WPS6658
Policy Research Working Paper 6658
Estimating the Effects of Credit Constraints
on Productivity of Peruvian Agriculture
Tiemen Woutersen
Shahidur R. Khandker
The World Bank
Development Research Group
Agriculture and Rural Development Team
October 2013
Policy Research Working Paper 6658
Abstract
This paper proposes an estimator for the endogenous Applying the estimator to a dataset on the productivity
switching regression models with fixed effects. The in agriculture substantially changes the conclusions
estimator allows for endogenous selection and for compared to earlier analysis of the same dataset.
conditional heteroscedasticity in the outcome equation.
This paper is a product of the Agriculture and Rural Development Team, Development Research Group. It is part of a
larger effort by the World Bank to provide open access to its research and make a contribution to development policy
discussions around the world. Policy Research Working Papers are also posted on the Web at http://econ.worldbank.org.
The authors may be contacted at skhandker @worldbank.org.
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Produced by the Research Support Team
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian
Agriculture
Tiemen Woutersen and Shahidur R. Khandker
Abstract. This paper proposes an estimator for the endogenous switching re-
gression models with …xed e¤ects. The estimator allows for endogenous selection and
for conditional heteroscedasticity in the outcome equation. Applying the estimator
to a dataset on the productivity in agriculture substantially changes the conclusions
compared to earlier analysis of the same dataset.
Keywords: Endogenous switching regression models, credit constraints.
JEL codes: C10, O16, O13, Q10, Q14.
Correspondence addresses: Department of Economics, Eller College of Management, University of
Arizona, P.O. Box 210108, Tucson, AZ 85721, woutersen@email.arizona.edu; Shahidur R. Khandker is
lead economist at the Development Research Group of the World Bank; his email address is skhand-
ker@worldbank.org. We thank Wesley Blundell, William J. Martin, Ming-sen Wang, and Roula Yazigi
for helpful comments and discussions.
1
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture2
1. Introduction
The endogenous switching regression model is useful when analyzing individuals
and …rms that switch between two regimes, for example, being credit constrained versus
being credit unconstrained. A credit constrained business may not be able to make the
necessary investments, which may lower the productivity of that business. Similarly, a
credit constrained farmer may not be able to purchase fertilizer or tools, which may also
cause the productivity to be lower. The decision to switch from one regime to the other
could also depend on unobserved factors, which would cause the state, such as being credit
constrained, to be endogenous.
A recent paper by Charlier, Melenberg and van Soest (2001) estimates several switch-
ing models. They …nd that the data rejects them all. The models that they reject include
s (1997) semi-parametric model. However, it might
a …xed e¤ects model and Kyriazidou’
be argued that the …xed e¤ects models that Charlier et al. (2001) and Guirkinger and
Boucher (2008) estimate do not adequately take the endogenous switching decision into
account. Also, Kyriazidou’s (1997) model does not allow for conditional time-varying
heteroscedasticity so it may not be that surprising that the data reject that model as
well.
We propose to generalize the existing …xed e¤ects and random e¤ects models to allow
for endogenous switching. This generalization will allow for conditional heteroscedasticity
in the outcome equation, a feature of almost any dataset. In particular, Maddala and
Nelson’s (1974) switching model is a special case of the proposed model and so is the
linear model with …xed e¤ects and heteroscedastic errors. The application we are inter-
ested in is agriculture …nancing in developing countries and micro nonfarm …nancing. In
particular, Guirkinger and Boucher (2008) estimate that removing the credit constraint
from constrained farmers would increase productivity by 26%. The number is based on an
estimate of a …xed e¤ects model. We extend this model with a selection equation and …nd
that the credit constraint has a much smaller impact on the estimated coe¢ cients of the
model, demonstrating the importance of having a selection equation. Two related papers
are Feder, Onchan and Raparla (1988) and Feder, Lau, Lin, and Luo (1990). There papers
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture3
argue that being credit constraint may very well be endogenous. Also, these papers do
not use individual e¤ects to control for the heterogeneity of the quality of the farmland
so that these papers di¤er from Guirkinger and Boucher (2008) and the present paper.
We note that switching models are not only useful for loan decisions but are also
useful for labor supply and household expenditure decisions. For example, Lee (1978)
and Adamchik and Bedi (2000) estimate a switching model to analyze wage di¤erences
between di¤erent sectors of the economy. We expect our extensions to be useful for such
applications as well. The methodology of this paper di¤ers from Wooldridge (1995),
who does not consider endogenous switching models. It also di¤ers from Semykinaa and
Wooldridge (2010), who use the inverse Mills ratio as an instrumental variable.
This paper is organized as follows. Section 2 introduces the model and states the
consistency and asymptotic normality result of our estimator. Section 3 applies the new
estimator to data on productivity in Peruvian agriculture and section 4 concludes.
2. Model and Theorem
In our application, farmers can be credit constrained or credit unconstrained. Being
credit constrained may reduce output of the farm since it may be more di¢ cult to buy
the relevant inputs such as fertilizer, machines, as well as to hire farm hands or specialized
workers. Thus, being credit constrained may reduce productivity. However, being credit
constrained and having low productivity could also be caused by a common unobserved
shock such as illness of the farmer. Thus, it is important to account for this sample
selection and that is what Maddala and Nelson’s (1974) “switching regression model with
endogenous switching” intends to do. In particular, their switching regression model has
a selection equation and an outcome equation. Let Wit be equal to one if the farmer i is
credit constrained in period t and zero otherwise. If the farmer i is not credit constrained
in period t; Wit = 0; then the productivity of the farm is
(0) 0 (0) (0)
Yi = Xit + fi + t + uit ; (1)
(0)
where Xit denotes the regressors, fi is an individual speci…c …xed e¤ect, is a time
(0)
dummy and uit is the error term. The models considered by Maddala and Nelson (1974)
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture4
or Maddala (1983) do not have …xed e¤ects or time dummies but we use those here.
Similar to the last equation, if the farmer i is credit constrained in period t; Wit = 1; then
the productivity of the farm is
(1) 0 (1) (1)
Yi = Xit + fi + t + uit ; (2)
(1) (1) (0)
where the …xed e¤ect fi and error term uit are in general di¤erent from fi and
(0)
uit in equation (1). Maddala and Nelson (1974) assume that the error terms in the
selection equation and in the outcome equation are jointly normal. This implies that
the error terms in the outcome equations do not have expectation zero conditional on
the regressors. Therefore, Maddala and Nelson (1974) and Maddala (1983) subtract the
inverse Mills ratio with a known coe¢ cient from the outcome equations. We also subtract
the inverse Mills ratio from the outcome equations. However, since we do not assume that
the error terms in the outcome equation are normally distributed we need to estimate the
coe¢ cient of the inverse Mills ratio. In particular, we propose the following procedure.
Let Qit denote the regressors of the selection equation of individual i in period t and
suppose we observe N individuals for T periods. Our procedure allows for predetermined
regressors (step 1A) or for exogenous regressors and correlated random e¤ects (step 1B).
Step 1A (Selection equation with predetermined regressors): Estimate a Probit model
with predetermined regressors. Let (^1 ; :::; ^T ) denote the quasi maximum likelihood
estimator, i.e.
P P
0
(^1 ; :::; ^T ) = arg max i t
ln[f ( t Qit )gWit f1 0
( t Qit )g1 Wit
]: (3)
N T
0
^ it = (^t Qit )
Using (^1 ; :::; ^T ); calculate R 1 (^t0Q )
it
for i = 1; :::; N and t = 1; :::; T:
Step 1B (Selection equation with correlated random e¤ects): Estimate a Probit model
with strictly exogenous regressors, constant slope coe¢ cients and correlated random ef-
fects. Let (^ ; ^1 ; :::; ^T ) denote the quasi maximum likelihood estimator, i.e.
P P PT PT
(^ ; ^1 ; :::; ^T ) = arg max i t
ln[f ( 0 Qit + t=1 0
t Qit )g
Wit
f1 ( 0 Qit + t=1 0
t Qit )g
1 Wit
]:
N T T T
(4)
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture5
PT ^0
(^ 0 Qit + T
1
t=1 t Qit )
Using (^ ; ^1 ; :::; ^T ); calculate R
^ it =
1 0
(^ Qit + T 1
P T ^0 for i = 1; :::; N and t =
t=1 t Qit )
1; :::; T:
Step 2: After step 1A or step 1B we need to di¤erence out the …xed e¤ect. For
(0)
every time period and every individual for which Wit = Wi;t 1 = 0; calculate Yit =
(0) (0) ^ it = R
^ it ^ i;t (0)
Yit Yi;t 1; Xit = Xit Xi;t 1; and R R 1: Next, regress Yit on a
constant, Xit , and ^ it : The constant takes care of the di¤erence in time dummies,
R
t t 1: For every time period and every individual for which Wit = Wi;t 1 = 1; calculate
(1) (1) (1) (1) ^ it :
Yit = Yit Yi;t 1 and regress Yit on a constant, Xit , and R
If the researcher is willing to make stronger assumptions, then other di¤erences can be
(1) (1) (1) (0) (0) (0)
used as well. In particular, de…ne l Yit = Yit Yi;t l ; l Yit = Yit Yi;t l ; l Xit =
Xit Xi;t l ; and ^ =R ^ it R
l Rit
^ i;t l for l = 1; :::T: Then de…ne the moment
0 P (0)
1
^ iT
i YiT XiT R ( T T 1)
B P (0) ^ C
B XiT f YiT XiT RiT ( T T 1 )g C
B Pi C
B R^ iT f Y (0) X R^ ( T 1 )g
C
1 B
B
i
P iT iT iT T C
C
g (0) ( ) = 2 YiT
(0)
2 XiT
^
2 RiT ( T T 2)
NBB P i
(0)
C
C
B X f Y X ^
R ( T 2 )g C
B Pi 2 iT 2 iT (0)
2 iT 2 iT T
C
@ ^
2 RiT f 2 YiT 2 XiT 2 RiT ( T T 2 )g
A
i
:::
0
where 1 is normalized to be zero and =f ; ; 2 ; :::; Tg . Let the moment for the other
outcome, g (1) ( ); be similarly de…ned, where 1 = 0, and = f ; '; 0
2 ; :::; T g : One can
use this general method of moment procedure instead of the least squares method in step
2 above but we do not consider this in further detail here. Also, in the application we
use a regressor in step 1A that is not used in step 2. This is usually called an exclusion
restriction.
We now state the assumptions.
Assumption 1 (Selection equation with predetermined regressors): Let E (Wit jQit ) =
0
( t Qit ). Let E fQit Q0
it g be nonsingular for t = 1; ::; T: Let the parameter space A
be compact; de…ne ! = f ; ; 1 ; :::; T ; ; ; ; 'g0 and let the true value !0 be in the
interior of A:
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture6
Assumption 1 allows for arbitrary correlation of the error in the selection equation
and also allows the variance of this equation to vary with time. De Jong and Woutersen
(2011) discuss dynamic binary choice models in more detail. An example that satis…es
assumption 1 is
p
Wit = Healthi1 + Harvestit (t + 1) + it t+1 (5)
where Healthi1 is the health of farmer i in period 1, Harvestit is the harvest of farmer
i in period t; and it is a standard normal error term that is i.i.d. conditional on the
regressors.
Assumption 2 (Selection equation with correlated random e¤ects): Let E (Wit jQi1; :::; QiT; ; vi ) =
1
PT
( 0 Qit + vi ) where vi = T 0
t=1 t Qit : Let the parameter space, B , be compact; de…ne
$=f ; ; 1 ; :::; T ; 1 ; :::; T; ; ; ; 'g0 , and let the true value $0 be in the interior of
B: Let E f(Qit vi )(Qit vi )0 g be nonsingular for t = 1; ::; T and all t 2 B:
This assumption allows for correlated random e¤ects since vi can depend on the re-
gressors. Such correlated random e¤ects were proposed by Chamberlain (1980). Mundlak
1
PT
(1978) lets the random e¤ect depend on the averages of the regressors, vi = 0 T t=1 Qit ;
and the last assumption also allows for that.
The next assumption is about an error term being uncorrelated with regressors, after
di¤erencing out the …xed e¤ect. De…ne
(0) (0) 0
"it = Yi ( Xit + Rit + t );
(1) (1) 0
"it = Yi ( Xit + Rit ' + t ); (6)
0
t Qit )
(
where Rit = 1 ( t0 Q ) is calculated if
it
step 1A (predetermined regressors) is used and
0 1
PT 0
( Qit + T Qit )
Rit = 1 1
( 0 Qit + T
PT t 0
t =1
if step 1B (correlated random e¤ects) is used.
t=1 t Qit )
(0) 0 (0) (1) 0
Assumption 3: Let Yi = Xit + Rit + t + "it if and only if Wit = 0: Let Yi = Xit +
(1) (0) (1)
Rit ' + t + "it if and only if Wit = 1: Let "it and "it be uncorrelated with Xit ;
(0) (1) (0)
Wit ; and Rit and let E ( "it ) = E ( "it ) = 0: Let var( "it j Xit ; Wit ; Rit ) > 0;
(1)
and var( "it j Xit ; Wit ; Rit ) > 0 for all Xit ; Wit ; and Rit : Let E [f(1; Xit ;
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture7
Wit ; Rit )(1; Xit ; Wit ; Rit )0 gjWit = Wi;t 1 = 0] be nonsingular for some t 2
f1; :::; T g and P (Wit = Wi;t 1 = 0) > 0: Let E [f(1; Xis ; Wis ; Ris )(1; Xis ; Wis ; Ris )0 gjWis =
Wi;s 1 = 1] be nonsingular for some s 2 f1; :::; T g and P (Wis = Wi;s 1 = 1) > 0:
Assumption 4: Let fQit ; Wit ; Xit ; Yit ; t = 1; :::; T g; i = 1; :::; T be i.i.d. across individuals.
Let E (jQit j4 ) < M; E (jWit j4 ) < M; E (jXit j4 ) < M; E (jYit j4 ) < M for all t = 1; ::; T , and
i = 1; :::; T where M < 1:
Kyriazidou (1997) imposes exchangability of the error terms. This implies that the
error terms are homoscedastic while the outcome equation in this paper allows for con-
ditional heteroscedasticity and the selection equation of assumption 1 allows for time-
varying variances as in the example above.1 In order to correct the standard errors for
our two step estimator, it is convenient to write the estimator as the maximum of an
objective function. This is similar to Heckman’s (1979) sample selection estimator. In
the application, however, we bootstrap the estimators. That is, we sample the data with
replacement and go through step 1A and step 2 for every dataset that we generated. The
objective function that is used to prove asymptotic normality of our estimator as well as
the asymptotic variance-covariance matrix is presented in the technical appendix.
Theorem 1 (Consistency and Asymptotic Normality):
Let assumptions 1 and 3-4 hold. Then
^ ! !0 and
!
p
p
!
N T (^ !0 ) ! N (0; A)
p
where A is positive semide…nite.
Let assumptions 2-4 hold. Then
^ ! !0 and
$
p
p
^
N T ($ $0 ) ! N (0; B)
p
where B is positive semide…nite.
1 Dustmann and Rochina-Barrachina (2007) discuss empirical identi…cation issues with Kyriazidou’s
estimator.
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture8
As Horowitz (2001, theorem 2.2) shows, bootstrapping an asymptotically normally
distributed estimator that can be represented by an in‡uence function yields a consistent
variance-covariance matrix and consistent con…dence intervals.2 In the application, we
bootstrap the estimator.
3. Productivity in Peruvian Agriculture
We apply the approach proposed above to a dataset about Peruvian agriculture. This
dataset contains information about whether the farmer was credit constrained, which
crops were grown on her/his farm, the amount of labor used, etc. The data was data
was collected in 1997 and 2003 and were previously analyzed by Guirkinger and Boucher
(2008). We follow their speci…cation and use regression coe¢ cients that are constant over
time. The only di¤erence between our speci…cation and Guirkinger and Boucher (2008)
is that we apply the methodology of the previous sections and use a selection equation to
account for the endogeneity. We report the results in Table (1). The …rst column reports
the …rst stage Probit regression. The second and third columns report columns (D) and
(E) in the original paper. The fourth and …fth columns report our estimates corresponding
to their original columns (D) and (E). The sixth and seventh columns are columns (F) and
(G) from the original paper. The last two columns are the corresponding estimates using
our method. The standard errors are calculated by bootstrapping the two-step estimation
together. We also implement a Wald test to compare the di¤erences between the credit
constrained farmers and the credit unconstrained farmers. We …nd that adding a selection
equation to the model shrinks the di¤erences between the coe¢ cients of the constrained
and unconstrained farmers. This …nding has important policy implications since the
e¤ect of being credit constrained is not as large as previously thought. Our statistical test
con…rms these …ndings. In particular, we used a Wald test with 11 degrees of freedom
to test the statistical di¤erence between the credit constrained farmers and the credit
unconstrained farmers. Using the speci…cation of the original paper, we …nd that the value
of the Wald test is 56.62 (comparing columns D and E) and 61.17 (comparing columns
F and G). Adding the selection equation reduces these numbers to 22.92 (comparing
2 Horowitz (2001, Theorem 2.2) averages gn (Xi ):
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture9
columns D’and E’
) and 25.96 (comparing columns F’and G’).3 Thus, the di¤erences do
not completely go away but are substantially reduced.
Next, we estimate that if credit constrained farmers were to become unconstrained
then productivity would increase by 10.6%, which is signi…cantly smaller than the es-
timate of 26% from Guirkinger and Boucher (2008).4 Moreover, this 10.6% increase is
not statistically signi…cant. A full comparison between our estimates and Guirkinger and
Boucher’s can be seen in Table 2. The second and third columns (B and B’) are estimates
for absolute productivity change by credit constrained type if the credit constraints were
removed. The fourth and …fth columns(C and C’) are relative productivity increases for
each group if they were to become unconstrained. The total estimated impact on produc-
tivity for removing credit constraints is found in the seventh and eighth columns (E and
E’), which includes our overall estimate of 10.6%.
Thus, applying the estimator to a dataset on the productivity in Peruvian agriculture
shows that the new estimator changes the conclusions compared to earlier results on the
same dataset. In particular, adding a selection equation to a model with …xed e¤ects
causes the coe¢ cients of the credit constrained farmers to be the quite similar to the
coe¢ cients of the unconstrained farmers.
4. Conclusion
We propose an estimator for the endogenous switching regression models with …xed ef-
fects. The estimator allows for endogenous selection and for conditional heteroscedasticity
in the outcome equation. Applying the estimator to a dataset on the productivity in Pe-
ruvian agriculture shows that the new, more general estimator substantially changes the
conclusions compared to the earlier analysis of the same dataset. In particular, adding a
selection equation to a model with …xed e¤ects causes the coe¢ cients of the credit con-
strained farmers to be similar to those of the unconstrained farmers, demonstrating the
importance of having a selection equation. Relaxing the single index assumption of the
selection equation by extending Altonji and Matzkin (2005) is left for future research and
3 The p-values of these for test were 0.000, 0.000, 0.0181, and 0.0066.
4 We use the same methodology to calculate the change in productivity as Guirkinger and Boucher
(2008) but we use the new estimator for the parameter value, using step 1A and step 2.
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture10
so is developing a model that allows for selection between more than two regimes.
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture11
5. Appendix: Consistency and Asymptotic Normality Results
In order to prove consistency and asymptotic normality of our two step estimator, it is con-
venient to write the estimator as the maximum of an objective function. Let assumptions
1 and 3-4 hold. De…ne
1 X
S (! ) = Si (! ) where
N i
P T T
1X 1X
Si (! ) = t
ln[f ( 0 Qit + 0
t Qit )g
Wit
f1 ( 0 Qit + 0
t Qit )g
1 Wit
]
T T t=1 T t=1
P
t (0) (0) 0 2
1( Yi observed) f Yi ( Xit + Rit + t )g
T
P
t (1) (1) 0 2
1( Yi observed) f Yi ( Xit + Rit ' + t )g :
T
@S (! )
Let @! j! =!0 denote the derivative of S (! ) with respect to ! and evaluated at the true
p
value !0 : Let denote the variance-covariance matrix of N @S (! )
@! j! =!0 : Remember that
! = f ; ; 1 ; :::; T ; ; ; ; 'g0 : Let H1 denote the second derivative of E fS (! )g with
0
respect to the vector = f 1 ; :::; Tg ; evaluated at the true value of ; i.e.
H1 = @ 2 E fS (! )g=@ @ 0 j = 0
: Similarly, let !subset = f ; ; ; ; ; 'g0 and
0
H2 = @ 2 E fS2 (!subset )g=@!subset @!subset j!subset =!subset;0 . Thus, the Hessian of E fS (! )g
has the following form,
H1 0
@ 2 E fS (! )g=@!@! 0 j!=!0 = :
0 H2
Note maximizing S (! ) with respect to ! is the same as maximizing
P P T T
1X 1X
i t
ln[f ( 0 Qit + 0
t Qit )g
Wit
f1 ( 0 Qit + 0
t Qit )g
1 Wit
]
N T T t=1 T t=1
with respect to and maximizing
P P
i t (0) (0) 0 2
1( Yi observed) f Yi ( Xit + Rit + t )g
T
N P
P
i t (1) (1) 0 2
1( Yi observed) f Yi ( Xit + Rit ' + t )g :
N T
…rst step estimator’ is equivalent to the estimator
with respect to !subset : Thus, our ‘
considered by Newey and McFadden (1994, example 1.2). Their conditions are satis…ed
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture12
so that ^ 0 = op (1): Next, note that
P P
i t (0) (0) 0 2
1( Yi observed) f Yi ( Xit + Rit + t )g
N P
P T
i t (1) (1) 0 2
1( Yi observed) f Yi ( Xit + Rit ' + t )g :
N T
is a concave function. The i.i.d. assumption and the assumption on the moments ensure
that this expression converges in probability to its expectation. The full rank assumption
then ensures that this expectation has a unique maximum at the true value. Thus,
all the assumptions of Newey and McFadden (1994, theorem 2.7) are satis…ed so that
^ subset
! !subset = op (1):
Concerning the asymptotic normality: Note that S (! ) is twice continuously di¤eren-
tiable. Interpret the …rst derivative as a moment and note that all the assumptions of
Newey and McFadden (1994, theorem 3.4) are satis…ed. The asymptotic normality follows
and
H1 1 0 H1 1 0
= :
0 H2 1 0 H2 1
The nonzero variation follows from the strictly positive variation of the error terms. The
matrix can be estimated using a sample analogue. In particular, de…ne
2
^ 1 = @ S (! ) j!=^
H !;
@ @ 0
^2 = @ 2 S (! )
H 0 !;
j!=^
@!subset @!subset
P P !
i
f @S i ( ) @Si ( )
g @ 0 @Si (!subset ) @Si ( )
N f @!subset g @ 0
i
^= P N @ P
!;
j!=^
@Si ( ) @Si (!subset ) @S2;i (!subset ) @S2;i (!subset )
N f @ g @!0 N f g @!subset =
i i
subset @!subset
and
^ 1
H 0 0 ^ 1
H
^= 1 ^ 1 :
0 ^ 1
H ^ 1
H 0
2 2
Theorem 4.5 by Newey and McFadden (1994) yields that ^ = + op (1):
Now suppose that assumption 2-4 hold. De…ne
1 X
S ($) = Si ($) where
N i
P PT PT
Si ($) = t
ln[f ( 0 Qit + t=1 0
t Qit )g
Wit
f1 ( 0 Qit + t=1 0
t Qit )g
1 Wit
T
P T T
t (0) (0) 0 2
1( Yi observed) f Yi ( Xit + Rit + t )g
T
P
t (1) (1) 0 2
1( Yi observed) f Yi ( Xit + Rit ' + t )g :
T
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture13
Remember that $ = f ; ; 1 ; :::; T ; 1 ; :::; T; ; ; ; 'g0 : The same reasoning as above
holds but now the consistency of the …rst step follows from Chamberlain (1980). The
function S ($) is twice continuously di¤erentiable and can again be consistently esti-
mated by its sample analogue. Also, the conditions of Horowitz (2001, theorem 2.2) are
satis…es since the estimator is asymptotically normally distributed and this normality fol-
lows from an averaging operator, in particular from applying the Lindeberg–Lévy central
P @Si (! ) P @ Si (! )
limit theorem to p1
N i @! and p1
N i @! .
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture14
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Table 1: Estimation results for productivity
Probit (D) (E) (D’) (E’) (F) (G) (F’) (G’)
(constant) Unconstrained Constrained Unconstrained Constrained Unconstrained Constrained Unconstrained Constrained
productivity productivity productivity productivity productivity productivity productivity productivity
b/se b/se b/se b/se b/se b/se b/se b/se b/se
A 0.00 -85.57 -130.62** -131.03 -134.65 -88.65 -116.20* -137.92 -122.15
(0.01) (58.78) (48.65) (96.25) (94.43) (59.57) (48.20) (93.92) (86.10)
K 14.45 182.67* 14.61 133.58
(13.26) (82.27) (38.59) (118.76)
K/A -24.28 645.98** 158.88 586.26
(127.11) (236.42) (210.46) (394.83)
Labor/A 7.72 -34.93 -18.42 -19.27
(42.06) (33.08) (98.43) (86.17)
Labor -0.01 -61.50 2.33 -45.55 -15.40
(0.02) (48.74) (38.08) (69.31) (58.54)
Dependency ratio 0.11 490.90 10.34 397.34 -67.39 696.21 29.14 472.43 14.82
(0.23) (418.87) (330.09) (610.32) (404.30) (404.46) (318.23) (596.20) (386.36)
Reg income -0.00 263.85 -14.79 49.97 -30.66 244.34 32.22 52.85 -37.26
(0.13) (167.80) (214.76) (346.38) (283.65) (171.22) (202.05) (356.85) (265.71)
Herd size 0.01 53.66** 40.89 42.73 52.57 56.55** 38.94 44.45 54.61
(0.01) (20.12) (21.76) (55.64) (53.32) (20.31) (21.03) (53.65) (49.71)
Rice 632.30* 93.30 763.05* 74.44 672.66* 115.48 713.98 114.22
(252.99) (147.59) (361.37) (276.05) (268.99) (146.88) (381.22) (268.85)
Cotton -279.51 -27.99 -616.28 -292.07 -236.15 -23.86 -681.16 -323.61
(223.06) (153.51) (340.81) (235.61) (226.56) (147.37) (363.86) (217.68)
Banana -374.69 754.11** -368.99 669.92 -395.52 759.00** -366.49 688.66
(267.39) (275.51) (575.70) (681.77) (272.64) (271.02) (589.59) (691.07)
Corn 61.04 -64.55 -0.29 -164.73 12.66 -38.69 -25.66 -137.48
(186.70) (117.97) (280.17) (188.64) (185.75) (116.87) (280.70) (193.14)
Durables -0.02* 5.03 4.83 24.98 -28.85 5.92* 6.38 23.62 -37.18
(0.01) (2.67) (28.11) (29.03) (44.61) (2.64) (26.34) (26.47) (45.08)
Constant 0.66*** 1493.80*** 977.59*** 406.41** 357.68* 1220.67*** 948.34*** 461.99** 374.78*
(0.14) (344.02) (262.72) (150.74) (158.21) (344.68) (248.31) (157.09) (157.97)
Title -0.41***
(0.10)
Network -1.25***
(0.19)
δ -532.09 421.59 -555.28 497.45
(667.13) (498.24) (693.75) (464.47)
Table 2: Counterfactuals: The impact of eliminating credit constraints on productivity and regional output
A B B’ C C’ D E E’
Type of Frequency Productivity Productivity Relative Relative Land Impact on Impact on
credit constraint in sample change change change change controlled regional output regional output
Quantity 23.50% 516.28 256.37 58.3% 28.90% 20.5% 11.90% 6.41%
rationed [176] [667.73] [4.5%] [15.7%]
Risk 15.50% 477.71 129.96 68.2% 18.56% 16.0% 10.90% 2.53%
rationed [175] [697.25] [4.7%] [16.2%]
Transaction cost 10.50% 412.75 160.29 49.0% 19% 7.8% 3.8% 1.52%
rationed [216] [620.77] [2.1%] [6.0%]
Constrained 49.50% 482.24 196.41 58.9% 24% 44.2% 26% 10.60%
[149] [657.27] [8.4%] [35.7%]