Climate Impact on Egyptian Agriculture: An Efficiency …
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than the one proposed by Cornwell et al. [50]. Additionally, it does not enforce any
parametric specification, yet it restricts the temporal pattern of inefficiency to be the
same for all productive units. Ahn et al. [52, 53] have proposed a different estimation methodology using Generalized Methods of Moments (GMM) to the [50, 51]
developed models, respectively. The authors have shown that GMM is performing
better because it is asymptotically efficient. Kumbhakar [54] proposed a Maximum
Likelihood (ML) estimation of a time-varying stochastic frontier model. A similar
model proposed by Battese and Coelli [55] termed as a time decay model.
The common characteristic among all the frontier models is that the intercept
has not been changed over productive units, which leads to misspecification in the
existence time-invariant unobservable factors, which cause that these factors may be
captured by the inefficiency term, resulting in producing biased estimates. Greene
[56] has introduced a model to solve this issue using a time-varying stochastic frontier model with unit-specific intercepts. In contrast with the previous models helps
to distinguish time-varying inefficiency from unit specific time-invariant unit heterogeneity. For this reason, Greene named these models as True Fixed Effects (TFE) or
True random effects (TRE). While the estimation of the TRE specification is computationally simple using simulation-based techniques, the ML estimation of the TFE
model needs to solve two main challenges related to nonlinear panel data models
estimation. The first is related to a computational challenge because of the large
size of the parameters space. However, Greene [56, 57] has provided evidence that
a Maximum Likelihood Dummy Variable (MLDV) methodology is feasible in the
case of a large number of nuisance parameters α i (N > 1000). The second challenge
is the incidental parameters problem, which is an inferential problem that is a result
of a larger number of units, compared to the length of the panel. We adopt a True
Fixed Effects (TFE) stochastic production function:
y it = α i + X
it β + ε it
(1)
ε it = v it − u it
(2)
where y it denotes the level of output of governorate i at time t, X it is a vector of input
costs of the ith governorate at time t. β is a vector of parameters to be estimated. Component α i in Eq. (1) is the random governorate specific effect, this specification allows
to disentangle time-varying inefficiency from unit specific time invariant unobserved
heterogeneity. The error term ε it in Eq. (2) can be decomposed into two components.
The first component, v it is a normally distributed disturbance capturing the random
variation in output due to statistical noise that occurs due to the unintended omission
of relevant variables from vector X it ; errors (measurement and approximation) associated with the choice of the functional form; unexpected stochastic the control of the
industry. Component v it is usually assumed to be symmetric, independent and identically distributed as N(0, σ
2
v ). The second component u it is a one-sided, non-negative
random variable, representing the stochastic shortfall of the i-th governorate output
from its production frontier, assumed to be independently distributed following a
613
than the one proposed by Cornwell et al. [50]. Additionally, it does not enforce any
parametric specification, yet it restricts the temporal pattern of inefficiency to be the
same for all productive units. Ahn et al. [52, 53] have proposed a different estimation methodology using Generalized Methods of Moments (GMM) to the [50, 51]
developed models, respectively. The authors have shown that GMM is performing
better because it is asymptotically efficient. Kumbhakar [54] proposed a Maximum
Likelihood (ML) estimation of a time-varying stochastic frontier model. A similar
model proposed by Battese and Coelli [55] termed as a time decay model.
The common characteristic among all the frontier models is that the intercept
has not been changed over productive units, which leads to misspecification in the
existence time-invariant unobservable factors, which cause that these factors may be
captured by the inefficiency term, resulting in producing biased estimates. Greene
[56] has introduced a model to solve this issue using a time-varying stochastic frontier model with unit-specific intercepts. In contrast with the previous models helps
to distinguish time-varying inefficiency from unit specific time-invariant unit heterogeneity. For this reason, Greene named these models as True Fixed Effects (TFE) or
True random effects (TRE). While the estimation of the TRE specification is computationally simple using simulation-based techniques, the ML estimation of the TFE
model needs to solve two main challenges related to nonlinear panel data models
estimation. The first is related to a computational challenge because of the large
size of the parameters space. However, Greene [56, 57] has provided evidence that
a Maximum Likelihood Dummy Variable (MLDV) methodology is feasible in the
case of a large number of nuisance parameters α i (N > 1000). The second challenge
is the incidental parameters problem, which is an inferential problem that is a result
of a larger number of units, compared to the length of the panel. We adopt a True
Fixed Effects (TFE) stochastic production function:
y it = α i + X
it β + ε it
(1)
ε it = v it − u it
(2)
where y it denotes the level of output of governorate i at time t, X it is a vector of input
costs of the ith governorate at time t. β is a vector of parameters to be estimated. Component α i in Eq. (1) is the random governorate specific effect, this specification allows
to disentangle time-varying inefficiency from unit specific time invariant unobserved
heterogeneity. The error term ε it in Eq. (2) can be decomposed into two components.
The first component, v it is a normally distributed disturbance capturing the random
variation in output due to statistical noise that occurs due to the unintended omission
of relevant variables from vector X it ; errors (measurement and approximation) associated with the choice of the functional form; unexpected stochastic the control of the
industry. Component v it is usually assumed to be symmetric, independent and identically distributed as N(0, σ
2
v ). The second component u it is a one-sided, non-negative
random variable, representing the stochastic shortfall of the i-th governorate output
from its production frontier, assumed to be independently distributed following a