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Identifying Factor Productivity by Dynamic Panel Data and Control Function Approaches: A Comparative Evaluation for EU Agriculture
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
GEWISOLA 2013 | 25 – 27 September
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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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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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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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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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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 𝑘
𝑖𝑡
+ 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 𝑘
𝑖𝑡
+ 𝑓 ℎ 𝑘𝑖,𝑡−1, 𝑚𝑖,𝑡−1, + 𝜀𝑖𝑡
where 𝜀𝑖𝑡 = 𝜉𝑖𝑡 + 𝑒𝑖𝑡.
• Now, we have two equations to identify the parameters
𝑦𝑖𝑡 = 𝛼 + 𝛽
1
𝑙𝑖𝑡 + 𝛽2 𝑘
𝑖𝑡
+ ℎ 𝑘𝑖𝑡, 𝑚𝑖𝑡 + 𝑒𝑖𝑡
𝑦𝑖𝑡 = 𝛼 + 𝛽1 𝑙𝑖𝑡 + 𝛽2 𝑘
𝑖𝑡
+ 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)
