Introduction

The Federal Minimum Wage was originally set up by President Franklin D. Roosevelt in 1945 at 40 cents an hour. Since then, the Federal Minimum Wage has increased multiple times, with the most recent occurrence happening in 2007, when it increased from $5.15 to $7.25 per hour (Mantel, 2014). However, many states have increased their minimum wage above the federal level. For example, California has a minimum wage set at $11 per hour and is incrementally increasing it every year till it reaches $15 in 2022 (Brainerd, 2018). As of today, 28 states (29 if you include Washington DC) have a higher minimum wage rate than the federal level. This has led to much debate of whether the Federal Minimum Wage should also be raised once more.

The effect of raising the minimum wage has been heavily debated. This debate usually revolves around the impact it will have economically. However, raising minimum wage might also have a causal relationship with improved mental health. Other studies not focused on minimum wage have found that there is a causal relationship with income and life satisfaction (Pischke, 2011). Since minimum wage raises the income level of the lowest paid workers, this may also lead to them having a more satisfying life, leaving them in a better mental state. Little research has been done on the impact minimum wage has on mental health in the United States; however, there has been relevant research done on the United Kingdom’s minimum wage. In one such study, Kronenber et al. (2017) looked at the impact of an increase in minimum wage on mental health. They found that there was a slight increase to mental health; however, these results were statistically insignificant. This led them to the conclusion that there was not enough evidence to prove that minimum wage influences mental health. Although, they say if the there was a larger increase in wages, there might be a more pronounced impact on mental health.

This paper aims to gain further insight into the possible positive or negative impact minimum wage has on mental health. By using a nationally representative survey, I will compare respondents’ self-reported days of poor mental health by states’ minimum wage rates.

Methods

Data

#----------------------------------------------------------------------------------------------#
#Project: Data Challenge 1                                                                     
#Author: Brandon Czuczor
#Program Name: 1_dataprep
#Data Used: BRFSS16_DC1.dta
#Created: 1/31/2018
#Last Revised & Notes: 

#Reminders: Set working directory.

#Contents: This file converts original data from Stata to R format and recodes variables for analysis
#----------------------------------------------------------------------------------------------#

#----------------------------------------------------------------------------------------------#
#Set Up and load data. Remember that after the first run you can comment out install.packages lines
#----------------------------------------------------------------------------------------------#

#________________________________________________________________________________________________________________#
#Set working directory
#If you are at school change to "C:/Users/czuczor.brandon/OneDrive - University of Wisconsin-La Crosse/ECO 307/DC1"
#If you are at home, change to "C:/Users/Brandon/OneDrive - University of Wisconsin-La Crosse/ECO 307/DC1"
#_________________________________________________________________________________________________________________

setwd("C:/Users/Brandon/OneDrive - University of Wisconsin-La Crosse/ECO 307/DC1")


#________________________________________________________________________________________________________________#
#----Get rid of # if your on another computer for the first time----#
#----Install packages
#install.packages("foreign")
#install.packages("tidyverse")
#_________________________________________________________________________________________________________________


#Library packages
library(foreign)
library(tidyverse)

#Import Data from Stata format to R
library(foreign)
BRFSS16 <- read.dta("BRFSS16_DC1.dta")


#-----------------------------------------------------------------------------------------------#
#Renaming variables that start with _ to get rid of the _.
#-----------------------------------------------------------------------------------------------#
names(BRFSS16)[names(BRFSS16) == "_state"] <- "fips"
names(BRFSS16)[names(BRFSS16) == "_finalwt"] <- "finalwt"

#-----------------------------------------------------------------------------------------------#
#fips = state numbers
#menthlth = number of days in past 30 days you had bad mental health
#income2 = household income level
#medcost = If you can afford medical costs
#addepev2 = If you have been told by a doctor that you have depression
#-----------------------------------------------------------------------------------------------#

Mwdata <- select(BRFSS16, fips, menthlth, income2, finalwt, medcost, addepev2)


#-----------------------------------------------------------------------------------------------#
#Merging my state policy
#-----------------------------------------------------------------------------------------------#

statepol <- read.csv("PolicyData_Czuczor.csv")

names(statepol)[names(statepol)== "X_state"] <- "fips"

Mwdata_statepol <- left_join(Mwdata, statepol, by="fips")

#Removing other dataframes
rm(BRFSS16, Mwdata, statepol)

#-----------------------------------------------------------------------------------------------#
#Recoding variables and label values for categorical variables
#-----------------------------------------------------------------------------------------------#


#Changing code 88 to 0, and 88/77 to NA
Mwdata_statepol$menthlth <- recode(Mwdata_statepol$menthlth, '88' = 0L)
Mwdata_statepol$menthlth <- as.numeric(recode(as.character(Mwdata_statepol$menthlth), "77" = "NA", "99" = "NA"))


#
Mwdata_statepol$income2 <- as.factor(Mwdata_statepol$income2)

#And define levels for the factor variable using the BRFSS codebook making sure you go in the same order as the values
levels(Mwdata_statepol$income2) <- c("Less than $10K", 
                                      "$10K to <$15K", 
                                      "$15K to <$20K", 
                                      "$20K to <$25K", 
                                      "$25K to <$35K",
                                      "$35K to <$50K",
                                      "$50K to <$75K",
                                      "$75K or more",
                                      "Don't Know",
                                      "Refused")


#med cost------------------------------------------------------
Mwdata_statepol$medcost <- as.factor(Mwdata_statepol$medcost)

#And define levels for the factor variable using the BRFSS codebook making sure you go in the same order as the values
levels(Mwdata_statepol$medcost) <- c("Yes", 
                                      "No", 
                                      "Don't know", 
                                      "Refused")

#Addepev2---------------------------------------------------------

  
Mwdata_statepol$addepev2 <- as.factor(Mwdata_statepol$addepev2)  
  levels(Mwdata_statepol$addepev2) <- c("Yes", 
                                       "No", 
                                       "Don't know", 
                                       "Refused")





#Drop observations with missing values on any of your variables by replacing my dataframe name with yours
#in the code below.
#Pay attention - if a ton of observations are dropped, you may have a problem here
Mwdata_statepol <- Mwdata_statepol %>% filter(complete.cases(.))

##################################################################################################
#Analytic sample is prepared. Proceed to 2_eda
##################################################################################################

The data used in this analysis is from the 2016 Behavioral Risk Factor Surveillance System (BRFFS) and the state by state 2016 minimum wage rates. The BRFSS is used because it is the largest continuously conducted health survey in the United States. For this study, MENTHLTH variable is the key outcome measure. MENTHLTH contains the respondents’ self-reported days of poor mental health over the past 30 days. Larger values in this variable indicate worse mental health. MENTHLTH is re-coded so that anyone who reported no poor mental health days are coded as 0. In addition, all respondents who reported they Don’t Know or Refused to answer are excluded. Minwage is the key independent variable. It is a continuous variable which contains the minimum wage in the respondents’ state in 2016. Figure 1 provides a map of the range of minimum wage in 2016.

Figure 1 Minimum Wage Rates, 2016

Figure 1 Minimum Wage Rates, 2016

In addition to these key measures, the analytic files include a measure for annual household income from all sources called INCOME2, which is an interval scale. Minwage should mostly affect people who have low household income; although, it should also impact some people who are in higher household income, such as children who live with their parents and are in low paying jobs. For this reason, I have kept it unrestricted. Another variable used is MEDCOST. MEDCOST contains the respondents’ responses to if there was a time in the past 12 months when they needed to see a doctor but could not because of cost. This is a nominal variable with the outputs being Yes, No, Don’t Know, Refused. Finally, the last variable used is ADDEPEV2. This is needed for many areas that have high depression rates also tend to have lower minimum wage rates, as can be seen in figure 2 (MMWR, 2010). This variable contains the respondents’ responses to if they were ever told that they have a depressive disorder, including depression, major depression, dysthymia, or minor depression. This is a nominal variable with the outputs being Yes, No, Don’t Know, Refused.

Figure 2 Adult Depression Rates by state, 2006-08

Figure 2 Adult Depression Rates by state, 2006-08

After this sample restriction and eliminating responses with missing data, the analytic samples contains 466191 observations. Graph 1 provides the weighted summary statistics for Minwage us BRFSS sampling weight finalwt. All other descriptive statistics and regressions will also apply this BRFSS sampling weight.

plot_data <- Mwdata_statepol %>%
  # income2
  group_by(Minwage) %>%
  summarize(meanMenthlth=weighted.mean(menthlth, finalwt))


graph1 <- ggplot(plot_data, aes(x= Minwage, y=meanMenthlth)) + geom_point()  +labs(
  x = "Minimum Wage (USD)",
  y = "Average Bad Mental Health Days",
  title = "Graph 1",
  subtitle = "Average Bad Mental Health Days Compared Minimum Wage, 2016",
  caption = "Data source: BRFSS, 2016"
) + geom_smooth(method=lm, se=FALSE, size = 2, color = "grey40") +
  scale_x_continuous(labels = function(Minwage){ paste0("$", Minwage, ".00") })

graph1 + theme_minimal() + theme(plot.caption = element_text(color = "gray30"),
                                plot.background = element_rect(fill = "grey97"))

Empirical Strategy

To estimate the impact of minimum wage on mental health, I compare the days of poor mental health to the minimum wage levels of each state. I start with Model 1, which is a simple regression using Ordinary Least Squares (OLS) and then weighted least square to account for the complex sampling structure of the BRFFS data.

Model 1 Simple Regression

\[menthlth_{i} = \beta_{0} + \beta_{1}minwage_{i}+\epsilon_{i}\] In this model, \(\beta_{1}\) is the is the estimated difference in days of poor mental health associated with a $1 difference in the state minimum wage. A negative \(\beta_{1}\) would indicate that an improvement to mental health.

This method attributes any differences between states’ mental health to minimum wage. This could produce a biased estimate, because other states may differ in other ways, which could affect their mental health. For instance, a state with a higher minimum wage might have more programs to help their citizens afford medical care. If this were to happen, it would have a negative bias to bad mental health days. This means it may be more likely to overestimate the impact of minimum wage in any reduction.

Model 2 Multiple Regression

\[menthlth_{i} = \beta_{0} + \beta_{1}minwage_{i} + \beta_{2}income_{i} + \beta_{3}medcost_{i} + \beta_{4}depression_{i}+\epsilon_{i}\] In model 2, I control for multiple variables that could create potential biases that were not account for in model 1. These variables are medcost, income and depression. First, Income is controlled for because a person who makes more should have better mental health. The next variable is medcost. This is used to address the potential difference in affordability of health care. The final variable used in this model is depression. This is controlled for because people without depression should have better mental health than those who have it. All these variables would have a negative bias to mental health and minimum wage. In Model 3, I control for household income, depression, and medcost, while allowing the effect of minimum wage to vary with household income.

Medcost and depression are variables with 4 categories (Yes, No, Don’t know, Refused). Income is an interval scale variable with 10 categories including Don’t Know and Refused. The omitted category is income below $10,000.

Model 3 Multiple Regression Allowing Minimum Wage Impact to Depend on Income

\[menthlth_{i} = \beta_{0} + \beta_{1}minwage_{i} + income_{i}\theta_{1} + minwage_{i} * income_{i}\theta_{2} + \beta_{2}medcost_{i} + \beta_{4}depression_{i}+\epsilon_{i}\]

Results

To start off, I initially look at the impact on mental health when using the variables of minimum wage and income. From this initial result, it appears that minimum wage has a relatively large impact in households with annual income of $25,000 and below as can be seen in Graph 2. Interestingly, it shows the greatest affect happened in the household income range of $10,000 to $15,000. If taking this graph literally, minimum wage helps to lower bad mental health days; however, when using regressions to try and solve this question, a different story arises.

plot_data2 <- Mwdata_statepol %>%
  group_by(Minwage, income2) %>%
  summarize(meanMenthlth=weighted.mean(menthlth, finalwt))

plot_data3 <- plot_data2 %>% filter(income2 == "Less than $10K" | 
                                      income2 == "$10K to <$15K" |
                                      income2 == "$15K to <$20K" |
                                      income2 == "$20K to <$25K")


#Plot
graph <- ggplot(plot_data3, aes(x= Minwage, y=meanMenthlth, colour = income2)) + geom_point()  +labs(
  x = "Minimum Wage (USD)",
  y = "Bad Mental Health Days",
  title = "Graph 2",
  subtitle = "Average Bad Mental Health Days Compared to Minimum Wage and Household Income, 2016",
  caption = "Data source: BRFSS, 2016",
  colour = "Household Income"
) + geom_smooth(method=lm, se=FALSE, size = 2) + 
  scale_colour_manual(values=c("brown3", "dodgerblue3", "chartreuse3", "gold3")) +
  scale_x_continuous(labels = function(Minwage){ paste0("$", Minwage) })

graph + theme_minimal() + theme(plot.caption = element_text(color = "gray30"),
                                plot.background = element_rect(fill = "grey97"))

The first regression I use is the simple regression from Model 1. The results from this regression can be seen in Table 1, which is separated by OLS and weighted by least square. As expected, both OLS and weighted least squares gave a negative number. For the rest of the models, I used the weighted least square version.

The weighted least square implies that for every dollar minimum wage is raised, there will be a decrease in bad mental health days by 0.111 days. This may seem rather small, but, if we recall from Graph 1 the average bad mental health days is 3.71, this result is statistically significant and relatively large. If we take this estimate literally, raising minimum wage appears to have relatively large positive impact to mental health.

simple <- lm(menthlth ~ Minwage, data = Mwdata_statepol)

#----------------------------------------------------------------------------------------------#
#Simple Regression - estimated using weighted least squares to account for sample design
#----------------------------------------------------------------------------------------------#
simpleW <- lm(menthlth ~ Minwage, data = Mwdata_statepol, weights = finalwt)

stargazer(simple, simpleW, title = "Table 1 Results from Model 1 Simple Regression", column.labels = c("OLS", "Weighted"), type = "html")
Table 1 Results from Model 1 Simple Regression
Dependent variable:
menthlth
OLS Weighted
(1) (2)
Minwage -0.074*** -0.111***
(0.012) (0.011)
Constant 4.046*** 4.687***
(0.101) (0.095)
Observations 466,191 466,191
R2 0.0001 0.0002
Adjusted R2 0.0001 0.0002
Residual Std. Error (df = 466189) 7.761 182.964
F Statistic (df = 1; 466189) 36.303*** 94.575***
Note: p<0.1; p<0.05; p<0.01

The estimate from Model 1 is promising; however, it is most likely to be biased, for it does not account for other variables that might also increase mental health. Model 2 and 3 account for these potential biases. Table 2 shows the estimate for both models. Interestingly, there is a large change to the estimate of the effectiveness of minimum wage in model 2. When we account for income, depression, and ability to afford medical cost, minimum wage appears to have barely any impact on increasing mental wellbeing. In fact, the value is so close to 0, it is statistically insignificant. If this result is taken literally, then it shows there is not significant evidence that minimum wage has an impact on mental health. This model is interesting but also lacking, for minimum wage should be more effective in lower income households, which it does not account for.

This is where we finally get to Model 3. In this model, I let the impact of minimum wage vary depending on income. This changes the estimate drastically. For a person in a household who earns less than $10,000 a year, each dollar minimum wage is increased lowers their bad mental health days by .536 days. The only other income level that minimum wage is statistically significant is in households that earn $15,000 through $20,000. In this group, each dollar minimum wage is increased lowers their bad mental health days by .247 days. All other income levels hover just above 0 and are not statistically significant. The most likely reason why households which earn $15,000 to $20,000 have an increase is they probably have one or more member who is earning below that $10,000 level.

If you recall from Graph 2, the results of the Model 3 contrast from what Graph 2 predicts. In Graph 2, it seems that an increase in minimum wage would have a positive impact to mental health for all people in households who earn less than $25,000 per year with the biggest benefit being in the range of $10,000 to $15,000. However, when all the other variables are added in Model 3, the impact only seems to affect the mental health of households earning less than $10,000 and households earning $15,000 to $20,000. In addition, the group expected to see the largest impact from minimum wage, $10,000 to $15,000, had a change which was statistically insignificant.

simpleW <- lm(menthlth ~ Minwage, data = Mwdata_statepol, weights = finalwt)
MultiRegW <- lm(menthlth ~ Minwage + income2 + medcost + addepev2, data = Mwdata_statepol, weights = finalwt)
AdvRegW <- lm(menthlth ~ Minwage + Minwage*income2 + medcost + addepev2,
             data = Mwdata_statepol, weights = finalwt)

stargazer(MultiRegW, AdvRegW, title = "Table 2 Results from Model 2 and 3", column.labels = c( "Model 2", "Model 3"), covariate.labels = c("Minwage", "$10K to <$15K", "$15K to <$20K", "$20K to <$25K", "$25K to <$35K",
                                 "$35K to <$50K", "$50K to <$75K","$75K or more", "Income Don't Know ", 
                                 "Income Refused to Provide", "Medcost No", "Medcost Don't Know",
                                 "Medcost Refused to Provide","Depression No", "Depression Don't Know",
                                 "Depression Refused to Provide",
                                 "Minwage * $10K to <$15K", "Minwage * $15K to <$20K", "Minwage * $20K to <$25K", 
                                 "Minwage * $25K to <$35K", "Minwage * $35K to <$50K", "Minwage * $50K to <$75K",
                                 "Minwage * $75K or more", "Minwage * Don't Know", 
                                 "Minwage * Refused to Provide"),
          type = "html")
Table 2 Results from Model 2 and 3
Dependent variable:
menthlth
Model 2 Model 3
(1) (2)
Minwage 0.016 -0.536***
(0.010) (0.045)
10K to <15K -1.097*** -5.970***
(0.070) (0.549)
15K to <20K -1.516*** -3.960***
(0.063) (0.507)
20K to <25K -1.975*** -6.515***
(0.061) (0.497)
25K to <35K -2.394*** -7.354***
(0.060) (0.476)
35K to <50K -2.566*** -6.836***
(0.057) (0.455)
50K to <75K -2.871*** -7.778***
(0.057) (0.447)
75K or more -3.055*** -8.324***
(0.053) (0.408)
Income Don’t Know -1.647*** -5.856***
(0.061) (0.485)
Income Refused to Provide -2.976*** -9.243***
(0.061) (0.475)
Medcost No -2.591*** -2.575***
(0.032) (0.032)
Medcost Don’t Know -1.807*** -1.791***
(0.249) (0.249)
Medcost Refused to Provide -2.213*** -2.243***
(0.399) (0.399)
Depression No -8.657*** -8.650***
(0.029) (0.029)
Depression Don’t Know -2.359*** -2.341***
(0.181) (0.181)
Depression Refused to Provide -6.950*** -6.961***
(0.414) (0.414)
Minwage * 10K to <15K 0.587***
(0.066)
Minwage * 15K to <20K 0.289***
(0.061)
Minwage * 20K to <25K 0.546***
(0.060)
Minwage * 25K to <35K 0.598***
(0.057)
Minwage * 35K to <50K 0.513***
(0.055)
Minwage * 50K to <75K 0.591***
(0.054)
Minwage * 75K or more 0.634***
(0.049)
Minwage * Don’t Know 0.506***
(0.058)
Minwage * Refused to Provide 0.752***
(0.056)
Constant 15.491*** 20.058***
(0.101) (0.376)
Observations 466,191 466,191
R2 0.212 0.212
Adjusted R2 0.212 0.212
Residual Std. Error 162.429 (df = 466174) 162.387 (df = 466165)
F Statistic 7,841.315*** (df = 16; 466174) 5,031.105*** (df = 25; 466165)
Note: p<0.1; p<0.05; p<0.01

Conclusion

This study examined the impact of State Minimum Wage rates on mental health. Prior research indicated a link between income and happiness; however, little evidence was available to indicate if minimum wage had a similar impact. Using cross-sectional data from the BRFSS, I find strong evidence that higher minimum wage rates increase mental health of respondents in households who make below $10,000 and between $15,000 to $20,000. All other household income levels showed no strong evidence of a positive or negative relationship to mental health. As such, it appears that minimum wage has a positive causal relationship to mental health for the poorest workers.

This analysis does have some potential limitations. First, BRFSS does not contain data on if its respondents work at minimum wage or not. Without this, there is a potential that the results are underestimated because it includes people that get paid at a higher rate. Another limitation is the estimate uses cross-sectional data. This means there could be preexisting differences from state to state that cause a difference in mental health that are not accounted for in the multiple regression models and are attributed to minimum wage.

Works Cited

Brainerd, J. (2018, January 02). Retrieved from http://www.ncsl.org/research/labor-and-employment/state-minimum-wage-chart.aspx

Kronenberg, C., Jacobs, R., & Zucchelli, E. (2017). The impact of the UK National Minimum Wage on mental health. SSM - Population Health, 3, 749-755. http://doi.org/10.1016/j.ssmph.2017.08.007

Mantel, B. (2014, January 24). Minimum wage. CQ Researcher, 24, 73-96. Retrieved from http://library.cqpress.com/

Morbidity and Mortality Weekly Report (MMWR). (2010, October 01). Retrieved from https://www.cdc.gov/mmwr/preview/mmwrhtml/mm5938a2.htm

Pischke, J. (2011). Money and Happiness: Evidence from the Industry Wage Structure. IZA Discussion Papers 5705, Institute for the Study of Labor (IZA). http://ideas.repec.org/p/iza/izadps/dp5705.html