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. 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 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 References [1] Adamchik, V., and V. Bedi (2000): “Wage di¤erentials between the public and the private sectors: Evidence from an economy in transition,” Labour Economics, 7: 203-224. [2] Altonji, J. G., Matzkin, R. L. (2005): “Cross section and panel data estimators for nonseparable models with endogenous regressors,” Econometrica, 73: 1053-1102. [3] Boucher, S. R., C. Guirkinger, and C. Trivelli (2009): “Direct Elicitation of Credit Constraints: Conceptual and Practical Issues with an Application to Peruvian Agri- culture,” Economic Development and Cultural Change, 57, 4: 609-640 . [4] Charlier, E., B. Melenberg, and A. van Soest (2001): “An analysis of housing expen- diture using semiparametric models and panel data,” Journal of Econometrics, 101, 71-107. [5] Chamberlain, G. (1980): “Analysis with qualitative data,” Review of Economic Stud- ies, 47: 225-238. [6] De Jong, R. M., and T. Woutersen (2011): “Dynamic Time Series Binary Choice,” Econometric Theory, 27: 673-702. [7] Dustmann, C., M. E. Rochina-Barrachina (2007): “Selection correction in panel data models: an application to the estimation of females’wage equations,” Econometrics Journal, 10: 263-293. [8] Feder, G., T. Onchan, T. Raparla (1988): “Collateral, guaranties and rural credit in developing countries: evidence from Asia,” Agricultural Economics, Vol. 2, 3: 231– 245. [9] Feder, G., Lau, L. J., Lin, J. Y., & Luo, X. (1990): “The relationship between credit and productivity in Chinese agriculture: a microeconomic model of disequilibrium,” American Journal of Agricultural Economics, 72(5), 1151-1157. [10] Guirkinger, C. and S. R. Boucher (2008) “Credit Constraints and Productivity in Peruvian Agriculture”, Agricultural Economics, 39: 295-308. Estimating the E¤ects of Credit Constraints on Productivity of Peruvian Agriculture15 [11] Heckman, J. J. (1979): “Sample Selection Bias as a Speci…cation Error,” Economet- rica, 47: 153-161. [12] Horowitz, J. L. (2001): “The Bootstrap,” in Handbook of Econometrics, Vol. 5, ed. by J. J. Heckman and E. Leamer. Amsterdam: North-Holland. [13] Kyriazidou, E. (1997): “Estimation of a Panel Data Sample Selection Model,”Econo- metrica, 65: 1335-1364. [14] Lee, L. (1978): “Unionism and Wage Rates: A Simultaneous Equations Model with Qualitative and Limited Dependent Variables,” International Economic Review, 19: 415-433. [15] Maddala, G. (1983): Limited-Dependent and Qualitative Variables in Econometrics, Econometric Society Monographs No. 3, Cambridge University Press, New York. [16] Maddala, G. S., and F. D. Nelson (1974): “Maximum likelihood methods for models of markets in disequilibrium,” Econometrica, 42: 1013-1030. [17] Mundlak, Y. (1978): “On the pooling of time series and cross section data,” Econo- metrica, 46: 69-85. [18] Newey, W. K., and D. McFadden (1994): “Large Sample Estimation and Hypothesis Testing,”in Handbook of Econometrics, Vol. 4, ed. by R. F. Engle and D. McFadden. Amsterdam: North-Holland. [19] Semykinaa, A., and J. M. Wooldridge (2010): “Estimating panel data models in the presence of endogeneity and selection,” Journal of Econometrics, 157: 375-380. [20] Wooldridge, J. M. (1995): “Selection corrections for panel data models under condi- tional mean independence assumptions,” Journal of Econometrics, 68: 115-132. 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%]