A reexamination of resource allocation responses to the 65-mph speed limit.

Greenstone, Michael

Michael Greenstone (*)

I. INTRODUCTION

In 1987 the federal government allowed states to raise speed limits from 55 mph to 65 mph on a single category of roads, rural interstates. Of the 47 states with rural interstate roads, 40 adopted the higher speed limit within a year. Garber and Graham (1990) and Ashenfelter and Greenstone (2002) document that the fatality rate on rural interstates increased dramatically subsequent to its introduction. These studies conclude that higher speed limits lead to higher fatality rates.

In a recent issue of Economic Inquiry, Lave and Elias (1997) (henceforth L&E) argue that the full effect of the 65-mph speed limit cannot be inferred by examining rural interstates in isolation from other roads. They conjecture that the higher speed limits caused reallocations of drivers and state police that counterbalanced the increased fatality rates on rural interstates. In particular, they posit that the reduced travel times available on rural interstates induced drivers to switch from dangerous side roads to the safer rural interstates. Additionally, they contend that the higher limits freed the state police from speed enforcement, which allowed them to concentrate on activities with greater impacts on fatality rates. Thus, L&E's hypothesis is that the full effect of an increase in the speed limit requires an examination of statewide fatality rates. Figure 1 graphically depicts L&E's hypothesis.

L&E present evidence in favor of their hypothesized causal chain. First, in support of the driver reallocation conjecture, they find that between 1986 and 1988 vehicle miles of travel (VMT) increased on rural interstates where the speed limit was increased to 65 mph. Second, they present anecdotal evidence in favor of the trooper reallocation conjecture. Third, they show that the introduction of the 65-mph limit was associated with a statistically significant decline in statewide fatality rates of 3.4%-5.1%. Thus, L&E's surprising conclusion is that through driver and trooper reallocations the 1987 increase in speed limits reduced fatality rates.

This study reexamines L&E's empirical results and is unable to confirm them. It shows that the statewide fatality rate declined by a statistically insignificant amount in adopting states after 1987. This finding holds when the specification is virtually identical to the one that L&E fit and when alternative specifications are estimated. Although this result directly contradicts L&E's primary finding, the source of the discrepancy cannot be determined because their data were unavailable.

It remains puzzling that the large increase in rural interstate fatality rates is not observable in statewide fatality rates. An explanation that potentially reconciles this finding with L&E's is that the increase on rural interstates was counterbalanced, but not swamped, by fatality declines induced by the hypothesized reallocations. Consequently, this article also explores whether the 65-mph speed limit caused the reallocations that are the conjectured sources of the statewide decline in fatality rates. If these links are not supported by the data, it indicates that the statistically insignificant decline in statewide fatality rates cannot be causally related to the two reallocations and, in turn, to the higher speed limit.

The links between the 65-mph speed limit and the two reallocations are tested separately. First, the results suggest that VMT did not increase on rural interstates where the speed limit was raised. This finding is derived from a regression on 1982-1990 data, whereas L&E only compared unadjusted means from 1986 and 1988. Moreover, it holds when the comparison is to rural interstates in states that did not adopt the higher limit and to both other states and other categories of roads. These results fail to provide an empirical basis for the driver reallocation conjecture.

Second, this article develops a test of the policing reallocation conjecture. In particular, fatality rates on roads where state troopers do and do not patrol are compared. The results indicate that the statistically insignificant statewide decline in adopting states is almost entirely explained by a decline in fatality rates on urban noninterstate roads. (1) According to a National Research Council (1984) report, local policing agencies (not the state police) are primarily responsible for enforcement and safety activities on these roads. Though the source of the decline in fatality rates on urban noninterstate roads is not transparent, it is evident that it cannot be causally related to higher speed limits.

L&E contributed a clever theoretical insight that all analyses of speed limits should test. This article's results suggest that the effect of the 1987 increase in speed limits on fatality rates can be determined by solely examining the roads where the higher limit applied: rural interstates. On these roads, fatality rates increased dramatically.

II. DATA SOURCES AND DISCREPANCIES

This reanalysis uses a data file that contains the same variables as L&E's file but covers a slightly shorter period (1982-1990 instead of 1976-1990). (2) The Federal Highway Administration provided annual VMT data at the state by road type level from 1982 onward. Fatality data were compiled from the U.S. Department of Transportation's Traffic Safety CD-ROM: 1996, Fatal Accident Reporting System, which contains a census of all fatal crashes and has state by road type identifiers. Data on state unemployment rates and the adoption dates of state-specific seat belt laws were also collected. All of the data, except the state-specific seat belt variables, were obtained in electronic form, which mitigates the possibility of human error.

An important advantage of my data file is that, unlike L&E's, it contains observations on annual fatalities and VMT for categories of roads below the state level. In the subsequent analysis, the data is analyzed separately for rural interstates, noninterstate roads in rural areas, urban interstates, and urban noninterstate roads. These four categories of roads together account for all VMT and traffic fatalities. These disaggregated data allow for a precise determination of the location and timing of changes in VMT and fatality rates. A STATA format version of this data file and the programs that produced the subsequent results are publicly available. (3)

Another major difference between the two data files is that L&E's has monthly observations, whereas my data is annual. Although the federal government does not collect monthly VMT data, L&E created monthly measures with four seasonal adjusters. (4) These constructed monthly measures are likely to understate the true variability in VMT because the adjusters are seasonal instead of monthly and are determined from national data not state data. Because L&E's data were unavailable, it was impossible to estimate the magnitude of this understatement and to identify additional discrepancies.

III. A REEXAMINATION OF STATEWIDE FATALITY RATES

This section reexamines L&E's claim that the statewide fatality rate declined in states that adopted the higher speed limit on rural interstates. Table 1 presents the results from regressions where the dependent variable is the natural log of the statewide fatality rate (i.e., fatalities per 100 million miles). The parameter of interest, called policy parameter in the table, is the regression coefficient from an indicator that equals one for observations from years and states when the 65-mph limit was in force on rural interstates. All specifications include a full set of state fixed effects, the state unemployment rate, and an indicator for whether a seat belt law was in force. The effects of the unemployment rate and the seat-belt law are allowed to vary by state.

Column (1) reports the results from a specification that is virtually identical to the one that L&E estimated. Here the sample is limited to the 40 states that adopted the 65-mph limit, so the policy parameter tests for a mean shift in the fatality rate after 1987. To control for other sources of changes in fatality rates (e.g., the increasing use of air bags in this period), state-specific linear time trends are included. The only differences between this specification and the one fit by L&E are that my data file contains annual observations (recall that L&E constructed monthly data) and covers a slightly shorter period, 1982-1990 (instead of 1976-1990).

The estimated policy parameter in column (1) indicates that the statewide fatality rate declined by 1.2% (measured in log points) in the years subsequent to the adoption of the 65-mph speed limit. (5) This estimate is dramatically smaller than the 5.1% decline that L&E report (619). Moreover, it has an associated t-statistic of 0.5, whereas L&E report a t-statistic of 3.2.

Although L&E only report results from the above specification, columns (2) and (3) present estimates from alternative specifications that further probe this relationship. These additional specifications are fit on a sample that includes the nonadopting as well as adopting states. This enlarged sample allows for potentially less restrictive modeling of unobserved time-varying factors. Column (2) drops the state-specific linear time trends but adds year indicators, which nonparametrically capture the year-specific component of variance common to adopting and nonadopting states. Column (3) includes both the state-specific trends and the year indicators. This specification is probably over-parameterized, but it is estimated to document the robustness of the results.

The fitting of these two specifications yields estimated effects that are slightly larger in magnitude than the column (1) estimate. However, conventional criteria would still judge them statistically indistinguishable from zero. When considered together, the three estimates suggest that the adoption of the 65-mph speed limit was not associated with a meaningful change in the statewide fatality rate. They contradict L&E's primary finding.

IV. DID THE 65-MPH SPEED LIMIT CAUSE REALLOCATIONS OF DRIVERS AND/OR POLICING RESOURCES?

Section III demonstrated that statewide fatality rates did not increase (and perhaps modestly declined) in states that adopted the 65-mph speed limit. Yet, Garber and Graham (1990) and Ashenfelter and Greenstone (2002) show that fatality rates increased on roads where the higher limit was introduced. How can these findings be reconciled? The increased fatality rate on rural interstates must be counterbalanced by a decline on other roads in adopting states. Are L&E correct to argue that the decline is due to driver and trooper reallocations induced by the 1987 adoption of the 65-mph speed limit?

Here I identify where the countervailing decline occurred and test whether it can be causally related to the 65-mph limit. The alternative is that it is due to unobserved factors that are unrelated to the speed limit on rural interstates. To preview the findings, the results suggest that the adoption of the higher speed limits is not associated with either of the reallocations. This removes the empirical basis for the connection between the higher speed limit on rural interstates and the reduced fatality rates on roads where the speed limit was unchanged. The logical conclusion is that the effect of the 1987 increase to 65 mph can be determined by examining rural interstates in isolation from other road types.

Driver Reallocation Conjecture

L&E claim that the increased speed limits on rural interstates induced drivers to switch to these roads. Their Table 1 shows that between 1986 and 1988, VMT on rural interstates grew faster in adopting states than in nonadopting ones or on other categories of roads within adopting states. To probe this result more rigorously, I use data from the entire 1982-1990 period and regression adjust VMT for observable determinants.

Table 2 presents the results from regressions where the dependent variable is the natural log of VMT The parameter of interest, again called policy parameter, is the regression coefficient from an indicator that is equal to one for observations from rural interstates in the years and states when the 65-mph limit was in force. All specifications include a full set of state by road type fixed effects, year by road type fixed effects, the state unemployment rate, and an indicator for whether a state seat belt law was in force. The year by road type indicators capture transitory determinants of VMT that are common to a road type in adopting and nonadopting states. The effect of the unemployment rate and the seat belt law are allowed to vary by state and road type.

For now, focus on the first panel where the sample is limited to observations from rural interstates. Here, the policy parameter tests for a mean shift in VMT on rural interstates in states that adopted the 65-mph speed limit relative to states that retained the 55-mph limit. The estimate in column (1) indicates that the relative change in rural interstate VMT was -1.7% (measured in log points). The parameter estimate's sign runs counter to the conjectured reallocation, but it would not be judged statistically significant by conventional criteria. In column (2), state by road type-specific, linear time trends are added to the specification. The estimate from this specification is now positive (2.7%) but remains statistically indistinguishable from zero.

The sample is enlarged to include observations on VMT from rural noninterstate, urban interstate, and urban noninterstate roads in the second, third, and fourth panels, respectively. The addition of these observations allows for another layer of comparisons--between road types within a state. Although L&E did not specify the road types from which they expected drivers to substitute to rural interstates, a natural assumption is that the increased traffic would come from other roads in the same region, that is, rural noninterstates. In contrast, urban roads are unlikely to be a substitute for rural interstates because they are located in entirely different regions of a state. In these specifications, the policy parameter captures the component of variance specific to rural interstates (relative to other roads in the same state) in adopting states (relative to nonadopters) in the years after 1987 (relative to earlier years).

The estimates fail to support the hypothesized increase in VMT on rural interstates in adopting states, regardless of whether the comparison is to rural noninterstates or either of the urban road types. In all three panels, the column (1) point estimates are actually negative, suggesting a substitution away from the roads with increased speed limits. However, conventional criteria would only reject zero when the comparison is to urban noninterstate roads. In column (2), none of the estimates can be distinguished from zero in a statistical sense. It is apparent that the many different comparisons that underlie these estimates have failed to produce any evidence that the higher speed limits caused a reallocation of traffic.

STATE POLICE REALLOCATION CONJECTURE

This subsection develops and implements a test of the state police reallocation conjecture. L&E argued that the increased speed limits on rural interstates allowed the state police, who are responsible for patrolling these roads, to reallocate resources from speed enforcement to unspecified activities that have a greater impact on fatality rates. Because direct evidence on the allocation of state troopers' time is unavailable, L&E presented anecdotal support for this conjecture. A logical prediction of this theory is that the reallocation of state police resources should affect fatality rates on roads where the state police patrol, but not on roads where local police agencies have primary enforcement responsibilities.

Here I separately examine changes in fatality rates on the four component categories of the statewide total: rural interstates, rural noninterstates, urban interstates, and urban noninterstates. This analysis allows for the determination of the source of the decline in fatality rates that counterbalanced the increase on rural interstates. If this decline occurred on urban roads--particularly urban noninterstate roads--it cannot be causally related to a reallocation of state police because they have minimal enforcement responsibilities on these roads (National Research Council, 1984).

Table 3 presents separate regression estimates of the effect of the 65-mph speed limit on the natural log of the fatality rate (i.e., fatalities per 100 million miles) by road type. The table is arranged identically to Table 1, and the specifications are the same as the ones that underlie the estimates in that table.

The first two panels of Table 3 report the results from rural interstates and rural noninterstates, respectively. The first panel-reveals that the introduction of the 65-mph speed limit was associated with an approximately 30% increase in fatality rates on rural interstates. This finding is robust across all three specifications and is consistent with prior research. In contrast, the second panel reveals that the higher limit was not associated with a meaningful change in fatality rates on rural noninterstates.

The final two panels are illuminating. The point estimates in the third panel indicate that there was a decline in fatality rates on urban interstates in states that adopted the 65-mph limit. However, conventional criteria would judge this decline statistically indistinguishable from zero. The estimates in the fourth panel indicate that the higher speed limit was associated with a roughly 17% decline in fatality rates on urban noninterstate roads. This estimate is robust across the three specifications and is precisely estimated in each of them. Because the state police have minimal enforcement responsibilities on these roads, this decline cannot be attributed to trooper reallocations and, in turn, to the increased speed limits on rural interstates.

Some back-of-the-envelope calculations reveal that the increase in fatality rates on rural interstates and decline on urban noninterstates together explain the statewide decline. In particular, the multiplication of a road type's pre-1987 fatality rate by its percentage change estimate (from Table 3) and its fraction of total fatalities yields its contribution to the change in the statewide fatality rate. On rural interstates (urban noninterstates), which accounted for 5% (35%) of traffic-related fatalities, the fatality rate was 1.50 (2.10).

The multiplication of these numbers indicates that rural interstates contributed a +0.023 change to the post-1986 change in adopting states' statewide fatality rate; the analogous number for urban noninterstates is -0.126. The sum of these two numbers (i.e., -0.103) divided by the preperiod statewide fatality rate (i.e., 2.67) implies that these two road types reduced the statewide fatality rate by 3.7%. Interestingly, this figure is in the middle of the range of estimates presented in Table 1 and is similar to L&E's estimate!

V. CONCLUSIONS

At least three empirical regularities have emerged from this analysis. First, statewide fatality rates declined modestly in states that adopted the 65-mph speed limit on rural interstates. Second, this statewide decline resulted from a sharp increase in fatality rates on rural interstates and a large decline in fatality rates on urban noninterstates. Third, this article is unable to find any evidence that the higher speed limit induced either of the reallocations that L&E posited. Together these three results suggest that the statewide decline in fatality rates in adopting states was not causally related to the 65-mph speed limit.

L&E have contributed an important theoretical insight that all analyses of increases in speed limits should test. In the case of the 1987 increase in speed limits, however, it appears that the effect on fatality rates can be determined by solely examining the roads where the changed speed limit applied. On these rural interstate roads, fatality rates increased dramatically.

TABLE 1

Proportionate (Log) Effect of the 65-mph Speed Limit on the Statewide
Fatality Rate

 65-mph Adopting All States
 States
Sample Includes (1) (2) (3)

Policy parameter -0.012 -0.047 -0.037
 (0.025) (0.035) (0.045)
[R.sup.2] 0.996 0.995 0.996
State fixed effects Yes Yes Yes
Year fixed effects No Yes Yes
State-specific linear Yes No Yes
 time trends

Note: The entries in the policy parameter row are the regression
coefficients from an indicator variable that equals one for observations
from states and years when the 65-mph speed limit was in force on rural
interstates. All models control for the state unemployment rate and
whether a seat- belt law was in force; the effect of both of these
factors is allowed to vary by state. Heteroskedastic consistent standard
errors are reported in parentheses. The column (1) regression was based
on 360 observations, and column (2) and (3) regressions were fit on 423
observations.
TABLE 2

Proportionate (Log) Effect of the 65-mph Speed Limit on VMT, by Road
Type

 (1) (2)

Rural interstates
 Policy parameter -0.017 0.027
 (0.030) (0.025)
 [R.sup.2] 0.999 0.999
Rural interstates and
 rural noninterstates
 Policy parameter -0.067 0.045
 (0.044) (0.034)
[R.sup.2] 0.999 0.999
Rural interstates and
 urban noninterstates
 Policy parameter -0.044 0.065
 (0.043) (0.040)
[R.sup.2] 0.999 0.999
Rural interstates and
 urban noninterstates
 Policy parameter -0.081 -0.013
 (0.041) (0.041)
[R.sup.2] 0.999 0.999
State by road type Yes Yes
 fixed effects
Year by road type Yes Yes
 indicators
State by road type-specific No Yes
 time trend

Notes: The policy parameter is the regression coefficient from an
indicator that equals one for observations from rural interstates when
the 65-mph speed limit applied. All models control for the state
unemployment rate and whether a seat belt law was in force; the effect
of both of these factors is allowed to vary at the state by road type
level. Heteroskedastic-consistent standard errors are reported in
parentheses. In the top panel the regressions are based on 423
observations. The regressions in the second through fourt panels were
estimated on 846 observations.
TABLE 3

Proportionate (Log) Effect of the 65-mph Speed Limit on the Fatality
Rate, by Road Type

 65-mph Adopting States All States
Sample Includes (1) (2) (3)

Rural interstates
 Policy parameter 0.264 0.314 0.283
 (0.099) (0.160) (0.200)
 [R.sup.2] 0.876 0.821 0.859
Rural noninterstates
 Policy parameter -0.010 -0.021 0.006
 (0.031) (0.066) (0.095)
 [R.sup.2] 0.997 0.995 0.996
Urban interstates
 Policy parameter -0.113 -0.103 -0.248
 (0.122) (0.111) (0.140)
 [R.sup.2] 0.720 0.698 0.751
Urban noninterstates
 Policy parameter -0.169 -0.168 -0.173
 (0.055) (0.056) (0.071)
 [R.sup.2] 0.967 0.965 0.972
State by road type fixed Yes Yes Yes
 effects
Year by road type fixed No Yes Yes
 effects
State by road Yes No Yes
 type-specific linear
 time trends

Notes: The entries in the policy parameter rows are the regression
coefficients from an indicator variable that equals one for observations
from states and years when the 65-mph speed limit was in force on rural
interstates. All models control for the state unemployment rate and
whether a seat belt law was in force; the effect of both of these
factors is allowed to vary by state and road type. Heteroskedastic-
consistent standard errors are reported in parentheses. The column (1)
regressions are based on 360 observatios for rural interstates, rural
noninterstates, and urban noninterstates and 341 observations for urban
interstates respectively. Column (2) and (3) regressions were fit on 423
observations for rural noninterstates and urban noninterstates, 421
for rural interstates, and 404 for urban interstates. There are fewer
observations for the latter two categories of roads because there are
zero fatalities on some state by road categories in individual years and
the dependent variable is the natural log of the fatality rate. The
results are insensitive to setting the dependent variable equal to an
arbitrarily small value for these observations and including an
indicator in the model that equals one for them.

(*.) I thank Orley Ashenfelter, David Card, Ted Gayer, David Lee, Helen Levy, Enrico Moretti, Katherine Ozment, and Anne Piehl for valuable comments. Hilary Hoynes generously shared a data file. Michael Park provided superb research assistance. The Industrial Relations Section at Princeton University, the Alfred P. Sloan Doctoral Dissertation Fellowship, and the Robert Wood Johnson Foundation generously supported this research.

(1.) Rural (urban) roadways pass through geographic areas with a population of less (greater) than 5000.

(2.) I was unable to obtain data from the federal government for the years 1976-1981.

(3.) To access the data file and programs: FTP to irs.princeton.edu, login as anonymous, and use your e-mail address as the password. The files are located in the directory /pub/highways and can be downloaded.

(4.) This was determined through personal communication with Charles Lave.

(5.) Throughout Tables 1, 2, and 3, White-corrected standard errors are presented to account for the presence of heteroskedasticity (White, 1980).

REFERENCES

Ashenfelter, O., and M. Greenstone. "Using Mandated Speed Limits to Measure the Value of a Statistical Life." Working paper, University of Chicago, January 2002.

Garber, S., and J. Graham. "The Effects of the New 65 Mile-per-Hour Speed Limit on Rural Highways Fatalities: A State-by-State Analysis." Accident Analysis and Prevention, 22(2), 1990, 137-49.

Lave, C., and P. Elias. "Resource Allocation in Public Policy: The Effects of the 65-MPH Speed Limit." Economic Inquiry, 35(3), 1997, 614-20.

U.S. National Research Council Transportation Research Board. Fifty-Five, a Decade of Experience. Washington, DC, 1984.

White, H. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity." Econometrica, 48(4), 1980, 817-38.

RELATED ARTICLE: ABBREVIATIONS

L&E: Lave and Elias

MPH: Miles per Hour

VMT: Vehicle Miles of Travel

Greenstone: NBER, and Assistant Professor, Department of Economics, University of Chicago, 1126 E. 59th St., Chicago, IL 60637. Phone 1-773-7029012, Fax 1-773-702-8490, E-mail mgreenst@midway. uchicago.edu