Estimation procedure

Maximum Likelihood (ML) estimations are performed in Ox 3.40 (Doornik, 2002) by using the package SFAMB (Stochastic Frontier Analysis using ModelBase)²⁴. The estimation procedure follows Battese and Coelli (1995) by estimating all the parameters in one step and Likelihood Ratio (LR) tests are conducted to test different hypotheses.

We estimate the translog production function by using a single equation. It is important to keep in mind that a potential problem associated with this procedure is that the parameter estimates may be subject to some simultaneity bias because inputs can hardly be regarded as really exogenous variables. However, given that we have cross-sectional data and use proxies for some inputs, we estimate a single equation²⁵.

On-farm income and production input variables are divided by their arithmetic means so that parameter estimates can be directly interpreted as production elasticities evaluated at sample means²⁶. The variable working capital is assumed to be a variable input, and the regularity conditions of the production function estimated, monotonicity, linearity and quasi-concavity in the variable input, are checked according to the following expressions (Table 19).

According to the literature that we consulted, the regularity conditions are rarely fulfilled globally in empirical work; however, if they are met for a sufficient number of the observed data points, it is considered “well-behaved” and interpretable (Berndt and Christensen, 1973).

On the other hand, Thijssen (1992), Salvanes and Tjotta (1996) and Sauer et al. (2006) have pointed out the importance of checking quasi-concavity in empirical applications.

24 SFAMB is a package written in Ox for estimating stochastic frontier production functions (Brummer, 2001).

25 If we had information about costs, we could estimate the production function using an equation system, incorporating cost share equations (Berndt and Christensen, 1973).

26 Each variable transformed will be represented with a M. Thus, for instance, the variable working capital LWC would be LWCM, where L means decimal logarithm.

Table 19

5.3.2 Dealing with endogeneity

Possible simultaneity between the financial variables and technical efficiency is an important issue; however, as developed in Section 3.2.4, Chapter III, it has been lightly studied. We are interested in checking whether the amount of credit or the condition of constrained is determined by the performance of farmers in the use of their inputs (technical efficiency).

We use the Durbin-Wu-Hausman test (Davidson and MacKinnon, 1993) to check simultaneity. First, we run a regression of the potential endogenous variable on all the exogenous variables and a set of instruments. Those instruments should be variables that are highly correlated to the potential endogenous variables but not with the term error of the original inefficiency model. Second, we run the original model by incorporating the residuals of the previous regression and check the significance of its parameter. The null hypothesis is no endogeneity, which means that the parameters of the residuals should not be significant²⁷. Thus, if the test is rejected, we ought to use instrumental variables; otherwise, our estimates will be inconsistent. In case of finding evidence of simultaneity, we correct the estimations by using fitted values of each model as instruments of the variable of interest.

The instruments used are the same both for the variable credit and for the variable credit constraint. The logarithm of on-farm income per hectare (Ln[Y/A]) is used as a proxy of

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household wealth; the idea behind of this variable is that high levels of household wealth decrease the necessity of borrowing. The quantity of owned land (OA) is used as a proxy of collateral so that a great amount of owned land could be seen by lenders as a signal of guarantee, increasing farmers’ chances of getting credit. The dummy variable relationship with productive organization (DOPR) is used as a proxy of social capital, understanding that the social-productive networks contribute to the access to credit.

Additionally, we use two variables that from a lender’s point of view can be proxies of the client’s potential quality. The variable credit scoring (CS)²⁸, and the variable DINDTYPE used as a signal of client quality in the future. DINDTYPE measures the historical payment behavior of farmers, taking values 1, 2, and 3 (the worst one). Thus, low values of DINDTYPE would be associated with higher possibilities of getting credit (Table 20).

Table 20

Instruments for the variables credit (CRED) and credit constraint (DCC)

Variable Definition Type Proxy

Logarithm of on-farm income per hectare Ln(Y/A) Continue Wealth

Own land OA Continue Collateral

Relationship with productive

organization DOPR Dummy 1 if farmer belongs to

productive organization Social Capital

Credit score CS Continue taking values between 1

and 4 (the worst one) Lender Perception Historical payment behavior of farmers DINDTYPE Categorical. 1,2 and 3, where 3 is

the worst

Signaling Source: Own definition

It is important to keep in mind that the expected effects mentioned in the previous paragraph are the result of getting credit. However, the amount of credit is the result of the interaction between demand and supply, so we can not expect that those effects are an absolute truth, at least in some of the variables mentioned, and they can go in the completely opposite direction. This is valid for the condition of credit constraint as well, because it is possible to define this condition as a situation of excess demand in the credit market²⁹.

28 This variable is used to measure creditworthiness and ranges from 1 (most) to 4 (least). This variable is calculated as the average of several subjective evaluations (each on a scale of 1 to 4) of the general cleanliness and order of the household’s dwelling and farm (see Chapter IV for a more detailed description of the variables used). This admittedly rough method of assessing creditworthiness is similar to methods that the Banco Estado has implemented in recent years in an attempt to reduce the administrative costs of delivering small rural credits.

29 Several papers that have studied the factors behind the condition of credit constraint by using Probit or Logit models have had difficulties interpreting the parameters in the model because those variables could explain the supply or demand side of the constraint.

5.4 Estimations and discussion