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A sturdy values analysis of motor vehicle fatalities

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Abstract

Understanding the major determinants of crash fatalities continues to be an important topic of investigation for safety researchers. Regression models using a vast number of explanatory variables are often used which result in a huge array of specifications. Results often vary among studies based on size of estimated coefficients and significance levels. To address this, we explore both significance and model sturdiness in regression models using Leamer’s s-values. This Bayesian technique allows us to address estimation uncertainty and model ambiguity over all possible subset regressions so as to evaluate the effect of key variables which we focus on as contributors to crash fatalities. These include cell phone use, fleet modernization, suicidal behavior, alcohol use, and speed limits.

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Notes

  1. See NHTSA (2016).

  2. See NHTSA (2016).

  3. See Loeb et al. (1994) for a more complete list and discussion of these contributing influences.

  4. See Blattenberger et al. (2013).

  5. An extensive review of the literature regarding the explanatory factors can be found in Loeb et al. (1994) and more recently in Fowles and Loeb (2019) and Blattenberger et al. (2013).

  6. See for example, Fowles et al. (2010).

  7. See CTIA (2011). By December 2015, the number of wireless subscriber connections rose to 377.9 million as per CTIA (2016).

  8. Strangely, the bans do not include hands-free devices even though research indicates that such devices have a similar adverse effect. See for example, Consiglio et al. (2003).

  9. See Fowles and Loeb (2019) and Blattenberger et al. (2013) for a full review of these papers.

  10. See also Fowles et al. (2013).

  11. A time trend was also considered as a potential regressor in the model. However, our measure of the age of the fleet (MCMY) was found to be almost perfectly correlated with a time trend, with a correlation coefficient of 0.99962.

  12. See Blattenberger et al. (2013) and Loeb et al. (1994) on this issue.

  13. The target of interest in a Bayesian regression setting is the posterior means for the \( \beta \) parameters. Mathematical developments for EBA are found in Leamer (1982).

  14. The Bayesian natural conjugate model sets the prior variance for the β’s = var(β) = v2Ik×k where Ik×k is the k by k identity matrix. Bounds are obtained via the scalar v2 which is set to the minimum or maximum expected R-square divided by k, see Leamer (2014, 2016) for details. Calculations are performed in the software R (R Development Core 2016). Also see Fowles (1988).

  15. A super pessimist prior is to exclude a variable from a regression, so the prior mean is at zero and the variance is zero as well (prior R-square zero). In this paper, we do not consider this kind of strict prior.

  16. Our method of imputing cell phone subscriptions correlates with the actual data with a correlation coefficient of 0.9943.

  17. The per se law refers to legislation that makes it illegal to drive a vehicle at a blood alcohol level at or above the specified BAC level. BAC is measured in grams per deciliter.

  18. See Office of the Federal Register (1980).

  19. See Blattenberger et al. (2009).

  20. Regional dummies were included as explanatory variables, but results are not shown in Table 2.

  21. See Leamer (2014).

  22. See Leamer (2014).

  23. Leamer’s decision rule in the selection of models requires the absolute values of s-values to be greater than 1 and the absolute value of t statistics for the full OLS model to be greater than 2. Conformity between the sign of t simple and t all is an additional factor in model selection although not necessarily required. However, when signs differ between these two values, additional information should be considered.

  24. It is important to note that all three cell phone variables are sturdy regardless as to one’s prior whether pessimistic, optimistic, or not having a preconceived notion at all. The results in Table 2 regarding cell phone subscriptions reveal an overall positive effect of cell phones on fatality rates, but the marginal effect is diminishing. (A pictorial representation of this is available from the authors.) One should remember that the nonlinear specification is the prior proposed by previous studies.

  25. Again, regional dummy variables are included in the analysis, but not shown in Fig. 3.

  26. For t statistics and s-values, the correlation is .89.

  27. All variables are standardized to mean 0 and variance 1 so as to allow for unit-free comparisons.

  28. See for example, Loeb et al. (2009), Fowles et al. (2010), and Fowles and Loeb (1992).

  29. See Breiman (2001).

  30. See Blattenberger et al. (2013).

  31. See Chaloupka et al. (1993) and Freeborn and McManus (2007).

  32. See Centers for Disease Control and Prevention, National Center for Injury Prevention and Control (2012).

  33. These are Region 9 states in our model.

  34. See Conner et al. (2001).

  35. A note is also due regarding the potential shortcomings in the paper. Clearly, alternative models, e.g., double log models among others, could be investigated. One’s initial prior establishes the structure of the model, and s-values can be viewed then to demonstrate whether they appear reasonable. Quality of data is another matter in which all empirical investigations are subject to. One is left with using the best available at the time, recognizing measurement, and sampling errors are prone to show up. The data used in this study are obtained from well-known sources (as indicated in “Appendix 1”) and are sensitive to such errors no more than in other studies.

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Author information

Authors and Affiliations

  1. Department of Economics, University of Utah, 260 S. Central Campus Drive, Gardner Commons 4100, Salt Lake City, UT, 84112, USA

    Richard Fowles

  2. Department of Economics, Rutgers University, 360 Dr. Martin Luther King Jr. Blvd, Hill Hall 813, Newark, NJ, 07102, USA

    Peter D. Loeb

Authors
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Correspondence to Richard Fowles.

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Appendices

Appendix 1: Data sources

Name

Data source

FATAL

Highway Statistics (various years), Federal Highway Administration, Traffic Safety Facts (various years), National Highway Traffic Safety Administration

MCMY

National Automobile Dealers Association (various years) and the National Household Travel Survey, US Department of Transportation.

PERSE

Digest of State Alcohol-Highway Safety Related Legislation (various years), Traffic Laws Annotated 1979, Alcohol and Highway Safety Laws: A National Overview 1980, National Highway Traffic Safety Administration

SPEEDHI

Highway Statistics (various years), Federal Highway Administration

BELT

Traffic Safety Facts (various years), National Highway and Traffic Safety Administration

BEER

US Census Bureau, National Institute on Alcohol Abuse and Alcoholism

MLDA

A Digest of State Alcohol-Highway Safety Related Legislation (various years), Traffic Laws Annotated 1979, Alcohol and Highway Safety Laws: A National Overview of 1980, National Highway Traffic Safety Administration, US Census Bureau

YOUNG

State Population Estimates (various years), US Census Bureau http://www.census.gov/population/www/estimates/statepop.html

CELLPOP

Cellular Telecommunication and Internet Association Wireless Industry Survey, International Association for the Wireless Telecommunications Industry

UNEMPLOY

Statistical Abstract of the United States (various years), US Census Bureau

REALINC

State Personal Income (various years), Bureau of Economic Analysis website http://www.bea.doc.gov/bea/regional/spi/dpcpi.htm

EDHS

Digest of Education Statistics (various years), National Center for Education Statistics, Educational Attainment in the United States (various years), US Census Bureau

EDCOLL

Digest of Education Statistics (various years), National Center for Education Statistics, Educational Attainment in the United States (various years), US Census Bureau

SUICIDE

Statistical Abstract of the United States (various years), US Census Bureau

REGION

US States 1: ME, NH, VT; 2: MA, RI, CT; 3: NY, NJ, PA; 4: OH, IN, IL, MI, WI, MN, IA, MO; 5: ND, SD, NE, KS; 6: DE, MD, DC, VA, WV; 7: NC, SC, GA, FL; 8: KY, TN, AL, MS, AR, LA, OK, TX; 9: MT, ID, WY, CO, NM, AZ, UT, NV; 10: WA, OR, CA; 11: AK, HI

Appendix 2: Descriptive statistics (primary variables, raw data)

Name

Mean

Median

Standard deviation

MCMY

1987.00

1987.01

10.10

CELLPOP

360.27

206.56

378.44

SPEED

65.06

65.00

6.65

PERSE

0.91

1.00

0.29

BEER

1.29

1.28

0.23

MLDA

20.74

21.00

0.76

BELT

0.75

1.00

0.43

EDHS

0.60

0.60

0.06

EDCOLL

0.16

0.15

0.05

REALINC

28,743.65

28,466.36

7227.34

YOUNG

0.20

0.19

0.03

SUICIDE

13.02

1.00

0.29

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Fowles, R., Loeb, P.D. A sturdy values analysis of motor vehicle fatalities. Empir Econ 60, 2063–2081 (2021). https://doi.org/10.1007/s00181-020-01826-2

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