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The effects of automobile recalls on the severity of accidents.

I. INTRODUCTION

The National Highway Traffic Safety Administration (NHTSA) reports in its 2009 annual report that in 2008, 37,261 people were killed in the 5,811,000 police-reported motor vehicle traffic crashes. More than 2.35 million people were injured, and 4,146,000 crashes involved property damage only (NHTSA 2009a). Most accidents were caused by drivers' mistakes or misbehavior. However, it cannot be underestimated that vehicle defects may play a role in causing accidents. With 20 million cars recalled during 2010 alone, the recent massive recalls by Toyota, and with the number of recalls consistently above 15 million during the last decade and a half, understanding the effects of recalls has become an important research and policy question. (1)

A safety defect is defined as "a problem that exists in a motor vehicle or item of a motor vehicle equipment that possesses a risk to motor vehicle safety, and may exist in a group of vehicles of the same design or manufacture, or items of equipment of the same type and manufacture." (2) To remove defective cars from the roads, the NHTSA requests vehicle manufacturers to recall them and fix the defects at no cost to the owners of the vehicles. The number of automobile recalls has sharply increased over the last two decades. Vehicle manufacturers issued 588 separate recalls involving 14.8 million vehicles in 2007, and the industry set a record of 30.8 million vehicles in 2004. Since then, the number has decreased and increased again. Toyota's recall crisis in 2010 has ignited sharp disputes over appropriate public safety policy, and the NHTSA has been criticized by lawmakers and car-safety groups for acting too slowly on complaints, while Toyota has been widely criticized by lawmakers and the public for hiding information on its vehicle defects. We believe that this puts the focus on the effectiveness of recall regulation: Are recalls effective in reducing accidental harm? If so, should our society spend more resources on this regulation? However, without quantitative evidence, any attempt to change public safety policies related to recalls is hard to defend. Clearly, if we find that recalls reduce accidental harm we can infer that manufacturers are putting on the road vehicles that are dangerous to the public, and that their systems to control the quality of their vehicles are passing the responsibility to find defects to the American drivers, something clearly unacceptable when happening in the numbers that we are seeing in the last years.

While vehicle recalls have been the object of study over the past two decades, most of that research has focused on particular aspects of recalls, such as their effect on demand, vehicle resale prices, firm valuation, liability verdicts, and initiation of recalls, rather than safety. (3) There is no quantitative evidence of the number of vehicle accidents caused by vehicle defects and how many potentially dangerous vehicles are on the U.S. roads everyday. (4) Furthermore, we do not know whether vehicle recalls are effective in reducing accidental harm. So far, there has been no empirical assessment of vehicle recall regulation related to safety.

There are a number of reasons why there are relatively few studies of the effect of recalls on safety. First, there is no direct link between recall, vehicle, and accident data, therefore researchers need to do this by themselves, and to analyze the effectiveness of recalls researchers should be able to identify potentially dangerous cars. Second, vehicles may have multiple defects, and recalls are issued over time. Therefore, even if an accident has been caused by a particular defect, we do not know which defect causes the accident. Third, defects have different levels of risks. Thus, it is very difficult to measure potential risks accurately and compare them. Fourth, there is no way to find out whether particular car owners have returned their cars to manufacturers to be fixed. Fifth, drivers' behavioral change is not observable before and after recalls. Sixth, the entire recall process is time consuming and very complicated. (5) Recently, Bae and Benftez-Silva (2011a) have developed a synthetic panel data model to investigate the effectiveness of recall regulation in terms of the number of accidents on the road. The basic argument of that work is that if the defects, which lead to recalls, directly or indirectly affect accidents, then one would expect recalls would lead to a reduction in the number of accidents. Their finding that indeed recalls reduce the number of accidents, complements our findings on the severity of those accidents.

This paper empirically investigates how recalls affect accident severity using publicly available accident and recall data from the NHTSA. There are two arguments suggesting that there would be a decrease in accident severity. First, behavioral response by drivers learning about the defect can make them more aware of the risks of driving the vehicle, and may induce greater care in driving, which reduces the harm if the defect leads to an accident, and greater care may also reduce the total number of accidents. The changed behavior persists until the driver has the defect repaired (if that is the case). Second, if the defect is a hazardous one, elimination of the defect may reduce the expected accident severity if a vehicle with the defect repaired is subsequently involved in an accident (even if the driver changes back to the level of care he exercised before learning about the defect through the announced recall).

The results of our analysis show that recalls reduce the severity of injuries in vehicle crashes. In particular, we find that if a recall for a new-year model is issued, then the severity of injuries of accidents continuously diminishes during the first year after the recall, something we do not find among cars not subject to major recalls. This is because defects are removed over time as drivers take corrective actions and possibly drivers increase their level of care until the defects are fixed. One clear policy implication is that both quick and timely recall actions should be taken and more detailed information on defects should be delivered to the owners of defective vehicles. Additionally, the government should make an effort to allow insurance companies to link, through the release of the Vehicle Identification Numbers (VIN) of recalled cars, the information on recalls to insured vehicles, prompting drivers to fix the problems on their cars to avoid higher premiums, and can also follow suggestions by some policy makers to include recall information on the registration renewal information that Departments of Motor Vehicles (DMVs) send to drivers. More broadly, given the large number of recalls and our findings, the government should consider reviewing the quality control system of car manufacturers who are putting potentially dangerous products on the roads in record numbers.

Section II of the paper presents a theoretical discussion on how recalls can reduce accidental harm, and discusses our identification strategy. Section III introduces the recall system and recent recall trends. The estimation strategy, using an ordered probit model, is discussed in Section IV, along with a discussion of our data and some summary statistics. Section V discusses estimation results, and our concluding remarks are presented in the final section of the paper.

II. VEHICLE RECALLS, SAFETY, AND MODEL IDENTIFICATION

This section studies two connected questions, and how they relate to our empirical analysis. First, we need to analyze the conditions under which recalls are efficient from the point of view of social welfare. Second, we need to analyze whether recalls reduce accidental harm and how recalls affect the distribution of injury severity of accidents.

The efficiency question needs to connect the marginal benefits of recalls with their marginal costs, where the former are measured by the monetized value of savings thanks to the possible reduction of the severity and the number of accidents resulting from an additional recall, while the marginal costs are the extra monetary costs of the additional recall. Recall costs can be comparatively easy to compute (even though costs linked to the loss of reputation and the consequences on future sales can be more difficult to calculate); however, the benefits side is more complex since the value of life is often involved in the calculation (Ashenfelter and Greenstone 2002; Kaplow and Shavell 1999; Posnerwer 1998).

Assume that the variable (H), representing accidental harm, properly reflects the value of life. Suppose that n is the number of accidents caused by defects, L is the injury severity per accident, and x is the variable that measures recall activity (0 [less than or equal to] x < [infinity]). For simplicity, assume that the marginal costs of an additional recall activity are constant (c). Then, the social costs of accidents are given by (6)

SC = H(x) + cx = n(x) x L(x) + cx.

To minimize the social costs of accidents, the marginal benefits should be equal to the marginal costs. Thus, the efficient level ([x.sup.*]) of recall activity can be found by solving the following equation which results from taking first derivatives:

H'(x) = -c [??] n'(x) x L(x) + n(x) x L'(x) = -c.

Given positive recall costs (c), recalls are not welfare-improving unless they reduce accidental harm. This means that there should be a reduction in accidental harm from either the reduction in the number of accidents (n'(x) < 0) or (and) the reduction in the severity of injury (L'(x) < 0). Bae and Benitez-Silva (2011a) show that recalls reduce the number of accidents, and this paper focuses on whether recalls reduce the severity of injuries (L'(x) < 0). Notice that a reduction in the number of accidents, and/or a reduction in the severity of those accidents does not guarantee that the level of optimal recalls from a societal perspective will be the actual level we observe, given that social costs are unlikely to be internalized by manufacturers, and the benefits for them are more likely to be linked with reputation and assessment of the consequences on future profits, not with the reduction of accidental harm. This suggests an important role for regulation and policy, which in part already exists, but that has not been at the forefront of the discussion given the lack of quantitative evidence on the benefits of recall activities.

The second question, however, is tricky to answer if the probability that a defect causes accidents is believed to be very small. Many industry people and some experts then believe that recalls do not save lives. (7)

To analyze this issue, we present a simple discussion which naturally leads to our identification strategy in the empirical analysis. Suppose that there is only one defect for a particular vehicle model. Also suppose that the manufacturer does not know the potential risk of the defect when it sells the vehicle to the consumer. When the consumer purchases the car, she assumes that the car is safe. Given this safety evaluation, she will choose her optimal levels of care when driving, [z.sup.*.sub.i], (0 [less than or equal to] [z.sub.i] [infinity]) such that her utility is maximized. In this situation the consumer will only know about the defect when the manufacturer finds it and issues a recall. Thus, there will be no change in her level of care until that recall is issued. This is illustrated as a horizontal line in the expected level of care before t = 0 in Figure 1. Suppose that a recall is announced at t = 0. Then, she may take the car to the dealer right away and fix it, or fix later and raise her level of care ([z'.sub.i]) until the defect is being fixed. Once the repair takes place, her level of care will return to the initial level ([z.sup.*.sub.i]). Therefore, the consumer's expected level of care ([z.sub.i]) diminishes and the probability that the car is being fixed (p([theta])) increases during the time period between t = 0 and t = j. (8) The time period could be a year or more than a year, depending on the recall and its risk.

Now, consider accidents that occur after the recall issuance. If the defect had not played any role in causing the accidents, then the severity of injuries would rather increase over time, at least up to t = j. This is because drivers reduce their levels of care as their cars are being fixed and they adjust their driving to a potentially hazardous situation. If the recall failed in terms of affecting neither drivers' levels of care nor the likelihood of taking corrective action, then the average severity level would not change between time 0 and time j. If these were true, then there would be no correlation between the severity of injuries and when the accidents occurred over time. If the recall were effective, then the severity of injuries would decrease at least up to time j. We do not know whether drivers raised their levels of care or took any corrective actions before the accidents or when the drivers returned to their original levels of care, therefore the exact length of the process analyzed is a random variable.

This discussion provides an identification strategy given the accident data we analyze. We focus on the accidents of a particular vehicle model. We check when the first recall for a year model was issued, and then observe when the accident occurred. For instance, we look at the Ford Taurus 2007-year model, that had its first recall in March 2007. Then, we observe an accident in which this vehicle model was involved, and when the accident occurred. If the accident occurred, say, in May 2007, then the accident occurred 2 months after the recall was issued. We observe all the accidents with the same vehicle model and observe when they occurred. Given our previous discussion, in order to argue for a role of recalls in the reduction of the severity of accidents, the average severity of accidents that occurred within 2 months must be greater than the average severity of accidents that occurred after 3, 4, or more months. This is because the probability that the defect of a particular vehicle is eliminated before the accident increases over time. (9) Accordingly, the severity must diminish over time if the recall is effective in reducing accidental harm. Thus, the severity would be negatively associated with the months passed after the recall. Therefore, we can expect that the longer the time since a recall issuance is, the lower the severity of injuries of an accident is, at least during a relatively short time (about a year in our empirical application) after the recall. Notice that this variable is identified through the variation in the sample of the time between the recall and the accident, and that is separately identified from a vintage control of the number of months between the launching of a model and the time of the accident, given the variation of time between the launching of the model and the recalls. Additionally, we would expect that in a sample of accidents by cars not subject to recalls we should see no significant decrease in the severity of accidents over time. Our empirical analysis tests these hypotheses.

III. THE U.S. RECALL SYSTEM AND TRENDS

The NHTSA has the authority to require vehicle manufacturers to issue recalls, whenever their vehicles possess any potential safety-related defect that could cause loss of vehicle control such as steering, braking, tire damage, or repeated stalling. However, the Federal Motor Vehicle Safety Standard regulates the vehicle industry, and manufacturers are asked to issue recalls if serious accidents occur or are expected because of potential defects. However, the manufacturers can initiate them whenever they find critical defects that might cause serious accidental harm. In that case, the manufacturers report detailed information on the corresponding defects to the NHTSA and begin to take actions for recall issuance. In many cases, the NHTSA may find the defects first (maybe because of complaints reported from owners of defective vehicles) and require the manufacturers to issue recalls, followed by its own investigation. The manufacturers may comply with the requirement and issue recalls. If they do not agree with the government's recall decision, they can resolve the disputes in court.

The owners of the vehicles may report complaints to either the manufacturers or the NHTSA. It does not matter whether the owners are injured or not in accidents. If the accidents occur and the defective problems are considered as a cause of the accidents, they can file a defect report directly to the NHTSA. Once the recalls are issued, they have to take their vehicles to the places assigned by the manufacturers to be repaired. The entire recall process is lengthy and time consuming, thus, it may take several years. (10) Once the recalls are announced, the manufacturers send notice letters to their customers and also announce them through the media so that the vehicles should be brought in and the defects fixed. After that, the Recall Management Division, part of the NHTSA, monitors the post-recall process. After the recalls are issued, then it may take several years again to finish all corrective procedures because it depends upon the vehicle owners. If the owners' addresses change and they do not notify of such a change, then there is no way for the manufacturers to send letters. The NHTSA requires manufacturers to submit "Quarterly Recall Reports" that contain detailed corrective actions in accordance with Federal Regulation, 573.6.

The recall system began its operation in 1966. Since then, the number of vehicle recalls has increased over time (Figure 2). In 1966, 58 recalls were issued, and by 2008 the number of recalls had increased to 684. The increase has been particularly sharp since the mid 1990s, and in the graph we can see the number of hazardous recalls but only up to 2001 when the government stopped reporting the hazard level of recalls. (11) Since each recall involves a different number of units, we can plot the average number of units per recall over time. Figure 3 shows the annual average units per recall. In 1981, a large number of vehicles were recalled. Other than that the average number of units per recall has increased during the 1990s and then decreased during the 2000s. For example, more than 58,000 vehicles per recall on average were issued in 1996. Since then, the number has decreased. In 2009, the average unit per recall was 33,000. Additionally, during the late 1990s and the early 2000s, there was a sharp increase in equipment recalls. In the 1990s hazardous recalls tend to be larger than the average recall.

Figure 4 shows the proportion of all total vehicles recalled initiated by domestic manufacturers, which up to the mid 1990s had fluctuated considerably every year moving from highs above 90% to as low as 50%. Since then, we can observe a sharp decline in the proportion of units recalled initiated by domestic manufacturers, a trend that reached a low point just above 40% in the last few years. In part this reflects the growing importance of foreign manufacturers in the U.S. car market, but also their push toward massive production which seems to be coming with a lowering of their quality, reaching a pinnacle with the ongoing recalls by Toyota. It is interesting to emphasize that a larger proportion of the recalls issued by foreign manufacturers are considered hazardous compared with domestic manufacturers. It is also important to emphasize that in Figure 4, we are not accounting for some very small manufacturers that recall very small number of vehicles, but the recalls represented in the figure account for almost all the vehicles actually recalled.

Figure 5 shows the evolution of the proportion of recalled vehicles that are mandatory, meaning that they have been initiated by the government and not the manufacturers. (12) This proportion has fluctuated considerably over time, and since the early 1990s, has consistently reached 60% of the vehicles recalled. Recalls can be quite costly for manufacturers and in some cases they seem reluctant to initiate the recall as they balance the cost and benefits of delaying action. Interestingly, if we just look at the proportion of recalls irrespective of number of vehicles involved (figure not shown), the proportion of mandatory recalls is never above 40%, and usually fluctuates between 20% and 30%, which indicates that mandatory recalls are usually also those with large number of units involved.

IV. ESTIMATION STRATEGY AND DATA

A. Empirical Model Setup

Given the nature of the data that we have access to, we can only analyze the effects of recalls if accidents of particular models actually occur. In our analysis, we use Police Accident Reports (PAR) provided by the NHTSA (1988-2007) through the General Estimates System (GES) which began operations in 1988. The GES obtains its data from a nationally representative sample selected from the estimated 6 million police-reported crashes which occur annually. (13) A nice feature of this data is that the system contains information on the severity of injuries of the people involved in the accidents. At the same time, it also contains information on vehicle models, and vehicle-year models, that are involved in the accidents. The latter information is the key that allows us to connect accidents data to the independently collected recall information, since recalls are specific to vehicle models. (14)

We want to see if recalls affect a person's injury level, conditional on an accident occurring. Therefore, the person i's injury level is [y.sup.*.sub.i], which is the dependent variable in our model. In fact, we do not have information on the exact injury level for the person. Fortunately, the GES has a categorical variable, [y.sub.i], indicating the severity of injury of a person in an accident. The variable is based on an unobserved continuous variable, [y.sup.*.sub.i] [member of] R. The variable appears as an ordered rating scale, and we use this information to measure accidental harm. Since the dependent variable is discrete and ordered, the ordered probit model is used for our analysis.

A number of reasons can explain the differences in the severity of injuries of individuals involved in accidents. We categorize the variables into four major determinants, and write

(1) [y.sup.*] = f([D.sub.i], [V.sub.i], [E.sub.i], [R.sub.i] | [A.sub.i] = 1)

where [D.sub.i] represents driver characteristics, [V.sub.i] refers to vehicle characteristics, [E.sub.i] indicates environmental factors, and [R.sub.i] stands for regulation factors including vehicle recalls. With this function being conditional on the accident that has happened, [A.sub.i] = 1. The dependent variable takes five values (0, 1, 2, 3, 4) corresponding to no injury, possible injury, non-incapacitating injury, incapacitating injury, and fatal injury (of drivers, passengers, or pedestrians). The ordered probit model is constructed as follows: (15)

(2) [y.sup.*] = [beta]'X + [epsilon], [epsilon]|X ~ N(0, 1)

(3) [y.sub.i] = [beta]'[X.sub.i] + [[epsilon].sub.i]

Let [[kappa].sub.1] < [[kappa].sub.2] < [[kappa].sub.J] be unknown cut points and define

(4) y = 0 if [y.sup.*] [less than or equal to] [[kappa].sub.1]

y = 1 if [[kappa].sub.1] < [y.sup.*] [less than or equal to] [[kappa].sup.2]

y = 2 if [[kappa].sub.2] < [y.sup.*] [less than or equal to] [[kappa].sup.3]

y = 3 if [[kappa].sub.3] < [y.sup.*] [less than or equal to] [[kappa].sup.4]

y = 4 if [y.sup.*] > [[kappa].sub.4].

[epsilon] is normally distributed across observations. The conditional distribution of y given X is

(5) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

The parameters [kappa] and [beta] are estimated by maximum likelihood (Gould and Sribney 1999). For each observation i, the log-likelihood function is

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

B. Recall Variable and Data Structure

We use 3 years of accident data from the GES, with all the detailed information on the accidents that occurred in 2005, 2006, and 2007 on U.S. roads. Each observation is by a person who is involved in an accident, either as a driver, a passenger, or a non-occupant, such as a pedestrian. Each observation shows the injury severity of that person and contains information on the vehicle related with the person. If the person is a driver, then the vehicle is her car. If she is a pedestrian, then the information is about the vehicle that injured her. However, the accident data does not contain any recall information, and there is no direct link between accidents and recalls. Therefore, we need to create a recall variable using data from the NHTSA for the 2005 to 2007 period. (16) We obtain information on each vehicle model's recall history, including the date, month, and year of each recall announcement for the particular vehicle-year model. (17) Since the cross-sectional accident data include the date that the accident occurred and each accident has information on the vehicle maker and the vehicle model involved, we can find when a recall for the vehicle model involved in the accident was issued.

We define the main recall variable of interest as "the months that have passed after a recall issuance," which appears with the name, RECALL, in the tables. For instance, if a recall for a particular year model is issued in January and a vehicle of this year model is involved in an accident next month, then the value of the variable is one. If the recall is issued in January and the accident occurs in March, then it is two. We measure the months elapsed during the first year after the issuance of the recall, and the maximum value of the recall variable is therefore 12. Having this definition, we see the relationship between the months elapsed and the severity of injury of the accident.

Vehicle recalls have a number of characteristics that make any empirical analysis very complex and require a number of important simplifications. For instance, each vehicle model contains multiple recalls, and some recalls are issued before and some after accidents occur. Furthermore, we do not know if a particular vehicle involved in the accident is the vehicle included in the recall. Thus, our estimation strategy requires us to eliminate the accidents that we cannot link to a particular recall. We enumerate here the main problems and the criteria we use to include or not the accident in our sample:

* Many vehicles may contain multiple defects, and manufacturers often issue more than one recall for a particular vehicle model. If two recalls were issued in a relatively short time period, it is hard to know which recall affected the accident, if it did, but since this happens quite often, if there are two or more recalls issued for a particular vehicle model within 3 months, we consider them as a single recall. Otherwise, we remove accidents with vehicle models that have multiple recalls within 4 and 18 months after the first recall, unless one of the recalls is minor (includes less than 10,000 units of that year model) and with some other exceptions that we will discuss below.

* We also require that the owners of the corresponding vehicle models should be able to respond to the issuance, but it is much harder for used car owners to know about recalls given that only if they are in the same State and do not change addresses will they be able to be linked. Furthermore, even for new car owners, if they change their addresses, then the recall notice might not reach them. Thus, we include only vehicle models launched in the 2005-2007 period we analyze in the data set, to all but guarantee that owners will receive the information.

* Given that we include only new-year vehicle models, the first recall should be issued within the first year, and the accident can occur up to a year after the recall was issued.

* The hazard levels of different recalls can be quite different, but for recalls after 2001 we do not have this information. Thus, we include accidents with vehicle models whose correction rates are at least 60%. The higher correction rate indicates that the defect is considered a riskier one. Notice that this correction rate is for vehicles already sold to individuals, it does not include vehicles not delivered to individuals and therefore may be already fixed by the manufacturer or the dealers. This justifies the use of the correction rate as a selection criteria. We discuss the sensitivity of our results to this criteria. It should not be surprising that if we take all recalls independent of correction rates the effects of recalls on severity will be smaller since many drivers will not know about the recalls yet and will not have taken them to be fixed. This selection criteria is in fact connected with the fact that we use new vehicle models since these vehicles are the ones more likely to get safety recalls corrected (Hoffer, Pruitt, and Reilly 1994; Rupp and Taylor 2002).

* Recalls often contain very different numbers of units. Some recalls contain a few hundreds, while others contain millions. In our analysis we include only recalls of more than 10,000 units.

Even after eliminating vehicle models following the criteria discussed above, approximately 700 observations are included in our sample.

C. Summary Statistics

Table 1 shows the severity levels of individuals involved in accidents over the 3 years we analyze. The first column shows the severity of accidents for new year models (2005, 2006, and 2007) that have their first recalls over these 3 years. Each accident occurred after its first recall was issued. More than 65% of individuals are not injured in accidents. Possible injury accounts for 13.55% of the accidents. Non-incapacitating and incapacitating injury represents 13.12% of the accidents. Less than 1% of individuals experience fatal accidents. The second set of columns shows the severity levels of the accidents, after excluding major recalls. Thus, the first set represents what we call recall accidents, while the second set shows non-recall accidents. (18) There are no major differences in the distribution of severities, except that as expected the accidents on cars subject to recalls have a slightly higher percentage of injuries. We would not expect, however, huge differences, so it seems we do not have a selection problem from the sample restrictions explained in the previous subsection. However, given the small number of fatalities, the results regarding this event should be taken with caution.

Other independent variables are included along with the recall variable in order to control for other sources of variation that can explain the severity of accidents. Drivers' behavior (or characteristics) is one of the most important factors that might affect the severity of injuries. To control for this, [D.sub.i] includes sex, age, whether any safety equipment was used, and whether alcohol was involved at the time of the crash. [V.sub.i] includes the variables that are not related to the vehicle defects, such as vehicle size, the vehicle role in the crash, and whether there were any contributing factors related to the vehicle. [E.sub.i] includes environmental factors surrounding the accident. [R.sub.i] includes recalls and speed limits. The definitions of the variables and their descriptions can be found in Table 2.

It is interesting to discuss some of these variables of interest. [RESTRAINT.sub.i] encodes what is documented on the PAR regarding occupant use of available vehicle restraints (i.e., lap and/or shoulder belt, child safety seat, and motorcycle helmet). About 12% of persons do not use any devices, while 88% of them wear a lap or shoulder seat belt. (19) With this information we construct a dummy variable, which takes the value of one if the person uses any one of the protective restraints. Therefore, we expect a negative relationship between the dependent variable and this variable. [ALCOHOL.sub.i] is a binary indicator that indicates whether alcohol was used by the person involved in the crash. [MOTORIST.sub.i] indicates the role of this person in the accident. If the person is a motorist, then it is one. If she is a non-motorist, then it is zero. Assuming that pedestrians are injured more severely conditional on being involved in accidents, a negative relationship is expected. To account for vehicle factors, the binary indicator [AUTOMOBILE.sub.i] is included because the degree of severity might be different, not because of vehicle defects, but because of vehicle non-defective factors, so it is important to distinguish between automobiles, motorcycles, light trucks, etc. [FACTOR.sub.i] indicates whether there were any vehicle factors that might have been the cause of the crash. The possible factors include tires, brake system, steering system, suspension, power train, exhaust system, and so on. The PAR data show whether one of these factors could have caused each accident. However, we do not know if they are coming from defects or just simply maintenance problems.

[SPEED_LIMIT.sub.i] shows actual posted speed limit in miles per hour. Half of the accident reports do not contain information on vehicles' travel speed at the time of crash, therefore, instead of missing many observations we include the speed limit, the maximum being 75 miles/hr and the minimum is 5. Given the nature of accidents that occurred in the parking lots or alleys we remove them from our sample. Regarding environmental factors, [ROADWAY.sub.i] identifies the location of the first harmful event. This is a dummy variable, and if the vehicle is on a roadway it takes the value 1. If the vehicle is off a roadway (or shoulder) or parking lane, then the value is 0. [STRAIGHT_ROAD.sub.i] identifies the horizontal alignment of the roadway in the immediate vicinity of the first harmful event. If the roadway is straight, then the variable is 1, otherwise it is 0. [GOOD_WEATHER.sub.i] measures the general atmospheric conditions. If there are no adverse conditions, then the value is 1. If it is rainy, sleety, snowy, foggy, or a similar poor condition, then the variable has the value of 0.

An important variable is [VINTAGE.sub.i], which measures the months between the October of the previous year in which the model was initially launched in the market and the time of the accident. For instance, if an accident occurred in January, the involved vehicle must have been purchased within 3 months. (20) If the accident occurred in December next year, then it must have been purchased during the last 15 months. The variable can take a value as high as 27 if a vehicle was recalled in December of the year in which it was launched, and the accident happened in the following December.

We present the summary statistics in Tables 3 and 4. Table 3 presents the sample of accidents linked to recalled vehicles, and Table 4 for those linked to vehicle models not subject to major recalls. In Table 3, the total number of observations is 701. The dependent variable, [SEVERITY.sub.i], has a mean of 0.6505, this means that the large majority of accidents have neither severe injuries nor fatal injuries. The mean statistics for the explanatory variables reveal that the average age in our sample of the individuals involved in accidents is 37.55. The number of males is larger than the number of females and most people have used some kind of restraint system. We also see in the table that only about 6.5% of accidents involve alcohol, so in a large majority of accidents intoxication was not a factor. Although not reported in the table, 69.8% of people were the drivers, while 27.92% were the passengers, and almost 97% are either drivers or passengers. Regarding the vehicle type, 51% of the accidents involved automobiles. Vehicle contributing factors are reported by policemen when they thought these were the possible causes of the accidents. However, we do not know whether the factors really come from the defective parts that brought about recall issuance. Only 3.1% was considered to have had possible contributing factors.

The key recall variable, [RECALL.sub.i], has an average of 7.06 months. Therefore, the accidents in the sample occurred on average 7 months after the first recalls were issued, and given the value of the [VINTAGE.sub.i] variable the accidents occurred on average 15 months after they were launched. Regarding speed limit, the average speed limit was 45 miles/hr. This is because the accidents in the sample occurred on the local streets as well as highways. Many environmental factors are considered. Most accidents occurred on local roads, on straight roadways, and when there were no weather-related problems. The average number of occupants in cars involved in the accidents in the sample was 1.48, which indicates that most drivers were alone in their vehicles at the time of crash.

In Table 4 we show the summary of the observations linked to vehicles not subject to major recalls. The number of observations is much higher at over 12,300. The main differences that we observe between the two samples is that the non-recalled sample is composed of a lower percentage of automobiles and more SUVs, light trucks, and other trucks, and there is a slightly longer time between the launching of the model and the accidents.

V. ESTIMATION RESULTS

The first set of estimation results is shown in Table 5. We present four models, MODEL 1 controls for the [RECALL.sub.i] measure but omits the variable [VINTAGE.sub.i], while MODEL 2 includes it because we are interested in assessing the consequences of controlling for the number of months the vehicle has been on the road, which could potentially explain the changes in the severity of the accidents. The two variables are separately identified as we explained above because of the variation in the sample across vehicle models from the time of the launching of the car to the time of the accident, and the independent variation from the time of the recall to the time of the accident. We also present a third model MODEL 3 which only controls for the vintage measure and leaves out our main recall control, to explore the possibility that the vintage effect could overwhelm any effect of our main variable of interest. We then compare the fit of the models using a pseudo-[R.sup.2] measure and the Bayesian Information Criteria (BIC), a scalar measure of fit, which is widely used to compare non-nested models (Long and Freese 2001). The pseudo-[R.sup.2] weakly supports MODEL 2, while the BIC is strongly in favor of the model without the vintage variable. Given their significance and interpretation, we prefer to show all results. (21) We also show another set of results, labeled MODEL 4, using the very different sample of accidents not linked to vehicle models subject to major recalls. For this set of accidents we can only control for the vintage effect. As we hypothesized earlier, if we find a significant and negative vintage effect with this sample any similar results in the recall sample would suggest that the recall variable was picking up a vintage effect and therefore we would not be able to convincingly argue that the effect on severity was linked to recalls.

Most of the signs across specifications are what we expected. (22) In Model 1, the severity of injuries decreases over time after recall issuance, and the coefficient is significantly different from zero at the 5% significance level. Therefore, the more months pass after a recall issuance, the lower the severity of injuries is. (23) With the second model, we reach the same conclusion and the recall variable is still significant although a bit smaller in magnitude, even though the variable, VINTAGE, is also negatively associated with the dependent variable but the effect is small and not statistically significant. Thus, after controlling for the vintage effect we still see the decrease in the severity of injuries over the first year. This reinforces our finding that recalls reduce the severity of injuries in the time period we analyze.

However, we could still wonder whether the vintage and the recall effects are separately identified, even if we have argued that independent sources of variation suggest theoretical identification of the model. That is why we present the results from Models 3 and 4. In MODEL 3, we only include the vintage effect, and while it becomes negative and significant at the 10% level, the coefficient decreases in magnitude considerably, and so does the fit of the model, suggesting that the recall variable certainly belongs in the model and captures variation that the vintage measure misses. In fact the vintage variable could be spuriously significant in this specification because of its correlation with the recall variable. To check this conjecture we estimate MODEL 4 using the sample of accidents not linked to major recalls. Here the vintage effect all but disappears, and while still negative the coefficient is very small and highly insignificant, showing that the recall effect on severity is not a vintage effect but a true relationship that links recalls with a decreased severity of the accidents of the vehicles. (24)

Regarding the other explanatory variables, the older the person is, the higher the severity is, while gender does not affect the severity of injuries. If a person uses any protective restraints, then she is injured less. Non-drunken persons are injured less. Regarding the variable, MOTORIST, motorists are less injured, while non-motorists, such as pedestrians, are more severely injured. Vehicle characteristics do not seem to affect severity much. While this might not be true in general as shown by the significant effects in MODEL 4, but when only new-year models are involved in accidents, this is plausible. Most environmental factors, except GOOD_WEATHER, appear not to be significant; this is probably because the data is constructed with only new-year models. When there are bad weather conditions, people are injured less.

Given the difficulty of interpreting the coefficients discussed above, Table 6 reports the marginal effects for all explanatory variables in MODEL I. The marginal effects for the categorical variables, such as the recall variable, explain the slopes of the probability curves at the point intersection with the vertical line of the average months (7.05) after recall issuance in the sample. This implies that for the average person as one more month passes after a recall issuance, the predicted probability of no injury increases by 1.31%. It also decreases the predicted probability of an incapacitating injury by 0.37%, and the probability of fatal injury by 0.03%. The marginal effects for the dummy variables are explained by the change in the predicted probability for a change in [x.sub.k] from 0 to 1. For instance, wearing protective devices, such as seat belts, increases the probability of no injury by 33% and decreases the predicted probability of an incapacitating injury by 13.8%, and of fatal injury by 2.06%. Thus, wearing seat belts has substantial impacts on safety, which is clearly consistent with most of the literature on seat-belt laws.

It is interesting to analyze the individual predicted probabilities with the different months after a recall; we show this in Tables 7a and 7b corresponding to model specifications 1 and 4. In Table 7a, if an accident occurred this month and the first recall was issued in the previous month, then the predicted probability that the person does not have any injury is 0.5741. For the person who is involved in an accident this month and her vehicle had a recall 12 months ago, the probability is 0.7187. The probability that the accident results in a non-incapacitating injury goes down from 17% to 10.77%, and the probability of resulting in an incapacitating injury goes down from 7.97% to 3.73% during the year after the recall. Finally, the probability of resulting in fatal injury also goes down (0.0054 vs. 0.0016). The last two results, however, should be taken with caution, given the small number of observations with these major injuries that we have in the data set of accidents linked to major recalls. Table 7b presents the same exercise but using MODEL 4 and the effect of the vintage variable, and not surprisingly all the probabilities are essentially unchanged as the cars involved in accidents grow older. We show these results graphically in Figures 6-8, which bring home the point that the recall effect is very strong, and the vintage effect essentially non-existent.

VI. CONCLUSIONS AND POLICY IMPLICATIONS

This paper analyzes the effects of recalls on vehicle safety in the United States, and in particular, we investigate whether recalls affect accidental harm measured by the degree of severity of the accidents. Our results show that recalls reduce the severity of injuries of individuals involved in motor vehicle accidents. We find that if a recall for a new-year model is issued, then the severity of injuries of accidents continuously diminishes during the first year after the recall. This can be because defects are removed over time but also (and) because drivers may increase their level of care until the defects are fixed. Our quantitative findings show that after recall issuance as time goes by, the predicted probability that a person does not have any injury increases, and the probability that a person has significant or fatal injuries becomes smaller, as the number of months passed increases. Because of data limitations, we have only included new vehicle models with one valid recall in the year and a half after the original recall, but given this evidence, we can say that recalls are effective for new-year models. All this shows that defective cars linked to serious accidents are put on the road every year by manufacturers and that an overhauling of the recall system and the quality control of new automobiles should be considered by policy makers. (25)

Given the need to know about a recall in order to act on it, every effort should be made to make owners aware of the possible defects of their vehicles. For example, in the year 2001, the IIHS (Insurance Institute for Highway Safety) submitted a petition to the NHTSA to ask for more information release. The petition was for inclusion of VINs in defect and noncompliance information reports. The institute insisted that if NHTSA were provided with the VINs of recalled vehicles at the beginning of recall issuance, drivers would know immediately whether they were driving potentially unsafe vehicles, and the information could even be taken into account by insurance companies when pricing insurance. This is especially true when customers purchase used cars, given that people do not know whether the used cars that they want to purchase were subject to recalls. Table 8 shows two recalls issued in 2005 and their correction rates quarterly reported by two major car makers. As this example illustrates, correction rates are much higher when recalls contain highly risky defects and they are issued within a year. Thus, both appropriate risk evaluations on risks and responsive actions are very important (see Bae and Benitez-Silva (2011b) for a more detailed discussion).

For a long time manufacturers have resisted any change that could lead to more awareness regarding recalls or affect correction rates (like asking the DMVs to include recall notices with the registration renewals of vehicles), arguing that they would result in a substantial administrative burden, but with unclear effects on safety. However, producing safer and higher quality cars should be much more important even to them. Over the last months of 2009 and the beginning of 2010, Toyota has recalled more than 6 million vehicles in the United States (9 million vehicles worldwide) because of acceleration problems and braking flaws. Regulators have linked 52 deaths to crashes allegedly caused by accelerator problems. According to a report, (26) Toyota recalls could cost up to $2 billion, with $1.1 billion for repairs and $0.9 billion in lost sales. As of March 2010, at least 89 class-action lawsuits have been filed against Toyota, which could also cost it at least $3 billion. If Toyota had taken recall actions in a more timely fashion and the important recall information had been immediately released to the public, then the costs would be much smaller. This is especially true when recalls are effective in reducing accidental harm.

Along with the work by Bae and Benitez-Silva (2011a) that finds that recalls reduce the number of accidents of particular models driven by particular types of drivers, we provide a first step toward understanding the effects of recalls on safety, the importance of which has increased given the prominence, size, and costs of vehicle recalls in the last years. Further research is needed to draw a more complete picture of the effects of recalls on safety, through analyzing the benefit-cost analysis of recalls, the effects of recalls on vehicle demand, measurement of accidental loss and the value of life, and the effects of recalls on manufacturers' reputation.

doi: 10.1111/j.1465-7295.2011.00425.x

ABBREVIATIONS

BIC: Bayesian Information Criteria

DMV: Department of Motor Vehicles

GES: General Estimates System

IIHS: Insurance Institute for Highway Safety

NHTSA: National Highway Traffic Safety Administration

PAR: Police Accident Reports

VIN: Vehicle Identification Numbers

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--. "What Makes Car Owners Actively Respond to Vehicle Recalls?" Manuscript, SUNY-Stony Brook and Hood College, 2011b.

Bates, H., H. Matthias, L. Michael, and O. Nick. "Motor Vehicle Recalls: Trends, Patterns and Emerging Issues." Omega: International Journal of Management Science, 35(2), 2007, 202-10.

Cameron, C. A., and P. K. Trivedi. Regression Analysis of Count Data. Cambridge: Cambridge University Press, 1998.

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Jarrel, G., and S. Peltzman. "The Impact of Product Recalls on the Wealth of Sellers." Journal of Political Economy, 93(3), 1985, 512-36.

Kaplow, L., and S. Shavell. "Economic Analysis of Law." NBER Working Paper No. 6960, 1999.

Long, S. J., and J. Freese. "Regression Models for Categorical Dependent Variables Using Stata." College Station, TX: Stata Corporation, 2001.

Marino, A. M. "A Model of Product Recalls with Asymmetric Information." Journal of Regulatory Economics, 12, 1997, 245-65.

NHTSA. "National Automotive Sampling System (NASS), General Estimates System (GES)." U.S. Department of Transportation, 1988-2007.

--. "Traffic Safety Facts, U.S. Department of Transportation." DOT HS 811 172, 2009a.

--. "Motor Vehicle Defects and Safety Recalls: What Every Vehicle Owner Should Know." 2009b.

Posnerwer, R. A. "Economic Analysis of Law, Aspen Law and Business," 1998.

Rhee, M., and P. Haunschild. "The Liability of Good Reputation: A Study of Product Recalls in the U.S. Automobile Industry.'" Manuscript, Stanford University, 2003.

Rupp, N. G., and C. R. Taylor. "Who Initiates Recalls and Who Cares'? Evidence from the Automobile Industry." Journal of Industrial Economics, L(2), 2002, 123-49.

Wooldridge, J. M. Econometric Analysis of Cross Section and Panel Data. Cambridge, MA: The MIT Press, 2002.

YONG-KYUN BAE and HUGO BENITEZ-SILVA *

* We are grateful to John Hause, Chris Swann, Chris Snyder, Sam Peltzman, Ioana Marinescu, Adam Copeland, Katja Seim, Selcuk Eren, Na Yin, Huan Ni, Caroline Austin, an anonymous referee, and the editor for their useful comments and suggestions. We also thank the participants of the Annual International Industrial Organization Conference held in Chicago, and the applied micro workshops at Florida State University, Drexel University, Cornell, Hood College, University of St. Gallen, and the IAE in Barcelona. H.B.-S. is also grateful to the Economics Departments at the University of Maryland and UPF for their hospitality during the completion of this paper. We bear sole responsibility for any remaining errors.

Bae: Assistant Professor, Department of Economics and Management, Hood College, 401 Rosemont Avenue, Frederick, MD 21701. Phone 1-301-696-3692, Fax 1301-696-3771, E-mail bae@hood.edu

Benitez-Silva: Associate Professor, Department of Economics and New York Center for Computational Science, SUNY-Stony Brook, Stony Brook, NY 11794. Phone 1-631-632-7551, Fax 1-631-632-7516, E-mail hugo.benitez-silva@sunysb.edu

(1.) While it is possible to find cases of large recalls which were linked to few complaints and even fewer accidents or fatalities, this should not be taken as evidence that these problems are not serious. If we naively believe that the probability of recall-related accidents are too low, and we leave in the hands of the manufacturers the mandate of not putting unsafe vehicles on the road, the price to pay will likely be preventable accidents, injuries, and lives. At the very least the profession should seriously tackle the question of understanding the effects of recalls. This paper is a rare step in this direction and we hope our work encourages others to research this issue.

(2.) NHTSA 2009b.

(3.) These papers include Bates et al. (2007); Crafton, Hoffer, and Reilly (1981); Hartman (1987); Hoffer, Pruitt, and Reilly (1994); Huble and Arndt (1996); Jarrel and Peltzman (1985); Marino (1997); Rupp and Taylor (2002); and Rhee and Haunschild (2003).

(4.) It is hard to identify the source of an accident given that both human error and vehicle defects can play a role. What seems clear from our analysis is that the severity of accidents after recalls is significantly decreasing over time, which points to the effectiveness of recalls.

(5.) The recall regulation and details about the recall process can be found on the website of the NHTSA: http://www.nhtsa.gov.

(6.) We follow the notation of Cooter and Ulen (2000), but the interpretation of x is different in our model.

(7.) of course, we fully understand that drivers' faults are one of the major sources of accidents. For more discussion on this, see Evans (2002).

(8.) For particular recalls and particular vehicles affected the expected level of care (and the probability of being fixed) need not decrease (increase) in a monotonic fashion; we are showing that case for illustrative purposes. In reality we could observe step functions as waves of owners find out about the recalls over time and adjust behavior and take their cars to be fixed.

(9.) The riskier the defect is, the more responsive the drivers are. Thus, the level of care diminishes over the relatively short time period and the correction rate increases at a greater speed. See Bae and Benitez-Silva (201 lb) for an analysis of the evolution of correction rates in the quarters after the issuance of a recall.

(10.) Recent information indicates that Toyota might have been aware of the problems with sudden acceleration on some its most popular vehicles for more than 7 years before it started to recall them.

(11.) Recalls can be of different types: vehicle, equipment, tire, and component recalls. In most cases when recalls are mentioned, it usually refers only to vehicle recalls. However, other types of recalls often contain hazard parts and (or) defective equipment. Recently, the recalls related to defective equipment have sharply increased. Recalls have different hazard ratings according to the potential risk levels. This information was available to the public in the past, but it is no longer the case. For additional discussions on these issues, see Bae and Benitez-Silva (2011a).

(12.) For more details, see Rupp and Taylor (2002), who emphasize that the recalls of new vehicle models are more likely to be initiated by the manufacturers.

(13.) Notice that the fact that we use data on reported accidents is another reason to restrict our analysis to newer models, given that the reporting behavior of owners of older vehicles might be quite different, and they might be less likely to file accident reports and notify the police about an event, especially if the damage is not too extensive. Another related issue has to do with whether recalled vehicles might be more likely to appear in the police reports than other vehicles, maybe because owners, assuming they know about the recall, are more likely to call the police after an accident. If this was the case we would be in the presence of a selection problem that could bias our coefficient of interest. While this is plausible, although unlikely to be a major issue, we cannot really control for this issue without access to the universe of data on all cars on the road.

(14.) There is no specific data on the accidents caused by recalls. There are owners' accident reports submitted to manufacturers and (or) the NHTSA, but we have no access to them.

(15.) Following the discussion in Cameron and Trivedi (1998), Greene (2000), and Wooldridge (2002).

(16.) All the detailed information on recalls are available in the NHTSA website. See http://www-odi.nhtsa.dot.gov.

(17.) It is important to emphasize that the recall information does not take the risk levels into account. In particular, the effects of hazard recalls on severity could show a more solid relationship between recalls and severity. The information was available to the public in the past, but it is no longer available.

(18.) The second set includes accidents by vehicles whose recalls were issued, but the units involved for those particular vehicle models are less than 10,000. The first set has vehicles whose recalls were major ones and each recall was issued in the first year.

(19.) This is consistent with the NHTSA data on seat belt usage. As of 2008, 83% of occupants wear their seat belts, regardless of new and used cars. Thus, the effect of new cars on wearing seat belts could be sizable.

(20.) Manufacturers begin to sell their new-year models from September in previous year. We do not know when particular owners purchased their cars and had accidents.

(21.) BIC is defined as [BIC.sub.k] = D([M.sub.k]) - d [f.sub.k], ln N, where k is a model, and D([M.sub.k]) is the deviance of the model [M.sub.k]. d [f.sub.k] is the degrees of freedom associated with the deviance. The difference in the BICs between models indicates which model is more likely to have generated the observed data. The BIC values are -3110.445 without VINTAGE and -3103.993 with it, respectively. The difference (6.452) between them indicates strong support for the model without the variable. Thus, our main results are linked to the specification shown in MODEL 1.

(22.) These [beta] parameters by themselves are of limited interest, and here we can only discuss their signs and statistical significance. Also we need to note that the explanatory variables only affect the predicted probabilities. Therefore, the interpretation of the tables should be understood as the effects of the explanatory variables on the likelihood of severity.

(23.) To check for a possible nonlinear relationship, we included the variable, RECALL_SQ, along with RECALL in the equation. The coefficients on the quadratic terms were not significant. We also added higher polynomial specifications on the recall and the vintage variables without any significant change in the results.

(24.) The sample of accidents of non-recalled vehicles has a smaller proportion of automobiles, and more sports utility vehicles and light/heavy trucks. We could wonder then whether the lack of significance of the vintage effect in MODEL 4 is due to the different composition of vehicles in the larger sample. To study this possibility, we re-estimated both models using only the sub-sample of automobiles; the results were essentially unchanged, with the recall effect becoming somewhat stronger and the vintage effect even smaller.

(25.) Recently, a bill is being considered in Congress that would allow the NHTSA to speed up the process of mandatory recalls which can now take months, and they are even considering requiring car manufacturers to install devices that would record what happened during an accident, similar to what is in place in airplanes. See "Highway safety agency wants more auto recall power," AP Press, May 6, 2010.

(26.) "Toyota counts rising cost of recall woes," AP Press, March 16, 2010.

TABLE 1
Severity Level of Accidents That Occurred in the Years 2005, 2006, and
2007

Severity level                    Freq    Percent     Cum       Freq

No injury (=0                    457         65.19    65.19   8,022
Possible injury (=1)              95         13.55    78.74   1,596
Non-incapacitating injury (=2)    92         13.12    91.86   1,502
Incapacitating injury (=3)        51          7.28    99.14   1,124
Fatal injury (=4)                  6          0.86   100.00      75
Total                            701 (a)    100.00   100.00  12,319 (b)

Severity level                   Percent      Cum

No injury (=0                       65.12     65.12
Possible injury (=1)                12.96     78.08
Non-incapacitating injury (=2)      12.19     90.27
Incapacitating injury (=3)           9.12     99.40
Fatal injury (=4)                    0.61    100.00
Total                              100.00    100.00

Note: The data set comes from the GES.

Only new-year vehicle models are included. Since the GES data are from
a probability sample of police-reported traffic  crashes, nationally
representative estimates can be obtained from these data. Refer to
"NASS GES Analytical Users Manual, 1988-2009" regarding the
methodology to do that.

(a) The total number of observations that include accidents linked to
recalled vehicles.

(b) The total number of observations that include accidents not linked
to recalled vehicles.

TABLE 2
Description of Variables

Variable                   Description                            Dummy

Dependent variable
  SEVERITY                 Injury categories                        N
Personal characteristics
  AGE                      Age of the person (years)                N
  MALE                     Gender: 1 if male, 0 if female           Y
  RESTRAINT                Use of any protective device: 1 if       Y
                             use, 0 if no use
  ALCOHOL                  Police-reported alcohol involvement:     Y
                             1 if drunk, 0 if not drunk
  MOTORIST                 The role of the person in the            Y
                             accident: 1 if motorist, 0 if
                             non-motorist
Vehicle characteristics
  AUTOMOBILE               Body type of the vehicle: 1 if           Y
                             automobile, 0 if other
  VEHICLE FACTOR           Vehicle factors: 1 if any factor, 0      Y
                             if no contributing factor
  VEHICLE ROLE             Vehicle role: I if striking vehicle,     Y
                             0 otherwise
Regulation factors
  RECALL                   Months that have passed since a          N
                             recall issuance
  RECALL_SQ                Square of RECALL                         N
  VINTAGE                  Months that have passed since            N
                             October in the previous year
  VINTAGE_SQ               Square of MONTH VINTAGE                  N
  VINTAGE_2                Months that have passed since            N
                             October in the previous year
                           (For non-recall accidents)               N
  SPEED_LIMIT              Actual posted speed limit (in miles      N
                             per hour)
Environmental factors
  HIGHWAY                  Inter-state highway: I if highway, 0     Y
                             if local
  ROADWAY                  The location of the first harmful        Y
                             event:
                           1 if the vehicle is on the roadway,
                             0 if it is off the roadway
  STRAIGHT_ROAD            1 if straight road, 0 if curved road     Y
  GOOD_WEATHER             The general weather conditions:
                           1 if it is good, 0 if there was any      Y
                             adverse condition
OCCUPANT_INVOLVED          Number of occupants involved             N
  ROAD_LANES               Number of road lanes                     N
  WEEKDAY                  Weekday: 1 if weekdays, 0 if             Y
                             weekends

TABLE 3
Summary Statistics for Recall Accidents

Variable                        Obs     Mean        SD      Min   Max

Dependent variable
  Severity                      701     0.6505     1.0152      0     4
Personal characteristics
  Age                           701    37.5578    16.1820     11    91
  Male                          701     0.6220     0.4852      0     1
  Restraint system use          701     0.8873     0.3164      0     1
  Alcohol involvement           701     0.0656     0.2478      0     1
  Motorist                      701     0.9672     0.1783      0     1
Vehicle characteristics
  Body type                     701     0.5136     0.5002      0     1
  Vehicle contributing factor   701     0.0314     0.1745      0     1
  Vehicle role                  701     0.5635     0.4963      0     1
Regulation factors
  Recall in months              701     7.0599     3.3414      1    12
  Recall squared                701    60.9914    46.4534      1   144
  Vintage in months             701    15.2810     4.3507      3    27
  Vintage squared               701   252.4108   139.1169      9   729
  Speed limit                   701    45.0927    13.6915      5    75
Environmental factors
  Highway                       701     0.1697     0.3757      0     1
  Relation to roadway           701     0.9415     0.2348      0     1
  Straight road                 701     0.8959     0.3057      0     1
  Weather conditions            701     0.8274     0.3782      0     1
  Occupants involved            701     1.4836     0.9358      0     9
  Number of travel lanes        701     2.9601     1.2495      1     7
  Weekday                       701     0.7575     0.4289      0     1

Variable                        Acronym

Dependent variable
  Severity                      SEVERITY
Personal characteristics
  Age                           AGE
  Male                          MALE
  Restraint system use          RESTRAINT
  Alcohol involvement           ALCOHOL
  Motorist                      MOTORIST
Vehicle characteristics
  Body type                     AUTOMOBILE
  Vehicle contributing factor   VEHICLE_FACTOR
  Vehicle role                  VEHICLE_ROLE
Regulation factors
  Recall in months              RECALL
  Recall squared                RECALL_SQ
  Vintage in months             VINTAGE
  Vintage squared               VINTAGE_SQ
  Speed limit                   SPEED_LIMIT
Environmental factors
  Highway                       HIGHWAY
  Relation to roadway           ROADWAY
  Straight road                 STRAIGHT_ROAD
  Weather conditions            GOOD_WEATHER
  Occupants involved            OCCUPANT_INVOLVED
  Number of travel lanes        ROAD_LANES
  Weekday                       WEEKDAY

TABLE 4
Summary Statistics for Non-Recall Accidents

Variable                          Obs      Mean       SD     Min   Max

Dependent variable
  Severity                      12,319    0.6715    1.0417      0     4
Personal characteristics
  Age                           12,319   37.9306   16.4014      0   102
  Male                          12,319    0.6121    0.4873      0     1
  Restraint system use          12,319    0.8971    0.3039      0     1
  Alcohol involvement           12,319    0.0472    0.2122      0     1
  Motorist                      12,319    0.9742    0.1586      0     1
Vehicle characteristics
  Body type                     12,319    0.3889    0.4875      0     1
  Vehicle contributing factor   12,319    0.0264    0.1603      0     1
  Vehicle role                  12,319    0.6014    0.4896      0     1
Regulation factors
  Vintage in Months             12,319   17.2785    7.0316      4    27
  Speed limit                   12,319   45.0889   13.6249      0    75
Environmental factors
  Highway                       12,319    0.1670    0.3730      0     1
  Relation to roadway           12,319    0.9574    0.2020      0     1
  Straight road                 12,319    0.8831    0.3213      0     1
  Weather Conditions            12,319    0.8146    0.3886      0     1
  Occupants involved            12,319    1.5229    1.1374      0    39
  Number of travel lanes        12,319    3.0370    1.3485      1     7
  Weekday                       12,319    0.7438    0.4365      0     1

Variable                        Acronym

Dependent variable
  Severity                      SEVERITY
Personal characteristics
  Age                           AGE
  Male                          MALE
  Restraint system use          RESTRAINT
  Alcohol involvement           ALCOHOL
  Motorist                      MOTORIST
Vehicle characteristics
  Body type                     AUTOMOBILE
  Vehicle contributing factor   VEHICLE_FACTOR
  Vehicle role                  VEHICLE_ROLE
Regulation factors
  Vintage in Months             VINTAGE
  Speed limit                   SPEED_LIMIT
Environmental factors
  Highway                       HIGHWAY
  Relation to roadway           ROADWAY
  Straight road                 STRAIGHT_ROAD
  Weather Conditions            GOOD_WEATHER
  Occupants involved            OCCUPANT_INVOLVED
  Number of travel lanes        ROAD LANES
  Weekday                       WEEKDAY

TABLE 5
Impact of Vehicle Recalls on the Severity of Accidents

                                 MODEL 1                MODEL 2

With                             RECALL                 RECALL
With                                                    VINTAGE

Personal characteristics
  AGE                       0.0062 (0.0029) **     0.0062 (0.0029) **
  MALE                      0.0077 (0.0958)        0.0075 (0.0958)
  RESTRAINT                -0.8589 (0.1882) ***   -0.8564 (0.1883) ***
  ALCOHOL                   0.8190 (0.1803) ***    0.8201 (0.1801) ***
  MOTORIST                 -0.6435 (0.2112) ***   -0.6502 (0.2123) ***
Vehicle characteristics
  AUTOMOBILE                0.0334 (0.0937)        0.0295 (0.0939)
  VEHICLE FACTOR           -0.1598 (0.2844)       -0.1608 (0.2829)
  VEHICLE ROLE             -0.0374 (0.0936)       -0.0379 (0.0936)
Regulation factors
  RECALL                   -0.0357 (0.0148) **    -0.0321 (0.0186) *
  VINTAGE                      --                 -0.0044 (0.0139)
  SPEED LIMIT               0.0002 (0.0039)        0.0002 (0.0039)
Environmental factors
  HIGHWAY                  -0.2248 (0.1400)       -0.2247 (0.1400)
  ROADWAY                  -0.0268 (0.1933)       -0.0294 (0.1935)
  STRAIGHT_ROAD             0.1101 (0.1552)        0.1083 (0.1554)
  GOOD_WEATHER             -0.2377 (0.1228) *     -0.2284 (0.1226) *
  OCCUPANT_INVOLVED         0.0206 (0.0473)        0.0215 (0.0475)
  LANES                     0.0002 (0.0387)       -0.0001 (0.0388)
  WEEKDAY                  -0.0664 (0.1047)       -0.0660 (0.1049)
  No. of OBS                      701                    701
  Pseudo [R.sup.2]               0.0841                 0.0842

                                 MODEL 3                MODEL 4

With
With                             VINTAGE                VINTAGE

Personal characteristics
  AGE                       0.0062 (0.0029) **     0.0018 (0.0007) **
  MALE                     -0.0030 (0.0956)       -0.2454 (0.0225) **
  RESTRAINT                -0.8565 (0.1879) ***   -0.7254 (0.0409) ***
  ALCOHOL                   0.8300 (0.1782) ***    0.7657 (0.0505) ***
  MOTORIST                 -0.6759 (0.2106) ***   -0.7079 (0.0512) ***
Vehicle characteristics
  AUTOMOBILE                0.0074 (0.0934)       -0.0535 (0.0231) **
  VEHICLE FACTOR           -0.1597 (0.2847)       -0.0639 (0.0669)
  VEHICLE ROLE             -0.0423 (0.0935)       -0.0882 (0.0229) ***
Regulation factors
  RECALL                          --                     --
  VINTAGE                  -0.0193 (0.0112) *     -0.0007 (0.0016)
  SPEED LIMIT              -0.0003 (0.0039)       -0.0002 (0.0010)
Environmental factors
  HIGHWAY                  -0.2185 (0.1403)        0.0913 (0.0346) *
  ROADWAY                  -0.0730 (0.1934)        0.0136 (0.0545)
  STRAIGHT_ROAD             0.1056 (0.1568)        0.0405 (0.0364)
  GOOD_WEATHER             -0.2321 (0.1216) *      0.0049 (0.0288)
  OCCUPANT_INVOLVED         0.0260 (0.0477)       -0.0273 (0.0108) **
  LANES                    -0.0008 (0.0388)       -0.0132 (0.0085)
  WEEKDAY                  -0.0801 (0.0112)       -0.0444 (0.0256)
  No. of OBS                     701                  12,319
  Pseudo [R.sup.2]             0.0821                 0.0484

Note: Standard errors are in parentheses. The Huber/White/sandwich
estimator of variance is used.

* Significant at the 10%; ** 5%; and *** 1% level.

TABLE 6
Marginal Effects from MODEL 1

Variable                                Ave_Change   P[y = 0]

AGE                     Marginal        0.0009       -0.0023
MALE                0 [right arrow] 1   0.0011       -0.0028
RESTRAINT           0 [right arrow] 1   0.1326        0.3316
ALCOHOL             0 [right arrow] 1   0.1270       -0.3175
MOTORIST            0 [right arrow] 1   0.1004        0.2511
AUTOMOBILE          0 [right arrow] 1   0.0049       -0.0123
VEHICLE_FACTOR      0 [right arrow] 1   0.0227        0.0568
VEHICLE_ROLE        0 [right arrow] 1   0.0055        0.0138
RECALL                  Marginal        0.0052        0.0131
SPEED_LIMIT             Marginal        0.0000       -0.0001
HIGHWAY             0 [right arrow] 1   0.0320        0.0799
ROADWAY             0 [right arrow] 1   0.0040        0.0099
STRAIGHT_ROAD       0 [right arrow] 1   0.0159       -0.0398
GOOD_WEATHER        0 [right arrow] 1   0.0359        0.0898
OCCUPANT_INVOLVED       Marginal        0.0030       -0.0076
LANES                   Marginal        0.0000       -0.0001
WEEKDAY             0 [right arrow] 1   0.0098        0.0246

Variable            P[y = 1]   P[y = 2]   P[y = 3]   P[y = 4]

AGE                  0.0006     0.0010     0.0006     0.0001
MALE                 0.0007     0.0012     0.0008     0.0001
RESTRAINT           -0.0422    -0.1309    -0.1380    -0.0206
ALCOHOL              0.0377     0.1246     0.1347     0.0205
MOTORIST            -0.0359    -0.1017    -0.1000    -0.0135
AUTOMOBILE           0.0032     0.0053     0.0035     0.0003
VEHICLE_FACTOR      -0.0162    -0.0246    -0.0149    -0.0011
VEHICLE_ROLE        -0.0036    -0.0059    -0.0039    -0.0003
RECALL              -0.0034    -0.0057    -0.0037    -0.0003
SPEED_LIMIT          0.0000     0.0000     0.0000     0.0000
HIGHWAY             -0.0228    -0.0345    -0.0210    -0.0016
ROADWAY             -0.0025    -0.0043    -0.0029    -0.0002
STRAIGHT_ROAD        0.0109     0.0172     0.0108     0.0009
GOOD_WEATHER        -0.0208    -0.0385    -0.0278    -0.0026
OCCUPANT_INVOLVED    0.0020     0.0033     0.0022     0.0002
LANES                0.0000     0.0000     0.0000     0.0000
WEEKDAY             -0.0063    -0.0106    -0.0071    -0.0006

Note: 0 [right arrow] 1 indicates that the variable is a dummy. All
others are continuous variables. Standard errors are excluded  from
the table.

TABLE 7
Predicted Probabilities

(a) RECALL Variable, Indicating Months Since Recall

Months since recall      1         2         3         4

Pr(y = 0|x)           0.5741    0.5881    0.6019    0.6156
Pr(y = 1|x)           0.1709    0.1683    0.1655    0.1625
Pr(y = 2|x)           0.1698    0.1639    0.1580    0.1522
Pr(y = 3|x)           0.0797    0.0748    0.0702    0.0657
Pr(y = 4|x)           0.0054    0.0049    0.0044    0.0040

Months since recall      5         6         7         8

Pr(y = 0|x)           0.6291    0.6425    0.6557    0.6688
Pr(y = 1|x)           0.1595    0.1562    0.1529    0.1494
Pr(y = 2|x)           0.1464    0.1406    0.1349    0.1293
Pr(y = 3|x)           0.0615    0.0574    0.0536    0.0500
Pr(y = 4|x)           0.0036    0.0032    0.0029    0.0026

Months since recall      9        10        11        12

Pr(y = 0|x)           0.6816    0.6942    0.7066    0.7187
Pr(y = 1|x)           0.1459    0.1422    0.1385    0.1346
Pr(y = 2|x)           0.1237    0.1183    0.1129    0.1077
Pr(y = 3|x)           0.0465    0.0433    0.0402    0.0373
Pr(y = 4|x)           0.0023    0.0021    0.0018    0.0016

(b) VINTAGE Variable, Indicating Months Since Launching of Model

Months since launch      1         2         3         4

Pr(y = 0|x)           0.6503    0.6506    0.6508    0.6511
Pr(y = 1|x)           0.1398    0.1398    0.1397    0.1397
Pr(y = 2|x)           0.1263    0.1262    0.1261    0.1260
Pr(y = 3|x)           0.0802    0.0801    0.0800    0.0799
Pr(y = 4|x)           0.0033    0.0033    0.0033    0.0033

Months since launch      5         6         7         8

Pr(y = 0|x)           0.6513    0.6516    0.6519    0.6521
Pr(y = 1|x)           0.1396    0.1395    0.1395    0.1394
Pr(y = 2|x)           0.1259    0.1258    0.1257    0.1256
Pr(y = 3|x)           0.0798    0.0797    0.0796    0.0795
Pr(y = 4|x)           0.0033    0.0033    0.0033    0.0033

Months since launch      9        10        11        12

Pr(y = 0|x)           0.6524    0.6527    0.6529    0.6532
Pr(y = 1|x)           0.1394    0.1393    0.1393    0.1392
Pr(y = 2|x)           0.1256    0.1255    0.1254    0.1253
Pr(y = 3|x)           0.0794    0.0793    0.0792    0.0791
Pr(y = 4|x)           0.0033    0.0032    0.0032    0.0032

TABLE 8
Quarterly Correction Rates for Two 2005 Recalls

  Auto-Maker                Ford (a)
  Year Model               2004, 2005
 Issue Dates               July 22, 2005
Units Involved               180,113

                  Units       Units      Correction
Year     Month    Fixed    Unreachable      Rate

2005       11    120,610      2,534        0.669
2005       12      --          --            --
2006        1    141,618      2,185        0.786
2006        2      --          --            --
2006        3      --          --            --
2006        4      --          --            --
2006        5    154,140      2,597        0.856
2006        6      --          --            --
2006        7      --          --            --
2006        8    160,376      2,210        0.890
2006        9      --          --            --
2006       10      --          --            --
2006       11    165,092      1,860        0.917
2006       12      --          --            --
2007        1      --          --            --
2007        2    168,647      1,576        0.936

  Auto-Maker             GMC / CHEVROLET (b)
  Year Model                 2000, 2001
 Issue Dates             October 19, 2005
Units Involved                316,591

                  Units       Units      Correction
Year     Month    Fixed    Unreachable      Rate

2005       11      --          --            --
2005       12      --          --            --
2006        1    68,937       8,612        0.218
2006        2      --          --            --
2006        3      --          --            --
2006        4    110,280      9,194        0.348
2006        5      --          --            --
2006        6      --          --            --
2006        7    169,186      9,471        0.534
2006        8      --          --            --
2006        9      --          --            --
2006       10    188,016      9,559        0.594
2006       11      --          --            --
2006       12      --          --            --
2007        1    206,817      9,461        0.653
2007        2      --          --            --

Source: http://www-odi.nhtsa.dot.gov/recalls/recallsearch.cfm.

(a) Campaign ID #: 05V270000, Initiation: ODI, Components: Electrical
system, wiring.

(b) Campaign ID #: 05V155000, Initiation: ODI, Components: Fuel
system, fuel pump.
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Author:Bae, Yong-Kyun; Benitez-Silva, Hugo
Publication:Economic Inquiry
Article Type:Abstract
Geographic Code:1USA
Date:Apr 1, 2013
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