First-Stage Estimation

Although the endogeneity-corrected estimates differ from the exogenous ones, they are no more likely to be correct if the probability of MUD is not appropriately estimated in the first stage. To address this concern I survey the general predictions of the first stage before turning to examine the validity of the instrumental variables. Tables 21 and 22 show the first-stage estimation results for females and males, respectively.

Asian males are less likely than whites to suffer from MUD, while black females are more likely. Among both males and females age is negatively correlated with the probability of having MUD, while individuals who are not currently married or never have been married are significantly more likely to have MUD. Living outside of a core-based statistical area (i.e., rural residence) is also negatively correlated with MUD among both genders. For males, college graduates and full time workers are significantly less

likely to have MUD. For females, having children is negatively associated with MUD.

However, among females education is uncorrelated with MUD, and income is

uncorrelated with MUD among both genders.³² The only control for financial resources that is significant among females is whether the respondent’s current household has a single phone line, an outcome that is positively correlated with MUD. Whether or not the respondent reports a disability is uncorrelated with MUD, which helps to alleviate

concerns of reverse-causality (i.e., that chronic poor health causes marijuana use that leads to MUD).

Table 21

First-Stage Probit Estimates of Marijuana Use Disorder for Females

Demographic Human Capital Other Substances Instrumental Variables

Slightly Disapprove -0.426^*** -0.434^*** -0.408^***

(0.079) (0.079) (0.086)

Strongly Disapprove -0.710^*** -0.716^*** -0.623^***

(0.117) (0.118) (0.121)

IV Significance 57.93^*** 58.24^*** 41.22^***

1st Stage {0.000} {0.000} {0.000}

IV Significance 2.67 1.940 1.890

2nd Stage {0.263} {0.379} {0.389}

Demographics

Black 0.134^* 0.120 0.282^***

(0.076) (0.077) (0.085)

Asian 0.034 0.068 0.272

(0.232) (0.231) (0.251)

32 Although it may seem odd that human capital is uncorrelated with MUD among females, these results are consistent with McGeary and French (2000) who find that education is uncorrelated with chronic drug use among both males and females, and that neither income nor employment status is correlated with chronic drug use among females. The negative correlation between employment and MUD among males is also consistent with McGeary and French (2000).

Table 21 (Cont.)

Demographic Human Capital Other Substances Demographics (cont.)

Table 21 (Cont.)

Demographic Human Capital Other Substances Human Capital (cont.)

Disable Collects SSI -0.008 0.059

(0.176) (0.186)

Income < $20,000 -0.012 -0.048

(0.103) (0.113)

Income $20–50,000 -0.048 -0.068

(0.107) (0.116)

Insurance 0.113 0.201^*

(0.109) (0.118)

Food Stamp 0.088 0.039

(0.074) (0.081)

Public Assistance 0.074 0.057

(0.071) (0.074)

Table 21 (Cont.)

Demographic Human Capital Other Substances

N 19,101

Notes. The dependent variable is a binary indicator for marijuana use disorder. All models control for year and quarter of interview. Omitted categories include white, age 50-64, married, no household members over 65, respondent lives in CBSA with population over 1 million, college education, did not work last week, family income $50,000-$75,000, and no phone lines in household. Omitted IV category refers to

“Neither agree nor disagree.” { } Indicates p-value for joint test of variable significance. 2nd-Stage Significance refers to the results of a heuristic test for excludability of the IVs from the 2nd stage, in which the IVs are included in an NLS regression of ER visits and tested for joint significance. Brackets contain

“true” number of observations represented by weighted estimates. Standard errors are in parentheses.

*p < 0.1 ^**p < 0.05 ^***p < 0.01.

Table 22

First-Stage Probit Estimates of Marijuana Use Disorder for Males

Demographic Human Capital Other Substances Instrumental Variables

Somewhat Disapprove -0.090 -0.092 -0.055

(0.108) (0.109) (0.109)

Strongly Disapprove -0.896^*** -0.887^*** -0.826^***

(0.106) (0.105) (0.105)

Table 22 (Cont.)

Demographic Human Capital Other Substances Demographics (cont.)

Table 22 (Cont.)

Demographic Human Capital Other Substances Human Capital (cont.)

Disable Collects SSI -0.039 -0.041

(0.139) (0.138)

Income < $20,000 -0.035 -0.008

(0.129) (0.138)

Income $20–50,000 -0.093 -0.090

(0.119) (0.127)

Insurance -0.082 -0.024

(0.109) (0.125)

Food Stamp 0.036 -0.022

(0.089) (0.092)

Public Assistance -0.057 -0.095

(0.105) (0.111)

Notes. The dependent variable is a binary indicator for marijuana use disorder. All models control for year and quarter of interview. Omitted categories include white, age 50–64, married, no household members over 65, respondent lives in CBSA with population over 1 Million, college education, did not work last week, family income $50,000-$75,000, and no phone lines in household. Omitted IV category refers to

“Neither agree nor disagree.” { } Indicates p-value for joint test of variable significance. 2nd-Stage Significance refers to the results of a heuristic test for excludability of the IVs from the 2nd stage, in which the IVs are included in an NLS regression of ER visits and tested for joint significance. Brackets contain

“true” number of observations represented by weighted estimates. Standard errors are in parentheses.

*p < 0.1 ^**p < 0.05 ^***p < 0.01.

All three other forms of substance use disorder are strongly and positively correlated with MUD, which is consistent with the positive omitted variables bias on βM

observed in the second stage. Given the large magnitude of these three coefficients relative to the other controls, it is likely that inclusion of the substance use disorder controls improves the accuracy of estimates of the linear index for MUD at the individual level, which should in turn improve the second stage estimates. This bolsters the case for the comprehensive substance use disorder specification being preferred to the human capital and demographic specifications.

Overall, the coefficients for the controls in the first stage do not seem problematic. However, consistency of the 2SNLS estimates requires that the

instrumental variables (IVs) are valid. Validity of the IVs requires both that they strongly correlated with the probability of MUD, conditional on all other control variables, and that conditional on all other control variables, they are uncorrelated with the error term for ER visits. Recall from section 4 that the single instrument (measured by two variables) is the respondent’s opinion of another adult trying marijuana once or twice.

Responses include “neither approve nor disapprove,” “somewhat disapprove,” and

“strongly disapprove.” Indicators for “somewhat” and “strong” disapproval are included in the first stage, with “neither approve nor disapprove” as the omitted category.

The first stage results suggest that the IVs are jointly significant among males and females. The chi-squared value for females is roughly 58 for both the demographic and human capital models, and diminishes to 41 in the substance use disorder specification.

For males the IVs have even more predictive power, with a chi-squared value of 71–72 in

the demographic and human capital specifications and 64 in the substance use disorder specification. These results suggest that the IVs are sufficiently strong.

The theoretical justification for exclusion of the IVs from the equation for ER visits rests on the assertion that conditional on all of the available controls it is reasonable to assume that one’s opinion of adults trying marijuana is independent of health or of other behavior that may lead to ER visits. Unfortunately, when the model is

just-identified, there is no formal empirical test that the instrumental variables are excludable from the equation for ER visits. One heuristic test used previously in the substance use literature is to include the instruments directly in an exogenous version of the second stage NLS model and test whether the IVs are jointly significant (see e.g., Kenkel &

Terza, 2001). Among females the IVs are jointly insignificant, with a p-value ranging from 0.26 to 0.39. However, among males the IVs are jointly significant in all three models. Interestingly, the IVs become more strongly correlated with ER visits after controls for human capital are added, and the controls for other forms of substance use disorder barely diminish this joint significance, such that the statistical case for

excludability is greatest in the least comprehensive model.

These results provide only circumstantial rather than direct evidence in favor of the instrument (for females) or against them (for males). However, the response of the IVs to the inclusion of additional controls among males suggests that the instrument is capturing statistical noise rather than any true underlying information about individual demand for ER visits. Moreover, the evidence suggests that the IVs are excludable among females, and the female estimates are broadly similar to those for males (with the

exception of βM in the final specification.) Therefore, I continue under the assumption that the IVs are valid. To provide more support for the 2SNLS estimates, I run several additional specifications. Results of these robustness checks are presented in the next section.