# The Role of the Federal Reserve in the U.S. Housing Crisis: A VAR Analysis with Endogenous Structural Breaks

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## Abstract

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## 1. Introduction

## 2. Previous Literature

## 3. Qu-Perron Method for Detecting Structural Breaks

- The $Sup\text{}LR$ test considers a likelihood ratio test for the null hypothesis of no structural break versus an alternative hypothesis of structural break with a pre-specified number of breaks, say $m$.
- The $UDmax$ test and the $WDmax$ test consider an equal weighting scheme and unequal weighting scheme, respectively, where weights depend on the number of regressors and the significance level of the tests. For these two tests, the alternative hypothesis is any number of breaks with some specified maximum.
- The $seq(l+1|l)$ test is a sequential test for the null hypothesis of $l$ breaks versus the alternative of $\left(l+1\right)$ breaks.

## 4. VAR Models, Data and Results

#### 4.1. VAR Models

#### 4.2. Data

#### 4.3. Discussion of Results

#### 4.3.1. Estimation of Break Dates—Pure Structural Change with No Linear Constraints

#### 4.3.2. Time Series Analysis for Subsamples—Pre and Post-Crisis

## 5. Concluding Remarks

## Author Contributions

## Funding

## Conflicts of Interest

## Appendix A

Variable | $\mathsf{\Delta}\mathbf{LRGDP}$ | $\mathsf{\Delta}\mathbf{LNHPA}$ | RIS | FFR | HS |
---|---|---|---|---|---|

ADF | −7.26202 | −3.6379 | −2.85346 | −3.556268 | −3.36324 |

p-value | (0.00) | (0.01) | (0.05) | (0.04) | (0.01) |

Regime 1: 2000Q1 to 2008Q4 | Regime 2: 2009Q1 to 2017Q4 | |||||
---|---|---|---|---|---|---|

$\mathsf{\Delta}\mathbf{LRGDP}$ | $\mathsf{\Delta}\mathbf{LNHPA}$ | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | $\mathsf{\Delta}\mathbf{LNHPA}$ | FFR | |

${\mathsf{\Delta}\mathrm{LRGDP}}_{\mathrm{t}-1}$ | 0.054966 | 0.255539 | 39.55285 | 0.29813 | 0.093042 | 0.863853 |

(0.80) | (0.52) | (0.03) | (0.03) | (0.88) | (0.60) | |

${\mathsf{\Delta}\mathrm{LNHPA}}_{\mathrm{t}-1}$ | 0.156347 | 0.927119 | 11.72112 | 0.04125 | 0.335293 | −0.30645 |

(0.02) | (0.00) | (0.04) | (0.26) | (0.06) | (0.51) | |

${\mathrm{FFR}}_{\mathrm{t}-1}$ | −3.27 × 10^{−5} | −0.00083 | 0.991962 | 0.000738 | 0.007349 | 1.19834 |

(0.96) | (0.45) | (0.00) | (0.81) | (0.61) | (0.00) | |

C | 0.002218 | 0.000584 | −0.51069 | 0.003188 | 0.002615 | −0.0175 |

(0.41) | (0.90) | (0.02) | (0.01) | (0.63) | (0.22) |

Regime 1: 2000Q1 to 2008Q4 | Regime 2: 2009Q1 to 2017Q4 | |||||
---|---|---|---|---|---|---|

$\text{}\mathsf{\Delta}\mathbf{LRGDP}$ | RIS | FFR | $\text{}\mathsf{\Delta}\mathbf{LRGDP}$ | RIS | FFR | |

${\mathsf{\Delta}\mathrm{LRGDP}}_{\mathrm{t}-1}$ | 0.040554 | 0.076589 | 31.24551 | 0.37202 | 0.067732 | 0.129445 |

(0.84) | (0.16) | (0.03) | (0.00) | (0.01) | (0.92) | |

${\mathrm{RIS}}_{\mathrm{t}-1}$ | 0.426163 | 1.026699 | 44.44523 | −0.013027 | 1.027946 | 6.305261 |

(0.00) | (0.00) | (0.00) | (0.95) | (0.00) | (0.00) | |

${\mathrm{FFR}}_{\mathrm{t}-1}$ | −0.00013 | −0.00052 | 0.991746 | 0.001413 | −0.00072 | 1.121703 |

(0.82) | (0.00) | (0.00) | (0.71) | (0.36) | (0.00) | |

C | −0.01765 | −0.00058 | −2.64146 | 0.003336 | −0.00075 | −0.1932 |

(0.02) | (0.77) | (0.00) | (0.55) | (0.52) | (0.00) |

Regime 1: 2000Q1 to 2008Q4 | Regime 2: 2009Q1 to 2017Q4 | |||||
---|---|---|---|---|---|---|

$\text{}\mathsf{\Delta}\mathbf{LRGDP}$ | HS | FFR | $\text{}\mathsf{\Delta}\mathbf{LRGDP}$ | HS | FFR | |

${\mathsf{\Delta}\mathrm{LRGDP}}_{\mathrm{t}-1}$ | −0.09751 | −859.179 | 24.57057 | 0.373026 | 3200.074 | −0.6239 |

(0.63) | (0.79) | (0.13) | (0.00) | (0.05) | (0.65) | |

${\mathrm{HS}}_{\mathrm{t}-1}$ | 1.41 × 10^{−5} | 1.08877 | 0.001189 | −1.69 × 10^{−7} | 0.967067 | 0.000114 |

(0.00) | (0.00) | (0.00) | (0.96) | (0.00) | (0.01) | |

${\mathrm{FFR}}_{\mathrm{t}-1}$ | 7.16 × 10^{−5} | −13.9219 | 1.003731 | 0.001343 | 4.362603 | 1.13993 |

(0.89) | (0.10) | (0.00) | (0.70) | (0.93) | (0.00) | |

C | −0.01865 | −124.352 | −2.28616 | 0.003091 | 31.38228 | −0.09831 |

(0.00) | (0.23) | (0.00) | (0.29) | (0.43) | (0.00) |

Pre-Crisis | Post-Crisis | |||||
---|---|---|---|---|---|---|

Model 1 | ||||||

${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LNHPAP}}$ | ${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LNHPAP}}$ | |

J-B test | 2.512118 | 8.217447 | 0.322027 | 5.913267 | 0.392461 | 0.205936 |

p-value | (0.28) | (0.02) | (0.85) | (0.05) | (0.82) | (0.90) |

Model 2 | ||||||

${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathrm{RIS}}$ | ${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathrm{RIS}}$ | |

J-B test | 0.326042 | 6.850346 | 0.860979 | 3.32965 | 0.383112 | 17.01102 |

p-value | (0.85) | (0.03) | (0.65) | (0.19) | (0.83) | (0.00) |

Model 3 | ||||||

${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathrm{HS}}$ | ${\epsilon}_{FFR}$ | ${\epsilon}_{\mathsf{\Delta}\mathrm{LRGDP}}$ | ${\epsilon}_{\mathrm{HS}}$ | |

J-B test | 0.992582 | 1.317416 | 1.56771 | 2.666512 | 0.373458 | 0.557175 |

p-value | (0.61) | (0.52) | (0.46) | (0.26) | (0.83) | (0.76) |

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1 | Bernanke (2005) put out the hypothesis that during the 1990s, a combination of diverse forces created a significant increase in the global supply of saving (emanating in large part from China and other Asian emerging market economies), which helped explain the persistently low longer-term interest rates in the mid-2000’s while the Federal Reserve was raising short-term interest rates. |

2 | Federal National Mortgage Association is commonly known as Fannie Mae while the Federal Home Loan Mortgage Corporation is known as the Freddie Mac. |

3 | A similar VAR model was also used by Ahamada and Sanchez (2013) in studying house price—macro relationship. Miles (2014) and McDonald and Stokes (2013c) used a standard 30-year mortgage rate in addition to the funds rate but arrived at different conclusions regarding the impact of long-term interest rate on house prices. Since our objective is to examine the role of the Federal Reserve and not the merit of global savings glut hypothesis, we decided against including long-term interest rate in our model. |

4 | Ahamada and Sanchez (2013) that applied Qu and Perron (2007) test to study house price-macro link also used 1960:Q1 as the starting point. However, their sample ended in 2009:Q3. |

5 | See Miles (2009) for a thorough literature review of studies that investigated structural breaks in relationship between housing and the rest of the economy over time. His own VAR analysis indicated that residential investment has become more important for the macroeconomy since the financial deregulation of the early 1980s. |

6 | The period of Great Moderation refers to the rule based monetary era from the mid-1980s until the early mid-2000s which was accompanied by substantial reduction in the volatility of macro variables such as real GDP, inflation and interest rate. |

7 | We found a fifth break date at 1977:Q4 only in Model 3 which coincided with the great inflation of the 1970s. |

8 | Furthermore, we find 1999:Q4 and 2008:Q4 to be significant break dates in Model 1 when we allow the covariance matrix of errors, in addition to the condition mean, to change across regimes. |

9 | $SIC\left(p\right)=\mathrm{ln}|\mathsf{\Sigma}\left(p\right)|+\frac{\mathrm{ln}T}{T}p{n}^{2}$ where, $\mathsf{\Sigma}\left(p\right)$ is the residual variance of the $VAR\left(p\right)$ model, $n$ is the number of variables in the $VAR$ model and $T$ is the total number of observations. The order of VAR is chosen by minimizing $SIC$ with respect to $p$. |

10 | In orthogonalized impulse responses, the underlying shocks are orthogonalized using the Cholesky decomposition. The main criticism of Cholesky orthogonalization is that the responses change drastically if the order of the variables change as the decomposition involves a triangular matrix (see Pesaran and Shin (1998) for details). |

11 | Even though the federal funds rate was close to 0% during 2009–2015, if the relationship between housing variables and the funds rate prevailed in the post-crisis period, it would have shown up in the impulse responses of housing variables when a shock was given to the interest rate, after controlling for other factors. |

12 | For sake of simplicity, we are presenting results at the intervals of 1, 5 and 10 respectively. |

**Figure 1.**Generalized Impulse Response Function (GIRF) of housing variables with respect to one SD positive shock to federal funds rate. FFR, $\mathsf{\Delta}\mathrm{LNHPA}$, RIS and HS denote the federal funds rate, house price inflation, residential investment share in GDP and housing starts respectively.

**Figure 2.**Generalized Impulse Response Function (GIRF) of housing market variable with respect to one SD positive shock to real GDP growth. $\mathsf{\Delta}\mathrm{LRGDP}$, $\mathsf{\Delta}\mathrm{LNHPA}$, RIS and HS denote real GDP growth, house price inflation, residential investment share in GDP and housing starts respectively.

test | $\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathsf{\Delta}\mathbf{LNHPA}$$,\text{}\mathbf{FFR}$ | $\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathbf{RIS}$$,\mathbf{FFR}$ | $\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathbf{HS}$$,\text{}\mathbf{FFR}$ |
---|---|---|---|

WDmax | 41.7334 | 61.0579 | 60.4645 |

$\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathsf{\Delta}\mathbf{LNHPA}$$,\text{}\mathbf{FFR}$ | $\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathbf{RIS}$$,\text{}\mathbf{FFR}$ | $\mathsf{\Delta}\mathbf{LRGDP}$$,\text{}\mathbf{HS}$$,\text{}\mathbf{FFR}$ | ||||
---|---|---|---|---|---|---|

Test | Test Statistic | Break Dates | Test Statistic | Break Dates | Test statistic | Break Dates |

Seq(1|0) | 34.103 | 1986Q4 | 42.133 | 1987Q1 | 36.601 | 1987Q1 |

(1986Q2–1987Q3) | (1986Q4–987Q2) | (1986Q4–1987Q2) | ||||

Seq(2|1) | 26.774 | 2008Q4 | 49.786 | 2008Q4 | 61.811 | 2008Q4 |

(2008Q3–2009Q1) | (2007Q2–2009Q2) | (2008Q2–2009Q2) | ||||

Seq(3|2) | 47.466 | 1969Q1 | 108.621 | 1969Q1 | 61.811 | 1977Q4 |

(1968Q3–1969Q3) | (1968Q3–1969Q3) | (1977Q3–1978Q1) | ||||

Seq(4|3) | 12.319 | 1978Q1 | 108.621 | 2000Q1 | 57.172 | 1969Q1 |

(1977Q3–1978Q3) | (1999Q2–2000Q4) | (1968Q3–1969Q3) | ||||

Seq(5|4) | 37.769 | 2000Q1 | 0.0000 | 1978Q1 | 38.209 | 1999Q4 |

(1997Q4–2001Q4) | (1977Q3–1978Q3) | (1998Q4–2000Q4) |

2000Q1–2008Q4 | 2009Q1–2017Q4 | ||||
---|---|---|---|---|---|

${\mathbf{\chi}}^{2}$ | p-Value | ${\mathbf{\chi}}^{2}$ | p-Value | ||

Model 1 | $FFR\nRightarrow \mathsf{\Delta}\mathrm{LNHPA}$ | 0.5662 | 0.45 | 0.2619 | 0.61 |

$\mathsf{\Delta}\mathrm{LRGDP}\nRightarrow \mathsf{\Delta}\mathrm{LNHPA}$ | 0.4174 | 0.52 | 0.0218 | 0.88 | |

Model 2 | $FFR\nRightarrow RIS$ | 11.3943 | 0.00 | 0.8318 | 0.36 |

$\mathsf{\Delta}\mathrm{LRGDP}\nRightarrow RIS$ | 1.9996 | 0.16 | 7.6998 | 0.01 | |

Model 3 | $FFR\nRightarrow HS$ | 2.6238 | 0.10 | 0.0084 | 0.93 |

$\mathsf{\Delta}\mathrm{LRGDP}\nRightarrow HS$ | 0.0722 | 0.79 | 3.8164 | 0.05 |

$\mathbf{Variance}\text{}\mathbf{Decomposition}\text{}\mathbf{of}\text{}\mathsf{\Delta}\mathbf{LNHPA}$ | ||||||||
---|---|---|---|---|---|---|---|---|

2000Q1 to 2008Q4 | 2009Q1 to 2017Q4 | |||||||

Period | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | $\mathsf{\Delta}\mathbf{LNHPA}$ | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | $\mathsf{\Delta}\mathbf{LNHPA}$ |

1 | 0.011811 | 9.941631 | 20.41247 | 69.64590 | 0.021438 | 0.221527 | 4.978330 | 94.80014 |

5 | 0.024322 | 8.397416 | 26.47954 | 65.12305 | 0.022839 | 0.540334 | 5.329699 | 94.12997 |

10 | 0.028097 | 7.124616 | 25.58334 | 67.29204 | 0.023209 | 3.644288 | 5.170177 | 91.18553 |

Variance Decomposition of RIS | ||||||||

Period | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | RIS | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | RIS |

1 | 0.001672 | 0.015145 | 14.35550 | 85.62936 | 0.000952 | 0.006853 | 1.357947 | 98.63520 |

5 | 0.004300 | 6.469207 | 22.97886 | 70.55193 | 0.002493 | 1.318683 | 19.84692 | 78.83440 |

10 | 0.006435 | 38.02760 | 12.57335 | 49.39906 | 0.003786 | 6.065616 | 23.07306 | 70.86132 |

Variance Decomposition of HS | ||||||||

Period | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | HS | S.E. | FFR | $\mathsf{\Delta}\mathbf{LRGDP}$ | HS |

1 | 92.77857 | 0.413013 | 28.71898 | 70.86800 | 61.83247 | 0.202954 | 5.018482 | 94.77856 |

5 | 237.0345 | 6.377980 | 22.87398 | 70.74804 | 141.9710 | 0.091849 | 20.82011 | 79.08804 |

10 | 359.5210 | 21.35389 | 16.52256 | 62.12355 | 192.1084 | 0.421875 | 23.92973 | 75.64839 |

© 2019 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/).

## Share and Cite

**MDPI and ACS Style**

Barari, M.; Kundu, S. The Role of the Federal Reserve in the U.S. Housing Crisis: A VAR Analysis with Endogenous Structural Breaks. *J. Risk Financial Manag.* **2019**, *12*, 125.
https://doi.org/10.3390/jrfm12030125

**AMA Style**

Barari M, Kundu S. The Role of the Federal Reserve in the U.S. Housing Crisis: A VAR Analysis with Endogenous Structural Breaks. *Journal of Risk and Financial Management*. 2019; 12(3):125.
https://doi.org/10.3390/jrfm12030125

**Chicago/Turabian Style**

Barari, Mahua, and Srikanta Kundu. 2019. "The Role of the Federal Reserve in the U.S. Housing Crisis: A VAR Analysis with Endogenous Structural Breaks" *Journal of Risk and Financial Management* 12, no. 3: 125.
https://doi.org/10.3390/jrfm12030125