Equilibrium real interest rates in Brazil: Convergence at last, but not quite.
| Autor | Fonseca, Marcelo |
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Introduction
After controlling inflation with the launch of the Real plan in 1994, Brazil was finally able to bring the real interest rate to a level close to zero at the end of 2019, just before the pandemic. This convergence was short-lived. In early 2022, the Selic rate was back to double digits and real rates were close to 5%. During most of the pandemic, the central bank policy rate (Selic rate) was at 2%, a record low. The effective real interest rate (360-PreDI Swap discount by 12-month inflation expectation) reached -0.75% in June 2020, the lowest level ever, and at the end of that August, it was slightly below zero. However, the easing cycle did not last long. The effective real interest rate increased throughout 2021, reaching 9.25% in December. Consensus expectations predict it will reach 11.50% in mid-2022.
In this paper we define the equilibrium interest rate as the one that stabilizes the economy, driving inflation to a target and the output gap to this potential level. Magud and Tsounta (2012) divide the methodologies used to calculate the equilibrium interest rate into two categories:
* Static methodologies:
- Consuming smoothing models;
- Uncovered interest parity;
* Dynamic methodologies:
- Hodrick-Prescott (HP) filter;
- Implicit common stochastic trend;
- Dynamic Taylor rule;
- Taylor rule with augmented inflation expectation;
- General equilibrium model.
This is the third paper to measure the equilibrium real interest rate in Brazil with different approaches, following Miranda and Muinhos (2003) and Muinhos and Nakane (2006).
Laubach and Williams (2003) focus on estimating the real interest rate--consistent with output equalizing potential and stable inflation--on a medium-run concept of price stability that does not consider the effects of short-run price and output fluctuations. Their purpose is to show that the time variation in the natural interest rate is important for analysis. Monetary policy performance and its real-time mismeasurement can significantly hamper macroeconomic stabilization.
Given a definition that considers deviation of output from potential, estimating the natural interest rate also entails finding the potential output. Moreover, since the natural interest rate and the trend growth rate are connected, Laubach and Williams (2003) must estimate both the level of potential output and its growth rate trend. Therefore, they use the Kalman filter to estimate these unobserved variables. Besides the Kalman filter, they model the cyclical dynamics of output and inflation using restricted VAR. Then, employing median-unbiased estimates of these coefficients, based on Stock and Watson (1998), they apply the maximum likelihood to estimate the remaining model parameters.
After estimating the model using quarterly US data from the period from 1961 to 2000, Laubach and Williams (2003) use simulations of the estimated model to assess the effects of natural interest rate mismeasurement. They find that mismeasurement leads to a significant deterioration in output stabilization, but has relatively modest effects on inflation stabilization.
Barcellos Neto and Portugal (2008) were the first to attempt to calculate the natural interest rates for Brazil using the Laubach and Williams method. However, since their estimation period ended in 2005, in the first stages of inflation targeting in Brazil, the outcome of the estimation shows a rate hovering around 10%, which is significantly higher than the range we expect nowadays.
Araujo and Silva (2014) also present some different methodologies to measure the Brazilian neutral real interest rate: i) statistical filters; and ii) a state-space macroeconomic model. They include variables such as the real exchange rate, credit default swap, and an international interest rate. In the period they consider, from 2002 to the end of 2012, they find the country's natural interest rate to be around 3.5%.
Perrelli et al. (2014) follow the same approach, trying to measure the equilibrium interest rate using statistical filters, short- and long-run estimation of IS curve micro-founded models, and even a state-space model similar to Goldfajn and Bicalho (2011), but none of the adopted methodologies are even close to Laubach and Williams (2003).
The objective of this paper is to measure the equilibrium interest rate in Brazil using different methodologies.
In the first, based on Schulz (2019), we combine static and dynamic approaches, starting with simple ones like the long-run real interest rate average, ending up in a dynamic Taylor rule in a fixed-effect panel with 27 emerging countries measured quarterly from 1995 to 2019. In this approach, we also include a simple Taylor rule and a Hodrick-Prescott filter.
The second, which is the core of the paper, is a version of the Laubach and Williams (2003) approach for Brazil. We consider the equilibrium interest rate and the output gap as state variables. One innovation is to include fiscal and credit variables as explanatory variables in the process. We also add the Brazilian risk premium and the US interest rates in the process to calculate the equilibrium real interest rate in Brazil. In addition, we test different methodologies to obtain the output gap, to improve the robustness of the measure of the equilibrium real rate.
The third approach is an update of those of Goldfajn and Bicalho (2011), Perrelli et al. (2014), and Augusto (2018), extending the period from 2003 to 2020 to gain a better view of the variables that allowed the recent real interest rate convergence to low levels.
The following section presents the Taylor rule methodology and the new variables that we include in the model. In the third section, we present our version of the Laubach and Williams (2003). In the fourth, we show the updated version of the short and long interest rate approach. In the fifth section we compare the effective interest rate with an average of the semi-Laubach Williams and an estimated Taylor rule. The last section is a summary and conclusion.
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Taylor rule approach
In this section, neutral interest rate (NIR) is estimated by four models: the long-term average of the real interest rate, the Hodrick and Prescott (HP) filter, a standard Taylor rule, and a dynamic Taylor rule--the latter, through a panel data regression with fixed effects, for the period 1995-2019 in quarterly terms. The results show that (a) Brazil's interest rate is high in neutral, nominal, and real terms (compared to other emerging economies); and (b) NIR has declined consistently over the past few decades.
2.1 Methodology
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Long-run real interest rate (RIR) Based on the model of Miranda and Muinhos (2003), NIR can be estimated as a long-term trend. In this case, we calculate the arithmetic mean of the RIR over a five-year period (20 quarters), with the final long-term RIR estimate being the average of the estimates for these four periods.
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HP filter NIR is estimated with the Hendrick Prescott filter using quarterly RIR data between 1985Q1 to 2025Q4. We use projections when available from the IMF or OECD; and when not, we stretch the value of the last period, so as to reduce possible distortions at the extremes (periods tending to 1995 and 2019) by the filter.
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Standard Taylor rule The Taylor rule is a standard monetary policy response in which the monetary authority reacts to an inflation deviation from the target or to an output deviation from the potential. A Taylor rule (generalized version) is given by
[i.sub.t] - [i.sup.*] = [a.sub.[pi]] ([[pi].sub.t] -...
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