Based on Hollingsworth et al (2017)

A Brief Summary

Main Questions:

How deaths and emergency room visits relate to the use of opioids and other drugs vary with macroeconomic conditions

What is the relationship between local economic conditions and drug-related adverse outcomes?

How serious adverse health outcomes related to opioid and other drugs vary with short-term fluctuations in macroeconomic conditions (specifically the local unemployment rate)?

Main Findings:

Generally found that there is a positive relationship between the unemployment rate and the opioid death and emergency room visits for opioids.

Strong evidence that opioid-related deaths and emergency room visits increase during times of economic weakness.

Negative economic shocks have larger adverse affects on drug related mortality and emergency room visits when conducted at the state (versus county) level.

Economic shocks were found to have the largest effect for white people.

Regress drug_deaths on unemp and gdp_per_capita

unemp: The coefficient of 3.38 represents that a one percentage increase in the unemployment rate is associated with a 3.38 increase in drug deaths per 100,000 people. (Note: This variable is significant at the 5% level of significance)

gdp_per_capita: The coefficient of 0.061 represents that a $1,000 increase in GDP per capita is associated with a 0.061 increase in drug deaths per 100,000 people. (Note: This variable is not significant at the 5% level of significance)

Based on the results, there is a procyclical relationship between the unemployment rate and drug-related mortality.

## 
## Call:
## lm(formula = drug_deaths ~ unemp + gdp_per_capita, data = Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -14.341  -7.597  -1.398   6.072  24.004 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     8.15620    9.52321   0.856   0.3961  
## unemp           3.38212    1.66699   2.029   0.0482 *
## gdp_per_capita  0.06121    0.13451   0.455   0.6512  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 9.197 on 47 degrees of freedom
## Multiple R-squared:  0.08313,    Adjusted R-squared:  0.04411 
## F-statistic: 2.131 on 2 and 47 DF,  p-value: 0.1301

unemp and gdp_per_capita Scatterplot

The variance of the regression error appears to be heteroskedastic. There seems to be variation of small and large differences between the fitted line and the observations. This indicates that our model likely would be more well suited to a non-linear model and therefore is suffering from heteroskedasticity.

Breusch-Pagan test

Based on the Breusch-Pagan test conducted below, a p-value of 0.046 means that we reject the null (homosked) in favor of the alternative (hetero) and have sufficient evidence that heteroskedasticity exists.

## 
##  studentized Breusch-Pagan test
## 
## data:  reg1
## BP = 6.1535, df = 2, p-value = 0.04611

White test for heteroskedasticity

Based on the White test conducted below, a p-value of 0.1862 means that we fail to reject the null (homosked) in favor of the alternative (hetero) and do not have sufficient evidence that heteroskedasticity exists.

Considering the results from the Breusch-Pagan and White tests conducted in questions 4 and 5, the results contradict each other. A likely reason why this might happen is the Breusch-Pagan test only checks for the linear form of heteroskedasticity, while the White test checks for many forms of heteroskedasticity.

## 
##  studentized Breusch-Pagan test
## 
## data:  reg1
## BP = 7.4968, df = 5, p-value = 0.1862

Significantly Correlated With the Error Variance

Hold

The standard errors change from those obtained in question 2 in a robust standard error model, by increasing. This does affect the conclusion about the relationship between macroeconomic conditions and drug-related mortality from question 2, but causes the variable to only be significant at the 10% level of significance (versus the 5%)

## 
## t test of coefficients:
## 
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)    8.156195   8.965363  0.9097  0.36760  
## unemp          3.382116   1.860587  1.8178  0.07548 .
## gdp_per_capita 0.061209   0.140711  0.4350  0.66556  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Explore the Relationship Between the Unemployment and Other Vars

When Looking At Three Different Models Produced Below, We Find Different Results:

Male Drug Deaths Regression:

unemp: The coefficient of 4.85702 represents that a one percentage increase in the unemployment rate is associated with a 4.85702 increase in male drug deaths per 100,000 men. (Note: This variable is significant at the 5% level of significance)

gdp_per_capita: The coefficient of 0.18368 represents that a $1,000 increase in GDP per capita is associated with a 0.18368 increase in male drug deaths per 100,000 men. (Note: This variable is not significant at the 5% level of significance)

Male White Drug Deaths Regression:

unemp: The coefficient of 5.4978 represents that a one percentage increase in the unemployment rate is associated with a 5.4978 increase in white male drug deaths per 100,000 white men. (Note: This variable is significant at the 5% level of significance)

gdp_per_capita: The coefficient of 0.1815 represents that a $1,000 increase in GDP per capita is associated with a 0.1815 increase in white male drug deaths per 100,000 white men. (Note: This variable is not significant at the 5% level of significance)

Alcohol Deaths Regression:

unemp: The coefficient of 0.897680 represents that a one percentage increase in the unemployment rate is associated with a 0.897680 increase in alcohol deaths per 100,000 people. (Note: This variable is significant at the 5% level of significance)

gdp_per_capita: The coefficient of 0.013462 represents that a $1,000 increase in GDP per capita is associated with a 0.013462 increase in alcohol deaths per 100,000 people. (Note: This variable is not significant at the 5% level of significance)

## 
## Call:
## lm(formula = male_drug_deaths ~ unemp + gdp_per_capita, data = Data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -19.56 -12.49  -2.52  10.00  32.27 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      4.6234    14.0869   0.328   0.7442  
## unemp            4.8570     2.4658   1.970   0.0548 .
## gdp_per_capita   0.1837     0.1990   0.923   0.3606  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 13.61 on 47 degrees of freedom
## Multiple R-squared:  0.08923,    Adjusted R-squared:  0.05047 
## F-statistic: 2.302 on 2 and 47 DF,  p-value: 0.1112
## 
## t test of coefficients:
## 
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)     4.62340    8.96536  0.5157  0.60848  
## unemp           4.85702    1.86059  2.6105  0.01209 *
## gdp_per_capita  0.18368    0.14071  1.3053  0.19813  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## lm(formula = male_white_drug_deaths ~ unemp + gdp_per_capita, 
##     data = Data)
## 
## Residuals:
##     Min      1Q  Median      3Q     Max 
## -22.156 -11.619  -2.303  11.050  41.631 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)  
## (Intercept)      3.2965    15.0459   0.219   0.8275  
## unemp            5.4978     2.6337   2.087   0.0423 *
## gdp_per_capita   0.1815     0.2125   0.854   0.3975  
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 14.53 on 47 degrees of freedom
## Multiple R-squared:  0.0955, Adjusted R-squared:  0.05701 
## F-statistic: 2.481 on 2 and 47 DF,  p-value: 0.09455
## 
## t test of coefficients:
## 
##                Estimate Std. Error t value Pr(>|t|)   
## (Intercept)     3.29649    8.96536  0.3677 0.714754   
## unemp           5.49776    1.86059  2.9549 0.004876 **
## gdp_per_capita  0.18145    0.14071  1.2896 0.203515   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Call:
## lm(formula = alcohol_deaths ~ unemp + gdp_per_capita, data = Data)
## 
## Residuals:
##    Min     1Q Median     3Q    Max 
## -7.423 -4.029 -1.201  2.562 19.589 
## 
## Coefficients:
##                Estimate Std. Error t value Pr(>|t|)
## (Intercept)    10.12794    6.24571   1.622    0.112
## unemp           0.89768    1.09328   0.821    0.416
## gdp_per_capita  0.01346    0.08822   0.153    0.879
## 
## Residual standard error: 6.032 on 47 degrees of freedom
## Multiple R-squared:  0.01445,    Adjusted R-squared:  -0.02749 
## F-statistic: 0.3446 on 2 and 47 DF,  p-value: 0.7103
## 
## t test of coefficients:
## 
##                 Estimate Std. Error t value Pr(>|t|)
## (Intercept)    10.127942   8.965363  1.1297   0.2643
## unemp           0.897680   1.860587  0.4825   0.6317
## gdp_per_capita  0.013462   0.140711  0.0957   0.9242