metadata: authors: 0: author: Woutersen, Tiemen
1: author: Khandker, Shahidur R.
count: Peru
docna: 0: docna: Estimating the effects of credit constraints
            on productivity of Peruvian agriculture
docty: Policy Research Working Paper
theme: Rural non-farm income generation,Rural services and infrastructure,Rural policies and institutions
majtheme: Rural development
subtopic: Climate Change and Agriculture,Rural Settlements,Urban Housing and Land Settlements,Crops and Crop Management Systems,Agricultural Economics,Urban Governance and Management,Urban Housing,Food Security,Municipal Management and Reform,Agricultural Growth and Rural Development
teratopic: Social Protections and Labor,Macroeconomics and Economic Growth,Education,Private Sector Development
abstracts: cdata!: This paper proposes an estimator for the
            endogenous switching regression models with fixed effects.
            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. This paper proposes
            an estimator for the endogenous switching re-gression models
            with fixed effects. 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.
geo_reg_key: 80475,80450,80469
repnme: repnme: Estimating the effects of credit
            constraints on productivity of Peruvian agriculture
display_title: Estimating the effects of credit
            constraints on productivity of Peruvian agriculture
listing_relative_url: /research/2013/10/18405278/estimating-effects-credit-constraints-productivity-peruvian-agriculture
topicv3: Agriculture and Food Security m1326205 435,Crop Production m1326627 174,Agricultural Credit m1327605 1962,Land and Housing m1327648 817,Rural Development m1504505 2667
publishtoextweb_dt: 2013-10-01T00:00:00Z
historic_topic: Social Protections and Labor,Macroeconomics and Economic Growth,Education,Private Sector Development
no_of_pages: 19
model_extractions: 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 switching regression models with fixed effects. 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.

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.

> _The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent._

Produced by the Research Support Team
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture Tiemen Woutersen and Shahidur R. Khandker<sup>�</sup> Abstract. This paper proposes an estimator for the endogenous switching regression 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 skhandker@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 switching models. They ...nd that the data rejects them all. The models that they reject include a ...xed e¤ects model and Kyriazidou’s (1997) semi-parametric model. However, it might 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 interested 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 where Xit denotes the regressors, fi<sup>(0)</sup> is an individual speci...c ...xed e¤ect, �� is a time dummy and u<sup>(0)</sup> it<sup>is the error term.The models considered by Maddala and Nelson (1974)</sup>
# 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 where the ...xed e¤ect fi<sup>(1)</sup> and error term u<sup>(1)</sup> it are in general di¤erent from fi<sup>(0)</sup> and u<sup>(0)</sup> it 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.

Using (^�1; :::; ^�T ); calculate R<sup>^</sup> it = 1���(^(�^t<sup>0</sup> �<sup><u>Q</u></sup> t<sup><u>0Qitit)</u>)fori = 1; :::; Nandt = 1; :::; T:</sup> Step 1B (Selection equation with correlated random e¤ects): Estimate a Probit model with strictly exogenous regressors, constant slope coe¢ cients and correlated random effects. Let (^�;<sup>^</sup> 1; :::;<sup>^</sup> T ) denote the quasi maximum likelihood estimator, i.e.

T T (^�;<sup>^</sup> 1; :::;<sup>^</sup> T ) = arg max <u>PNi PT t</u><sup>ln[f�(�0Qit+</sup> <u>PTt=1</u> t<sup>0Qit)gWitf1��(�0Qit+</sup> <u>PTt=1</u> t<sup>0Qit)g1�Wit]:</sup> (4)
’ ~~i~~ <u>-—&(4</u> ~~—~~ _ A

- _A — AS

-— A

A A KK A ae A A A _ A —~ _A —~ _A O(y

-—

K A 8 A -A B-A’ 6- kK -kK_ A A -A B-A’ 6—k =K-— A A -A B-A’ 6-K -K_ A —A B-A 0- K -K_ A A —A B-A 6- K -K_ A A —A B-A 0- K -—K_ 0 ~~—_~~ 0 B,O,K ,.,8 6 T 6 A, Py T yey T (3) fC)
.

UT UT &(y ~~-~~ a, By Y gree Y iS) — — 0,4, 7,2 fC) (S) A =A —~ BAN +A 6+AK A =A —adA +A + Ar <u>oY</u> —&(y <u>oY</u> ~~<u>=</u>~~ —8(y ~~_~~ T B 0K a A A A A A (A (A (A A A A (A A A A A A A A
Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture7 �Wit; �Rit)(1; �Xit; �Wit; �Rit)<sup>0</sup> 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)<sup>0</sup> 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(jQitj<sup>4</sup> ) < M; E(jWitj<sup>4</sup> ) < M; E(jXitj<sup>4</sup> ) < M; E(jYitj<sup>4</sup> ) < 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 conditional heteroscedasticity and the selection equation of assumption 1 allows for timevarying variances as in the example above.<sup>1</sup> 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 where �A is positive semide...nite.

Let assumptions 2-4 hold. Then 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.<sup>2</sup> 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’).<sup>3</sup> 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 estimate of 26% from Guirkinger and Boucher (2008).<sup>4</sup> 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 productivity 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 effects. The estimator allows for endogenous selection and for conditional heteroscedasticity in the outcome equation. Applying the estimator to a dataset on the productivity in Peruvian 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 constrained 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.
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-%y ~~=~~ {A —~ BA +A 64+AK -{A -aA +A + Ar
YY — ~~——l1~~ (A — ~~_——l1~~ (A

-{A —- BA +A 6+AK -{A -aA +A + Ar

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Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture13 Remember that $ = f�; �; �1; :::; �T ; 1; :::; T ; �; �; �; 'g<sup>0</sup> : The same reasoning as above holds but now the consistency of the ...rst step follows from Chamberlain (1980). The function S<sup>�</sup> ($) is twice continuously di¤erentiable and � can again be consistently estimated 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 follows from an averaging operator, in particular from applying the Lindeberg–Lévy central <u>1</u> @Si(!) <u>1</u> @S<sup>�</sup> i(!�) limit theorem to ~~p~~ N Pi @! and ~~p~~ N Pi @ �! .