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Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach

  • Ricardo Quineche EMAIL logo
Published/Copyright: September 13, 2021
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Studies in Nonlinear Dynamics & Econometrics
From the journal Studies in Nonlinear Dynamics & Econometrics Volume 26 Issue 5

Abstract

This paper empirically examines the long-run relationship between consumption, asset wealth and labor income (i.e., cay) in the United States through the lens of a quantile cointegration approach. The advantage of using this approach is that it allows for a nonlinear relationship between these variables depending on the level of consumption. We estimate the coefficients using a Phillips–Hansen type fully modified quantile estimator to correct for the presence of endogeneity in the cointegrating relationship. To test for the null of cointegration at each quantile, we apply a quantile CUSUM test. Results show that: (i) consumption is more sensitive to changes in labor income than to changes in asset wealth for the entire distribution of consumption, (ii) the elasticity of consumption with respect to labor income (asset wealth) is larger at the right (left) tail of the consumption distribution than at the left (right) tail, (iii) the series are cointegrated around the median, but not in the tails of the distribution of consumption, (iv) using the estimated cay obtained for the right (left) tail of the distribution of consumption improves the long-run (short-run) forecast ability on real excess stock returns over a risk-free rate.

Keywords: asset return forecasting; cay ; quantile cointegration; quantile regression; stationarity
Corresponding author: Ricardo Quineche, The Kenneth C. Griffin Department of Economics, The University of Chicago, Chicago, IL, USA; and Economic Studies, Central Reserve Bank of Peru, Lima, Peru, E-mail:

Acknowledgments

The author is grateful to the Editor in Chief, Professor Bruce Mizrach, and an anonymous Referee for useful suggestions that significantly improved the paper. Further, the author greatly appreciates useful comments of Stéphane Bonhomme, Emily Chen, Agustin Gutierrez, Eyo Herstad, Takuma Habu, Ali Hortaçsu, Shanon H. Hsu, Fulin Li, Jimena Montoya, Guillaume Pouliot, Harald Uhlig, and participants in the Research Seminar at The University of Chicago. Any errors are responsibility of the author.

  1. Author contribution: The author has accepted responsibility for the entire content of this submitted manuscript and approved submission.

  2. Research funding: None declared.

  3. Conflict of interest statement: The author declares no conflicts of interest regarding this article.

Appendix A: Data details

The consumption data is the sum of personal consumption expenditures on non-durables and services excluding shoes and clothing, and it is obtained from US Department of Commerce, Bureau of Economic Analysis, NIPA Table 2.3.5. The asset wealth data is net worth of households and nonprofit organizations series provided by the Board of Governors of the Federal Reserve System, Flow of Funds Accounts, Table B.1, series FL152090005.Q. Labor income data is obtained from NIPA Table 2.1. To construct the after-tax labor income series, we sum wage and salary disbursements (line 3), personal current transfer receipts (line 16) and employer contributions to employee pension and insurance funds (line 7) minus personal and employer contributions for government social insurance (line 25 + line 8), and taxes. Taxes are constructed as follows: (personal current taxes (line 26)) × [(wage and salary disbursements (line 3))/(wage and salary disbursements (line 3)) + proprietor’s income with inventory valuation and capital consumption adjustments (line 9) + rental income of persons with capital consumption adjustment (line 12) + personal dividend income (line 15) + personal interest income (line 14)]. We use the price index for personal consumption expenditure (2012 = 100) as price deflator, which is obtained from NIPA Table 2.1. Population series comprises can be found in NIPA Table 2.1.

Appendix B: Unit root tests and robustness of empirical results

Table B1:

Unit root tests.

Variable MZ α GLS MSBGLS MZ t α GLS ADFGLS
Consumption −3.136 0.326 −1.023 −1.014
Labor income −4.003 0.335 −1.341 −1.178
Asset wealth −11.484 0.205 −2.359 −2.290

  1. *, ** and *** denote rejection of the null hypothesis with a significance level of 0.1, 0.05 and 0.01, respectively.

Table B2:

t n (τ) test statistic for consumption for different sub-samples.

Sub-sample: τ
1952Q1− 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1998Q3 1.78 0.95 0.26 −0.13 −0.19 −0.3 −0.18 −1.65 −1.18
2003Q3 1.87 1.30 0.71 0.22 0.44 −0.22 −0.72 −1.96 −1.51
2008Q3 2.01 1.19 0.49 −0.58 −0.41 −0.87 −1.22 −2.93** −2.26
2013Q3 2.38 0.75 −0.13 −0.85 −2.06 −1.37 −1.37 −3.32*** −3.54***
2018Q3 2.23 1.04 −0.07 −1.36 −1.45 −1.61 −1.64 −3.65*** −3.18***

  1. *, ** and *** denote rejection of the null hypothesis with a significance level of 0.1, 0.05 and 0.01, respectively.

Table B3:

t n (τ) test statistic for labor income for different sub-samples.

Sub-sample: τ
1952Q1− 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1998Q3 1.21 1.04 0.44 0.59 0.17 −0.18 −1.70 −2.59** −2.58**
2003Q3 1.36 0.81 0.71 0.71 0.45 0.12 −1.41 −1.33 −0.25
2008Q3 0.84 0.23 −0.50 −0.47 −1.65 −2.20 −2.60** −1.48 −1.09
2013Q3 −0.02 −0.40 −1.10 −1.41 −2.57 −2.87** −2.83** −1.50 −1.24
2018Q3 1.09 −0.02 −0.30 −0.15 −1.55 −2.85** −3.04** −1.73 −1.65

  1. *, ** and *** denote rejection of the null hypothesis with a significance level of 0.1, 0.05 and 0.01, respectively.

Table B4:

t n (τ) test statistic for asset wealth for different sub-samples.

Sub-sample: τ
1952Q1− 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1998Q3 0.42 0.69 −0.14 −0.43 −1.09 −0.19 −0.05 −0.33 0.55
2003Q3 −1.66 −0.80 0.50 0.02 0.49 1.060 1.6 0.81 2.20
2008Q3 −1.93 −1.35 −0.77 −1.27 −1.48 −0.77 0.84 0.32 1.79
2013Q3 −1.85 −1.10 −0.58 −0.77 −0.23 0.31 1.66 0.96 1.38
2018Q3 −1.62 −0.75 −0.55 −0.38 0.59 0.73 1.57 0.78 1.27

  1. *, ** and *** denote rejection of the null hypothesis with a significance level of 0.1, 0.05 and 0.01, respectively.

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2020-0059).

Received: 2020-05-20
Accepted: 2021-08-26
Published Online: 2021-09-13

© 2021 Walter de Gruyter GmbH, Berlin/Boston

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Transition from the Taylor rule to the zero lower bound
  4. A note on change in persistence of U.S. city prices
  5. Instability in regime switching models
  6. Testing for exuberance in house prices using data sampled at different frequencies
  7. Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach
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https://doi.org/10.1515/snde-2020-0059
Keywords for this article
asset return forecasting; cay; quantile cointegration; quantile regression; stationarity

Articles in the same Issue

  1. Frontmatter
  2. Research Articles
  3. Transition from the Taylor rule to the zero lower bound
  4. A note on change in persistence of U.S. city prices
  5. Instability in regime switching models
  6. Testing for exuberance in house prices using data sampled at different frequencies
  7. Consumption, aggregate wealth and expected stock returns: a quantile cointegration approach
  8. A family of nonparametric unit root tests for processes driven by infinite variance innovations
  9. Prediction of stock index of two-scale long short-term memory model based on multiscale nonlinear integration
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