Identification of monetary shocks through the yield curve: Evidence for Brazil.
| Autor | Filho, Adonias Evaristo da Costa |
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Introduction
This paper derives a new measure of monetary shocks for Brazil, based on changes of the yield curve around monetary policy decisions. To obtain this new measure, first we estimate the Diebold and Li (2006) model with nominal yields. Then, we use the latent variables of this model to obtain the new shock series, which are used to assess the impact of monetary policy on the economy, through local projections.
This approach, therefore, takes into account variations of the whole yield curve around monetary policy announcements, rather than only short-term rates. Particularly after the Global Financial Crisis (GFC) of 2008, a number of countries used forward guidance and large-scale asset purchases (LASP) to try to stimulate their economies in the context of the lower bound of nominal interest rates. Forward guidance is usually associated with actions taken by central banks to influence interest rate expectations over the medium term. LASP policies, in turn, try to reduce long-term interest rates by reducing the term premium. The approach used in this paper has the advantage of capturing these dimensions of policy and can, therefore, be applied both to conventional and unconventional times. This approach follows recent research of Inoue and Rossi (2018) and Kortela and Nelimarkka (2020).
The literature on identification of monetary shocks is vast. Christiano et al. (1999) provide an early summary of identification based on the recursiveness assumption of VARs. In this approach, the main idea is that the policy interest rate reacts contemporaneously to output and inflation, but these variables react with a lag to innovations or exogenous movements in interest rates. Identification based on VAR with sign restrictions developed from Uhlig (2005). The dynamic stochastic general equilibrium (DSGE) literature, departing from Smets and Wouters (2007), identifies monetary shocks as the residuals of Taylor rules. Another approach, based on the narrative method of Romer and Romer (2004), regresses the policy rate on forecasts of GDP and inflation, and their revisions relative to previous quarters. These forecasts and revisions capture the endogenous component of monetary policy, while the residuals are taken as a shock measure, i.e., movements in the policy rate that do not reflect the state of the economy.
The idea of using financial market data, particularly fed fund futures, to identify monetary shocks can be traced back to Rudebusch (1998), Bagliano and Favero (1999), Kuttner (2001), and Faust et al. (2004). This identification scheme has the advantage of capturing the forward-looking behavior of monetary policy. This approach evolved to identification of monetary shocks based on exogenous changes in the principal components or factors extracted from a cross-section of interest rates. Gurkaynak et al. (2005) use a target and a path factor--this one closely related to the statements of the Fed--finding that long-term yields are very sensitive to the latter. Barakchian and Crowe (2013) develop a monetary shock measure extracting factors from fed fund futures. They use the first factor, interpreted as a level shock, to identify the responses of output and inflation to monetary policy. A recent example of this approach is Altavilla et al. (2019), who extract factors from changes in yields from one month to ten years around the press releases and conferences of the European Central Bank. They study the effects of monetary policy on stock prices, inflation-linked swaps, and the euro-dollar exchange rate.
Relative to the approach of extracting factors to measure monetary shocks, the approach in this paper estimates the Diebold and Li (2006) model, based on Inoue and Rossi (2018) and Kortela and Nelimarkka (2020). The advantage is that in the factor approach, the loadings are relatively unrestricted, while the Diebold and Li (2006) model imposes more discipline on the loadings (Diebold et al., 2005).
Recent papers often use high-frequency identification, based on intraday financial data around announcements (Gertler and Karadi, 2015; Nakamura and Steinsson, 2018; Jarocinski and Karadi, 2020). Ramey (2016) reviews the literature on macroeconomic shocks, including several approaches to identify monetary shocks. For Brazil, Costa Filho (2017) reviews the empirical evidence, and derives measures based on the methods of Romer and Romer (2004) and Barakchian and Crowe (2013).
Identification of monetary shocks from the yield curve is based on the idea that the term structure contains important information on the expected path of future interest rates and changes in the perception of risk and uncertainty in the economy by financial market participants (Inoue and Rossi, 2019). This information is lost in other approaches to identify shocks. While Brazil has never experienced zero-lower-bound episodes, identifying monetary shocks through the yield curve is likely more informative about other dimensions of monetary policy announcements. For instance, shifts in the whole yield curve are associated not only to changes in short-term policy rates, but also to the expected future path of short-term interest rates conveyed through communication from the central bank.
The content of this paper is of interest to financial market participants, policymakers, and academics, having both practical and theoretical consequences.
The rest of the paper is organized as follows. Section 2 describes the Diebold and Li (2006) model. Section 3 presents the data. Section 4 shows the results of the estimation. Section 5 estimates the effects on inflation, measures of economic activity, and the real exchange rate through local projections. Section 6 estimates the effects on the economy considering the latent variables in all months, regardless of whether monetary policy meetings occurred or not. Section 7 presents a comparison with other monetary shocks in the literature. Finally, section 8 concludes.
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Diebold and Li (2006) model
In the Diebold and Li (2006) model, the yield curve is a function of three unobservable factors (level, curvature, and slope). Given some restrictions on the factor loadings, these can be interpreted as long-, medium-, and short-term factors, respectively. The model is given by the following function:
[mathematical expression not reproducible] (1)
where [r.sub.[tau],t] is the annualized zero-coupon interest rate of maturity [tau]. For the sake of standardization, we express bond maturities in months ([tau] = 1, 3, 6, 12, 18, 24, 30, 36, 48, 60, 120), not years. This follows Diebold and Li (2006), Diebold et al. (2006), and Caldeira et al. (2010), who express bond maturity in months.
[L.sub.t], [S.sub.t], and [C.sub.t] are the level, slope, and curvature factors, respectively, and [lambda] is a constant that governs the exponential rate of decay of the loadings. The greater this parameter, the faster is the decay of long-term maturities. The loading on the first factor is constant, affecting all interest rates in the same way, so it determines the level of the curve. The loading on the slope factor affects short rates more than long rates, and the loading of the curvature factor exerts more impact on medium-term rates.
The model is expressed in state space form and estimated by maximum likelihood using the Kalman Filter, following Diebold et al. (2006). Caldeira et al. (2010) defend the estimation of the Diebold-Li model using only one step and making use of the Kalman filter as opposed to the two-step method, since it leads to efficient parameter estimates, as the measurement and state equations are estimated jointly, and also due to the fact that in the one-step estimation there is no need to assume a particular value for the decay parameter [lambda].
Departing from Equation (1) for [tau] = 1, 3, 6, 12, 18, 24, 30, 36, 48, 60, and 120 months, the measurement equations are given by
[r.sub.t] = [LAMBDA][f.sub.t] + [[epsilon].sub.t], (2)
where
[mathematical expression not reproducible],
[LAMBDA] is the 11 x 3 matrix whose [tau]th row is
[mathematical expression not reproducible],
and where [f.sub.t] = [[L.sub.t] [S.sub.t] [C.sub.t]]' and
[mathematical expression not reproducible].
The state equations form a VAR(1):
([f.sub.t] - [mu]) = A ([f.sub.t-1] - [mu]) + [[xi].sub.t] (3)
where [[mu].sub.L], [[mu].sub.S], and [[mu].sub.c] denote the means of the factors and [f.sub.t] = [[L.sub.t] [S.sub.t] [C.sub.t]]',
[mathematical expression not reproducible]
and [mu] = [[[mu].sub.L] [[mu].sub.S] [[mu].sub.C]]', so that Equation (3) can be specified in more detail as
[mathematical expression not reproducible]. (4)
For the errors, the assumption is that the terms in the measurement equations are not cross-correlated, but can be correlated in the state equations. Therefore, it is allowed that the covariance between the level, slope, and curvature factors may be different from zero. In other words, it is assumed that the [[[xi].sup.j].sub.t] are mutually correlated, while the [[epsilon].sub.([tau],t)] are mutually independent and uncorrelated with [[[xi].sup.j].sub.t], for j = L,S,C.
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Data
To estimate the Diebold-Li model, nominal yields of eleven maturities are used: 1-month, 3-month, 6-month, 1-year, 1.5-year, 2-year, 2.5-year, 3-year, 4-year, 5-year, and 10-year. The data is on a daily basis, ranging from the beginning of 2004 to the end of 2019, encompassing 4,174 observations. The series used in the estimation were downloaded from Bloomberg, with the following tickers: PREDI30, PREDI90, PREDI180, PREDI360, PREDI540, PREDI720, PREDI900, PREDI1080, PREDI1440, PREDI1800 and PREDI2520 Index. Figure 1 depicts most series used in the estimation.
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Results
Table 1 presents the estimated coefficients of the Diebold-Li model presented in Section 2.
For the estimation, the initial values of the level ([[mu].sub.L] = 12), slope ([[mu].sub.S] = 1), and curvature ([[mu].sub.C] = 0.7) are set at their empirical counterparts. The...
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