本研究目的是在使用半母數分析焦慮和憂鬱的嚴重程度與老年人的時薪之間的關係。我們假說是適度的焦慮可能會增加薪水,其焦慮程度和薪水關係呈倒 U 型,一定程度的焦慮會迫使人們在工作中更加積極並提高工資,但是過度焦慮則可能會影響工作績效並降低工資。然而,憂鬱對工資的影響可能呈負相關,當一個人越憂鬱時,他們的工作表現就越差,得到的薪水就越少。本研究使用部分線性模型來驗證焦慮和憂鬱對不同性別工人時薪的影響。數據主要來自美國 2006-2016 年美國 the Health and Retirement Study(HRS)。我們使用 Heckman 兩階段模型來解決潛在的選擇偏差問題。第一階段模型使用 Probit 模型來估計個人是否參與工作。這裡的因變量是一個二元虛擬變量,自變量是影響個人決定工作與否的外生變量。根據 Probit模型,我們計算出樣本的 inverse Mill's ratio 來修正樣本選擇偏差。第二階段模型是半母數模型,以工資為主要預測因素,以疾病為結果變量。為了解決選擇偏差的問題,在方程中加入 inverse Mill's ratio。半母數模型中疾病對 IV 廻歸的誤差項來處理潛在的內生性,且其殘差可去除 IV 無法解釋的疾病變異以及其他解釋變量所造成的內生影響。2010 年的分析結果顯示,在伴有一定程度的焦慮和憂鬱時,男性其工資會先上升後下降,而嚴重的焦慮和憂鬱症狀會再次增加男性的工資。由於焦慮和憂鬱越加嚴重,女性的工資隨之下降,顯示出女性的工資有疾病懲罰的跡象。根據這項研究發現,女性通常比男性較容易感受更多的焦慮和憂鬱,另外,我們提出懷疑,有可能出現嚴重心理疾病的工人多報工資的情況而影響結果。

The purpose of this study was to analyze the relationship between anxiety and depression and hourly earnings in older adults using semiparametric analysis. Our hypothesis is that a certain criterion of anxiety may increase wages. The relationship between anxiety level and wages is inverted U-shaped. A certain degree of anxiety will force people to be more active at work and increase wages, but excessive anxiety may affect job performance and reduce salary. However, the effect of depression on wages can be negatively correlated, with the more depressed a person is, the worse their job performance and the less pay they get. This study uses a partial linear model to examine the effects of anxiety and depression on the hourly wages of workers by gender. The data mainly come from the Health and Retirement Study (HRS) in the United States from 2006 to 2016. We use a Heckman two-stage model to address potential selection bias. The first stage model uses the Probit model to estimate whether an individual is involved in the work. The dependent variable here is a binary dummy variable, and the independent variable is an exogenous variable that affects an individual's decision to work or not. According to the Probit model, we calculate the inverse Mill's ratio of the sample to correct for sample selection bias. The second-stage model is a semiparametric model with wages as the main predictor and disease as the outcome variable. To address the problem of selection bias, we add the inverse Mill's ratio to the equation. The error term of the regression of disease on IV in the semiparametric model is used to deal with potential endogeneity, and its residual can remove the endogenous effect of disease variation that cannot be explained by IV and other explanatory variables. The results of the 2010 analysis showed that when accompanied by a certain degree of anxiety and depression, males’ wages first rose and then fell, and severe disease increased males’ wages again. Females’ wages fell as anxiety and depression increased, showing signs that females’ wages were punished by disease. According to the findings of this study, females are generally more likely to experience higher levels of anxiety and depression than males, and we raise suspicions that over reporting of wages by workers with severe mental illness may affect the results.

TABLE OF CONTENTS:
I. INTRODUCTION.................1
II. LITERATURE REVIEW.................2
III. DATA .................6
3.1 DEMOGRAPHIC CHARACTERISTICS .................6
3.2 OUTCOME VARIABLE.................7
3.2.1 EMPLOYMENT.................7
3.2.2 DEPRESSION AND ANXIETY SYMPTOMS.................8
3.3 PRIMARY PREDICTOR VARIABLE.................12
3.4 INSTRUMENTAL VARIABLE.................20
IV. VARIABLE SPECIFICATION AND METHODOLOGY ....................21
V. RESULTS.................24
VI. CONCLUSION.................45
VII. REFERENCE .................48
VIII. APPENDIX .................51

LIST OF TABLES:
Table 1 Weighted summary statistics for disease of male potential
workers in 2010 ..........................................................................13
Table 2 Weighted summary statistics for disease of female potential
workers in 2010...........................................................................14
Table 3 Weighted summary statistics for anxiety of workers in 2010
(by gender) ..................................................................................18
Table 4 Weighted summary statistics for depression of workers in 2010
(by gender) ..................................................................................19
Table 5 Exogenous disease and log wage: partially linear model in 2010
(By gender and disease) .............................................................26
Table 6 Endogenous disease and log wage–partially linear model: the
augmented regression approach in 2010 (By gender and
disease).........................................................................................32
Table 7 Endogenous disease and log wage–partially linear model:
Robustness check (By gender and disease) ..............................39
Table 8 Endogenous disease and log wage–partially linear model:
Robustness check without outlier (By gender and disease)....42

LIST OF FIGURES:
Figure 1 The percentage of elderly males’ depression in the U.S.............9
Figure 2 The percentage of elderly females’ depression in the U.S..........9
Figure 3 The percentage of elderly males’ anxiety in the U.S. ...............11
Figure 4 The percentage of elderly females’ anxiety in the U.S. ............11
Figure 5 Densities of wage for elderly workers in the U.S. in 2010 (by
gender)..........................................................................................16
Figure 6 Density of wage: suffering anxiety versus not suffering anxiety
in the U.S. in 2010: (a)male (b)female .......................................16
Figure 7 Density of wage: suffering depression versus not suffering
depression in the U.S. in 2010: (a)male (b)female ....................16
Figure 8 Semiparametric estimates of the effects of anxiety on log real
wage: Exogenous–males..............................................................28
Figure 9 Semiparametric estimates of the effects of anxiety on log real
wage: Exogenous–females...........................................................28
Figure 10 Semiparametric estimates of the effects of depression on log
real wage: Exogenous–males......................................................29
Figure 11 Semiparametric estimates of the effects of depression on log
real wage: Exogenous–females...................................................29
Figure 12 Semiparametric estimates of the effects of anxiety on log real
wage: Endogenous–males...........................................................35
Figure 13 Semiparametric estimates of the effects of anxiety on log real
wage: Endogenous–females........................................................35
Figure 14 Semiparametric estimates of the effects of depression on log
real wage: Endogenous–males....................................................36
Figure 15 Semiparametric estimates of the effects of depression on log
wage: Endogenous–females........................................................36
Figure 16 Semiparametric estimates of the effects of anxiety on log wage:
Robustness check–males.............................................................40
Figure 17 Semiparametric estimates of the effects of anxiety on log wage:
Robustness check–females..........................................................40
Figure 18 Semiparametric estimates of the effects of depression on log
wage: Robustness check–males..................................................41
Figure 19 Semiparametric estimates of the effects of depression on log
wage: Robustness check–females...............................................41
Figure 20 Semiparametric estimates of the effects of anxiety on log wage:
Robustness check without outlier–males ..................................43
Figure 21 Semiparametric estimates of the effects of anxiety on log wage:
Robustness check without outlier–females ...............................43
Figure 22 Semiparametric estimates of the effects of depression on log
wage: Robustness check without outlier–males........................44
Figure 23 Semiparametric estimates of the effects of depression on log
wage: Robustness check without outlier–females ....................44

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