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Distributional and Efficiency Impacts of Increased US Gasoline Taxes

Distributional and Efficiency Impacts of Increased US Gasoline Taxes
Distributional and Efficiency Impacts of Increased US Gasoline Taxes

667

American Economic Review 2009, 99:3, 667–699

https://www.sodocs.net/doc/2717578349.html,/articles.php?doi =10.1257/aer.99.3.667

For several reasons, reducing automobile-based gasoline consumption is a major US public policy issue. Gasoline use generates environmental externalities. In 2004, approximately 22 per-cent of US emissions of carbon dioxide—the principal anthropogenically sourced “greenhouse gas” contributing to global climate change—derived from gasoline use. Other environmental externalities from gasoline combustion include the impacts from emissions of several “local” air pollutants such as carbon monoxide, nitrogen oxides, and volatile organic compounds. Reduced gasoline use could lead to improved air quality and associated benefits to health.1, 2 In addition, gasoline consumption accounts for 44 percent of the US demand for crude oil, and the nation’s dependence on crude oil makes the United States vulnerable to changes in world oil prices ema-nating from disruptions in the world oil market. Some analyses claim that this vulnerability is not accounted for in individual consumption decisions and thus represents another externality from

1

Ian W. H. Parry and Kenneth A. Small (2005) and the National Research Council (2002) examine the various externalities from gasoline use and offer estimates of the overall marginal damages. The former study estimates the overall external cost from US gasoline consumption (including effects relating to local pollution, climate change, con-gestion, and accidents ) to be about 75 cents per gallon in year-2000 dollars. This suggests that US taxes on gasoline are below the efficiency-maximizing level, since the federal tax plus average state tax totals 41 cents.2

The extent of the health improvement from improved air quality depends on both the reduction in gasoline use and possible changes in pollution per gallon of gasoline used. Air districts currently in compliance with air pollution regulations under the 1990 Clean Air Act amendments might well respond to reductions in gasoline use by relaxing “tailpipe” emissions requirements, that is, on the allowable emissions per unit of fuel combusted. This would offset the air-quality and health improvements from reduced gasoline consumption.

Distributional and Efficiency Impacts of

Increased US Gasoline Taxes

By Antonio M. Bento, Lawrence H. Goulder, Mark R. Jacobsen, and Roger H. von Haefen*

We examine the impacts of increased US gasoline taxes in a model that links the markets for new, used, and scrapped vehicles and recognizes the consider-able heterogeneity among households and cars. Household choice parameters derive from an estimation procedure that integrates individual choices for car ownership and miles traveled. We find that each cent-per-gallon increase in the price of gasoline reduces the equilibrium gasoline consumption by about 0.2 percent. Taking account of revenue recycling, the impact of a 25-cent gasoline tax increase on the average household is about $30 per year (2001 dollars ). Distributional impacts depend importantly on how additional revenues from the tax increase are recycled. (JEL D12, H22, H25, L62, L71)

* Bento: Department of Applied Economics and Management, Cornell University, 424 Warren Hall, Ithaca, NY 14853 (e-mail: amb396@https://www.sodocs.net/doc/2717578349.html, ); Goulder: Department of Economics, Stanford University, Landau Economics Bldg., Stanford, CA 94305 (e-mail: goulder@https://www.sodocs.net/doc/2717578349.html, ); Jacobsen: Department of Economics, University of California at San Diego, 9500 Gilman Drive, San Diego, CA 92093 (e-mail: m3jacobs@https://www.sodocs.net/doc/2717578349.html, ); von Haefen: Department of Agricultural and Resource Economics, North Carolina State University, 4338 Nelson Hall, Raleigh, NC 27695 (e-mail: rhhaefen@https://www.sodocs.net/doc/2717578349.html, ). We are grateful to David Austin, Tim Bresnahan, Don Fullerton, Michael Greenstone, Ken Small, James Sweeney, Kenneth Train, Kurt van Dender, Frank Wolak, and three anonymous referees for very helpful sugges-tions, and to Emeric Henry for his important contributions to the econometric efforts. We also thank the William and Flora Hewlett Foundation and Stanford’s Precourt Institute for Energy Efficiency for financial support.

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JUnE 2009 gasoline consumption.3 The various externalities provide a potential rationale for public policy oriented toward gasoline consumption.

Recently, analysts and policymakers have called for new or more stringent policies to curb gasoline consumption. The US Senate recently passed a bill that would raise corporate average fuel economy (CAFE) standards for passenger vehicles for the first time since 1985. The stan-dards would be increased from the current 27.5 miles per gallon to 35 miles per gallon by 2020. The 2005 Energy Bill includes tax credits for households purchasing relatively fuel-efficient vehicles such as hybrid cars. The California State Assembly recently enacted AB 1493, which mandates carbon dioxide emissions that would require significant improvements in automobile fuel economy. Other proposals include subsidies to retirements of older (gas-guzzling) vehicles and increments to the federal gasoline tax.4

This paper examines the gas tax option, employing an econometrically based multimarket simulation model to evaluate the policy’s efficiency and distributional implications. We investi-gate the impacts of increased US gasoline taxes on fuel consumption, relating these impacts to changes in fleet composition (shifts to higher mileage automobiles) and vehicle miles traveled (VMT). We also evaluate the economy-wide costs of higher gasoline taxes, and explore how the costs are distributed across households that differ by income, region of residence, race, and other characteristics. We consider how the distribution of impacts depends on the ways revenues from the tax are returned to the private sector.

Some prior studies have examined the impact of gasoline taxes by estimating the demand for gasoline as a function of gasoline price and household income. For example, Jerry A. Hausman and Whitney K. Newey (1995) use household-level data on gasoline consumption to estimate deadweight loss from gasoline taxes, while Sarah E. West and Roberton C. Williams III (2004, 2005) use such data to assess the distributional impacts of gasoline taxes and the optimal gaso-line tax.

Other studies infer the demand for gasoline from automobile choice and utilization models. For example, James Berkovec (1985), Fred L. Mannering and Clifford Winston (1985), Kenneth E. Train (1986), and West (2004) estimate the household’s discrete automobile purchase decision and its continuous choice of VMT. Following Jeffrey A. Dubin and Daniel L. McFadden (1984), these authors account for the connections between these two choices, although the cross-equa-tion restrictions implied by a unified structural model of behavior are not imposed.

A third set of studies focuses on supply-side phenomena—in particular, the impacts of policies on new car production and the composition of the automobile fleet, and the associated effect on gasoline consumption. In contrast with the previously mentioned studies, this third set consid-ers explicitly the imperfectly competitive nature of the new car market and the pricing behavior of new car producers. For example, Steven T. Berry, James Levinsohn, and Ariel Pakes(1995); Pinelopi K. Goldberg (1998); and David H. Austin and Terry M. Dinan (2005) develop models of new car market that combine supply decisions by imperfectly competitive producers with dis-crete demand choices by households. The latter two studies explore impacts of automobile poli-cies on the new car market. Goldberg (1998) and Andrew M. Kleit (2004) analyze tighter CAFE standards; Austin and Dinan (2005) examine CAFE standards and a gasoline tax increase.

The present study differs from earlier work in several ways. First, in contrast with nearly all prior work,5 this analysis considers supply and equilibrium not only in the new car market, but in

3 See, for example, National Research Council (2002).

4 The general public appears to be growing increasingly supportive of stronger measures to curb gasoline use. A February 2006 new York Times/CBS News Poll found that a majority of Americans would support a higher gasoline tax if it reduced global warming or made the United States less dependent on foreign oil.

5 One exception is Berkovec (1985), who develops a model with interactions among these markets. His model assumes pure competition among auto producers, however.

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VOL. 99 nO. 3669 the used car and scrap markets as well. The wider scope helps provide a more complete picture of the impact of a gasoline tax. In addition, addressing the equilibrium in all three car markets enables us to capture important dynamic effects. Higher gasoline taxes are likely to cause an increase in the share of relatively fuel-efficient cars among new cars sold. The extent to which the fuel-efficiency of the overall(new and used car) fleet improves will depend on the rate at which the newer, more efficient cars replace older cars. This depends on the relative size of the stocks of new and used cars and the rate at which older cars are taken out of operation (scrapped). By considering the new, used, and scrapped car markets, the model is able to consider the dynamics of changes in fleet composition and related short- and long-run impacts on gasoline consump-tion. As in Goldberg (1995), Berry, Levinsohn, and Pakes(1995), Amil K. Petrin (2002), and Austin and Dinan (2005), we consider the imperfectly competitive nature of the new car market. In contrast with these studies, however, we connect this market to the used and scrap markets. This allows us to consider how policies affect the entire fleet of cars and associated demands for gasoline.

A second major difference from earlier work is the model’s ability to capture distributional effects. The model considers over 20,000 households that differ in terms of income, family size, employment status (working or retired), region of residence, and ethnic background. This enables us to trace distributional impacts in several important dimensions. All household demands stem from a consistent, utility maximization framework, enabling us to measure distributional impacts in terms of theoretically sound welfare indexes. Prior studies have examined distribu-tional effects by focusing on how gasoline expenditure shares differ across income groups.6 In contrast, the present model considers not only the expenditure-side impacts but also the ways that the government’s disposition of gas tax revenue influences the distribution of policy impacts. Finally, the model differs in its econometric approach to estimating consumer demand for automobiles, VMT, and gasoline. Berkovec (1986), Mannering and Winston (1986), Goldberg (1998), and West (2004) account for the connections between the automobile purchase and use (VMT)decisions by employing sequential, two-step estimators. Their approach accounts for correlations between the discrete and continuous choice margins but ignores the cross-equation restrictions implied by a unified behavior model. In contrast, we adopt a full-information, one-step structural approach that simultaneously estimates these choice dimensions within a utility-theoretic framework that permits us to recover sound welfare estimates.7 In addition, we assume that all parameters entering preferences vary randomly across households. Random coefficients allow us to account for correlations in the unobservable factors influencing a household’s dis-crete car choice and continuous VMT demand, while simultaneously allowing for more plausible substitution patterns among automobiles (McFadden and Train 2000; David S. Bunch, David Brownstone, and Thomas F. Golub 1996).

The rest of the paper is organized as follows. Section I describes the equilibrium simulation model. Section II outlines the model’s data sources, with emphasis on the data employed to esti-mate household demands for vehicles and travel. Section III presents our approach for estimating

6 See James M. Poterba (1989, 1991) for expenditure-based estimates of the incidence of gasoline taxes.

7 A difficulty with welfare measurement from two-step estimators is that each step yields a different set of estimates for the same parameters. Each set may have different welfare implications for the same policy. One-step estimators generate a single set of parameter estimates and therefore avoid this difficulty. To our knowledge, the only other auto-mobile study to incorporate a one-step procedure is that of Ye Feng, Don Fullerton, and Li Gan (2005). Other studies have estimated the demand for automobiles separately from the demand for gasoline and VMT. Berry, Levinsohn, and Pakes (2004) and Petrin (2003) focus on the demand for automobiles; Hausman and Newey (1995), Richard L. Schmalensee and Thomas M. Stoker (1999), and West and Williams (2005) concentrate on the demand for gasoline. Austin and Dinan (2005) obtain demand functions for cars by calibrating the parameters of their simulation model to be consistent with internal estimates by General Motors.

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households’ automobile purchase and driving decisions. Section IV presents and interprets results from simulations of a range of gasoline tax policies. Section V offers conclusions.

I. Model Structure

A. Overview

The economic agents in the model are households, producers of new cars, used car suppliers, and scrap firms. The model considers the car-ownership and VMT decisions of 20,429 house-holds. The ownership and VMT decisions are made simultaneously in accordance with utility maximization.

The model distinguishes cars according to age, class, and manufacturer. Table 1 displays the different car categories, which imply 350 distinct cars of which 284 appear in our dataset and simulation.8

The used car market equates the supply of used cars remaining after scrapping with the demand for ownership of those cars. Producers of new cars decide on new car prices in accordance with Bertrand (price ) competition. These producers consider households’ demand functions in deter-mining optimal pricing. Price markups reflect the various price elasticities of demand for cars as well as the regulatory constraints posed by existing CAFE standards.

The model solves for a sequence of market equilibria at one-year intervals. Car vintages are updated each year, so that last year’s new cars become one-year-old cars, last year’s one-year-old cars become two-year-old cars, etc. Once a car is scrapped, it cannot reenter the used car market. Characteristics of given models of new cars change through time, as described in Section IV. In particular, producers change the fuel economy of new models in a manner consistent with profit maximization.

B. Household Demands

Households obtain utility from car ownership and use, as well as from consumption of other commodities. The utility from driving depends on characteristics of the automobile as well as VMT. Each household has exogenous income; most households also are endowed with cars. If a household has a car endowment, it chooses whether to hold or relinquish (sell or scrap ) that car;

8

The number of distinct cars increases over time as some unique new models become old and enter the used car fleet.

Table 1—Included Car Types

Classes Age categories Manufacturers Compact

New cars Ford Luxury compact 1–2 years old Chrysler

Midsize 3–6 years old General Motors Fullsize

7–11 years old Honda Luxury mid /fullsize 12–18 years old

Toyota

Small SUV Other Asian Large SUV European

Small truck Large truck Minivan

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if it relinquishes the car it also decides whether to purchase a different car (new or used). If a household does not have a car endowment, it chooses whether to purchase a car.

If household i owns car j, its utility can be expressed by

(1)U ij=U ij(z j, M i, x i),

where z j is a vector of characteristics of car j, and M i and x i, respectively, refer to household i’s vehicle miles traveled and its consumption of the outside (or Hicksian composite) good. The household’s utility conditional on choosing car j can be expressed through the following indirect utility function:

(2)V ij=V′ij+μiεij

with

(3)V′ij=V′ij( y i?r ij, p ij M,p ix, z j, z i, z ij ),

where

y i=income to household i,

r ij=rental price of car j to household i,

p ij M=per-mile operating cost,

p ix=price of the outside good, x,

z i=vector of characteristics of household i,

z ij=vector of characteristics of household i, interacted with characteristics of car j.

Household income y i is devoted toward purchasing a car (or cars9), car operation, and the pur-chase of the outside good. We treat car purchases as rentals, so that payments are spread over many years. The household budget constraint can then be written as:

(4)y i=r ij+p ij M M i+p ix x i.

If a household owns a vehicle, the stream of rental income from that vehicle is included in its income. A household that chooses to retain its existing car effectively makes a rental payment equal to its implicit rental income from that car. Income also includes the household’s share of profits to new car producers, government transfers, and capital gains or losses resulting from changes in automobile prices.10 The government transfer component of income includes revenue from the gasoline tax and adjusts as policy changes.

9 In Section III we discuss how we allow for multiple car ownership.

10 If a household is endowed with one vehicle of type j entering the period, its gain is computed as: (r

j′?r j)(1 ?θj)+ 1/2 (r j′?r j)(θj?θj′), where r j and r j′, respectively, denote the rental price of car j in the reference and policy-change cases, and θj and θj′ represent the probability of the car’s being scrapped in the two cases. The first term represents the

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The operating cost p ij M includes the fuel cost (including gasoline taxes), as well as maintenance and variable insurance costs. The rental price r ij accounts for depreciation, registration fees, and fixed insurance costs. As indicated in expression (2) above, indirect utility includes the random component μiεij, where ε has a type I extreme-value distribution (following the econometric model) and μ is a scale parameter. We assume the household chooses the vehicle (or vehicles) yielding the highest conditional utility, given V′ and the random error. The probability that a given car j maximizes utility for household i is

(5)exp a V′ij__μi b/∑k exp a V′ik___μi b.

The indirect utility function V ij can be differentiated following Roy’s identity to yield the optimal choice of miles traveled, M ij, conditional on the purchase of car j. Aggregate automobile and VMT demand are the sum of these micro decisions. In specifying aggregate demand for automobiles, we treat each individual in our sample as a representative of a subpopulation of like individuals and sum up the probabilities. Similarly for aggregate VMT demand, we sum up each individual’s probability-weighted VMT demand for each car.

C. Supply of new Cars

Each of the seven producers in the model sets prices for its fleet of automobiles to maximize profits, given the prices set by its competitors and subject to fleet fuel economy constraints. Thus, we assume Bertrand competition. Producers face less than perfectly elastic demands for their cars: that is, two new cars of the same class can sell at different prices if produced by different firms. The producer problem accounts for the presence of CAFE standards. These standards require that each manufacturer’s fleet-wide average fuel economy be above a certain level in each of two general categories of cars: “light trucks” and “passenger cars.” The classes in the passenger car category are nonluxury compact, nonluxury midsize, nonluxury fullsize, luxury compact, and luxury midsize/fullsize. Those in the light truck category are small truck, large truck, small SUV, large SUV/van, and minivan.11

In the following, the subscript k refers to the cars made by a particular manufacturer. The boldface vector p includes prices of the cars made by all seven manufacturers.12T and C denote the sets of cars (for a given manufacturer) in the light truck and passenger car categories, respec-tively;

_e T and _e C refer to the efficiency requirements for light trucks and passenger cars; and e k is the fuel economy of car k. A given producer chooses a vector of prices, p k, and a vector of individual-model fuel economies, e k, to maximize profit:

(6)max{ p

k , e k }

k

( p k?c k(e k ))q k( p, e)

gain in the value of the car owned, while the second is an adjustment to the gain that accounts for the change in the probability that the car is scrapped.

11 We remove a small (fixed) fraction of the largest vehicles from CAFE in order to incorporate the fact that the very largest trucks and SUVs are exempt from CAFE standards.

12 The purchase price is the same as the present value of rental prices over the life of the car.

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BEnTO ET AL.: IMpACTS Of InCREASED US GASOLInE TAxES subject to:

∑ k ∈C

q k _____ ∑ k ∈C

q k __ e k ≥ _ e C and ∑

k ∈T

q k _____ ∑ k ∈T

q k

__ e k

≥ _ e T ,where p k and c k refer to the purchase price and marginal cost, respectively, of a particular car and

q k is the demand as a function of all prices.13 For any given model k , marginal cost is a function of e k , the chosen level of fuel economy for that car. Each producer’s solution to (6) determines the quantities of vehicles sold in each class. Producers can alter fuel economy and the mix of vehicles, but cannot introduce new vehicle classes, exit existing vehicle classes, or alter attributes like weight and horsepower that determine class.

The solution to (6) requires a demand function (which is given within the model by the sum of individual demands from (5)) and a cost function. To identify the cost function parameters, we employ data on automobile markups, prices, and quantities sold, along with our estimated house-hold demand elasticities for different automobiles. The relationship between production cost and fuel economy is taken from engineering estimates of the incremental costs of fuel economy from the National Research Council (2002). These relationships pose the technological and cost con-straints under which producers in the model choose optimal levels of fuel economy. (Details are provided in the Appendix, available online at https://www.sodocs.net/doc/2717578349.html,/articles.php?doi=10.1257/aer.99.3.667.)

We must solve the constrained optimization problem for all of the firms simultaneously, since the residual demand curve faced by a given firm depends on the prices set by the others. The solution method is discussed in Section IE below.

D. Used Car and Scrap Markets

The Used Car Market .—In the model, “used car” refers to all cars that are neither new nor scrapped. The available supply of used cars of a particular vintage (i.e., model year ) is the total stock of that vintage operating in the previous year less those that are scrapped. The total sup-ply of all used cars in the current period is the aggregate supply from the previous period net of the vehicles scrapped, plus an increment to the supply representing the cars that were new in the previous period. Let ? refer to a given manufacturer and class of vehicle. For each manufacture-class category ?, the quantity of used cars evolves according to (7)

q ?, t +1 U = (1 ? θ?) q ?, t U

+ q ?, t n

,where q ?, t U and q ?, t n

refer to the quantity of used and new cars of the manufacturer-class combina-tion ? available in year t , and θ? represents the average probability that used cars of type ? are scrapped. This scrap rate will depend on the car’s expected resale value if kept in operation. We discuss the specification of θ? in the next section.

Each used car type, or age-manufacturer-class combination, has a different rental price. The model determines the set of rental prices that clears the used car market, that is, that causes every

13

Our treatment ignores some complexities of the CAFE regulations. The actual regulations allow for intertemporal banking and borrowing: the standard can be exceeded in one year if the firm overcomplies in another. In addition, some manufacturers can, and do, elect to pay a fine rather than meet the standards, and others are not in fact constrained by the standards. Work in progress (Mark R. Jacobsen 2006) addresses these issues.

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car to be sold. Household demands for used cars come from household demands computed as in (5). Since the demand for a given used car will depend on the rental prices of all used cars (and

on new car prices), all used car rental prices need to be solved simultaneously.

The Scrap Market.—We assume that households will scrap a car when the scrap value exceeds the resale value. However, each car (age-manufacturer-class combination) in our model actually represents a group of cars of varying quality and value, some of which may fall under the cutoff for scrapping even if the average car in the group does not. To allow for scrapping of some cars of a given type, we assign a scrap probability to each car. The scrap decision depends on p j, the purchase price or resale value of a used car. Today’s purchase price is the discounted sum of future rental prices, adjusted for the possibility that a car will be scrapped (and earning no rental price) before reaching each progressively older age. The household has myopic expectations: it assumes that future rental values will be the same as the current-period rental values of older vintages of the same vehicle type. Changes in the gasoline tax affect scrap decisions through their effects on purchase prices.14 When this value changes as a result of a change in the gasoline tax, so does the probability of scrap.

In terms of the resale value for each used car, the scrap probability θj is modeled simply as (8)θj=b j(p j )ηj,

where b j is a scale parameter used for calibration and ηj is the elasticity controlling the change in scrap probability as the price of the car changes. Scrap rates increase with car age and are cali-brated to 0.05, 0.06, 0.09, and 0.20 for the four categories of used cars. These values are derived from the distribution of car age in the data (see online Appendix for details).

E. Solution Method

To solve the model, we must obtain the full vector of new and used car rental prices for a par-ticular year that satisfies the following conditions: (i) every available (not scrapped) used car has a buyer (or retainer), and (ii) for every new car producer, the first-order conditions for constrained profit maximization are satisfied.15 Note that the second requirement is a function of all prices, not just new car prices. We determine overall demands for a given car by aggregating across households their probability-weighted demands for that car.

The solution method embeds the used car problem within the broader problem of solving for both used and new car prices. Specifically, we solve for the used car prices that satisfy require-ment (i), conditional on a set of posited prices for the new cars. We then adjust the new car prices in an attempt to meet condition (ii), and solve again for used car prices that meet requirement (i) conditional on the adjusted new car prices. We repeat this procedure until conditions (i) and (ii) are met within a desired level of accuracy.16

14 Here it is relevant that we are simulating a permanent and constant change to the gasoline tax. If the policy involved government committing to a path of varying gasoline taxes in the future, for example, a more complex model-ing of expected future prices might be called for.

15 Note that the calibration procedure is embedded in a baseline simulation, before the introduction of an increment to the gasoline tax. The values of calibrated parameters (determining new car supply and costs, and used car scrap rates) are then saved and introduced into the policy simulation, solved as described in this section.

16 The oligopolistic structure of the new car market involves both multiple products and multiple producers. Under these conditions, theory leaves open the possibility of nonuniqueness. We have tested for nonuniqueness by random-izing starting values over a uniform distribution, and in these experiments the model has always converged to one solution.

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VOL. 99 nO. 3675 The government’s revenue from gasoline taxes is returned to households according to the various “recycling” methods described in Section IV. Government revenues and transfers are mutually dependent: the level of transfers affects household demands and government revenues, while the level of revenues determines the transfer level consistent with the government’s bud-get constraint. Thus, solving the model also requires that we determine the equilibrium level of government revenue and transfers. The overall solution is a set of prices for each car that simultaneously clears all markets, and an aggregate transfer level that equals the government’s revenues from the gasoline tax. To solve the multidimensional system we use Broyden’s method, a derivative-based quasi-Newton search algorithm.

II. Data

Our dataset has two main components: (i) a random sample of US households’ automobile ownership choices from the 2001 national Household Travel Survey(NHTS), and (ii) new and used automobile price and nonprice characteristics from Wards Automotive Yearbook, The National Automobile Dealer’s Association (NADA)Used Car Guide, and the Department of Energy (DOE) https://www.sodocs.net/doc/2717578349.html, Web site. By merging these two types of information, we obtain an unusually rich dataset, one that allows us to consider household choices among a wide range of new and used cars and that permits us to distinguish households along many important dimen-sions. In the Appendix, we offer details on how we merged the datasets and constructed needed variables.

A. The nHTS Sample

The 2001 NHTS consists of 26,038 households living in urban and rural areas of the United States. With the help of Department of Transportation (DOT) staff, we obtained the confidential NHTS data files containing relevant data for our analysis. For each household, we have informa-tion on income, automobile holdings (by make, model, and year), and vehicle miles traveled. In addition, we have data on the household’s demographic characteristics (including household size, composition, gender, education, and employment status) and geographical identifiers (including the state, metropolitan statistical area, and zip code of residence).

After cleaning the data, our final sample consists of 20,429 households from the original 26,038. Table 2 presents major demographic statistics of our final sample.

B. The Automobile Sample

The 1983–2002 Wards Automobile Yearbook provided most of the car and truck characteris-tics used in our analysis. Automobile characteristics include horsepower, weight, length, height, width, wheelbase, and city and highway miles per gallon (MPG) by make, model, and year for all cars and trucks sold during this period. We obtained information on car and truck prices from the NADA monthly Used Car Guide. We used price information from the April 2001 and 2002 editions of the guide, which we obtained in electronic format. Each edition contained the manufacturer’s suggested retail price and current resale price (a weighted average of recent transaction prices) for all new and used cars and trucks dating back to 1983. As indicated in the Appendix, we calculated depreciation based on changes in prices for a given car over the 2001–2002 period.

Combining information from the Wards and NADA datasets yielded a vector of prices and various automobile characteristics for roughly 4,500 automobiles distinguished by manufacturer, model, and year. We aggregated these data into the seven manufacturer categories, ten class

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categories, and five age categories in Table 1. We used a weighted geometric mean formula to aggregate price and nonprice characteristics within each make, class, and age category, where the weights were proportional to the holdings frequencies in the NHTS.

Table 3 displays statistics on miles per gallon, horsepower, and rental price from our data. The data show significant MPG differences across classes and age categories. A new compact, for example, is 1.48 times more efficient than a large SUV. The newest compacts yield 1.47 more miles per gallon than those in the oldest age category. In contrast, the newest midsize and large SUVs are less fuel-efficient than the older models. As for horsepower, most of the increases apply to compacts and full size cars. Average horsepower of compacts increased 60 percent, and a verage horsepower of full size cars rose 75 percent. Differences in rental price are most

Table 2—Sample Demographic Statistics from the 2001 NHTS—20,429 Observations Variable

Mean (SD )Household size

2.490 (1.34) Number of adults ≥ 18 years old 1.861 (0.69) Number of adults ≥ 65 years old 0.380 (0.67) Number of children ≤ 2 years old 0.096 (0.32) Number of children 3–6 years old 0.136 (0.41) Number of children 7–11 years old 0.185 (0.49) Number of children 12–17 years old 0.211 (0.54) Number of workers 1.272 (0.95) Number of females

1.033 (0.52)Average age among adults (≥ 18)49.560 (16.8)Household income (2001 $s )

56,621 (43,276)Household breakdown

Percentage

1 male adult, no children, not retired 5.711 female adult, no children, not retired 7.881 adult, no children, retired

10.302+ adults w / average age ≤ 35, no children, not retired

7.102+ adults w / average age > 35 and ≤ 50, no children, not retired 8.432+ adults w / average age > 50, no children, not retired 9.042+ adults w / average age ≤ 67, no children, retired 9.292+ adults w / average age > 67, no children, retired 8.471+ adults w / youngest child < 3 years old 8.691+ adults w / youngest child 3–6 years old 7.651+ adults w / youngest child 7–11 years old 8.641+ adults w / youngest child 12–17 years old 8.85White household respondent a 85.60Black household respondent 7.62Hispanic household respondent 6.25Asian household respondent

2.17Adults with high school diplomas 89.40Adults with four-year college degrees 30.50Resident of MSA < 250k 7.62Resident of MSA 250–500k 8.22Resident of MSA 500k–1m 8.30Resident of MSA 1–3m 22.20Resident of MSA > 3m 32.50Nonresident of MSA

21.10Household income ≤ $25,000

22.80Household income ≤ $50,000 and > $25,00033.30Household income ≤ $75,000 and > $50,00019.80Household income > $75,000

24.10

a

The white, black, Hispanic, and Asian percentages sum to more than 100 percent because some respondents have multicultural backgrounds.

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substantial for new cars, due to the particularly rapid depreciation of new luxury vehicles. Older cars have much lower rental prices, and these prices are more similar across classes.

C. Calculation of Rental prices and per-Mile Operating Costs

Two important variables we must construct from our data are the automobile rental prices and per-mile operating costs (the “price per mile” variable in Section I ) for all 284 autos. The under-lying inputs to these prices and costs differ by region as well as automobile type. For household i owning car j , the rental price is given by

Table 3—Automobile Characteristics

Characteristic Compact Luxury compact Midsize Fullsize Luxury mid /full Small SUV Large SUV /van Trucks and minivans Total

Miles per gallon a All car ages 29.73 (27.8, 35.6)24.18 (22.2, 26.9)27.16 (24.2, 31.0)25.57 (22.6, 30.5)23.65 (21.3, 25.0)23.75 (17.8, 27.0)20.04 (16.6, 26.8)22.19 (16.8, 27.7)24.39 (16.6, 35.6) Model years 2001–200230.29 (28.0, 32.8)24.47(22.9, 26.9)26.90 (24.2, 30.5)25.61 (23.0, 28.0)23.70 (23.0, 24.2)24.17 (21.9, 26.4)19.08 (17.2, 22.5)21.51 (16.8, 25.9)24.15 (16.8, 32.8) 1999–200030.32 (28.1, 35.6)24.45 (23.1, 26.8)27.29 (25.1, 29.7)25.79 (22.6, 28.0)23.86 (23.0, 24.4)23.80 (19.8, 27.0)18.21 (16.7, 19.6)22.07 (18.8, 26.3)24.18 (16.7, 35.6)

1995–199830.02 (28.4, 32.1)24.24 (22.3, 26.4)27.50 (25.4, 29.8)25.51 (23.0, 27.8)24.29 (23.3, 25.0)23.44 (19.6, 26.3)19.60 (16.6, 23.7)22.01 (17.7, 27.2)24.44 (16.6, 32.1)

1990–199429.21 (27.8, 30.4)23.81 (22.2, 26.3)26.74 (25.2, 30.0)25.37 (23.5, 28.8)22.91 (21.3, 24.0)22.67 (17.8, 24.9)20.90 (17.2, 26.0)21.80 (17.6, 26.0)24.08 (17.2, 30.4)

1983–198928.82 (28.2, 29.4)23.94 (22.6, 26.1)27.38 (24.3, 31.0)25.56 (23.8, 30.5)23.23 (22.1, 24.3)24.84 (23.3, 26.3)22.88 (18.1, 26.8)23.75 (20.0, 27.7)25.14 (18.1, 31.0)

Horsepower/100 All car ages 1.286 (0.88, 1.78) 2.275 (1.56, 3.63) 1.530 (0.98, 1.96) 1.726 (0.86, 2.21) 2.177 (1.42, 2.81) 1.531 (1.02, 1.95) 1.909 (0.88, 2.59) 1.665 (0.94, 2.79) 1.719 (0.86, 3.63) Model years 2001–2002 1.526 (1.34, 1.78) 2.621 (1.64, 3.63) 1.787 (1.65, 1.96) 2.123 (1.97, 2.21) 2.463 (2.13, 2.81) 1.763 (1.65, 1.95) 2.391 (2.15, 2.59) 2.023 (1.40, 2.79) 2.036 (1.34, 3.63)

1999–2000 1.454 (1.23, 1.68) 2.488 (1.70, 3.45) 1.682 (1.58, 1.80) 1.917 (1.50, 2.07)

2.376 (2.10)

1.648 (1.45, 1.88)

2.271 (2.12, 2.52) 1.920 (1.34, 2.63) 1.932 (1.23,

3.45)

1995–1998 1.342 (1.09, 1.47) 2.414 (1.75, 3.38) 1.597 (1.47, 1.72) 1.835 (1.41, 2.07) 2.237 (2.01, 2.53) 1.554 (1.35, 1.83) 2.024 (1.86, 2.17) 1.633 (1.09, 2.06) 1.773 (1.09, 3.38)

1990–1994 1.152 (1.05, 1.24) 2.075 (1.60, 2.54) 1.418 (1.28, 1.54) 1.469 (0.90, 1.74) 1.952 (1.83, 2.11) 1.467 (1.29, 1.59) 1.476 (0.90, 1.77) 1.430 (1.07, 1.78) 1.516 (0.90, 2.54)

1983–19890.955 (0.88, 1.03) 1.777 (1.56, 2.15) 1.166 (0.98, 1.41) 1.212 (0.86, 1.36) 1.637 (1.42, 2.01) 1.164 (1.02, 1.27) 1.244 (0.88, 1.46) 1.243 (0.94, 1.51) 1.270 (0.86, 2.15)

Rental price/1000 All car ages 2.570 (0.38, 6.84) 5.959 (0.55, 26.6) 2.749 (0.38, 8.55) 3.029 (0.39, 8.67) 5.680 (0.45, 21.4) 3.141 (0.42, 7.81) 4.289 (0.43, 14.4) 3.149 (0.26, 8.32) 3.681 (0.26, 26.6) Model years 2001–2002 5.798

(5.14, 6.84)15.94 (7.23, 26.6) 6.528 (5.65, 8.55)7.463 (6.84, 8.67)14.45 (11.8, 21.4) 6.823 (6.12, 7.81)10.27 (7.92, 14.4) 6.750 (4.78, 8.32)8.792 (4.78, 26.6)

1999–2000 3.258 (2.14, 4.24) 6.819 (3.74, 12.6) 3.274 (2.10, 4.72) 3.628 (3.13, 4.52) 5.712 (3.99, 8.69) 3.724 (3.11, 4.35) 4.566 (2.20, 7.69) 3.850 (2.91, 5.24) 4.237 (2.10, 12.6)

1995–1998 2.320 (1.62, 3.27) 4.506 (2.59, 5.72) 2.420 (1.68, 3.18) 2.521 (2.06, 3.17) 3.823 (2.54, 5.61) 2.884 (2.20, 3.58) 3.638 (2.53, 5.66) 2.842 (1.94, 3.68) 3.051 (1.62, 5.72)

1990–19940.972 (0.72, 1.29) 1.679 (1.11, 2.34) 1.015 (0.73, 1.33) 1.019 (0.75, 1.26) 1.317 (0.86, 1.79) 1.259 (0.98, 1.74) 1.253 (0.69, 2.04) 1.118 (0.74, 1.51) 1.186 (0.69, 2.34)

1983–1989

0.503 (0.38, 0.67)0.850 (0.55, 1.31)0.509 (0.38, 0.67)0.491 (0.39, 0.64)0.714 (0.45, 1.21)0.589 (0.42, 0.82)0.676 (0.43, 1.31)0.514 (0.26, 0.73)0.585 (0.26, 1.31)

notes: Minimum and maximum values reported in parentheses. The categories small truck, large truck, and minivan have been aggregated in this table.a

Weighted harmonic mean of EPA test miles per gallon estimates.

JUnE 2009 678THE AMERICAn ECOnOMIC REVIEW

(9)r i j=D j+ 0.85 I ij A+f i j+R p j,

where

D j=depreciation in the real value of car j,

I ij A=household i’s annual insurance costs for car j,

f i j=household i’s automotive registration fees for car j, and

R =real interest rate.

Thus, the one-year rental price of a car is the sum of depreciation, insurance, and registration costs, plus the forgone real return on the principal value of the car.17 For the real interest rate, R, we use a value of 3.89 percent, the 2001 average daily real rate on 30-year T-Bills. We include insurance costs in both the rental price (associated with the choice of car) and the per-mile oper-ating cost (associated with VMT). Representatives from State Farm Insurance suggested to us that roughly 85 percent of auto insurance premiums are fixed and independent of VMT. Hence, 85 percent of insurance costs appear in the rental price formula, while the remainder is allocated to operating costs.

The rental prices are included in the household utility function relative to the price of the out-side good (cost of living) faced by each household. We incorporate a cost of living index for 363 distinct regions that, together with differences in insurance and registration fees, reflects varia-tion across households in the effective rental price of vehicles.18

The per-mile operating cost, p ij M, is expressed by:

(10)p ij M=( p i gas/M pG j*)+n j+ 0.15 I ij M,

where

gas=household i’s per gallon price of gasoline,

p

i

MpG j=miles per gallon for car j,

n j=per-mile maintenance and repair costs for car j, and

I ij M=household i’s per-mile insurance costs for car j.

The price of gasoline (and therefore operating cost) varies among households based on differ-ences across 363 distinct regions of residence. The average after-tax gasoline price faced by households in 2001 ranged from $1.19 (Albany, GA) to $1.86 per gallon (San Francisco).

17 If the household has purchased the car using a loan, this term can be equivalently interpreted as the interest pay-ment on that loan.

18 Further details about the regional cost of living index are provided in the Appendix; it varies by a factor of 1.77 across households.

BEnTO ET AL.: IMpACTS Of InCREASED US GASOLInE TAxES

VOL. 99 nO. 3679 III. Estimation of Household Ownership and Utilization Decisions

A. The Econometric Model

Challenges.—Two overarching concerns influenced our approach to estimating household automobile demand. The first was our desire to integrate consistently the car ownership and uti-lization decisions. Such integration is crucial for generating consistent estimates of welfare costs from gasoline taxes. The second concern arose from an important feature of the data: households frequently own more than one car. In the 2001 NHTS, 41.5 percent of households own zero or one car, another 43.6 percent own two cars, and the remaining 14.9 percent own three or more autos. This implies that many households have a potentially enormous number of auto bundles from which to choose. If, for example, there are J different cars and trucks and we consider only bundles consisting of no more than two cars, there are 1 +J+J(J+ 1)/2 bundles that house-holds can potentially choose. With our automobile dataset consisting of 284 composite cars and trucks, there are 40,755 distinct bundles that households might choose (and this large number ignores all bundles with three or more autos).19

As discussed in the introduction, nearly all past efforts to integrate automobile ownership and utilization decisions have relied on reduced-form, sequentially estimated models. Our struc-tural approach estimates simultaneously the decisions on both margins. To account for different households owning different quantities of cars, we adopt a variation of Igal E. Hendel (1999) and Jean-Pierre H. Dubé’s (2004)repeated discrete-continuous framework. In the context of automobile choice, the framework assumes that a household’s ownership and utilization choices arise from separable choice occasions. On each choice occasion, the household makes a discrete choice of whether to own one of J automobiles. If an auto is chosen, the household conditionally decides how much to drive it during the year. To account for ownership of multiple automo-biles, households have multiple choice occasions on which different automobile services may be demanded. Intuitively, different choice occasions in our framework correspond to different primary tasks or purposes for which households might demand automobile services (e.g., com-muting to work, family travel, shopping excursions, or any combination thereof). We assume their number depends on the number of adults in a given household.20

Our approach to modeling automobile demand has advantages and drawbacks. Its main advan-tages are that it consistently links ownership and utilization decisions and reduces the dimension of the households’ choice set on a given choice occasion to J+ 1 alternatives (J autos and the no-auto alternative). The latter feature makes our approach econometrically tractable with our 284 composite auto dataset. It also has the virtue of allowing for households to own several cars.

A main drawback is that it does not allow for interaction effects among the fleet of autos held by households—for example, a four-person household’s utility from holding a second minivan being less than holding a single minivan. To account for such interactions, one would need to regard bundles of automobiles, rather than individual cars, as the objects of choice. As suggested

19 Past transportation applications have addressed this dimensionality problem by randomly sampling from the full set of choice alternatives in estimation. As discussed in Train (1986), such an approach works only with restric-tive fixed parameter logit and nested logit models. We cannot adopt this sampling approach in our model because, as described below, our model employs random coefficients to introduce correlations in the unobservables entering the discrete and continuous choice margins. Moreover, although the sampling approach solves the dimensionality problem in estimation, it does not solve the problem in a simulation model, where the full choice set would need to be employed to construct aggregate automobile demands.

20 There is some evidence in the nonmarket valuation literature that the specification of the number of choice occa-sions, as long as it is larger than the chosen number of goods, does not have significant effects on estimated welfare measures (von Haefen, D. Matthew Massey, and Wiktor L. Adamowicz 2005). Moreover, we do not expect that it has much, if any, effect on the relative efficiency rankings of policies.

JUnE 2009

680THE AMERICAn ECOnOMIC REVIEW above, however, such an approach would require substantially more aggregation of cars beyond what we have pursued.21 This would rule out significant product differentiation and thus severely limit our ability to account for the imperfectly competitive nature of the automobile industry. In addition, it would compel us to put a limit of two on the number of cars owned by any household, which would eliminate from our sample those households likely to be most affected by changes in gasoline taxes.

Specifics .—Our repeated discrete-continuous model of automobile demand works as follows. Household i (i = 1, … , n ) is assumed to have a fixed number of choice occasions, T i . We let T i equal the number of adults in each household plus one.22 On choice occasion t , household i is assumed to have preferences for car j ( j = 1, … , J ) that can be represented by the following con-ditional indirect utility function:(11) V i t j = V ′i j + μi εi t j ,

where V ′ij = ? 1 ___ λi exp a ? λi a y i /T i ? r ij

________ p ix b b ? 1 ___ βij

exp a αij + βij p ij M ___ p ix b + τij , αij = ? α i T z ij

α , βij = ? e xp ( ? β i T z i j β

), λi = exp ( ? λ i T z i λ), τij = ? τi T z i

j τ, and

μi = exp ( μ i *

),and where ( y i , r ij , p ij M , p ix ) are household i’s income, rental price for the j th auto, utilization

(or VMT ) price for the j th car, and the Hicksian composite commodity price, respectively; ( z i j α , z i j β, z i j τ) are alternative automobile characteristics (including make, age, and class dummies

that control for unobserved attributes 23) interacted with household demographics; z i λ

contains just household characteristics; ( ? α i , ? β i , ? λ i , ? τi , μ i *

) are parameters that vary randomly across house-holds; and εi t j contains additional unobserved heterogeneity that varies randomly across house-holds, automobiles, and choice occasions.24 If the household decides, instead, not to rent a car (i.e., automobile 0), its conditional indirect utility function is:

21

Feng, Fullerton, and Gan’s (2005) bundling approach aggregates all automobiles into one of two composites—cars and trucks.22

The 2001 NHTS indicates that 11.1 percent of households have more automobiles than the number of adults. For the 1.84 percent of households with more autos than the number of adults plus one, we set the number of choice occa-sions equal to the number of held autos. 23

Berry, Levinsohn, and Pakes (1995, 2004) use alternative specific constants for every automobile to control for unobserved characteristics. Given the highly nonlinear-in-parameters structure of our conditional indirect utility functions, we could not estimate a model with a full set of alternative specific constants, and instead adopted a more parsimonious specification with make, age, and class dummies as in Goldberg (1995).24

The level of income in the budget constraint associated with each choice occasion is the household’s income divided by the number of choice occasions. This assures that overall spending is consistent with the household’s total

VOL. 99 nO. 3681

BEnTO ET AL.: IMpACTS Of InCREASED US GASOLInE TAxES (12)

V it 0 = ? 1 ___ λi

exp a ? λi a y i /T i _____ p ix b b + φ i T z i

φ + μi εit 0,where z i φ

and φi are individual characteristics and parameters, respectively. The rational house-hold is assumed to choose the alternative that maximizes its utility on each choice occasion. Assuming each εi t j ( j = 0, … , J ) can be treated as independent draws from the normalized type I extreme value distribution, the probability that individual i chooses alternative j on choice

o ccasion t condition on the model’s structural parameters is (13)

Pr it ( j ) = exp (V ′ij /μi )

___________ ∑ k

exp (V ′ik /μi )

.

Assuming the household chooses automobile j , Roy’s identity implies that the household’s

conditional VMT demand is (14)

M itj = exp a αij + βij a p ij M ___ p ix

b + λi a y i /T i ? r ij ________ p ix b b .We assume the analyst imperfectly observes M itj due to measurement error in our data.25, 26 The

analyst observes ? M itj = M itj + ηitj , where ηitj is an independent draw from the normal distribu-tion with mean zero and standard deviation σi = exp ( σ i * ).27 The likelihood of observing ?

M itj

conditional on the model parameters is (15)

l ( ? M itj | j chosen, j ≠ 0) = 1 _______ (2π)1/2σi

exp a ? 1__ 2 a ? M itj ? M itj ________ σi b 2 b .Given our assumed structure, the full likelihood of household i ’s automobile demand conditional

on δ = ( ? α i , ? β i , ? λ i , ? τi , φi , μ i * , σ i * ) is then (16)

L i = ∏ t =1

T i

c ∏ j =0

J

P r it ( j ) 1 itj

∏ j =1

J

l ( ? M itj | j chosen

) 1 itj d ,where 1itj is an indicator function equal to one if car j is chosen on individual i ’s t th choice occa-sion, and zero otherwise.

income.

25

Because the 2001 NHTS elicited VMT in part by asking respondents to recall their past driving behavior, we believe it is appropriate to account explicitly for measurement error in reported VMT.26

Our assumption that some disturbances capture preference heterogeneity while others pick up measurement error makes our model conceptually similar to the Gary Burtless and Hausman (1978) two-error discrete-continuous model that is frequently used in nonlinear budget constraint applications.27

Following Dubin and McFadden (1984), past automobile applications assume some degree of correlation between ηitj and the type I extreme value errors in the discrete choice model. Similar to King (1980), we instead assume that these disturbances are independent, and introduce correlations between the discrete and continuous choices through random parameters as described below.

JUnE 2009

682THE AMERICAn ECOnOMIC REVIEW B. Estimation Strategy

Past econometric efforts to model vehicle ownership and derived VMT demand decisions have used variations of Dubin and McFadden’s (1984) sequential estimation strategy that accounts for the induced selectivity bias in derived VMT demand with a Heckman-like (1979) correction factor. We employ a full-information estimation approach that accounts for correlations in the unobserved determinants of choice across discrete and continuous dimensions through random parameters (McFadden and Train 2000). Intuitively, random parameters allow unobserved varia-tions in taste to influence automobile ownership decisions and VMT demand decisions. We allow all parameters, δ = ( ? α i , ? β i , ? λ i , ? τi , φi , μ i

* , σ i * ), to be distributed multivariate normal with mean _ δ and variance-covariance matrix Σδ. This approach is more general than earlier random coefficient discrete-continuous applications (e.g., Mervyn King 1980; Feng, Fullerton, and Gan 2005) that include only one random parameter. The more general specification offers a far richer degree of unobserved preference heterogeneity to influence households’ ownership and use decisions than previous applications.28

Given the nonlinear nature of our likelihood function, the large number of households and sites in our dataset, and the potentially large number of parameters on which we wish to draw inference, classical estimation procedures such as maximum simulated likelihood (Christian Gourieroux and A. Monfort 1996) would be exceptionally difficult, if not impossible, to imple-ment. In light of these computational constraints, we adopt a Bayesian statistical perspective and employ a variation of Greg M. Allenby and Peter J. Lenk’s (1994) Gibbs sampler estimation procedure, which is less burdensome to implement in our application.29

The Bayesian framework assumes that the analyst has initial beliefs about the unknown parameters ( _ δ , Σδ) that can be summarized by a prior probability distribution, f ( _ δ

, Σδ). When the analyst observes a set of choices x , she combines this choice information with the assumed data-generating process to form the likelihood of x conditional on alternative values of ( _ δ , Σδ), L (x | _ δ , Σδ). The analyst then updates her prior beliefs about the distribution of ( _ δ , Σδ) to form a posterior distribution for ( _ δ , Σδ) conditional on the data, f ( _ δ , Σδ | x ). By Bayes’s rule, f ( _ δ , Σδ | x ) is proportional to the product of the prior distribution and likelihood, i.e., f ( _ δ , Σδ | x ) = f ( _ δ , Σδ)L (x | _ δ , Σδ)/D, where D is a constant. In general, f ( _ δ

, Σδ | x ) will not have an analyti-cal solution, and thus it is difficult to derive inference about the moments and other relevant prop-erties of ( _

δ

, Σδ) conditional on the data. However, Bayesian econometricians have developed a number of Markov Chain Monte Carlo (MCMC ) procedures to simulate random samples from f ( _ δ , Σδ | x ), and in the process draw inference about the posterior distribution of ( _ δ , Σδ).Following Allenby and Lenk (1994), we specify diffuse priors for ( _ δ , Σδ) and use a Gibbs sampler with an adaptive Metropolis-Hastings component to simulate from f ( _ δ

, Σδ | x ). By decomposing the parameter space into disjoint sets and iteratively simulating from each set con-ditionally on the others, the Gibbs sampler generates simulations from the unconditional poste-rior distribution after a sufficiently long burn-in. The implementation details of the algorithm are described in the Appendix.

28

For example, under our random coefficients specification, a household that is relatively insensitive to utilization costs and horsepower when purchasing a car will likewise be relatively insensitive to these factors when driving it.29

Although the Bayesian paradigm implies a very different interpretation for the estimated parameters relative to classical approaches, the Bernstein–von Mises theorem suggests that the posterior mean of Bayesian parameter estimates, interpreted within the classical framework, are asymptotically equivalent to their classical maximum likeli-hood counterparts. Following Train (2003), we interpret this result as suggesting that both approaches should generate qualitatively similar inference, and thus the analyst’s choice of which to use in practice can be driven by computational convenience.

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BEnTO ET AL.: IMpACTS Of InCREASED US GASOLInE TAxES

One further dimension of our estimation approach is worth noting. Because of the large number of households in our dataset (n= 20,429) and our desire to account for differences in automobile demand across different household types (e.g., single males, two-adult households with and without children, retired couples), we stratified the sample into 12 groups based on demographic characteristics and estimated separate models within each strata. In addition to decomposing a computationally burdensome estimation problem on a large data-set into a series of more manageable estimation problems on smaller datasets, stratification allows us to better account for observable and unobservable differences among households.

C. Empirical Results

For all 12 strata, we obtain precisely estimated posterior mean values for (_δ ,Σδ).30 Many of

the parameters that are common across the 12 strata vary in magnitude considerably, suggesting

that there is significant preference heterogeneity across the different subpopulations. We also

find that the diagonal elements of Σδare generally large, suggesting considerable preference heterogeneity within each stratum as well. The latter preference heterogeneity and the highly

nonlinear structure of our preference function mean that the estimated parameters do not have

a simple economic interpretation. Thus, instead of focusing on the estimated parameters, we

examine the various elasticities they imply. We display these elasticities in Table 4, broken down

by household and automobile types. Our cross-section estimation implies that these should be

interpreted as long-run elasticities.

The first column of Table 4 reports the elasticity of gasoline use with respect to gasoline price.

In the “All” and “By household” panels, the elasticities allow for responses in both VMT and car

choice (and associated fuel economy). In the “By auto” panel, the elasticities are conditional on

car choice. Across all households and cars, we obtain a mean estimate of ?0.35. The estimated

elasticities are larger for families with children and owners of trucks and SUVs. D. J. Graham

and Stephen Glaister’s (2002) survey of past studies indicates long-run elasticities in the United

States ranging from ?0.23 to ?0.80. Kenneth A. Small and Kurt Van Dender’s (2007) more

recent state-level analysis produces a central estimate of ?0.33.

The second column of the table shows the elasticity of gasoline use with respect to income.

On average, we find estimates of around 0.76. The elasticity is highest for families with children

and owners of new vehicles. Graham and Glaister report long-run estimates in the range of 1.1

to 1.3.31

The third column reports car ownership elasticities with respect to the own rental price. For

new cars, rental price elasticities should track purchase price elasticities if rental and purchase

prices vary proportionally. Our results imply mean rental price elasticities of ?0.88 for all vehi-

cles and ?1.97 for new vehicles only. Luxury cars, large SUVs, and large trucks, which have the

highest rental prices, have the highest rental price elasticities among automobile classes.

Our estimated elasticities with respect to rental prices are smaller in absolute magnitude than

those found in some studies, such as Berry, Levinsohn, and Pakes (1995), which obtained elas-

ticities ranging from ?3 to ?4.5. A plausible explanation is that the objects of choice in our

study are not individual make-models but automobile composites (i.e., make-model combina-

tions aggregated by age, class, and make). This aggregation implies that we have only 59 new

30 Parameter estimates for each of the 12 strata are reported in the Appendix.

31 Although our estimated income elasticities are lower than in much of the previous literature, we note that our stratification of the sample allows parameters controlling income effects to vary among types of households, which may yield a more accurate estimation of income effects than in prior (mainly time-series) work.

JUnE 2009

684THE AMERICAn ECOnOMIC REVIEW

cars in our dataset, not the 200–300 cars typically found in other applications. By collapsing

make-models into composite cars, we reduce the number of channels for substitution.

Much of the work estimating these elasticities has focused exclusively on new vehicles (e.g., Berry, Levinsohn, and Pakes 1995; Petrin 2002). These studies have generally employed multiple years of automobile sales data and controlled for the potential endogenity of price arising from unobserved car characteristics.32 In contrast, we have a single household-level cross section and control for unobserved product characteristics through class, make, and age dummies that vary across household types.

32

For example, Berry, Levinsohn, and Pakes (1995) employ 20 years of market-level data for new make-model combinations, and use alternative specific constants and instrumental variables to identify price effects.

Table 4—Posterior Mean Long-Run Elasticity Estimates

Elasticity of gasoline use wrt price a

Elasticity of gasoline use wrt income a

Car ownership elasticity wrt rental price VMT elasticity

wrt operating

cost a

All

? 0.350.76

? 0.82? 0.74By household

Retired

? 0.320.61? 0.93? 0.69 Not retired, no children ? 0.320.68? 0.72? 0.69 Not retired, with children ? 0.39

0.96

? 0.85

? 0.83

By auto By class All cars Compact

? 0.270.83

? 0.65? 0.59

Luxury compact ? 0.300.78? 1.25? 0.64 Midsize ? 0.280.74? 0.67? 0.60 Fullsize

? 0.290.75? 0.73? 0.63 Luxury midsize /fullsize ? 0.300.79? 1.25? 0.63 Small SUV ? 0.290.93? 0.73? 0.63 Large SUV /van ? 0.320.88? 0.98? 0.69 Small truck ? 0.340.78? 0.62? 0.72 Large truck ? 0.310.79? 0.85? 0.66 Minivan ? 0.310.85? 0.77? 0.65 New cars Compact

? 0.28 1.14? 1.44? 0.60 Luxury compact ? 0.270.76? 3.14? 0.46 Midsize ? 0.290.95? 1.58? 0.60 Fullsize

? 0.29 1.04? 1.77? 0.61 Luxury midsize /fullsize ? 0.280.83? 3.04? 0.47 Small SUV ? 0.26 1.86? 1.58? 0.55 Large SUV /van ? 0.34 1.06? 2.30? 0.69 Small truck ? 0.370.91? 1.32? 0.75 Large truck ? 0.32 1.05? 1.69? 0.65 Minivan ? 0.310.98? 1.67? 0.63By age

New cars

? 0.30 1.10? 1.97? 0.63 1- 2-year-old cars ? 0.290.79? 1.01? 0.63 3- 6-year-old cars ? 0.270.76? 0.73? 0.59 7- 11-year-old cars ? 0.300.75? 0.28? 0.65 12- 18-year-old cars

? 0.31

0.83

? 0.13

? 0.68

a Elasticities in the By Auto panel are conditional on car choice.

BEnTO ET AL.: IMpACTS Of InCREASED US GASOLInE TAxES

VOL. 99 nO. 3685

A close comparison with data types and results from other studies suggests that our smaller elasticities might also reflect limitations from cross-sectional data and are not likely, due to a fail-ure to adequately control for unobserved car characteristics. Our elasticities are similar in mag-nitude to those reported in Berry, Levinsohn, and Pakes (2004) and Train and Winston (2007), studies that employ household-level cross-sectional data and control for price endogeneity with alternative specific constants and instrumental variables.33 In addition, Goldberg (1995), using five years of household-level data and an identification strategy comparable to ours, finds elas-ticities for make-models that are similar in magnitude to those of Berry, Levinsohn, and Pakes (1995). 34 Combined, these results suggest that our estimates control sufficiently for endogeneity of price but may reflect limitations from the cross section of data used.

The final column of the table reports long-run VMT elasticities with respect to operating costs. Across all households and cars, the average elasticity is ?0.74. This elasticity is lower for new cars than for older vehicles. Older cars are disproportionately owned by lower-income house-holds, which exhibit higher VMT elasticities. Because gasoline makes up slightly less than half of per-mile operating costs, our average estimate implies an average VMT elasticity with respect to the price of gasoline of ?0.34. In their survey, Graham and Glaister report that, from prior studies, the average estimate for this long-run elasticity is ?0.30, while Small and van Dender report an estimate closer to ?0.1. Both sets of authors note that existing estimates are quite sen-sitive to the data and modeling assumptions employed, and thus the caveats mentioned earlier concerning the limitations of cross-sectional data may apply here as well. Past applications that (like ours) use disaggregate household data to control for endogenous vehicle choice tend to find larger elasticities than aggregate time series or panel data studies that combine household and commercial demand for highway VMT (Mannering 1986).

IV. Simulation Results

A. Assumptions Underlying the Simulation Dynamics

The simulation model generates a time path of economic outcomes over ten years at one-year intervals. As mentioned, the model solves in each period for the market-clearing new and used car prices. We assume that household incomes grow at an annual rate of 1 percent. In all simu-lations, the pre-tax price of gasoline is $1.04 and is taken as exogenous and unchanging over time.35

B. Baseline Simulation

The baseline simulation offers a reference scenario with which we compare the outcomes from various gasoline tax policies. Consistent with historical trends, we assume in this simulation that automobile horsepower and weight increase at an annual rate of 5 percent. In our central case, we calibrate the baseline fuel economy technology to the “Path 1” assumptions of the National Research Council (2002) regarding improvements in fuel economy: over a ten-year period, such improvements range from 11 percent for compacts to 20 percent for large SUVs. As part of a

33 Train and Winston use a cross section of household-level data involving 200 new cars, and find average elasticities for new cars ranging from ?1.7 to ?3.2.

34 We explored the sensitivity of estimates to several alternative specifications and estimation strategies. In particu-lar, we experimented with allowing the income coefficient to vary across car classes and age groups, and restricting a subset of parameters to be fixed across the sample. None of these alternatives generated elasticities significantly differ-ent from those in Table 4.1.

35 Preexisting federal taxes are $0.185, and average state taxes are $0.225.

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686THE AMERICAn ECOnOMIC REVIEW

sensitivity analysis below, we adopt in the baseline the more optimistic National Academy of Sciences (NAS) “Path 3” assumptions regarding growth in baseline fuel economy technology. In our policy simulations, producers adjust fuel economy away from these baseline technologies following equation (6) above.

Table 5 displays the equilibrium quantities of new and used cars under the baseline simulation. Our reference case overpredicts the size of the vehicle fleet by about 8 percent, ranging from 5 percent for midsize cars to 14 percent for small trucks.

C. Impacts of Gasoline Tax Increases under Alternative Recycling Methods

Here we present results from simulations of permanent increases in gasoline taxes. We start by focusing on the impacts of a tax increase of 25 cents per gallon (other tax increases are con-sidered below ) under the following alternative ways of recycling the additional revenues from the tax increase:

? “flat” recycling: revenues are returned in equal amounts to every household.

? “Income-based” recycling: revenues are allocated to households according to each house-hold’s share of aggregate income.

? “VMT-based” recycling: revenues are allocated as a lump sum according to each house-hold’s share of aggregate vehicle miles traveled in the baseline.Recycling could be accomplished by the government’s mailing rebate checks to households on an annual basis. The shares of total revenues going to different households depend on baseline values and thus do not depend on behavioral responses to the gasoline tax.Aggregate Impacts

Gasoline Consumption. Table 6 presents the impacts of this policy on gasoline consumption. In the short run (year 1), the percentage reduction is about 5.1 percent under flat and income-based recy-cling, and about 4.5 percent under VMT-based recycling. Compared with other recycling methods,

Table 5—Baseline Fleet Composition Year 1

Year 10New

Used All cars in operation New Used All cars in operation Class

Compact

4.9844.6849.66

5.2749.5254.79 Luxury compact 0.22 4.44 4.660.26 2.79 3.05 Midsize 2.6327.5830.21 2.8227.3030.12 Fullsize

1.3216.3217.64 1.4914.6416.13 Luxury mid /full 0.328.308.620.39 4.67 5.06 Small SUV 1.3210.6511.97 1.411

2.9914.40 Large SUV 1.1015.9317.02 1.3012.9214.23 Small truck 1.2710.2611.54 1.3512.251

3.60 Large truck 2.1719.8322.00 2.4222.162

4.58 Minivan 1.3212.7414.06 1.4513.621

5.07Total

16.65

170.73

187.39

18.15

172.87

191.03

note: Units are millions of privately owned cars in operation.

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精神分裂症患者在怎样的情况下会自杀

精神分裂症患者在怎样的情况下会自杀 精神分裂症是最常见的一种精神病。早期主要表现为性格改变,如不理采亲人、不讲卫生、对镜子独笑等。病情进一步发展,即表现为思维紊乱,病人的思考过程缺乏逻辑性和连贯性,言语零乱、词不达意。精神分裂症患者随时有可能出现危险行为,这主要是指伤人毁物、自伤自杀和忽然出走。这些危险行为是受特定的精神症状支配的.那么精神分裂症患者在什么情况下会自杀呢? 被害妄想:这是所有精神病人最常见的症状之一,多数病人采取忍耐、逃避的态度,少数病人也会“先下手为强”,对他的“假想敌”主动攻击。对此,最重要的是弄清病人的妄想对象,即:病人以为是谁要害他。假如病人的妄想对象是某个家里人,则应尽量让这位家属阔别病人,至少不要让他与病人单独在一起。 抑郁情绪:精神分裂症病人在疾病的不同时期,可能出现情绪低落,甚至悲观厌世。特别需要留意的是,有相当一部分自杀成功的病人,是在疾病的恢复期实施自杀行为的。病人在精神病症状消除以后,因自己的病背上了沉重的思想包袱,不能正确对待升学、就业、婚姻等现实问题,感到走投无路,因此选择了轻生。对此,家属一定要防患于未然,要尽早发现病人的心理困扰,及时疏导。 对已经明确表示出自杀观念的病人,家属既不要惊慌失措,也不要躲躲闪闪,要主动与病人讨论自杀的利弊,帮助病人全面、客观地评估现实中碰到的各种困难,找出切实可行的解决办法。 另外,这种病人在自杀之前,是经过周密考虑,并且做了充分预备的,例如写遗书、收拾旧物、向家人离别、选择自杀时间、预备自杀工具等。这类病人的自杀方式也是比较温顺的,多数是服药自杀。因此,他需要一定的时间来积攒足足数目的药物,这时就能看出由家属保管药品的重要性了。只要家属密切观察病人的情绪变化,是不难早期发现病人的自杀企图的。 药源性焦虑:抗精神病药的副作用之一是可能引起病人莫名的焦躁不安、手足无措,并伴有心慌、出汗、恐惧等。这些表现多是发作性的,多数发生在下午到傍晚时分,也有的病人在打长效针以后的2?3天内出现上述表现。这种时间上的规律性,有助于家属判定病人的焦虑情绪是否由于药物所致。病人急于摆脱这种强烈的痛苦,会出现冲动伤人或自伤,这些行为只是为了发泄和解脱,并不以死为终极目的。家属可以在病人发作时,给他服用小剂量的安定类药物,或者在医生的指导下,调整抗精神病药的剂量或品种,这样就可以有效地控制病人的焦虑发作。 极度兴奋:病人的精神症状表现为严重的思维紊乱、言语杂乱无章、行为缺乏目的性,这类病人也可能出现自伤或伤人毁物。由于病人的兴奋躁动是持续性的,家属有充分的思想预备,一般比较轻易防范。家属要保管好家里的刀、剪、火、煤气等危险物品,但最根本的办法,是使用大剂量的、具有强烈镇静作用的药物来控制病人的兴奋。假如在家里护理病人确有困难,则可以强制病人住院治

女性警惕五种常见外阴疾病

女性警惕五种常见外阴疾病 *导读:女性的阴部柔软,脆弱,不好好呵护就容易受伤。外阴损伤是常见的外阴疾病,常因遭到猛烈碰撞导致。此外,还有外阴损伤、尖锐湿疣、外阴肿瘤等外阴疾病女性也要警惕。…… *1、外阴损伤 外阴损伤是女性常见的症状之一。发病原因多数为骑跨式跌伤,如骑男式自行车时意外的急刹车,或上下车时阴部遭到猛烈碰撞,外阴部位受到暴力打击等等。 在这种情况下,外阴部有严重的挫伤,可有疼痛,能见到皮下淤血或血肿。 *2、*尖锐湿疣 尖锐湿疣是一种性传播疾病,一般与不洁性交有关。发病时,外阴瘙痒,分泌物增加。早期外阴部的皮肤、粘膜粗糙不平,随后可摸到小结节或肿块,样子为毛刺状,或者像大小不等的菜花状、鸡冠花状的灰白色肿物,多分布在小阴唇的内侧、大小阴唇之间的唇间沟、会阴和肛门。 *3、假性湿疣 假性湿疣不是性传播疾病。在阴唇内侧可以看到有小米粒大小的淡红色疹子,两侧对称,分布均匀。 *4、*外阴肿瘤 女性外阴的良性肿瘤,如乳头瘤、纤维瘤等,并不多见。它

们是生长在大阴唇外侧的单个肿瘤。 常见的恶性肿瘤是“外阴鳞状上皮癌”。在外阴部能摸到硬结或肿物,常伴有疼痛或瘙痒,有的病人在外阴部位,还会长有经久不愈的溃疡。 *5、*外阴白色病变 外阴白色病变,也称为“慢性外阴营养不良”。 有一种外阴白色病变,一般发生在30~60岁的妇女,主要症状是外阴奇痒难忍,抓破以后伴有局部疼痛。外阴皮肤增厚,颜色多为暗红色或粉红色中夹杂有界限清晰的白色斑块。 如果发现有外阴白斑,应当去详细检查治疗。过去,曾经认为它可以癌变,所以主张早期切除。现在,虽然医生们已经不主张早期切除,但是,还是要病人积极治疗。 有白色病变的人,更要保持外阴部位的清洁干燥,不要用肥皂或其他刺激性药物清洗外阴,也不要用手去搔抓,不要吃辛辣的食物,衣服要宽大,不要穿不透气的人造纤维内裤。

脐带血间充质干细胞的分离培养和鉴定

脐带血间充质干细胞的分离培养和鉴定 【摘要】目的分离培养脐带血间充质干细胞并检测其生物学特性。方法在无菌条件下用密度梯度离心的方法获得脐血单个核细胞,接种含10%胎牛血清的DMEM培养基中。单个核细胞行贴壁培养后,进行细胞形态学观察,绘制细胞生长曲线,分析细胞周期,检测细胞表面抗原。结果采用Percoll(1.073 g/mL)分离的脐血间充质干细胞大小较为均匀,梭形或星形的成纤维细胞样细胞。细胞生长曲线测定表明接后第5天细胞进入指数增生期,至第9天后数量减少;流式细胞检测表明50%~70%细胞为CD29和CD45阳性。结论体外分离培养脐血间充质干细胞生长稳定,可作为组织工程的种子细胞。 【关键词】脐血;间充质干细胞;细胞周期;免疫细胞化学 Abstract: Objective Isolation and cultivation of mesenchymal stem cells (MSCs) in human umbilical cord in vitro, and determine their biological properties. Methods The mononuclear cells were isolated by density gradient centrifugation from human umbilical cord blood in sterile condition, and cultured in DMEM medium containing 10% fetal bovine serum. After the adherent mononuclear cells were obtained, the shape of cells were observed by microscope, then the cell growth curve, the cell cycle and the cell surface antigens were obtained by immunocytochemistry and flow cytometry methods. Results MSCs obtained by Percoll (1.073 g/mL) were similar in size, spindle-shaped or star-shaped fibroblasts-liked cells. Cell growth curve analysis indicated that MSCs were in the exponential stage after 5d and in the stationary stages after 9d. Flow cytometry analysis showed that the CD29 and CD44 positive cells were about 50%~70%. Conclusions The human umbilical cord derived mesenchymal stem cells were grown stably in vitro and can be used as the seed-cells in tissue engineering. Key words:human umbilical cord blood; mesenchymal stem cells; cell cycle; immunocytochemistry 间充质干细胞(mesenchymal stem cells,MSCs)在一定条件下具有多向分化的潜能,是组织工程研究中重要的种子细胞来源。寻找来源丰富并不受伦理学制约的间充质干细胞成为近年来的研究热点[1]。脐血(umbilical cord blood, UCB)在胚胎娩出后,与胎盘一起存在的医疗废物。与骨髓相比,UCB来源更丰富,取材方便,具有肿瘤和微生物污染机会少等优点。有人认为脐血中也存在间充质干细胞(Umbilical cord blood-derived mesenchymal stem cells,UCB-MSCs)。如果从脐血中培养出MSCs,与胚胎干细胞相比,应用和研究则不受伦理的制约,蕴藏着巨大的临床应用价值[2,3]。本研究将探讨人UCB-MSCs体外培养的方法、细胞的生长曲线、增殖周期和细胞表面标志等方面,分析UCB-MSCs 作为间充质干细胞来源的可行性。

我的精神分裂症形成和发展史

出生前背景 母亲是地道、淳朴、专一,文化程度不高的农村主妇,父亲是当地的混混,好色成性,道德观念淡薄,无责任感,为非作歹,攻击性强,专横,常聚众斗殴,浪荡无比。他的放荡从和母亲接姻前持续到今。从母亲断断断断续的回忆中我恍知我没呱呱落地前就已有不寻常的经历,失职的母亲怀着我和父亲怄气经常绝食威胁,奢望唤醒父亲的为父为夫的责任感。可怜的女人,痴痴的等待,身心俱损终换不来一时的真爱。他从不掩饰自己的劣迹,而是将其当作显示自己无限魅力和能耐的招牌加以渲染,毫无顾忌在当众谈论。 童年背景 除父母,还有两兄,我是幼女,相比较受宠爱。 爷爷 奶奶,传统的封建妇女,极重男轻女,从未给过我好脸色。爷爷、奶奶在家中居从属地位,对我没产生至关重要的影响。 儿时家里很穷,主要靠母亲支撑维系家族。她非常辛苦,在纺织厂,三班制。歇工还要步行到七八公里外的田地里劳作。很难照顾到我们的感受,她所能做的就是竭尽所能维系家庭的完整,让我们能生存下去。与此同时,她还要忍受父亲周而复始的背叛,虐待、暴打。生活不如意加之贫困无比,让她难免脾气暴躁,我是她时常爆发时的接纳对象。如此妇女,受封建思想灌输至深,永远铭记自己要恪守妇道,她始终如一的忠诚与父亲,永不离弃他,爱护他,疼爱他(她比父亲年长些,父亲相貌俊秀,而母亲姿色平平)。我可怜而鄙视她,丈夫如果某天一改往日作贱她的口吻,她会像孩子似的受宠若惊的心花怒放。 父亲霸道无比,家里人人惧怕他,他无比自恋。除了母亲,伤害最深的是大哥,每天无缘无故的遭受父亲的暴打。他性情多变,无法揣摩,吃饭时一家人欢声笑语,吃完饭看看大哥不顺眼他操起皮鞭就抽。看到大哥在皮鞭下嚎哭,新的皮鞭疤痕烙在旧疤痕上,我和二哥感到恐惧,怜悯大哥,然而我们是无助的,谁也不能阻挡皮鞭的落下。尽管如此,父亲当时在我心目中是高大的,令人崇拜的,对我产生的正负影响也是最强烈的。他多才多艺,知识渊博,开明,前卫,聪明,而母亲相比之下平庸很多,她每天只是起早贪黑的工作,思想保守,愚昧,无任何才华而言。 童年,虽说不是幸福的,但也算不上痛苦。 童年转青春期阶段 邻居是一个恶老太婆,和当时大多传统村妇一样,没知识、没修养也没教养。她确实很恶,不允许她看不顺眼的小孩从她家旁边的小巷经过,她不喜欢我。每次我冒险经过她都会如同恶狗样在我刚出现在她视野中就开始狂吠,连同我的老祖宗也一起骂,持续到我再次从原路返回,躲到家里,她的吠声还要延续十分钟。 被爱妄想出现在五年级,应该更早些。我喜欢上一个家境优越的的男生,尽管那时他已经有“女朋友”。从爱上他那刻起我就很明确他也是爱我的,他和同桌说话其实余光是在看我,尽管没有任何证实,我非常明确他就是偷偷看我的。即使在上课,即使他没有和同桌说话,我感觉他在狠狠的想着我。他回答老师的提问也暗示着对我的爱意。比如他的回答里有“她”,那就是暗示他说的是我。或是我读书看到书上的“他”字样,心便狂喜的乱跳,认为这是我暗恋对象给我的暗示,他一直在我身边! 妄想形成初期就有泛化倾向,我似乎对自己相貌无限自信,觉得自己是最美的,一上街满街的男孩都为我的美貌所折服,他们都不由自主的盯着我看,我的一举一动都被他们密切关注着,一出门便有那么多双眼睛注视着我。

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