Errors-in-Variables Bounds in a Tobit Model of Endogenous Protection.

• Author: Gawande, Kishore

Kishore Gawande [*]

Alok K. Bohara [+]

The errors-in-variables (EIV) problem is pervasive in econometrics but has not received the attention it deserves, perhaps because it is difficult to resolve. The first objective of this paper is to demonstrate the effectiveness of recently developed methods to deal with the EIV problem in models with censoring. The second objective of this paper is to empirically examine, in light of the EIV problem, theories of endogenous protection that have become important in trade theory in their ability to explain why nations do not follow the traditional economic maxim of free trade. These theories emphasizing political-economic factors have gained momentum based on a set of empirical studies that have sought to prove their validity. Whether inferences about the theories of endogenous protection are gravely affected by errors in variables is examined using data on U.S. nontariff barriers with respect to nine developed countries. The theoretical developments in Kiepper (1988) and Klepper and Learner (1984) are combined with a result from Levine (1986), which usefully extends the use of EIV diagnostics to a model with censoring.

1. Introduction

   The predominantly nonexperimental nature of economic data compels the use of proxies, imperfectly measured variables, and dirty data. This paper is motivated by the cogent arguments in favor of sensitivity analyses made by Leamer (1983, 1985). In this paper the recent theoretical advances in the errors-in-variables (EIV) literature by Klepper and Leamer (1984) and Klepper (1988), which have focused on the linear regression model, are applied to a Tobit model via a result in Levine (1986).

   The empirical literature on endogenous protection provides a rich context within which to study the sensitivity of inferences to the EIV problem. Studies of endogenous protection based on the seminal empirical work of Pincus (1975), Caves (1976), Ray (1981), and Baldwin (1985), and among others, have significantly influenced traditional thinking in the area of trade. It is a prime example of empirical work that has led theoretical development and continues to influence it. But inferences from econometric studies of endogenous protection are suspected to be fragile because there is widespread use of proxies and variables that are poorly measured. The EIV problem is not specific to just the variables measured with error. The extensive use of mismeasured variables and proxies may lead to spurious estimates on even well-measured variables.

   This paper seeks to make two contributions. First, using cross-country and cross-industry data on nontariff barriers, the sensitivity of inferences about the validity of theories of endogenous protection to classical errors in variables is investigated. Second, the applicability of the EIV methodology to limited-dependent variable models is demonstrated. The paper proceeds as follows. In section 2, the choice of regressors is motivated, an endogenous protection equation is estimated, and inferences are made under the presumption that there are no errors in variables. In section 3, the EIV methodology and its extension to the Tobit model is described. In section 4, two kinds of EIV analyses are performed, one that leads to bounds on estimated coefficients and another that exposes those inferences that are fragile on account of errors in variables. Section 5 concludes.

2. Inferences About Endogenous Protection Theories

   Empirical Specification

   Trade protection in the United States has been modeled in the empirical literature as including four components: (i) a self-interested political component that is a response to protectionist pressures, which is substantially influenced by the lobbying efforts of private agents, (ii) an altruistic political component influenced by welfare-oriented motives of the government, (iii) a retaliatory component that serves as a strategic deterrent against undesirable protectionist policies of its partners, and (iv) a component motivated by comparative advantage. Their empirical relevance has been demonstrated by Caves (1976), among others, using tariff data from the Kennedy round, by Ray (1981) and Baldwin (1985) using tariff data during the Tokyo round of cuts, and by Trefler (1993) using aggregate U.S. NTB (non-tariff barrier) data from 1983.

   A feature of this study is the use of bilateral cross-industry NTB data between the United States and nine developed partner countries. NTBs include all trade barriers other than ad valorem tariffs. Prominent examples of NTBs are antidumping duties to thwart dumping below fair price, countervailing duties to counter partner's export subsidies, quotas whose licences may be distributed to domestic agents, and voluntary export restraints where the partner country voluntarily restricts its exports. Leamer (1990) provides an exhaustive taxonomy of nearly 50 NTBs. After the Tokyo round tariff cuts, the new protectionism in developed countries took the form of NTBs. In the United States, their use sharply escalated after 1979 and continued to rise through the 1980s. Data from 1983 are used in this study and capture a period in which the use of NTBs was widespread.

   NTBs are measured in this study as coverage ratios; that is, the fraction of imports covered by some NTB or other. Following Baldwin's framework, the specification employed in the econometric analysis is

   [N.sub.ij] = [X1.sub.ij][[alpha].sub.1] + [X2.sub.ij][[alpha].sub.2] + [X3.sub.ij][[alpha].sub.3] + [[[beta]N.sup.*].sub.ij] + [[D.sup.*].sub.j][[gamma].sub.j] + [[varepsilon].sub.ij],

   [[varepsilon].sub.ij] [sim] N(0, [[sigma].sup.2]), i = 1, [ldots], 435, j = 1,[ldots], 9. (1)

   United States NTBs on good i against country j, [N.sub.ij], are determined by a self-interested political component, whose variables are represented by the vector [X1.sub.ij], an altruistic political component represented by [X2.sub.ij] the theory of comparative costs represented by [X3.sub.ij], and an offensive component, [[[beta]N.sup.*].sub.ij], designed to thwart foreign NTBs. Country-effect dummy variables are included in [[D.sup.*].sub.j]. The parameters [[alpha].sub.1], [[alpha].sub.2], [[alpha].sub.3], and [beta] are assumed stable across industries and countries, and Equation 1 is estimated by pooling industry and country data. Here, cross-industry data at the four-digit SIC level of disaggregation are pooled across nine countries: Belgium, Finland, France, Germany, Italy, Japan, the Netherlands, Norway, and the United Kingdom. The errors [[varepsilon].sub.ij] are assumed to be homoskedastic across countries and goods.

   The choice of regressors in Equation 1 is influenced by Baldwin's study but also includes newly constructed variables, and an additional model, namely, the strategically retaliatory model. Table 1 shows the association of regressors with the underlying theory and the expected sign on each coefficient. The Appendix details the construction of the variables.

   (i) Strategic retaliation: The aim of using retaliatory NTBs, as opposed to employing them for purely protectionist purposes, is to deter undesirable foreign trade policy at minimum domestic cost. In a game-theoretic political economy model based on fairly real-world assumptions, Baldwin (1990) shows the existence of optimal nonnegative retaliatory trade barriers. His argument is motivated by the ability of retaliatory measures to discourage special-interest pressures in the foreign country that led to the formation of the foreign trade barrier in the first place. Grossman and Helpman (1995) describe a model with a noncooperative trade-war equilibrium and a bargaining equilibrium resulting from trade talks. In Baron's (1997) case study of the Kodak-Fujifilm trade war, the use of normarket strategies such as applying pressure on the government to impose sanctions is highlighted using a bargaining model. Although these theories about retaliation and bargaining are more properly tested using relative levels of protection in the two countries, the use of foreign NTBs as a regressor can be used to infer whether the United States retaliates against high NTBs abroad (positive sign on [[N.sup.*].sub.ij]) or whether high NTBs abroad are an indication of greater bargaining strength in the partner country (negative sign on [[N.sup.*].sub.ij]).

   (ii) Special-interest or pressure group model: The special-interest group model associated with Olson (1965) and Pincus (1975), and subsequently formalized by Brock and Magee (1978) and Findlay and Wellisz (1982), suggests measures of special-interest pressure. The concentration ratio (CONC4) and measures of scale economies (SCALE) have traditionally been used as proxies for special-interest pressures because the stakes from protection are highest in industries with a high degree of concentration or scale economies. In addition to these proxies, a more direct measure of pressure--corporate PAC (Political Action Committee) campaign contributions scaled by industry value added (PACCVA83)--is employed and presumed to be positively related to the level of protection. More recently, protection has been modeled by Grossman and Helpman (1994) as the outcome of a menu auction, in which industry lobbies each bid on a menu of trade tax vectors. The government then sets a specific trade tax vector and collects from eac h lobby its bid on that specific vector. In their model, which abstracts from market structure issues, the prediction is that the inverse import penetration ratio (CONS/[M.sub.ij]) should be positively related to protection. [1]

   (iii) Adding machine model: The adding machine model due to Caves (1976) focuses on the voting strength of the industry and suggests that number of employees (NE82) and degree of unionization (UNION) in that industry and the industry's labor intensity (LABINT82) are all positively related to the level of NTBs. The number of states in which production is located (REPRST) is another...