This document summarizes a presentation on identifying factor productivity in EU agriculture using dynamic panel data and control function approaches. The presentation compares these two recently proposed production function estimators and evaluates their plausibility for agricultural data. Estimates from applying both methods to farm-level panel data from 8 EU countries find that materials is the most important production factor in EU field crop farming, with an estimated production elasticity of around 0.7. The estimates of factor prices vary substantially across countries.

1. 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 + 𝜀𝑖𝑡
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
𝜀 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 + 𝜀𝑖𝑡
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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-100-50050100150200
Shadowpriceofworkingcapital(%)
DK FR DEE DEW IT PL SK UK
excludes outside values
Shadow interest rate of materials (%):
distributions per country

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-100102030405060
Shadowwage(EUR/hour)
DK FR DEE DEW IT PL SK UK
excludes 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 = 𝛼 𝑋 𝑥𝑖𝑡 − 𝛼 𝑋 𝜌𝑥𝑖𝑡−1 + 𝜌𝑦𝑖𝑡−1 + 𝛾𝑡 − 𝜌𝛾𝑡−1
𝑋
+ 1 − 𝜌 𝜂𝑖 + 𝜀𝑖𝑡
• Alternatively:
𝑦𝑖𝑡 = 𝜋1𝑋
𝑋
𝑥𝑖𝑡 + 𝜋2𝑋
𝑋
𝑥𝑖𝑡−1 + 𝜋3 𝑦𝑖𝑡−1 + 𝛾𝑡
∗
+ 𝜂𝑖
∗
+ 𝜀𝑖𝑡
∗
subject to the common factor restrictions that 𝜋2𝑋
= −𝜋1𝑋
𝜋3
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 = 𝑖 𝑡 𝜔𝑖𝑡, 𝑘𝑖𝑡 and 𝑘𝑖𝑡 evolves 𝑘𝑖𝑡+1 = 1 − 𝛿 𝑘𝑖𝑡 + 𝑖𝑖𝑡, with 𝛿=
depreciation rate
• Given monotonicity we can write 𝜔𝑖𝑡 = ℎ 𝑡 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 = ℎ 𝑡 𝑖𝑖𝑡, 𝑘𝑖𝑡 into production function gives
𝑦𝑖𝑡 = 𝛼 𝐴
𝑎𝑖𝑡 + 𝛼 𝐿
𝑙𝑖𝑡 + 𝛼 𝑀
𝑚𝑖𝑡 + 𝜙 𝑡 𝑖𝑖𝑡, 𝑘𝑖𝑡 + 𝜀𝑖𝑡
• 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 𝜙 𝑡 and candidate value for 𝛼 𝐾, 𝜔𝑖𝑡 is computed for all t
2. Regress 𝜔𝑖𝑡 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 𝑘𝑖𝑡 𝜉𝑖𝑡 = 0 consistent estimate of 𝛼 𝐾 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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-100-95-90-85-80-75-70-65-60-55
Shadowpriceoffixedcapital(%)
DK FR DEE DEW IT PL SK UK
excludes outside values
Shadow interest rate of fixed capital (%):
distributions per country

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-.0005
0.0005
Shadowpriceofland(EUR/ha)
DK FR DEE DEW IT PL SK UK
excludes 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 + 𝛽1 𝑙𝑖𝑡 + 𝛽2 𝑘𝑖𝑡 + 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 + 𝛽1 𝑙𝑖𝑡 + 𝛽2 𝑘𝑖𝑡 + 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1, + 𝜀𝑖𝑡
where 𝜀𝑖𝑡 = 𝜉𝑖𝑡 + 𝑒𝑖𝑡.
• Now, we have two equations to identify the parameters
𝑦𝑖𝑡 = 𝛼 + 𝛽1 𝑙𝑖𝑡 + 𝛽2 𝑘𝑖𝑡 + ℎ 𝑘𝑖𝑡, 𝑚𝑖𝑡 + 𝑒𝑖𝑡
𝑦𝑖𝑡 = 𝛼 + 𝛽1 𝑙𝑖𝑡 + 𝛽2 𝑘𝑖𝑡 + 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1, + 𝜀𝑖𝑡

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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 𝜀𝑖𝑡|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)