Econometric Analysis of Homelessness in the United States

Econometric Analysis of Homelessness in the United States Ryan Vyskocil Dr. Trees Fall 2015

Vyskocil 1 Table of Contents I. Introduction... 2 II. Equations and Variables.. 3 III. Initial Regression. 5 IV. Second Regressions... 8 V. Analysis 11 VI. Tests of Assumptions: Heteroscedasticity. 13 VII. Correcting for Heteroscedasticity... 16 VIII. Tests of Assumptions: Multicollinearity.. 20 IX. Correcting for Heteroscedasticity... 21 X. Tests of Assumptions: Autocorrelation... 28 XI. Conclusion... 29 XII. Appendix.. 31

Vyskocil 2 I. Introduction In this project, I am looking to analyze how state expenditures on mental health care affect the rate of homelessness within each state. I will be looking at 2014 point in time estimates of homelessness in the United States, and will be analyzing cross-sectional data collected by state. With my dependent variable being rate of homeless per 10,000 persons by state, the main independent variable I will be analyzing is mental healthcare expenditures per mentally ill patient. When speaking with non-profits in the Capital Region, Such as Cares Inc., I have found that many local homelessness organizations identify mental illness as a root cause of homelessness; and while I will be including rate of mental illness as a control variable in my regression, I am curious to find out how state spending on mental healthcare affects the rate of homelessness within each state. I hypothesize that greater state mental healthcare spending per mentally ill person will decrease the rate of homelessness within a state. Moreover, the independent control variables I will be analyzing include the following: Rate of Mental Illness, Veteran Percentage, Unemployment Rate, State and Local Welfare Spending per capita, Average Rental Costs, and Federal Rental Assistance per capita. I suspect that I will have multicollinearity between State and Local Welfare and Federal Rental Assistance, so I will run two separate regressions, one including Federal Rental Assistance as a control, and one including State and Local Welfare Spending.

Vyskocil 3 II. Equation and Variables The equations for the regressions that will be run are as follows: HOME=β1+β2MentEx+β3MentRa+β4 Vet+β5Rent+β6UnEm+β7FedRent HOME=β1+β2MentEx+β3MentRa+β4 Vet+β5Rent+β6UnEm+β7Welfare Ho: β2<0 Variable Name Variable Description Data Source Anticipated Slope HOME MentEx MentRa Dependent Variable Data is measured as a rate by state as number of homeless per 10,000 persons (January 2014) State Mental Health Agency Mental Health Services Expenditures in millions of dollars/number of mentally ill adults per state (2013) Percentage of Adults with any kind of Mental Illness (2015 report based on data collected in 2012) http://ww w.endhomel essness.org /page/- /files/state_ of_homeles sness_2015_ FINAL_onlin e.pdf http://kff.org /other/stateindicator/sm haexpenditures / http://www. mentalhealth america.net/ sites/default/ files/parity% 20or%20Dis parity%2020 15%20Repor t.pdf Statistical Significant N/A N/A N/A Practical Significance Negative Significant Medium Positive Significant Medium

Vyskocil 4 Variable Name Variable Description Data Source Anticipated Slope Veteran Rent UnEm Welfare FedRent Veteran Population as a percentage of entire state population (2014) Average rental cost of a 2 Bedroom Rental Unit at the Fair Market Rate (2014) Rate of unemployment (2014) Combined State and Local Welfare Spending/State population (2014) Federal Rental Assistance measured is total dollars spent for each state/total population of each state (2014) http://www. va.gov/vetda ta/veteran_p opulation.as p https://www. health.ny.go v/diseases/ai ds/ending_th e_epidemic/ docs/key_res ources/housi ng_and_sup portive_servi ces/out_of_r each_2014.p df http://www. bls.gov/lau/l astrk14.htm http://www. usgovernme ntdebt.us/co mpare_state _spending_2 015b40a http://www.c bpp.org/rese arch/housing /nationaland-statehousingdata-factsheets?fa=vi ew&id=3586 #map Statistical Significant Positive Significant High Positive Significant High Positive Positive Not Significant Not Significant Practical Significance Low Low Negative Significant Low

Vyskocil 5 III. Initial Regressions Regression with State and Local Welfare Spending as a Control: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.734 a.539.477 12.1360493952 54902 a. Predictors: (Constant), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), 2 BR FMR Average Rental Cost (2014), State and Local Spending per Capita (2014) Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -81.134 28.855-2.812.007 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012) -.001.004 -.036 -.267.790 3.078 1.259.284 2.446.019 Rate of Veterans (2014) -.598 1.579 -.047 -.379.707 2 BR FMR Average Rental Cost (2014) State and Local Spending per Capita (2014).032.010.446 3.040.004.021.008.412 2.449.018 Unemployment Rate (2014).449 1.424.034.315.754 a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil 6 Regression with Federal Rental Assistance as a Control: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.828 a.685.642 10.03885 a. Predictors: (Constant), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), Mental Health Expenditures (in millions), Federal Rental Assistance Per Capita (2014), Rate of Veterans (2014), 2 BR FMR Average Rental Cost (2014) Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -54.144 24.296-2.228.031 Mental Health Expenditures (in millions) Rate of Mental Illness (2015 report based on data from 2011-2012).000.002 -.017 -.154.879 1.712 1.068.158 1.603.116 Rate of Veterans (2014) 1.080 1.538.084.702.486 2 BR FMR Average Rental Cost (2014) Federal Rental Assistance Per Capita (2014).024.009.330 2.626.012.123.024.669 5.118.000 Unemployment Rate (2014) -.647 1.237 -.049 -.523.604 a. Dependent Variable: Estimated Homeless per 10,000 (2014) After running these initial regressions, many of the signs in each of the two runs did not match my hypothesized predictions. Additionally, many of the independent variables that I predicted to be statistically significant were not, including mental health expenditures, which was the main independent variable I

Vyskocil 7 am analyzing. Rather than accepting the data and results as truth and concluding my initial hypothesis was incorrect, I decided to look more closely at the data. The first thing I discovered was that the District of Colombia, which was included in my initial regression, is a significant outlier that needs to be removed from the group of observations. I came to this conclusion after looking at the two scatter plots which are displayed below; Washington DC has a homelessness rate which is significantly greater than every other state observation. Additionally, Washington DC receives much more Federal Rental Assistance and State/Local Welfare spending per capita. For these reasons, Washington DC was skewing the data to make the slopes of each of these two control variables positive. If, in reality, these slopes were positive, this would signify that increased federal rental assistance and state/local spending per capita actually increases the rate of homelessness within a state.

Vyskocil 8 Additionally, I realized that the significant T values for mental health expenditures in each of the two regressions were much closer to one than I initially suspected. This led me to believe that state mental healthcare expenditures have no effect on the rate of homelessness within a state. Being that I am looking to prove that mental illness is in fact a root cause of homelessness and that states should spend more money on mental health care, I found another variable that I decided to include in my regression. The name of this variable is TreatedMI, and it is described as the percentage of adults with a mental illness within each state that received some sort of treatment over the past calendar year (Mental Health America 2015). In looking at this new variable, I hypothesize that an increased percentage of adults who receive treatment for their mental illness will in fact decrease the rate of homelessness within a State. IV. Second Regressions The equations for the new regressions that will be run without including Washing DC as an observation are as follows: HOME=β1+β2MentEx+β3MentRa+β4 Vet+β5Rent+β6UnEm+β7FedRent+ β8treatedmi HOME=β1+β2MentEx+β3MentRa+β4 Vet+β5Rent+β6UnEm+β7Welfare+ β8treatedmi Ho: β2<0 and β8<0

Vyskocil 9 Regression with State and Local Welfare Spending as a Control: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.727 a.528.449 6.66848137092 5258 Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -15.678 18.738 -.837.408 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012).000.002.030.218.828 1.266.725.220 1.746.088 Rate of Veterans (2014).904.881.126 1.027.310 2 BR FMR Average Rental Cost (2014) State and Local Spending per Capita (2014).023.006.566 3.605.001.007.005.229 1.328.191 Unemployment Rate (2014) -.797.838 -.111 -.951.347 TreatedMI -.470.198 -.310-2.374.022 a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil 10 Regression with Federal Rental Assistance as a Control: Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.721 a.520.440 6.72647414831 7498 a. Predictors: (Constant), Federal Rental Assistance Per Capita (2014), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Mental Illness (2015 report based on data from 2011-2012), Unemployment Rate (2014), Rate of Veterans (2014), 2 BR FMR Average Rental Cost (2014) Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -11.619 19.626 -.592.557 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012).002.002.108.879.384 1.162.730.202 1.592.119 Rate of Veterans (2014).957.927.133 1.032.308 2 BR FMR Average Rental Cost (2014).023.007.572 3.409.001 Unemployment Rate (2014) -.976.912 -.136-1.070.291 TreatedMI -.484.216 -.319-2.236.031 Federal Rental Assistance Per Capita (2014).028.028.170 1.007.320 a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil 11 After running each of these two regressions, I decided to focus on the regression that includes Federal Rental Assistance per capita as a control variable, rather than the regression that includes state and local welfare spending per capita. First of all, I believe that this independent variable is a better control for the main independent variable I am analyzing because federal rental assistance is provided to families and individuals that cannot afford to pay their current monthly rent. For this reason, one would expect the amount of assistance per capita to have an effect on the number of homeless persons in a state, as such assistance is meant to keep families and individuals off of the streets and in reasonable rental units. Moreover, while both the federal rental assistance and state/local spending per capita turned out to be statistically insignificant (both having p values well over.05,) the regression with federal rental assistance as a control had a greater statistical significance of my main X. For these reasons, I have decided to focus on the second of these two regressions when providing my analysis. V. Analysis The R Squared value of this regression is.520. This means that the independent variables in this regression explain 52% of the variation in the rate of homelessness among each of the states. Moreover, the only independent variables that are statistically significant in this regression are average monthly rental cost and percentage of adults with a mental illness who receive treatment; Mental Health

Vyskocil 12 Expenditures, Rate of Mental Illness, Rate of Veterans, Federal Rental Assistance, and Unemployment were all found to be statistically insignificant. Average Monthly rental costs has a p value of.001, and has a β5 value of 0.023. This means that for every dollar increase in a states average monthly rental cost, the number of homeless persons per 10,000 people will increase by.023. This essentially means that an increase of $44 in rental cost will result in the rate of homelessness in a state increasing by 1 person, making the variable practically significant. In regards to the other significant independent variable, the percentage of adults with a mental illness who receive treatment, the p value is within the range of statistical significance at.031. The sign of this variable s coefficient is negative, signifying that there exists a negative relationship between the percentage of adults who have a mental illness who receive treatment and the rate of homelessness within a state. The coefficient is -0.484, which tells us that for every one percentage increase in the percentage of mentally ill adults who receive treatment, the number of homeless person per 10,000 people will decrease by.484. I believe that this statistically is practically significant as well, because it shows the importance of treating mental illness. Unlike my main independent variable, which measures how much money a state spends on mental healthcare costs per mentally ill person, this independent variable merely measures what percentage of mentally ill persons actually receive treatment for their conditions.

VI. Tests of Assumptions: Heteroscedasticity Vyskocil 13 Initially, I ran a visual test for Heteroscedasticity by squaring the unstandardized residuals from my regression and then graphing these values in a scatter plot against each of my independent variables. Heteroscedasticity exists when an independent variable affects the spread of your residuals; essentially meaning that as the value of an independent variable changes, certain value ranges of the independent variable have a smaller spread of residuals while others have a larger spread. Of all of my visual tests, the above scatter plot was the only test that

Vyskocil 14 seemed to visually exhibit heteroscedasticity. This plot displays the relationship between the Average Rental Cost control variable and the size of the residual squared. To look further into this possible issue, I then ran the Glejser Test which uses the absolute value of the residuals and measures the causal effect of each variable on this value. In other words, the absolute value of the residuals become the dependent variable in the regression and the dependent variables remain the same. The results of the test can be seen below. As I initially suspected, Average Rental Costs is the only variable that is statistically significant, and it seems to explain 29 percent of the variation in the residuals. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.543 a.294.177 3.74512 a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), 2 BR FMR Average Rental Cost (2014), Federal Rental Assistance Per Capita (2014)

Vyskocil 15 Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -7.663 10.927 -.701.487 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012).000.001 -.071 -.479.635 -.081.406 -.031 -.200.843 Rate of Veterans (2014).255.516.077.494.624 2 BR FMR Average Rental Cost (2014) Federal Rental Assistance Per Capita (2014).009.004.474 2.330.025.011.015.152.741.463 Unemployment Rate (2014).252.508.076.497.622 TreatedMI.043.120.061.354.725 a. Dependent Variable: RESABSS I then used a different equation of the Glejser Test to ensure that the Average Rental Costs does in fact exhibit heteroscedasticity; rather than running a regression with my original dependent variables, I calculated the square root of each dependent variable and ran a regression to analyze the effect of these new values on the residual. The results are seen below. The average rental cost variable does again seem to exhibit heteroscedasticity, as the R square value is.294, and the variable has a significant T value of.022.

Vyskocil 16 Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.542 a.294.196 3.70166 a. Predictors: (Constant), TreatedMISQR, FEDRENTSQR, MentExSqR, RateMISQR, VETSQR, RENTSQR Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -17.217 19.893 -.865.392 MentExSqR -.022.068 -.048 -.319.752 RateMISQR -.349 3.466 -.015 -.101.920 VETSQR 11.600 26.343.067.440.662 RENTSQR.556.234.476 2.375.022 FEDRENTSQR.278.315.160.882.382 TreatedMISQR.229 1.360.026.168.867 a. Dependent Variable: RESABSS VII. Correcting for Heteroscedasticity It is important to try and correct for heteroscedasticity because this condition may negatively affect the R square values and statistical significance of variables in the regression. In order to correct for this failed assumption, I attempted to transform the data by dividing each variable by the value of the variable that was causing heteroscedasticity (Average Rental Costs). After doing this I re-ran my regression using these new values, and the results may be seen below.

Vyskocil 17 Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1.393 a.154.013.00668 a. Predictors: (Constant), Rent2, MentEx2, FedRent2, UnEm2, Vet2, TreatedMI2, MentRa2 b. Dependent Variable: HOME2 Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant).025.006 3.892.000 MentEx2.002.002.152.989.328 MentRa2.702.625.586 1.124.267 Vet2 1.160.855.448 1.356.182 FedRent2.008.024.056.335.739 UnEm2 -.661.731 -.188 -.904.371 TreatedMI2 -.264.182 -.521-1.456.153 Rent2-15.472 14.940 -.561-1.036.306 a. Dependent Variable: HOME2 We must then re-run our tests for heteroscedasticity in order to determine if we did in fact correct for the issue that was affecting our data. In order to do this, I re-ran the Glejser Test using the new absolute values of the regression run with the transformed data. The results of the test may be seen below.

Vyskocil 18 Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1.451 a.203.070.0038627 a. Predictors: (Constant), Rent2, MentEx2, FedRent2, UnEm2, Vet2, TreatedMI2, MentRa2 b. Dependent Variable: RESABS2 Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant).013.004 3.363.002 MentEx2.000.001 -.038 -.254.801 MentRa2 -.093.361 -.131 -.259.797 Vet2.377.494.244.762.450 FedRent2.008.014.093.571.571 UnEm2 -.044.422 -.021 -.105.917 TreatedMI2 -.040.105 -.132 -.381.705 Rent2-6.376 8.633 -.388 -.739.464 a. Dependent Variable: RESABS2 After running this test, it appears that heteroscedasticity is still affecting the transformed data. This is because once we multiply the initial problematic variable (Average Rental Costs) back through the entire equation, the beta and significance values for the constant become the values that signify slope and statistical significance for the original problematic variable (Average Rental Costs). This being the case, the significant T value for this independent variable is.002 meaning that it is still statistically significant in explaining the variation in the residuals. From here, it starts to become clear that heteroscedasticity in this case may not be correctable;

Vyskocil 19 we may therefore have to accept the low level of heteroscedasticity present in our initial regression. As can be seen below, the Renal Cost variable only accounts for 26.5% of the variation in the residual; while this is not an ideal situation, I do not believe that this case of heteroscedasticity is severe enough to discard the results of the regression and remove the variable from our equation. Model Summary b Model R R Square Adjusted R Square Std. Error of the Estimate 1.515 a.265.250 3.57586 a. Predictors: (Constant), 2 BR FMR Average Rental Cost (2014) b. Dependent Variable: RESABSS Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -3.863 2.101-1.839.072 2 BR FMR Average Rental Cost (2014).010.002.515 4.159.000 a. Dependent Variable: RESABSS

Vyskocil 20 VIII. Tests of Assumptions: Multicollinearity Correlations Mental Estimated Health 2 BR FMR Federal Homeless Expenditures Rate of Average Rental Unempl Treated per per Mentally Mental Rate of Rental Assistance oyment Mentally 10,000 ill Illness Veterans Cost Per Capita Rate Ill Pearson Correlation Estimated Homeless per 10,000 Mental Health Expenditures per Mentally ill 1.000.289 -.142 -.091.648.337.078 -.350.289 1.000 -.259 -.014.391.304.033.112 Rate of Mental Illness -.142 -.259 1.000.353 -.462 -.269.014.159 Rate of Veterans -.091 -.014.353 1.000 -.331 -.444 -.171.165 2 BR FMR Average Rental Cost Federal Rental Assistance Per Capita.648.391 -.462 -.331 1.000.575.134 -.288.337.304 -.269 -.444.575 1.000.290.134 Unemployment Rate.078.033.014 -.171.134.290 1.000 -.327 TreatedMI -.350.112.159.165 -.288.134 -.327 1.000 After running different tests on my data, some of my variables do seem to exhibit signs of being multicollinear, meaning that some of my variables move together in a straight line relationship. The easiest way to identify multicollinearity is to create a Pearson Correlation table on SPSS while running a regression. By doing this, one is able to identify the correlation relationship between each set of variables. The values in the table range from 0-1, with 0 signifying that absolutely no multicollinearity is present, and 1 signifying that the variables move together exactly. In class, we identified any variable with a Pearson Correlation value greater

Vyskocil 21 than.3 as at risk of exhibiting multicollinearity. All of the relationships between variables that fall above this.3 threshold are highlighted above. Of the 21 variable relationships that could exhibit multicollinearity, 8 of the correlation values fall within this threshold, but non fall above the value of.6 which would indicate that there is strong multicollinearity which is skewing my data. The existence of multicollinearity in my regression will not affect my R square value, which was.520, but it may very well affect the significance values (t stat and significant t value); it is therefore important that we transform our data in order to correct for multicollinearity in the data. IX. Correcting for Multicollinearity After analyzing the different cases of multicollinearity that my variables exhibit, I concluded that to transform the data, I would have to completely change the scope of my variables; I believe that this would do more harm to the story than good, so I chose to not transform any variables. Rather than this approach, I began to pull different variables from my regression to see what results different combinations of variables yielded. First off, I removed the Federal Rental Assistance variable from my regression; the results are seen below. In doing so, my R square remained high at.508 and the same two variables, percent treatment of mental illness and average rental costs, remained statistically significant. The only difference between my last regression and this one is that the significance of the rate of mental illness independent variable increased significantly (p value of.111), but it did not increase enough to consider the variable statistically significant.

Vyskocil 22 Additionally, almost all multicollinearity was removed from my regression. The only variable that continues to consistently display multicollinearity is the average rental cost variable, as it seems to be collinear with Mental Health Expenditures, Rate of Mental Illness, and the Rate of Veterans. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.713 a.508.440 6.727503856277718 a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), 2 BR FMR Average Rental Cost (2014) Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) -17.039 18.875 -.903.372 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012).002.002.112.915.365 1.188.729.207 1.629.111 Rate of Veterans (2014).609.860.085.708.483 2 BR FMR Average Rental Cost (2014).027.006.669 4.866.000 Unemployment Rate (2014) -.600.832 -.083 -.721.475 TreatedMI -.371.185 -.244-2.005.051 a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil 23 Correlations Estimated Mental Health Rate of 2 BR FMR Homeless Expenditures Mental Rate of Average Unemploy Treated per 10,000 per Mentally ill Illness Veterans Rental Cost ment Rate MI Pearson Correlation Estimated Homeless per 10,000 Mental Health Expenditures per Mentally ill Rate of Mental Illness 1.000.289 -.142 -.091.648.078 -.350.289 1.000 -.259 -.014.391.033.112 -.142 -.259 1.000.353 -.462.014.159 Rate of Veterans -.091 -.014.353 1.000 -.331 -.171.165 2 BR FMR Average Rental Cost.648.391 -.462 -.331 1.000.134 -.288 Unemployment Rate.078.033.014 -.171.134 1.000 -.327 TreatedMI -.350.112.159.165 -.288 -.327 1.000 Next I decided to remove the Average Rental Cost variable from my regression to see how the results may be affected. Realistically, it is not ideal to remove two variables from my regression because it is important to have enough control variables to paint an accurate picture of how the main independent variable affects the dependent variable, but I was curious as to how this removal would affect my regression. The results are seen below. The R square value decreases to.237 and the p value of my main independent variable, mental health expenditures, decreases to.017, making the variable statistically significant; however the sign on this variable is positive, which is the opposite of my initial hypothesis. This result means that as for every $1 increase in mental healthcare expenditures per mentally ill

Vyskocil 24 patient, the number of homeless persons actually increases by.005 per every 10,000 people. This beta value is not, in my opinion, practically significant though because it would mean that the rate of homelessness in a state would only increase by 1 person for every 10,000 people as a result of every additional $200 spent on each individual mentally ill person. Also, multicollinearity is almost nonexistent in this regression, with only two Pearson Correlation values slightly above the of 0.3 target value. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.487 a.237.151 8.28161322218 2546 a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012) Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) 40.352 18.141 2.224.031 Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012).005.002.344 2.472.017.162.860.028.189.851 Rate of Veterans (2014) -.295 1.034 -.041 -.286.777 Unemployment Rate (2014) -.539 1.024 -.075 -.527.601 TreatedMI -.624.218 -.411-2.856.007 a. Dependent Variable: Estimated Homeless per 10,000 (2014)

Vyskocil 25 Correlations Estimated Mental Health Rate of Homeless Expenditures Mental Rate of Unemploym Treated per 10,000 per Mentally ill Illness Veterans ent Rate MI Pearson Correlation Estimated Homeless per 10,000 Mental Health Expenditures per Mentally ill 1.000.289 -.142 -.091.078 -.350.289 1.000 -.259 -.014.033.112 Rate of Mental Illness -.142 -.259 1.000.353.014.159 Rate of Veterans -.091 -.014.353 1.000 -.171.165 Unemployment Rate.078.033.014 -.171 1.000 -.327 TreatedMI -.350.112.159.165 -.327 1.000 Finally I decided to reintroduce the Federal Rental Assistance variable into my regression, while continuing to leave out the Average Rental Cost variable. The results are seen below. The R square of this regression is.387 and the only two variables that are statistically significant are the percentage of adults with a mental illness who receive treatment and the federal rental assistance per capita. My main independent variable is once again very close to being statistically significant,.083, but remains practically insignificant with a beta value of.003. The Federal Rental Assistance variable is statistically significant with a p value of.002, and has a beta values of.081. This means that for every $1 increase in Federal Rental Assistance per capita, the number of homeless persons per 10,000 people increases by.081. This value definitely has some sort of practical significance because it means that the number of homeless persons increase by one person for every $12.34 increase in Federal Rental Assistance per capita within a state. More importantly, the

Vyskocil 26 variable describing the percentage of adults with a mental illness who receive treatment is very statistically and practically significant. With a T statistic of 4.043, this variable is most definitely statistically significant within the regression; and with a beta value of -.848, we can conclude that for every percentage increase in the number of mentally ill adults who receive treatment, the number of homeless persons per 10,000 decreases by.848, which is nearly one person. Being that the mean of all of my observations is 18.03 homeless persons per 10,000 people, a decrease of nearly one person for every one percentage increase in treatment of adult mental illness is a very significant finding. Also, multicollinearity is not very prevalent in this regression, with only four Pearson Correlation values slightly above the cusp of 0.3. Model Summary Model R R Square Adjusted R Square Std. Error of the Estimate 1.622 a.387.301 7.51141552270 3936 a. Predictors: (Constant), Federal Rental Assistance Per Capita (2014), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Mental Illness (2015 report based on data from 2011-2012), Unemployment Rate (2014), Rate of Veterans (2014)

Vyskocil 27 Coefficients a Unstandardized Coefficients Standardized Coefficients Model B Std. Error Beta t Sig. 1 (Constant) 31.841 16.662 1.911.063 Mental Health Expenditures per Mentally ill.003.002.233 1.777.083 Rate of Mental Illness.522.787.091.663.511 Rate of Veterans 1.113 1.033.155 1.077.288 Unemployment Rate -1.672.993 -.232-1.684.099 TreatedMI -.848.210 -.560-4.043.000 Federal Rental Assistance Per Capita.081.025.501 3.238.002 a. Dependent Variable: Estimated Homeless per 10,000 (2014) Correlations Estimated Mental Health Rate of Unempl Federal Rental Homeless Expenditures Mental Rate of oyment Treated Assistance per 10,000 per Mentally ill Illness Veteran Rate MI Per Capita Pearson Correlation Estimated Homeless per 10,000 Mental Health Expenditures per Mentally ill 1.000.289 -.142 -.091.078 -.350.337.289 1.000 -.259 -.014.033.112.304 Rate of Mental Illness -.142 -.259 1.000.353.014.159 -.269 Rate of Veterans -.091 -.014.353 1.000 -.171.165 -.444 Unemployment Rate.078.033.014 -.171 1.000 -.327.290 TreatedMI -.350.112.159.165 -.327 1.000.134 Federal Rental Assistance Per Capita.337.304 -.269 -.444.290.134 1.000

Vyskocil 28 X. Tests of Assumptions: Autocorrelation Model Summary b Adjusted R Std. Error of the Model R R Square Square Estimate Durbin-Watson 1.721 a.520.440 6.72647414831 7500 2.167 a. Predictors: (Constant), TreatedMI, Mental Health Expenditures per Mentally ill (2013), Rate of Veterans (2014), Unemployment Rate (2014), Rate of Mental Illness (2015 report based on data from 2011-2012), 2 BR FMR Average Rental Cost (2014), Federal Rental Assistance Per Capita (2014) b. Dependent Variable: Estimated Homeless per 10,000 (2014) Normally Autocorrelation is not an issue for complex regressions run using cross-sectional data, but it is still necessary to test for this assumption to ensure that it is not affecting my data. To do so, I selected to calculate the Durbin-Watson statistic when I ran my initial regression on SPSS. As is displayed above, my Durbin- Watson value is 2.167. This value can range from 0-4, and the closer it is to two, the more sure we are that autocorrelation is not affecting the data. Initially, being that the statistic is 2.167, we can be fairly certain that the data does not exhibit autocorrelation, but to ensure that this is true, we must create a Durbin-Watson d statistic chart and plot our statistic within one of the ranges of this chart. To do this I used my number of observations and number of independent variables along with a Durbin-Watson critical value chart to find my dl and du statistics. After calculating these values and creating the chart below, it is clear that the data does not exhibit autocorrelation, as the Durbin-Watson statistic above, 2.167, falls in the middle region of the chart. This signifies that autocorrelation is not present.

Vyskocil 29 XI. Conclusions After analyzing the collected data using econometric techniques, a few different conclusions can be made. First and foremost, the data used for this report is definitely not the strongest data to analyze the effect of mental health expenditures on homelessness. The ideal means of analyzing my hypothesis would be to analyze homelessness data collected by fifty cities throughout the United States, but aggregating this sort of data was simply unrealistic considering the scope of and resources available for this report. Moreover, it may be concluded that the amount of money a state spends on mental healthcare per mentally ill patient does not explain any variation in the rate of homelessness within a state. That being said, it is very clear that the percentage of adults with a mental illness who actually receive treatment for their illness does significantly affect the rate of homelessness within a state. I believe that this speaks

Vyskocil 30 volumes about how we approach mental illness in the United States. While this report only deals with how mental illness affects homelessness, it is clear that policy solutions that deal with mental illness must be most focused on diagnosing and reaching all adults that have a mental illness. To do this, programs must be focused on educating the public regarding the importance of treatment, and must go beyond simply increasing funding to mental healthcare programs that are inefficient in terms of reaching a large portion of the population. Furthermore, although the variable was both heteroscedastic and collinear with multiple variables, it seems that Average Rental Costs play a large role in determining the rate of homelessness within a given state. Being that in every regression this variable had a significant T stat and accounted for a large part of the R square value, it may be concluded that the main cause of homelessness in the United States seems to be purely economic in nature. Being that this variable is practically significant, with homeless person per 10,000 people increasing by one person for every $44 increase in average rent, it becomes clear that a large part of what is causing people to be homeless in the United States is that they either lack a stream of income, or do not have a large enough stream of income to afford rental costs within their region of the nation. Homelessness is a very difficult topic to understand due to the many different perceived causes of homeless; but it is important that reports like these are done because although homelessness affects a very small percentage of the nation, it is a pressing public problem that needs to be addressed in many regions of the nation.

Vyskocil 31 XII. Appendix Estimated Homeless per 10,000 (2014) Mental Health Expenditures per Mentally ill (2013) Rate of Mental Illness (2015 report based on data from 2011-2012) Rate of Veterans (2014) 2 BR FMR Average Rental Cost (2014) Federal Rental Assistance Per Capita (2014) State and Local Spending per Capita (2014) Unemploy ment Rate (2014) Percentage of adults with any mental illness who received treatment (2015 report based on data from 2011-2012) ALABAMA 9.41 $501.43 19.32 8.53% $683.00 $111.15 $371.18 6.8 40.3 ALASKA 24.22 $2,500.52 18.94 9.96% $1,125.00 $95.01 $1,628.81 6.8 36.2 ARIZONA 15.59 $1,504.77 18.83 7.91% $911.00 $47.98 $415.96 6.9 37.6 ARKANSAS 9.90 $311.44 19.81 8.40% $653.00 $81.24 $471.96 6.1 46.2 CALIFORNIA 29.37 $1,234.28 17.68 4.77% $1,354.00 $130.58 $1,172.60 7.5 35.7 COLORADO 18.72 $744.79 18.12 7.72% $916.00 $79.91 $597.48 5 41.5 CONNECTICU 12.37 $1,701.75 16.71 5.93% $1,197.00 $206.30 $1,056.53 6.6 46.5 DELAWARE 9.63 $706.21 18.26 8.35% $1,044.00 $115.43 $748.17 5.7 47.8 DC 117.59 $1,994.24 19.44 4.53% $1,469.00 $632.88 $1,973.01 7.8 FLORIDA 20.88 $150.61 19.87 7.96% $1,008.00 $77.16 $417.23 6.3 35.4 GEORGIA 16.36 $433.18 18.99 7.46% $809.00 $96.46 $475.37 7.2 34.8 HAWAII 48.73 $998.88 17.48 8.52% $1,640.00 $138.78 $774.89 4.4 26.5 IDAHO 12.87 $224.26 20.58 8.10% $692.00 $52.00 $428.27 4.8 47.9 ILLINOIS 10.18 $610.83 15.86 5.60% $902.00 $150.54 $931.64 7.1 42.7 INDIANA 9.05 $482.98 19.87 7.22% $729.00 $77.16 $606.35 6 41.1 IOWA 10.05 $1,037.26 18.4 7.46% $689.00 $63.08 $514.95 4.4 44.3 KANSAS 9.58 $944.88 18.2 7.62% $746.00 $60.95 $516.53 4.5 49.9 KENTUCKY 11.53 $379.37 19.47 7.49% $660.00 $104.00 $589.11 6.5 45.6 LOUISIANA 9.91 $393.78 19.28 7.10% $804.00 $135.06 $516.16 6.4 35.9 MAINE 20.49 $2,182.25 20.05 9.57% $842.00 $165.40 $827.01 5.7 50.1 MARYLAND 13.15 $1,332.33 17.93 7.32% $1,297.00 $162.14 $937.02 5.8 43 MASSACHUSE 31.48 $826.20 17.38 5.63% $1,252.00 $278.86 $1,349.07 5.8 52.7 MICHIGAN 12.34 $867.18 19.81 6.64% $748.00 $83.55 $736.64 7.3 42.5 MINNESOTA 15.35 $1,392.69 17.18 6.76% $856.00 $94.55 $989.52 4.1 45.3 MISSISSIPPI 7.43 $378.98 20.27 7.36% $707.00 $119.90 $434.19 7.8 34.9 MISSOURI 12.01 $2,548.13 18.99 8.15% $744.00 $85.26 $412.30 6.1 44.8 MONTANA 17.05 $1,453.17 18.92 9.74% $705.00 $67.41 $683.87 4.7 46.1 NEBRASKA 16.08 $687.65 17.89 7.62% $701.00 $71.75 $744.09 3.3 51 NEVADA 37.18 $759.57 16.05 8.03% $1,001.00 $70.80 $634.00 7.8 30.9 NEW HAMPSH 10.37 $963.00 18.53 8.57% $1,049.00 $131.14 $753.69 4.3 49.8 NEW JERSEY 13.06 $1,891.25 14.66 4.79% $1,296.00 $170.06 $1,208.30 6.6 36.9 NEW MEXICO 13.17 $827.00 19.59 8.22% $774.00 $71.44 $527.43 6.5 43.9 NEW YORK 40.81 $1,833.20 18.61 4.52% $1,293.00 $274.74 $1,149.59 6.3 38.9 NORTH CARO 11.56 $779.54 16.84 7.79% $747.00 $79.65 $683.83 6.1 45.4 NORTH DAKO 17.01 $703.78 17.21 7.76% $738.00 $75.73 $676.15 2.8 38.7 OHIO 10.20 $678.43 19.64 7.47% $720.00 $122.65 $853.88 5.7 47.4 OKLAHOMA 10.81 $333.33 21.88 8.70% $689.00 $73.49 $489.94 4.5 41.5 OREGON 30.64 $1,156.89 20.89 8.35% $846.00 $90.67 $856.37 6.9 44.7 PENNSYLVAN 11.99 $2,077.34 17.99 7.34% $901.00 $120.28 $1,024.46 5.8 48 RHODE ISLAN 11.28 $721.62 18.8 6.82% $928.00 $274.84 $1,137.25 7.7 46.4 SOUTH CARO 10.46 $401.45 19.56 8.64% $756.00 $80.91 $393.17 6.4 46.8 SOUTH DAKO 10.37 $655.46 17.77 8.44% $680.00 $78.53 $586.05 3.4 47 TENNESSEE 14.38 $578.65 20.25 7.73% $729.00 $92.22 $534.40 6.7 43.4 TEXAS 10.57 $344.68 16.86 6.23% $872.00 $66.74 $385.80 5.1 36.1 UTAH 10.47 $476.11 22.35 5.16% $794.00 $42.14 $509.70 3.8 43.2 VERMONT 24.88 $1,902.08 19.39 7.76% $1,007.00 $159.60 $1,117.21 4.1 57.1 VIRGINIA 8.43 $709.32 17.5 9.38% $1,088.00 $92.84 $588.50 5.2 51.3 WASHINGTON 26.12 $732.31 20.77 8.55% $970.00 $99.84 $764.71 6.2 44.4 WEST VIRGINIA 10.88 $568.19 21.88 9.04% $665.00 $92.96 $540.45 6.5 47.7 WISCONSIN 10.52 $834.06 17.98 7.19% $767.00 $66.69 $851.05 5.5 41.3 WYOMING 12.96 $819.54 19.6 8.51% $768.00 $58.20 $513.56 4.3 40