Formally defining as the inflation rate in period t and

Formally, defining as the inflation rate in buy MLN2238 t and the nominal interest rate, the behavior of the economy can be represented by two equations, one on the demand side, called the IS curve, and the other on the supply side, the Phillips curve.where is the inflation rate at period t, defined as the percentage change in the price level between t−1 and t; is the output gap; is the expected inflation rate at period t over t+1 inflation; is the expected output gap at t over period t+1 output gap; R is the short-run nominal interest rate. In Addition, and are errors terms obeying the following structures, respectively:, and are independent and identically distributed random variables (i.i.d), with mean zero, variances and , respectively. The Phillips curve in Eq. (2) is derived from an explicit optimization problem in a context of monopolistic competition, in which each firm sets its price level subject to future adjustments. The main difference of this proposition in relation to the original Phillips curve is the inclusion of the variable regarding future expected inflation rate, . So, this is a forward looking process instead of the traditional backward looking process, . Also, note that the coefficient of the output gap is decreasing in the degree of rigidities in prices and represents possible supply shocks. To close the model specification we need a core equation that determines interest rate, which is in our case the COPOM reaction function. In the model proposed by Clarida et al. (1999) there is an innovation in relation to the traditional Taylor Rule (1993). More precisely, inflation expectation is explicit and a forward-looking process. As highlighted by the authors, this monetary policy rule responds to the expected inflation rather than to past inflation. The innovation makes it more consistent with the overall model represented by Eqs. (1)–(4). Hence, Eq. (5) is the focus of our next section and of our empirical work.
Empirical evidence on reaction functions estimates A seminal work about monetary policy rules with inflation targeting is Taylor (1993). It highlights the determination of the interest rate as a monetary instrument to achieve the inflation target. According to the author, policymakers should identify relevant variables for the economy\'s price stability. By managing the interest rate in response to changes in these variables, policymakers would achieve price stability in the economy. The first estimates made by Taylor (1993) considered a simple linear reaction function that expressed the behavior of interest rates. His estimates for the United States for the period 1987–1992 had as main characteristic explaining variables like the deviation of inflation from its equilibrium value (or target), and the deviation from real output relative to its potential level. The proposed function was:where i is the Federal Funds interest rate; r* is the equilibrium real interest rate; π is the inflation rate (from GDP deflator); π* is the inflation target; and y is the percentage deviation of real output in relation to the potential output (output gap). The author\'s empirical results show that the predicted interest rate was a close approximation to the actual interest rate in the U.S. economy for the period 1987–1992. Note that Taylor points to a target or equilibrium inflation rate of 2%. The U.S. Federal Reserve (Fed) would respond to deviations from the actual inflation rate from the equilibrium level of 2% and to deviations of output based on a backward-looking process. Despite his notorious contribution, the Taylor\'s Rule (1993) lacked variables that account for future expectations about inflation and output. To address this deficiency, several studies have modified slightly the Taylor\'s reaction function. Among the pioneering works, Judd and Rudebush (1998) estimated a reaction function for the Fed during three different institutional presidents. The purpose of work was to evaluate the hypothesis that the turnovers of central bank presidents might also influence monetary policy. Their first estimate was of Taylor\'s reaction function in order to use it as baseline. As expected, this function did not adhere well to the overall data sample. It means that each one of the Central Bank administration had its own way of conducting monetary policy. To adjust the reaction function to capture such change in administration, the authors assumed that the authorities did not react instantaneously to economic changes. This assumption led the authors to propose the following reaction function specification