Welfare Wednesday as an Environmental Cue

somewhat peculiar. 19 They find a positive correlation between welfare day and the AMA rate, but give no sense—either in levels as in Figure 2 or as a marginal effect— of the magnitude of their result. The day dummies indicate that AMAs are more likely to occur on the weekend. A hypothesis test on the equality of the six day dummies is rejected at the one percent level χ 2 = 46.9, and an equality test for the five weekday dummies can be rejected as well χ 2 = 13.1. However, as noted, the difference between the weekday dummies and the weekend there is no statistical difference between Saturday and Sunday is attributa- ble to the nature of hospital discharge planning. AMAs are evaluated relative to planned discharges, which fall on the weekend because of reduced staff and community-based clo- sures. AMAs do not respond in a similar way on the weekend since it is believed that the decision to leave AMA has very little to do with the hospital staff or community support. Ceteris paribus, the homeless are more likely to leave the hospital AMA, and the interaction term suggests that there is only a very small check effect for the homeless—as anticipated given that welfare receipt should be quite low for this group. 20 HIV positive IDUs are more likely to leave AMA. AMAs are more likely to occur in the last week of the month and the first week of the month the omitted cat- egory relative to the two middle weeks an equality test on the two middle weeks can- not be rejected; χ 2 = 0.07.

VII. Welfare Wednesday as an Environmental Cue

As a final test of the link between welfare payments and drug use, we investigate whether individuals induced to leave AMA by Welfare Wednesday are more likely to subsequently use drugs than IDUs who leave the hospital on a planned discharge. We implement this test by estimating the effect of leaving AMA on the likelihood of rapid readmission to the hospital readmission within 14 days and the likelihood of that readmission being due to a drug overdose using Welfare Wednesday as an instrument for leaving AMA. Specifically, we estimate: 3 READMISSION it +1 = f α + α 1 AMA it + α 3 Z it + υ it 4 OVERDOSE it +1 = f ζ + ζ 1 AMA it + ζ 3 Z it + η it where READMISSION equals one if the ith individual was admitted to the hospital on the t +1th admission within 14 days following the tth admission; OVERDOSE equals one if the ith individual was admitted to the hospital on the t+1th admission with a primary diagnosis of a drug overdose, AMA is as previously defined; Z are vectors of controls which include all information in Equation 2 except the Welfare Wednesday variable; υ and η are disturbance terms. 19. For instance, the AMA rate for non-IDUs in their sample is 1.3 percent—identical to the AMA rate for the hospital as a whole. 20. We also tested for welfare receipt by estimating Equation 2 for the nonhomeless and included an interac- tion term between welfare Wednesday and HIV status. HIV positive IDUs may be more likely to be on Disability I or II, which yield a much higher benefit rate see Section II. But, the results indicate that the AMA check effect is the same for HIV positive patients as for HIV negative patients. There may simply be insuffi- cient variation among the nonhomeless in welfare benefits; the results from our interviews support this conclu- sion recall 18 of the 22 patients on income assistance were receiving Disability I or II with only four on basic. Riddell and Riddell 153 Note that Equations 3 and 4 do not require “complete spells.” Individuals are defined as equaling zero for both dependent variables if they have not been readmitted to the hospital or with an overdose within 14 days of the admission of interest. That would therefore include individuals who were readmitted, for example, two months follow- ing the initial discharge as well as individuals who were never seen in the data again. As a robustness check for Equation 2, we estimate the readmission regression using alternative definitions of the dependent variable such as readmission within seven days and readmission within one month, and also by using a set of duration models. 21 Recall that many overdoses all fatal but also most nonfatal are unobserved to us; some individuals who leave AMA may overdose, but not be subsequently admitted to the hospital and thus do not appear in the data. Unlike the analysis in Section V, where it is difficult to be certain what the implications of unobserved overdoses are for the results, our estimates here will understate any check effect. We use Welfare Wednesday as an instrument for AMA. It is plausible to believe that the impact of leaving AMA on future outcomes such as drug use is not the same for everybody. In the presence of heterogeneous impacts, we cannot estimate the aver- age causal effect of leaving AMA for the IDU population. We can, however, estimate the Local Average Treatment Effect LATE of leaving AMA on subsequent readmis- sion and overdose outcomes, where the LATE refers to the subset of the population whose behavior was influenced by Welfare Wednesday Imbens and Angrist 1994; Heckman 1997. There are three conditions that must hold for a consistent LATE estimator: a Welfare Wednesday has a direct effect on leaving AMA, b leaving the hospital on a Wel- fare Wednesday only affects readmissionoverdoses through its effect on increasing the probability of leaving AMA, and c the monotonicity assumption Imbens and Angrist 1994. Figure 2 offers evidence in favor of the first condition. The second condition should be met given that the date on which you become ill that is, whether you are in the hospital around a Welfare Wednesday is an exogenous event. Alternatively stated, we believe there is no reason to expect a relationship between the day of the week that you leave the hospital on a planned discharge and subsequent health outcomes. It might be tempting to think that individuals leaving the hospital on a planned discharge on Welfare Wednesday are more likely to binge following welfare receipt. But, imagine two IDUs, both of whom receive social assistance—one who is properly discharged on the Monday preceding Welfare Wednesday, and one who is properly discharged on the Welfare Wednesday. Both individuals will receive their welfare payment on the Wednesday, both will be in the community following receipt, and both may be subject to cravings. We see no plausible reason to expect that the individual properly discharged on welfare day is any more or less likely to binge than the individual properly dis- charged on the Monday preceding welfare day. The third condition implies that Welfare Wednesday can only induce people to leave AMA who would not otherwise, and does not induce people to stay in the hospital until a planned discharge who otherwise would leave AMA—the latter of which seems highly unlikely. Table 4 presents the results. Beginning with the readmission regression, note the mean of the dependent variable: 11 percent of IDUs are readmitted to the hospital 21. In the hazard models, the spell of interest is an “out-of-hospital” spell time from the tth admission to the tth +1 admission. Overall, all results strongly point toward the same conclusion. The Journal of Human Resources 154 Riddell and Riddell 155 Table 4 Estimates of the Change in Probability of Readmission Overdose Readmission of Length of Stay Variable Readmission Readmission Same Diagnosis on Readmission Probit IV Probit Probit IV Probit Probit IV Probit OLS IV Left against medical advice 0.133 0.354 0.006 0.072 0.092 0.231 −0.979 8.51 0.013 0.101 0.002 0.016 0.010 0.050 0.603 2.31 Homeless 0.008 −0.020 −0.001 −0.006 0.004 −0.013 −1.69 −3.22 0.018 0.021 0.005 0.003 0.011 0.011 1.00 1.37 Female −0.014 — −0.005 −0.004 −0.004 −0.005 0.914 0.809 0.008 0.017 0.003 0.003 0.005 0.006 0.534 0.587 0.009 HIV positive 0.054 0.047 0.001 −0.002 0.015 0.015 0.822 0.486 0.010 0.011 0.002 0.002 0.005 0.007 0.621 0.648 Log likelihood −1515.1 −1582.3 −245.8 −239.7 −863.1 −931.4 — — χ 2 295.2 161.0 63.5 75.7 347.8 211.2 — — Adjusted R 2 — — — — — — 0.08 0.08 Number of observations 4,760 2,328 Notes: Huber-White standard errors are in parentheses. Statistical significance is denoted by for 1 percent level, for 5 percent level, and for 10 percent level. Instrumental variable regressions use Welfare Wednesday as an instrument for leaving the hospital against medical advice. The dependent variables are: “readmission” equals one if the patient was readmitted within two weeks from the admission of interest mean = 0.111, “overdose readmission” equals one the patient was readmitted with a prin- cipal diagnosis of a drug overdose following the admission of interest mean = 0.016, “same readmission” equals one if the patient was readmitted with the identical principal diagnosis as that of the admission of interest mean = 0.057, and “length of stay” is the number of days in the hospital on the admission following the admission of inter- est mean = 9.37. All regressions also include controls for age and its square, gender, primary diagnosis of illness, hospital ward treated on, length of stay in hospital and its square, three week-of-month, six day-of-the-week, 11 calendar-month, and four year dummies. All probit-based estimates are presented as marginal effects, and are evaluated at the mean of the relevant covariate. The source is a census of hospital admissions of injection drug-users admitted over fiscal years 1996 to 2000 at St. Paul’s Hospital in Vancouver. within two weeks 8 percent within one week and 16 percent within one month. The simple probit model indicates that leaving AMA increases the likelihood of readmis- sion within two weeks by 13 percentage points. 22 However, the IV estimate is much higher with an estimated impact of around 35 percentage points. 23 From the overdose regression, a similar story emerges. Based on the simple probit, leaving AMA implies just under a one percentage point increase in the likelihood of a subsequent overdose, which is understated given that there are likely individuals who leave AMA and subsequently overdose but are not admitted to the hospital. When we instrument for AMA, the LATE is seven percentage points. Overall, the LATE estimates suggest that those IDUs induced to leave AMA because of Welfare Wednesday are more likely to subsequently binge on drugs than IDUs leaving the hospital on a planned discharge. 24 It is possible that this result is picking up a type of income effect; specifically, it is the IDUs receiving welfare pay- ments who are induced to leave. However, we are confident that social assistance receipt is extremely high among this population. We believe the more convincing explanation is that Welfare Wednesday is an environmental cue for some IDUs. A seven percentage point increase in the probability of an overdose due to Welfare Wednesday strikes us as a troubling result—particularly if this finding can be extrap- olated to those individuals induced to leave AMA by Welfare Wednesday who over- dose fatally or overdose nonfatally but survive without admission to the hospital. However, an important question remains: what can be said about the remaining 28 35 − 7 = 28 percentage points of the Welfare Wednesday induced readmission effect? The fact that one in ten IDUs are readmitted to the hospital within two weeks almost two in ten within one month itself is striking, and illustrates the strain on the health care system that this population creates. The further finding that Welfare Wednesday may generate a situation where IDUs have a one in three chance of return- ing to the hospital within two weeks is, we believe, astounding. But to fully appreci- ate the implications of the results we need to know how much of the 28 percentage points is binging versus planned behavior unrelated to drug use such as paying rent. To address this issue, we offer the following evidence. First, we asked the Ministry of Human Resources about check theft—an area of concern in the United States. 25 About 1 percent of checks go missing, which includes both lost checks and stolen checks. Unfortunately, the Ministry was unable to provide us with the incidence of missing checks for IDUs or for Disability Level II recipients for example, which could be much higher. Thus, we can make no concrete conclusions about IDUs want- ing to pick up their checks for fear of theft, although the incidence of theft appears much lower than in the United States. 22. The estimate using a one week definition is 11 percentage points. The result that patients who leave AMA are readmitted sooner than planned discharge cases has been shown previously in both Canada and the United States. Anis et al. 2002 estimate the latter relationship and find a positive correlation, but do not tie readmission or any other outcome such as drug overdose for that matter to Welfare Wednesday. 23. The results are very similar if we use a linear probability model. For the linear IV case, the F-stat from the first stage is 19.03. 24. There is no statistically significant difference in the mean overdose rate between patients discharged properly on Welfare Wednesday relative to patients discharged properly on Nonwelfare Wednesdays. 25. According to Social Security Online see www.ssa.gov, check theft has doubled in the last 10 ten years in the United States. The Journal of Human Resources 156 We also have some evidence on the incidence of direct deposit. While the Ministry told us that, overall, direct deposit is very common in British Columbia, based on our experience with this population, and our interview-based study none on direct deposit the use of direct deposit is rare among IDUs. In fact, many do not have bank accounts. It may therefore be the case that individuals leave the hospital to cash their check, pay bills, and then return thereafter without using drugs. On the other hand, due to variation in when Welfare Wednesday falls within the month, our results con- trol for general end-of-the-month effects such as paying rent. The findings also indi- cated that individuals were no more likely to leave AMA in the last week of the month relative to the first week of the month. Moreover, in our interview-based study, 16 of the 22 IDUs on income assistance had the housing component of their check mailed directly to their hotel, an option offered by the Ministry. One final complexity is that B.C. law has a provision where the support component of an individual’s income assistance payment can be reduced by time spent in the hos- pital. The Ministry appears to rely entirely on patients themselves informing the Ministry of a hospital stay. As far as we can tell, there is no enforcement mechanism. In particular, because there is no information-sharing agreement between hospitals and the Ministry of Human Resources, hospital staff are not permitted to notify welfare workers that a patient is in the hospital without that patient’s consent. Nevertheless, if the threat is viewed as credible, this could be an additional reason for the AMA check effect. As a final piece of evidence, we conduct two more analyses. First, we estimate the same regression as in the above cases of Equations 3 and 4, but with a dependent vari- able that is defined as equaling one if the individual is readmitted to the hospital with the identical principal diagnosis as they had on the initial visit. 26 If planned behavior unrelated to drug use is driving the results, we should see patients readmitted with the same medical condition. The third column of Table 4 presents the results. We see that 23 of the remaining 28 percentage point effect is driven by individuals being re- admitted with the identical principal diagnosis. But these results can only be taken so far. For some medical conditions—such as pneumonia, endocarditis heart valve infection, osteomyelitis bone infection, and septicemia blood infection, among others—the illness is so serious that the individual’s behavior outside the hospital is largely irrelevant: They will be back in the hospital with the same condition regard- less of their drug use or lack thereof. To further pursue the above results, we examine length of a stay in the hospital, a common proxy in the medical literature for the severity of an illness. In particular, we ask whether individuals induced to leave AMA by Welfare Wednesday have longer lengths of stay on their next admission. For this analysis, we condition on being re- admitted that is, only uses the 941 individuals for whom we have longitudinal infor- mation, which amounts to 2,328 admission observations. The final column of Table 4 presents the results. From OLS estimation, we see a negative correlation between leaving AMA and the length of your next hospital stay— not a surprising result given that patients who leave AMA are, in general, completing 26. For this analysis, we use the full ICD codes up to the five-digit level as opposed to the broad categories defined in Table 1 or more aggregated ICD coding, and thus the dependent variable only equals one if the principal diagnosis is truly identical. Riddell and Riddell 157 treatment relating to their prior admission. The IV regression, however, yields very different results. Patients induced to leave AMA by Welfare Wednesday have rela- tively longer hospital stays—by around eight days, a very large effect relative to the mean of around nine days. This suggests that such individuals are engaging in behav- ior that negatively affects their health status. Drug use, and particularly heavy drug use, is a prime candidate. For instance, many IDUs have a central-venous catheter an intravenous line leading to the heart in place for antibiotics. Individuals leaving the hospital AMA would still have the central-venous catheter in place, and would likely use this line if they were to inject drugs, thereby exposing themselves to complica- tions such as further infection or an air embolism air in the blood stream, which can be fatal. 27 Overall, we do not have sufficient evidence to conclude whether any of the remaining 28 percentage points is of drug-related policy concern or is purely a check administration issue, but the length of stay findings suggest the former. 28 It should be emphasized that even if all of the 28 percentage points is planned behav- ior unrelated to drug consumption, attention from policy-makers is still required. Many of the patients involved have a severe medical condition, and thus even a few days out of the hospital can be highly problematic or fatal. Moreover, there is a pub- lic cost, given that the AMA will likely cause a setback in the patient’s recovery leading to a longer overall stay in hospital than would have otherwise occurred. As well, the 26 percent AMA rate is a constant source of frustration and morale prob- lems among hospital staff.

VIII. Summary and Policy Discussion