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    • Note that the two functional forms

    2018-11-07

    Note that the two functional forms of the inflation tax curve are obtained as particular cases of the following function: The two particular cases are as follows: (a) constant semi-elasticity: a1=1, a2>0; constant elasticity: a2=0. The functional form (13) also encompasses other possibilities that are not restricted to the above two cases. The inflation tax elasticity (ɛ) with respect to the inflation rate is given by: This elasticity may be either negative or positive, depending upon the tax curve parameters and the inflation rate. That is, the functional form (13) is flexible enough to allow the data to reveal the shape of the inflation tax curve. Fig. 4 shows how the inflation tax revenue and the (continuous) inflation rate evolved in Brazil during the period 1947–2003. The former increased from 1947 to mid-1960s, when it began to decrease until the beginning of the 1970s. Thereafter a new upward phase began, which ended with the Real Plan in 1994. Note that while the inflation tax revenue peaked during the 1960s, inflation peaked during the 1990s. Indeed, inflation was substantially higher during the latter period, when hyperinflation was going on. This evidence strongly suggests the occurrence of important financial innovations during the sample period, which sharply decreased the betaxolol of the inflation tax for a given inflation rate. Fig. 5 displays four different scatter plots between the (continuous) inflation rate (x-axis) and the associated inflation tax revenue (y-axis), according to the way each variable is measured. Note that the two graphs in the left half side do not show any obvious relationship between the two variables. However, the graphs placed on the right half side are more revealing concerning the shape of the inflation tax curve. In both cases inflation is measured in log terms and a clear positive relationship arises. The double-log specification seems to provide a slightly better fit, although it also suggests the possibility of a non-linear relationship.
    Empirical results Table 1 shows the ADF unit root test results for the inflation tax revenue, the inflation rate (measured in continuous terms) and associated transformations. The tests on the level of the variables do not reject the hypothesis of a unit root in all cases. However, the null is rejected when they are expressed in first differences, which means that all variables seem to be I(1). This result opens the possibility of estimating the inflation tax curve using a cointegration framework. In order to uncover the format of the inflation tax curve, a general-to-specific model selection strategy is used (see Hendry, 1995). The general unrestricted equilibrium correction model is as follows:where n is usually set at 2 and ST stands for a specific split trend. For example, ST70 indicates a time trend beginning in 1970. Note that the resulting split trend is an essential part of the model, since it acts as a proxy for (persistent) financial innovation, an unobservable variable according to economic theory, as argued in the last section. Indeed, as Fig. 4 strongly suggests, financial innovation was substantial during the period under analysis and it is a key factor in the inflation tax curve, given that it decreases the tax base for a given inflation rate. Therefore, it is likely to cause a structural break in the link between the inflation rate and the inflation tax revenue. Its exclusion from the model would yield a misspecification. Finally, note that (15) encompasses the possibility of a split trend with several breaks. This possibility makes theoretical sense since financial innovation could have evolved at different paces during the sample. For instance, the higher the inflation rate, the bigger the incentive for agents to come up with more money saving innovations. Eq. (16) shows the final selected specification (called Model 1 in Table 2). The variables are cointegrated, as indicates the significant lagged inflation tax revenue coefficient, suggesting a long-run relation among them. The model passes all diagnostic tests. Moreover, recursive estimates as well as recursive Chow tests show that parameters are stable and no obvious structural break is found. Those are significant results not only due to the long sample involved, but also due to the fact that during this period the Brazilian economy experienced significant changes and was subjected to large and frequent economic shocks, including several stabilization plans, most of them with heterodox features.T=52 (1952–2003); ; R2=0.98; DW=2.04; AR 1–2: F(2,36)=0.32 (0.73); ARCH 1–1: F(1,36)=0.65 (0.42); Hetero: F(23, 14)=0.32 (0.99); Normality: χ2(2)=1.59 (0.45); RESET: F(1, 37)=0.07 (0.79).