I. INTRODUCTION

In recent years, federal and local governments have implemented a preponderance of fiscal policies in the form of temporary tax cuts and subsidies, with US examples including the Car Allowance Rebate System (CARS, or "Cash for Clunkers"), federal and state hybrid and electric car subsidies, federal and state first-time homebuyer credits, bonus depreciation schedules on new investments, and state- and locality-specific sales tax holidays. The prevalence of such policies, which I heretofore refer to as "holidays" to denote their transitory nature, reflects often (though certainly not always) bipartisan support. Republicans may like lowering taxes, if only temporarily, while Democrats may like a policy that benefits consumers without sacrificing the government's long-run ability to raise revenue. For instance, Transportation Secretary Ray LaHood lauded Cash for Clunkers for both "giving the auto industry a shot in the arm" as well as providing "good news for ... consumers' pocketbooks." (1) Moving from federal to state policy, Robyn, Cohen, and Henchman (2011) observe that sales tax holidays "enjoy broad political support, with backers arguing that holidays ... provide benefits to low-income consumers [and] improve sales for retailers, create jobs, and promote economic growth."

This bipartisan appeal of holidays reflects the dual objectives of holidays: (a) to increase economic activity in the targeted market and (b) to provide tax relief and value to consumers. While many previous studies have addressed holidays' efficacy with regards to stimulating economic activity, this article complements those efforts by providing a theoretical and empirical framework for assessing their efficacy with regards to the goal of providing value to consumers. In particular, I compare a holiday's cost to the government against its benefit to consumers, as measured by compensating variation, to assess a holiday's impact on consumer welfare and Kaldor-Hicks efficiency.

A salient feature of each of the holidays listed above is the targeting of a durable commodity. This commonality is unlikely to be mere coincidence, as the exchange of durables is more readily delayed or accelerated in order to take advantage of a temporarily preferential fiscal treatment. (2) Such timing behavior falls in the first tier of Joel Slemrod's (1992) "hierarchy of behavioral responses to taxation," and the prediction of significant timing response is borne out in empirical analyses of sales tax holidays (Cole 2012), Cash for Clunkers (Copeland and Kahn 2013; Mian and Sufi 2012), expiring hybrid vehicle subsidies (Sallee 2011), and the temporary bonus depreciation on capital goods (House and Shapiro 2008). (3)

The focus on these large timing responses has led analysts to conclude that holidays are cost-ineffective in terms of government cost per genuinely new (not time-shifted) purchase, though they may be effective at increasing short-run activity. However, these statements address only the first of the holiday's dual goals: how effective are holidays at promoting economic activity? This article instead addresses the other goal: how effective are holidays at providing value to consumers? A simple example demonstrates that the two "efficiency" concepts may bear little relationship to one another. Consider the case in which consumers did not change their behavior in response to a holiday. The holiday merely transfers money from the government to those consumers who were already planning to purchase during the holiday. Under these circumstances the policy would fail miserably in terms of government cost per genuinely new purchase, or time-shifted purchase for that matter, but would be relatively effective at achieving the goal of providing value to consumers. (4)

The article makes three primary contributions. The first is to provide a tractable theoretical framework for describing the welfare effects and Kaldor-Hicks efficiency of holidays. Owing to the durability of a holiday's targeted commodity, the effects of the policy are inherently dynamic in nature. As such the welfare effects of temporary tax reforms have often been assessed using the toolkit of macroeconomics, with examples including Judd (1985), Judd (1987), and Strulik and Trimborn (2010). I instead utilize properties of the envelope theorem in the context of intertemporal consumer durable choice, an approach that captures consumers' welfare effects in terms of compensated demand curves and does not require assumptions about the precise nature of consumers' utility (e.g., the intertemporal elasticity of substitution) or the durable good's depreciation process. (5)

I then define a few convenient demand concepts that enable a holiday's inherently dynamic effects to be expressed in terms of static, "partial equilibrium" analyses in the markets for three distinct "subgoods." The first subgood reflects the quantity that would have been purchased in a constant tax regime, the second reflects the quantity that is time-shifted to the holiday period, and the third reflects the new quantity that would not have been purchased (in any period) without the holiday. This reframing enables me to describe the holiday's price, quantity, and welfare effects not in terms of phase diagrams and dynamic simulations, but with graphical representations that would be intuitive to even an undergraduate public finance student. I hope that this reframing and these figures provide pedagogical value for the discussion and analysis of a variety of temporary fiscal policies.

Using this framework, I show that theory alone is ambiguous with regards to a holiday's impact on Kaldor-Hicks efficiency. This result may be surprising given that holidays often reduce distortionary tax rates, albeit for a short time only, and leave all other periods' and goods' tax rates unchanged. In that case one might expect that the holiday increases Kaldor-Hicks efficiency as the excess burden of taxation is reduced (or eliminated) for at least some window of time. However, I show that the ambiguity arises from the competing efficiency effects in two of the subgood markets. First, the holiday may reduce distortion in the "new good" submarket, with the typical pro-efficiency effects of a tax cut. Second, the holiday introduces distortion in the "time-shifted" submarket, with an efficiency effect comparable to that of a distortionary subsidy. For instance, if the holiday temporarily reduced a tax rate from 5% to 0%, would more shifting occur than if the holiday reduced the rate from 5% to 4.9%? If so, consumers face shadow costs of shifting that imply that the loss in tax revenues exceeds consumers' compensating variation.

The article's second contribution is methodological in nature. I derive structural equations for the three subgood demand concepts that are consistent with intuitive constant price elasticity assumptions, and subsequently derive the corresponding formulas for a holiday's welfare effects. While these formulas are more complex than those that would arise from more basic approximations, such precision and internal consistency are warranted because of the fact that welfare effects depend so critically on the precise shapes of the demand functions. For instance, two different sets of demand functions may be in complete agreement with regards to the share of holiday sales that are new versus time-shifted; however, they may have completely different implications with regards to the holiday's Kaldor-Hicks efficiency.

These formulas benefit from the fact that they depend only upon readily observed and reliably estimated policy and demand parameters. These parameters are specific to the good and holiday in question; therefore, the proposed method does not require assumptions regarding the external validity of parameters such as consumers' intertemporal elasticity of substitution, assumptions that are often necessary in a "macro-style" dynamic analysis. Nor does the methodology rely on an estimate of the policy's long-run cumulative impact on economic activity. In principle an estimate of this long-run effect would be useful for assessing welfare effects--in practice, it is unlikely to be estimable with much precision. I derive these structural formulas with the intent that they prove useful for empiricists who are interested in the welfare effects of a variety of holiday policies.

The third contribution of the paper is to fill a gap in the policy analysis of holidays. Using the method described above, I generate the first estimates of the Kaldor-Hicks efficiency of two different policies: Cash for Clunkers and states' sales tax holidays. While both policies have been criticized for reasons ranging from administrative complexity to equity concerns to their ineffectiveness at increasing economic activity, I also estimate that they are inefficient from a welfare-economics, Kaldor-Hicks perspective. Merging this article's theory of welfare effects with data from Mian and Sufi (2012) and Busse et al. (2012), I estimate that Cash for Clunkers provided at most $0.47 in consumers' compensating variation for every $1 of government spending. (6)

Using estimates from Cole (2012), I estimate that states' sales tax holidays on computers provide an average of only $0.77 in consumers' compensating variation for every $1 of foregone tax revenue. (7)

The paper is organized as follows. Section II models the welfare effects of tax holidays using the subgood concepts previously described. I also use this theoretical framework to compare and contrast a holiday's efficiency at "increasing economic activity" versus "providing value to consumers." Section III derives the explicit structural formulas for the demand concepts and the corresponding welfare effects. Section IV applies the methods to estimate the welfare effects of Cash for Clunkers and states' sales tax holidays. Section V concludes with a summary of the results, a discussion of their applicability to other policy contexts, and suggestions for future research.

II. A THEORETICAL FRAMEWORK

Consider a good y that is purchased over multiple periods indexed by t [member of] [OMEGA]. The good is originally taxed at a rate of [[tau].sub.noth] in all periods, where [[tau].sub.noth] may be greater than, less than, or equal to 0. Assuming that supply is perfectly elastic at a price of [bar.p], the equilibrium price paid by consumers is [p.sub.noth] = (1 + [[tau].sub.noth]) [bar.p] in all periods. I now wish to describe the welfare effects of a policy that reduces the tax to [[tau].sub.h] < [[tau].sub.noth] in the holiday period t = h and leaves the tax unchanged in all other periods. The policy reduces the period-h consumer price to [p.sub.h] = (1 + [[tau].sub.noth]) [bar.p], increases the equilibrium quantity in period h, and (weakly) decreases the quantities in all other periods as consumers time-shift purchases. This general framework can encapsulate a variety of temporary policies including tax cuts, subsidies, and other fiscal policies that are not explicitly framed as tax cuts or subsidies but effectively act as such by temporarily changing consumer prices.

The assumption of perfectly elastic supply simplifies the analysis since producer surplus is 0 both before and after a holiday is enacted. However, the assumption is unnecessary for attaining the qualitative efficiency results, in particular the competing efficiency effects in the new versus time-shifted submarkets. Perfectly elastic supply implies that consumers receive the full incidence of the holiday's effect on prices, and therefore represents the best possible case for consumers. (8)

For parsimony, I also assume that that there are no income effects with respect to demand for y, no cross-price effects with non-y goods, and no externalities. This latter assumption is perhaps most contentious in the context of a holiday, which presumably aims to increase consumption of the targeted good due to the existence of some social benefit that exceeds private benefit. It is well understood how to incorporate externalities into a welfare analysis, so I maintain the "no externality" assumption in order to focus on the less understood divergence between a holiday's private value to consumers and cost to government. The presence of an externality does not negate the relevance of private welfare effects in a comprehensive cost-benefit analysis--it simply implies that these estimates are an insufficient but necessary component of the complete analysis. If the no externality assumption leads to a negative efficiency finding, then an advocate's burden for justifying the holiday is heavier to the extent that a larger positive externality is required to make up the difference. (9,10)

A. Demand Concepts

Given a price [p.sub.h] in the holiday period and a common price [p.sub.noth] in all nonholiday periods, let [y.sub.t]([P.sub.h], [p.sub.noth]) be the demand for y in period t. (11) To make the welfare effects of a holiday as clear as possible, let us define the following key demand concepts.

* C([p.sub.noth]) gives the demand in period h if the price were a constant [p.sub.noth] in all periods. It is defined by

(1a) C ([p.sub.noth]) [equivalent to] [y.sub.h] [p.sub.noth], [p.sub.noth]). for all [p.sub.noth].

* N([p.sub.h], [p.sub.noth]) is the long-run cumulative growth arising from the holiday, or more precisely, it is the increase in the present value ("present" as of period h) of demand relative to the present value if the price were [p.sub.noth] in all periods. It is defined by

(1b) N([p.sub.h], [p.sub.noth]) [equivalent to] [summation over (t [member of] [OMEGA])] [(1 + R).sup.-(t-h)]

x ([y.sub.t] ([y.sub.t] ([p.sub.h], [p.sub.noth]) - [y.sub.t] ([p.sub.noth], [p.sub.noth]))

for all [p.sub.h] and [p.sub.noth], where R is the government's discount rate. By construction this demand concept is equal to 0 whenever [p.sub.h] = [p.sub.noth]; therefore, the equilibrium quantity prior to the implementation of the holiday is N([p.sub.noth], [p.sub.noth]) = 0, whereas the post-implementation quantity is some value N([p.sub.h], [p.sub.noth]) [greater than or equal to] 0.

* T([p.sub.h], [p.sub.noth]) is the portion of [y.sub.h] attributable to time-shifted purchases, or more precisely, it is the magnitude of the decrease in the present value of demand in non-h periods relative to the present value if the price were [p.sub.noth] in all periods. It is defined by

(1c) T([p.sub.h], [p.sub.noth]) [equivalent to] - [summation over (t [member of] [OMEGA], t [+ or -] h)] [(1 + R).sup.-(t-h)] x [(.sub.yt] ([p.sub.h], [p.sub.noth]) - [y.sub.t] ([p.sub.noth], [p.sub.noth])).

for all [p.sub.h] and [p.sub.noth]. By construction, this demand concept is also equal to 0 whenever [p.sub.h] = [p.sub.noth]; therefore, the equilibrium quantity prior to the implementation of the holiday is T([p.sub.noth], [p.sub.noth]) = 0. The post-implementation quantity is instead some value T([p.sub.h], [p.sub.noth]) [greater than or equal to] 0.

These definitions imply that

(2) [y.sub.h] ([p.sub.h], [p.sub.noth]) [equivalent to] C ([p.sub.noth]) + N ([p.sub.h], [p.sub.noth]) + T ([p.sub.h], [p.sub.noth])

for all [p.sub.h] and [p.sub.noth]. Hence period-h demand is decomposed into the quantity that would have been purchased under a constant tax regime (C) and the short-run growth in sales that arise due to the holiday (N + T). The short-run growth itself can be decomposed into the portion that is "time-shifted" from non-h periods to period h (T) and the portion that is genuinely "new" and would not have occurred in any period without the temporary tax cut (N). (12)

Demand for C is perfectly inelastic with respect to changes in [p.sub.h], but this is not true of the demand for N and T. These demand functions will generally slope downwards as a reflection of diminishing marginal utility of consumption. However, it is worth noting that the marginal utility schedules in the context of a temporary tax reduction may bear little resemblance to those in the context of a permanent change in prices. In particular, marginal utility in the context of a holiday will reflect various shadow costs associated with shifting purchases that would have ideally occurred in periods other than the holiday.

First, consumers may generally prefer "smooth" to "lumpy" intertemporal consumption flows. (13) Second, consumers face heterogeneous shopping costs that make shopping in some periods more convenient than others. (14) Third, consumers may face liquidity constraints that make it difficult to purchase goods at a time other than the originally planned period, and only a sufficiently low holiday price incentivizes the consumer to shift. (15) Fourth, deterioration of infrequently purchased consumer durables may lead the optimal replenishment period to fall during a nonholiday period. (16) These four examples are not intended to provide an exhaustive list of the costs of shifting purchases. They do however illustrate that even though these shadow costs are nonpecuniary, they will nonetheless affect consumers' reservation price for shifting purchases and their willingness to pay for the holiday. (17)

B. Graphical Interpretation of Welfare Effects

The virtue of the demand definitions given above is that a holiday's multiperiod effects can be expressed solely in terms of the period-h demand concepts C, N, and T. I derive analytical expressions for a holiday's welfare effects in the next subsection, but first explain the theory's intuition via a simple graphical analysis of each demand concept.

Figure 1 diagrams a holiday's welfare effects on the C submarket. By construction, the demand for C is perfectly inelastic with respect to changes in [p.sub.h], given a fixed value of [p.sub.noth]. Within this submarket, the holiday therefore results in pure transfers from the government (the area denoted "-G" in the figure) to consumers ("+CV", for "compensating variation"), and these transfers have no net effect on social surplus.

Figure 2 diagrams the welfare effects associated with the holiday's effect on the N submarket. Holding constant [p.sub.noth], the downward sloping demand curve shows consumer's marginal benefit of N, whereas the horizontal line at [bar.p] shows producers' marginal cost (i.e., supply) of N. At N = 0, the equilibrium quantity prior to holiday implementation, consumers' marginal benefit of N is given by (1 + [[tau].sub.noth]) [bar.p] whereas the marginal cost of producing additional N is given by [bar.p]. If [[tau].sub.noth] > 0, as is the case in Figure 2, then reductions in the holiday-period price can reduce the distortionary wedge between supply and demand for N and the holiday has the pro-efficiency effect typical of any distortion-reducing tax cut. As drawn consumers and government both enjoy gains, with consumer gains ("+CV" in the Figure) arising from the lower after-tax price for N, and government gains ("+G") arising from the fact that [[tau].sub.h] > 0 and equilibrium quantity has increased above the original equilibrium quantity N = 0. A "full" holiday with [[tau].sub.h] = 0 will instead yield the government zero N-related tax revenues, though it is worth noting that the efficiency gains in the N-submarket are maximized at [[tau].sub.h] = 0. At this tax rate the submarket's deadweight loss triangle is entirely eroded. If [[tau].sub.h] < 0, the government replaces a distortionary tax on N with a distortionary subsidy, and the net effect on the submarket's deadweight loss is theoretically ambiguous.

The possibility for efficiency gains in the TV-submarket hinges on the existence of a distortionary wedge between supply and demand prior to the holiday's implementation. Recall that the demand function in Figure 2 plots N([p.sub.h], [p.sub.noth]) for a given value of [p.sub.noth]. If the nonholiday tax rate is 0 as opposed to some strictly positive value, then demand for N is lower than that shown in Figure 2. In fact, supply and demand for N are equal at the equilibrium quantity N = 0. In this context, a reduction in the holiday-period tax rate to some [[tau].sub.h] < 0 necessarily increases dead-weight loss as the government subsidizes N and distorts the previously undistorted submarket.

Figure 3 diagrams the welfare effects associated with the holiday's effect on the T submarket, with the area labeled "+CV" denoting gains to consumers, and the area labeled "-G" denoting decreases in government revenues. The x-axis of the diagram shows the quantity of T units bought and sold; however, the downward sloping demand curve T([p.sub.h], [p.sub.noth]) shows how demand for T varies with the difference between [p.sub.h] and [p.sub.noth]. This is because of the fact that the difference between holiday and nonholiday prices shows consumers' marginal benefit of incremental T units. Analogously, producers' marginal cost of production is equal to 0 for all quantities of T. The difference between holiday and nonholiday prices reflects the per unit government cost for a given level of T. For example, if [[tau].sub.noth] = 10% and [[tau].sub.h] = 6%, then the government only loses out on the 4% tax that would have been assessed in the original purchase period but is not assessed during the holiday.

At T = 0, the equilibrium quantity prior to holiday implementation, there is in fact no wedge between supply and demand. Consumers' marginal benefit and producers' marginal cost of additional T are both 0. For T greater than 0 consumers' marginal benefit is actually negative. This arises from the fact that, under the constant-tax policy and for a given present value of [y.sub.t] quantities, consumers have optimally allocated that present value across periods. Consumers must therefore be compensated in order to time-shift purchases, but this is precisely what the holiday does. In essence the holiday acts as a subsidy of T and the submarket experiences the standard anti-efficiency effects of a distortionary subsidy that drives equilibrium quantity above the socially efficient quantity. (18) Unlike the new purchase submarket, the time-shifted submarket's anti-efficiency effects stem from distortions between the holiday and nonholiday prices; therefore, a holiday induces deadweight loss in the T submarket regardless of whether the nonholiday tax rate is positive, negative, or zero.

The figures illustrate an important result of the theory, namely that the net effect of a holiday on Kaldor-Hicks efficiency is theoretically ambiguous. A holiday increases deadweight loss if the social surplus loss in the time-shifted submarket exceeds the social surplus gain in the new purchase submarket. This ambiguity is itself noteworthy because a reduction in distortionary taxes typically decreases the excess burden of taxation.

The previous discussion does not hold government revenue fixed, though the net effect on efficiency is unchanged under lump sum compensation. Therefore the potential for a reduction in Kaldor-Hicks efficiency does not rely on any assumptions regarding the government's reliance upon other distortionary tax instruments, a result that stands in contrast to insights based on the optimal tax designs of Atkinson and Stiglitz (1976) or Ramsey (1927). Both approaches would assign equal tax rates in all periods, (19) and therefore predict less efficient market outcomes upon implementation of a holiday. However, both of these optimal tax approaches assume that the government must satisfy a revenue constraint subject to a fixed amount of lump sum taxation. The Kaldor-Hicks measure of efficiency employed herein makes no such assumptions; therefore, it is informative in several ways.

First, it may be of inherent interest if the analyst does not consider the government budget constraint binding, or alternatively, does not consider the lump-sum tax instrument fixed. Second, it may capture the first-order welfare effects of a holiday-type policy while remaining theoretically tractable and agnostic with regards to other distortionary tax instruments. Third, it may be considered an upper bound estimate on the holiday's welfare effects if the government maintains revenue neutrality via increases in other distortionary taxes. Therefore an anti-efficiency finding in the lump-sum compensation context is all the more damning for an alternative policy counterfactual with non-lump-sum compensation.

C. Analytical Expression of Welfare Effects

In order to derive analytical expressions for the welfare effects of holidays, it will prove useful to define a few inverse demand concepts that are closely related to the earlier demand concepts.

* p([y.sub.h], [p.sub.noth]) gives the period-h inverse demand for [y.sub.h] holding constant [p.sub.noth]. It is implicitly defined by

(3a) [y.sub.h] [equivalent to] [y.sub.h] (p ([y.sub.h], [p.sub.noth]), [p.sub.noth]).

* [p.sup.N] (N, [p.sub.noth]) is the holiday-period price that yields a certain quantity of N demand holding constant [p.sub.noth]. It is implicitly defined by

(3b) [p.sub.h] [equivalent to] [p.sup.N] (N([p.sub.h], [p.sub.noth]), [p.sub.noth]).

Note that [p.sup.N] (0, [p.sub.noth]) = [p.sub.noth] for all [p.sub.noth]. Therefore, the equilibrium value of [p.sup.N] prior to implementation of the holiday is given by [p.sub.noth]. In contrast, the equilibrium value following holiday implementation is given by [p.sub.h].

* [DELTA][p.sup.T] (T, [p.sub.noth]) is the difference in holiday and nonholiday prices that yields a certain T demand holding constant [p.sub.noth]. It is implicitly defined by

(3c) [p.sub.h] -[p.sub.noth] [equivalent to] [DELTA][p.sup.T] (T ([p.sub.h], [p.sub.noth]), [p.sub.noth]).

Note that [DELTA][p.sup.T] (0, [p.sub.noth]) = 0 for all [p.sub.noth]. Therefore, the equilibrium value of [DELTA][p.sup.T] prior to implementation of the holiday is 0. In contrast, the equilibrium value following holiday implementation is given by [p.sub.h] - [p.sub.noth].

Using the definitions, the welfare effects of the holiday are given in the next propositions.

PROPOSITION la. Employing the envelope theorem to the choice of consumer durables and invoking the previously defined demand concepts, the consumer's compensating variation for the holiday is given by

(4a) CV = - ([p.sub.h] - [p.sub.noth]) C ([p.sub.noth])

(4b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(4c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

PROPOSITION 1b. Invoking the previously defined demand concepts, the change in government revenues because of the holiday is given by

(5a) [DELTA]G = ([p.sub.h] - [p.sub.noth]) C ([p.sub.noth])

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

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

Proofs. See Appendix.

The "a" lines of Equations (4) and (5) correspond to a holiday's effects on consumer welfare and government revenues in the C-submarket in Figure 1, respectively. The "b" lines correspond to the effects in the N-submarket in Figure 2, and the "c" lines to the effects in the T-submarket in Figure 3.

The Kaldor-Hicks measure of economic efficiency, which I denote as [DELTA]SS to denote the change in social surplus, is given by the sum CV + DELTA]G.

PROPOSITION 1c. The change in social surplus is given by

(6a) [DELTA]SS = 0

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

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

Proof. Equation (6a) is the sum of Equations (4a) and (5a). Equation (6b) is the sum of Equations (4b) and (5b). Equation (6c) is the sum of Equations (4c) and (5c).

If the government budget constraint is fixed, [DELTA]SS is an accurate measure of the impact on social surplus only if the government compensates via lump sum taxation. (20) If that is not the case and the government compensates with increases in other distortionary taxes, [DELTA]SS misstates the true effect on social surplus. In fact the [DELTA]SS measure generally overestimates the true change in social surplus assuming that the government's marginal cost of funds for the compensating and distortionary tax instrument is greater than 0. (21)

D. Comparing Efficiency Concepts

[DELTA]SS can also be expressed in terms of the holiday and nonholiday tax rates, along with a few readily interpretable reduced-form parameters. In particular consider the following:

(7a) g = N ([p.sub.h], [p.sub.noth]) + T ([p.sub.h], [p.sub.noth])/C ([p.sub.noth])

is the short-run growth in period h because of the holiday;

(7b) [s.sup.N] = ([p.sub.h], [p.sub.noth])/N ([p.sub.h], [p.sub.noth]) + T ([p.sub.h], [p.sub.noth]) and

(7c) [s.sup.T] = T ([p.sub.h], [p.sub.noth])/N ([p.sub.h], [p.sub.noth]) + T ([p.sub.h], [p.sub.noth])

are the shares of short-run growth attributable to new versus time-shifted shifted units, with

[s.sup.N] [member of] [0, 1], [s.sup.T] [member of] [0, 1], and [s.sup.N] + [s.sup.T] = 1;

(7d) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

is the ratio of realized to maximum potential consumer surplus in the N submarket, with [f.sup.N] [member of] [0, 1]; and

(7e) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

is the ratio of realized to maximum potential consumer surplus in the T submarket, with [f.sup.T] [member of] [0, 1]. (22)

With these definitions, [DELTA]SS can be written as

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

Equation (8) shows that the sign of [DELTA]SS is the same as the sign of ([[tau].sub.h]/[[tau].sub.noth] - [[tau].sub.h]) [s.sup.N] 4- [f.sup.N] [s.sup.N] - (1 - [f.sup.T]) [s.sup.T]. Interestingly, a ceteris paribus change in growth, g, has no effect on the sign of [DELTA]SS. Instead, higher growth implies only that the magnitude of [DELTA]SS is higher, whether [DELTA]SS be positive or negative. In contrast, [s.sup.N], [s.sup.T], [f.sub.N], and [f.sup.T] each affect the likelihood that the temporary tax reduction is efficiency-enhancing. In particular, a higher share of new purchases (or conversely, a lower share of time-shifted purchases) increases [DELTA]SS, as do higher [f.sup.N] and [f.sup.T]. (23)

In an effort to compare the current welfarebased concept of efficiency against an activity-based concept, let us now consider a commonly cited statistic, cost to the government per genuinely new (not time-shifted) unit. For instance, Edmunds.com received significant media attention (and a rebuttal from the Obama White House) for its estimate that Cash for Clunkers cost the government $24,000 per incremental car purchase. Cole (2012) employs such a measure in his analysis of sales tax holidays on computers, and in fact estimates that the government's cost per new computer exceeded the price of the computers themselves. (24) In terms of the reduced-form parameters, this alternative measure is given by

(9) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where a lower measure of [absolute value of [DELTA]G]/N presumably indicates greater efficiency.

Like [DELTA]SS, [absolute value of [DELTA]G]/N is more efficient if [s.sup.N] is larger. In contrast to [DELTA]SS however, [absolute value of [DELTA]G]/N decreases with g. This arises from the fact that a large portion of the government's cost arises from the C units that would have been purchased even in the absence of the holiday. A higher g does not change this portion of the government's cost, but holding constant [s.sup.N] and [s.sup.T] does imply that more new purchases were induced by the cut; therefore, the government pays less per newly incentivized purchase.

Most notable in this alternative efficiency measure are the absences of [f.sup.N] and [f.sup.T]. Therefore, [s.sup.N] and [s.sup.T] (along with the readily observable [[tau].sub.h], [[tau].sub.noth], [bar.p], and g) are sufficient statistics for pinning down an "activity"-based efficiency measure such as [absolute value of [DELTA]G]/N. In contrast, [s.sup.N] and [s.sup.T] are insufficient for estimating [DELTA]SS and are instead sufficient only in determining its upper and lower bounds. At best [f.sup.N] =[f.sup.T] = 1, in which case [DELTA]SS is positive if the good was originally taxed (i.e., if [[tau].sub.noth] > 0). At worst [f.sup.N] = [f.sup.T] = 0, in which case [DELTA]SS is negative if [[tau].sub.noth] < 0 or [[tau].sub.noth] > 0 and [s.sup.T] > [[tau].sub.h]/[[tau].sub.noth]. (25)

The absences of [f.sup.N] and [f.sup.T] from [absolute value of [DELTA]G]/N and inclusion in [DELTA]SS also imply that the two efficiency measures may bear little relationship to one another. The activity-based measure does not factor in consumers' willingness to pay for a holiday whereas the Kaldor-Hicks measure does. For instance a large value of [s.sup.T] may yield a high (inefficient) [absolute value of [DELTA]G]/N, but [DELTA]SS may nonetheless be positive (efficient) if [f.sup.N] and [f.sup.T] are sufficiently large. More generally, there exist infinitely many demand functions that will yield the same [s.sup.N] and [s.sup.T] for a holiday, and therefore will have the same estimated impacts on economic activity; however, the demand functions in this set may have [f.sup.N] and [f.sup.T] values anywhere from 0 to 1. The result is that two different demand functions from within this set may have dramatically different estimates of Kaldor-Hicks efficiency. In fact, for a given [s.sup.N] and [s.sup.T], two different demand functions may not even agree upon the sign of [DELTA]SS, much less the magnitude. These observations help motivate the next endeavor, to construct a structural demand model that pins down consumers' compensating variation given the data that is available around a holiday.

III. ESTIMATION OF WELFARE EFFECTS

Two general challenges arise when estimating the statistics necessary for holiday efficiency analysis. The first is definitional in nature, namely that different researchers may apply different definitions to what they consider a "new" versus a "time-shifted" purchase. For instance, consider an individual who purchases a car during Cash for Clunkers. She would not have purchased the car in the absence of the program, which may lead the analyst to allocate that purchase to "new" sales. On the other hand, she would have also bought the car if the program were instituted on a permanent basis, but in a period other than the actual Cash for Clunkers window. The fact that she purchased during the specific program window rather than this alternative period indicates that the program induced some timing behavior and that the analyst should allocate that purchase to "time-shifted" sales.

The second challenge is empirical in nature. Even conditional upon using the new and time-shifted concepts defined earlier as N and T, data will not distinguish between those sales that fall in the C, N, and T categories. In principle one could measure the sales in all periods and compare these values to the hypothetical sales that would have occurred absent the holiday, with the difference in these cumulative sales amounts equaling N. T would then equal the difference between the short-run effect during the holiday window itself and the long-run cumulative effect.

In practice however, only the short-run effect is likely to be estimable with much confidence. The long-run effect requires the summation of effects across periods, a process that mechanically increases the confidence interval around the cumulative effect's estimate. This statistical issue is noted in both House and Shapiro (2008) and Mian and Sufi (2012), the latter of which estimates with relative confidence the large short-run impact of Cash for Clunkers on car sales during the Cash for Clunkers window itself. The authors also estimate that the program's long-run effect on cumulative sales is close to 0, but the confidence interval around this cumulative point estimate is large. The authors reject the null hypothesis that the long-run cumulative effect on sales is 50% of the initial short-run impact, but cannot reject that the long-run impact is generally somewhere between 0% and 50%. Clearly however, Cash for Clunkers' efficacy depends on whether this number is closer to 0% or closer to 50%.

When even a data set and empirical methodology as impressive as those employed by Mian and Sufi cannot provide the necessary precision, the importance of a robust structural approach is evident. I therefore proceed by deriving a set of analytically tractable demand functions for C, N, and T that are based on constant elasticity assumptions. To be clear, I cannot assert that these functions are the "right" ones--if they are not, the estimated efficiency effects that arise from them will be incorrect. However, constant elasticity has an intuitive appeal that leads to its broad application in structural models. Furthermore, the constant elasticity assumption can always be tested (and rejected, if need be) under the right circumstances and with sufficient data. I in fact perform such a test in my subsequent analysis of computer sales tax holidays and cannot reject the assumption.

These demand functions are relatively more complex than those that would arise from an alternative structural assumption such as linearity. However, I contend that use of the precise demand functions implied by constant elasticity, as opposed to simpler first- or second-order approximations, is especially warranted in an analysis of Kaldor-Hicks efficiency because the welfare effects depend so critically on the shapes on the demand functions. (26)

A. Structural Demand

The structural model that I now present relies on two assumptions--that demand has constant elasticity with respect to a permanent (i.e., all period) change in prices, and that demand has constant elasticity with respect to a change in only the holiday period price. Formally these assumptions are:

(10a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

(10b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [epsilon] is the "permanent" price elasticity of the good and [gamma] is the "residual" holiday price elasticity that is unexplained by the permanent price elasticity, [epsilon] and [gamma] are both weakly negative, with [gamma] < 0 implying that demand reacts more strongly when [p.sub.h] changes but other periods' prices are unchanged. These assumptions are sufficient for pinning down precise relationships between prices and the [y.sub.h], C, N, and T demand concepts.

PROPOSITION 2. Assumptions (10a) and (10b) imply that:

(11a) [y.sub.h] ([p.sub.h], [p.sub.noth]) = z [([p.sub.h].sup.[epsilon]] [([p.sub.h]/[p.sub.noth]).sup.[gamma]],

(11b) C([p.sub.noth]) = z [([p.sub.noth]).sup.[epsilon]],

(11c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

and

(11d) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII],

where z is a constant.

Proof. See Appendix.

The permanent price elasticity [epsilon] can be estimated outside of the temporary tax cut context using standard methods. The demand parameters z and [gamma] are identified via estimates of the constant-tax-regime quantity (C) and the short-run holiday-induced growth (g). (27) The method for identifying C is straight-forward. For instance, a researcher may look at the holiday-granting jurisdiction's quantities preceding the implementation of the holiday, or alternatively, look at a comparable, non-holiday-granting jurisdiction's quantities. The implicit assumption would be that these quantities estimate the quantity of sales that would have occurred in the holiday-granting-jurisdiction had the holiday not been enacted, g is then identified by comparing this hypothetical quantity to the actual holiday quantity. Of critical importance, both C and g are estimable with greater precision and confidence than long-run cumulative growth.

B. Estimated Welfare Effects

Plugging the structural demand equations into Equations (4) and (5), and taking advantage of the identities given in footnote 27, a holiday's welfare effects are given by

(12) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

and

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

These expressions have two primary virtues: (a) they rely on five pieces of reliably estimable information ([[tau].sub.noth], [[tau].sub.h], [epsilon], g, and [bar.p]C, the pretax spending in the absence of the holiday) and (b) they are internally consistent with intuitive constant elasticity assumptions. It is my hope that these formulations will prove useful toward analysis of a broad range of temporary fiscal policies.

For the sake of completeness, the structural demand equations imply that the previously discussed activity-based measure of efficiency is given by

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

Whether or not this measure exceeds [bar.p] is a natural criterion for assessing the activity-based efficiency of a holiday. After all, if the cost-to-government per new unit is greater than [bar.p], then the government could have directly purchased the new units and given them away at lower total cost. The formulation above demonstrates an important implication for the activity-based measure--it is greater than [bar.p] for any [epsilon] > - 1, less than [bar.p] for any [epsilon] < - 1, and equal to [bar.p] if [epsilon] = - 1. Note that these statements hold for any estimated level of growth, which in turn suggests that the activity-based efficiency measure will be quite sensitive to the estimate of permanent price elasticity [epsilon]. If the analyst's activity-based efficiency criterion is simply based on whether [absolute value of [DELTA]G]/N exceeds [bar.p], then the outcome is predetermined by the value of [epsilon], regardless of the extent of the holiday's price or growth effects.

IV. APPLICATIONS

To demonstrate the methodology's broad applicability, I now estimate the welfare effects of two different holiday-type policies. The first is Cash for Clunkers, the second is a sales tax holiday on computers. The two policies differ on several dimensions beyond simply the targeted commodity. Sales tax holidays are explicitly framed as temporary tax cuts, whereas Cash for Clunkers was framed as a temporary voucher program. Sales tax holidays are implemented at the state level, where the size of the holiday discount depends on the state's nonholiday sales tax rate, while Cash for Clunkers was implemented at the federal level and voucher amounts and eligibility criteria did not vary across states. The federal government's cost of Cash for Clunkers is directly measurable, whereas the cost of sales tax holidays must be inferred from estimates of new versus time-shifted sales.

Despite these differences, the two policies share salient features such that this paper's methods are readily applicable. Both policies target a durable good and therefore incentivize significant time-shifting. Furthermore, previous empirical exercises have estimated that consumers realized the entire incidence of both the sales tax holiday tax cut and the Cash for Clunkers vouchers, thus validating the prior assumption of perfectly elastic supply. (28)

A. Cash for Clunkers

Cash for Clunkers was a $2.85 billion federal program in July and August 2009. It offered program participants a voucher for either $3,500 or $4,500 if the individual traded in a car with sufficiently low gas mileage for a car with sufficiently high gas mileage. Whether an individual received the $3,500 or $4,500 voucher depended on the difference in mileages between the turned-in "clunker" and the purchased new car. The traded-in clunker was then scrapped to ensure its removal from the US auto fleet. (29)

The welfare analysis of Cash for Clunkers relies on empirical results from Mian and Sufi (2012) and Busse et al. (2012). The former focuses on the economic activity generated by Cash for Clunkers, the latter on the extent to which consumers realized the full incidence of the program's vouchers. Both pieces of information are necessary but insufficient for estimating welfare effects without the structure provided in this article.

Estimates from Mian and Sufi (2012) imply 120% short-run growth in voucher-eligible car sales during the Cash for Clunkers window. (30) The authors' point estimate of the effect on cumulative sales through 1 year is close to zero, implying that virtually all of the short-run growth consisted of time-shifted sales. However, the authors acknowledge that the confidence interval around this long-run effect is quite large. For my welfare analysis, I employ the article's implied short-run growth rate of 120% but allow the permanent price elasticity to dictate the share of said growth that stems from time-shifting. (31)

Busse et al. (2012) estimate that customers received the entirety of the voucher's incidence. The authors also point out that the voucher receipt required the forfeiture of the clunker; therefore, the net discount to consumers is given by the difference between the voucher value and the value of the forfeited clunker. The average voucher value was $4,210 but the average voucher value net of trade-in value was only $2,390, jointly implying that forfeited clunkers had an average trade-in value of $1,820. These numbers compare to an average price of $22,592 for a new vehicle purchased under Cash for Clunkers. (32) Assuming that the voucher value is untaxed by a state and that the forfeited clunker would have reduced a purchaser's sales tax liability if traded in at another time, then Cash for Clunkers reduced consumers' effective price of purchasing a car by 2,390/22,592 [approximately equal to] 10.6 %. (33)

Table 1 shows the estimated effect on car purchases under two different assumptions regarding permanent price elasticity. Panel A uses [epsilon] = -0.87 while Panel B uses [epsilon] = -3.31. The former is the McCarthy (1996) estimate of the price elasticity for new vehicle purchases. (34) The latter implies that half of the short-run growth was attributable to genuinely new, not time-shifted, purchases. Mian and Sufi (2012) statistically rejects that half of the short-run growth was attributable to new purchases, so [epsilon] = -3.31 bounds the true permanent elasticity. Within each [epsilon]-panel, the effects are estimated for three preexisting tax circumstances: a low 0% tax, a medium 5.71% tax, and a high 10.25% tax. These values reflect the range of US sales tax rates in 2009, where 5.71% is a weighted average across the United States. (35) I consider [epsilon] = -0.87 and a preexisting tax of 5.71% to be the base case scenario while [epsilon] = -3.31 and a preexisting tax of 10.25% is a best case scenario.

Column 1 shows the preexisting tax rate, whereas Column 2 shows a consumer's effective tax rate after accounting for the program's 10.6% reduction in consumer price. Columns 3 and 4 show the estimated share of new versus time-shifted sales, respectively. Given an estimated growth in sales, these estimates depend upon the relative price of a car during versus not during the Clunkers window, not the price level itself. Thus the estimates do not vary within a panel, though they do change as e changes between panels. Given the vastly different estimates of time-shifted sales between panels, it is no surprise that the government cost per new car (the last Column) also differs tremendously between panels. (36) The estimates in Panel A are around $25,000 per car, slightly larger than Edmunds.com's $24,000 estimate. The estimates in Panel A exceed the average tax- and voucher-exclusive car price of $22,592, implying that the government could have directly bought the new cars at lower cost, though the result is expected given that the permanent price elasticity has magnitude less than one. The cost per new car is only about a third as large under the [[tau].sub.s] = - 3.31 scenarios in Panel B, thus demonstrating the activity-based efficiency measure's high sensitivity to the permanent price elasticity.

Table 2 instead shows the estimated welfare effects for each permanent price elasticity and sales tax scenario. Column 2 shows the effects on consumer's compensating variation arising from the program's 10.6% reduction in consumer price. Larger preexisting taxes lead to larger estimates of compensating variation. In the base case I estimate that consumers gained $1.17 billion in compensating variation. This stands in contrast to the $2.85 billion spent by the federal government (Column 3). State tax revenues are also estimated to have decreased (see Column 4), but only slightly so in the base case.

In each scenario considered in the Table, the net cost to government (federal and state) far exceeds consumers' compensating variation; therefore, each scenario's net change in social surplus (i.e., the value in Column 5) is negative. In the base case Cash for Clunkers is estimated to have created $1.69 billion in additional deadweight loss in the economy. Even in the best case scenario the program is estimated to have created fully $1.36 billion in additional deadweight loss. (37) Column 6 frames the welfare effects alternatively, showing consumers' compensating variation as a fraction of government cost. In the base case scenario, the program provided consumers only $0.41 in compensating variation for every $1 of government cost. In the best case scenario the consumer valuation ratio only rises to $0.47.

The only prior estimate of the program's welfare effects is a back-of-the-envelope calculation in Abrams and Parsons (2009). (38) The difference between their consumer welfare and mine rests on three methodological differences. First, Abrams and Parsons assume that forfeited clunkers are only worth $1,000 on average, a perfectly acceptable (and it turns out conservative) estimate given that the actual value of $1,820 was only known 3 years later following the considerable empirical effort of Busse et al. (2012). Second, they assume that the market for cars is undistorted prior to the program's implementation. If this is not true, as in states that levy sales taxes, then the Abrams and Parsons methodology misses out on potential efficiency gains in the genuinely new car submarket.

Finally, and most importantly, the Abrams and Parsons methodology assumes that consumers gain surplus of 1/2 of the voucher's value (net of forfeited clunker value). The authors acknowledge that this assumption requires "invoking some linearity and constant distribution across the demand function." (p. 2) The structural methodology employed herein instead implies that the value is much higher at approximately 69%. (39) The divergence stems primarily from the current methodology's recognition that many vouchers, 45% of them in fact, went to consumers who would have bought during the program's window anyway. While the surplus value to new and time-shifting consumers was in fact close to 50% of the net voucher value, the surplus to consumers who would have bought anyway is precisely 100% of the net voucher value. My estimates of compensating variation would be fully 27% lower under the Abrams and Parsons assumption, which translates to a downward bias in compensating variation of fully $301 million even assuming that the market is initially undistorted. (40) This large bias demonstrates the importance of using this article's structural methodology as opposed to linear approximations.

As previously discussed, the methods in this paper only account for the private welfare effects of a temporary fiscal policy. Proponents of Cash for Clunkers would contend that both time-shifted and new sales provided external benefits, time-shifted sales to the extent that the economy's resources were underutilized, new units to the extent that a more fuel efficient fleet would reduce environmental damage. The existence of said externalities does not eliminate the relevance of private welfare effects in a complete cost-benefit analysis--instead, it implies that private welfare effects are a necessary but insufficient component of the complete analysis. The evidence in support of the program's stimulative effect is generally weak (see Copeland and Kahn 2013; Gayer and Parker 2013; Mian and Sufi 2012), but let us consider its environmental impact. Using the base case social welfare loss of $1,685 billion and assuming the program eliminated the Li, Linn, and Spiller (2013) lower bound estimate of 9.0 million tons of C[O.sub.2], then Cash for Clunkers was efficient only if the external cost of a ton of C02 is at least $187. Assuming instead that the program eliminated the authors' upper bound estimate of 28.2 million tons of C[O.sub.2], then it was efficient only if the external cost of a ton of C[O.sub.2] is at least $60. This latter value is greater than the $39 cost estimated by the Interagency Working Group on Social Cost of Carbon. (41)

B. Sales Tax Holidays

In 2012, 18 US states held sales tax holidays. The holidays temporarily eliminate sales taxes on select goods, with most occurring for a few days during the back-to-school shopping period. They most commonly target clothing, computers, and school supplies, though some states employ holidays on other goods ranging from energy efficient products to hurricane preparedness items to firearms. (42) The current analysis draws upon the results of Cole (2012), an empirical study of computer sales tax holidays in nine US states in 2007. Table 3 shows Cole's estimates of holiday price elasticities and the nonholiday tax rates on computers in each state, along with my calculation of the large, implied holiday growth.

The structural welfare formulas in Equations (12) and (13) rely on the constant elasticity assumptions in Equations (10a) and (10b). A multi-state holiday, which targets a common good but features different holiday discounts across states, provides an opportunity to test these assumptions. Under a null hypothesis of constant elasticities, the natural log of the gross holiday-induced growth should be proportional to the natural log of the nonholiday tax-inclusive price. Figure 4 shows this relationship for the nine states in Cole (2012). While the usual caveats apply to a sample of only nine observations, the proportional relationship cannot be rejected. (43)

Table 4, Panel A provides the estimated new share ([s.sup.N]) and time-shifted share ([s.sup.T]) using this article's structural demand functions, the growth estimates from Table 3, and an assumption that each state's demand has a permanent price elasticity of [epsilon] = -0.842 as estimated in Cole (2012). Although the states have different nonholiday tax rates and holiday-induced growth rates, the time-shifted share is relatively constant at around 90%. The lowest time-shift share is 88.8% in both Louisiana and New Mexico, the two states with the smallest growth rates. These states require relatively smaller magnitude [gamma]'s in order to explain the growth that occurred in excess of that predicted by [epsilon] alone, hence the lower [s.sup.T] values.

The table also provides estimates of the activity-based efficiency measure [absolute value of [DELTA]G]/ ([bar.p]N), the government cost per dollar of new spending. Like [s.sup.N] and [s.sup.T] these ratios are similar across states, ranging from 1.116 to 1.160 with an average of 1.138. The fact that these ratios are in excess of 1 imply that the governments could have bought the new computers and given them away at a smaller revenue cost than the holiday.

Panel B provides the same estimates but under an assumption that each state has a larger permanent price responsiveness of [epsilon] = -1.83, the price elasticity of computers from Greenwood and Kopecky (2013). As expected, the larger magnitude [epsilon] increases each state's estimated share of new purchases, with an average [s.sup.N] increase of 83% relative to Panel A. The new [epsilon] dramatically lowers [absolute value of [DELTA]G]/ ([bar.p]N) in each state, with the average now 0.603 across states, though this is no surprise given the prior observation that any [epsilon] less than (greater than) one in magnitude will have a [absolute value of [DELTA]G]/ ([bar.p]N) value greater than (less than) one. Interestingly, this change in e also reverses the states' rankings in terms of [absolute value of [DELTA]G]/ ([bar.p]N). Louisiana and Tennessee were the most and least efficient, respectively, in Panel A; in Panel B, they are instead least and most efficient. (44) In sum, it is clear that estimates of a holiday's activity-based efficiency are quite sensitive to [epsilon].

Table 5 presents the estimated welfare effects, where each state's compensating variation (Column 2), cost to government (Column 3), and change in social surplus (Column 4) are normalized by the state's holiday-period tax revenues under the original constant-tax regime. Panel A presents the estimates for the baseline of [epsilon] = -0.842, in which case the average normalized compensating variation is 1.411, the average normalized government cost is -1.860, and the average normalized change in social surplus is --0.449. In each and every state the losses to the government exceed consumers' compensating variation, leading to a net decrease in social surplus. In net holidays generate an average of only $0.77 in compensating variation for every $1 of foregone tax revenue (see Column 5) as the inefficiencies associated with subsidization of time-shifted units significantly outweigh any efficiencies associated with the elimination of the tax distortion on genuinely new units.

Comparing across states, compensating variation and the change in government revenues are positively and negatively correlated with nonholiday tax rates, respectively. (45) This is not surprising given that a holiday is more of a boon to consumers in high tax states, but will also cost the high-tax government more revenue. In net however, social surplus losses are largest in high tax states. This stands in contrast to Panel A in Table 4, which showed that holidays were more efficient in high tax states according to the activity-based efficiency measure.

Panel B in Table 5 provides the welfare estimates under the [epsilon] = - 1.83 alternative. This change in [epsilon] does not affect the compensating variation estimates but reduces the magnitude of the government's estimated revenue losses. In net each state's change in social surplus remains negative, though less so (in magnitude) compared with Panel A. Larger magnitude permanent price elasticity therefore makes the holidays appear relatively more efficient by both activity-based and welfare-based criteria, though the welfare-based measure is much less sensitive to e. Comparing across states, the change in e does not change the Panel A finding that higher tax states have larger social surplus losses, whereas the change in e completely reversed the correlation between tax rates and activity-based efficiency. (46)

V. CONCLUSION

While temporary fiscal policies may induce response along a potentially efficiency-enhancing "new purchase" margin, they also induce response along an efficiency-decreasing "time-shift" margin. As such the net effect on Kaldor-Hicks efficiency is theoretically ambiguous. To rectify this situation I presented a structural model that is internally consistent with constant demand elasticities and relies only upon reliably estimable information. Using this framework I estimate that two different policies, Cash for Clunkers and states' sales tax holidays, are both Kaldor-Hicks inefficient. Both policies cost government significantly more than consumers received in compensating variation.

While the methods presented herein can be applied to other policies, the specific empirical results should not be generalized. For instance, the degree to which consumers react to and value a sales tax holiday on clothing (or an expiring hybrid car subsidy, or a temporary first-time homebuyer credit, etc.) will depend on their clothing-specific preferences and willingness to delay or expedite clothing purchases. There is no reason to expect these preferences will align with those for fuel-efficient cars or computers. Therefore a fruitful avenue of policy-relevant research would be to use this paper's techniques to estimate the efficiency effects of other temporary fiscal policies that induce responses along the same new and time-shifted margins.

Given that holidays may not pass muster in terms of Kaldor-Hicks efficiency, additional research may address their prevalence. Externalities are an unsatisfactory explanation if the external benefit arises from new as opposed to time-shifted purchases-why not lower the tax rate or subsidize in all periods, even by a small amount, and avoid the inefficient distortions associated with time-shifting? On the other hand, time-shifting may be desirable if the market is slack and there is social benefit to stimulus. This argument carries weight for policies such as Cash for Clunkers, but even so, it does not imply that the private welfare effects should be ignored. The stimulus argument carries little weight for policies like sales tax holidays that tend to occur at regularly scheduled intervals, not just periods when the market is weak.

Perhaps the intent of holidays is not to increase economic efficiency but rather to target certain favored portions of the population. In terms of the current analysis, I have estimated the aggregate compensating variation across all consumers. If only a preferred portion of the population shops during holidays, but consumers are evenly affected by tax increases that compensate for lost revenues, then holidays may provide distributional benefits. Or perhaps the story behind holidays is one of political economy or psychology. Holidays garner significant attention from consumers, producers, the media, and voters. Perhaps it is the salience of a large but brief policy change, especially in comparison to a small, permanent, but more efficient change, that makes holiday policies so popular.

doi: 10.1111/ecin.12223

APPENDIX: PROOFS

Proof of Proposition 1a

Applying the envelope theorem to the consumer's expenditure minimization problem, the benefit of a marginal change in [p.sub.h] is - [y.sub.h]([p.sub.h], [P.sub.noth]). This result is shown as equation 14.41 (p. 632) of the Just, Hueth, and Schmitz (2004) treatment of intertemporal economic welfare analysis in the context of a durable good. Therefore:

(A1a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A1b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A1c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A1d) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A1e) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The first step relies on the decomposition of [y.sub.h] given in Equation (2). The second follows from integration by parts. The third relies on the facts that N([p.sub.noth], [p.sub.noth]) = 0 and T([p.sub.noth], [p.sub.noth]) = 0. Finally the last step is obtained from integration by substitution and uses the implicit definitions of the [p.sup.N] and [DELTA][p.sup.T] functions given in Equations (3b) and (3c), respectively.

Proof of Proposition lb

The government's tax revenue changes due to: changes in the quantities sold in non-/; periods; changes in the quantity sold in hand changes in the per-unit tax collected in h. The present value of the change in revenues is given by

(A2a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2c) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A2d) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

The first step relies on the subgood definitions given in Equation (1). The second gathers subgood quantity terms.

The third relies on the facts that N([p.sub.noth], [p.sub.noth]) = 0 and T([p.sub.noth], [p.sub.noth]) = 0

Proof of Proposition 2

Assumption (10b) states that

(A3a) [partial derivative] ln [y.sub.h]([p.sub.h], [p.sub.noth])/[partial derivative][p.sub.h] = [epsilon] + [gamma] + [gamma].

Integrating over [p.sub.h] therefore implies that

(A3b) ln [y.sub.h]([p.sub.h], [p.sub.noth]) = ([epsilon] + [gamma])ln[p.sub.h] + [f.sub.1]([p.sub.noth])

where [f.sub.1] is a function that depends on [p.sub.noth] but not [p.sub.h]. Assumption (10a) holds for all f including h; therefore Equations (10a) and (10b) together imply that

(A4a) [partial derivative] ln [y.sub.h]([p.sub.h], [p.sub.noth])/[partial derivative][p.sub.noth] = -[gamma].

Integrating over [p.sub.noth] therefore implies that

(A4b) ln [y.sub.h]([p.sub.h], [p.sub.noth]) = -[gamma] ln [p.sub.noth] + [f.sub.2]([p.sub.h])

where [f.sub.2] is a function that depends on [p.sub.h] but not [p.sub.noth]. In net, Equations (A3b) and (A4b) are both satisfied if and only if

(A5) [y.sub.h] ([p.sub.h], [p.sub.noth]) = z[([p.sub.h]).sup.[epsilon]][([p.sub.h]/[p.sub.noth]).sup.[gamma]]

where z is a constant.

The definition of C given in Equation (la), together with the previous result, imply that

(A6a) C ([p.sub.noth]) = [y.sub.h] ([p.sub.noth], [p.sub.noth])

(A6b) = z[([p.sub.noth]).sup.[epsilon]].

Before moving on to the derivation of the new and time-shifted demands, it will prove useful to define [y.sup.*.sub.t] (p) as the Hicksian demand in period t as a function of the entire vector of [p.sub.t] prices, p. Note that the [y.sub.t]([p.sub.h], [p.sub.noth]) functions hold prices constant in non-h periods; therefore, their partials are related to those of the [y.sup.*.sub.t](p) functions according to

(A7a) [partial derivative][y.sub.t]([p.sub.h], [p.sub.noth])/[partial derivative][p.sub.h] = [partial derivative][y.sup.*.sub.t](p)/[partial derivative][p.sub.h]

for all t and

(A7b) [partial derivative][y.sub.t]([p.sub.h], [p.sub.noth])/[partial derivative][p.sub.noth] = [summation over (s[member of][OMEGA],S[not equal to] [partial derivative][y.sup.*.sub.t](p)/[partial derivative][p.sub.s].

for all t. Furthermore Young's Theorem implies that

(A7c) [partial derivative][y.sup.*.sub.h](p)/[partial derivative][p.sub.t] = [(1 + R).sup.-(t-h)] [partial derivative][y.sup.*.sub.t](p)/[partial derivative][p.sub.h].

Combining these properties therefore implies that

(A7d) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

With this final result in mind, we now proceed to the derivation of T. Taking the partial of its definition in Equation (1c),

(A8a) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

(A8b) = -[partial derivative][y.sub.h]([p.sub.h], [p.sub.noth])/[partial derivative][p.sub.noth]

(A8c) = z[gamma][([p.sub.h]).sup.[epsilon]+[gamma]][([p.sub.noth]).sup.-[gamma]- 1].

Integrating this expression and accounting for the boundary condition T([p.sup.noth], [p.sub.noth]) = 0 then yields

(A9) T([p.sub.h], [p.sub.noth]) = z[([p.sub.h]).sup.[epsilon]] ([gamma]/1 + [epsilon] + [gamma]) (777Z7)

x ([([p.sub.h]/[p.sub.noth]).sup.1+[gamma]] - [([p.sub.h]/[p.sub.noth]).sup.- [epsilon]]).

Finally, N can be solved for using the [y.sub.h] decomposition

identity in Equation (2) along with the previous results:

(A10a) N([p.sub.h], [p.sub.noth]) = [y.sub.h] (([p.sub.h], [p.sub.noth]) - C{[p.sub.noth]) - T([p.sub.h]/[p.sub.noth])

(A10b) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII].

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Ching, A., M. Clark, T. Dutta, and Y. Zhu. "Comment on Abrams and Parsons: CARS Is Hardly a Clunker." The Economists' Voice, 7(1), 2010, 1-2.

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--. "Sales Tax Holidays: Timing Behavior and Tax Incidence." PhD dissertation. University of Michigan, Ann Arbor, MI, 2009.

--. "Christmas in August: The Effects of Sales Tax Holidays on Computer Purchases." Working Paper, 2012.

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--. (1987). "The Welfare Cost of Factor Taxation in a Perfect-Foresight Model." Journal of Political Economy, 95(4), 1987, 675-709.

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Li, S., J. Linn, and E. Spiller. "Evaluating Cash-for-Clunkers: Program Effects on Auto Sales and the Environment." Journal of Environmental Economics and Management, 65(2), 2013, 175-93.

McCarthy, P. "Market Price and Income Elasticities of New Vehicle Demands." Review of Economics and Statistics, 78(3), 1996, 543-47.

Mian, A., and A. Sufi. "The Effects of Fiscal Stimulus: Evidence from the 2009 'Cash for Clunkers' Program." Quarterly Journal of Economics, 127(3), 2012, 1107-42.

Mikesell, J. "State Sales Tax Holidays: The Continuing Triumph of Politics over Policy." State Tax Notes, July 10, 2006.

Ramsey, F. "A Contribution to the Theory of Taxation." Economic Journal, 37, 1927,47-61.

Robyn, M., M. Cohen, and J. Henchman. "Sales Tax Holidays: Politically Expedient but Poor Tax Policy." Journal of State Taxation, 29(6), 2011, 45-56.

Ruano, M. "Why Sales Tax Holiday Critics Are Wrong." State Tax Notes, September 29, 2008.

Sallee, J. "The Surprising Incidence of Tax Credits for the Toyota Prius." American Economic Journal: Economic Policy, 3(2), 2011, 189-219.

Slemrod, J. "Do Taxes Matter? Lessons from the 1980's." American Economic Review, 82(2), 1992, 250-56.

Strulik, H., and T. Trimbom. "Anticipated Tax Reforms and Temporary Tax Cuts: A General Equilibrium Analysis." Journal of Economic Dynamics and Control, 34(10), 2010,2141-58.

(1.) July 27, 2009 press release, http://www.nhtsa.gov/ About+NHTSA/Press+Releases/2009/Transportation+ Secretary+Ray+LaHood+Kicks+Off+CARS+Program+ Encourages+Consumers+to+Buy+More+Fuel-Efficient+ Cars+and+Trucks, last accessed December 10, 2014.

(2.) For instance, it is hard to imagine a policymaker proposing a brief holiday on a product as meritorious and delicious, but short-lived, as Greek yogurt.

(3.) While Mian and Sufi (2012) directly addresses Cash for Clunkers, the article also notes the existence of significant timing response to the first-time homebuyer credits.

(4.) More precisely, the holiday would provide consumers just as much value as an unrestricted cash payment in the amount of the tax savings.

(5.) See Just, Hueth, and Schmitz (2004, 629-35), for a rigorous description of the envelope theorem approach to welfare analysis in the case of consumer durables.

(6.) Mian and Sufi (2012) estimate the policy's impact on short- and long-run economic activity, while Busse et al. (2012) estimate the policy's price effects. Both pieces of information are necessary, but not sufficient, for estimating welfare effects.

(7.) The Hawkins and Mikesell (2001) critique of sales tax holidays asks "Would customers/taxpayers prefer a $12 tax cut delivered by a check in the mail or to have to spend roughly $200 (assuming a 6 percent tax rate) during a particular week of the year on the specifically exempted goods to receive the same financial benefit?" This article provides the methodological framework for actually answering this rhetorical question.

(8.) If supply is less than perfectly elastic, the pre-tax price will rise during the holiday period and suppliers will share the holiday's incidence. Consumers' compensating variation will be smaller but the change in producer surplus will be greater than 0.

(9.) If external benefits exist, they are likely to differ between new and time-shifted units. The methodology proposed herein helps distinguish between these two quantities.

(10.) In the Introduction I contrasted this article's approach against less tractable macroeconomic approaches. To be clear, they are not perfect substitutes. Macroeconomic analysis is particularly well suited for dealing with two distinct issues: dynamics and general equilibrium effects. The reframing that I propose herein is well suited for dealing with the former but not the latter; therefore, my reframing most accurately captures the welfare effects of "small" holiday policies. This is why I have expressly avoided any implication that the framework applies to, for instance, George W. Bush's "temporary" income tax cuts.

(11.) The demand function is indexed by t; therefore, a period's demand may respond differentially to changes in [p.sub.h] depending upon its proximity to the holiday period. Indexing by t also allows for seasonal variation.

(12.) A simple example clarifies the demand concepts. Ignoring discounting, suppose there are three periods with a common tax rate and demand of 5 in each period (i.e., [y.sub.1] = [y.sub.2] = [y.sub.3] = 5). Upon implementation of a holiday in period two, [y.sub.1] and [y.sub.3] each drop to 3 while [y.sub.2] jumps to 12. The short-run (i.e. holiday period) increase in sales is 12-5 = 7 while the long-run increase is 18 - 15 = 3. In this case C = 5 (the original demand in period two), T = 4 (the 4 units shifted to period two, 2 from period one and 2 from period three), and N = 3 (the number of period two sales that would not have occurred in any period without the holiday).

(13.) For instance, consumers would likely gain more utility from one additional unit being purchased in three consecutive periods rather than three units being purchased in one period. However, in order to benefit from a holiday's temporarily preferential fiscal treatment, the latter purchasing pattern is required.

(14.) For example, a small subsidy may not have lured a consumer to the car dealer during the inconveniently timed Cash for Clunkers window, whereas the consumer did make the time to shop for the program's sizable maximum rebate of $4,500.

(15.) Liquidity constraints may be most relevant for low income families, a group that many temporary tax cuts are presumably intended to benefit. For instance, if this month's rent is supposed to come out of the month's first paycheck and the kids' school clothes are supposed to come out of the month's second paycheck, it may be difficult for the credit-constrained family to take advantage of a three-day sales tax holiday on clothing that falls at the beginning of the month.

(16.) For instance, suppose it is June, a sales tax holiday on computer purchases will occur in August, and the family computer is 3 years old and has slowed to a crawl. A small reduction in the sales tax rate is insufficient to bother suffering through two more months of 2001-esque download speeds; however, the $50 in savings associated with a larger tax cut may be sufficient.

(17.) These shadow costs are consumer analogs to firms' internal adjustment costs in the House and Shapiro (2008) analysis of bonus depreciation policies.

(18.) Even if supply were not perfectly elastic, producers' marginal cost would equal 0 at T = 0; therefore, the holiday would still have the anti-efficiency effect of a distortionary subsidy, though the incidence of the subsidy would fall upon both consumers and producers.

(19.) Alvarez et al. (1992) addresses the desirability of intertemporally consistent tax rates in a framework similar to that of Atkinson and Stiglitz (1976). Ramsey (1927) would assign equal tax rates in all periods assuming that each period's demand has the same elasticity, an altogether reasonable assumption.

(20.) If the compensation actually occurs, the change in government revenues is 0 and the change in consumers' compensating variation, inclusive of the additional lump sum tax, is given by CV + [DELTA]G. The total effect on social surplus is still given by CV + [DELTA]G.

(21.) See Lecture 12 in Atkinson and Stiglitz (1980).

(22.) The maximum value of [f.sup.N] = 1 (or [f.sup.T] = 1) attains if consumers gain a net surplus of [p.sub.noth] - [p.sub.h] for each and every marginal unit of N (or T). The minimum value of [f.sup.N] = 0 (or [f.sup.T] = 0) attains if consumers gain a net surplus of 0 for each and every marginal unit of N (or T).

(23.) More precisely, [DELTA]SS increases with [s.sup.N] if ([[tau].sub.h]/[[tau].sub.noth] - [[tau].sub.h]) + [f.sup.N] + (1 - [f.sup.T]) > 0. This is necessarily true if [[tau].sub.h] [greater than or equal to] 0. If [[tau].sub.h] < 0, then the holiday may or may not induce additional deadweight loss in the N submarket as that subgood becomes subsidized. In that case a larger [s.sup.N] may actually imply a larger loss in social surplus.

(24.) Reports on job stimulus programs are also often accompanied by the statistic "cost per new job." See for instance the Brookings Institute's recent analysis assessing the job stimulus impact of Cash for Clunkers (Gayer and Parker 2013). Cash for Clunkers is compared and other job stimulus programs are specifically ranked upon their respective cost per new job metric.

(25.) For instance, [s.sup.T] > [[tau].sub.h]/[[tau].sub.noth] is necessarily true if [[tau].sub.noth] > 0, [[tau].sub.h], [less than or equal to] 0, and [s.sup.T] > 0.

(26.) For instance, linear subgood demand curves would necessarily imply [f.sup.N] = [f.sup.T] = 1/2, regardless of factors such as the policy's effect on price or the holiday-induced growth. Constant elasticity assumptions are flexible enough to allow the data on a holiday's impact to influence the estimates of consumers' marginal benefits of consumption.

(27.) z and [gamma] are identified by the following structural relationships: z = C[([p.sub.noth]).sup.[epsilon]] and [gamma] = (ln (1 + g)/ln (1 + [[tau].sub.h]/1 + [[tau].sub.noth])) - [epsilon].

(28.) Cole (2009) estimates "full pass-through or mild over-shifting of the sales tax on computers." Busse et al. (2012) "find that dealers passed 100% of the rebate through to consumers" during Cash for Clunkers.

(29.) Gayer and Parker (2013) provide an overview of the program's implementation and subsequent analyses.

(30.) More precisely, the authors estimate that "approximately 370,000 cars were purchased under the program during July and August 2009 that would not have been purchased otherwise" (p. 1109). Comparing this estimate to the approximately 677,000 total vouchers redeemed over the window implies a short-run growth rate in voucher-eligible cars of 120%.

(31.) As discussed in footnote 27, estimates of the short run growth g, the relative holiday and nonholiday prices, and the permanent price elasticity [epsilon] identify the "residual" holiday elasticity [gamma]. These demand parameters can then be used in the structural demand Equations (11a)-(11d) to apportion total holiday sales among C, N, and T.

(32.) The $4,210 value is calculated by the author using the National Highway Traffic Safety Administration's database of paid claims. The $2,390 value is from Busse et al. (2012, Table 10). The $22,592 average price is also from Busse et al. (2012).

(33.) In reality, states differed with respect to their sales tax treatment of vouchers and trade-ins; however, these differences have second-order effects on the program's effect on consumer prices, whereas the voucher value (net of the clunker's trade-in value) has a first-order effect.

(34.) Analyses more recent than McCarthy (1996) estimate the price elasticities for specific models of car, which predictably have more elastic demand relative to the broader car market.

(35.) 5.71% is the weighted average of the sales tax rate in 50 states plus the District of Columbia, weighted by the number of new vehicles sold in each jurisdiction in 2009. 2009 tax rates are from the Tax Foundation website. 2009 new vehicle sales are from the National Automobile Dealers Association 2010 State of the Industry Report. 10.25% reflects the sales tax rate in Chicago in 2009.

(36.) These estimates account for both federal government cost and the program's indirect effect on states' tax revenues. The change in

state tax revenues is given by - [[tau].sub.s] x (2,390) x (C + T) + [[tau].sub.s] x (22, 592 - 2,390) x N, where [[tau].sub.s] is the state's tax rate. The state loses revenue on the C and T units that would have been sold even without Cash for Clunkers since the per vehicle tax base is $2,390 (the difference between the voucher value and the clunker trade-in value) lower. On the other hand, the state gains revenue from tax levied on the N units that would not have occurred without the program.

(37.) The scrapped clunkers had an estimated value of $1.23 billion. Even if they were resold by the government as opposed to scrapped, the program would still have resulted in additional deadweight loss.

(38.) Ching et al. (2010) critiques the Abrams and Parsons (2009) article's assessment of the program's external benefits but not its methodology for estimating consumer welfare.

(39.) This percentage is estimated as consumers' compensating variation divided by the product of the number of vouchers redeemed and the difference in consumer prices with and without the vouchers.

(40.) The downward bias is $319 ($332) million assuming a preexisting tax rate of 5.71% (10.25%).

(41.) $39 is the Interagency Working Group on Social Cost of Carbon (2013) estimated cost per ton for 2015, estimated using a 3% discount rate and measured in 2011 dollars. The estimated cost drops to $12 per ton using a 5% discount rate and rises to $61 per ton using a 2.5% discount rate. The Group also publishes estimates based on the 95th percentile of its simulations "to represent the higher-than-expected economic impacts from climate change further out in the tails of the [simulation] distribution" (p. 12). Using a 3% discount rate, the estimated cost under this scenario is $116 per ton. The Group reports these costs in 2007 dollars, whereas the costs provided here reflect the Environmental Protection Agency's conversion to 2011 dollars. See http://www.epa.gov/climatechange/EPAactivities/ economics/scc.html, last accessed December 10, 2014.

(42.) Cole (2008) describes the history of US sales tax holidays. The Federation of Tax Administrators maintains a list of holidays on its website. Brunori (2001), Hawkins and Mikesell (2001), Mikesell (2006), and Robyn et al. (2011) offer criticisms of sales tax holidays, while Ruano (2008) defends them.

(43.) Figure 4 includes the result of OLS with a constant. The constant has a f-stat of only -0.40, so strict proportionality cannot be rejected. The addition of a second-order polynomial term to the regressors lowers the Adjusted [R.sup.2] from 0.596 to 0.589, further supporting the null hypothesis.

(44.) The correlation between tax rates and [absolute value of [DELTA]G]/ ([bar.p]N) switches from -0.728 in Panel A to +0.712 in Panel B.

(45.) The correlation between tax rates and CV/[G.sub.0] is +0.831. It is -0.828 between tax rates and [DELTA]G/[G.sub.0].

(46.) The correlation between tax rates and the normalized change in social surplus goes from -0.825 in Panel A to -0.799 in Panel B.

MARK D. PHILLIPS, I received valuable comments from Jim Aim, Gary Becker, Adam Cole, Brian Hill, William Hubbard, Kenneth Judd, Ed Kleinbard, Ethan Lieber, Victor Lima, Bruce Meyer, Casey Mulligan, Kevin Murphy, Olivia Wills, the editor, and two anonymous referees, along with workshop and conference participants at the 2012 National Tax Association Annual Conference, the 2013 Lincoln Institute Junior Scholars Program, the USC Gould School of Law's Center in Law, Economics, and Organization, and the USC Price School of Public Policy.

Phillips: Sol Price School of Public Policy, University of Southern California, Ralph and Goldy Lewis Hall, 300, Los Angeles, CA 90089. Phone 213-740-0210, Fax 213-740-0001, E-mail [email protected]

TABLE 1
New Versus Time-Shifted Cash for Clunkers Purchases

                                           Shifted    Govt. Cost per
               Effective    New Purchase   Purchase       New Car
                Tax Rate      Share of      Share       Purchased:
Preexisting   During Cash     Growth:     of Growth:  [absolute value
Tax Rate      for Clunkers   [S.sup.N]    [S.sup.T]   of [DELTA]G]/N
(1)               (2)           (3)          (4)            (5)

A. Estimates based on [epsilon] = -0.87

0.00%           -10.58%        0.176        0.824        $ 24,805
5.71%            -5.48%        0.176        0.824         24,931
10.25%           -1.41%        0.176        0.824         25,031

B. Estimates based on [epsilon] = -3.31

0.00%           -10.58%        0.500        0.500         $ 8,749
5.71%            -5.48%        0.500        0.500          7,959
10.25%           -1.41%        0.500        0.500          7,330

TABLE 2
Welfare Effects and Efficiency of Cash for Clunkers

Preexisting     Consumers'     Federal      Change in
Tax Rate       Compensating   Govt. Cost   State Govt.
                Variation                   Revenues
(1)                (2)           (3)           (4)

                     $ millions

A. Estimates based on [epsilon] = -0.87

0.00%             1,111         -2,851           0
5.71%             1,174         -2,851          -8
10.25%            1,225         -2,851         -15

B. Estimates based on [epsilon] = -3.31

0.00%             1,111         -2,851           0
5.71%             1,174         -2,851         146
10.25%            1,225         -2,851         262

                                  CV/[absolute
Preexisting      Change in      value of [DELTA]G]
Tax Rate       Social Surplus     (2)/[absolute
                (2)+(3)+(4)     value of (3)+(4)]
(1)                 (5)                (6)

                 $ millions

A. Estimates based on [epsilon] = -0.87

0.00%              -1,740              0.39
5.71%              -1,685              0.41
10.25%             -1,641              0.43

B. Estimates based on [epsilon] = -3.31

0.00%              -1,740              0.39
5.71%              -1,531              0.43
10.25%             -1,364              0.47

TABLE 3
Computer Sales Tax Holidays, 2007

                   Holiday      Tax     Holiday
State             Elasticity    Rate    Growth
(1)                  (2)        (3)       (4)

Alabama             -19.1        4%      73.5%
Georgia             -20.4        4%      78.5%
Louisiana           -11.0        4%      42.3%
Massachusetts       -22.9        5%     109.0%
Missouri            -21.6      4.225%    87.6%
New Mexico          -12.5        5%      59.5%
North Carolina      -24.7        4%      95.0%
South Carolina      -21.5        6%     121.7%
Tennessee           -27.6        7%     180.6%

Notes: "Holiday elasticity" and "tax rate" come from Cole
(2012). Tables 5 and 1, respectively. "Holiday growth" is the
author's calculation and inferred from these first two values
using Cole's definition of "elasticity."

TABLE 4
New Versus Time-Shifted Purchases during
Computer Sales Tax Holidays

                                 Shifted        Govt. Cost per
                 New Purchase   Purchase           $ of New
                   Share of     Share of          Purchases:
                   Growth:       Growth:     [absolute value of
State             [S.sup.N]     [S.sup.N]   [DELTA]G] / ([bar.p]N)
(1)                  (2)           (3)               (4)

A. Estimates based on [epsilon] = -0.842

Alabama             0.080         0.920             1.144
Georgia             0.077         0.923             1.141
Louisiana           0.112         0.888             1.160
Massachusetts       0.081         0.919             1.132
Missouri            0.077         0.923             1.138
New Mexico          0.112         0.888             1.151
North Carolina      0.070         0.930             1.135
South Carolina      0.092         0.908             1.129
Tennessee           0.092         0.908             1.116

B. Estimates based on [epsilon] = -1.83

Alabama             0.149         0.851             0.595
Georgia             0.142         0.858             0.598
Louisiana           0.220         0.780             0.572
Massachusetts       0.145         0.855             0.612
Missouri            0.140         0.860             0.603
New Mexico          0.212         0.788             0.582
North Carolina      0.127         0.873             0.608
South Carolina      0.162         0.838             0.615
Tennessee           0.154         0.846             0.636

TABLE 5
Welfare Effects and Efficiency of Computer Sales Tax Holidays

                        Consumers'            Change in Tax
State             Compensating Variation/   Revenues/Original
                   Original Tax Revenue        Tax Revenue
(1)                         (2)                    (3)

A. Estimates based on [epsilon] = -0.842
Alabama                    1.331                 -1.676
Georgia                    1.352                 -1.724
Louisiana                  1.198                 -1.376
Massachusetts              1.474                 -2.002
Missouri                   1.389                 -1.808
New Mexico                 1.272                 -1.529
North Carolina             1.419                 -1.884
South Carolina             1.523                 -2.105
Tennessee                  1.740                 -2.640

B. Estimates based on [epsilon] = -1.83
Alabama                    1.331                 -1.625
Georgia                    1.352                 -1.673
Louisiana                  1.198                 -1.330
Massachusetts              1.474                 -1.933
Missouri                   1.389                 -1.753
New Mexico                 1.272                 -1.469
North Carolina             1.419                 -1.830
South Carolina             1.523                 -2.020
Tennessee                  1.740                 -2.528

                  Change in Social
                  Surplus/Original     CV/[absolute value
State               Tax Revenue         of [DELTA]G](2)/
                      (2)+(3)        [absolute value of (3)]
(1)                     (4)                    (5)

A. Estimates based on [epsilon] = -0.842
Alabama                -0.345                 0.794
Georgia                -0.372                 0.784
Louisiana              -0.178                 0.871
Massachusetts          -0.528                 0.736
Missouri               -0.419                 0.768
New Mexico             -0.257                 0.832
North Carolina         -0.464                 0.754
South Carolina         -0.582                 0.723
Tennessee              -0.900                 0.659

B. Estimates based on [epsilon] = -1.83
Alabama                -0.294                 0.819
Georgia                -0.321                 0.808
Louisiana              -0.132                 0.900
Massachusetts          -0.458                 0.763
Missouri               -0.364                 0.793
New Mexico             -0.197                 0.866
North Carolina         -0.410                 0.776
South Carolina         -0.497                 0.754
Tennessee              -0.787                 0.689