- Email: [email protected]
Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments
Economics Letters xxx (xxxx) xxx
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments Woon Wook Jang College of Government and Business, Yonsei University, 1 Yonseidae-gil, Wonju, Gangwon-Do 220-710, South Korea
article
info
Article history: Received 28 June 2019 Accepted 7 September 2019 Available online xxxx JEL classification: E43 E44 E52 E58
a b s t r a c t This study uses structural vector autoregression models to examine the monetary policy (MP) effects on risk aversion, uncertainty, and inflation. MP shocks are identified with high-frequency external instruments, rather than Cholesky decomposition. The instruments include asset price changes in the 30-minute window around FOMC announcements and their decomposition into three orthogonal factors. The impulse-response analysis results are consistent with the standard MP effects theory, unlike with the Cholesky decomposition method. © 2019 Elsevier B.V. All rights reserved.
Keywords: Risk aversion Uncertainty Monetary policy Structural vector autoregression High-frequency data
1. Introduction Bekaert et al. (2013) decomposed the volatility index (VIX) into risk aversion (RA) and uncertainty (UC) components, and studied the monetary policy (MP) effects on the RA and UC for the pre-crisis period using a structural vector autoregressive (SVAR) framework. They showed a tightening MP counter-intuitively decreased the RA and UC for almost the first half-year, which increased in values from the second half, to reach the maxima after 20 and 21 months of the shock, respectively. Hahn et al. (2017) extended the analysis to the post-crisis period using the ‘‘shadow short rates’’ as the MP stance measures, to find that the mixed results of Bekaert et al. (2013) persisted even during that period. Since the RA and UC variables are decomposed from fastchanging financial asset prices reflecting market information, the initial negative impact on the RA and UC and the long-delayed positive response of those values can be puzzling. This could be due to the timing restriction imposed by the SVAR models’ Cholesky decomposition identification adopted in the above-mentioned papers. Gertler and Karadi (2015) indicate a ‘‘simultaneity’’ problem of a SVAR model when incorporating financial variables. Specifically, a change in MP might influence the financial variables, but those values could affect the decision
E-mail address: [email protected].
of the Federal Open Market Committee (FOMC). Generally, information changing the MP and financial variables simultaneously can render the Cholesky decomposition method inadequate. This paper adopts an external instrument variable (IV) approach to identify SVAR models (for an introduction, see Mertens and Ravn (2013) and Gertler and Karadi (2015)). For external instruments, we use the measurements of various asset price changes in the 30-min window around each FOMC meeting from 1991 to 2015. These measurements provide unexpected MP shocks, and their use for identification would render the endogenous variable ordering in the SVAR models irrelevant. In addition to the RA and UC, we include an inflation measure in our SVAR models to see whether the external IV approach resolves the ‘‘price puzzle’’ of increasing price level after a tightening MP shock. Finally, in line with Swanson (2018), we identify three independent MP effects from high-frequency data and use them as the external instruments to see the effects of each factor on the RA, UC, and inflation. In contrast to the findings of Bekaert et al. (2013) and Hahn et al. (2017), empirical analysis shows that the RA and UC increase instantly to one standard deviation MP shock, with the responses staying positive for about a quarter, and the effects disappearing thereafter. The results also show no price puzzle in the external IV approach; the forward guidance and large-scale asset purchases factors of MP shocks have stronger effects on the RA and UC than the federal fund rate factor.
https://doi.org/10.1016/j.econlet.2019.108675 0165-1765/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
2
W.W. Jang / Economics Letters xxx (xxxx) xxx
Fig. 1. Three MP factors effects: Federal fund rate, forward guidance, and LSAPs.
In what follows, Section 2 explains the data and introduces the MP effects decomposition method of Swanson (2018), Section 3 introduces the high-frequency external instruments identification method of SVAR models, Section 4 shows the empirical results, and Section 5 discusses the direction for future work. 2. Risk appetite data and measures, and MP identification effects We use the U.S. government bond spot rates from Gürkaynak et al. (2007). For inflation measure (INF), we use the year-onyear changes in price levels computed from the Federal Reserve Economic Data monthly consumer price index for all urban consumers. 2.1. RA and UC Following Bekaert et al. (2013), we project the future onemonth realized variances (RVARt +22 , computed from the fiveminute intraday S&P 500 index data) onto the implied variance (VIXt2 , the squared CBOE VIX) and the past one-month realized variances (RVARt ). Eq. (1) shows the projection results based on the daily data from January 1990 to December 2015 (the Newey–West serial correlation corrected standard errors are in parentheses). Then, the fitted value is defined as the UC measure, and the difference between the squared VIX, and UC is defined as the RA measure. RVARt +22 = −0.00006 + 0.33743VIX 2 t + 0.28685RVARt
(0.0002)
(0.07249)
Swanson (2018) defined the FG factor as ‘‘the component of FOMC announcements that conveys information about the future path of short-term interest rates above and beyond changes in the target federal funds rate itself’’. Likewise, the LSAP factor was defined as the ‘‘effects on the yield curve that are above and beyond the usual effects of changes in forward guidance’’. Following these definitions, Swanson (2018) placed restrictions on factor decomposition. Fig. 1 shows the time-series of the three factors, where the values of LSAP factor were multiplied by minus one, so that negative values indicate a lax monetary policy like the FFR and FG factors. By comparing Fig. 1 with some FOMC events, we can confirm that the decomposition is meaningful; for example, the ‘‘QE 1’’ of March 18, 2009; ‘‘Operation Twist’’ of September 21, 2011; and ‘‘Taper Tantrum’’ around the middle of 2013. For more details about the factor correspondence to FOMC announcements, refer to the explanation in Swanson (2018). 3. External instrument identification of SVAR model Let yt be an n × 1 vector of observables including the MP mp indicator variable yt . For expositional simplicity, assume that yt follows a SVAR (1) process as in Eq. (2) and a reduced-form representation as in Eq. (3): Ayt = Byt −1 + ut
(2)
(1)
(0.10146)
2.2. Identification of MP effects: FFR, FG, and LSAP factors We obtained asset price changes in the 30-min window around each FOMC announcement (10 min before and 20 min after the announcement) from staff at the Federal Reserve Board. This high-frequency data include the federal funds futures contracts (the current- and three-month maturities), Eurodollar futures contracts (the second-, third-, and fourth-quarter maturities), and Treasury bond yields (two-, five-, and ten-year maturities) for the period 1991–2015. Following Swanson (2018), we extract the first three principal component factors of the high-frequency asset price changes and transform them to identify three independent MP effects, the FFR factor, FG factor, and LSAPs factor. A change in FFR contains information for the future path of its own values. However,
yt = Cyt −1 + et ,
(3) −1
where A, B, and C are n × n coefficient matrices s.t. C = A B; ut is an n × 1 vector of unobservable structural shocks with zero mean and identity covariance matrix; and et = Dut is a reduced-form residual with D = A− 1 . ˆ Dˆ ′ provides n(n + An estimated covariance matrix Eˆ [et et ′ ] = D 1)/2 identifying restrictions; however, n(n − 1)/2 restrictions are required to identify the whole system. Here, the standard Cholesky decomposition restriction assumes that A is a lower triangular matrix, leading to n(n − 1)/2 restrictions. Alternatively, we use the external instruments identification approach, explained as follows. [ mp ]′ [ mp ]′ Consider partitioning yt = yt y∗′ , ut = ut u∗′ , and t t
[
mp
]′
et = et e∗′ , where the terms with superscript ‘‘mp’’ denote t an MP indicator, a structural MP shock, and a reduced-form MP equation residual, respectively, and the terms with ‘‘∗’’ denote the
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
W.W. Jang / Economics Letters xxx (xxxx) xxx
3
Fig. 2. Impulse response function analysis: Cholesky decomposition vs. external instrument. Note: The dotted line and shaded area represent 68% and 95% confidence interval, respectively, drawn with 10,000 replications.
other n − 1 variables. Since the external instruments approach does not consider the ordering in the variables of yt , ut , and et , the mp terms need not be the first element of each variable. Let zt be a mean zero external IV correlated with MP shock mp ut , but orthogonal to the other n − 1 shocks u∗t , s.t. E
[
mp zt ut
]
∗
]
[
=ρ
E z t ut = 0 where ρ is an unknown scalar. mp We compute the impulse-response to a monetary shock of ut , and let d denote the column in matrix D corresponding to the mp impact of the structural policy shock of ut . Then, for our purpose, we need to identify mp
yt = Cyt −1 + dut
]′
]′
If we partition d = dmp d∗′ , then with E [zt et ] = ρ dmp d∗′ mp ′ and E [zt et ] = E [zt et zt e∗′ t ] , following Mertens and Ravn (2013),
[
[
we can derive d∗ dmp
[
=
E zt e∗t
[
]
mp
E zt et
]
(4)
Here, we can estimate the right-hand side of Eq. (4) from the mp regression of the reduced-form residuals et and e∗t respectively on external instrument zt . In addition, Gertler and Karadi (2015) derived a formula for dmp , and so we can identify d∗ separately from d∗ /dmp . In our empirical analysis, following Gertler and Karadi (2015), we use the one-year government bond spot rate (GS1) as an mp MP indicator yt , and the (high-frequency) federal funds futures contract of three-month maturity (FF4) as an external instrument zt . The other endogenous variables in the vector of y∗t are the RA, UC, and INF. Additionally, to find the effects of the FFR, FG, and LSAP on RA, UC, and INF, we sequentially replace the GS1–FF4 combination with the GS–FFR, GS5–FG, and GS10–LSAP combinations (here, GS5 and GS10 are the five- and ten-year government bond spot rates.) These combinations are based on
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
4
W.W. Jang / Economics Letters xxx (xxxx) xxx
Fig. 3. Impulse response function analysis with three factors of MP effects as external instruments. Note: The dotted line and shaded area represent 68% and 95% confidence interval, respectively, drawn with 10,000 replications.
the event-study regression results of Swanson (2018), where the FFR factor affects mostly short-maturity bonds, and the FG and LSAP factors affect mid- and long-term bonds, respectively. 4. Empirical results Fig. 2 shows the difference between the impulse-responses of SVAR models using the Cholesky decomposition method (columns A and B) and those using high-frequency external instruments; that is, GS1–FF4 (column C). In column A, we replicate the results of Bekaert et al. (2013) and Hahn et al. (2017) using real FFR for the conventional MP period, and Wu and Xia’s (2016) shadow short rates for the unconventional MP period as an MP stance. Column B also uses the Cholesky decomposition as in column A, but with one difference: that the one-year government bond spot rate (GS1) is used as the MP stance as in column C, to compare the role of the high-frequency external instrument with that of the Cholesky decomposition. In column C, we use GS1 as an MP indicator
and the three-month ahead high-frequency federal funds futures contract (FF4) as an external MP instrument; that is, GS1–FF4. All the daily data are averaged and converted into monthly data; the high-frequency FOMC event date data are also converted to monthly basis following the transform method of Gertler and Karadi (2015). We estimated the SVAR models with two lags selected using the Bayesian and Hannan–Quinn information criteria respectively. The dotted line and shaded area in each panel of Fig. 2 represent 68% and 95% confidence intervals, respectively, drawn with 10,000 replications. The RA and UC responses in column A to one standard deviation MP shock are typical results of Bekaert et al. (2013) and Hahn et al. (2017), that is, initial negative and medium-run positive responses. The INF response also shows a typical price puzzle: a positive initial price-level response after a tightening MP shock. The results in column B, from using GS1 as an MP stance instead of federal funds and shadow short rates, are qualitatively the same as those in column A. When we adopt the external instrument approach in column C, however, the RA and UC increase instantly after a positive MP
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
W.W. Jang / Economics Letters xxx (xxxx) xxx
shock, remain for about half a year, and then disappear. Furthermore, the INF decreases after a tightening MP shock, indicating that the price puzzle can be resolved. Gertler and Karadi (2015) chose the GS1–FF4 pair as the MP indicator/external instrument because this combination might capture the effects of both target rate change and MP forward guidance. However, they did not decompose the two effects. In this paper, we separately apply the FFR and FG factors as instruments. In addition, we apply the LSAP factor as an instrument, and report the results in Fig. 3. Columns A, B, and C of Fig. 3 show respectively the responses of the MP indicator RA, UC, and INF to one standard deviation MP shocks (GS1, GS5, and GS10, respectively) using external instruments (FFR, FG, and LSAP, respectively). To compare the responses of each variable to the three different MP indicator shocks (with its corresponding instrument), we adjust the vertical axis of each row to the same scale. Fig. 3 shows that the RA and UC responses to the GS5–FG shock are the highest, followed by those to the GS10–LSAP shock. Interestingly, the RA and UC response to the GS1–FFR shock is minimal. However, all the RA and UC responses (in columns A, B, and C) show an initial positive response, as in column C of Fig. 2. The inflation response to the GS5–FG shock is negative and the highest, followed by that to the GS1–FFR shock. However, the response to the GS10–LSAP shock is significantly positive for about one quarter, implying that the termination of purchases of mortgage-backed securities and long-term Treasuries increases the price level. This is also consistent with intuition, since tapering shocks increase bond yields, with inflation expectation taking a significant portion of that yield.
5
5. Direction for future work This paper used external instruments for model identification. We used the 30-minute window data of the three-month federal funds futures contract around each FOMC announcement as an external MP instrument. As another instruments, we also applied the three independent factors of the MP effects extracted from high-frequency data. We then compared the RA, UC, and inflation responses to each of the different MP shocks. However, since unconventional MPs have been implemented during the post-crisis period, each variable might have responded differently depending on the period considered. Further research is required on this issue to identify the MP factor needed for an economy facing different environments. References Bekaert, G., Hoerova, M., Lo Duca, M., 2013. Risk, uncertainty and monetary policy. J. Monetary Econ. 60, 771–788. Gertler, Karadi, 2015. Monetary policy surprises, credit costs, and economic activity. Am. Econ. J. Macroecon. 7 (1), 44–76. Gürkaynak, R.S., Sack, B., Wright, J., 2007. The U.S. Treasury yield curve: 1961 to the present. J. Monetary Econ. 54 (8), 2291–2304. Hahn, J., Jang, W.W., Kim, S., 2017. Risk aversion, uncertainty, and monetary policy in zero lower bound environments. Econom. Lett. 156 (2017), 118–122. Mertens, K., Ravn, M.O., 2013. The dynamic effects of personal and corporate income tax changes in the United States. Amer. Econ. Rev. 103 (4), 1212–1247. Swanson, E., 2018. Measuring the effects of federal reserve forward guidance and asset purchases on financial markets, NBER Working Paper 23311. Wu, J.C., Xia, F.D., 2016. Measuring the macroeconomic impact of monetary policy at the zero lower bound. J. Money Credit Bank. 48 (2–3), 253–291.
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
Contents lists available at ScienceDirect
Economics Letters journal homepage: www.elsevier.com/locate/ecolet
Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments Woon Wook Jang College of Government and Business, Yonsei University, 1 Yonseidae-gil, Wonju, Gangwon-Do 220-710, South Korea
article
info
Article history: Received 28 June 2019 Accepted 7 September 2019 Available online xxxx JEL classification: E43 E44 E52 E58
a b s t r a c t This study uses structural vector autoregression models to examine the monetary policy (MP) effects on risk aversion, uncertainty, and inflation. MP shocks are identified with high-frequency external instruments, rather than Cholesky decomposition. The instruments include asset price changes in the 30-minute window around FOMC announcements and their decomposition into three orthogonal factors. The impulse-response analysis results are consistent with the standard MP effects theory, unlike with the Cholesky decomposition method. © 2019 Elsevier B.V. All rights reserved.
Keywords: Risk aversion Uncertainty Monetary policy Structural vector autoregression High-frequency data
1. Introduction Bekaert et al. (2013) decomposed the volatility index (VIX) into risk aversion (RA) and uncertainty (UC) components, and studied the monetary policy (MP) effects on the RA and UC for the pre-crisis period using a structural vector autoregressive (SVAR) framework. They showed a tightening MP counter-intuitively decreased the RA and UC for almost the first half-year, which increased in values from the second half, to reach the maxima after 20 and 21 months of the shock, respectively. Hahn et al. (2017) extended the analysis to the post-crisis period using the ‘‘shadow short rates’’ as the MP stance measures, to find that the mixed results of Bekaert et al. (2013) persisted even during that period. Since the RA and UC variables are decomposed from fastchanging financial asset prices reflecting market information, the initial negative impact on the RA and UC and the long-delayed positive response of those values can be puzzling. This could be due to the timing restriction imposed by the SVAR models’ Cholesky decomposition identification adopted in the above-mentioned papers. Gertler and Karadi (2015) indicate a ‘‘simultaneity’’ problem of a SVAR model when incorporating financial variables. Specifically, a change in MP might influence the financial variables, but those values could affect the decision
E-mail address: [email protected].
of the Federal Open Market Committee (FOMC). Generally, information changing the MP and financial variables simultaneously can render the Cholesky decomposition method inadequate. This paper adopts an external instrument variable (IV) approach to identify SVAR models (for an introduction, see Mertens and Ravn (2013) and Gertler and Karadi (2015)). For external instruments, we use the measurements of various asset price changes in the 30-min window around each FOMC meeting from 1991 to 2015. These measurements provide unexpected MP shocks, and their use for identification would render the endogenous variable ordering in the SVAR models irrelevant. In addition to the RA and UC, we include an inflation measure in our SVAR models to see whether the external IV approach resolves the ‘‘price puzzle’’ of increasing price level after a tightening MP shock. Finally, in line with Swanson (2018), we identify three independent MP effects from high-frequency data and use them as the external instruments to see the effects of each factor on the RA, UC, and inflation. In contrast to the findings of Bekaert et al. (2013) and Hahn et al. (2017), empirical analysis shows that the RA and UC increase instantly to one standard deviation MP shock, with the responses staying positive for about a quarter, and the effects disappearing thereafter. The results also show no price puzzle in the external IV approach; the forward guidance and large-scale asset purchases factors of MP shocks have stronger effects on the RA and UC than the federal fund rate factor.
https://doi.org/10.1016/j.econlet.2019.108675 0165-1765/© 2019 Elsevier B.V. All rights reserved.
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
2
W.W. Jang / Economics Letters xxx (xxxx) xxx
Fig. 1. Three MP factors effects: Federal fund rate, forward guidance, and LSAPs.
In what follows, Section 2 explains the data and introduces the MP effects decomposition method of Swanson (2018), Section 3 introduces the high-frequency external instruments identification method of SVAR models, Section 4 shows the empirical results, and Section 5 discusses the direction for future work. 2. Risk appetite data and measures, and MP identification effects We use the U.S. government bond spot rates from Gürkaynak et al. (2007). For inflation measure (INF), we use the year-onyear changes in price levels computed from the Federal Reserve Economic Data monthly consumer price index for all urban consumers. 2.1. RA and UC Following Bekaert et al. (2013), we project the future onemonth realized variances (RVARt +22 , computed from the fiveminute intraday S&P 500 index data) onto the implied variance (VIXt2 , the squared CBOE VIX) and the past one-month realized variances (RVARt ). Eq. (1) shows the projection results based on the daily data from January 1990 to December 2015 (the Newey–West serial correlation corrected standard errors are in parentheses). Then, the fitted value is defined as the UC measure, and the difference between the squared VIX, and UC is defined as the RA measure. RVARt +22 = −0.00006 + 0.33743VIX 2 t + 0.28685RVARt
(0.0002)
(0.07249)
Swanson (2018) defined the FG factor as ‘‘the component of FOMC announcements that conveys information about the future path of short-term interest rates above and beyond changes in the target federal funds rate itself’’. Likewise, the LSAP factor was defined as the ‘‘effects on the yield curve that are above and beyond the usual effects of changes in forward guidance’’. Following these definitions, Swanson (2018) placed restrictions on factor decomposition. Fig. 1 shows the time-series of the three factors, where the values of LSAP factor were multiplied by minus one, so that negative values indicate a lax monetary policy like the FFR and FG factors. By comparing Fig. 1 with some FOMC events, we can confirm that the decomposition is meaningful; for example, the ‘‘QE 1’’ of March 18, 2009; ‘‘Operation Twist’’ of September 21, 2011; and ‘‘Taper Tantrum’’ around the middle of 2013. For more details about the factor correspondence to FOMC announcements, refer to the explanation in Swanson (2018). 3. External instrument identification of SVAR model Let yt be an n × 1 vector of observables including the MP mp indicator variable yt . For expositional simplicity, assume that yt follows a SVAR (1) process as in Eq. (2) and a reduced-form representation as in Eq. (3): Ayt = Byt −1 + ut
(2)
(1)
(0.10146)
2.2. Identification of MP effects: FFR, FG, and LSAP factors We obtained asset price changes in the 30-min window around each FOMC announcement (10 min before and 20 min after the announcement) from staff at the Federal Reserve Board. This high-frequency data include the federal funds futures contracts (the current- and three-month maturities), Eurodollar futures contracts (the second-, third-, and fourth-quarter maturities), and Treasury bond yields (two-, five-, and ten-year maturities) for the period 1991–2015. Following Swanson (2018), we extract the first three principal component factors of the high-frequency asset price changes and transform them to identify three independent MP effects, the FFR factor, FG factor, and LSAPs factor. A change in FFR contains information for the future path of its own values. However,
yt = Cyt −1 + et ,
(3) −1
where A, B, and C are n × n coefficient matrices s.t. C = A B; ut is an n × 1 vector of unobservable structural shocks with zero mean and identity covariance matrix; and et = Dut is a reduced-form residual with D = A− 1 . ˆ Dˆ ′ provides n(n + An estimated covariance matrix Eˆ [et et ′ ] = D 1)/2 identifying restrictions; however, n(n − 1)/2 restrictions are required to identify the whole system. Here, the standard Cholesky decomposition restriction assumes that A is a lower triangular matrix, leading to n(n − 1)/2 restrictions. Alternatively, we use the external instruments identification approach, explained as follows. [ mp ]′ [ mp ]′ Consider partitioning yt = yt y∗′ , ut = ut u∗′ , and t t
[
mp
]′
et = et e∗′ , where the terms with superscript ‘‘mp’’ denote t an MP indicator, a structural MP shock, and a reduced-form MP equation residual, respectively, and the terms with ‘‘∗’’ denote the
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
W.W. Jang / Economics Letters xxx (xxxx) xxx
3
Fig. 2. Impulse response function analysis: Cholesky decomposition vs. external instrument. Note: The dotted line and shaded area represent 68% and 95% confidence interval, respectively, drawn with 10,000 replications.
other n − 1 variables. Since the external instruments approach does not consider the ordering in the variables of yt , ut , and et , the mp terms need not be the first element of each variable. Let zt be a mean zero external IV correlated with MP shock mp ut , but orthogonal to the other n − 1 shocks u∗t , s.t. E
[
mp zt ut
]
∗
]
[
=ρ
E z t ut = 0 where ρ is an unknown scalar. mp We compute the impulse-response to a monetary shock of ut , and let d denote the column in matrix D corresponding to the mp impact of the structural policy shock of ut . Then, for our purpose, we need to identify mp
yt = Cyt −1 + dut
]′
]′
If we partition d = dmp d∗′ , then with E [zt et ] = ρ dmp d∗′ mp ′ and E [zt et ] = E [zt et zt e∗′ t ] , following Mertens and Ravn (2013),
[
[
we can derive d∗ dmp
[
=
E zt e∗t
[
]
mp
E zt et
]
(4)
Here, we can estimate the right-hand side of Eq. (4) from the mp regression of the reduced-form residuals et and e∗t respectively on external instrument zt . In addition, Gertler and Karadi (2015) derived a formula for dmp , and so we can identify d∗ separately from d∗ /dmp . In our empirical analysis, following Gertler and Karadi (2015), we use the one-year government bond spot rate (GS1) as an mp MP indicator yt , and the (high-frequency) federal funds futures contract of three-month maturity (FF4) as an external instrument zt . The other endogenous variables in the vector of y∗t are the RA, UC, and INF. Additionally, to find the effects of the FFR, FG, and LSAP on RA, UC, and INF, we sequentially replace the GS1–FF4 combination with the GS–FFR, GS5–FG, and GS10–LSAP combinations (here, GS5 and GS10 are the five- and ten-year government bond spot rates.) These combinations are based on
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
4
W.W. Jang / Economics Letters xxx (xxxx) xxx
Fig. 3. Impulse response function analysis with three factors of MP effects as external instruments. Note: The dotted line and shaded area represent 68% and 95% confidence interval, respectively, drawn with 10,000 replications.
the event-study regression results of Swanson (2018), where the FFR factor affects mostly short-maturity bonds, and the FG and LSAP factors affect mid- and long-term bonds, respectively. 4. Empirical results Fig. 2 shows the difference between the impulse-responses of SVAR models using the Cholesky decomposition method (columns A and B) and those using high-frequency external instruments; that is, GS1–FF4 (column C). In column A, we replicate the results of Bekaert et al. (2013) and Hahn et al. (2017) using real FFR for the conventional MP period, and Wu and Xia’s (2016) shadow short rates for the unconventional MP period as an MP stance. Column B also uses the Cholesky decomposition as in column A, but with one difference: that the one-year government bond spot rate (GS1) is used as the MP stance as in column C, to compare the role of the high-frequency external instrument with that of the Cholesky decomposition. In column C, we use GS1 as an MP indicator
and the three-month ahead high-frequency federal funds futures contract (FF4) as an external MP instrument; that is, GS1–FF4. All the daily data are averaged and converted into monthly data; the high-frequency FOMC event date data are also converted to monthly basis following the transform method of Gertler and Karadi (2015). We estimated the SVAR models with two lags selected using the Bayesian and Hannan–Quinn information criteria respectively. The dotted line and shaded area in each panel of Fig. 2 represent 68% and 95% confidence intervals, respectively, drawn with 10,000 replications. The RA and UC responses in column A to one standard deviation MP shock are typical results of Bekaert et al. (2013) and Hahn et al. (2017), that is, initial negative and medium-run positive responses. The INF response also shows a typical price puzzle: a positive initial price-level response after a tightening MP shock. The results in column B, from using GS1 as an MP stance instead of federal funds and shadow short rates, are qualitatively the same as those in column A. When we adopt the external instrument approach in column C, however, the RA and UC increase instantly after a positive MP
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.
W.W. Jang / Economics Letters xxx (xxxx) xxx
shock, remain for about half a year, and then disappear. Furthermore, the INF decreases after a tightening MP shock, indicating that the price puzzle can be resolved. Gertler and Karadi (2015) chose the GS1–FF4 pair as the MP indicator/external instrument because this combination might capture the effects of both target rate change and MP forward guidance. However, they did not decompose the two effects. In this paper, we separately apply the FFR and FG factors as instruments. In addition, we apply the LSAP factor as an instrument, and report the results in Fig. 3. Columns A, B, and C of Fig. 3 show respectively the responses of the MP indicator RA, UC, and INF to one standard deviation MP shocks (GS1, GS5, and GS10, respectively) using external instruments (FFR, FG, and LSAP, respectively). To compare the responses of each variable to the three different MP indicator shocks (with its corresponding instrument), we adjust the vertical axis of each row to the same scale. Fig. 3 shows that the RA and UC responses to the GS5–FG shock are the highest, followed by those to the GS10–LSAP shock. Interestingly, the RA and UC response to the GS1–FFR shock is minimal. However, all the RA and UC responses (in columns A, B, and C) show an initial positive response, as in column C of Fig. 2. The inflation response to the GS5–FG shock is negative and the highest, followed by that to the GS1–FFR shock. However, the response to the GS10–LSAP shock is significantly positive for about one quarter, implying that the termination of purchases of mortgage-backed securities and long-term Treasuries increases the price level. This is also consistent with intuition, since tapering shocks increase bond yields, with inflation expectation taking a significant portion of that yield.
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5. Direction for future work This paper used external instruments for model identification. We used the 30-minute window data of the three-month federal funds futures contract around each FOMC announcement as an external MP instrument. As another instruments, we also applied the three independent factors of the MP effects extracted from high-frequency data. We then compared the RA, UC, and inflation responses to each of the different MP shocks. However, since unconventional MPs have been implemented during the post-crisis period, each variable might have responded differently depending on the period considered. Further research is required on this issue to identify the MP factor needed for an economy facing different environments. References Bekaert, G., Hoerova, M., Lo Duca, M., 2013. Risk, uncertainty and monetary policy. J. Monetary Econ. 60, 771–788. Gertler, Karadi, 2015. Monetary policy surprises, credit costs, and economic activity. Am. Econ. J. Macroecon. 7 (1), 44–76. Gürkaynak, R.S., Sack, B., Wright, J., 2007. The U.S. Treasury yield curve: 1961 to the present. J. Monetary Econ. 54 (8), 2291–2304. Hahn, J., Jang, W.W., Kim, S., 2017. Risk aversion, uncertainty, and monetary policy in zero lower bound environments. Econom. Lett. 156 (2017), 118–122. Mertens, K., Ravn, M.O., 2013. The dynamic effects of personal and corporate income tax changes in the United States. Amer. Econ. Rev. 103 (4), 1212–1247. Swanson, E., 2018. Measuring the effects of federal reserve forward guidance and asset purchases on financial markets, NBER Working Paper 23311. Wu, J.C., Xia, F.D., 2016. Measuring the macroeconomic impact of monetary policy at the zero lower bound. J. Money Credit Bank. 48 (2–3), 253–291.
Please cite this article as: W.W. Jang, Risk aversion, uncertainty, and monetary policy: Structural vector autoregressions identified with high-frequency external instruments. Economics Letters (2019) 108675, https://doi.org/10.1016/j.econlet.2019.108675.