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Unconventional U.S. Monetary Policy: New Tools, Same Channels?^{ †}

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## Abstract

**:**

## 1. Introduction

## 2. Econometric Framework

#### 2.1. Data

#### 2.2. The TVP-SV-VAR Model with a Cholesky Structure

#### 2.3. Bayesian Inference

#### General Prior Setup and Implementation

#### 2.4. Structural Identification

## 3. Empirical Results

#### 3.1. How Do Term Spread and Monetary Policy Shocks Affect Output Growth and Inflation?

#### 3.2. The Transmission of Monetary Policy and Term Spread Shocks

#### 3.3. Do Effects Vary over Time?

#### 3.4. Did Term Spread and Monetary Policy Shocks Matter Historically?

#### 3.5. Robustness and Extensions

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A. Structural Identification

## Appendix B. A Brief Sketch of the Markov Chain Monte Carlo Algorithm

- Sample ${\mathit{a}}^{T}={({\mathit{a}}_{1},\dots ,{\mathit{a}}_{T})}^{\prime}$ and ${\mathit{b}}^{T}={({\mathit{b}}_{1},\dots ,{\mathit{b}}_{T})}^{\prime}$ using the algorithm of Carter and Kohn (1994).
- Sample ${\mathit{h}}^{T}={({h}_{1},\dots ,{h}_{T})}^{\prime}$ and the corresponding parameters of Equation (7) through the algorithm put forth in Kastner and Frühwirth-Schnatter (2013). A brief description of this algorithm is provided in Appendix C.

## Appendix C. Sampling Log-Volatilities

- Sample ${\mathit{h}}_{i,-1}|{r}_{it},{\mu}_{i},{\rho}_{i},{\sigma}_{ih},{\mathsf{\Psi}}_{it}$ or ${\tilde{h}}_{ij,-1}|{r}_{ij},{\rho}_{i},{\sigma}_{ih},{\mathsf{\Psi}}_{it}$, all without a loop (AWOL). Here, ${\mathsf{\Psi}}_{it}={({c}_{it},{a}_{is,t},\dots ,{a}_{ii-1,t},{\mathit{b}}_{i1,t},\dots ,{\mathit{b}}_{ip,t})}^{\prime}$ is a vector of stacked coefficients and ${\mathit{h}}_{i,-1}={({h}_{i2},\dots ,{h}_{iT})}^{\prime}$. Following Rue (2001), ${\mathit{h}}_{i,-1}$ can be written in terms of a multivariate normal distribution:$${\mathit{h}}_{i,-1}\sim \mathcal{N}({\mathsf{\Omega}}_{{h}_{i}}^{-1}{\mathit{c}}_{i},{\mathsf{\Omega}}_{{h}_{i}}^{-1}).$$Similarly, the normal distribution corresponding to the non-centered parameterization is given by:$${\tilde{\mathit{h}}}_{i,-1}\sim \mathcal{N}({\tilde{\mathsf{\Omega}}}_{{h}_{i}}^{-1}{\tilde{\mathit{c}}}_{i},{\tilde{\mathsf{\Omega}}}_{{h}_{i}}^{-1}).$$The corresponding posterior moments are:$${\mathsf{\Omega}}_{{h}_{i}}=\left(\begin{array}{ccccc}\frac{1}{{s}_{{r}_{ij,2}}^{2}}+\frac{1}{{\sigma}_{ih}^{2}}& \frac{-{\rho}_{i}}{{\sigma}_{ih}^{2}}& 0& \dots & 0\\ -\frac{{\rho}_{i}}{{\sigma}_{ih}^{2}}& \frac{1}{{s}_{{r}_{i,3}}^{2}}+\frac{1+{\rho}_{i}}{{\varsigma}_{i}^{2}}& -\frac{{\rho}_{i}}{{\sigma}_{ih}^{2}}& \ddots & \vdots \\ 0& -\frac{{\rho}_{i}}{{\sigma}_{ih}^{2}}& \ddots & \ddots & 0\\ \vdots & \ddots & \ddots & \frac{1}{{s}_{{r}_{ij,T-1}}^{2}}+\frac{1+{\rho}_{i}}{{\sigma}_{ih}^{2}}& \frac{-{\xi}_{ij}}{{\sigma}_{ih}^{2}}\\ 0& \dots & 0& -\frac{{\rho}_{i}}{{\sigma}_{ih}^{2}}& \frac{1}{{s}_{{r}_{ij,T}}^{2}}+\frac{1}{{\sigma}_{ih}^{2}}\end{array}\right)$$$${\mathit{c}}_{i}=\left(\begin{array}{c}\frac{1}{{s}_{{r}_{ij,2}}^{2}}({\tilde{y}}_{ij,2}^{2}-{m}_{{r}_{ij,2}})+\frac{{\mu}_{i}(1-{\rho}_{i})}{{\sigma}_{ih}^{2}}\\ \vdots \\ \frac{1}{{s}_{{r}_{ij,T}}^{2}}({\tilde{y}}_{ij,T}^{2}-{m}_{{r}_{ij,T}})+\frac{{\mu}_{i}(1-{\rho}_{i})}{{\sigma}_{ih}^{2}}\end{array}\right).$$Multiplying by ${\sigma}_{ih}^{2}$ yields the moments for the non-centered parameterization: ${\tilde{\mathsf{\Omega}}}_{i}={\sigma}_{ih}^{2}{\mathsf{\Omega}}_{{h}_{ij}}$ and ${\tilde{\mathit{c}}}_{ij}={\sigma}_{ih}^{2}{\mathit{c}}_{ij}$. Finally, the initial states of ${\mathit{h}}_{i}^{T}$, ${h}_{i1}$ and ${\tilde{h}}_{i1}$ are obtained from their respective stationary distributions.
- Obtain the parameters of Equation (7) and Equation (A8). Since we impose a non-conjugate Gamma prior on ${\sigma}_{ih}$, we employ a Metropolis-within-Gibbs algorithm to sample ${\mu}_{i},{\rho}_{i}$ and ${\sigma}_{i}$ for both parameterizations. For the centered variant, we simulate ${\mu}_{i}$ and ${\rho}_{i}$ with a single Gibbs step, and ${\sigma}_{i}^{2}$ is sampled through an MH step. For the non-centered parameterization, we sample ${\rho}_{i}$ with MH and the other parameters with Gibbs steps.
- Sample the mixture indicators with inverse transform sampling. Note that we can rewrite Equation (A8) as:$${e}_{it}^{2}-{h}_{it}={\tilde{\xi}}_{it},\phantom{\rule{3.33333pt}{0ex}}{\tilde{\xi}}_{it}\sim \mathcal{N}({m}_{ir,t},{s}_{it}^{2}).$$This allows us to compute the posterior probabilities that ${r}_{it}=j$, which are given by:$$p({r}_{it}=c|\u2022)\propto p({r}_{it}=c)\frac{1}{{s}_{ik}}\mathrm{exp}\left(-\frac{({\tilde{\xi}}_{it}-{m}_{ik})}{2{s}_{{r}_{it}}^{2}}\right),$$

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1. | Data on real GDP growth (GDPC96), CPI inflation (CPALTT01USQ661S), the effective federal funds rate (FEDFUNDS) calculated as the quarterly average of daily rates, 10-year-government bond yields to proxy long-term interest rates (IRLTLT01USQ156N), net worth of households and nonprofit organizations resembling consumer wealth (TNWBSHNO) deflated by the personal income deflator (PCECTPI) and net interest rate margins for large U.S. banks (USG15NIM) are from the Fred database, https://research.stlouisfed.org/fred2/. Data on commercial banks’ assets (FL764090005.Q, FL474090005.Q), deposits (FL763127005.Q, FL764110005.Q FL763131005.Q, FL763135005.Q, FL762150005.Q) are from the financial accounts database of the Federal Reserve System, https://www.federalreserve.gov/releases/z1/current/. By and large, all transformed data are stationary according to an augmented Dickey–Fuller test. |

2. | See, for example, Cogley and Sargent (2005), who in response to the criticism raised by Sims (2001), extended their TVP framework put forward in Cogley and Sargent (2002) to allow for stochastic volatility. |

3. | In fact, experimenting with stationary state equations for ${\mathit{a}}_{it}$ and ${\mathit{b}}_{it}$ leaves our results qualitatively unchanged. |

4. | |

5. | Another strand of the literature proposes factor augmented VARs (FAVARs) with drifting parameters and stochastic volatility (Korobilis 2013). While FAVARs provide a flexible means of reducing the dimensionality of the estimation problem at hand, they could also lead to problems with respect to identification and structural interpretation of the underlying shocks. |

6. | Since we estimate the model on an equation-by-equation basis, ${\widehat{\mathit{V}}}_{a}$ and ${\widehat{\mathit{V}}}_{b}$ are block diagonal matrices. |

7. | There is a huge literature on the identification of conventional monetary policy shocks, but a consensus seems so far out of reach. Alternatively, one could use recursive identification, such as heavily used in the early literature; see, e.g., (Christiano et al. 2005). Recursive identification got criticized recently because of the stark underlying assumptions about the information set of the respective central bank and the unrealistic timing of the shocks, especially when also dealing with financial data. Since then, a number of authors proposed the use of external instruments, based on either the narrative approach (Romer and Romer 2004) or high frequency information (Gertler and Karadi 2015; Miranda-Agrippino and Ricco 2017). However, also, this literature came under criticism, since as pointed out by Hamilton (2018), Fed announcements provide not only information about a policy action, but about the Fed’s assessment of future economic conditions, and these effects are not easily separated. An approach to separate these effects is provided in Miranda-Agrippino (2016) and Nakamura and Steinsson (2018). |

8. | One aspect of monetary policy that we do not capture directly is forward guidance. There is a fast-growing literature assessing the effects of forward guidance; see, e.g., McKay et al. (2016), who present a theoretical model in which the power of forward guidance is highly sensitive to the assumption of complete markets. More recently, Nakamura and Steinsson (2018) provided an external instrument that measures also changes in the path of future interest rates in response to Fed announcements, which allows one to capture forward guidance effects empirically. |

9. | More specifically, an unexpected monetary expansion can be expected to drive up inflation and therefore inflation expectations. This in turn implies long-rates to decrease less strongly than short rates, causing a widening of the yield curve (Benati and Goodhart 2008). |

10. | In the case that the Fed purchases assets directly from the banking sector, the proceeds would be charged to the banks’ reserve balances with the Fed, leaving deposits untouched. The positive restriction on deposit growth is warranted since part of the Fed’s purchases directly concern the private non-banking sector. |

11. | To be precise, the narrative shock is transformed to quarterly frequency by simply averaging over the corresponding months. The monetary policy shock corresponds to the smoothed structural shocks. In general, residuals of the VAR are more volatile due to the inherent iid assumption, which is why we opted for smoothing the shocks, facilitating visual comparison to the more persistent narrative shocks. |

12. | All results are based on 500 draws from the full set of 15,000 posterior draws that have been collected after a burn-in phase of 15,000 draws. |

13. | These are based on the National Bureau of Economic Research (NBER) dating of recessions, available at http://www.nber.org/cycles.html. The full history of impulse responses over time and for all variables is available from the authors upon request. |

14. | Responses are to be interpreted as the reaction of a variable to a hypothetical 100-bp monetary policy/term spread shock independent of the actual value of the FFR during that period. |

15. | Data on shadow assets (FL504090005.Q, FL674090005.Q, FL614090005.Q) are from the financial accounts database of the Federal Reserve System, http://www.federalserver.gov/releases/z1/about.htm. |

**Figure 1.**Term spread and monetary policy shock. Notes: The plot in the left panel shows the identified term spread shock. Vertical bars refer to the launch of the Clinton debt buyback program and the three LSAP programs. The middle panel shows the monetary policy shock along with the narrative monetary policy shock of Romer and Romer (2004). The right panel shows the evolution of the term spread and the federal funds rate (realized data).

**Figure 2.**Impulse response functions. Notes: Posterior median responses to an expansionary monetary policy shock (−100 bp) and shock to the term spread (−100 bp) along with 50% (dark blue) and 68% (light blue) credible bounds. Results shown as averages over three periods, pre-crisis from 1991Q1–2007Q3, global financial crisis from 2007Q4–2009Q2 and its aftermath from 2009Q3–2015Q1.

**Figure 3.**Impulse response functions. Notes: Posterior median responses to an expansionary monetary policy shock (−100 bp) and shock to the term spread (−100 bp) along with 50% (dark blue) and 68% (light blue) credible bounds. Results shown as averages over three periods, pre-crisis from 1991Q1–2007Q3, global financial crisis from 2007Q4–2009Q2 and its aftermath from 2009Q3–2015Q1.

**Figure 4.**Elasticity of cumulative response to the size of shock on impact. Notes: The figure shows the ratio of the cumulative response of particular variable to the impact shock of the conventional monetary policy shock (black, solid line) and the spread shock (red, dashed line). Elasticities are in absolute terms. The shaded grey area indicates the period of the recession associated with the global financial crisis.

**Figure 5.**Historical decomposition of time series. Notes: Historical decomposition of time series based on the posterior median. The overall contribution of all shocks except the term spread and monetary policy shock in red. Contributions of the monetary policy shock and the term spread shock in blue and yellow, respectively. The shaded grey area indicates the period of the recession associated with the global financial crisis.

**Figure 6.**Impulse responses with shadow assets. Notes: Posterior median responses to an expansionary monetary policy shock (−100 bp) and shock to the term spread (−100 bp) along with 50% (dark blue) and 68% (light blue) credible bounds. Results shown as averages over three periods, pre-crisis from 1991Q1–2007Q3, global financial crisis from 2007Q4–2009Q2 and its aftermath from 2009Q3–2015Q1. Results based on inclusion of assets of the shadow banking sector instead of commercial banks’ assets.

**Figure 7.**Elasticity of cumulative response to size of shock on impact; investment growth included. Notes: The figure shows the ratio of the cumulative response of a particular variable to the impact shock of the conventional monetary policy shock (black, solid line) and the spread shock (red, dashed line). Elasticities are in absolute terms. The shaded grey area indicates the period of the recession associated with the global financial crisis.

Shock | Channel | Aggregate Demand | ||||||
---|---|---|---|---|---|---|---|---|

${\mathrm{i}}_{s}$ | sp | $\Delta \mathrm{wealth}$ | nim | $\Delta \mathrm{banks}\_\mathrm{assets}$ | $\Delta \mathrm{banks}\_\mathrm{deposits}$ | $\Delta \mathrm{p}$ | $\Delta \mathrm{gdp}$ | |

Monetary Policy | ↓ | ↑ | ↑ | ↑ | ↑ | ↑ | ↑ | ↑ |

Term Spread | 0 | ↓ | ↑ | ↓ | demand ↑/supply ↓ = ? | ↑ | ↑ | ↑ |

Monetary Policy Shock | ||||

1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | 1991Q1–2015Q1 | |

Real GDP growth | 0.10 | 0.10 | 0.08 | 0.10 |

Inflation | 0.06 | 0.04 | 0.04 | 0.06 |

Consumer wealth growth | 0.07 | 0.08 | 0.07 | 0.07 |

Short-term interest rate | 0.07 | 0.07 | 0.06 | 0.07 |

Banks’ deposit growth | 0.10 | 0.10 | 0.09 | 0.10 |

Banks’ asset growth | 0.13 | 0.11 | 0.10 | 0.12 |

Term spread | 0.11 | 0.13 | 0.10 | 0.11 |

Net interest rate margin | 0.08 | 0.09 | 0.07 | 0.08 |

Term Spread Shock | ||||

1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | 1991Q1–2015Q1 | |

Real GDP growth | 0.08 | 0.07 | 0.07 | 0.08 |

Inflation | 0.10 | 0.05 | 0.08 | 0.09 |

Consumer wealth growth | 0.13 | 0.08 | 0.10 | 0.12 |

Short-term interest rate | 0.12 | 0.06 | 0.09 | 0.11 |

Banks’ deposits | 0.11 | 0.08 | 0.10 | 0.11 |

Banks’ assets | 0.11 | 0.09 | 0.10 | 0.11 |

Term spread | 0.12 | 0.06 | 0.09 | 0.11 |

Net interest rate margin | 0.17 | 0.10 | 0.12 | 0.15 |

Correlation of Shadow Assets with Baseline | ||||||

Monetary policy shock | Term spread shock | |||||

1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | 1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | |

Real GDP growth | 0.976 | 0.969 | 0.968 | 0.984 | 0.979 | 0.948 |

Inflation | 0.957 | 0.991 | 0.914 | 0.963 | 0.950 | 0.938 |

Wealth | 0.996 | 0.998 | 0.997 | 0.995 | 0.996 | 0.994 |

Short-term interest rate | 0.994 | 0.999 | 0.978 | 1.000 | 0.999 | 1.000 |

Banks’ deposits | 0.775 | 0.658 | 0.768 | 0.930 | 0.694 | 0.810 |

Banks’ assets | 0.934 | 0.956 | 0.926 | 0.497 | 0.457 | 0.625 |

Term spread | 0.999 | 0.999 | 0.996 | 0.990 | 0.978 | 0.988 |

Net interest rate margin | 0.996 | 0.994 | 0.994 | 0.930 | 0.694 | 0.786 |

Average Correlation of Different Cholesky Orderings with Baseline | ||||||

Monetary policy shock | Term spread shock | |||||

1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | 1991Q1–2007Q3 | 2007Q4–2009Q2 | 2009Q3–2015Q1 | |

Real GDP growth | 0.999 | 0.995 | 0.999 | 0.998 | 0.997 | 0.990 |

Inflation | 0.998 | 0.998 | 0.995 | 0.996 | 0.998 | 0.995 |

Wealth | 0.999 | 0.999 | 0.999 | 1.000 | 1.000 | 0.999 |

Short-term interest rate | 0.999 | 0.989 | 1.000 | 1.000 | 1.000 | 1.000 |

Banks’ deposits | 0.998 | 0.993 | 0.998 | 0.998 | 0.984 | 0.986 |

Banks’ assets | 0.998 | 0.997 | 0.999 | 0.999 | 0.997 | 0.961 |

Term spread | 1.000 | 0.996 | 1.000 | 0.999 | 0.997 | 1.000 |

Net interest rate margin | 1.000 | 0.998 | 0.999 | 0.987 | 0.954 | 0.837 |

© 2018 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

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**MDPI and ACS Style**

Feldkircher, M.; Huber, F.
Unconventional U.S. Monetary Policy: New Tools, Same Channels? *J. Risk Financial Manag.* **2018**, *11*, 71.
https://doi.org/10.3390/jrfm11040071

**AMA Style**

Feldkircher M, Huber F.
Unconventional U.S. Monetary Policy: New Tools, Same Channels? *Journal of Risk and Financial Management*. 2018; 11(4):71.
https://doi.org/10.3390/jrfm11040071

**Chicago/Turabian Style**

Feldkircher, Martin, and Florian Huber.
2018. "Unconventional U.S. Monetary Policy: New Tools, Same Channels?" *Journal of Risk and Financial Management* 11, no. 4: 71.
https://doi.org/10.3390/jrfm11040071