# The Determinants of the U.S. Consumer Sentiment: Linear and Nonlinear Models

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## Abstract

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## 1. Introduction

## 2. Literature Review

## 3. Data

- University of Michigan Consumer Sentiment Index is a monthly survey of U.S. consumer confidence levels conducted by the University of Michigan. It is based on telephone surveys that gather information on consumer expectations regarding the overall economy.
- Bloomberg Barometer Startups Global Index measures both the occurrence and level of historical and recent venture activity for U.S.-based startups excluding biotechnology. The index is a gauge of startup activity that equally considers capital raised, deal count, first financings, and exit count.
- Business Confidence Index provides information on future developments, based upon opinion surveys on developments in production, orders, and stocks of finished goods in the industry sector.
- Dow Jones Sustainability United States 40 Index is composed of U.S. sustainability leaders as identified by Sustainable Asset Management (SAM) through a corporate sustainability assessment. The index represents the top 20% of the largest 600 U.S. companies in the Dow Jones Sustainability U.S. Index based on long-term economic, environmental, and social criteria.
- Morgan Stanley Capital International (MSCI) Global Energy Efficiency Index includes developed and emerging market large-, mid-, and smallcap companies that derive 50% or more of their revenues from products and services in energy efficiency.
- MSCI USA ESG leaders index is a capitalization weighted index that provides exposure to companies with high Environmental, Social, and Governance (ESG) performance relative to their sector peers.
- Personal Income in Billions is the income that persons receive in return for their provision of labor, land, and capital used in current production and the net current transfer payments that they receive from business and from government.
- S&P Carbon Efficiency Index is designed to measure the performance of companies in the S&P 500, while overweighting or underweighting those companies that have lower or higher levels of carbon emissions per unit of revenue.
- S&P Consumer Finance Index provides liquid exposure to mortgage real estate investment trusts (REITs), thrifts and mortgage finance companies, diversified and regional banks, consumer finance or data processing services companies trading on U.S. stock exchanges.
- S&P Municipal Bond Education Index consists of bonds in the S&P Municipal Bond Index from the Higher Education and Student Loan Sectors.
- U.S. unemployment rate is defined as the percentage of unemployed people who are currently in the labor force. In order to be in the labor force, a person either must have a job or have looked for work in the last four weeks.

## 4. Empirical Models and Results

#### 4.1. Multicollinearity Analysis

#### 4.2. Random Matrix Theory Analysis

#### 4.3. Regression Analysis

#### 4.4. Regime Switching Model

#### 4.5. Gradient Descent Algorithm

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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Variables | Coefficient | Uncentered | Centered |
---|---|---|---|

Variance | VIF | VIF | |

CONSTANT | 0.000016 | 2.104995 | NA |

BSTARTUP GLOBAL INDEX | 0.001203 | 1.168882 | 1.091751 |

BUSINESS CONFIDENCE INDEX | 3.815532 | 1.397339 | 1.393706 |

DOW JONES SUSTAINABILITY U.S. INDEX | 0.258094 | 28.59277 | 26.83816 |

MSCI GLOBAL ENERGY EFFICIENCY INDEX | 0.019746 | 4.335034 | 4.266459 |

MSCI USA LEADERS INDEX | 0.469852 | 51.01655 | 46.83093 |

PI IN BILLIONS | 0.217360 | 1.470266 | 1.057801 |

SP500 CARBON EFFICIENT | 0.561725 | 63.97503 | 58.49727 |

SP CONSUMER FINANCE INDEX | 0.029068 | 4.852076 | 4.697568 |

SP MUNICIPAL BOND EDUCATION | 0.106374 | 1.533979 | 1.301741 |

UNEMPLOYMENT RATE IN % | 0.015123 | 1.240514 | 1.095568 |

Dependent Variable: University of Michigan Consumer Sentiment Index | |||
---|---|---|---|

Linear Regression Model 1 | Linear Regression Model 2 | ||

Undifferentiated Variables | OLS Coefficients | Differentiated Variables | OLS Coefficients |

CONSTANT | −0.004706 | CONSTANT | 0.0004816 |

BSTARTUP GLOBAL INDEX | 0.008914 ‡ | BSTARTUP GLOBAL INDEX (-1) | −0.058823 |

BUSINESS CONFIDENCE INDEX | 2.172408 ‡ | BUSINESS CONFIDENCE INDEX (-1) | 5.759300 ** |

DOW JONES SUSTAINABILITY US INDEX | −0.283084 | DOW JONES SUSTAINABILITY (-1) | 1.048775 *** |

MSCI GLOBAL ENERGY EFFICIENCY INDEX | −0.317548 | MSCI GLOBAL ENERGY EFFICIENT INDEX (-1) | −0.699981 *** |

MSCI USA LEADERS INDEX | 2.048021 ** | MSCI USA LEADERS INDEX (-2) | −0.427186 |

PI IN BILLIONS | −0.104973 | PI IN BILLIONS (-4) | −1.231945 ** |

SP500 CARBON EFFICIENT | −1.135460 | SP 500 CARBON EFFICIENT (-2) | 0.643324 |

SP CONSUMER FINANCE INDEX | 0.077979 | SP CONSUMER FINANCE_INDEX (−3) | −0.274214 ** |

SP MUNICIPAL BOND EDUCATION | −0.125058 | SP MUNICIPAL BOND EDUCATION (-2) | 0.524653 |

UNEMPLOYMENT RATE IN % | −0.447830 **,‡ | UNEMPLOYMENT RATE IN % (-3) | 0.318304 * |

Adjusted R-squared | 0.071882 | Adjusted R-squared | 0.234387 |

Sum squared resid | 0.203433 | Sum squared resid | 0.161595 |

F-statistic | 1.906158 | F-statistic | 4.459419 |

Prob(F-statistic) | 0.051960 | Prob(F-statistic) | 0.000032 |

Dependent Variable: University of Michigan Consumer Sentiment Index | |||
---|---|---|---|

Variables (First Sub-Period) | OLS Coefficients | Variables (Second Sub-Period) | OLS Coefficients |

CONSTANT | 0.011538 | CONSTANT | −0.000718 |

BSTARTUP GLOBAL INDEX (-1) | −0.185552 ** | BSTARTUP GLOBAL INDEX (-1) | 0.041828 |

BUSINESS CONFIDENCE INDEX (-1) | 7.983167 * | BUSINESS CONFIDENCE INDEX (-1) | 3.726710 |

DOW JONES SUSTAINABILITY (-1) | 1.420353 *** | DOW JONES SUSTAINABILITY (-1) | 0.538998 * |

MSCI GLOBAL ENERGY EFFICIENT INDEX (-1) | −1.024799 *** | MSCI GLOBAL ENERGY EFFICIENT INDEX (-1) | −0.294351 |

MSCI USA LEADERS INDEX (-2) | 0.206585 | MSCI USA LEADERS INDEX (-2) | −1.348939 |

PI IN BILLIONS (-4) | −1.420226 * | PI IN BILLIONS (-4) | −0.342955 |

SP 500 CARBON EFFICIENT (-2) | 0.093590 | SP 500 CARBON EFFICIENT (-2) | 1.342124 |

SP CONSUMER FINANCE_INDEX (-3) | −0.408050 ** | SP CONSUMER FINANCE_INDEX (-3) | −0.085687 |

SP MUNICIPAL BOND EDUCATION (-2) | 0.538481 | SP MUNICIPAL BOND EDUCATION (-2) | 0.514044 |

UNEMPLOYMENT RATE IN % (-3) | 0.765796 ** | UNEMPLOYMENT RATE IN % (-3) | −0.224393 |

Adjusted R-squared | 0.372938 | Adjusted R-squared | 0.015380 |

Sum squared resid | 0.084147 | Sum squared resid | 0.054434 |

F-statistic | 4.211591 | F-statistic | 1.090595 |

Prob(F-statistic) | 0.000000 | Prob(F-statistic) | 0.388141 |

Dependent Variable: University of Michigan Consumer Sentiment Index | ||
---|---|---|

Variables | RS Coefficients (Regime 1) | RS Coefficients (Regime 2) |

CONSTANT | 0.010338 * | −0.011795 |

BSTARTUP GLOBAL INDEX | −0.025739 | −0.027302 |

BUSINESS CONFIDENCE INDEX | −1.263362 | 12.07068 ** |

DOW JONES SUSTAINABILITY | 0.752385 | −0.751735 |

MSCI GLOBAL ENERGY EFFICIENCY | −0.272709 | −0.638802 * |

MSCI USA LEADERS INDEX | 0.322006 | 3.966401 *** |

PI IN BILLIONS | 0.191583 | −4.290645 *** |

SP 500 CARBON EFFICIENT | −1.077221 | −1.702474 |

SP CONSUMER FINANCE_INDEX | 0.471282 ** | −0.355529 |

SP MUNICIPAL BOND EDUCATION | 0.842489 * | −2.616637 *** |

UNEMPLOYMENT RATE IN % | −0.397643 ** | −0.381531 |

Sum squared resid | 0.212884 | |

Probabilities Parameters | 0.774284 | 0.427532 | 1.811054 | 0.0701 |

**Table 5.**Constant simple transition probabilities and constant expected durations of the regime-switching regression.

Constant Simple Transition Probabilities | ||
---|---|---|

$P\left(i,k\right)=P(s\left(t\right)=k|s\left(t-1\right)=i)$ | ||

$\left(row=i/column=j\right)$ | ||

1 | 2 | |

1 | 0.684446 | 0.315554 |

2 | 0.684446 | 0.315554 |

Constant Expected Durations | ||

1 | 2 | |

3.169033 | 1.461035 |

Number of iterations: 2000 | ||||||

Error tolerance for Theta: 0.05 | ||||||

Tolerance for the cost function: 0.05 | ||||||

Initial guess for Theta: zeros (1, 11) | ||||||

Learning rate for gradient descent algorithm: 0.1 | ||||||

Error = 0.00076494 | ||||||

Least-square estimate of Theta: | ||||||

Theta = 0.001 | ||||||

0.0917 0.2379 0.3196 0.2878 0.3837 −0.0344 0.0101 0.0702 −0.0015 −0.2995 0.3034 |

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## Share and Cite

**MDPI and ACS Style**

El Alaoui, M.; Bouri, E.; Azoury, N.
The Determinants of the U.S. Consumer Sentiment: Linear and Nonlinear Models. *Int. J. Financial Stud.* **2020**, *8*, 38.
https://doi.org/10.3390/ijfs8030038

**AMA Style**

El Alaoui M, Bouri E, Azoury N.
The Determinants of the U.S. Consumer Sentiment: Linear and Nonlinear Models. *International Journal of Financial Studies*. 2020; 8(3):38.
https://doi.org/10.3390/ijfs8030038

**Chicago/Turabian Style**

El Alaoui, Marwane, Elie Bouri, and Nehme Azoury.
2020. "The Determinants of the U.S. Consumer Sentiment: Linear and Nonlinear Models" *International Journal of Financial Studies* 8, no. 3: 38.
https://doi.org/10.3390/ijfs8030038