 0.910

RTS 0.056 0.431 0.984 RTS 0.002 0.323 0.984

ACF vs DP ACF vs DPK 0.962 0.922 0.884 K 0.834 0.916 0.892L 0.940 0.986 0.962 L 0.852 0.844 0.649

RTS 1.000 1.000 0.998 RTS 0.984 0.992 0.934

Note: Value is the % of bootstrap reps where ACF coeff is less than OLS, LP, or DP coef. A valueeither above 0.95 or below 0.05 indicates that coefficients are significantly different from each other.


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Section 6

Gandhi, Navarro, and Rivers (2013)


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Gandhi, Navarro, and Rivers(2013)

• Show that control function method is notnonparametrically identified when there are flexibleinputs

• Propose alternate estimate that uses data on inputshares and information from firm’s first order condtiion

• Show that value-added and gross output productionfunctions are incompatible

• Application to Colombia and Chile


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Assumptions

1 Hicks neutral productivity Yjt = eωjt+εjtFt(Ljt,Kjt,Mjt)2 ωjt Markov, εjt i.i.d.3 Kjt and Ljt determined at t− 1, Mjt determined flexibly at

t• K and L play same role in the model, so after this slide I

will drop L

4 Mjt = Mt(Ljt,Kjt, ωjt), monotone in ωjt


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Reduced form• Let h(ωjt−1) = E[ωjt|ωjt−1], ηjt = ωjt − h(ωjt−1)• log output

yjt =ft(kjt,mjt) + ωjt + εjt=ft(kjt,mjt) + h(M−1

t−1(kjt−1,mjt−1))︸︷︷︸=ht−1(kjt−1,mjt−1)

+ηjt + εjt

• Assumptions imply

E[ηjt| kjt, kjt−1,mjt−1, ...kj1,mj1︸︷︷︸=Γjt

] = 0

• Reduced form

E[yjt|Γjt] =E[ft(kjt,mjt)|Γjt] + ht−1(kjt−1,mjt−1) (1)

• Identification: given observed E[yjt|Γjt] is there a uniqueft, ht−1 that satisfies (3)?


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Example: Cobb-Douglas 1

• Let ft(k,m) = βkk + βmm• Assume firm is takes prices as given• First order condition for m gives

m = constant + βk1 − βm

k + 11 − βm

ω

• Put into reduced form

E[yjt|Γjt] =C + βk1 − βm

kjt + βm1 − βm

E[ωjt|Γjt] + ht−1(kjt−1,mjt−1)

(2)

• ω Markov and ωjt−1 = M−1t−1(kjt−1,mjt−1) implies

E[ωjt|Γjt] =E[ωjt|ωjt−1 = M−1t−1(kjt−1,mjt−1)] =

=ht−1(kjt−1,mjt−1)


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Example: Cobb-Douglas 2

• Which leaves

E[yjt|Γjt] =constant + βk1 − βm

kjt + 11 − βm

ht−1(kjt−1,mjt−1)

(3)

from which βk, βm are not identified

• Rank condition fails, E[mjt|Γjt] is colinear withht−1(kjt−1,mjt−1)

• After conditioning on kjt, kjt−1,mjt−1, only variation inmjt is from ηjt, but this is uncorrelated with theinstruments


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Identification from first orderconditions 1

• Since m flexible, it satisfies a simple static first ordercondition,

ρt =pt∂Ft∂ME[eεjt ]eωjt

logρt = log pt + log ∂Ft∂M (kjt,mjt) + log E[eεjt ] + ωjt

• Problem: prices often unobserved, endogenous ω• Solution: difference from output equation to eliminateω, rearrange so that it involves only the value ofmaterials and the value of output (which are oftenobserved)

sjt︸︷︷︸≡log

ρtMjtptYjt

= logGt(kjt,mjt)︸︷︷︸≡

(Mt

∂Ft∂M

)/Ft

+ log E[eεjt ]︸︷︷︸E

−εjt


Paul Schrimpf


ACF estimator


Empirical example




Empirical results


• Identifies elasticity up to scale, GtE and εjt whichidentifie E

• Integrating,

∫ mjt

m0

Gt(kjt,m)/m = ft(kjt,mjt) + ct(kjt)

identifies f up to location• Output equation

yjt =∫ mjt

m0

Gt(kjt,m)/m − ct(kjt) + ωjt + εjt

−ct(kjt) + ωjt = yjt −∫ mjt

m0

Gt(kjt,m)/m − εjt︸︷︷︸

≡Yjt


Paul Schrimpf


ACF estimator


Empirical example




Empirical results


where the things on the right have already beenidentified

• Identify ct from

Yjt = − ct(kjt) + ht(Yjt−1, kjt−1) + ηjt


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Value added vs gross production

• Value added:

VAjt =ptYjt − ρtMjt

=ptFt(Kjt,Mt(Kjt, ωjt))eωjt+εjt − ρtMt(Kjt, ωjt)

• Envelope theorem implieselasticityYeω ≈ elasticityVAeω (1 − ρtMjt

ptYjt)

Problems• Production Hicks-neutral productivity does not implyvalue-added Hicks-neutral productivity

• Ex-post shocks εjt not accounted for in approximation


Paul Schrimpf


ACF estimator


Empirical example




Empirical results

Empirical results

• Look at tables• Value-added estimates imply much more productivitydispersion than gross (90-10) ratio of 4 vs 2


Paul Schrimpf

Grieco andMcDevitt(2017)

Amiti andKonings (2007)

DoraszelskiandJaumandreu(2013)

References

Part III

Selected applications andextensions


Paul Schrimpf




References

7 Grieco and McDevitt (2017)

8 Amiti and Konings (2007)

9 Doraszelski and Jaumandreu (2013)


Paul Schrimpf




References

Section 7

Grieco and McDevitt (2017)


Paul Schrimpf




References

Grieco and McDevitt (2017)

https://www.ftc.gov/sites/default/files/documents/public_events/fifth-annual-microeconomics-conference/grieco-p_0.pdf






Paul Schrimpf




References

Model details

• Timing:1 Quality chosen qit = q(kit, ℓit, xit, ωi,t−b)2 Production occurs, ωit revealed to firm3 Hiring chosen ℓi,t+1 − ℓit = hit = h(kit, ℓit, xit, ωit)

• ω follows Markov process:

E[ωi,t−b|Ii,t−b] = E[ωi,t−b|ωi,t−1] & E[ωit|Ii,t] = E[ωit|ωi,t−b

and ωit = E[ωit|ωi,t−1] + ηit = g(ωi,t−1) + ηit


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References

Moment conditions• Control function assumption: hiring is a monotonicfunction of ω

hit = h(kit, ℓit, xit, ωit)

soωit = h−1(kit, ℓit, xit, hit)

• Substitute into production function:

yit =αqqit + βkkit + βℓℓit + h−1(kit, ℓit, xit, hit) + εityit =αqqit + Φ(kit, ℓit, xit, hit) + εit

• Evolution of ω

ωit =yit − αqqit − βkkit − βℓℓit − εit = g(ωi,t−1) + ξit=g(Φ(kit−1, ℓit−1, xit−1, hit−1) − βℓℓit−1 − βkkit−1) + ξit

• Moment conditions:

E[εit|qit, kit, ℓit, xit, hit] = 0

E[ξit|kit, ℓit, xit, kit−1, ℓit−1, xit−1] = 0


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References

Estimation

1 Estimate, αq, Φ from

yit = αqqit + Φ(kit, ℓit, xit, hit) + εit

by semiparametric regression2 Estimate βk, βℓ

• Let ω(β)it = Φ(kit, ℓit, xit, hit) − βkkit − βℓℓit• For each β estimate g()

yit − αqit − βkkit − βℓℓit = g(ω(β)it−1) + ξit + εit︸︷︷︸≡ηit(β)

by nonparametric regression• Minimize empirical moment condition for η

β = arg min( 1NT

∑

it

kitηit(β))2 + ( 1NT

∑

it

ℓitηit(β))2


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References

• Should hemoglobin level be controlled for whenmeasuring quality?

• Anemia (low hemoglobin) is risk-factor for infection• Anemia can be treated through diet, iron supplements

(pills or IV), EPO, etc• Are dialysis facilities responsible for this treatment?• In 2006-2014 data average full-time dieticiens = 0.5,

average part-time = 0.6


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References

Measurement error• Simplified setup:

y = α q + ε

q unobserved, observe q = q + εq with E[εq|q = 0]• Then plim αOLS = α Var(q)

Var(q)+Var(εq)• If d = d(q) + εd with E[εd|q] = 0 and E[εdεq] = 0, then

plim α IV = α

• Is E[εdεq] = 0 a good assumption?• Paper argues E[εdεq] = O(1/(patients per facility))


Paul Schrimpf




References

• Estimation details:Step 1: Estimate αq

yjtE[y|hjt, ijt, kjt, ℓjt, xjt] = αq(qjtE[q|hjt, ijt, kjt, ℓjt, xjt]) + εjt

• Drop observations with hjt = 0 (not invertible)• Okay here, because selecting on ω, and residual, εjt is

uncorrelated with ω• Problematic in last step? No, see footnote 49

Step 2: Estimate βk, βℓ from

yjt + αq + βkkjt + βℓℓjt = g(ωjt−1(β)) + ηjt + εjt

• Only have ωjt−1(β) when hjt−1 = 0, okay because εjt andηjt are uncorrelated with ωjt−1, would be problem ifusing ωjt

• Nothing about selection — number of centers, 4270, vscenter-years, 18295, implies there must be entry and exit


Paul Schrimpf




References

Results

• Estimate implications:• Holding inputs constant, reducing infections by one per

year requires reducing output by 1.5 patients• Cost of treatment ≈ $50, 000, so one infection

≈ $75, 000• Holding output constant, reducing infections by one per

year requires hiring 1.8 more staff• Cost of staff ≈ $42, 000, so one infection ≈ $75, 000


Paul Schrimpf




References

• Would like to see some results related to productivitydispersion e.g.

• Decompose variation in infection rate into: productivityvariation, incentive variation, quality-quantity choices,and random shocks

• Compare strengthening incentives vs closing leastproductive facilities as policies to increase quality


Paul Schrimpf




References

Section 8

Amiti and Konings (2007)


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References

Overview

• Effect of reducing input and output tariffs onproductivity

• Reducing output tariffs affects productivity byincreasing competition

• Reducing input tariffs affects productivity throughlearning, variety, and quality effects

• Previous empirical work focused on output tariffs;might be estimating combined effect

• Input tariffs hard to measure; with Indonesian data onplant-level inputs can construct plant specific inputtariff


Paul Schrimpf




References

Methodology

• Estimate TFP using Olley-Pakes• Output measure is revenue ⇒ may confound

productivity and markups

• Estimate relation between TFP and tariffs

log(TFPit) =γ0 + αi + αtl(i) + γ1(output tariff)tk(i)++ γ2(input tariff)tk(i) + εit (4)

• k(i) = 5-digit (ISIC) industry of plant i• l(i) = island of plant i

• Explore robustness to:• Different productivity measure• Specification of 4• Endogeneity of tariffs

http://unstats.un.org/unsd/cr/registry/regcst.asp?Cl=27&Lg=1


Paul Schrimpf




References

Data and tariff measure

• Indonesian annual manufacturing census of 20+employee plants 1991-2001, after cleaning 15, 000 firmsper year

• Input tariffs:• Data on tariffs on goods, τjt, but also need to know

inputs• 1998 only: have data on inputs, use to construct input

weights at industry level, wjk• Industry input tariff =

∑j wjkτjt


Paul Schrimpf




References

Results

• Look at tables• Input tariffs have larger effect than output, γ1 ≈ −0.07,γ2 ≈ −0.44

• Robust to:• Productivity measure• Tariff measure• Including/excluding Asian financial crisis

• Less robust to instrumenting for tariffs• Qualitatively similar, but larger coefficient estimates

• Explore channels for productivity change• Markups (maybe), product switching/addition (no),

foreign ownership (no), exporters (no)


Paul Schrimpf




References

Section 9

Doraszelski and Jaumandreu (2013)


Paul Schrimpf




References

Overview

• Estimable model of endogenous productivity, whichcombines:

• Knowledge capital model of R&D• OP & LP productivity estimation

• Application to Spanish manufacturers focusing on R&D• Large uncertainty (20%-60% or productivity

unpredictable )• Complementarities and increasing returns• Return to R&D larger than return to physical capital

investment


Paul Schrimpf




References

Model (simplified) 1

• Cobb-Douglas production:

yit = βllit + βkkit + ωit + εit

• Controlled Markov process for productivity,p(ωit+1|ωit, rit),

ωit = g(ωit−1, rit−1) + ξit

• Labor flexible and non-dynamic• Value function

V(kt, ωt, ut) = maxi,r

Π(kt, ωt) − Ci(i, ut) − Cr(r, ut)+

+ 11 + ρE [V(kt+1, ωt+1, ut+1)|kt, ωt, i, r, ut]


Paul Schrimpf




References

Model (simplified) 2• u scalar or vector valued shock• u not explicitly part of model, but identification

discussion (especially p10 and footnote 6) implicitlyadds it

• u independent of? k, l? across time?

• Control function incorporating Cobb-Douglasassumption (and perfect competition):

ωit = h(lit, kit,wit−pit;β) = λ0+(1−βl)lit−βkkit+(wit−pit)

• Form moments based on

yit = βllit+βkkit+g (h(lit−1, kit−1,wit−1 − pit−1;β), rit−1)+ξit+εitεit

• No collinearity because:• Parametric h• Variation in k, r due to u

• Estimated model adds


Paul Schrimpf




References

Model (simplified) 3

• Material input instead of labor for control function• h based on imperfect competition

• Comparison to OP, LP, ACF


Paul Schrimpf




References

Results

• Look at tables and figures• Large uncertainty (20%-60% or productivityunpredictable )

• Complementarities and increasing returns• Return to R&D larger than return to physical capital


Paul Schrimpf




References

Ackerberg, D., K. Caves, and G. Frazer. 2006. “Structuralidentification of production functions.” URLhttp://mpra.ub.uni-muenchen.de/38349/.

Ackerberg, D., C. Lanier Benkard, S. Berry, and A. Pakes.2007. “Econometric tools for analyzing marketoutcomes.” Handbook of econometrics 6:4171–4276. URLhttp://www.sciencedirect.com/science/article/pii/S1573441207060631. Ungated URLhttp://people.stern.nyu.edu/acollard/Tools.pdf.

Ackerberg, Daniel A., Kevin Caves, and Garth Frazer. 2015.“Identification Properties of Recent Production FunctionEstimators.” Econometrica 83 (6):2411–2451. URLhttp://dx.doi.org/10.3982/ECTA13408.

Aguirregabiria, Victor. 2017. “Empirical IndustrialOrganization: Models, Methods, and Applications.” URLhttp://www.individual.utoronto.ca/vaguirre/courses/eco2901/teaching_io_toronto.html.

http://mpra.ub.uni-muenchen.de/38349/

http://www.sciencedirect.com/science/article/pii/S1573441207060631


http://people.stern.nyu.edu/acollard/Tools.pdf

http://dx.doi.org/10.3982/ECTA13408

http://www.individual.utoronto.ca/vaguirre/courses/eco2901/teaching_io_toronto.html

http://www.individual.utoronto.ca/vaguirre/courses/eco2901/teaching_io_toronto.html


Paul Schrimpf




References

Amiti, Mary and Jozef Konings. 2007. “Trade Liberalization,Intermediate Inputs, and Productivity: Evidence fromIndonesia.” The American Economic Review 97 (5):pp.1611–1638. URLhttp://www.jstor.org/stable/30034578.

Aw, Bee Yan, Xiaomin Chen, and Mark J. Roberts. 2001.“Firm-level evidence on productivity differentials andturnover in Taiwanese manufacturing.” Journal ofDevelopment Economics 66 (1):51 – 86. URLhttp://www.sciencedirect.com/science/article/pii/S0304387801001559.

Blundell, R. and S. Bond. 2000. “GMM estimation withpersistent panel data: an application to productionfunctions.” Econometric Reviews 19 (3):321–340. URLhttp://www.tandfonline.com/doi/pdf/10.1080/07474930008800475.

http://www.jstor.org/stable/30034578



http://www.tandfonline.com/doi/pdf/10.1080/07474930008800475

http://www.tandfonline.com/doi/pdf/10.1080/07474930008800475


Paul Schrimpf




References

Bond, Steve and Måns Söderbom. 2005. “Adjustment costsand the identification of Cobb Douglas productionfunctions.” IFS Working Papers W05/04, Institute forFiscal Studies. URLhttp://ideas.repec.org/p/ifs/ifsewp/05-04.html.

Doraszelski, Ulrich and Jordi Jaumandreu. 2013. “R&D andProductivity: Estimating Endogenous Productivity.” TheReview of Economic Studies 80 (4):1338–1383. URLhttp://restud.oxfordjournals.org/content/80/4/1338.abstract.

Foster, L., J.C. Haltiwanger, and C.J. Krizan. 2001. “Aggregateproductivity growth. Lessons from microeconomicevidence.” In New developments in productivity analysis.University of Chicago Press, 303–372. URLhttp://www.nber.org/chapters/c10129.pdf.

http://ideas.repec.org/p/ifs/ifsewp/05-04.html

http://restud.oxfordjournals.org/content/80/4/1338.abstract

http://restud.oxfordjournals.org/content/80/4/1338.abstract

http://www.nber.org/chapters/c10129.pdf


Paul Schrimpf




References

Foster, Lucia, John Haltiwanger, and C. J. Krizan. 2006.“Market Selection, Reallocation, and Restructuring in theU.S. Retail Trade Sector in the 1990s.” The Review ofEconomics and Statistics 88 (4):pp. 748–758. URLhttp://www.jstor.org/stable/40043032.

Gandhi, A., S. Navarro, and D. Rivers. 2013. “On theIdentification of Production Functions: HowHeterogeneous is Productivity?” URL https://sites.google.com/site/econsalvador/Research/production_9_25_13_FULL.pdf?attredirects=0.

Grieco, Paul L. E. and Ryan C. McDevitt. 2017. “Productivityand Quality in Health Care: Evidence from the DialysisIndustry.” The Review of Economic Studies 84 (3):1071–1105.URL http://dx.doi.org/10.1093/restud/rdw042.


https://sites.google.com/site/econsalvador/Research/production_9_25_13_FULL.pdf?attredirects=0



http://dx.doi.org/10.1093/restud/rdw042


Paul Schrimpf




References

Javorcik, Beata Smarzynska. 2004. “Does Foreign DirectInvestment Increase the Productivity of Domestic Firms?In Search of Spillovers through Backward Linkages.” TheAmerican Economic Review 94 (3):pp. 605–627. URLhttp://www.jstor.org/stable/3592945.

Kortum, Samuel and Josh Lerner. 2000. “Assessing theContribution of Venture Capital to Innovation.” The RANDJournal of Economics 31 (4):pp. 674–692. URLhttp://www.jstor.org/stable/2696354.

Levinsohn, James and Amil Petrin. 2003. “EstimatingProduction Functions Using Inputs to Control forUnobservables.” The Review of Economic Studies 70 (2):pp.317–341. URL http://www.jstor.org/stable/3648636.

Maican, F.G. 2006. “Productivity dynamics, r&d, andcompetitive pressure.” ECONOMIC STUDIES DEPARTMENTOF ECONOMICS SCHOOL OF BUSINESS, ECONOMICS ANDLAW UNIVERSITY OF GOTHENBURG .





Paul Schrimpf




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Olley, G.S. and A. Pakes. 1996. “The dynamics of productivityin the telecommunications equipment industry.”Econometrica 64 (6):1263–1297. URLhttp://www.jstor.org/stable/2171831.

Söderbom, Måns, Francis Teal, and Alan Harding. 2006. “TheDeterminants of Survival among African ManufacturingFirms.” Economic Development and Cultural Change54 (3):pp. 533–555. URLhttp://www.jstor.org/stable/10.1086/500030.

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http://onlinelibrary.wiley.com/doi/10.1111/j.1467-6419.2010.00631.x/full



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