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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
โข 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?
โข Unique and current set of production elasticities for 8 farm-level data sets at the EU country level
โข Some evidence on shadow prices
โข Conclusions
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Two problems of identification
A general production function:
๐ฆ๐๐ก = ๐ ๐ด๐๐ก , ๐ฟ๐๐ก , ๐พ๐๐ก, ๐๐๐ก + ๐๐๐ก + ํ๐๐ก
with
y Output
A Land
L Labour
K Capital (fixed)
M Materials (Working capital)
๐ Farm- & time-specific factor(s) known to farmer, unobserved by analyst
ํ Independent & identically distributed noise
i, t Farm & time indices
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Two problems of identification
Collinearity problem โข If variable and intermediate inputs are chosen simultaneously factor use across farms varies only with ๐ (Bond & Sรถderbom 2005; Ackerberg et al. 2007)
Production elasticities for variable inputs not identified!
Endogeneity problem โข ๐ likely correlated with other input choices โข Need to take ฯ into account in order to identify ๐, as ๐๐๐ก + ํ๐๐ก
is not i.i.d No identification of ๐ possible if ฯ is not taken into account!
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Traditional approaches to solve the
identification problems
1. Ordinary Least Squares: forget it. Assume ฯ is non-existent.
โ Bias: elasticities of flexible inputs too high (capture ฯ)
2. โWithinโ (fixed effects): assume we can decompose ฯ in
โ Assumption plausible?
โ Bias: elasticities too low as signal-to-noise is reduced
โ 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
โ current (exogenous) variation in input use by lagged adjustment to
past productivity shocks (Arellano & Bond 1991; Blundell & Bond 1998)
โข feasible if input modifications s.t. adjustment costs (Bond & Sรถderbom 2005)
โข plausible for many factors (e.g. labour, land or capital ) but less so for intermediate inputs
โ one way to allow costly adjustment: ๐๐๐ก = ๐๐๐๐กโ1 + ๐๐๐ก, with ๐ < 1
โ dynamic production function with lagged levels & differences of inputs
as instruments in a GMM framework (Blundell & Bond 2000)
โ Bias: hopefully small. Adresses both problems if instruments induce
sufficient exogenous variation
๐ autoregressive parameter
๐๐๐ก mean zero innovation
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Recent solutions to solve the
identification probems
4. Control Function approach
โ assume ฯ evolves along with observed firm characteristics (Olley/Pakes
1996, Econometrica)
โ materials a good control candidate for ฯ (Levinsohn & Petrin 2003)
โ further assume: (a) M is monotonically increasing in ฯ & (b) factor
adjustment in one period
1. Estimate โcleanโ A & L by controlling ฯ with M & K
2. Recover M & K from additional timing assumptions
โ solves endogeneity problem if control function fully captures ฯ โข productivity enhancing reaction to shocks less input use violating (a)
โข some factors (e.g. soil quality) might evolve slowly violating (b)
โ collinearity problem not solved โข 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
โข OLS: Highly implausible results at sample means
โข Within: Interaction terms not sig. in the majority of cases
โข BB: No straightforward implementation, as assumption of linear
addivitity of the fixed effects is violated
โข 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 (โฌ/h): distributions per country
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Conclusions
โข Adjustment costs relevant for important inputs in agricultural production โ LP and BB identification strategies a priori plausible
โข LP plausible results combined with FADN data but is a second-best choice โ corrected upward (downward) bias in OLS (Whithin-OLS) regressions
โ conceptual problems in identifying flexible factors
โข BB only performed well with regard to materials
โข Materials most important production factor in EU field crop farming (prod.
elasticity of ~0.7)
โข Fixed capital, land and labour usually not scarce
โข Shadow price analysis reveals heterogenous picture โ Credit market imperfections: Funding constraints (DEE, IT) vs. overutilisation
(DEW, DK)? Effects of financial crisis?
โ Low labour remuneration (except DK)
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Future research
โข Estimated shadow prices as starting point for analysis of
drivers & impacts
โข Extension to other production systems (e.g., dairy)
โข Examine other identification strategies
โข Wooldridge (2009) is a promising candidate
โข unifies LP in a single-step efficiency gains
โข solves collinearity problem
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The END.
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Appendix
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Blundell/Bond in detail
โข Substituting ๐ฃ๐๐ก = ๐๐ฃ๐๐กโ1 + ๐๐๐ก and ๐๐๐ก = ๐พ๐ก + ๐๐ + ๐ฃ๐๐ก into the production
function implies the following dynamic production function
๐ฆ๐๐ก = ๐ผ๐๐ฅ๐๐ก โ ๐ผ๐๐๐ฅ๐๐กโ1 + ๐๐ฆ๐๐กโ1 + ๐พ๐ก โ ๐๐พ๐กโ1๐
+ 1 โ ๐ ๐๐ + ํ๐๐ก
โข Alternatively:
๐ฆ๐๐ก = ๐1๐๐
๐ฅ๐๐ก + ๐2๐๐
๐ฅ๐๐กโ1 + ๐3๐ฆ๐๐กโ1 + ๐พ๐กโ + ๐๐
โ + ํ๐๐กโ
subject to the common factor restrictions that ๐2๐ = โ๐1๐๐3 for all X.
(allows recovery of input elasticities)
โข Farm-specific fixed effects removed by FD, allows transmission of ๐ to
subsequent periods
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Olley Pakes and Levinsohn/Petrin in
detail
โข Log investment (๐๐๐ก) as an observed characteristic driven by ๐๐๐ก:
โข ๐๐๐ก = ๐๐ก ๐๐๐ก , ๐๐๐ก and ๐๐๐ก evolves ๐๐๐ก+1 = 1 โ ๐ฟ ๐๐๐ก + ๐๐๐ก, with ๐ฟ=
depreciation rate
โข Given monotonicity we can write ๐๐๐ก = โ๐ก ๐๐๐ก , ๐๐๐ก
โข Assume: ๐๐๐ก = ๐ธ ๐๐๐ก|๐๐๐กโ1 + ๐๐๐ก,
โ ๐๐๐ก is an innovation uncorrelated with ๐๐๐ก used to identify capital
coefficient in the second stage
โข Idea
1. control for the influence of k and ฯ
2. recover the true coefficient of k as well as ฯ in the second stage
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Olley/Pakes and Levinsohn/Petrin
continued
โข Plugging ๐๐๐ก = โ๐ก ๐๐๐ก , ๐๐๐ก into production function gives
๐ฆ๐๐ก = ๐ผ๐ด๐๐๐ก + ๐ผ๐ฟ๐๐๐ก + ๐ผ๐๐๐๐ก + ๐๐ก ๐๐๐ก , ๐๐๐ก + ํ๐๐ก
โข ๐ is approximated by 2nd and 3rd order polynomials of i and k in the first stage
โข Here parameters of variable factors are obtained by OLS
โข Second stage:
1. using ๐๐ก and candidate value for ๐ผ๐พ, ๐ ๐๐ก is computed for all t
2. Regress ๐ ๐๐ก on its lagged values to obtain a consistent predictor of that part of ฯ that is free of the innovation ฮพ (โcleanโ ๐๐๐ก)
3. using first stage parameters together with prediction of the โcleanโ ๐๐๐ก and ๐ธ ๐๐๐ก๐๐๐ก = 0 consistent estimate of ๐ผ๐พ 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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-10
0-9
5-9
0-8
5-8
0-7
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 (โฌ/ha): distributions per
country
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The Wooldridge-Levinsohn-Petrin
approach
โข Unifies the Olley/Pakes and Levinsohn/Petrin procedure within a
IV/GMM framework
โ Estimation in a single step
โ Analytic standard errors
โ Implementation of translog is straightforward
โข Suppose for parsimony:
๐ฆ๐๐ก = ๐ผ + ๐ฝ1๐๐๐ก + ๐ฝ2๐๐๐ก +๐๐๐ก + ๐๐๐ก, and remember
๐๐๐ก = โ ๐๐๐ก , ๐๐๐ก ,
โ Now assume:
๐ธ ๐๐๐ก|๐๐๐ก , ๐๐๐ก , ๐๐๐ก , ๐๐,๐กโ1, ๐๐,๐กโ1 , ๐๐,๐กโ1, โฆ , ๐๐1, ๐๐1 , ๐๐1 = 0
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The Wooldridge-Levinsohn-Petrin
approach
โข Again, assume: ๐๐๐ก = ๐ธ ๐๐๐ก|๐๐๐กโ1 + ๐๐๐ก and
๐ธ ๐๐๐ก|๐๐๐ก , ๐๐,๐กโ1, ๐๐,๐กโ1 , ๐๐,๐กโ1, โฆ , ๐๐1, ๐๐1 , ๐๐1
= ๐ธ ๐๐๐ก|๐๐๐กโ1 = ๐ ๐๐๐กโ1 = ๐ โ ๐๐,๐กโ1, ๐๐,๐กโ1,
โข Plugging into the production function gives
๐ฆ๐๐ก = ๐ผ + ๐ฝ1๐๐๐ก + ๐ฝ2๐๐๐ก + ๐ โ ๐๐,๐กโ1, ๐๐,๐กโ1, + ํ๐๐ก
where ํ๐๐ก = ๐๐๐ก + ๐๐๐ก.
โข Now, we have two equations to identify the parameters
๐ฆ๐๐ก = ๐ผ + ๐ฝ1๐๐๐ก + ๐ฝ2๐๐๐ก + โ ๐๐๐ก , ๐๐๐ก + ๐๐๐ก
๐ฆ๐๐ก = ๐ผ + ๐ฝ1๐๐๐ก + ๐ฝ2๐๐๐ก + ๐ โ ๐๐,๐กโ1, ๐๐,๐กโ1, + ํ๐๐ก
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The Wooldridge-Levinsohn-Petrin
approach
โข And
๐ธ ๐๐๐ก|๐๐๐ก , ๐๐๐ก , ๐๐๐ก , ๐๐,๐กโ1, ๐๐,๐กโ1 , ๐๐,๐กโ1, โฆ , ๐๐1, ๐๐1 , ๐๐1 = 0
๐ธ ํ๐๐ก|๐๐๐ก , ๐๐,๐กโ1, ๐๐,๐กโ1 , ๐๐,๐กโ1, โฆ , ๐๐1, ๐๐1 , ๐๐1 = 0.
โข Unknown function โ approximated by low-order polynomial and ๐
might be a random walk with drift.
โข Estimation:
โ Both equations within a GMM framework, or
โ Second equation by IV-estimation and instrument for ๐ (Petrin and
Levinsohn 2012)