Price Gap and Welfare

Transcription

1 APPENDIX D Price Ga and Welfare Derivation of the Price-Ga Formula This aendix details the derivation of the rice-ga formula (see chaters 2 and 5) under two assumtions: (1) the simlest case, where there are no systematic differences in the cost of living between the home country and the country chosen as a comarator, and (2) the more comlicated case, where there are systematic differences. The first case is not realistic and is reviewed only in order to start with a simle formula, so as to build realism (and comlication) ste by ste. ase 1: No Systematic ost-of-living Difference Let i be the international rice of roduct i, which is assumed as fixed in international markets. Later on, we will discuss in what sense this assumtion is not realistic and how to amend it to something more realistic. Also, let t i and t i be the ad-valorem tariffs alied to roduct i in the home () and comarator () countries, resectively. Let i be the domestic rice of roduct i on the home market and i its domestic rice in the comarator country. Assume that a non-tariff measure (NTM) is imosed by the home country on widgets, for which we will omit the index i, and let a be the ad-valorem equivalent (AVE) of that NTM, in fractional form (that is, the AVE in ercent form is 100 times a). 179

2 180 Streamlining Non-Tariff Measures No NTM is imosed on widgets in the comarator country, which is why we chose it. We do not know a but will determine it using information that is available, which is essentially the domestic rice of widgets and other roducts in the home and comarator markets and tariff rates alies to widgets and other roducts in the home and comarator markets. Formally, the home rice of widgets is determined by = * ( 1 + a) (1) where a is unknown, and its rice in the comarator market by = *( 1 + (2) In (1) and (2), everything is observed excet a. Therefore, we can take the ratio of the two and obtain = * a) * (3) On the left-hand side (LS) is the ratio of domestic rices observed in the home and comarator markets, which is the main iece of evidence we use in the rice-ga calculation. If the home rice of widgets is three times their rice in the comarator market, the ratio of the LS is 3. On the right-hand side is an exression involving the common international rice, *, which can be eliminated, and tariffs. We can invert this exression to isolate (1 + a), obtaining: = 1+ a (4) or a = 1. (5) That is, the AVE of the NTM on widgets is calculated as the ratio of the home and comarator rices of widgets urged of the effect of tariffs.

3 Price Ga and Welfare 181 The reason for taking tariffs into account is as follows. Suose that observed domestic rices in the home and comarator countries, converted into US dollars at the current exchange rate, are $16.2 and $12.0, resectively, and tariffs are 20 ercent and 5 ercent resectively. Without tariff adjustment, the estimated AVE would be a unadjusted = = or 35.0 ercent, suggesting that the NTM imosed on widgets raises their home rice by 35.0 ercent. owever the tariff-adjusted AVE is 16. 2/ 20 / 100) a tariff-adjusted = 1 = / / 5/ 100) 12/ = or ercent. That is, almost half of the difference in the rice of widgets between the home and comarator markets is accounted for by the difference in tariff rates. Attributing the whole rice difference to the NTM would be flat wrong. ase 2: Systematic ost-of-living Difference Now suose that there are unobserved or hard-to-measure factors that raise the cost of living (OL) in the home country to a level that is systematically higher than in the comarator country. These factors can include transortation costs, landlockedness, ort inefficiency, and so on as long as they are not themselves due to NTMs. Let λ be the common rice-raising factor affecting all roducts. Then (1) becomes = * λ ) a) (6) whereas (2) is unchanged. ombining (6) and (2) as we did in (5), we have a = λ) 1. (7) So now we have two unknowns to determine: α and λ. For that, we need some additional information. That information will be obtained by looking at rice differences for other roducts, referably not subject to any cost-raising NTMs (finding such roducts is art of the difficulty of this exercise). Suose we have found 30 such roducts, and let and

4 182 Streamlining Non-Tariff Measures be their average rices on the home and comarator markets, resectively. We can write so, after maniulation, = * λ) = * λ) v, λ= 1. (8) Thus, we now calculate the rice ga in two stes: Ste 1. alculate the OL adjustment λ factor using (8). Ste 2. alculate the rice ga using domestic rices, tariffs, and the estimate of λ obtained from ste 1. In the examle above, a OL adjustment of 18 ercent would be enough to wie out comletely the estimated AVE of the NTM, meaning that the initial rice difference of 35 ercent on widgets would be exlained roughly in half by tariffs and in half by systematic OL differences. An Econometric Aroach The rice-ga method can be likened to an econometric aroach known as difference in differences (DID), and the analogy may hel readers who are familiar with econometrics to understand how it works. Assume that we have rice data for a samle of roducts, defined at the S6 level of the armonized system s nomenclature, and a samle of countries (more than two, unlike before). Some of those roducts are covered by the NTM in some but not all of the countries, but there are roduct-country combinations without any rice-raising NTM. The DID regression estimates the correlation between rices (the deendent variable, in log form) with exlanatory variables including tariffs and dummy (binary zero/one) variables marking the resence of NTMs. Let k be a roduct, i a country, and n a tye of NTMs (say, n = A means an SPS, n = B a TBT, and so on). Let I = 1 ikn 0 if NTM n is imosed by country i on roduct k otherwise.

5 Price Ga and Welfare 183 The DID regression equation has the form ( ) ln = aln 1+ t b I d i d k u (9) i i n n= A,... where u i is an error term. Fixed effects d i and d k control resectively for systematic cost-of-living differences across countries and for the fact that we are literally comaring ales and oranges in the regression since we are ooling over roducts. If the samle is declared as a anel with roducts as the anel s individuals, the econometrics software will transform the rice data by subtracting the mean samle rice of each roduct, in effect converting rices into rice gas. Using hats to denote econometric estimates, the estimated AVE of NTM n across countries and roducts is Derivation of the Welfare Formula ikn AVE = bˆn n e 1. (10) This aendix section details the derivation of the formula maing rice changes into welfare changes, under the assumtion that the utility function is such that there is an equivalence between welfare changes and monetary income changes that is not affected by olicy changes (this is true, for instance, when the utility function is quasi-linear). When analyzing referential tariff reductions, much of the comlication in welfare calculations comes from the differential treatment of referential vs. non-referential artners, which induces trade-diversion effects in addition to trade-creation ones. By contrast, most NTMs though not all are alied on an MFN (most favored nation) basis, so there are no trade-diversion issues. The most imortant excetions are quotas and tariff-quotas alied as art of referential agreements, for examle, in the context of agricultural roducts in EU references, but those tend to get hased out. Accordingly, in what follows, we will treat only the case of NTMs alied on an MFN basis. Let Δ < 0 be the change in the domestic rice generated by the elimination of an NTM, and let Δ > 0 be the corresonding increase in domestic consumtion of the roduct in question. The effect of eliminating the NTM on consumer surlus is the sum of the rectangular and triangular areas (the total area ABD in figure 2.2 in chater 2). That is, using the formula for the area of a right-angle triangle as an aroximation to any non-linear demand curve: 1 ΔW = 0 ( { Δ) + ( Δ) Δ 2{ + + ik (11)

6 184 Streamlining Non-Tariff Measures We know that the elasticity of demand, in algebraic form, is 0 Δ ε= < 0 (12) 0 Δ So the change in consumtion, Δ, can be exressed in terms of the elasticity of demand and the change in the rice, Δ. Δ Substituting (13) into (11) gives Δ ε (13) = Δ ΔW = 0( Δ)+ 0εΔ 2 0 Δ 1 Δ = ε = Ea 0 E0εa 2 ε a (14) = Ea which is the formula in the text. Note that, in this formula, all real quantities (which are not observed) have been relaced by monetary ones (which are observed), by multilying 0 by 0. 2 The ost of Irreversible Decisions This aendix section shows how to handle irreversible decisions and low-robability risks of large losses, highlighting the sensitivity of calculations to the data. ase 1: Real Otions and Irreversible Decisions Traditional cost-benefit analysis consists of relacing uncertain magnitudes by the exected value and then comaring them. owever, when some otions are irreversible, this can be gravely misleading, as was shown by enry (1974). is celebrated article was motivated by a demand from the French ministries of equiment and transort to evaluate, using costbenefit analysis, a decision to cut through the forest of Rambouillet to build a highway around Paris. enry showed that, with the decision to

7 Price Ga and Welfare 185 destroy a forest being irreversible, the analysis could not be correctly reduced to a comarison of exected costs and benefits. To see why, consider the following examle. Suose that a domestic firm is losing money, and that the government is weighing the otion to suort it with some measure whose cost to society just matches its benefit to the firm, which means that it nets out in the calculation of social welfare. There are two eriods, today (the first or current eriod, marked by the subscrit 0) and tomorrow (the second eriod, market by the subscrit 1). Profits and losses incurred tomorrow are discounted at rate r, and d = 1/(1 + r) is the discount factor. The firm s current rofit is π0. In the second eriod, its rofit is a random variable π ~ with distribution with π < 0 and π + < 0. Assume that π %π = π + with rob. with rob. 1 A1. π0 < 0 + A2. π + ( 1 ) π < 0 + A3. π + δπ > 0 0 Assumtion A1 means that the firm s current rofit is negative, and A2 means that its exected rofit over the two-eriod horizon is also negative. Without government suort, the firm closes down. But why should the government suort it? Suose that the government behaves like a rational shareholder. If it lets the firm close down, the ayoff is zero with certainty. If it lends suort, the firm will remain in business but, by A2, face more exected losses in the second eriod. A simle cost-benefit analysis suggests that the government should terminate suort to the firm at once. This reasoning is wrong. In eriod 2, if the state of nature is unfavorable (π ~ = π ) the government will let the firm close down and lose nothing. If it is favorable, then it will internalize the firm s rofit (π ~ = π + > 0). Thus, if the government suorts the firm today, its exected ayoff for the two eriods is Whereas if it does not, its ayoff is π suort = π 0 + δπ + (15) π let down = 0 (16)

8 186 Streamlining Non-Tariff Measures By A3, the government is better off suorting the firm. The reason is that in doing so it kees the otion of closing it down tomorrow, if the state of nature turns out to be bad, but enjoying ositive rofits if it is good. By closing down the firm today, it forecloses the ossibility of enjoying the ositive rofits tomorrow. Thus, keeing the suort today is like holding an otion on a stock. That otion has a value that can be calculated using otion-ricing techniques (see Dixit and Pindyck 1994 for technical details). There are many alications of this rincile, for instance, to environmental decisions. The next section of this aendix considers a slight variant where a decision tree reaches a terminal node when a olicy decision triggers a certain event. ase 2: An Irreversible Risk onsider the following situation. A sanitary and hytosanitary (SPS) regulation rohibits the imort of a lant that may carry an invasive micro-organism. If the regulation was relaxed (a binary decision), there would be an annual robability of a disease outbreak equal to, and the monetary cost of the outbreak, which would be irreversible, would be L. This cost includes the resent value, in monetary terms, of all damages inflicted to the economy and the environment. For instance, if the industry was wied out by the outbreak, L would include the resent value of all future lost roduction. The rohibition s annual cost to domestic roducers, who would otherwise use the lant as an inut, is. Let V I be the value to the government of sticking to the regulation, and V O the value of eliminating it. Also let d = 1/(1 + r) be the discount factor. We have Suose that V O < V 1. Then VI δmax VI; VO V L ( 1 ) δmax V ; V (17) = + { } = + { } O I O VI = + δv = /( 1 δ) V = L+ ( 1 ) δv O I δ = L ( 1 ) 1 δ (18) So we must have

9 Price Ga and Welfare 187 δ L ( 1 ) < 1 δ 1 δ (19) or, after rearrangement, L 1 δ < 1 δ( 1 ). (20) The LS is the resent discounted value of an infinite stream of costs,, what the economy would suffer if the regulation was maintained forever. The RS is the cost of facing, year after year, the robability of an outbreak costing L, which is what the economy would face if the regulation was eliminated. If, after substituting estimated values for,, and L, the three key arameters, the inequality is as shown in (20), the regulation should be maintained. If it is reversed, the regulation should be eliminated. ow should the arameters,, and L be estimated? Rough estimates of and L should be obtained from roducers and government authorities. As for, it is the robability that, absent the rohibition, an infected lant would be imorted. Suose that N lants are imorted each year and n are tested for the disease by sanitary authorities at the border, and if a single lant tests ositive, the whole shiment is destroyed. Assume for simlicity that all imorts arrive in one shiment of N lants, n of which will be tested. The robability of imorting at least one infected lant and having none testing ositive is the roduct of two indeendent robabilities: (1) the robability of none testing ositive in the samle tested, and (2) the robability of at least one being infected in the samle not tested. Suose that the ex-ante robability of any given lant being infected is q. Let us call the first event (nondetection) ND. Its robability is that of having exactly zero success (a success is a lant testing ositive) in n trials given a robability of success (infection) equal to q. This robability is given by the binomial formula, with k = 0: n Pr( ND) ( ) k q k q n k = 1 (21) This boils down to (1 q) n. By the same reasoning, the second robability is one minus the robability of having no infection in the nontested art of the shiment, that is, 1 (1 q) N n. Thus, N n n = 1 ( 1 q) ( 1 q). (22)

10 188 Streamlining Non-Tariff Measures A note of caution must be stated. ow sensitive are the calculations to assumtions? The answer is, very sensitive, and in ways which may sound surrising. To see this, consider the following examle. Suose that annual exort sales are $4.4 million. Assume, as a first aroximation, that this is all value-added (as if the roduction was organic agriculture), and that the regulation cuts 10 ercent from this total. Thus, the annual loss in value added is $440,000. This is. Assume that an outbreak would cost the industry $23 million. Furthermore, assume that the industry imorts 30,000 lants each year and that the quarantine service tests 2 ercent of them. Finally, let the discount rate be 7 ercent. The resent discounted value of the regulation s cost, /(1 d ), is $6.7 million. Suose first that the robability of infection of any given lant is 1/100,000. Then the exected cost of lifting the regulation is $19 million. That is, even without counting the environmental damage, the damage the industry would inflict on itself by taking the risk of an infection would far outweigh the ossible benefit. By contrast, suose now that the robability of infection of any given lant is 1/20. Then the exected cost of lifting the regulation is zero. This may seem very odd. The reason is that, with a robability of infection of 1/100,000, samling at a 2 ercent rate has a very low robability of catching an infected lant (less than 1 ercent), while imorting 30,000 of them carries a substantial risk (25 ercent). By contrast, with a robability of 1/20, samling at 2 ercent is very efficient: the robability of catching an infected lant is almost 100 ercent. Thus, even though the robability of infection is also very high (even closer to 100 ercent), the testing is sufficiently reliable to rule out undetected infection. In fact, the testing acts like a rohibition, because, with such a high robability of infection, all shiments test ositive and are destroyed. References Dixit, Avinash, and R. Pyndick Investment Under Uncertainty. Princeton, NJ: Princeton University Press. enry, laude Investment Decisions Under Uncertainty: The Irreversibility Effect. American Economic Review 64 (6):