Deciphering the impact of voluntary export restraints (VERs): A view through two analytic lenses

~)

Pergamon

Socio-Econ. Plann. Sci. Vol. 29, No. 4, pp. 325-335, 1995

0038-0121(95)00019-4

Elsevier Science Ltd. Printed in Great Britain

Deciphering the Impact of Voluntary Export Restraints (VERs): A View Through Two Analytic Lenses R I C H A R D M C G O W A N 1 and T H O M A S V A U G H A N 2 ~University of Scranton, The Provost's Office, Scranton, PA 18510, U.S.A. 2St Joseph's University, College of Business and Administration, Philadelphia, PA 19131, U.S.A.

Abstract--The economicand political components of trade issues are usually analyzed separately. The "success" of a particular trade policy is then analyzedthrough a particular lens. In this paper, the effect that Voluntary Export Restraints (VERs) had on the textile and steel industries will be examined from both an instrumental framework(ARIMA Time SeriesInterventionAnalysis) and expressiveframework (Stakeholder Analysis) in order to capture the economicand political aspects of this policy.

INTRODUCTION Throughout the postwar era, the U.S. has created a complex process for dealing with international trade issues. Industries, which have been hurt by imports, seek relief by appealing to Congress on the grounds of unfair trading practices. Congress may react to these appeals by placing a quota or tariff on the offending imported product. The Executive branch often vetoes these sanctions as being "anti-free trade" but presses trading partners to curtail their imports of the "offending" product. The eventual outcome is to offer some relief to industries hard hit by imports in the form of a VER (Voluntary Export Restraint). Thus, the process involves Congressional action, followed by Executive restraint in order to "satisfice" the various economic and political forces that are unleashed by trading issues (see Fig. 1). Although there are many examples of VERs, the two examined here are the voluntary export quotas that were placed on textiles and steel products in 1981 and 1984, respectively. Both of these VERs provide excellent opportunities to study the complex process by which such structures are instituted while examining their effectiveness from two very different points of view. Murray Edelman contends that political acts are both instrumental and expressive [12]. The current research explores Edelman's concept. The instrumental component involves an empirical analysis that will probe the substance of a voluntary export quota-viz, the VERs effect on employment and production within the relevant industry. The expressive analysis will use Freeman's stakeholder model which probes the image or public perception of the VER policy regardless of its actual effect [131. Previously, we examined the effect of voluntary automobile import quotas by Japan on domestic auto sales [16]. This analysis concluded that there was no increase in domestic auto sales due, in part, to aggressive advertising by Japanese manufacturers. It enabled them to maintain established market share. We here extend that analysis. In the case of textiles and steel, aggressive advertising by exports to the U.S. is absent. In fact, the International Garment Workers of America commissioned a series of "informercials" exhorting U.S. consumers to buy American products. Our analysis should therefore demonstrate the effectiveness of VERs devoid of the impact of counter advertising. The paper proceeds in this sequence. First, a chronology is presented of those events leading to the establishment of a VER on textiles and steel products. Second, the method (ARIMA Time Series Intervention Analysis) and results of our empirical analysis are presented. Third, a public reaction to the imposition of the VER will be analyzed using Freeman's stakeholder model [13]. 325

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The paper concludes with an assessment of VERs using the insights provided by the combined results of both analyses. TEXTILES AND STEEL VERs: A C H R O N O L O G Y Textiles In 1956, the U.S. textile industry first sought protection against Japanese textile imports. Textile unions organized a boycott of those stores that sold Japanese goods, while Congress threatened to enact a strict quota on all Japanese textiles. As a result, Japan did consent to a 5 yr VER agreement on textiles. As part of this agreement, the Japanese agreed not increase their market share by more than 1%/yr during the period of the agreement. However, Hong Kong and Korea quickly sought to fill the gap left by the Japanese, resulting in U.S. textile producers now looking for relief from manufacturers in these countries. In 1961, responding to pressure from textile manufacturers, the U.S. government, along with European officials, convened a conference under G A T T t auspices to provide a framework for all trade in cotton textiles. The resulting Long Term Agreement (LTA) allowed any importing nation to ask any exporting nation for a VER. The exporter had 30 days to respond with an acceptable proposal or face an outright quota [19]. When the LTA came up for renewal in 1973, the U.S. demanded that additional fibers such as woollens and synthetics be covered as a part of a new VER agreement. This new type of agreement, which was first signed in 1974, came to be known as a Multifiber Agreement (MFA). These MFAs were 3 yr agreements where the growth rates for any particular fiber were specified, but importing countries could not force exporting countries to reduce their exports from one year to another. However, by 1981, the decline in the U.S. textile industry had become serious enough that the MFA to be renewed in that year seriously restricted growth rates by pegging them to growth in the domestic textile markets of the importing country. This new MFA also allowed a country to establish global quotas for some items [9], thus creating the most severe restrictions on textile imports during the post-war era. Certainly, this agreement should have, to some extent, reduced the loss of textile workers' jobs and, perhaps, even had a positive effect on employment in the industry. To be sure, it set the tone for future policy actions involving the U.S. textile industry. Steel In many ways, the controversy surrounding steel imports parallels the story of textile imports, yet differs from it in significant ways. Since 1959, the U.S., once a major steel exporter, has been a net steel importer. However, it was not until 1968, that the industry was able to pass a quota bill in Congress that represented a reasonable threat to steel importers. In response to this threat, Japan and the major European steel producers announced a 3 yr VER for carbon steel going to the U.S. The quota legislation was subsequently withdrawn by the steel industry's Congressional representatives. The VER agreement was renewed again in 1971. Meanwhile, U.S. producers of speciality steel also began to protest the dumping of Japanese and European products. As a result, a three year quota on these types of steel was agreed to in 1976. In 1977, with both South Korea and Brazil moving aggressively into steel markets, the Carter administration, responding to steel protectionist pressures, instituted a trigger price mechanism (TPM). The TPM established a price floor for steel products, which was based on Japanese costs (since the Japanese were considered the most efficient producers). If steel was priced below these levels, it was considered "dumped" and would not be allowed into the U.S. The net effect of this action was to raise prices of steel in the U.S. It also enabled the Japanese to capture the American import market since European production costs were higher than those of the Japanese. By 1984, the TPM mechanism had completely broken down. The Reagan Administration responded to new calls for protection of the steel industry by announcing a "national policy for the steel industry." This policy included a new VER agreement with the major producers, but also put into statue a fair import target of 17-20.2% of the U.S. steel market. This target was certainly the most restrictive public policy action undertaken in an effort to protect the U.S. steel industry. tGeneral Agreement on Tariffs and Trade.

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Industry and Union Concerns: "Unfair" Trading Practices

l

Congressional Action: Quotas, Tariffs on imports

Executive Branch Actions: 1.) "Cooling Off"; Veto 2.) Negotiate with Trading Partners

VER Agreement: 1.) 2-3 years 2.) Renewal Process

Fig. 1. Voluntary Export Restraint (VER) process.

Whether or not it actually stemmed the loss of jobs in the industry will be examined in the next section.

THE EMPIRICAL ANALYSIS This section describes the empirical analysis conducted to assess the VER's impact on employment within both the U.S. textile and steel industries. The analysis is based on a quasi-experimental design. Data

Four time series constitute the data set, as follows: 1. 2. 3. 4.

Monthly Monthly Monthly Monthly

employment within the U.S. textile industry from 1977 to 1984 [3]. production for the U.S. textile industry from 1977 to 1984 [8]. employment within the U.S. steel industry from 1980 to 1987 [3]. production for the U.S. steel industry from 1980 to 1987 [7].

Method

Intervention analysist (also known as interrupted time series analysis) was here used to analyze each time series [15]. This technique is consistent with a quasi-experimental research design [5], and non-stationary, serially correlated data [2]. It enables a researcher to assess the impact of an intervention on an operating system or social process. The intervening event is used to break the time series into pre-event and post-event segments. Here, the intervention is the VER while the t Intervention analysis has been used to assess: the impact of new traffic laws [6]; gun control legislation [10, 23]; pollution abatement legislation [1]; the use of the breathalyzer in convicting drunk drivers [20]; the impact of excise tax increases on cigarette sales [17]; and the assessment of physician practice pattern [22].

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180000 1 6 0 0 0 0 ~ 140000 120000 100000 80000 60000 40000 20000 0 :::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 77 77 77 78 78 79 79 7g 80 80 81 81 82 82 62 83 83 84 84 84 Time

Fig. 2. U.S. textiles employment(197744). social process is the level of employment and production within the U.S. textile and steel industries. All intervention models are of the type:

L = I~ + Nt, where Yt is the observed series of the phenomena under investigation, It is the intervention component, a binary indicator with the value of 0 in the pre-intervention segment and 1 in the post-intervention segment. Nt is the "noise" or error component. The time series Yt is thus composed of noise or errors and an intervention (see the Appendix for further clarification). Procedure Data analysis was executed in two stages. The initial investigation focused on the time series that enumerated employment and production in both the textile and steel industries. Those parameters representing the rate of change and the aggregate change in employment, subsequent to the VER, were estimated first. A secondary analysis examined the effect the VER had on production in the two industries. Employment and the VERs for the textile and steel industries The time series of employment for the U.S. textile industry (see Fig. 2) was identified as an Auto Regressive Integrated Moving Average (ARIMA) model (1,1,0) (1,1,0)6. Regular and seasonal differencing achieved stationarity in the series. The AR (auto regressive) parameters were estimated and statistically tested with the following results: ~b~ = -0.161 (t = 3.09) and

(])6 =

0.85 (t = 15.65).

The time series of employment for the U.S. steel industry (see Fig. 4) was also identified as an Auto Regressive Integrated Moving Average (ARIMA) model (1,1,0) (1,1,0)6 with the following results for its AR parameters: ~bl = --0.364 (t = --2.84) and ~b6= 0.91 (t = 17.23). The MA (moving average) parameter was found to be: q~j = -0.260 (t = -2.71).

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25000

20000

15000 number of articles(000s)

10000

5000

..': :7: ":': :':" -'::" :':: :'.: -';'" :-"" .'::: ;;;: ; ' " ::': :::: :::: :::: :::: " : : ::: '::" " " : """ ':': " l : ::' 77 77 77

78 78 79 79 79 80 80

81 81 82 82

82 83 83

84 84 84

Time

Fig. 3. U.S. textile production (1977-84). The dynamic model postulated for both cases was: Yt = { o B / ( 1

-- 3B)}S~ r) + N t ,

where ~ and ~o are the rate of change and the level of change parameters, respectively, Yt is the filtered series, B is the back space operator used to achieve a stationary mean and variance, and S~r) is the binary variable that introduces the intervention into the series. It assumes the values: S~r) = 0 when t < T, or S~r) = 1 when t > T, where T is the initial month of the V E R agreement. This model is consistent with the hypothesis of a gradual increase in employment subsequent to the VER. For textile employment, the following parameters were estimated: ~ = 0 . 1 6 (t = 0.43) and ~o = 13,873 (t = 0.95); while, for steel employment, we found: ~ = 0.09 (t = 0.58) and ~ = 24,675 (t = 0.74). For both the textile and steel industries, these statistics indicate that the level of 25000

20000

15000 Employment

10000

5000

0

H J I l l l . . . i , H I : n l i l =

80 80 80 81 81 82 82 82 83 83 84 84 85 85 85 86 86 87 87

Time

Fig. 4. U.S. steel employment (1980-87).

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Richard McGowan and Thomas Vaughan 70000 60000 50000

number of tons

40000 30000 20000 10000 0

~ = j i I ~ = ~ I = = = I ~ | | = I ~ = I ~ i ~ j ~ I = = = = I = = = = ~ = m = = l ~ = = = ~ t | = = j = = = ~ = ~ = = = j I = I ~ I = = = = ~ = = = = i = ~ l = ~ = I = I = = = H i = , g l , = , , , , = = | H = H H H H i I , | . , I . ° , , , . , ° m H I H I H I H I H H H I H I H I H I H I I ' l l H l l = ' | ' ' | O ' ' '

80

80

80 81

81

82 82 82 83 83

84 84

85 85

85

86 86

87

87 87

Time

Fig. 5. U.S. steel production (1980-87). employment did increase following the VER, although the increase was not significant. Moreover, the lack of significance in the rate of change of the parameters demonstrates that the level of employment will itself not be significant. An alternative hypothesis here might be that employment in the U.S. steel and textiles industries might increase in reaction to an increase in demand for but a few time periods following intervention. The dynamic model consistent with this hypothesis is: Y, = ogBS~T) + N~,

where S~r) = 0 when t < T or S~r) = 1 when t t> T, and T is again the initial month of the VER agreement. Applying this model, the following parameters were estimated for textiles employment: = 14,211 (t = 2.68), while we found co = 7964 (t = 2.76) for steel employment. These results indicate that, during the period of time immediately following the VER, there was a slight increase in employment vs a considerable drop prior to the VER agreement. A possible explanation for this outcome might be that consumers built stockpiles of foreign steel and textiles, thereby decreasing their purchase of domestic steel and textiles leading, in turn, to unemployment prior to the imposition of the VER. In the months following imposition, production of U.S. steel and textiles did increase, thus raising employment slightly. However, when consumers of steel and textiles realized that the VER would not have an affect on the availability of foreign steel and textiles, the domestic markets returned to their previous positions. Overall, the results disclose that the VER stabilized unemployment in these industries, but will likely not return those unemployed workers to their workplaces. Production and the VERs for the textile and steel industries

One possible explanation for the lack of increase in employment for the domestic textile and steel industries is that the VER gave them an opportunity to become more productive by substituting capital for labour. Under such conditions, a policy of returning workers would be, at best, only partially accomplished, depending on the extent to which capital was substituted for labor in new production processes. Evaluation of this possibility required use of the time series for production by the textile and steel industries. For the textile industry, the time series was identified as an (0,1,1) (1,1,0)12 A R I M A model (see Fig. 3). The MA parameter was estimated to be 0~ = 0.32 (t = 4.25) while the AR parameter was ~bl2= 0.573 (t = 8.65). For the steel industry, the time series was identified as an (1,1,1) (1,1,0)12 A R I M A model (see Fig. 5). The estimate for the MA parameter was 01 = 0.25 (t = 3.65) while the AR parameters were: c,bl = 0.38 (t = 2.97) and ~bl~= 0.705

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(t = 11.25). If substantial substitution of capital for labor had occurred in either industry following the VER, production would have increased gradually to a statistically significant level, but with a concomitant increase in employment. The dynamic model consistent with this hypothesis would be: Yt = {coB/(1 -- 6B)}S~ r) + N,, where all parameters are as previously defined. Using this model, the following parameters were estimated for textile employment: 6 = - 0 . 2 5 (t = 0.85) and ~o = 4967 (t = 1.21). Corresponding values for steel employment were as follows: 6 = - 0 . 5 6 , (t = 0.79) and ~o = 8675 (t = 0.84). These results suggest that there was an increase in production but that it was not statistically significant. Moreover, the rate of change parameter was negative, indicating that, over time, production actually fell, although it was not a statistically significant decrease. Consequently, the absence of an increase in employment in these two industries, following the VER agreements, apparently cannot be attributed to increases in productivity in either the textile or steel industries. Alternative to this hypothesis might be that domestic production of steel and textiles would increase in reaction to short-term increases following the intervention. The dynamic model consistent with this hypothesis is again:

Yt = ogBS~r~ + N,. Textiles production for this case yielded: e~ = 5127 (t = 3.21), while, for steel production, the following parameters were generated: ~o = 7964 (t = 2.76). These results suggest that, in reaction to the VER, there was an increase in production for a very short period of time. As we saw with the employment data, perhaps consumers built up stockpiles of foreign steel and textiles, thereby decreasing their domestic purchases. In the months after the imposition, domestic production did increase, but only enough for these markets to return to their previous states. In summary, our empirical results establish that VERs, although celebrated as shrewd U.S. trade policy, have apparently been more symbolic than substantive. In both the textile and steel industries, VERs increased neither employment nor production. Yet, in the latest round of G A T T talks, VER agreements continue to be made [4]. The following section will attempt to explain why VERs remain popular with both public policy makers as well as businesspersons in affected industries. S T A K E H O L D E R ANALYSIS Although VERs failed to restore employment in the two industries studied here, these agreements still enjoy acceptance to the extent that both have been extended twice. In an attempt to reconcile the actual outcome of VERs with their persistent image of success, Freeman's technique of stakeholder analysis is employed. In doing so, stakeholders for each of the industries were divided into opposing and advocating groups. See Figs 6 and 7 for a "mapping" of these groups.

Stakeholder analysis of the textile industry Opposing groups. The Retail Trade Action Coalition (RITAC) is certainly the most powerful and vocal group in leading the opposition to any sort of restrictions on textile imports. RITAC's argument revolves around the inflationary impact that protectionist measures can have on the price of clothing for the American consumer. Obviously, RITAC would prefer a VER rather than an outright quota on textile imports since it permits retailers to import textiles from the cheapest sources. While the exporting countries have much less of a voice in influencing U.S. trade policy, there are some elements of the VER that should be emphasized. First, textile exporters to the U.S. are generally developing countries who are using textiles as a base for industrial development. Second, the number of such countries has been increasing and their nature changing. This has required U.S. authorities to continuously negotiate VERs with these new producers, making the enforcement of VERs for textiles quite involved. Finally, since a VER is a "voluntary" action, it allows these

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governments to preserve national pride in that they have been active partners in determining details of the agreements, such as the nature and levels of restrictions. For the Executive branch of government, the VER is an almost ideal instrument for dealing with textile controversies. Although the VER has not provided a permanent solution to industry issues, it is symbolic enough to show that government is being responsive to the industry. At the same time, it allows the Executive branch to proclaim its belief in free-trade, which is a popular national ideology. In general, the President plays the role of mollifying Congress while trying to assure trading partners (especially, friendly developing countries) that U.S. markets will remain open to them. Advocating groups. Besieged by foreign competition, the U.S. textile industry has sought protection from Ibreign competition. In this regard, the VER can prevent further erosion of market share, at least for some textile products. Perhaps, a brief respite from competition would offer U.S. textile manufacturers time to "retool", and thus become more competitive. However, the ARIMA analysis of production figures presented earlier suggest that this is not likely to happen. For the textile unions, the preferred solution would be an outright quota to limit the market share of foreign firms. However, as long as Congress cannot override the Executive branch's objection to outright quotas, a VER will suggest to members that the union is working to preserve their jobs. Tip O'Neill's observation that "all politics is local" appears valid in the case of VERs for the textile industry. The role of local and state governments has become significant in relation to trade issues through laws that permit only the purchase of American made clothing for state employee uniforms, etc. This type of activity has caused tension between local and federal officials where the latter claim this protectionism violates GATT agreements. On the other hand, it places additional pressure on foreign textile producers to agree a VER arrangement [14].

Stakeholder analysis of the steel industry Opposing groups. Much of what was stated about opposing stakeholder groups of the textile industry can be repeated for the steel industry. There are, however, a few significant differences.

Opposing Groups

Public Policy Measures: Restrictions on Textile Imports

Advocating Groups

Fig. 6. A stakeholdermap of the 1993 U.S. textile industry.

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Opposing Groups

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Public Policy Measures: Restrictions on Steel Imports

Advocating Groups

Fig. 7. A stakeholder map of the 1993 U.S. steel industry.

The most obvious involves the type of countries exporting steel to the U.S. Rather than developing, these are countries with advanced economies searching for markets to " d u m p " excess steel production. Since these countries generally compete with the U.S. in a variety of other industries, they become easier targets for protectionism. They are also eager to enter VER agreements in order to avoid outright quotas. It is important to note here that consumers of steel have an increasing array of products available to them such as plastics and metal substitutes. As a result, large users of steel, such as auto manufacturers and builders, may protest a VER agreement, but not quite as vigorously as they would have in the past. Advocating groups. The primary difference between the advocating groups of the textile and steel industries is the role of state and local government in protecting the latter. For example, both California and New Jersey, hardly steel producing states, both require that all state construction use U.S.-produced steel, while all state automobiles be made from U.S. steel. These policies are in no way isolated. Thus, while steel producing states such as Pennsylvania and Ohio have passed laws to protect "local" industry, "buying American" has become a requirement for many state governments. DISCUSSION Can this view of the past be helpful in predicting the future of these two industries' protectionist activity? One issue might be the attitude of the Clinton administration towards protecting ailing industries. Even after 3 yr in office, it is far from clear what trade policy the administration will pursue [18]. We have seen here that the Executive branch's traditional stance regarding trade is one of compromiser. At issue is the value of being seen as a defender of free trade, or as a protector of the American worker. The current VER agreement covering steel ended in 1992. Since no new

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agreement has been reached, one of the Clinton Commerce Department's first acts was to issue $2.6 billion in import duties on steel from 19 countries [11]. These countries include all members of the European Community (EC) as well as Japan, Canada, Korea and Brazil. Hence, the VER agreement for steel products appears to have broken down, at least temporarily, while domestic steel, along with its allies, have won a significant political victory. As for the textile industry, can it expect treatment similar to that realized by the steel industry? Based on our analysis, this appears unlikely. In this regard, the primary importers of textiles are developing countries with less competitive economies. Further to this, the Congressional delegation representing the textile interest is presently not as geographically cohesive as that representing steel. However, the Clinton administration may look upon requests from Southern textile makers in a more favorable light than previous administrations. A major conclusion of this analysis is that the application of classical economic theory in the development of public policy may be insufficient, if used in isolation. The various VER agreements are considered successful, not because they provide additional employment for either the textile or steel industries, but because they "satisficed" industry stakeholders. The VER exemplifies what is, according to Edelman, a condensation symbol [12]. It condenses into one political event a sign of reassurance as well as a promise of a return to greatness for these industries. This implies that it is more the needs, the hope and the anxieties of people rather than intellect, that actually decipher a political act in a time of hardship.

REFERENCES 1. D. Aaronson, C. T. Dienes and M. C. Mushenko. Changing the public drunkeness laws: the impact of decriminalization. Law Soc. Rev. 12, 405-436 (1978). 2. G. E. P. Box and G. C. Tiao. Intervention analysis with applications to economic and environmental problems. J. Amer. Statist. Assoc. 70, 70-79 (1975). 3. Bureau of Labor Statistics. Employment and Earning Reports, Monthly Reports of U.S. Industries compiled by Department of Labor, U.S. Government Printing Office Washington, DC (1977-87). 4. Business Week, The New Round of GATT Talks. 12/20/93, p.56. 5. D. T. Campbell and J. C. Stanley. Experimental and Quasi-Experimental Design for Research. Rand McNally & Co., Chicago (1963). 6. J. T. Campbell and H. L. Ross. The Connecticut crackdown on speeding time series data in quasi-experimental analysis. Law Soc. Rev. 3, 35-53 (1965). 7. Department of Commerce. The U.S. Steel Industry, Monthly Reports complied by the Commerce Department, U.S. Government Printing Office Washington, DC (1980-87). 8. Department of Commerce. The U.S. Textile Industry, Monthly Reports complied by the Commerce Department, U.S. Government Printing Office Washington, DC (1977-84). 9. I. M. Destler. American Trade Politics. Institute for International Economics and the Twentieth Century Fund, New York (1992). 10. S. J. Deutsch and F. B. Alt. The effect of Massachusetts' Gun Control Law on gun related crimes in the City of Boston. Eval. Q. 1, 543-568 (1977). 11. The Economist. Steel trade. 30 Jan 65 (1993). 12. M. Edelman. The Symbolic Uses of Politics. University of Illinois Press, Urbana, IL (1970). 13. R. E. Freeman. Strategic Management: A Stakeholder Approach. Pitman Marshfield, MA (1984). 14. J. M. Kline. State Government Influence in U.S. International Economic Policy. D.C. Heath, Lexington, MA (1983). 15. R. McCleary and R. A. Hay. Applied Time Series for the Social Sciences. Sage Publications, Beverly Hills, CA (1980). 16. R. McGowan and T. Vaughan. Deciphering the Japanese automobile import quota. Policy Studies Jl 16, 413-425 (1988). 17. R. McGowan. Public policy measures and cigarettes sales: an ARIMA intervention analysis. Res. Corporate Soc. Perform. Policy l l , 151-179 (1989). 18. New York Times. Clinton trade policy: so far little is new 2 Feb, DI (1994). 19. G. L. Stockhausen. Threats of Quotas in International Trade. Greenwood Press, New York (1988). 20. H. L. Ross, D. T. Campbell and G. V. Glass. Determining the effects of a legal reform: the British breathalyzer crackdown of 1967. Am J. PubL Hlth 71, 370~375 (1981). 21. G. C. Tiao, G. E. P. Box and W. J. Hamming. Analysis of Los Angeles photochemical smog data: a statistical overview. J. Air Pollut. Control Ass. 25, 260-268 (1975). 22. T. Vaughan and D. Szeto. The diffusion of medical practice patterns in a community hospital. Socio-Econ. Plann. Sci. 22, 51-55 (1988). 23. F. E. Zimring. Firearms and federal law: The Gun Control Act of 1968. J. Lgl. Stud. 4, 133-198 (1975).

APPENDIX Intervention analysis requires the identification of an Auto Regressive Integrated Moving Average (ARIMA) model that replicates each time series analyzed. In ARIMA notation, a model

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is specified with two shorthand descriptors, (p,d,q) and (P,D,Q). The first element (p) represents the auto regressive term; the second element (d) is the degree of differencing required to achieve stationarity; and the third term (q) is the extent of the moving average associated with random shocks. The second notational array (P,D,Q) designates analogous terms, except these are associated with seasonality. The ARIMA model is tested against observed series until a statistically adequate model is identified. Adequacy of the model is confirmed after an examination of the autocorrelation and partial autocorrelation functions of the series, and when a statistical analysis of the residuals indicates that they constitute a time series of white noise [21]. When an appropriate ARIMA model is specified, it is used to filter that series. At this point, a dynamic model, consistent with the postulated intervention effect is formulated. This dynamic model corresponds to the hypothesis, as its formulation specifies the configured change in the level of white noise produced by the intervention. Once formulated, the dynamic model is fitted to the residual series, its parameters are estimated, and each is evaluated using the technique suggested by Box and Tiao [2].