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How Much Can We Trust Causal Interpretations of Fixed-Effects Estimators in the Context of Criminality?

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Abstract

Researchers are often interested in estimating the causal effect of some treatment on individual criminality. For example, two recent relatively prominent papers have attempted to estimate the respective direct effects of marriage and gang participation on individual criminal activity. One difficulty to overcome is that the treatment is often largely the product of individual choice. This issue can cloud causal interpretations of correlations between the treatment and criminality since those choosing the treatment (e.g. marriage or gang membership) may have differed in their criminality from those who did not even in the absence of the treatment. To overcome this potential for selection bias researchers have often used various forms of individual fixed-effects estimators. While such fixed-effects estimators may be an improvement on basic cross-sectional methods, they are still quite limited when it comes to uncovering a true causal effect of the treatment on individual criminality because they may fail to account for the possibility of dynamic selection. Using data from the NSLY97, I show that such dynamic selection can potentially be quite large when it comes to criminality, and may even be exacerbated when using more advanced fixed-effects methods such as Inverse Probability of Treatment Weighting (IPTW). Therefore substantial care must be taken when it comes to interpreting the results arising from fixed-effects methods.

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Notes

  1. Poisson regressions are used given the dependant variable in each specification is a count variable. Negative Binomial specifications could also be used in such contexts, with an analogous discussion to the one presented here.

  2. Thanks to an anonymous reader for pointing this paper and selection out.

  3. Numerous papers have argued that smoking can act as a gateway drug to harder drugs (Torabi et al. 1993; Chen et al. 2002; Fleming et al. 1989). However, this claim is often supported by showing that smoking is simply correlated with a higher likelihood of harder drug use later on. Clearly, this association is subject to the critique that is the subject of this paper.

  4. However, standard errors are clustered by individual, meaning the standard errors are adjusted for the fact that observations for the same individual are not statistically independent across panel periods. In terms of the equations above, the residual r ij terms are not assumed to be independent, rather they are allowed to have an arbitrary correlation within individual (but are independent across individuals).

  5. Gang status in a given panel year was determined by whether the respondent answered yes to the question “Have you been a member of a gang since last interviewed?”

  6. Smoking status in a given panel year was determined by whether the respondent answered yes to the question “Have you smoked a cigarette since last interviewed?”

  7. Technically, these estimates are called a conditional fixed-effects estimates, but will be referred to simply as a fixed-effects estimator here for brevity. Coefficients on the other included time varying regressors are also omitted for brevity. Note that the number of observations and number of persons shown at the bottom of Table 3 indicate that individuals for whom the dependant variable (i.e. crime count for each category) is zero in all panel years do not contribute to the estimates.

  8. McKinnish (2008) has argued that fixed-effects estimators can also suffer from bias toward zero due to a type of measurement error attenuation bias in instances where the treatment in question has both transitory and longer-term components, but where only the longer-term component is expected to have a substantial impact on the outcome of interest. Given the treatments of interest here—gang participation, marriage, and smoking—this concern is relatively minor in this analysis.

  9. All specifications also include each individual’s age and age squared, along with indicators for panel year. Gordon et al. (2004) actually use negative binomial regressions. Poisson regressions are used here since there is some variation in each individual’s “exposure” in each panel year, as the time between interviews varied between individuals. It is more straightforward to incorporate such variable exposure in Poisson regressions. However, all results in this paper are qualitatively equivalent using negative binomial specifications as done by Gordon et al. (2004).

  10. Moreover, if anything, gang status has a stronger connection to criminality using the NSLY97 data than the delinquency data used by Gordon et al. (2004). This likely has to do with the fact that the oldest youth in the data set used by Gordon et al. (2004) were 16, while the youth in the NLSY97 data used here range from 15 years old (the youngest cohort in the first panel year) up to 24 years old (the oldest cohort in the 2005 panel). Given criminality generally rises during these ages, it should not necessarily be unexpected to find a stronger association between gang status and criminality in this data set covering a larger age range.

  11. See Hernan et al. (2000) and Robins et al. (2000) for particular examples.

  12. This Hierarchical Linear Model method was introduced by Bryk and Raudenbush (1992) and has been used in a very similar context to this (but without IPTW weights) by Horney, Osgood, and Marshall (1995).

  13. Hierarchcial Linear Modeling software (HLM 6.0) must be used to estimate this empirical model when period specific individual weights are used, as standard fixed-effects estimation routines require individuals to have the same weight in each panel year.

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Acknowledgments

The author thanks Eric Helland, Shawn Bushway, Ray Paternoster, Brian Johnson, and Serkan Ozbeklik, as well as the comments of three anonymous referees and the editors Alex Piquero and James Lynch for encouragement and helpful suggestions on earlier drafts of this project.

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Bjerk, D. How Much Can We Trust Causal Interpretations of Fixed-Effects Estimators in the Context of Criminality?. J Quant Criminol 25, 391–417 (2009). https://doi.org/10.1007/s10940-009-9073-y

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