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    • As regards the tax problem there are two distinct types

    2018-10-25

    As regards the tax problem, there are two distinct types of variables. The impact of each input X on tax collection y depends on the magnitude of the coefficient β, which indicates whether these variables expand or contract the frontier, i.e., whether they increase or decrease the municipal tax collection. Z are variables that may explain the distance between the observed tax collection and the estimated efficient frontier, while δ are the corresponding coefficients to be estimated. If δ>0, the variable contributes to distancing the municipal tax revenue from the efficient frontier, while a negative sign implies that the variable acts to reduce inefficiency. In the case under study, the oil royalties are the variable of interest among the set of covariates. The model defined by Eqs. (3) and (4) can be linearized and synthesized according to the following system: As Battese and Coelli (1995) highlight, both equations must be estimated simultaneously by maximum likelihood. The reason is that a two-stage procedure with ordinary least squares is inconsistent, because in the first stage, the inefficiency components are estimated as a regression error, i.e., under the assumption that they are white noise. However, the second-stage estimation involves specifying a regression model to explain such effects, violating ex post the assumption that they are i.i.d. in the previous stage. Thus, following Battese and Coelli\'s (1995) recommendation, the equations are simultaneously estimated by maximum likelihood. The technical efficiency (TE) of each municipality i in year t can be defined by the ratio , where is the estimated tax revenue on the efficient frontier (U=0). Therefore: The technical efficiencies TE measure the distance of each municipality from the efficient frontier and vary, by design, between zero and one. The closer to one, the more efficient the municipality and, therefore, the higher its tax effort. For example, if TE=0.75, then this municipality collects 25% less than it these would obtain if the internal sources of inefficiency were corrected.
    Data and results In order to estimate the tax production function, it is necessary to select some measures of inputs that reflect the municipal effort in collecting taxes. This paper employs the personnel expenditures as a proxy for labor and the capital expenditures as a proxy for capital in the tax production function. The idea is to capture the municipal effort in managing the activities related to tax collection. Papers that employ the efficient production frontier to assess tax collection usually base the inputs on fiscal capacity, that is, on local economic variables (GDP, population, etc.), without taking into account the effort of the government. This paper adopts a different strategy and employs another set of inputs, following the argument that they indirectly reflect the level of effort made by municipal administrations to collect taxes. Given the available information, both capital and personnel expenditures are direct functions of the inputs employed in tax collection. However, due to legal restrictions, in Brazilian municipalities, the mayor observes the fiscal revenue before implementing personnel and capital expenditures, which would make such variables endogenous. Moreover, some normative restrictions (like Fiscal Responsibility Act) forbid the free float of personnel and capital expenditures. This could introduce a bias of reverse causality in the estimates, since the estimated tax collection affects the Municipal outlay. In order to overcome this problem, the lagged personnel and capital expenditures are used as instruments for personnel and capital expenditures, respectively. This allows correcting the bias of reverse causality and simultaneity that comes from the aforementioned restrictions, under the identification hypothesis that the past inputs (expenditures) are uncorrelated with unobservable determinants of present output (taxes). The specification of the production function is an important issue. According to Sauer et al. (2006), the functional form must possess certain desirable properties and the most important ones are theoretical flexibility and global consistency. A flexible functional form should be able to mimic arbitrarily different productive structures from an appropriate choice of parameters. On the other hand, a functional form has global consistency if it allows the reproduction of the theoretical properties of an expected economic relationship, from the appropriate choice of parameters. The theoretical consistency requires that the production function is: (i) monotonically non-decreasing in inputs; (ii) single-valued for each observation; and (iii) quasi-concave, which means a convex production-possibility set. The theoretical consistency must be the only restriction imposed on the production function, the functional form of which should be as flexible as possible.