# Asymmetric Wealth Effect between US Stock Markets and US Housing Market and European Stock Markets: Evidences from TAR and MTAR

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Cointegration

#### 2.1. Cointegration in Financial Markets

#### 2.2. Cointegration in Housing Market

## 3. Research Results and Discussion

_{01}presents a “one-way relationship” with the US markets.

_{01}and the coefficient ${\Phi}^{-}$ is significant at the 10% level, supporting our Hypothesis 3 for these indices.

## 4. Research Methodology

#### 4.1. Sample, Data and Hypothesis

**Hypothesis**

**1.**

**Hypothesis**

**2.**

**Hypothesis**

**3.**

#### 4.2. Linear Cointegration Analysis

#### 4.3. Threshold Cointegration Analysis

#### 4.4. Asymmetric Error Correction Model with Threshold Cointegration

## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

- Agoraki, Maria-Eleni, Dimitris Georgoutsos, and Georgios Kouretas. 2019. Capital Markets Integration and Cointegration: Testing for the Correct Specification of Stock Market Indices. Journal of Risk and Financial Management 12: 186. [Google Scholar] [CrossRef] [Green Version]
- Ambrose, Brent, Esther Ancel, and Mark Griffiths. 1992. The fractal structure of real estate investment trust returns: A search for evidence of market segmentation and nonlinear dependency. Journal of the American Real Estate and Urban Economics Association 20: 25–54. [Google Scholar] [CrossRef]
- Arshanapalli, Bala, and John Doukas. 1993. International stock market linkages: Evidence from the pre- and post-October 1987 period. Journal of Banking and Finance 17: 193–208. [Google Scholar] [CrossRef]
- Arshanapalli, Bala, John Doukas, and Larry Lang. 1995. Pre and Post-October 1987 Stock Market Linkages between U.S. and Asian Markets. Pacific-Basin Finance Journal 3: 57–73. [Google Scholar] [CrossRef]
- Bahmani-Oskooee, Mohsen, and Tsung-Pao Wu. 2017. Housing prices and real effective exchange rates in 18 OECD countries: A bootstrap multivariate panel Granger causality. Economic Analysis and Policy 60: 119–26. [Google Scholar] [CrossRef]
- Bahmani-Oskooee, Mohsen, and Seyed Hesam Ghodsi. 2018. Asymmetric causality between the U.S. housing market and its stock market: Evidence from state level data. Journal of Economic Asymmetries 18: e00095. [Google Scholar] [CrossRef]
- Balke, Nathan, and Thomas Fomby. 1997. Threshold cointegration. International Economic Review 38: 627–45. [Google Scholar] [CrossRef] [Green Version]
- Byers, David, and David Peel. 1993. Some evidence of interdependence of national stock markets and the gains from international portfolio diversification. Applied Financial Economics 3: 239–42. [Google Scholar] [CrossRef]
- Chan, Kung-Sik. 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics 21: 520–33. [Google Scholar] [CrossRef]
- Cheung, Yin-Wong, and Lilian Ng. 1992. Stock Price Dynamics and Firm Size: An Empirical investigation. The Journal of Finance 47: 1985–97. [Google Scholar] [CrossRef]
- Choudhry, Taufiq, Lin Lu, and Ke Peng. 2007. Common Stochastic Trends among Far East Stock Prices: Effects of the Asian Financial Crisis. International Review of Financial Analysis 16: 242–61. [Google Scholar] [CrossRef]
- Dickey, David, and Wayne Fuller. 1979. Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association 74: 427–31. [Google Scholar]
- Ding, Haoyuan, Terence Tai-Leung Chong, and Sung Park. 2014. Nonlinear Dependence between Stock and Real Estate Markets in China. Economics Letters 124: 526–29. [Google Scholar] [CrossRef] [Green Version]
- Enders, Walter. 2004. Applied Econometric Time Series. New York: John Wiley & Sons, Inc. [Google Scholar]
- Enders, Walter, and Clive Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16: 304–11. [Google Scholar]
- Enders, Walter, and Pierre Siklos. 2001. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19: 166–76. [Google Scholar] [CrossRef] [Green Version]
- Engle, Robert, and Clive Granger. 1987. Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica 55: 251–76. [Google Scholar] [CrossRef]
- Fama, Eugene, and James MacBeth. 1973. Risk, return, and equilibrium: Empirical tests. Journal of Political Economy 81: 607–36. [Google Scholar] [CrossRef]
- Fuller, Wayne. 1976. Introduction to Statistical Time Series. New York: Wiley, State Publisher. [Google Scholar]
- Ghosh, Asim, Reza Saidi, and Keith Johnson. 1999. Who Moves the Asia-Pacific Stock Markets: U.S. or Japan? Empirical Evidence Based on the Theory of Cointegration. The Financial Review 34: 159–70. [Google Scholar] [CrossRef]
- Gomes, Luís, Vasco Soares, Sílvio Gama, and José Matos. 2018. Long-term memory in Euronext stock indexes returns: An econophysics approach. Business and Economic Horizons 14: 862–81. [Google Scholar] [CrossRef] [Green Version]
- Granger, Clive. 1981. Some properties of time series data and their use in econometric model specification. Journal of Econometrics 16: 121–30. [Google Scholar] [CrossRef]
- Granger, Clive, and Tae-Hwy Lee. 1989. Investigation of production, sales, and inventory relationships using multicointegration and non-symmetric error correction models. Journal of Applied Economics 4: 145–59. [Google Scholar] [CrossRef]
- Green, Richard. 2002. Stock prices and house prices in California: New evidence of a wealth effect? Regional Science and Urban Economics 32: 775–83. [Google Scholar] [CrossRef]
- Grubel, Herbert. 1968. Internationally Diversified Portfolios: Welfare Gains and Capital Flows. The American Economic Review 58: 1299–314. [Google Scholar]
- Gueye, Ghislain Nono. 2021. Pitfalls in the cointegration analysis of housing prices with the macroeconomy: Evidence from OECD countries. Journal of Housing Economics 51: 101748. [Google Scholar] [CrossRef]
- Hatemi-J, Abdulnasser. 2008. Tests for cointegration with two unknown regime shifts with an application to financial market integration. Empirical Economics 35: 497–505. [Google Scholar] [CrossRef]
- Ibbotson, Roger, and Laurence Siegel. 1984. Real estate returns: A comparison with other investments. AREUEA Journal 12: 219–42. [Google Scholar] [CrossRef]
- Kanas, Angelos. 1998. Linkages between the US and European equity markets: Further evidence from cointegration tests. Applied Financial Economics 8: 607–14. [Google Scholar] [CrossRef]
- Kasa, Kenneth. 1992. Common stochastic trends in international stock markets. Journal of Monetary Economics 29: 95–124. [Google Scholar] [CrossRef]
- Kim, Suk-Joong. 2005. Information Leadership in the Advanced Asia-Pacific Stock Markets: Return, Volatility and Volume Information Spillovers from the US and Japan. Journal of the Japanese and International Economies 19: 338–65. [Google Scholar] [CrossRef] [Green Version]
- Kwiatkowski, Denis, Peter Phillips, Peter Schmidt, and Yongcheol Shin. 1992. Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics 54: 159–78. [Google Scholar] [CrossRef]
- Lee, Sang Bin, and Kwang Jung Kim. 1994. Does the October 1987 crash strengthen the co-movement in stock price indexes. Quarterly Review of Economics and Business 3: 89–102. [Google Scholar]
- Li, Xiao-Lin, Tsangyao Chang, Stephen Miller, Mehmet Balcilar, and Rangan Gupta. 2015. The co-movement and causality between the U.S. housing and stock markets in the time and frequency domains. International Review of Economics & Finance 38: 220–33. [Google Scholar] [CrossRef] [Green Version]
- Liow, Kim Hiang. 2006. Dynamic relationship between stock and property markets. Applied Financial Economics 16: 371–76. [Google Scholar] [CrossRef]
- Liu, Crocker, David Hartzell, Wylie Greig, and Terry Grissom. 1990. The integration of the real estate market and the stock market: Some preliminary evidence. The Journal of Real Estate Finance and Economics 3: 261–82. [Google Scholar] [CrossRef]
- Liu, Yu-Shao, and Chi-Wei Su. 2010. The relationship between the real estate and stock markets of China: Evidence from a nonlinear model. Applied Financial Economics 20: 1741–49. [Google Scholar] [CrossRef]
- Los, Cornelis, and Bing Yu. 2008. Persistence characteristics of the Chinese stock markets. International Review of Financial Analysis 17: 64–82. [Google Scholar] [CrossRef]
- MacKinnon, James. 2010. Critical Values for Cointegration Tests. Queen’s Economics Department Working Paper, No. 1227. Kingston: Queen’s University, Department of Economics. [Google Scholar]
- Matos, José, Sílvio Gama, Heather Ruskin, and José Duarte. 2004. An econophysics approach to the Portuguese Stock Index PSI-20. Physica A: Statistical Mechanics and its Applications 342: 665–76. [Google Scholar] [CrossRef]
- McCord, Michael, Daniel Lo, John McCord, Peadar Thomas Davis, and Martin Haran. 2019. Measuring the cointegration of housing types in Northern Ireland. Journal of Property Research 36: 343–66. [Google Scholar] [CrossRef]
- Phillips, Peter, and Pierre Perron. 1988. Testing for a Unit Root in Time Series Regression. Biometrika 75: 335–46. [Google Scholar] [CrossRef]
- Phylaktis, Kate, and Fabiola Ravazzolo. 2005. Stock Market Linkages in Emerging Markets: Implications for International Portfolio Diversification. Journal of International Financial Markets, Institutions and Money 15: 91–106. [Google Scholar] [CrossRef]
- Quan, Daniel, and Sheridan Titman. 1997. Commercial real estate prices and stock market returns: An international analysis. Financial Analysts Journal 53: 21–34. [Google Scholar] [CrossRef]
- Shen, Chung-Hua, Chien-Fu Chen, and Li-Hsueh Chen. 2007. An empirical study of the asymmetric cointegration relationships among the Chinese stock markets. Applied Economics 39: 1433–45. [Google Scholar] [CrossRef]
- Sim, Sung-Hoon, and Byoung-Ky Chang. 2006. Stock and real estate markets in Korea: Wealth or credit–price effect. Journal of Economic Research 11: 99–122. [Google Scholar]
- Srivastava, Aman. 2007. Cointegration of Asian Markets with US Markets: International Diversification Perspectives. Global Business Review 8: 251–65. [Google Scholar] [CrossRef]
- Stehle, Richard. 1997. An Empirical Test of the Alternative Hypotheses of National and International Pricing of Risky Assets. Journal of Finance 32: 493–502. [Google Scholar] [CrossRef]
- Sun, Changyou. 2011. Price dynamics in the import wooden bed market of the United States. Forest Policy and Economics 13: 479–87. [Google Scholar] [CrossRef]
- Taylor, Mark, and Ian Tonks. 1989. The internationalisation of stock markets and the abolition of U.K. exchange control. Review of Economics and Statistics 71: 332–36. [Google Scholar] [CrossRef]
- Tong, Howell, and Kok Sing Lim. 1980. Threshold Autoregression, Limit Cycles and Cyclical Data. Journal of the Royal Statistical Society Series B 42: 245–92. [Google Scholar] [CrossRef]
- Tong, Howell. 1978. On a threshold model. In Pattern Recognition and Signal Processing. Edited by C. Chen. NATO ASI Series E: Applied Sciences; Alphen aan den Rijn: Sijthoff & Noordhoff, vol. 29, pp. 575–86. ISBN 9789028609785. [Google Scholar]
- Tong, Howell. 1983. Threshold Models in Nonlinear Time SeriesAnalysis. Lecture Notes in Statistics No. 21. New York: Springer. [Google Scholar]
- Tsai, I-Chun, Cheng-Feng Lee, and Ming-Chu Chiang. 2012. The asymmetric wealth effect in the US housing and stock markets: Evidence from the threshold cointegration model. The Journal of Real Estate Finance and Economics 45: 1005–20. [Google Scholar] [CrossRef]
- Worzala, Elaine, and Kerry Vandell. 1993. International direct real estate investments as alternative portfolio assets for institutional investors: An evaluation. Paper presented at the 1993 AREUEA Meetings, Anaheim, CA, USA, June 28–July 1. [Google Scholar]
- Xu, Xiaojie, and Yun Zhang. 2023. Cointegration between housing prices: Evidence from one hundred Chinese cities. Journal of Property Research 40: 53–75. [Google Scholar] [CrossRef]
- Yang, Tracy, and Jamus Jerome Lim. 2004. Crisis, Contagion, and East Asian Stock Markets. Review of Pacific Basin Financial Markets and Policies 7: 119–51. [Google Scholar] [CrossRef]
- Yule, Udny. 1926. Why do we sometimes get nonsense-correlations between time series?—A study in sampling and the nature of time series. Journal of the Royal Statistical Society 89: 11–63. [Google Scholar] [CrossRef]

Statistics | Freddie Mac | DJIA | SPX | FTSE | STOXX |
---|---|---|---|---|---|

Mean | 23.624 | 11,244.93 | 1287.64 | 5090.34 | 2570.72 |

Std. Deviation | 25.348 | 6581.62 | 736.25 | 1580.65 | 986.25 |

Minimum | 0.225 | 2293.62 | 294.87 | 1990.20 | 807.74 |

Maximum | 72.990 | 28,538.44 | 3363.00 | 7687.77 | 5059.11 |

Skewness | 0.656 | 0.7817 | 0.8175 | −0.3929 | −0.0730 |

Kurtosis | −1.275 | 0.040 | 0.097 | −1.007 | −0.461 |

Indexes | ADF | PP | KPSS |
---|---|---|---|

p-Value | p-Value | Test-Statistic Value | |

Freddie Mac | 0.597 | 0.5937 | 1.0925 *** |

DJIA | 0.5661 [5] | 0.4887 [4] | 2.3051 [4] *** |

SPX | 0.5007 [5] | 0.5221 [4] | 2.2070 [4] *** |

FTSE | 0.4757 [5] | 0.5013 [4] | 1.8786 [4] *** |

STOXX | 0.6464 [5] | 0.6533 [4] | 1.3059 [4] *** |

Panel A—Results of Linear Cointegration Tests: Values of Test Statistics | |||||||||||

Index Pairs | None | Drift | Trend | ||||||||

${\tau}_{1}$ | ${\tau}_{2}$ | ${\phi}_{1}$ | ${\tau}_{3}$ | ${\phi}_{2}$ | ${\phi}_{3}$ | ||||||

Freddie/DJIA | −1.740 | −1.735 | 1.520 | −1.974 | 1.411 | 2.101 | |||||

Freddie/SPX | −1.710 | −1.705 | 1.465 | −1.964 | 1.382 | 2.063 | |||||

SPX/FTSE | 0.645 | 0.715 | 0.764 | −0.194 | 2.157 | 2.710 | |||||

SPX/STOXX | 0.795 | 0.873 | 1.411 | −0.827 | 2.536 | 2.743 | |||||

DJIA/FTSE | −0.314 | −0.271 | 0.399 | −1.211 | 1.771 | 2.284 | |||||

DJIA/STOXX | 0.043 | 0.088 | 0.717 | −1.449 | 1.986 | 2.246 | |||||

Panel B—Statistical Tests: Critical Values for Test Statistics | |||||||||||

None | Drift | Trend | |||||||||

1% | 5% | 10% | 1% | 5% | 10% | 1% | 5% | 10% | |||

${\tau}_{1}$ | −2.58 | −1.95 | −1.62 | ${\tau}_{2}$ | −3.46 | −2.88 | −2.57 | ${\tau}_{3}$ | −3.99 | −3.43 | −3.13 |

${\phi}_{1}$ | 6.52 | 4.63 | 3.81 | ${\phi}_{2}$ | 6.22 | 4.75 | 4.07 | ||||

${\phi}_{3}$ | 8.43 | 6.49 | 5.47 |

Panel A | ||||||||

Freddie/DJIA | Freddie/SPX | |||||||

Item | TAR | Consistent TAR | MTAR | Consistent MTAR | TAR | Consistent TAR | MTAR | Consistent MTAR |

Lag | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

Threshold | 0 | 0.421 | 0 | 0.065 | 0 | −1.09 | 0 | 0.187 |

${\rho}_{1}$ (coef+) | −0.001 | 0.009 | −0.022 | −0.054 ** | −0.016 | −0.005 | −0.025 | 0.049 |

${\rho}_{1}$ statistic value | (−0.046) | (0.379) | (−1.318) | (−1.988) | (−0.559) | (−0.187) | (−0.855) | (0.860) |

${\rho}_{2}$ (coef−) | −0.030 * | −0.032 * | −0.011 | −0.006 | −0.054. | −0.071 * | −0.046. | −0.049 * |

${\rho}_{2}$ statistic value | (−1.671) | (−1.905) | (−0.430) | (−0.342) | (−1.892) | (−2.371) | (−1.551) | (−2.210) |

AIC | −229.744 | −230.688 | −228.853 | −231.070 | 116.660 | 114.866 | 117.329 | 115.057 |

BIC | −212.871 | −213.815 | −211.980 | −214.197 | 133.533 | 131.739 | 134.202 | 131.930 |

Q_{LB} (LB test_4) | 0.997 | 0.999 | 0.987 | 0.986 | 0.619 | 0.742 | 0.638 | 0.395 |

Q_{LB} (LB test_8) | 0.796 | 0.823 | 0.758 | 0.624 | 0.771 | 0.761 | 0.815 | 0.661 |

Q_{LB} (LB test_12) | 0.732 | 0.748 | 0.686 | 0.658 | 0.911 | 0.889 | 0.943 | 0.894 |

H0: no CI | 1.404 | 1.870 | 0.969 | 2.059 | 1.932 | 2.827 | 1.601 | 2.731 |

p-value | 0.250 | 0.159 | 0.383 | 0.132 | 0.150 | 0.063 | 0.206 | 0.069 |

H0: SAP | 0.975 | 1.891 | 0.116 | 2.264 | 0.914 | 2.6610 | 0.269 | 2.474 |

p-value | 0.326 | 0.172 | 0.734 | 0.135 | 0.341 | 0.106 | 0.605 | 0.118 |

Panel B | ||||||||

SPX/FTSE | SPX/STOXX | |||||||

Lag | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

Threshold | 0 | −0.136 | 0 | 0.004 | 0 | −0.143 | 0 | −0.037 |

${\rho}_{1}$ (coef+) | 0.105 | 0.104 * | 0.084 | 0.094 | 0.038 | 0.040 | 0.003 | 0.007 |

${\rho}_{1}$ statistic value | (1.879) | (2.033) | (1.588) | (1.782) | (1.802) | (1.947) | (0.165) | (0.409) |

${\rho}_{2}$ (coef-) | −0.088 | −0.134 * | −0.095 | −0.106 | −0.031 | −0.04 | 0.019 | 0.036 |

${\rho}_{2}$ statistic value | (−1.537) | (−2.149) | (−1.52) | (−1.73) | (−1.269) | (−1.579) | (0.707) | (0.647) |

AIC | −299.651 | −302.832 | −298.448 | −299.971 | −359.686 | −361.218 | −354.981 | −355.02 |

BIC | −282.778 | −285.959 | −281.574 | −283.098 | −342.813 | −344.345 | −338.108 | −338.147 |

Q_{LB} (LB test_4) | 0.995 | 0.995 | 0.951 | 0.934 | 0.961 | 0.956 | 0.962 | 0.951 |

Q_{LB} (LB test_8) | 0.994 | 0.993 | 0.979 | 0.971 | 0.791 | 0.821 | 0.732 | 0.743 |

Q_{LB} (LB test_12) | 1.000 | 0.998 | 0.999 | 0.998 | 0.609 | 0.613 | 0.527 | 0.545 |

H0: no CI | 3.373 | 5.007 | 2.766 | 3.536 | 2.568 | 3.340 | 0.257 | 0.276 |

p-value | 0.038 * | 0.008 ** | 0.067 | 0.032 * | 0.081 | 0.039 * | 0.7736 | 0.759 |

H0: SAP | 6.674 | 9.941 | 5.461 | 7.000 | 4.828 | 6.368 | 0.219 | 0.256 |

p-value | 0.011 * | 0.002 ** | 0.021 * | 0.009 ** | 0.030 * | 0.013 * | 0.641 | 0.614 |

Panel C | ||||||||

DJIA/FTSE | DJIA/STOXX | |||||||

Lag | 3 | 3 | 3 | 3 | 3 | 3 | 3 | 3 |

Threshold | 0 | 0.159 | 0 | −0.009 | 0 | −0.124 | 0 | −0.002 |

${\rho}_{1}$ (coef+) | 0.032 | 0.061 | 0.025 | 0.032 | 0.022 | 0.025 | −0.019 | −0.02 |

${\rho}_{1}$ statistic value | (0.561) | (1.03) | (0.518) | (0.683) | (0.987) | (1.111) | (−0.927) | (−0.992) |

${\rho}_{2}$ (coef−) | −0.084 | −0.094 | −0.128 * | −0.162 * | −0.038 | −0.043 | 0.022 | 0.027 |

${\rho}_{2}$ statistic value | (−1.593) | (−1.877) | (−2.057) | (−2.475) | (−1.564) | (−1.737) | (0.772) | (0.916) |

AIC | −267.038 | −269.068 | −268.754 | −270.962 | −326.23 | −327.1 | −324.112 | −324.505 |

BIC | −250.165 | −252.195 | −251.881 | −254.089 | −309.357 | −310.227 | −307.239 | −307.632 |

Q_{LB} (LB test_4) | 0.999 | 0.997 | 0.961 | 0.968 | 0.999 | 0.999 | 0.999 | 0.998 |

Q_{LB} (LB test_8) | 0.977 | 0.987 | 0.955 | 0.94 | 0.812 | 0.802 | 0.697 | 0.668 |

Q_{LB} (LB test_12) | 0.995 | 0.998 | 0.992 | 0.991 | 0.724 | 0.727 | 0.607 | 0.585 |

H0: no CI | 1.536 | 2.544 | 2.387 | 3.499 | 1.789 | 2.221 | 0.751 | 0.943 |

p-value | 0.2194 | 0.083 | 0.096 | 0.033 * | 0.172 | 0.113 | 0.474 | 0.393 |

H0: SAP | 2.483 | 4.488 | 4.176 | 6.389 | 3.480 | 4.343 | 1.406 | 1.788 |

p-value | 0.118 | 0.036 * | 0.043 * | 0.013 * | 0.065. | 0.039 * | 0.238 | 0.184 |

Panel A | ||||||||

Freddie/DJIA | Freddie/SPX | |||||||

Item | DJIA.est | DJIA.t | Freddie.est | Freddie.t | SPX.est | SPX.t | Freddie.est | Freddie.t |

(Intercept) | 0.012 | 0.552 | 0.023 | 0.251 | −0.002 | −0.082 | 0.026 | 0.297 |

${\mathsf{\alpha}}_{1}^{+}$ | 0.02 | 0.088 | 2.551 * | 2.584 | 0.137 | 0.615 | 2.046 * | 2.220 |

${\mathsf{\alpha}}_{2}^{+}$ | 0.374 | 1.674 | −0.131 | −0.135 | 0.594 ** | 2.665 | 0.421 | 0.457 |

${\mathsf{\alpha}}_{3}^{+}$ | 0.185 | 0.812 | −0.148 | −0.15 | 0.092 | 0.416 | −0.306 | −0.334 |

${\mathsf{\alpha}}_{4}^{+}$ | −0.331 | −1.601 | −0.713 | −0.791 | −0.256 | −1.236 | −0.675 | −0.788 |

${\mathsf{\alpha}}_{1}^{-}$ | −0.401 * | −2.266 | 1.686 * | 2.186 | −0.335 | −1.846 | 1.943 * | 2.594 |

${\mathsf{\alpha}}_{2}^{-}$ | −0.311 | −1.583 | 0.141 | 0.165 | −0.362 | −1.823 | −0.547 | −0.668 |

${\mathsf{\alpha}}_{3}^{-}$ | 0.058 | 0.267 | 0.278 | 0.295 | 0.259 | 1.23 | 0.891 | 1.025 |

${\mathsf{\alpha}}_{4}^{-}$ | 0.263 | 1.213 | −0.129 | −0.137 | 0.121 | 0.573 | −0.618 | −0.709 |

${\mathsf{\beta}}_{1}^{+}$ | −0.013 | −0.301 | −0.087 | −0.456 | −0.036 | −0.800 | −0.086 | −0.468 |

${\mathsf{\beta}}_{2}^{+}$ | 0.011 | 0.268 | 0.016 | 0.089 | 0.024 | 0.573 | 0.014 | 0.079 |

${\mathsf{\beta}}_{3}^{+}$ | 0.014 | 0.344 | −0.094 | −0.532 | 0.014 | 0.331 | −0.084 | −0.486 |

${\mathsf{\beta}}_{4}^{+}$ | −0.010 | −0.250 | 0.027 | 0.152 | 0.006 | 0.141 | 0.022 | 0.129 |

${\mathsf{\beta}}_{1}^{-}$ | 0.074 * | 2.362 | 0.356 ** | 2.610 | 0.065 | 1.942 | 0.356 * | 2.583 |

${\mathsf{\beta}}_{2}^{-}$ | 0.010 | 0.315 | −0.149 | −1.056 | 0.006 | 0.169 | −0.109 | −0.762 |

${\mathsf{\beta}}_{3}^{-}$ | 0.001 | 0.039 | 0.352 * | 2.468 | −0.004 | −0.122 | 0.338 * | 2.366 |

${\mathsf{\beta}}_{4}^{-}$ | 0.002 | 0.056 | −0.258 | −1.825 | 0.018 | 0.534 | −0.245 | −1.760 |

${\mathsf{\Phi}}^{+}$ | 0.005 | 0.340 | −0.010 | −0.163 | 0.000 | −0.026 | 0.014 | 0.233 |

${\mathsf{\Phi}}^{-}$ | −0.012 * | −2.102 | −0.034 | −1.421 | −0.011 | −1.911 | −0.036 | −1.526 |

${\mathrm{H}}_{01}:\text{}{\mathsf{\alpha}}_{1}^{+}={\mathsf{\alpha}}_{2}^{+}$ = 0 for all lags | 1.591 | [0.14] | 3.276 ** | [0.00] | 1.563 | [0.14] | 3.652 ** | [0.00] |

${\mathrm{H}}_{02}:\text{}{\mathsf{\beta}}_{1}^{+}={\mathsf{\beta}}_{2}^{+}$ = 0 for all lags | 0.844 | [0.57] | 1.602 | [0.13] | 0.684 | [0.7] | 1.564 | [0.14] |

Panel B | ||||||||

SPX/FTSE | SPX/STOXX | |||||||

Item | FTSE.est | FTSE.t | SPX.est | SPX.t | STOXX.est | STOXX.t | SPX.est | SPX.t |

(Intercept) | −0.014 | −0.727 | −0.024 | −1.198 | −0.027 | −1.119 | −0.018 | −0.88 |

${\mathsf{\alpha}}_{1}^{+}$ | 0.568 | 1.925 | 0.881 ** | 2.949 | 0.431 | 1.38 | 0.464 | 1.776 |

${\mathsf{\alpha}}_{2}^{+}$ | −0.315 | −1.087 | −0.341 | −1.163 | −0.436 | −1.525 | −0.260 | −1.087 |

${\mathsf{\alpha}}_{3}^{+}$ | −0.042 | −0.144 | 0.06 | 0.203 | 0.197 | 0.698 | 0.151 | 0.639 |

${\mathsf{\alpha}}_{4}^{+}$ | 0.432 | 1.49 | 0.114 | 0.388 | 0.092 | 0.327 | −0.046 | −0.192 |

${\mathsf{\alpha}}_{1}^{-}$ | −0.904 ** | −2.628 | −0.829 * | −2.378 | −0.486 | −1.329 | −0.464 | −1.515 |

${\mathsf{\alpha}}_{2}^{-}$ | 0.333 | 0.996 | 0.252 | 0.744 | 0.054 | 0.147 | −0.073 | −0.236 |

${\mathsf{\alpha}}_{3}^{-}$ | 0.345 | 0.987 | 0.181 | 0.511 | 0.278 | 0.772 | 0.234 | 0.776 |

${\mathsf{\alpha}}_{4}^{-}$ | −0.608 | −1.702 | −0.496 | −1.371 | 0.244 | 0.679 | 0.298 | 0.991 |

${\mathsf{\beta}}_{1}^{+}$ | −0.225 | −0.809 | −0.261 | −0.925 | −0.121 | −0.352 | −0.162 | −0.562 |

${\mathsf{\beta}}_{2}^{+}$ | 0.534 | 1.952 | 0.784 ** | 2.827 | 0.817 * | 2.388 | 0.808 ** | 2.818 |

${\mathsf{\beta}}_{3}^{+}$ | 0.04 | 0.146 | 0.111 | 0.402 | 0.082 | 0.238 | 0.056 | 0.195 |

${\mathsf{\beta}}_{4}^{+}$ | −0.399 | −1.511 | −0.271 | −1.013 | −0.168 | −0.521 | −0.172 | −0.635 |

${\mathsf{\beta}}_{1}^{-}$ | 0.665 | 1.918 | 0.442 | 1.26 | 0.336 | 0.763 | 0.216 | 0.586 |

${\mathsf{\beta}}_{2}^{-}$ | −0.320 | −0.966 | −0.435 | −1.293 | −0.119 | −0.264 | −0.195 | −0.516 |

${\mathsf{\beta}}_{3}^{-}$ | −0.266 | −0.793 | 0.033 | 0.097 | −0.218 | −0.477 | −0.060 | −0.158 |

${\mathsf{\beta}}_{4}^{-}$ | 0.527 | 1.578 | 0.623 | 1.841 | −0.091 | −0.204 | −0.123 | −0.329 |

${\mathsf{\Phi}}^{+}$ | −0.046 | −0.738 | 0.008 | 0.128 | 0.028 | 0.840 | 0.041 | 1.477 |

${\mathsf{\Phi}}^{-}$ | 0.134 | 1.791 | 0.122 | 1.619 | −0.025 | −0.219 | 0.055 | 0.563 |

${\mathrm{H}}_{01}:\text{}{\mathsf{\alpha}}_{i}^{+}={\mathsf{\alpha}}_{i}^{-}$ = 0 for all lags | 1.692 | [0.11] | 1.960 | [0.06] | 0.968 | [0.47] | 1.123 | [0.35] |

${\mathrm{H}}_{02}:\text{}{\mathsf{\beta}}_{i}^{+}={\mathsf{\beta}}_{i}^{-}$ = 0 for all lags | 1.345 | [0.23] | 1.576 | [0.14] | 0.845 | [0.56] | 1.139 | [0.34] |

Panel C | ||||||||

DJIA/FTSE | DJIA/STOXX | |||||||

Item | FTSE.est | FTSE.t | DJIA.est | DJIA.t | STOXX.est | STOXX.t | DJIA.est | DJIA.t |

(Intercept) | −0.018 | −0.911 | −0.017 | −0.841 | −0.021 | −0.814 | −0.008 | −0.386 |

${\mathsf{\alpha}}_{1}^{+}$ | 0.705 ** | 2.653 | 0.775 ** | 2.885 | 0.538 * | 2.114 | 0.351 | 1.675 |

${\mathsf{\alpha}}_{2}^{+}$ | 0.100 | 0.399 | 0.172 | 0.679 | −0.151 | −0.577 | 0.003 | 0.015 |

${\mathsf{\alpha}}_{3}^{+}$ | 0.126 | 0.505 | 0.159 | 0.631 | 0.233 | 0.921 | 0.165 | 0.794 |

${\mathsf{\alpha}}_{4}^{+}$ | 0.347 | 1.399 | 0.123 | 0.49 | 0.122 | 0.480 | 0.146 | 0.701 |

${\mathsf{\alpha}}_{1}^{-}$ | −0.407 | −1.157 | −0.150 | −0.421 | 0.110 | 0.305 | 0.273 | 0.918 |

${\mathsf{\alpha}}_{2}^{-}$ | 0.659 | 1.868 | 0.210 | 0.588 | 0.077 | 0.214 | −0.209 | −0.706 |

${\mathsf{\alpha}}_{3}^{-}$ | 0.091 | 0.254 | −0.151 | −0.418 | −0.009 | −0.023 | −0.128 | −0.413 |

${\mathsf{\alpha}}_{4}^{-}$ | −0.770 * | −2.181 | −0.608. | −1.705 | −0.127 | −0.327 | −0.006 | −0.018 |

${\mathsf{\beta}}_{1}^{+}$ | −0.343 | −1.375 | −0.308 | −1.224 | −0.295 | −0.913 | −0.126 | −0.473 |

${\mathsf{\beta}}_{2}^{+}$ | 0.308 | 1.212 | 0.296 | 1.151 | 0.455 | 1.441 | 0.403 | 1.551 |

${\mathsf{\beta}}_{3}^{+}$ | 0.006 | 0.022 | 0.104 | 0.412 | 0.107 | 0.337 | 0.083 | 0.317 |

${\mathsf{\beta}}_{4}^{+}$ | −0.430 | −1.781 | −0.357 | −1.463 | −0.268 | −0.880 | −0.388 | −1.545 |

${\mathsf{\beta}}_{1}^{-}$ | 0.098 | 0.273 | −0.254 | −0.695 | −0.399 | −0.888 | −0.653 | −1.765 |

${\mathsf{\beta}}_{2}^{-}$ | −0.722 | −1.977 | −0.339 | −0.918 | −0.138 | −0.302 | 0.098 | 0.260 |

${\mathsf{\beta}}_{3}^{-}$ | −0.004 | −0.011 | 0.232 | 0.621 | 0.032 | 0.063 | 0.149 | 0.354 |

${\mathsf{\beta}}_{4}^{-}$ | 0.926 * | 2.581 | 0.905 * | 2.495 | 0.444 | 0.871 | 0.341 | 0.811 |

${\mathsf{\Phi}}^{+}$ | −0.007 | −0.145 | 0.029 | 0.587 | 0.035 | 1.021 | 0.019 | 0.658 |

${\mathsf{\Phi}}^{-}$ | 0.135 | 1.881 | 0.039 | 0.54 | 0.016 | 0.308 | 0.065 | 1.485 |

${\mathrm{H}}_{01}:\text{}{\mathsf{\alpha}}_{i}^{+}={\mathsf{\alpha}}_{i}^{-}$ = 0 for all lags | 1.870 | [0.07] | 1.295 | [0.25] | 0.780 | [0.62] | 0.691 | [0.70] |

${\mathrm{H}}_{02}:\text{}{\mathsf{\beta}}_{i}^{+}={\mathsf{\beta}}_{i}^{-}$ = 0 for all lags | 1.799 | [0.09] | 1.402 | [0.20] | 0.711 | [0.68] | 1.158 | [0.33] |

Zone | Stock Market | Housing Market |
---|---|---|

US | DJIA SPX | Freddie Mac |

Europe | STOXX FTSE | – |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2023 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Coelho, P.; Gomes, L.; Ramos, P.
Asymmetric Wealth Effect between US Stock Markets and US Housing Market and European Stock Markets: Evidences from TAR and MTAR. *Risks* **2023**, *11*, 124.
https://doi.org/10.3390/risks11070124

**AMA Style**

Coelho P, Gomes L, Ramos P.
Asymmetric Wealth Effect between US Stock Markets and US Housing Market and European Stock Markets: Evidences from TAR and MTAR. *Risks*. 2023; 11(7):124.
https://doi.org/10.3390/risks11070124

**Chicago/Turabian Style**

Coelho, Pedro, Luís Gomes, and Patrícia Ramos.
2023. "Asymmetric Wealth Effect between US Stock Markets and US Housing Market and European Stock Markets: Evidences from TAR and MTAR" *Risks* 11, no. 7: 124.
https://doi.org/10.3390/risks11070124