Identifying Sibling Influence on Teenage Substance Use

II. Literature Review

We begin with a brief survey of the literature on family influences on risky behaviors, particularly substance use, drawing across the social sciences.⁴

Developmental psychologists and sociologists were first to investigate the importance of social environment on adolescent development and behavior. Although some perceive peer group influence as the single most important factor shaping a child’s behavior (Harris 1998), a number of psychologists continue to emphasize the primacy of the family in shaping a child’s attitudes and behaviors (Jessor and Jessor 1977; Kandel 1980; Barnes 1990).

Within the family, the psychology literature suggests two main mechanisms through which siblings may influence each other. The first one is that a sibling, most likely the younger one, may see his older sibling as a role model to observe, imitate, and use in shaping his notions about what types of behaviors are suitable (Widmer 1997; Buhrmester 1992; Rodgers and Rowe 1988; Bikchandani et al. 1992). In the context of risky behaviors, Patterson (1984) argues that siblings are more likely to learn these type of behaviors from each other when they have conflict ridden and aggressive relationships, because these promote antisocial behavior.

The second mechanism, which we refer to as the “opportunity hypothesis,” suggests that siblings influence each other’s behaviors by providing opportunities (friends and settings) for substance use and sexual intercourse. In contrast to Patterson’s hypothesis, this mechanism is more likely to occur with siblings who have better and warmer relationships, share friends, and hence engage in risky behavior together. For the purpose of our study, it is important to note that most of the literature surveyed here argues that the pattern of influence runs from the older to the younger child (Buhrmester 1992; Rodgers and Rowe 1988).

Although the economics literature does not focus specifically on siblings interactions, it also offers some rationales for conformity in behavior, which can be applied to siblings. For example, in his social distance model, Akerlof (1997) represents social interaction as a mutually beneficial trade between agents. Agents occupy a location in the social space, which is partly inherited. The model creates incentives for agents to interact with those that are close in the social space, thus possibly explaining their tendency to conform to the behavioral norms of those who share their inherited social location.

In addition to the theoretical work reviewed above, a large number of studies have investigated social influence on youth behavior empirically. However, most of these papers provide evidence of large correlations between siblings in a variety of behaviors, without necessarily devising a strategy for distinguishing causality from the effect of common unobserved factors. For example, Duncan et al. (2001) examine sibling correlations in measures of delinquency for a sample of adolescents in grades 7 through 12 using Add Health data. The sample includes genetically differentiated siblings within a family, peers, grade mates, and neighbors, thus allowing the authors to compare correlations in the same behavior across different types of relationships. The correlations are highest for siblings, especially for twins, thus suggesting a large scope for family influences. Using the same data set, Slomkowski et al. (2005) find that both genetic and environmental factors contribute to similarities between siblings’ smoking behavior. On the environmental side, parental behavior has been shown to be a source of imitation, although studies, such as Conger and Reuter (1996) and Windle (2000), show that it is less potent than sibling influences. Averett et al. (2011) do not examine sibling correlations but do show that having an older sibling increases substance use. Controlling for measures of parental supervision has little effect on the strength of this effect.

Researchers have also used data about the quality of the relationship between siblings to study sibling influences. For example, using the Arizona Sibling Study, Rowe and Gulley (1992) find that correlations in substance use and delinquent behavior are higher when interactions are warmer, less conflict-ridden, and more frequent, and when siblings have more mutual friends and are of the same gender. Although these results do not directly test for the presence of a direct sibling influence, they are consistent with one, as suggested by the opportunity hypothesis described above. Overall, however, results based on this type of data are mixed and often contradictory.⁵

Although some of the studies mentioned above control for a large array of family and parental characteristics and some find interactions that are consistent with a sibling effect, the sibling effects they estimate could reflect the impact of unobserved common factors. A few studies, mostly in economics, attempt to identify a sibling causal effect by using instrumental variables strategies. One of them, Oettinger (2000), estimates linear probability models of high school graduation of an older sibling on the probability that the younger sibling graduates and vice versa in the NLSY97. He finds that sibling influence runs mostly from the older to the younger sibling but his identification strategy relies on exclusion restrictions that seem questionable.⁶

Ouyang (2004) develops a dynamic model of the older and younger siblings’ behaviors. Her model allows for state dependence and for the older sibling’s behavior to contemporaneously affect that of the younger sibling. She estimates the model with NLSY97 data on cigarettes, marijuana, and alcohol consumption and finds strong evidence of a sibling effect. In contrast with our approach, however, she does not allow for individual specific unobserved heterogeneity and proxies family specific heterogeneity with the older sibling’s smoking history.

Finally, Harris and Lopez-Valcarel (2008) propose an interesting theoretical model in which siblings learn about whether smoking is desirable by observing their siblings’ decisions. They allow the decision not to smoke to have a different effect than the decision to smoke cigarettes. Using data on smoking behavior of family members from supplements to the CPS, they estimate a multivariate probit model in which the number of one’s siblings who smoke appears on the righthand side. They find a powerful sibling influence as well as some evidence that the positive effect of smoking is stronger than the deterrent effect of not smoking. However, their estimates imply that the variance of the error component that affects the behavior of all siblings is zero. That is, conditional on a limited set of observables, sibling effects account for the entire sibling correlation in smoking. We suspect that their finding of powerful sibling effects may be due in part to problems in separately identifying the common factors that influence smoking from the sibling influence.⁷

In sum, there are good theoretical reasons for believing that substance use and other behaviors of adolescents are causally influenced by siblings. However, the strong similarity in the behavior of siblings may be due to genes and shared environments, as well as a direct influence of one sibling on another. To date, little is known about the relative contribution of these mechanisms, let alone the precise nature of sibling interactions.

III. The NLSY97 Data

The empirical analysis uses the first eight rounds of the National Longitudinal Survey of Youth 1997 (NLSY97), a panel study of men and women who were between 12 and 16 years of age at the end of 1996. In the first round, the NLSY surveyed 8,984 individuals originating from 6,819 households in the United States. Because the sample design selected all household residents in the appropriate age range, the NLSY97 original cohort includes 1,892 households with more than one respondent. Using information about the relationship between the different respondents of the same household, we created a sample of pairs of biological siblings.

For every year since 1997, the NLSY97 contains extensive information about a wide range of risky behaviors. We focus on smoking cigarettes, drinking alcohol, using marijuana, and using cocaine and/or other hard drugs.⁸ The substance-use questions are administered directly by the respondent into a computer. The interviewer cannot observe the responses. The main outcome we analyze is whether the individual reports having engaged at all in the particular behavior since the last interview date. For example, for smoking, the variable takes the value 1 if the respondent reports having smoked since the last interview, and 0 otherwise. For each behavior, we construct this variable from two NLSY97 variables. The first and most important one is a dummy variable indicating whether the respondent has engaged in the behavior since the last date of interview. When it is available (usually in the first few survey rounds), we also use a second dummy variable, which indicates whether the respondent has ever engaged in the specified behavior. This second variable allows checking the consistency of some of the answers to the first question, as well as filling in some of the missing observations. These questions were not asked in every year. Web Appendix A reports the exact name, reference numbers, and survey years of the variables we used. The substance use information is first available in 1998 (1999 for cocaine and hard drug use), and we select those observations that are part of uninterrupted sequences of nonmissing answers. Because individuals do not answer questions about all behaviors in every round, the analysis sample is slightly different for each behavior. In the case of cigarette smoking for example, the analysis sample is composed of 1,650 pairs of siblings, for whom we have between one and six rounds of observations.

We also estimate models that use reports of the number of days the person engaged in the behavior in the previous month to construct an indicator for high consumption and an indicator for low consumption. We present results based on five consumption categories.

The younger siblings are between 15 to 19 years old when they enter our analysis sample while the older siblings are between 16 and 20. The average age of the younger sibling is 16.04, while the average age of the older sibling is 18.06. We use all pairs with adjacent birth orders (i.e., the first-born with the second-born and the second-born with the third-born if we have the three oldest siblings in our sample). A total of 1,456 pairs come from two-sibling families, while 176, 12, and 6 come from three, four, and five sibling families respectively.⁹ Our sample is 24 percent Black and 23 percent Hispanic. The high minority proportions stem from the fact that we use supplemental and military samples along with the cross-sectional sample. Unless we indicate otherwise, descriptive statistics and multivariate analyses we report are unweighted, and we do not account for nonrandom attrition.¹⁰

In all of our empirical work, we control for a set of individual and environmental characteristics. These consist of race, gender, AFQT percentile score, education completed by age 19, number of siblings, birth order dummies, mother’s education, and a dummy for whether the child lived with both biological parents at age 12. We also include three dummy variables describing aspects of the individual’s environment up to age 12. These consist of an indicator for whether the respondent ever heard gun shots or saw someone get shot at with a gun, an indicator for whether her house was broken into, and a third indicator for whether she ever was a frequent victim of bullying.¹¹ As a sensitivity check, we experimented with using the child’s report of the percentage of his peers who engage in the behavior as an additional control, although the behavior of the child may influence his choice of peers. In some models, the explanatory variables include an indicator for whether the two siblings have the same residence and measures of parenting styles and the degree to which the child is influenced by parents and siblings. We use these variables as controls and as determinants of the strength of the direct sibling influence.¹²

We provide further details about variable construction and sample selection in Web Appendix A. Appendix Table 1 reports the age distribution of the sample. Appendix Table A2 reports unweighted and weighted descriptive statistics for the explanatory variables used in our analysis.

IV. Sibling Correlations in Substance Use

To set the stage, we document the strong relationship in substance use among siblings. Table 1 reports the mean values of the substance use measures for males, females, and the combined sample. The values are high for many of the behaviors. For example, 61 percent of the males and 58 percent of the females report drinking alcohol during the previous year. Twenty-five percent of the males and 19 percent of the females report using marijuana. The figure is about 40 percent for cigarette smoking. About 6 percent of the sample reports having used hard drugs in the previous year. The unweighted means are similar to the weighted means. (See Web Appendix Table 1.) The fractions who used the substance one or more days in the past month are lower, not surprisingly. Web Appendix Table 2 shows that incidence of the behaviors tends to increase with age until about age 20. The fractions of older siblings who engage in the behavior in all years and who engage in the behavior in some years are 0.21 and 0.42 (respectively) for smoking, 0.33 and 0.54 for drinking, 0.06 and 0.43 for marijuana, and 0.005 and 0.19 for hard drugs. The “some years” group plays a key role in distinguishing between family correlations and sibling effects.

In Table 2, we use a regression to summarize the relationship between substance use of the sibling pairs when they were the same age. Specifically, we report OLS estimates of ρ from the regression

(1)

where and are the behaviors of the younger and older siblings at age a, respectively, j is the siblings’ age gap, is a set of age dummies for the younger sibling, and X² is a vector of controls that refer to the younger sibling and that are listed in Section III. We also report estimates with controls excluded. Throughout the paper, the superscripts 1 and 2 indicate whether a variable refers to the older sibling or the younger sibling, respectively.

The results are striking. Consider smoking cigarettes. If the older sibling smoked, the probability the young sibling smoked shifts by 0.226. This value is very large relative to the sample mean of about 0.4. With controls, the shift in the probability remains large at 0.17. In the case of marijuana, if the older sibling smoked at a given age, the probability that the younger sibling used marijuana at that age increases by 0.157, which is very large relative to the sample mean of about 0.22. Having an older sibling who uses hard drugs shifts the probability for the younger sibling by 0.092. This shift is larger than the unconditional mean of 0.06. In all cases, adding control variables weakens the relationship to some degree but a strong relationship remains.

We also present separate results for brother pairs and sister pairs. The relationship across siblings tends to be larger for sister pairs. Below we explore whether the size of the peer effect depends on the gender composition of the pair.

In the remainder of the paper, we address the key but difficult question of whether the sibling correlations are due, at least in part, to a causal effect of the older sibling’s behavior.

V. A Joint Dynamic Probit Model of Substance Use and Sibling Influences

In this section we present the joint dynamic model of substance use that underlies much of the econometric analysis. We begin with the behavioral model and then turn to the econometric specification and estimation issues.

Consider a sibling pair. The variables and are the ages of the older and younger siblings in year t: We leave family subscripts implicit throughout the paper. We focus here on the case in which y is a binary choice.

Let be the difference between the perceived benefit and the cost of , including the opportunity costs of foregoing other goods.¹³ is determined by

(2)

The older sibling chooses if and chooses otherwise. Thus

(3)

The net benefit of depends on a set of covariates X¹, the vector of age dummies indicating whether the older sibling is aged a in year t, the family-specific component ε and the person-specific component for the older sibling, is a transitory error component affecting the older sibling in period t.

The benefit of also depends on , the lagged choice of the older sibling. The dependence parameter γ¹ reflects two mechanisms. The first one is the effect of habit formation and informational effects. The second one is the effect of the information the parent has about the child, as well as the positive or negative influence of the parents’ reaction, on the net benefit of y¹t to the older sibling. In principle, the net benefit of y¹t could depend on through a direct peer influence from the younger to the older sibling or because the parental response to the behavior of the younger child affects the older sibling. We assume that both of these effects are 0 and leave out of Equation 3.

The younger sibling faces a similar problem, except that the net benefit of his behavior also depends directly on the action of his older sibling in t and t -1. He chooses if and otherwise. Thus

(4)

where v² is a component specific to the younger sibling and is a transitory error component for the younger sibling at time t. The variable is the older sibling’s age in the previous period, X² is a set of observed covariates, and is a vector of age dummies for the younger sibling.

The main parameters of interest, π² and λ², capture the direct influence of the older sibling on the younger sibling. We do not attempt to identify the specific mechanisms that underlie them. However, a brief discussion of what these mechanisms might be is in order. The coefficient λ² on the lagged behavior of the older sibling may reflect information provision about how to get and use the substances of interest, as well as about the consequences of substance use. It also will pick up an effect on the preferences and expectations of the younger sibling about norms of behavior.¹⁴ In addition, it will reflect how the parent’s reaction to signals they receive about substance use of the older sibling in t – 1 affects the costs and benefits to substance use by the younger sibling in t.

The coefficient π² on the contemporaneous behavior of the older sibling may reflect any and all of these mechanisms. However, it also may pick up a direct effect of on opportunities for the younger sibling to get and use substances, as stressed by the opportunity hypothesis. This might be particularly important for younger siblings once they are old enough to be seriously at risk to use substances but too young to easily get access to them on their own. Because we assume that the older sibling influences the behavior of the younger sibling but not vice versa, we are implicitly assuming that the younger child observes before choosing .

Below we place restrictions on the distributions of and over time and across siblings. Without loss of generality, v¹ and the corresponding component v² for the younger sibling are assumed to be uncorrelated.

To complete the model, we assume that substance use is 0 for all individuals if a_t £ A₀ where A₀ is the minimum age of initiation. Let and be the years in which the older sibling and the younger sibling reach age A₀: At age A₀, the behavior of the older sibling is determined by

(5)

where is the year in which the older sibling reaches A₀. On the other hand, the younger sibling’s behavior at A₀ depends on the behavior of the older sibling and is given by

(6)

Thus, the behavioral model consists of Equations 4–6.

The econometric model also contains Equations 3 and 4. But we do not observe behavior at the minimum age of initiation. Consequently, in the econometric model we replace Equations 5 and 6 with approximate equations for the behavior of the older and younger siblings in the year we first observe them. The choice of in year , the first year we observe the older sibling, is determined by

(7)

The corresponding equation for the younger sibling is

(8)

where is the first year we observe the behavior of the younger sibling.¹⁵ From now on, the subscript 0 refers to parameters for the first year of observation. In the above equation, and are the sibling-influence parameters. Each is the sum of two components. The first component of is the direct effect of on holding the prior behavior of the younger sibling constant. These components of and are directly analogous to π² and 벂 but they will be larger if the influence of older sibling’s behavior is stronger at younger ages. (We allow the sibling influence parameters to depend on age in Section VI.B.) The second components of and capture the continuing influence of the behavior of the older sibling in prior periods on . This lagged influence will be part of and because and are correlated with lags of the older sibling’s behavior, which influence through the state dependence term . The term appears in Equation 4 (when ), but it is excluded from Equation 8 because we do not observe it.

The coefficients on the age controls and X also are allowed to differ between the equations for the first observations and the equations for the later periods, both because they may depend on age and because they will pick up lagged influences in Equations 7 and 8. They also differ between the older and younger siblings.

The model generalizes easily to allowing the sibling influence parameters to depend on other observables. Below we experiment with allowing the sibling influence parameters to depend on the gender mix of the sibling pair, on the gap in age between the younger and older sibling, and on whether they share the same residence in models with and π² constrained to zero. The psychology literature suggests that these parameters could depend on “ family process” variables characterizing the relationships between the parent and child and between the siblings. We did not explore this possibility using the joint dynamic probit model because results using the correlated random effects regressions suggest lack of power to identify the interaction effects. (See Section VIII.B.)

We assume the sibling pair specific error component ε is . The person specific error components v¹ and v² are and , respectively. They are independent across siblings. The error components and are N(0‚ 1). They are independent across siblings and years. One might expect temporal variation in factors such as stresses within the family (eg., parental unemployment, marital conflict, parental substance abuse) or variation in access to drugs or alcohol in a neighborhood or in a school to lead and to covary conditional on ε and thus violate this assumption. We experienced numerical difficulties in estimating a version of the model with a common iid sibling pair specific shock. We strongly suspect that, in order to identify the model with contemporaneous sibling influences without strong restrictions on the error structure, one needs to observe powerful time-varying exogenous determinants of substance use that influence one’s own behavior but not one’s sibling. Unfortunately, we do not observe such variables. We believe that the estimates of the contemporaneous peer influence parameters and π² will be biased upward if common transitory shocks are important.

In our main specification, we restrict the factor loadings α on the family effect ε and the factor loadings δ on the individual effects v¹ and v² to equal 1 in all equations. Note, however, that we allow the variances of v¹ and v² to differ.¹⁶ Our results are not sensitive to replacing the assumption that ε is normally distributed with a three point discrete distribution. We ran into numerical problems when we attempted to increase the number of points beyond 3.¹⁷ In Section VI.G.3, we consider an alternative, less restrictive error specification. We estimate the models by maximum likelihood.¹⁸

VI. Results for the Joint Dynamic Probit Model

We now turn to estimates of the joint dynamic probit model. In Section VI.A, we start with our baseline model specification, which assumes that sibling influences operate through but not . That is, it restricts the contemporaneous sibling influence parameters and π² to 0. It also excludes age interactions. In Section VI.B, we allow the model parameters to depend on age. In Section VI.C, we examine whether the sibling influence parameters depend on the gender mix, on the age difference between the siblings, or on their coresidence. In Section VI.D, we add contemporaneous sibling influences. In Section VI.E, we simulate the effect of an exogenous switch in the behavior of the older sibling from 0 to 1 in period on the time paths of substance use of the older and younger siblings. In Section VI.F, we use the baseline model to address the fundamental question of how much of the sibling correlation in substance use is causal. Finally, in Section VI.G, we discuss various checks for specification bias and robustness to alternative model specifications.

E. The Dynamic Response to the Older Sibling’s Substance Use

1. Model with lagged sibling effects

The estimates of the parameters of the dynamic probit model refer to effects on the latent variable index rather than to effects on the probability of substance use. Furthermore, they do not provide a quantitative sense of how persistent the effects are. To address these issues, we use the bias corrected estimates of the baseline model to simulate the effect of an exogenous switch in the behavior of the older sibling from0 to 1 in period on the time paths of substance use of both the older and younger siblings.²⁶ In Section VI. E.2, we simulate the models with both contemporaneous and lagged sibling effects.

Figure 1A presents the results for smoking using the model in the first column of Table 3. The vertical axis measures the change in behavior relative to the baseline probability. The horizontal axis measures the time period relative to , so 0 corresponds to . Web Appendix Tables 9A and 9B report point estimates and standard errors. These are based on a parametric bootstrap method.²⁷

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Figure 1

Effect of Shifting the Older Sibling’s Probability of Substance Use From 0 to 1 on the Older and Younger Siblings’ Probabilities of Behavior, Relative to Baseline (Based on Dynamic Probit Model)

Note: The solid line and the broken line represent the effects on the probabilities of behavior, relative to baseline, of the older sibling and of the young sibling, respectively. Error bars show the 90% confidence intervals. The x-axis measures the number of periods after the exogenous change in the older sibling’s behavior. Baseline probabilities for smoking in the first and last period displayed on the graphs are, respectively: 0.4091(0.0116) and 0.4269(0.0135) for the older sibling, and 0.3311 (0.0118) and 0.3860 (0.0309) for the younger sibling. For drinking, they are 0.5699 (0.0104) and 0.7227 (0.0113) for the older sibling and 0.4486 (0.0128) and 0.5860 (0.0290) for the younger sibling. For smoking marijuana, they are 0.2482 (0.0101) and 0.1968 (0.0098) for the older sibling and 0.2067 (0.0098) and 0.2814 (0.0343) for the younger sibling. We display the confidence interval bars for the responses of the older sibling and younger sibling slightly to left and slightly to right of the number of period after the exogenous change in the older siblings’ behavior.

We begin with the older sibling’s response. The solid line in the graph reports the effect of exogenously switching from 0 to 1 on the time path of the average value of , relative to the baseline average for . The vertical bars represent 90 percent²⁸. To be more specific, for each older sibling, we first set to 1 in , simulate forward, and take the average of for the values of t reported at the top of each column of Web Appendix Table 9a and on the horizontal axis of Figure 1a. We repeat the procedure with set to 0 in , take the difference in the two averages for each value of t, and then divide by baseline value in the top row of Web Appendix Table 9. confidence bands. One can see that the exogenous change in smoking behavior from 0 to 1 in raises the probability of smoking one year later by 0.508 (0.047) of the baseline value (0.409). The effect is 13.6 percent of the baseline value two years later and essentially dies out after four periods.

The broken line in the graph displays the effect on the time path of , relative to the baseline average of , of a one-time exogenous shift in the smoking behavior of the older sibling from 0 to 1 in , with the distribution of the future behavior of the older siblings unaffected. Smoking among older siblings increases smoking among younger siblings in by 0.10 (0.077) of the baseline value.²⁹ This is 19.7 percent of the effect of the older sibling’s behavior in on his own behavior in the next period. The value is 0.025 (0.017) in the second period. The effect on the probability that the younger sibling smokes relative to baseline is essentially zero after three years.³⁰

Figure 1B displays simulations for drinking using the bias corrected point estimates in Table 3, Column 2. For the older sibling, drinking last year raises the probability of drinking this year by 0.296 (0.031) of the baseline value, which is 0.570. After three periods, the effect is only 0.011 (0.003) of the baseline value. An exogenous change in the drinking behavior of the older sibling in increases drinking among younger siblings by 0.217 (0.057) of the baseline probability (0.449). The effect on the younger sibling is essentially zero after three periods.

Figure 1C shows that marijuana use by the older sibling in increases the probability that the older sibling uses marijuana one year later by .649 (.078) of the baseline probability of 0.248. The effect on the older sibling’s behavior is 0.033 (0.010) three years later and close to 0 after that. The bias corrected estimates imply that a onetime exogenous shift in the smoking behavior of the older sibling from 0 to 1 in increases the probability that the younger sibling uses marijuana in by 0.236 (0.091) of the baseline value. The effect on the younger sibling is 0.010 after two periods.

Web Appendix Table 10 reports the results of dynamic simulations based on the model with age interactions. We are particularly interested in how the responses depend on the age of the younger sibling at the time of the shock. Because response parameters depend not only on age but also on whether the shock occurs in or a later period, we first contrast the response using the sample of younger siblings who were 15 at with the response of those who were 17 at . In the case of cigarettes, the results show that the effect on behavior at is substantially larger for 15-year-olds than 17-yearolds: 0.163 versus 0.109. This is also true for alcohol and marijuana. We have not attempted to use simulation to estimate the bias in the sibling influence parameters in the model with age interactions. We suspect the sibling effect estimates for cigarettes are biased upward by perhaps 30 percent and that the bias is small for alchohol and marijuana. For all three outcomes, the effects are essentially zero after three periods.³¹

Overall, the effects of substance use by the older sibling in one period on the younger sibling are substantial but they die out fairly quickly. It is important to note that most of our parameter estimates indicate that the peer influence is biggest in the equation for the first observation on the younger sibling. For this reason, when we simulate the average effect of exogenously shifting the behavior of the older sibling from no substance use in all periods to substance use in all periods, we find only modest effects on the behavior of the younger sibling for .

2. Model with both contemporaneous and lagged sibling effects

To assess the dynamic impact of the contemporaneous and lagged sibling effects, we used the bias corrected estimates to perform three different counterfactual simulations. First, we exogenously switch the behavior of the older sibling from 0 to 1 in period . Second, we exogenously switch the behavior of the older sibling from 0 to 1 in period . Finally, we switch the behavior of the older sibling from 0 to 1 in both .

Table 5 reports the results of this exercise for smoking, drinking, and smoking marijuana. Looking at smoking first, we see that an exogenous shift in smoking behavior among older siblings from0 to 1 at leads to an increase in the probability of the younger sibling smoking by 0.072 at and this effect dies out quickly. In contrast, shifting the older sibling’s smoking at raises the probability that the youngest sibling smokes by 0.198 immediately, by 0.112 in the next period and 0.033 two periods later. This persistence is higher than what we found in the model with only a lagged effect in part because λ², the sibling effect of when t > t_min, is larger than in the specification with only the lagged effect (0:122 versus 0.068). Finally, shifting the older sibling’s smoking from 0 to 1 in both and increases the probability that the younger sibling smokes in by 0.272 and by 0.131 at , which is approximately equal to the sum of the effects of shifting and of shifting separately.

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Table 5

Bias Corrected Effect of Shifting the Older Sibling’s Probability of Behavior from 0 to 1 on the Younger Sibling’s Probabilities of Behavior Relative to Baseline (Based on Dynamic Probit Model with both Contemporaneous and Lagged Sibling Effects)

The second panel reports the simulation results for drinking. In line with the estimates discussed above, for drinking, the sibling effect mostly operates with a lag. This can be seen in the table, which indicates that shifting the older sibling’s drinking behavior from 0 to 1 in raises the probability that the younger sibling drinks at by 0.224, whereas shifting the older sibling’s drinking behavior from 0 to 1 at only raises the probability that the younger sibling drinks in the same period by 0.056.

Finally, the results for marijuana reveals a substantial effect of the older sibling’s behavior both contemporaneously and in the next period. Shifting the older sibling’s behavior from 0 to 1 in raises the probability that the younger sibling smokes marijuana in by 0.196. Shifting the older sibling’s behavior in raises this probability by 0.357 of the baseline probability (0.21). These effects fade away very quickly however and are basically null after two periods.

VII. A Joint Dynamic Ordered Probit Model with Many Categories

The degree of state dependence and the strength of the peer influence are likely to depend on the amount of substance use. In this section, we propose and implement a simple way to allow for flexible forms of nonlinearity in the dynamic behavior of substance use and sibling influence while continuing to allow for sibling pair effects and individual effects. Expanding from two categories (0,1) to an arbitrary number of categories, the equations for the latent variables and become

with thresholds q₁, q₂, . . ., q_{M - 1}, where M is the number of categories and category m= 1 corresponds to zero consumption. The equation for is identical to (5). The equation for is

(9)

The values of are determined by the indicator function for m= 1, by for 2 ≤ m ≤ M − 1, and for m=M. The variable is determined by in the same fashion. For simplicity of presentation and in anticipation of the empirical work, we have excluded the contemporaneous variables , from the equations for . The state dependence parameters and should increase with m if the positive influences of habit, social connections, and information on the propensity to engage in substance use are increasing in the quantity consumed in the previous period. If the size of the sibling influence is positive and increasing in the intensity of the older sibling’s behavior, then the sibling influence parameters and will be increasing in m.

By including a large number of groups, one can accommodate an arbitrary nonlinear relationship between substance use today and own past substance use, as well as past substance use by the older sibling. Of course, with a large number of categories, freely estimating the thresholds q along with the γ and λ parameters would be hopeless without a very large sample. However, one can restrict these parameters to lie on a flexible but relatively parsimonious function, such as a linear spline with a number of break points less than M.

Note that Fortin and Lemieux (1998) proposed the use of an ordered probit model with a large number of categories as a way to allow for arbitrary nonlinearity in the link between a continuous variable (the wage in their case) and a latent variable. The latent variable is an index of regressors plus an error term. Essentially, the ordered probit model provides a model of the probability that the continuous variable falls in a particular interval. Our model is very different in that it involves a system of equations with dynamics and unobserved heterogeneity. Basically, we are combining the idea of specifying the category-specific parameters parsimoniously with the idea of using the ordered categorical response model with a large number of categories as the specification for the link function relating y to the observed and unobserved variables that determine the latent variable y^*. Our approach seems well-suited to the estimation of nonlinear dynamic panel data models with unobserved heterogeneity.

We have estimated models for days of use of cigarettes, alcohol, and marijuana last month using five categories (M= 5). For all three substances, the categories are 0, 1–7, 8–14, 15–22 and 23–30 days of use.³⁵ We restrict the γ and λ parameters to lie on a linear spline with two breakpoints in slope but leave the thresholds qm, m= 1, . . .,M - 1, free. The changes in slope occur at 8 and eighteen days.³⁶ We use the simulation procedure described in Section V.A to quantify the bias that might arise from treatment of the first period. The only difference is that here we use the ordered probit specification rather than the probit specification.³⁷

The estimates of the parameters of the spline functions and the variance parameters are in Web Appendix Table 15. We also report the bias corrected estimates of the sibling influence parameters, which form the basis of the discussion that follows. The spline function estimates are used to compute the implied values of the state dependence parameters (γ) and sibling influence parameters (λ) for m= 2 to 5 (Table 7). In keeping with the binary probit results, we find that both family heterogeneity and individual heterogeneity are important for all three outcomes. We also find substantial state dependence for both the older sibling and the younger sibling. The 24 state dependence parameters are all positive. They also are increasing in m in all cases, with the exception that is less than for drinking.

The bias corrected sibling influence parameters are all positive with the exception of category 5 for marijuana. The size of increases in m through category 4 in the cases of smoking and drinking and through category 3 in the case of marijuana, but the effects are smaller for the highest category for all three outcomes. Many of the point estimates of are substantial relative to the corresponding values of , the state dependence for the older sibling. However, the standard errors of the are large, which is the price that is paid for the five-category model. After the bias correction, the estimates are statistically significant at the 10 percent level or better in only 3 of the 12 cases. The sibling effect in later periods is smaller, and the point estimates are negative in several cases. The ordered probit findings are broadly consistent with the binary case, but the bias correction makes more of a difference, particularly for drinking.

Figure 2 graphs simulations of the effect of exogenously shifting the older sibling’s substance use in from 0 to one of the two highest categories (with equal probability) on substance use in subsequent periods.³⁸ The effects are relative to the baseline probabilities. Panels A–D refer to cigarettes. One period later, the shift raises the low consumption (1–7 days) probability for the older sibling by 0.24 and the high consumption (23–30 days) probability by 0.55 relative to the baseline averages. The effects become very close to 0 after four periods. The shift in the older sibling’s behavior increases the probability that the younger sibling is in the low consumption category by 0.15 (0.059) relative to baseline. It increases consumption in the high consumption category by 0.33 (0.145) relative to baseline, and the effects are monotonically increasing. The sibling effects are very small after two years.

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Figure 2

Effect of Shifting the Older Sibling’s Probability of Substance Use from 0 to 1 of the Two Highest Categories (with Equal Probability) on the Older and Younger Siblings’ Probabilities of Consumption, Relative to Baseline (Based on Ordered Probit Model with 5 Categories)

Note: The solid line and the broken line represent the effects on the probabilities of behavior, relative to baseline, of the older sibling and of the young sibling, respectively. Error bars show the 90% confidence intervals. The x-axis measures the number of periods after the exogenous change in the older sibling’s behavior. Baseline probabilities for smoking on 1–7 days a month in the first and last period shown in the graphs are: 0.0860 (0.004) and 0.0892(0.004) for the older sibling and 0.0946(0.004) and 0.0927(0.005) for the younger sibling. In the same order, for smoking on 8–14 days: 0.0203(0.001), 0.0216(0.001), 0.0207(0.001) and 0.0227 (0.002). For smoking on 15–22 days: 0.0320(0.003), 0.0348(0.003), 0.0310(0.003), 0.0364(0.004). For smoking on 23–30 days: 0.1914 (0.009), 0.2358 (0.010), 0.1153 (0.007), 0.2444(0.035). For drinking on 1–7 days: 0.3421 (0.010), 0.4106(0.010), 0.2959(0.011), 0.3901(0.019). For drinking on 8–14 days: 0.0569 (0.003), 0.0979 (0.004),0.0345(0.002), 0.0908(0.012). For drinking on 15–22 days: 0.0335 (0.003), 0.0707 (0.005), 0.0159 (0.002), 0.0654(0.012). For drinking on 23–30 days: 0.0140 (0.002), 0.0395(0.004), 0.0045 (0.001), 0.0354(0.011). For marijuana on 1–7 days: 0.0881(0.006), 0.0805 (0.006), 0.0874 (0.005), 0.1044 (0.012). For marijuana on 8–14 days: 0.0887(0.006), 0.0811(0.006), 0.012 3(0.002), 0.0176(0.005). For marijuana on 15–22 days: 0.0209(0.002), 0.0198(0.002), 0.0177(0.002), 0.0287 (0.006). For marijuana on 23– 30 days: 0.0400(0.004), 0.0407(0.004), 0.0248(0.003), 0.0675(0.027). We display the confidence interval bars for the responses of the older sibling and younger sibling slightly to left and slightly to right of the number of years after the exogenous change in the older siblings’ behavior.

In the case of alcohol (Figure 2 E–H), the shift increases the older sibling’s drinking relative to baseline by 0.272 (0.034) in the low category, 0.745 (0.11) in the 8–14 category, and 1.23 (0.22) in the high category. The corresponding effects on the younger sibling are 0.067 (0.177) in the low category, 0.22 (.415) in the 8–14 day category, and 0.51 (0.873) in the high category. These effects are substantial, but are also imprecise.

In the case of marijuana (Figure 2 I–L), the corresponding effects are 0.77, 1.07, and 1.44 for the older sibling and 0.10 (0.164), 0.146 (0.223) and 0.252 (0.33) for the younger sibling. The fact that the effects are much larger in the highest category makes sense. However, the effects decay to essentially 0 after three years.

Overall, the results for the five-category ordered probit model are qualitatively consistent with those for the binary probit specification but are less precise. The point estimates indicate that the sibling effect is increasing in the older sibling’s consumption, but they are statistically significant only for smoking. The results provide strong evidence that the probability of substance use and the quantity of substance use today depend positively on one’s consumption level in prior periods.

VIII. Using Correlated Random Effects Regression to Estimate the Sibling Effect

We supplement the investigation of sibling effects based on the joint dynamic probit model with a simple regression approach. Correlated random effects (CRE) estimates of the direct effect of older siblings on younger siblings’ behavior are based on the following linear least squares projection equation:

(10)

The intuition is that if and have the same relationship with the error term that determines , then the coefficient on identifies the part of the link in the behavior of siblings that is due to common unobserved influences, leaving β₂ as the sibling effect. In Web Appendix C, we discuss in detail the assumptions on the above model that are required for β₂ to equal the sibling influence parameter λ² in the case in which y is continuous. The basic argument carries over to the case in which y is a binary choice. The assumptions include no state dependence, covariance stationarity of , and the symmetry restriction . Furthermore, the effects of ε or v¹ on must not vary with the age of the older sibling and the influence of ε on must not vary with the age of the younger sibling . The estimates of the dynamic probit model show substantial state dependence, and the presence of the terms and are enough to lead to age dependence in the influence of the error components on and in a nonlinear binary choice model such as (3) and (4).³⁹

We also consider the case in which both contemporaneous and lagged behaviors of the older sibling influence the younger child with coefficients λ²⁰ and λ², respectively. Consider the following projection equation:

(11)

In this case, we need to make two additional assumptions for β₂ and β₃ to capture λ² and λ²⁰. These assumptions are that and are independent across siblings at all leads and lags and that is serially uncorrelated. If any of these assumptions fail, then in general β₂ ≠ λ² and β₃ ≠ λ²⁰ in (11).

If only the assumption of no serial correlation fails, one still can estimate an average of λ² and λ²⁰ by using the regression

(12)

to test for sibling effects, as we do below. Finally, if one uses (10) when (11) is correct, then the coefficient on will pick up part of the effect of , but one will still detect sibling influences.

A. Results Using the CRE Approach

Table 8 presents estimates of sibling effects using the correlated random effect model discussed above. Each column refers to a different outcome. The top panel presents estimates of our main specification, which we refer to as Model 1. Model 1 is a variant of (10) for the case in which is binary and the control variables X and age dummies are added:

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Table 8

Marginal Effects of the Older Sibling’s Behavior on the Younger Sibling’s Behavior (Correlated Random Effects Model)

(13)

In the middle panel, we replace in the equation above with . We refer to this specification as Model 2. In the bottom panel, we allow for the possibility of a contemporaneous influence. We replace with (Model 3). The peer influence coefficient on in Model 3 is likely to be positively biased if transitory environmental factors are correlated across siblings. It also may be positively biased as the result of an interview effect when the sibling interviews occur on the same day.⁴⁰

We report marginal effects of the row variables on the probability that based on MLE probit estimates of β₁, β₂, and the other parameters in the model. Standard errors are clustered at the household level.⁴¹

Column 1 refers to smoking. The results for Model 1 indicate that raises the smoking probability by 0.062 (0.026). This estimate is statistically significant and is equal to 15.6 percent of the mean probability. The marginal effect of is 0.085 (0.018), so about 3/5th of the link between the older sibling’s past smoking and the younger sibling’s current smoking is due to common influences and 2/5th is due to the sibling effect. The results for Model 2 and Model 3 suggest an even stronger causal sibling effect on smoking.

For drinking, the estimates of Model 1 indicate that raises the probability of drinking by about 0.054 (0.024), which is 9.1 percent of the mean probability. The link due to common influences is 0.118 (0.018). The evidence for a causal effect in the case of marijuana is weak. The estimates are positive, but are statistically significant only in the case of Model 3, which allows for a contemporaneous influence of the older sibling on the younger one.

The point estimates for use of hard drugs are positive and substantial relative to the sample mean. For example, the marginal effect of is 0.011 (0.019) for Model 1 while the sample mean is 0.062. However, the effect is not statistically significant. We obtain even larger estimates using Model 2 and Model 3. Overall, the results for hard drugs suggest a positive causal effect but are too noisy to support strong conclusions.⁴²

IX. Conclusion

Parents frequently implore their older children to set a good example for younger brothers and sisters. Social scientists, particularly psychologists, have long been interested in the influences that siblings have on each other. Many studies, including ours, have found strong sibling correlations in a variety of behaviors, including substance use, that are robust to the inclusion of a rich set of controls. The difficult question is whether these correlations reflect causal influences or result from shared genes and environment. To identify causal effects, we use panel data and the key assumption that older siblings influence younger siblings but not vice versa. We rely primarily on a joint dynamic probit model and a joint dynamic ordered probit model that allow for state dependence and nonstationarity. Our use of a multiple equation dynamic ordered response models with large numbers of categories but restrictions on the category specific model parameters as a way to allow for nonlinear state dependence in the presence of unobserved heterogeneity may have other applications.

The point estimates of the sibling effect for smoking, drinking, and marijuana are almost always positive but the estimates are also noisy. They are statistically significant for drinking and marijuana using the dynamic probit model and for cigarette smoking using the ordered probit model. We also find a positive effect for hard drugs but the coefficients are not statistically significant. For the most part, the effects are largest in the equation for the first observation for the younger sibling. Although in many cases we find fairly large effects of past behavior on the latent variable that determines substance use, the effect on the younger sibling of a one-time shift in the behavior of the older sibling dies out fairly quickly. Simulations using the dynamic probit model indicate that only a small fraction of the large sibling correlation in substance use is causal although the estimates of the fractions are noisy.

We also report probit regressions motivated by the correlated random effects literature, subject to a number caveats. These results indicate that smoking, drinking, and, more tentatively, marijuana use by the older sibling increase the probability that the younger sibling engages in these behaviors. Combining the evidence from the different estimation approaches and different substances, we conclude that there is a modest positive sibling effect on substance use but that only a small part of the sibling correlation in substance use is causal.

There is a substantial research agenda. First, the analysis should be repeated with additional data sets containing panel data on substance use for large samples. These are steep data requirements. Add Health, which has been used in some previous studies of sibling links in risky behavior, is a natural possibility. The availability of genetic markers that influence substance use could be incorporated, building on some of the work discussed in Fletcher and Lehrer (2011). However, the time between interviews makes Add Health less than ideal. Second, other behaviors, including positive behaviors such as volunteering and study time, could be examined. Third, as evidence accumulates on the dynamic interrelationship among the use of different substances, it would be desirable to revisit our analysis of sibling effects in models with multiple substances. The question of “gateway” drugs is salient in policy discussions of drug law reform but given limited information in the data it is hard to quantify the linkages without strong a priori information about which linkages are most likely. Finally, while we do identify a causal effect, we do not make much progress in identifying the mechanisms underlying it. Statistical power is a serious problem, at least in the NLSY97, but a more structured approach in which the researcher constrains the way in which parental characteristics and home environment measures alter the strength of the sibling effect on a multiple set of behaviors may be worth trying.