Separating the Productive and Measurement Effects of Substance Use on Skill

Separating the Productive and Measurement Effects of Substance Use on Skill Josh Kinsler, University of Georgia, jkinsler@uga.edu Ronni Pavan, University of Rochester, ronni.pavan@rochester.edu October 31, 2016 Project Description - INCOMPLETE 1 Introduction Annual marijuana use among twelfth graders in the US has increased by approximately 60% since the early 1990s. Additionally, the share of twelfth graders who perceive great risk in regular marijuana usage has dropped from 80% to less than 40% over the same time frame. Marijuana is not the only substance high schoolers abuse, with nearly 20% reporting the use of other illicit drugs over the past year and 40% consuming alcohol over the last thirty days. 1 These numbers are alarming, given the recent trend in marijuana decriminalization and the negative associations between substance use, cognition, mental health, and ultimately, student outcomes. 2 However, correlations between these measures and substance use do not necessarily inform us on the causal impact of drugs. Moreover, cross-sectional analyses can be quite misleading when the underlying processes are dynamic. For this project, we propose a new framework for estimating the effects of substance use on human capital formation of high school students. We focus on high school because this is a period of both significant investment in human capital and high drug use. 3 Our work builds on an extensive literature examining the impact of drug use on human capital. When considering human capital, it is natural to think about the cognitive and non-cognitive skills that an individual brings to the labor market. Indeed, much of the literature focuses on the impact that substance abuse has on labor market outcomes. With few exceptions, researchers surprisingly find either positive or negligible impacts of drug use on wages and employment. 4 However, as Register et al. 2001) notes, this literature treats education as exogenous when examining wage and employment outcomes. This is problematic since conditioning on an individual s education likely obscures the impact that drug use had on human capital formation at earlier stages. More importantly, if the goal is to understand the impact of drug use on human capital formation, it is critical to consider the direct impact of drug use on formal education since this is a time of significant investment. This is not a new insight, as a large and growing literature explores the impact of substance use on school dropout and attainment rates. Two of the earliest studies, Yamada et al. 1996) and Bray et al. 2000), find 1 All statistics are derived from survey data publicly provided by the Monitoring the Future study of American youth. The data can be found at http://www.monitoringthefuture.org/data/14data.html#2014data-drugs. 2 For example, data from the 2009 National Youth Risk Behavior Survey show a negative association between alcohol and other drug use and academic achievement after controlling for sex, race/ethnicity, and grade level. The full report can be found at http://www.cdc.gov/healthyyouth/health_and_academics/pdf/alcohol_other_drug.pdf 3 In the 1997 National Longitudinal Survey of Youth NLSY97), the fraction of individuals who used marijuana in the last year rises above 20% at age 16, but begins to decline after age 19. 4 See Kaestner 1991), Kaestner 1994), Gill and Michaels 1992), Register and Williams 1992), Buchmueller and Zuvekas 1998), French et al. 2001), DeSimone 2002), MacDonald and Pudney 2000), MacDonald and Pudney 2001), van Ours 2007). 1

that marijuana use reduces the likelihood of graduating high school. However, neither of these studies address the endogeneity of drug use. Register et al. 2001) and Chatterji 2006) examine the impact of illicit drug use on schooling attainment, instrumenting for drug use with state drug policies. Both papers find negative and significant impacts, but the instruments used for identification have been questioned due to their weak relationship with drug use. The study by van Ours and Williams 2009) relies on timing assumptions and the structure imposed by a bivariate duration model to identify a negative impact of marijuana on attainment rates, while McCaffrey et al. 2010) uses a propensity score matching approach to identify the impact of marijuana on drop out rates. Even if these final two papers were able to deal fully with endogeneity, it is difficult to understand the mechanism through which past drug use affects dropout and attainment. The channel most researchers have in mind is that drug use leads to poor performance, however other potential channels include incarceration or expulsion. We are aware of only one paper in the literature that explicitly studies the link between drug use and student performance. Pacula et al. 2003) finds a significant impact of marijuana use on standardized test scores using a fixed effects model. 5 This approach allows researchers to mitigate the spurious impact of unobserved individual ability, i.e., low performing students are more likely to consume drugs. Similar to the fixed effects approach, our method for identifying the impact of substance use on human capital utilizes panel data to capture the effect of unobserved heterogeneity. However, we do not restrict unobserved heterogeneity, or human capital, to be fixed over time and explicitly allow it to vary endogenously with past substance use. Furthermore, our method can simultaneously incorporate several cognitive measures, such as grades, failure rates, etc., allowing us to condense skill information across a large number of outcomes in a data driven manner. By incorporating instruments into a panel data model, we can also address concerns with contemporaneous endogeneity, allowing the movement between skills and drug use to be correlated over time even after controlling for the impact of past unobserved heterogeneity. Finally, we allow drug use to potentially influence our ability to measure human capital and illustrate under what conditions we can separately identify the effect of substance abuse on skill accumulation versus skill measurement. Substance use may have a direct effect on cognitive measures due to its impact on effort and motivation. However, we are primarily interested in understanding whether this impact is persistent over time, i.e., whether the use of drugs permanently reduces an individual s human capital. We argue in Section 3 that a standard fixed effect model primarily identifies the impact of drug use on our ability to measure human capital. Although the measurement channel is important, the persistent effect of drug use has potentially more serious implications for labor market outcomes and individual welfare. The key challenge in our approach is separately identifying the productive and measurement effects of drug use. We discuss the intuition for identification in a simplified version of our model. We provide two separate identification strategies, one which relies on the availability of instruments and one that does not. As noted earlier, researchers have questioned the strength of the instruments typically employed in the literature; thus, it is critical to have an approach that does not rely solely on these instruments. We then describe how we plan to generalize the proofs for the full specification. Our identification approaches suggests a generalized method of moments GMM) estimation procedure that will be utilized to recover the parameters of the production function of skills jointly with the temporary and persistent impacts of substance use. We use the 1997 National Longitudinal Survey of Youth NLSY97) to estimate our model, which has several advantages over the data used in prior literature. First, it includes complete high school transcripts for a large number of individuals, more than 6000 students, which can be linked with yearly observations on substance use. High school in the US typically lasts four years, making our panel longer than the data used in the past to analyze scholastic performance see for example Pacula et al. 2003), Engberg and Morral 2006)). Second, the NLSY97 transcript data is extraordinarily rich, containing not only information on whether the students progress on time, but also information on the number and types of classes that the students take each term, with their corresponding grades. Using a method similar to Cunha and Heckman 5 Engberg and Morral 2006) also uses a fixed effects approach to estimate the effect of marijuana on school attendance. 2

2008) and Cunha et al. 2010), we will be able to simultaneously use all of this information, condensing the scholastic variables into a single index that may be interpreted as the cognitive skills of the student while in school. Although the NLSY97 high school transcript data has been publicly available for several years, to our knowledge, it has not been used to study the impact of substance use on educational outcomes. Mezza and Buchinsky 2014) and Alford 2014) use the NLSY97 data to explore the impact of substance abuse on educational attainment and employment, but do not use the transcript data. Pacula et al. 2015) uses the NLSY97 to study how the consumption of cannabis is influenced by medical marijuana legislation, but does not explore impacts on educational outcomes. We supplement the the NLSY97 data with state level information on drug prices, sales taxes, and law enforcement policies. This data is collected from various sources and is explained in greater detail in Section 2. In order to link this information with the NLSY97 data, we will need to apply for and gain access to the NLSY97 geocode data. In the next section, we discuss the NLSY97 in more detail. In Section 3, we present the econometric model that we propose to use for our baseline analysis and discuss how we plan to identify and estimate the model. In Section 4, we discuss the time-line for the project and our short and long term goals. We also connect this project to our other scientific contributions. In Section 5, we outline the project s broader impacts. Finally, in Section 6, we review the results from our prior NSF support, the organization and management for this project, and how we will evaluate the success of this project. 2 The Model In this section, we present a model of skill acquisition and substance use. The model is designed to estimate the dynamic impact of substance use on human capital formation when substance use affects our ability to assess skills in the short term. This implies that in our model the long term impact of drug use on achievement can be potentially stronger or milder) than what the short term impact may imply. The model is similar in spirit to the ones presented in Cunha and Heckman 2008) and Cunha et al. 2010). We assume there exists a latent unobserved factor, human capital in our framework, that transitions over time according to a skill production function. Although we cannot observe human capital directly, we observe noisy measures of it each period. The key innovation of our model relative to Cunha and Heckman 2008) and Cunha et al. 2010) is to allow unobserved human capital to be correlated with other factors that enter both the skill production function and measurement system. As we document below, allowing for this type of correlation in the model threatens identification for even the most basic production functions. The potential for substance use to affect both skill production and skill measurement is understandable. Substance use can have permanent and lasting effects on an individual s cognition cite). Additionally, substance abuse can affect performance on exams or school attendance through its short term impacts on physical health. However, there are many other settings where observed or unobserved factors affects both skill transitions and skill measurements. Consider, for example, the setting in Cunha et al. 2010). Noncognitive skills play an important role in the production of cognitive skills. However, there is significant evidence that non-cognitive skills, such as persistence or reliability, can also impact test taking effort, particularly for low-stakes exams. Altering the measurement system in Cunha et al. 2010) to accommodate this impact of non-cognitive skill on cognitive skill measurement would undercut the identification argument. Note that this is true regardless of whether non-cognitive skill is observed. A goal of this paper is to show why identification fails in this setting and to provide potential solutions to the identification problem. In this paper, we focus on the simpler case where variables that affect skill measurement and are potentially correlated with the main unobservable captured by the test) are observed. We develop two versions of the model. In the first version, we assume the availability of instruments, i.e., variables correlated with the decision to use drugs but not with contemporaneous shocks to skills. Notice that our definition of what constitute an instrument is less strict than what usually used in the literature. We allow, for example, 3

this variable to be correlated with the unobserved skill of the agent and only require it to be uncorrelated with the contemporaneous evolution of this skill. Because the power of some of the instruments that we will use have been questioned in the literature, we also develop a simplified version of the model where we assume that no instrument is available. Accordingly, the second version of our model relies on stronger assumptions regarding the timing of events. While the proposed models will be used to estimate the impact of a vector of substances on cognitive skills, we discuss identification when the use of only one substance is included. The generalization of the proof is straightforward as long as there exists a valid instrument for each additional substance. The details are available in an online appendix. 2.1 The Baseline Model Let H t be a student s unobserved cognitive skills at time t, where t = {1,.., T }. Skills evolve over time and are affected by the consumption of substances D t. We assume that the law of motion of unobserved skills is: H t+1 = α 0t H t + α 1t D t + π t+1 1) where π t+1 is assumed to be independent of both H t and D t. If H t were observed, then we could estimate α 1t directly since we have assumed π t+1 and D t are independent. This approach would be similar to the valueadded models regularly used to evaluate school and family inputs in test score production. However, H t is not observed, complicating identification. Further complicating identification will be the contemporaneous relationship between D t and H t that we introduce below. Finally, our assumption that the production function is linear is a strong one. Yet, even for this basic model, identification is difficult to establish. 6 Although skills are unobserved, we have access to J imperfect skill measures M j t such that: M j t = H t + λ j 1t D t + u j t 2) where we assume that u j t is independent of H t across time and measures. λ j 1t captures the impact drug use has on our ability to measure skill directly. This effect is distinct from α 1t, which captures the impact that substance use has on an individual s ability to accumulate additional skill. In the more standard approach introduced by Cunha and Heckman 2008) and Cunha et al. 2010), λ j 1t is assumed to be zero. In other words, the measurement equations are not allowed to depend directly on any variables that are correlated with the evolution of the underlying latent variables. The final piece of the model is the equation that governs the use of substances: D t+1 = d 0t D t + d 1t H t+1 + d 2t Z t+1 + η t+1 3) where η t+1 is independent of all other variables. Z t+1 is a set of instruments that influence D t+1 but are independent of η t+1, π t+1 and u j t+1 for all t and j. Plausible candidates are drug prices, related state taxes and other types of state policies. These variables are discussed in detail in the data section. Note that we require Z t+1 to be independent of η t+1, π t+1 and u j t+1 but not necessarily of H t+1. Indeed, if Z t+1 is correlated across time, a likely occurrence since state policies change infrequently, we expect it to be correlated with H t+1. A cursory examination of Equation 1) would suggest that we do not allow for endogeneity in our model given that we assume that π t+1 is independent of both H t and D t. However, this is not the case, a fact that is evident if we re-write Equation 1) in terms of observables, ) M j t+1 = λ j 1t+1 D +1 t+1 + α 0t λ j M j t + +1 0t α 1t λj 1t D t + ɛ j t+1. 6 Equation 1) indicates that substance use at time t has an impact on skills at time t + 1. As we explain later, this model is isomorphic to a model with a contemporaneous effect of drugs. 4

The newly defined error term ɛ j t+1 is a function of π t+1, u j t and u j t+1 and is therefore correlated with both D t+1 and M j t. An alternative way to illustrate the endogeneity problem inherent in our model is to re-define human capital as H t = H t + α 1t D t. α 0t Re-writing Equations 1) and 2) in terms of H t we obtain: and H t+1 = α 0t Ht + α 1,t D t+1 + π t+1 M j t = H t + λ j 1t D t + u j t where α 1,t = α1,t+1 α 0,t+1 and λ j 1t = λj 1t λj 0t α1t α 0t. In this equivalent model, skills clearly affect contemporaneous substance use, and vice versa, inducing a simultaneity problem. This alternative setup also maintains the possibility that the permanent and measurement effects of substance use are different and is achieved without loss of generality. 7 We prefer our initial definition of human capital H t relative to H t because it describes directly the long run, or persistent, component of scholastic performance. The presence of Z t+1 in the decision to use drugs is critical to our first identification strategy. Recall that the innovation in our model is to allow D t to affect the measurement of H t. But because D t and H t are related according to equation 3), it is impossible to identify the impact of substance use on skill measurement λ j 1t ) without a source of exogenous variation in D t. Z t provides this necessary source of exogenous variation which then enables us to clean the measurement system of the impact of substance abuse. This ultimately brings us back to the identification setting of Cunha and Heckman 2008). Identification. In this section, we present a strategy for identifying the proposed model. We illustrate identification assuming D t is uni-dimensional, however, ultimately we will define D t as a four-dimensional vector that includes consumption of marijuana, cocaine, alcohol and cigarettes. As noted earlier, our identification strategy extends to this multivariate setting and can be seen in the online appendix. To see how to identify the uni-dimensional model, we first rewrite Equations 1) and 3) in terms of predetermined observables in order to avoid simultaneity biases: ) )) M j t+1 = λ j 1t+1 d 0t + +1 + λj 1t+1 d 1t α 1t α 0tλ j 1t D t + D t+1 = + +1 + λj 1t+1 d 1t d 0t + d 1t ) α0t α 1t α 0tλ j 1t M j t + λ j 1t+1 d 2tZ t+1 + v j m,t 4) )) D t + d 1tα 0t λ j M j t + d 2t Z t+1 + v j d,t 5) 0t ) ) where v j m,t = +1 + λj 1t+1 d 1t π t+1 + λ j 1t+1 η t+1 α0t λ j λ j 1t+1 d 1t + +1 u j t + u j t+1 and vj d,t = d 1tπ t+1 + 0t η t+1 d1tα0t u j λ t. OLS estimation of these regressions would lead to inconsistent estimates of the reduced j 0t form coefficients due to the bias induced by measurement error. 8 As an example, M j t will be correlated with 7 Notice that in this alternative set-up, we can still formulate a parallel with the standard approach. Assuming that λj 1t λ j = α 1t, α 0t 0t which implies λ j 1t = 0, results in a measurement equation that does not include any endogenous variable, as in Cunha and Heckman 2008). This restriction imposes a proportionality between the measurement impact λ j 1t and the long run impact α 1t of substance use. 8 Note that Equation 4) looks like a typical value-added test score model where the coefficient on drug use would be the parameter of interest. However, even if the coefficient on drug use were correctly identified, it does not provide direct information on the structural parameters of the model and is instead a combination of the temporary effect, the permanent effect, and other parameters. 5

v j m,t through u j t as specified in Equation 2). Nevertheless, we have assumed access to multiple measures of cognitive skills, indexed by j, and therefore can identify the coefficients using one measure as an instrument for another as, for example, in Cunha and Heckman 2008)). With the reduced form coefficients identified, the next step is to show how to map them to the structural parameters of the model. For simplicity we rewrite all the reduced form coefficients: M j t+1 = A j,t D t + B j,t M j t + C j,t Z t+1 + v j m,t 6) D t+1 = E j,t D t + F j,t M j t + G j,t Z t+1 + v j d,t such that A j,t = ) )) λ j 1t+1 d 0t + +1 + λj 1t+1 d 1t α 1t α 0tλ j 1t ) B j,t = +1 + λj 1t+1 d α0t 1t C j,t = λ j 1t+1 d 2t 7) )) d 0t + d 1t E j,t = α 1t α 0tλ j 1t F j,t = d 1tα 0t G j,t = d 2t The following step by step analysis describes how to identify the underlying structural parameters from the reduced form coefficients. 1. Normalize the scale of the unobserved variables by setting λ 1 0t = 1 for all time periods. This is without loss of generality. 2. Consider time t equations, which involve all parameters indexed by t and some indexed by t+1. Notice that G j,t and C j,t identify the parameters d 2t and λ j 1t+1. 3. The ratio F 1,t /F j,t identifies for all j and therefore d 1tα 0t. 4. Consider B j,t = λj 0t+1 α0t looking at j = 1 we can also identify λ1 0t+1 α0t λ 1 0t 5. The known at this stage) object + λj 1t+1 d1tα0t. The second term λj 1t+1 d1tα0t A j,t λ j 1t+1 Ej,t has already been identified so = α 0t. From d 1t α 0t we can also recover d 1t. = λ j 0t+1 λ j 1t+1 6. Using E j,t and the previous result we can obtain d 0t. α 1t α0tλj 1t ) identifies α 1t α0tλj 1t. 7. At this stage, we have identified d 0t, d 1t, d 2t, α 0t,, λj 0t+1 and λj 1t+1, plus the combination of parameters α 1t α0tλj 1t for all t < T. Notice that this means that we have identified λ j λ j 0T and λj 1T. 0t No other period T parameters are left to identify. 8. Consider any t > 1. From t = t 1, we have already recovered λ j 1t +1 = λj 1t and therefore we can use α 1t α0tλj 1t to recover α 1t. We have now identified all time t parameters, where t > 1. 9. Without further assumptions, we cannot separately identify all the λ j 11 and α 11. We can only identify their combination α 11 α01λj 11 λ j 01 or, written in a different way, λ 1 11 λj 11. λ j 01 6

10. Notice that the lack of identification of the first period parameters does not spill over to the other periods. It is therefore quite natural to propose a few alternative normalization to pin down these remaining parameters: a) A natural approach is to normalize the temporary impact for one measure, say λ 1 11. A relatively harmless normalization is to assume that λ 1 11 = λ 1 12 such that the temporary impact of drug use is the same in the first two periods for at least one meansure. b) A corollary of this normalization is that a model with time invariant parameters is fully identified. c) An alternative normalization is to set one λ j 11 equal to zero or equal to a different λj 11. d) A final strategy, not a normalization, is to specify more completely the initial conditions. We can define the initial condition D 1 = d 10 H 1 + d 20 Z 1 + η 1 and assume that Z 1 is uncorrelated with H 1. Estimation. Equations 4) and 5) provide the foundation for our estimation strategy. If we stack all periods, we can define M j = {M j T,..., M j 2 }, D = {D T,..., D 2 }, and Z = {Z T,..., Z 2 }. Using the lag operator L we can also define X j = {LD, LM j, Z} and W j = {LM 1,..., LM j 1, LM j+1,..., LM J, LD, Z}. Stacking all j, we can define X = {X 1,..., X J } and W = {W 1,..., W J }. Using these newly defined matrices and a similarly defined vector of unobservables) we can rewrite Equations 4) and 5) as: M = β M Ω)X + V m D = β D Ω)X + V D where Ω is the vector of structural parameters, and use the following orthogonality conditions to estimate the model using GMM: EM β M Ω)X) W ) = 0 ED β D Ω)X) W ) = 0. In the empirical analysis, we will examine the robustness of the results under different assumptions/normalizations. 2.2 Alternative Approach In a second version of the model, we explore the types of assumptions required to estimate the impact of substances on cognitive skills in the absence of instruments. To identify the model, we will need to impose stronger assumptions on the timing of events. In particular, we will replace Equation 3) with an equation in which drug use is a function of past period skills and not present period skills. This is a strong assumption that basically means any co-movement of drugs and skills must be caused by drugs. Note that this assumption is not very different from the one required for the estimation of fixed effect type models. In a fixed effect model, reverse causality is assumed to be driven by a time invariant unobservable. In this model, the endogeneity is driven by last period s unobserved skills. Formally, we assume that the drug use equation is: D t+1 = d 0t D t + d 1t H t + η t+1 3 ) Writing Equations 1) and 3 ) in terms of observables makes the identification strategy clear: ) M j t+1 = λj 0t+1 α 0t M j t + +1 α 1t α 0t λ j 1t D t + λ j 1t+1 D t+1+ ++1 π t+1 α 0t +1 uj t u j t+1 7

and D t+1 = d 0t d 1t λ j 1t ) D t + d 1t λ j M j t d 1t 0t λ j u j t + η t+1. 0t Again, we need to instrument M j t with a different measure in order to correct for the effect of measurement error. The mapping from the reduced form coefficients to the structural parameters is very similar to the steps described above, and even in this case we need to make an extra normalization on the λ 1 11 in order to identify all the first period parameters. Note that it is not possible to directly estimate the impact of substance use on school outcomes without controlling for past outcomes and past drug use. Moreover, controlling for these past variables still only allows for the direct identification of the temporary impact of drug use from the coefficient of D t+1. One approach in the literature see for example Bray et al. 2000) or Register et al. 2001)) is to estimate a regression using past drug use as an instrument for recent drug use. This would not necessarily identify a well defined parameter as both past and present drug use should be included in the specification. One interesting application of this model is to show precisely what fixed effect models would estimate in this context. While we have not yet worked out the details of this analysis, it seems reasonable to expect that regressions like those in Table 6 are likely to identify something close to λ j 1t+1. The fixed effect strategy identifies the impact of drug use on cognitive measures by looking at how skill measures change when substance use changes. This seems closely related to the temporary impact of drugs. As part of our project we plan to investigate this further both analytically and through simulations. The estimation of this version of the model will follow the same strategy as the previous version. Close with a discussion of FE and OLS approaches... 3 Data Our project will be based primarily on the National Longitudinal Survey of Youth 1997 NLSY97). The NLSY97 consists of a nationally representative sample of approximately 9,000 youths who were 12 to 16 years of age as of December 31, 1996. Young people continue to be interviewed on an annual basis. We gather information on demographic and family related variables, substance use, scholastic experience, and cognitive skills. We supplement the NLSY data with information on drug prices and policies at the state level. The model section will explain precisely how these exogenous variables will be used in estimation. In the following subsections, we provide a basic summary of the data and then present descriptive analysis of the correlations between cognitive measures and substance use. This descriptive analysis is of interest per se, since by using the panel dimension of the data we can shed new light on the impact of drug use. Many of the most compelling contributions to the substance abuse literature use similar fixed effect regressions to mitigate endogeneity bias. 9 However, our panel is both longer and reflects a more recent cohort of students. In all the following analyses, we include NLSY97 respondents with valid high school transcripts who attended high school since the last interview. Our sample consists of 6,196 individuals and 19,250 observations in total. The high school transcript data is merged with NLSY97 survey data using information on the actual high school term dates and survey dates. Demographics and family related variables. In our analysis, we use information on the gender, race, age of the students mother at birth, paternal and maternal education, and family income and assets in 1997). In Table 1 we report the summary statistics for this class of variables. The sample is evenly split between male and female respondents, and includes significant proportions of non-white students. The family background variables indicate significant variability in home environments associated with parental education and earnings. 9 See for example Kaestner 1994), Pacula et al. 2003), and Engberg and Morral 2006) 8

Table 1: Summary Statistics - Demographics Observations Means Std Deviations % Male 6,196 0.51 % White 6,196 0.54 % Black 6,196 0.25 Age Mother at 1st Birth 5,742 22.93 4.85 Father s Years of Schooling 5,253 12.87 4.20 Mother s Years of Schooling 5,885 12.70 3.74 Family Income in 1997 4,526 48,819 42,295 Family Assets in 1997 4,309 105,429 141,311 Data are from the NLSY97. Only individuals with at least one term of high school transcripts are included. Substance use. The NLSY97 collects information on the use of several substances. Although the goal of our project is to identify how consumption of illicit substances impacts cognitive skills, we also consider the effects of other substance use that is highly correlated with illicit drugs. Thus, we incorporate alcohol, tobacco, marijuana and cocaine into our analysis. Cocaine is catch-all category for other illicit substances that the survey does not distinguish between, e.g., crack, heroin, or amphetamines. 10 The survey asks respondents whether they used these substances since the last interview, and if so, how frequently they were used in the last month for cocaine it is the yearly frequency). It is important to note that approximately 0.5 % individuals refuse to respond to questions about drug use. While this could be interpreted as a signal of substance use, we take a conservative approach and treat these observations as missing. In Table 2, we report summary statistics for these variables. Among the substances considered, alcohol is the most prevalent, with 50% of respondents reporting positive consumption since the last interview. Close to one quarter of the respondents report using marijuana since the last interview, while only 6% report using cocaine or other illicit drugs. With the condition of having consumed some amount of the drug since last interview, marijuana actually appears to be a more intensely used substance relative to alcohol among high school students. Finally, respondents who report positive cocaine consumption use the drug approximately once per week. 11 10 The exact wording of the survey question is: Excluding marijuana and alcohol, since the date of last interview, have you used any drugs like cocaine or crack or heroin, or any other substance not prescribed by a doctor, in order to get high or to achieve an altered state?" 11 The average number of days between interviews is 382, or 54.5 weeks. 9

Table 2: Summary Statistics - Substance Use Observations Mean Std Deviation Since the last interview, the respondent has ingested Y=1/N=0): Tobacco 15,648 0.35 0.48 Alcohol 18,956 0.50 0.50 Marijuana 18,551 0.22 0.41 Cocaine 15,838 0.06 0.23 Days in the last month the respondent ingested: Tobacco 5,447 13.77 13.20 Alcohol 9,489 3.74 5.16 Marijuana 3,988 6.98 9.94 Times since the last interview the respondent ingested: Cocaine 895 54.05 117.36 Data are from the NLSY97. The sample consists of individuals with at least one term of high school transcripts who were enrolled in high school since the last interview. Use of one substance does not preclude the use of other substances. In fact, we expect that students who consume alcohol may be more likely to consume marijuana or cocaine. This assertion is supported by Table 3, which presents pairwise correlations in the use of these substances. All correlations are large and statistically significant. The strong relationship between the use of the various substances implies that it is not possible to investigate the impact of one substance on human capital formation in isolation. Moreover, if drug use and human capital formation are dynamic processes, a contemporaneous link between one substance and cognitive skills could actually reflect the long term influence of a different substance from prior periods. Table 3: Correlation in Substance Use Tobacco Alcohol Marijuana Cocaine Tobacco 1.00 Alcohol 0.43 1.00 Marijuana 0.45 0.40 1.00 Cocaine 0.24 0.20 0.37 1.00 Data are from the NLSY97. The sample consists of individuals with at least one term of high school transcripts who were enrolled in high school since the last interview. Scholastic experience and cognitive skills. The primary measures of cognitive skills are taken from respondents high school transcripts. In the spring of 2000, high school transcripts were collected for NLSY97 respondents born in 1980 and 1981 who provided written permission to contact their schools. A second phase of high school transcript collection began in 2004 and included respondents born between 1982 and 1984 who had provided written permission to contact their schools. The high schools, both public and private, were asked to provide the respondent s transcript, along with course descriptions and information about the school s grading scale. The collection of high school transcripts is available for approximately 6,200 students, or nearly 70% of the original cohort. We collapse the transcript data into yearly observations so that it is consistent with the rest of the NLSY97 data. We concentrate our analysis on students grade point average GPA), whether students have failed any classes, total credits accrued, and the fraction of these credits in advanced classes. Note that because credit 10

systems vary considerably across schools, we transform all credits into the equivalent Carnegie credit units to ensure that they are comparable across schools. One Carnegie credit is defined as the credits earned for a class that meets every day for one period for an entire school year. We also collect information on the Peabody Individual Achievement Test PIAT) test scores and suspensions, both of which come from the survey and not from the high school transcripts. The PIAT is one of the most widely used brief assessments of academic achievement with demonstrably high test-retest reliability and concurrent validity. 12 Table 4 shows the summary statistics for these skill measures. The average GPA in our sample is 2.71, with slightly lower values in math and verbal courses. Students accumulate close to 6.5 Carnegie credits per year, with about half of these credits dedicated to math and verbal courses. Finally, 33% of students fail at least one course per year. Table 4: Summary Statistics - Educational Variables Observations Mean Std Deviation GPA 18,830 2.71 0.76 GPA in Math Courses 17,066 2.46 0.88 GPA in Verbal Courses 18,211 2.65 0.86 Total Credits 19,250 6.29 3.41 Fraction Advanced Credits 18,830 0.06 0.13 Fraction Math Credits 16,560 0.20 0.14 Fraction Verbal Credits 17,894 0.30 0.20 Failed any Class 19,250 0.33 0.47 Have Been Suspended 17,811 0.10 0.30 PIAT 4,524 78.33 16.69 Data are from the NLSY97. The sample consists of individuals with at least one term of high school transcripts who were enrolled in high school since the last interview. Other data sets. While we utilize only the NLSY97 in the descriptive analysis below, we have also collected additional variables that are correlated with substance use but not with shocks to cognitive skills. These variables will be useful for identifying the model outlined in Section 3. The types of variables include state legislation regarding substance use, states sales taxes for alcohol and cigarettes, and prices. Information for alcohol and tobacco is readily available from groups such as impacteen http://www.impacteen.org/) and the Tax Foundation http://taxfoundation.org/). More challenging is information regarding marijuana and cocaine. Data on marijuana is collected from the website http://www.theweedblog.com, which provides detailed information on state marijuana laws, such as whether medical marijuana is prohibited or if marijuana is decriminalized. For cocaine, we rely on the The Drug Enforcement Administration s System to Retrieve Information from Drug Evidence DEA - STRIDE). STRIDE is a database of drug exhibits sent to DEA laboratories for analysis. While STRIDE is not a representative sample of drugs available in the United States, it reflects all evidence submitted to DEA laboratories for analysis. The DEA established this on-line dataset to provide ready access to drug seizure data. Key variables in the STRIDE data include the type of drug purchased, the quantity purchased, and price. We exclude any cocaine transaction above 500 grams and trim transactions where the price is below $10 p/gm or over $500 p/gm. We then generate average price by state and year. The data also includes cocaine seizures. We calculate total seizures by state and year as a possible supply shock. We stress that we do not argue that these variables are uncorrelated with past cognitive skills but only with unpredictable shocks to skills that might occur each year. Because these instruments are persistent over time and very often are time invariant), they will naturally be correlated with past skills. Furthermore, 12 During the first 6 waves, respondents not yet in high school and at least 13 years old in 1997 from round 2) were administered the PIAT test. Because of the age limitation, approximately 1,500 individuals took the test starting in round 2. 11

because skills cannot be directly measured, controlling for past measures of skills does not make these variables valid instruments. Similar variables have been used in DeSimone 2002), Pacula et al. 2003), Chatterji 2006), although under different identifying assumptions. Among others, McCaffrey et al. 2010) finds that some of these instruments are not very strong; for this reason in the next section we also develop a version of our model that relies only on the longitudinal nature of the data to identify the parameters of interest. 3.1 Descriptive Evidence In this section, we examine the correlations between substance use and cognitive measures in the NLSY97. Our cognitive skill measures are summarized in Table 3. We analyze how these variables correlate with the use of tobacco, alcohol, marijuana or cocaine since the date of last interview. We selected these drug use measures because they appear to better capture the correlation with cognitive skills and are consistent with each other. In all regressions, standard errors are clustered at the individual level. Table 5 displays the Ordinary Least Squares OLS) coefficients for each measure of substance use. Each column in the upper and lower panels represents a separate regression that also includes controls for survey year, age, gender and race. 13 As expected, marijuana use is negatively associated with most measures positively to suspensions and failures), although its effect is not statistically significant in the PIAT test and in how credits are distributed across different classes. Cocaine has effects similar to marijuana, although its impact is larger for the PIAT test and for the fraction of advanced classes. Alcohol, on the other hand, is either not important or positively associated with skills, as seen in the PIAT test, failures, total credits, and the fraction of advanced credits. Although this result is somewhat surprising, we suspect that it is generated by a spurious correlation between social skills, alcohol consumption, and cognitive skills. Finally, tobacco is very negatively associated with cognitive skills, much more so than marijuana or cocaine use. This correlation might seem surprising, but it is very likely generated by a confounding factor. 13 Controlling for additional variables such as family income and assets, maternal and paternal education or mother s age at birth does not drastically change the results but significantly reduces the number of observations. 12

Table 5: OLS Results GPA Math GPA Verbal GPA % Advanced Credits % Math Credits Marijuana -0.120-0.125-0.109-0.314-0.394 0.020) 0.024) 0.023) 0.328) 0.376) Alcohol 0.006-0.006-0.007 1.342 0.413 0.016) 0.020) 0.018) 0.288) 0.286) Cocaine -0.118-0.092-0.125-1.049-0.437 0.030) 0.038) 0.034) 0.495) 0.636) Tobacco -0.231-0.211-0.248-2.948-0.444 0.018) 0.022) 0.020) 0.307) 0.326) Observations 15242 13678 14723 15242 13165 % Verbal Credits Total Credits Failed Any Suspended PIAT Marijuana -0.157-0.379 0.054 0.062-0.374 0.511) 0.074) 0.012) 0.009) 0.941) Alcohol -0.246 0.143-0.025-0.004 3.117 0.391) 0.058) 0.009) 0.006) 0.681) Cocaine -0.882-0.235 0.057 0.053-2.897 0.796) 0.115) 0.019) 0.015) 1.741) Tobacco 0.297-0.541 0.111 0.058-3.248 0.453) 0.064) 0.010) 0.007) 0.787) Observations 14379 15599 15599 14963 3308 Data are from the NLSY97. The sample consists of individuals with at least one term of high school transcripts who were enrolled in high school since the last interview. Drug regressors are indicators for use since the date of last interview. Regressions include controls for survey year, age, gender and race. Standard errors are clustered at the individual level. In Table 6, we present results from fixed effect regressions where, again, each column in the upper and lower panels reflects a separate regression. In the next section, we argue that fixed effects regressions are unable to identify the long term impact of drug use. However, this type of approach has been used to remove time invariant individual unobservables that might create a spurious negative correlation between drug use and cognitive skills. For example, students who are unobservably less prone to devote time to studying may be more likely to use that time to consume drugs. As expected, the magnitude of the impact of all substances decreases in this specification. In this analysis, the use of any of the four substances is negatively correlated with GPA even alcohol), and the impact of tobacco use has declined much more relative to the other drugs. None of the substance use indicators are statistically significant when the dependent variable is total credits or how these credits are divided between mathematical and verbal subjects. Alcohol and marijuana are positively associated with advanced classes, while tobacco is negatively associated. All substances are positively associated with failing at least one class, although cocaine and tobacco are not statistically significant. Only marijuana is positively related to suspensions, while no variable predicts PIAT. 13

Table 6: Fixed Effects Results GPA Math GPA Verbal GPA % Advanced Credits % Math Credits Marijuana -0.043-0.053-0.011 0.488-0.636 0.015) 0.023) 0.018) 0.288) 0.527) Alcohol -0.044-0.030-0.058 0.946-0.075 0.012) 0.019) 0.015) 0.236) 0.427) Cocaine -0.101-0.074-0.088 0.061-0.441 0.022) 0.034) 0.027) 0.425) 0.784) Tobacco -0.034-0.057-0.047-0.859 0.515 0.015) 0.022) 0.018) 0.279) 0.505) Observations 15242 13678 14723 15242 13165 % Verbal Credits Total Credits Failed Any PIAT Suspended Marijuana -0.963-0.004 0.032 0.010 0.033 0.637) 0.093) 0.012) 0.622) 0.008) Alcohol -0.581 0.038 0.032 0.203 0.008 0.529) 0.077) 0.010) 0.484) 0.006) Cocaine 0.737-0.090 0.018-0.310-0.001 0.939) 0.137) 0.018) 0.903) 0.011) Tobacco 0.004-0.131 0.015 0.239 0.007 0.621) 0.091) 0.012) 0.587) 0.007) Observations 14379 15599 15599 3308 14963 Data are from the NLSY97. The sample consists of individuals with at least one term of high school transcripts who were enrolled in high school since the last interview. Drug regressors are indicators for use since the date of last interview. Regressions include controls for survey year, age, gender and race. Standard errors are clustered at the individual level. While the results vary considerably across specification and cognitive measures, these two tables suggest that a negative correlation exists between most substances and cognitive measures. The key results are that the correlation of alcohol with skill reverses when we compare cross-sectional variation to individual variation; the negative correlation between substance use and skill drops dramatically when controlling for individual effects, and marijuana is the drug that most often results in a negative and statistically significant effect. We have discussed above additional variables instruments) that are arguably orthogonal to the shocks to skills. While we cannot currently link these variables to the NLSY97 respondents, it is inappropriate to use these instruments in the above analysis since they are likely correlated with skills through lagged substance use. In the model we develop in the next section, these variables will be used as exclusion restrictions, once the impact of past skills and substance use is properly accounted for. 4 Discussion In this proposal, we show that there is strong evidence that substance use is negatively related to cognitive skills. This association remains, albeit smaller in magnitude, after controlling for time invariant individual 14

characteristics. We present a model that will allow us to separately identify temporary and persistent effects of substance use on cognitive skills. While we can show identification of the model with one drug, it is a short term goal to extend the identification proof to a N dimensional vector of substances. Then the model will be estimated in its two forms, with and without the instruments discussed in Section 2, and under different identifying assumptions for the identification of the first period parameters. For example, we will experiment with modeling the initial condition or restricting how the parameters can vary over time. The structural estimates will then be utilized to understand how much of the cross-sectional correlations are due to reverse causality, temporary effects, and permanent effects. We will then simulate data and understand what alternative approaches like straight" IV or fixed effect regressions may be identifying in the actual data. We expect this part of the project to be completed within the first two years. According to the National Institute on Drug Abuse, in 2013 an estimated 24.6 million Americans aged 12 or older - 9 percent of the population - used an illicit drug in the past month. Also in 2013, an estimated 19.8 million Americans aged 12 or older used marijuana in the past month. The U.S. Department of Justice estimates that illicit drug use costs America close to 200 billion dollars per year, with the majority of these costs being driven by losses in productivity. The productivity costs associated with drug use are primarily the result of a reduction in labor force participation and incarceration. Both labor supply and criminal behavior have strong links with schooling and human capital. If illicit drug use has large and persistent impact on human capital formation during high school, it is likely that the productivity costs of illicit drug use are considerably higher than those proposed by the Department of Justice. 15

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