This paper aims to investigate

This paper aims to investigate this thing – that oil revenues are reducing the fiscal effort of the benefiting municipalities – through the estimation of an efficient tax production frontier based on Battese and Coelli (1995). We include political variables in the inefficiency equation, with the purpose of assessing whether partisan preferences of locals help to explain inefficiency scores. As an additional contribution, we address the endogeneity of inputs by adopting the lagged independent variable in the production function as instrument to correct the bias of reverse causality and/or simultaneity between inputs and outputs. This paper is structured as follows, besides this introduction. Section 2 presents the methodology; and Section 3 provides the data and results. The final section presents some concluding remarks.
Methodology Aigner et al. (1977) originally developed the Stochastic Production Frontier method to study the technical efficiencies of firms. The fundamental idea is to estimate a frontier that represents the potential (or optimal) production of a particular set of productive units and observe how each one is positioned relative to this frontier. Considering i=1, ⋯, I firms, the basic model is:where X is the vector of inputs, y is a measure of product, and β is the vector of parameters to be estimated, which describes how production responds to changes in inputs. The production unexplained by the model (random error) is decomposed into two parts. The U component reflects the fact that the product of each unit has its upper bound on the production frontier and possesses non-negative truncated distribution (U≥0); usually, one assumes a half-normal distribution, such that U∼N+(μ, σ2). V is a random component that is assumed to be independent and identically distributed (i.i.d.), representing shocks beyond the unit\'s control, such that and . The V component means that the frontier itself may vary randomly between firms or over time for the same firm. The rationale behind the stochastic frontier model can be employed to study a “tax production function.” The tax capacity of a governmental entity can be estimated according to factors that are under its control (U) or beyond Allosteric control (V). Thus, the efficiency measure can be derived from U, as follows: Since U has non-negative distribution, TE∈[0, 1]. Fig. 1 allows us to observe the efficiency measures. The greater the distance U, the closer to zero the technical efficiency TE. This means that the municipality producing y would be able to “produce” more taxes with the same amount of input X. Moreover, as U→0, TE→1, indicating that the unit (municipality) is close to the tax-efficient frontier. The frontier\'s position varies stochastically according to the random error V. If V is positive, the stochastic frontier exceeds the value of the deterministic one. This is represented by the solid curve, which does not consider the occurrence of exogenous shocks. The opposite occurs if V is negative. The position of the stochastic frontier as V≠0 is indicated by . In Fig. 1, municipality i\'s position is above the deterministic frontier, indicating that the unit experienced a positive shock. Battese and Coelli (1995) develop a stochastic frontier model for panel data in which the inefficiency terms are parameterized from a set of explanatory variables. Thus, y is the production of unit i, i=1, ⋯, I, at time t, t=1, ⋯, T. If X is the (1×K) vector of inputs and β is the (K×1) vector of parameters to be estimated, the model can be expressed in the following functional form:V are i.i.d. random errors such that . U are non-negative random components that possess normal distribution truncated at zero, representing the technical production inefficiencies. They are expressed by: Thus, , where Z are the explanatory variables of technical inefficiencies and δ is an (M×1) vector of coefficients to be estimated. W∼N(0, σ2) is a random variable truncated at point −Zδ.