# Consumer Sentiment in the United States and the Impact of Mental Disorders on Consumer Behavior—Time Trends and Persistence Analysis

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## Abstract

**:**

## 1. Introduction

## 2. Data

## 3. Methodology and Results

#### 3.1. Unit Root Methods

#### 3.2. ARFIMA (p, d, q) Model

#### 3.3. Granger Causality Test

#### 3.4. FCVAR Model

## 4. Concluding Comments

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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$d=0$ | ${x}_{t}$ process is short memory |

$d>0$ | ${x}_{t}$ process is long memory |

$d<0.5$ | ${x}_{t}$ is covariance stationary |

$d\ge 0.5$ | ${x}_{t}$ is non-stationary |

$d<1$ | ${x}_{t}$ is mean-reverting |

$d\ge 1$ | ${x}_{t}$ is not mean-reverting |

Data Analyzed | Sample Size (Year) | Model Selected | d | Std. Error | Interval | I(d) |
---|---|---|---|---|---|---|

Mental Health Time Series | ||||||

Mental and substance use disorders | 30 | ARFIMA (2, d, 0) | 1.26 | 0.241 | [0.87, 1.66] | I(1) |

Anxiety disorders | 30 | ARFIMA (2, d, 1) | 0.65 | 0.402 | [−0.01, 1.31] | I(0), I(1) |

Depressive disorders | 30 | ARFIMA (2, d, 0) | 0.31 | 0.277 | [−0.15, 0.77] | I(0) |

Bipolar disorders | 30 | ARFIMA (0, d, 0) | 0.97 | 0.160 | [0.71, 1.23] | I(1) |

Eating disorders | 30 | ARFIMA (0, d, 2) | 1.16 | 0.189 | [0.85, 1.47] | I(1) |

Schizophrenia | 30 | ARFIMA (0, d, 0) | 1.15 | 0.133 | [0.93, 1.37] | I(1) |

Alcohol use disorders | 30 | ARFIMA (1, d, 0) | 1.35 | 0.163 | [1.09, 1.62] | I(1) |

Substance use disorders | 30 | ARFIMA (1, d, 0) | 1.38 | 0.141 | [1.15, 1.61] | I(1) |

Consumer Sentiment Time Series | ||||||

Consumer Sentiment Index | 30 | ARFIMA (0, d, 0) | 0.95 | 0.168 | [0.68, 1.23] | I(1) |

Direction of Causality | Lags ^{1} | Prob. | Decision | Outcome |
---|---|---|---|---|

Mental and substance use disorders → Consumer Sentiment Index | 3 | 0.0246 | Reject null | Mental and substance use disorders influence Consumer Sentiment Index |

Consumer Sentiment Index → Mental and substance use disorders | 3 | 0.2535 | Do not reject null | Consumer Sentiment Index does not influence mental and substance use disorders |

Anxiety disorder → Consumer Sentiment Index | 9 | 0.0000 | Reject null | Anxiety disorder influences Consumer Sentiment Index |

Consumer Sentiment Index → Anxiety disorder | 9 | 0.2858 | Do not reject null | Consumer Sentiment Index does not influence anxiety disorder |

Depressive disorder → Consumer Sentiment Index | 2 | 0.5171 | Do not reject null | Depressive disorder does not influence Consumer Sentiment Index |

Consumer Sentiment Index → Depressive disorder | 2 | 0.4195 | Do not reject null | Consumer Sentiment Index does not influence depressive disorder |

Bipolar disorder → Consumer Sentiment Index | 1 | 0.9210 | Do not reject null | Bipolar disorder does not influence Consumer Sentiment Index |

Consumer Sentiment Index → Bipolar disorder | 1 | 0.4771 | Do not reject null | Consumer Sentiment Index does not influence bipolar disorder |

Eating disorders → Consumer Sentiment Index | 1 | 0.8963 | Do not reject null | Eating disorders do not influence Consumer Sentiment Index |

Consumer Sentiment Index → Eating disorder | 1 | 0.5036 | Do not reject null | Consumer Sentiment Index does not influence eating disorders |

Schizophrenia → Consumer Sentiment Index | 9 | 0.0182 | Reject null | Schizophrenia influences Consumer Sentiment Index |

Consumer Sentiment Index → Schizophrenia | 9 | 0.9980 | Do not reject null | Consumer Sentiment Index does not influence schizophrenia |

Alcohol use disorder → Consumer Sentiment Index | 9 | 0.0000 | Reject null | Alcohol use disorder influences Consumer Sentiment Index |

Consumer Sentiment Index → Alcohol use disorder | 9 | 0.4464 | Do not reject null | Consumer Sentiment Index does not influence alcohol use disorders |

Substance use disorders → Consumer Sentiment Index | 9 | 0.5773 | Do not reject null | Substance use disorders do not influence Consumer Sentiment Index |

Consumer Sentiment Index → Substance use disorders | 9 | 0.0604 | Do not reject null | Consumer Sentiment Index does not influence substance use disorders |

^{1}We used the Akaike information criterion to detect the number of lags.

$\mathit{d}\ne \mathit{b}$ | Cointegrating Equation Beta | ||
---|---|---|---|

Var1 | Var 2 | ||

Panel I: Mental and substance use disorders (Var1) vs. Consumer Sentiment Index (Var2) | $d=1.525\left(0.424\right)$ $b=1.525(0.352$) | 1.000 | –0.146 |

${\u2206}^{d}\left(\left[\begin{array}{c}Mentalandsubstanceusedisorders\\ ConsumerSentiment\end{array}\right]-\left[\begin{array}{c}15.465\\ 76.697\end{array}\right]\right)={L}_{d}\left[\begin{array}{c}\u20130.008\\ 1.931\end{array}\right]{\nu}_{t}+{\displaystyle \sum _{i=1}^{2}}{\widehat{\mathsf{\Gamma}}}_{i}{\mathsf{\Delta}}^{d}{L}_{d}^{i}({X}_{t}-\mu )+{\epsilon}_{t}$ | |||

Panel II: Anxiety (Var1) vs. Consumer Sentiment Index (Var 2) | $d=1.239\left(0.424\right)$ $b=1.239(0.210$) | 1.000 | –0.050 |

${\u2206}^{d}\left(\left[\begin{array}{c}Anxiety\\ ConsumerSentiment\end{array}\right]-\left[\begin{array}{c}5.606\\ 72.983\end{array}\right]\right)={L}_{d}\left[\begin{array}{c}\u20130.062\\ 1.204\end{array}\right]{\nu}_{t}+{\displaystyle \sum _{i=1}^{2}}{\widehat{\mathsf{\Gamma}}}_{i}{\mathsf{\Delta}}^{d}{L}_{d}^{i}({X}_{t}-\mu )+{\epsilon}_{t}$ | |||

Panel III: Schizophrenia (Var 1) vs. Consumer Sentiment Index (Var2) | $d=0.058\left(0.192\right)$ $b=0.058(0.003$) | 1.000 | –0.002 |

${\u2206}^{d}\left(\left[\begin{array}{c}VSchizophrenia\\ ConsumerSentiment\end{array}\right]-\left[\begin{array}{c}0.472\\ 78.812\end{array}\right]\right)={L}_{d}\left[\begin{array}{c}2.929\\ 360995.240\end{array}\right]{\nu}_{t}+{\displaystyle \sum _{i=1}^{2}}{\widehat{\mathsf{\Gamma}}}_{i}{\mathsf{\Delta}}^{d}{L}_{d}^{i}({X}_{t}-\mu )+{\epsilon}_{t}$ | |||

Panel IV: Alcohol use disorders (Var 1) vs. Consumer Sentiment Index (Var2) | $d=0.954\left(0.000\right)$ $b=0.954(0.000$) | 1.000 | –0.085 |

${\u2206}^{d}\left(\left[\begin{array}{c}Alcoholusedisorders\\ ConsumerSentiment\end{array}\right]-\left[\begin{array}{c}3.154\\ 92.281\end{array}\right]\right)={L}_{d}\left[\begin{array}{c}\u20130.05\\ 3.309\end{array}\right]{\nu}_{t}+{\displaystyle \sum _{i=1}^{2}}{\widehat{\mathsf{\Gamma}}}_{i}{\mathsf{\Delta}}^{d}{L}_{d}^{i}({X}_{t}-\mu )+{\epsilon}_{t}$ |

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**MDPI and ACS Style**

Monge Moreno, J.T.; Monge, M.
Consumer Sentiment in the United States and the Impact of Mental Disorders on Consumer Behavior—Time Trends and Persistence Analysis. *Mathematics* **2023**, *11*, 2981.
https://doi.org/10.3390/math11132981

**AMA Style**

Monge Moreno JT, Monge M.
Consumer Sentiment in the United States and the Impact of Mental Disorders on Consumer Behavior—Time Trends and Persistence Analysis. *Mathematics*. 2023; 11(13):2981.
https://doi.org/10.3390/math11132981

**Chicago/Turabian Style**

Monge Moreno, Jesús Tomás, and Manuel Monge.
2023. "Consumer Sentiment in the United States and the Impact of Mental Disorders on Consumer Behavior—Time Trends and Persistence Analysis" *Mathematics* 11, no. 13: 2981.
https://doi.org/10.3390/math11132981