Identifying Factor Productivity by Dynamic Panel Data and Control

Function Approaches: A Comparative Evaluation for EU Agriculture

by Martin Petrick and Mathias Kloss

Mathias Kloss

Economics Cluster Seminar Wageningen UR | 3 October 2013

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Stagnating agricultural productivity

growth in Europe

Source: Coelli & Rao 2005, p. 127.

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Stagnating agricultural productivity

growth in the EU

Source: Piesse & Thirtle 2010, p. 171.

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Outline

• An insight into recent innovations in production function estimation

Comparative evaluation of 2 recently proposed production function estimators

How plausible are these for the case of agriculture?

• Unique and current set of production elasticities for 8 farm-level data sets at the EU country level

• Some evidence on shadow prices

• Conclusions

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Two problems of identification

A general production function:

𝑦𝑖𝑡 = 𝑓 𝐴𝑖𝑡 , 𝐿𝑖𝑡 , 𝐾𝑖𝑡, 𝑀𝑖𝑡 + 𝜔𝑖𝑡 + 휀𝑖𝑡

with

y Output

A Land

L Labour

K Capital (fixed)

M Materials (Working capital)

𝜔 Farm- & time-specific factor(s) known to farmer, unobserved by analyst

휀 Independent & identically distributed noise

i, t Farm & time indices

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Two problems of identification

Collinearity problem • If variable and intermediate inputs are chosen simultaneously factor use across farms varies only with 𝜔 (Bond & Söderbom 2005; Ackerberg et al. 2007)

Production elasticities for variable inputs not identified!

Endogeneity problem • 𝜔 likely correlated with other input choices • Need to take ω into account in order to identify 𝑓, as 𝜔𝑖𝑡 + 휀𝑖𝑡

is not i.i.d No identification of 𝑓 possible if ω is not taken into account!

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Traditional approaches to solve the

identification problems

1. Ordinary Least Squares: forget it. Assume ω is non-existent.

– Bias: elasticities of flexible inputs too high (capture ω)

2. “Within” (fixed effects): assume we can decompose ω in

– Assumption plausible?

– Bias: elasticities too low as signal-to-noise is reduced

– Collinearity problem not adressed

time-specific shock

farm-specific fixed effect

remaining farm- and time specific shock

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Recent solutions to solve the

identification probems

3. Dynamic panel data modelling

– current (exogenous) variation in input use by lagged adjustment to

past productivity shocks (Arellano & Bond 1991; Blundell & Bond 1998)

• feasible if input modifications s.t. adjustment costs (Bond & Söderbom 2005)

• plausible for many factors (e.g. labour, land or capital ) but less so for intermediate inputs

– one way to allow costly adjustment: 𝜐𝑖𝑡 = 𝜌𝜐𝑖𝑡−1 + 𝑒𝑖𝑡, with 𝜌 < 1

– dynamic production function with lagged levels & differences of inputs

as instruments in a GMM framework (Blundell & Bond 2000)

– Bias: hopefully small. Adresses both problems if instruments induce

sufficient exogenous variation

𝜌 autoregressive parameter

𝑒𝑖𝑡 mean zero innovation

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Recent solutions to solve the

identification probems

4. Control Function approach

– assume ω evolves along with observed firm characteristics (Olley/Pakes

1996, Econometrica)

– materials a good control candidate for ω (Levinsohn & Petrin 2003)

– further assume: (a) M is monotonically increasing in ω & (b) factor

adjustment in one period

1. Estimate “clean” A & L by controlling ω with M & K

2. Recover M & K from additional timing assumptions

– solves endogeneity problem if control function fully captures ω • productivity enhancing reaction to shocks less input use violating (a)

• some factors (e.g. soil quality) might evolve slowly violating (b)

– collinearity problem not solved • Solutions by Ackerberg et al. (2006) and Wooldridge (2009)

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Data

FADN individual farm-level panel data made available by EC

Field crop farms (TF1) in Denmark, France, Germany East, Germany

West, Italy, Poland, Slovakia & United Kingdom

T=7 (2002-2008) (only 2006-2008 for PL & SK)

Cobb Douglas functional form (Translog examined as well)

Annual fixed effects included via year dummies

Estimation with Stata12 using xtabond2 (Roodman 2009) & levpet

estimator (Petrin et al. 2004)

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Cobb Douglas production elasticities

Blundell/Bond

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Cobb Douglas production elasticities

LevPet

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Elasticity of materials LevPet

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Elasticity of materials:

Comparison of estimators (LevPet)

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Returns to scale LevPet

Point estimates

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Returns to scale LevPet

Not sig. different from 1 displayed as 1

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Examining the Translog specification

• OLS: Highly implausible results at sample means

• Within: Interaction terms not sig. in the majority of cases

• BB: No straightforward implementation, as assumption of linear

addivitity of the fixed effects is violated

• LevPet: No straightforward implementation, as M & K are assumed to

be additively separable

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-10

0-5

00

50

10

015

020

0

Sha

dow

price o

f w

ork

ing c

apita

l (%

)

DK FR DEE DEW IT PL SK UKexcludes outside values

Shadow interest rate of materials (%):

distributions per country

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-10

010

20

30

40

50

60

Sha

dow

wage

(E

UR

/hou

r)

DK FR DEE DEW IT PL SK UKexcludes outside values

Shadow wage (€/h): distributions per country

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Conclusions

• Adjustment costs relevant for important inputs in agricultural production – LP and BB identification strategies a priori plausible

• LP plausible results combined with FADN data but is a second-best choice – corrected upward (downward) bias in OLS (Whithin-OLS) regressions

– conceptual problems in identifying flexible factors

• BB only performed well with regard to materials

• Materials most important production factor in EU field crop farming (prod.

elasticity of ~0.7)

• Fixed capital, land and labour usually not scarce

• Shadow price analysis reveals heterogenous picture – Credit market imperfections: Funding constraints (DEE, IT) vs. overutilisation

(DEW, DK)? Effects of financial crisis?

– Low labour remuneration (except DK)

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Future research

• Estimated shadow prices as starting point for analysis of

drivers & impacts

• Extension to other production systems (e.g., dairy)

• Examine other identification strategies

• Wooldridge (2009) is a promising candidate

• unifies LP in a single-step efficiency gains

• solves collinearity problem

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The END.

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Appendix

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Blundell/Bond in detail

• Substituting 𝑣𝑖𝑡 = 𝜌𝑣𝑖𝑡−1 + 𝑒𝑖𝑡 and 𝜔𝑖𝑡 = 𝛾𝑡 + 𝜂𝑖 + 𝑣𝑖𝑡 into the production

function implies the following dynamic production function

𝑦𝑖𝑡 = 𝛼𝑋𝑥𝑖𝑡 − 𝛼𝑋𝜌𝑥𝑖𝑡−1 + 𝜌𝑦𝑖𝑡−1 + 𝛾𝑡 − 𝜌𝛾𝑡−1𝑋

+ 1 − 𝜌 𝜂𝑖 + 휀𝑖𝑡

• Alternatively:

𝑦𝑖𝑡 = 𝜋1𝑋𝑋

𝑥𝑖𝑡 + 𝜋2𝑋𝑋

𝑥𝑖𝑡−1 + 𝜋3𝑦𝑖𝑡−1 + 𝛾𝑡∗ + 𝜂𝑖

∗ + 휀𝑖𝑡∗

subject to the common factor restrictions that 𝜋2𝑋 = −𝜋1𝑋𝜋3 for all X.

(allows recovery of input elasticities)

• Farm-specific fixed effects removed by FD, allows transmission of 𝜔 to

subsequent periods

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Olley Pakes and Levinsohn/Petrin in

detail

• Log investment (𝑖𝑖𝑡) as an observed characteristic driven by 𝜔𝑖𝑡:

• 𝑖𝑖𝑡 = 𝑖𝑡 𝜔𝑖𝑡 , 𝑘𝑖𝑡 and 𝑘𝑖𝑡 evolves 𝑘𝑖𝑡+1 = 1 − 𝛿 𝑘𝑖𝑡 + 𝑖𝑖𝑡, with 𝛿=

depreciation rate

• Given monotonicity we can write 𝜔𝑖𝑡 = ℎ𝑡 𝑖𝑖𝑡 , 𝑘𝑖𝑡

• Assume: 𝜔𝑖𝑡 = 𝐸 𝜔𝑖𝑡|𝜔𝑖𝑡−1 + 𝜉𝑖𝑡,

– 𝜉𝑖𝑡 is an innovation uncorrelated with 𝑘𝑖𝑡 used to identify capital

coefficient in the second stage

• Idea

1. control for the influence of k and ω

2. recover the true coefficient of k as well as ω in the second stage

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Olley/Pakes and Levinsohn/Petrin

continued

• Plugging 𝜔𝑖𝑡 = ℎ𝑡 𝑖𝑖𝑡 , 𝑘𝑖𝑡 into production function gives

𝑦𝑖𝑡 = 𝛼𝐴𝑎𝑖𝑡 + 𝛼𝐿𝑙𝑖𝑡 + 𝛼𝑀𝑚𝑖𝑡 + 𝜙𝑡 𝑖𝑖𝑡 , 𝑘𝑖𝑡 + 휀𝑖𝑡

• 𝜙 is approximated by 2nd and 3rd order polynomials of i and k in the first stage

• Here parameters of variable factors are obtained by OLS

• Second stage:

1. using 𝜙𝑡 and candidate value for 𝛼𝐾, 𝜔 𝑖𝑡 is computed for all t

2. Regress 𝜔 𝑖𝑡 on its lagged values to obtain a consistent predictor of that part of ω that is free of the innovation ξ (“clean” 𝜔𝑖𝑡)

3. using first stage parameters together with prediction of the “clean” 𝜔𝑖𝑡 and 𝐸 𝑘𝑖𝑡𝜉𝑖𝑡 = 0 consistent estimate of 𝛼𝐾 by minimum distance

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Elasticity of materials:

Comparison of estimators (BB)

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Comparison of estimators - East German field

crop farms: marginal return on materials

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0-9

5-9

0-8

5-8

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5-7

0-6

5-6

0-5

5

Sha

dow

price o

f fixe

d c

apita

l (%

)

DK FR DEE DEW IT PL SK UKexcludes outside values

Shadow interest rate of fixed capital (%):

distributions per country

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-.000

50

.000

5

Sha

dow

price o

f la

nd

(E

UR

/ha)

DK FR DEE DEW IT PL SK UKexcludes outside values

Shadow land rent (€/ha): distributions per

country

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The Wooldridge-Levinsohn-Petrin

approach

• Unifies the Olley/Pakes and Levinsohn/Petrin procedure within a

IV/GMM framework

– Estimation in a single step

– Analytic standard errors

– Implementation of translog is straightforward

• Suppose for parsimony:

𝑦𝑖𝑡 = 𝛼 + 𝛽1𝑙𝑖𝑡 + 𝛽2𝑘𝑖𝑡 +𝜔𝑖𝑡 + 𝑒𝑖𝑡, and remember

𝜔𝑖𝑡 = ℎ 𝑘𝑖𝑡 , 𝑚𝑖𝑡 ,

– Now assume:

𝐸 𝑒𝑖𝑡|𝑙𝑖𝑡 , 𝑘𝑖𝑡 , 𝑚𝑖𝑡 , 𝑙𝑖,𝑡−1, 𝑘𝑖,𝑡−1 , 𝑚𝑖,𝑡−1, … , 𝑙𝑖1, 𝑘𝑖1 , 𝑚𝑖1 = 0

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The Wooldridge-Levinsohn-Petrin

approach

• Again, assume: 𝜔𝑖𝑡 = 𝐸 𝜔𝑖𝑡|𝜔𝑖𝑡−1 + 𝜉𝑖𝑡 and

𝐸 𝜔𝑖𝑡|𝑘𝑖𝑡 , 𝑙𝑖,𝑡−1, 𝑘𝑖,𝑡−1 , 𝑚𝑖,𝑡−1, … , 𝑙𝑖1, 𝑘𝑖1 , 𝑚𝑖1

= 𝐸 𝜔𝑖𝑡|𝜔𝑖𝑡−1 = 𝑓 𝜔𝑖𝑡−1 = 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1,

• Plugging into the production function gives

𝑦𝑖𝑡 = 𝛼 + 𝛽1𝑙𝑖𝑡 + 𝛽2𝑘𝑖𝑡 + 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1, + 휀𝑖𝑡

where 휀𝑖𝑡 = 𝜉𝑖𝑡 + 𝑒𝑖𝑡.

• Now, we have two equations to identify the parameters

𝑦𝑖𝑡 = 𝛼 + 𝛽1𝑙𝑖𝑡 + 𝛽2𝑘𝑖𝑡 + ℎ 𝑘𝑖𝑡 , 𝑚𝑖𝑡 + 𝑒𝑖𝑡

𝑦𝑖𝑡 = 𝛼 + 𝛽1𝑙𝑖𝑡 + 𝛽2𝑘𝑖𝑡 + 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1, + 휀𝑖𝑡

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The Wooldridge-Levinsohn-Petrin

approach

• And

𝐸 𝑒𝑖𝑡|𝑙𝑖𝑡 , 𝑘𝑖𝑡 , 𝑚𝑖𝑡 , 𝑙𝑖,𝑡−1, 𝑘𝑖,𝑡−1 , 𝑚𝑖,𝑡−1, … , 𝑙𝑖1, 𝑘𝑖1 , 𝑚𝑖1 = 0

𝐸 휀𝑖𝑡|𝑘𝑖𝑡 , 𝑙𝑖,𝑡−1, 𝑘𝑖,𝑡−1 , 𝑚𝑖,𝑡−1, … , 𝑙𝑖1, 𝑘𝑖1 , 𝑚𝑖1 = 0.

• Unknown function ℎ approximated by low-order polynomial and 𝑓

might be a random walk with drift.

• Estimation:

– Both equations within a GMM framework, or

– Second equation by IV-estimation and instrument for 𝑙 (Petrin and

Levinsohn 2012)