I. INTRODUCTION

One of the most notable economic events since World War II is the proliferation of preferential trade agreements (PTAs), including free trade agreements (FTAs) and customs unions (CUs). The study of such agreements has followed fundamentally two paths, one normative and one positive. The normative path is whether or not PTAs are welfare-improving (see Bagwell and Staiger 1997, 2005; Bond, Riezman, and Syropoulos 2004). A full survey of this literature is beyond the scope of this paper, but see Baldwin (2007) for an excellent survey.

The second path, which is "positive," examines what factors explain and predict which pairs of countries have PTAs. Building on the work of Krugman (1991a, 1991b) and Frankel (1997), Baier and Bergstrand (2004), or BB, introduced asymmetric absolute and relative factor endowments into a Krugman-type increasing-returns/monopolistic-competition model to show theoretically that the net utility gains from a bilateral PTA depend on two countries' economic sizes and their economic similarity, bilateral distance, and relative factor endowments. Using a single cross-section for 1996, BB employed a probit analysis to show that these economic factors that tend to improve on net a country-pair's utility from a PTA also tend to increase the pair's probability of having a PTA. Egger and Larch (2008), Chen and Joshi (2010), and Baldwin and Jaimovich (2012) confirmed BB's findings and showed that additional variables--such as preexisting PTAs--also tend to increase the likelihood of a pair of countries having an agreement. (1)

Despite the proliferation of PTAs over the past 60 years, there is still considerable scope for further formations or enlargements of PTAs. Governments' policy makers have long been looking for a "road map" to guide them toward selection of PTA partners for enlarging existing arrangements or forming new ones; limited resources and political obstacles have inevitably constrained governments to sequencing such formations and enlargements rather than pursuing them simultaneously. Ideally, such a road map should be consistent with improving the net economic welfare of members. This study attempts to explain and predict (in-sample) the actual timing of formations and enlargements of all PTAs among 10,518 pairings of 146 countries for 57 years from 1950 through 2006 based upon a parsimonious structure inspired by a simple economic model. Moreover, to gauge the potential usefulness of this exercise for future formations and enlargements, we also show how our approach predicts PTA events well out-of-sample, based primarily on economic considerations. The results suggest that most PTA formations and enlargements are influenced by factors that tend to increase pairs' economic welfare.

In econometrics, the analysis of the time elapsed until a certain event occurs is referred to as duration analysis. Duration analysis has its origin in survival analysis, which refers to the survival time of a subject in a particular state. In our context, this refers to the survival of a country-pair in the state of "No-PTA." Central to such analyses is the hazard rate, which in our context emphasizes the conditional probability of a country-pair leaving the state of No-PTA conditional upon having been in this state for a particular duration. The latter emphasizes the inherently dynamic nature of duration analysis, cf., Abbring and van den Berg (2002), de Ree and Nillesen (2009), and Wooldridge (2010). So, the key difference of this paper from the existing literature is predicting the specific year of a PTA formation/enlargement event (or a window of years leading up to the event), in-sample and out-of-sample, using a parsimonious econometric model motivated by economic and political variables. (2)

In this paper, we first address how one might interpret the decision of a pair of countries to form/enlarge a PTA in some year conditional upon not having had a PTA until that year. This discussion informs us about the determinants of the "hazard rate" (without economic covariates), which is the probability of a country-pair leaving the No-PTA state in a year conditional upon having been without a PTA up until that year. Classic distributions determining hazard rates include the Weibull and log-logistic distributions, which yield that such hazard rates are functions of time trends. However, a simple time trend in the absence of economic covariates can explain only 11 % of the variation in the PTA events. Second, most economic duration analyses are concerned with the influence of time-invariant or time-varying economic covariates that "shift" the hazard rate in any year. Drawing upon the recent literature on economic determinants of PTAs noted above, we motivate the inclusion of several economic and political covariates that likely influence the probability of two countries forming/enlarging a PTA in any particular year, conditional upon not having a PTA until that year. These covariates include three measures of geography, four measures of economic size and relative factor endowments, four measures of the influences of other PTAs, and six political variables. These covariates have an explanatory power of up to 44% when measured by the pseudo-[R.sup.2] (up to 49% including fixed effects). They predict (in-sample) up to 57% of the 1,560 bilateral PTA events in the period 1950-2006 among the 10,518 pairings of 146 countries within a 10-year window leading up to the date of entry (up to 72% when including fixed effects). The same models predict up to 26% (39% with country-pair fixed effects) of the PTA events in the very year they occurred. (3)

Third, our model also performs well out-of-sample. Taking only the periods up through 2000 for the estimation, the model predicts up to 66% of the 284 PTAs concluded from 2001 through 2006 in the year the PTAs were concluded, and up to 82% in a 5-year window up until the actual formation of the PTAs. The out-of-sample predictions are worse when only the years up through 1989 were used for estimation and the out-of-sample period was quite long (1990-2006), but then the regressions are informed by only 523 PTA events that happened prior to 1990. We close the study with an evaluation of the influence of multilateralism on PTA timing and of the successfulness of the model for predicting in particular the Canada-United States Free Trade Agreement (CUSFTA), the North American Free Trade Agreement (NAFTA), the formation of the original European Economic Community (EEC) and subsequent enlargements, and the model's most likely PTA events in the post-sample period of 2007-2013.

The remainder of the paper is organized as follows. Section II motivates the use of an econometric duration model to analyze the timing of PTA (formation/enlargement) "events." Section III motivates the time-invariant and time-varying economic, political, and historical determinants of the hazard rate. Section IV describes the data. Section V provides the empirical results. Section VI provides the predictive analysis. Section VII concludes.

II. MOTIVATION FOR A DURATION ANALYSIS OF TIME-TO-PTA

A. Analyzing PTA Status versus Timing of PTAs

Figure 1 illustrates the years in which PTA events occurred, summarizing the (cumulative) number of bilateral trade agreement "membership events" for all years from 1950 through 2006 in which some new "membership" occurred (either a new agreement or an enlargement), according to information mainly provided by the World Trade Organization (WTO). (4) The WTO categorization (labeled there regional trade agreements, or RTAs) includes two-way preferential agreements, FTAs in goods, FTAs in services, and CUs. (5) We focus on memberships at the country-pair level and avoid redundant observations by counting events such as the membership of France and (West) Germany in the original EEC as a single new membership "event" (instead of two events) and the enlargement of the original EEC to include the United Kingdom as five new membership events instead of ten events. (6) Accordingly, the events should not be interpreted as just new PTAs that have been formed, since we also count as new memberships ones that are brought about through enlargements of existing PTAs. In this study, we do not separate our empirical sample into "new PTAs" versus "enlarged PTAs." We also show in Figure 1 the subset of PTA events that include only FTAs and CUs.

The figure suggests that there have been years with strong and weak membership activity over time. The number of all PTA membership "events" concluded since 1950 rose to 1,560 until the end of 2006, that is, 14.83% of the 10,518 country-pairs and 0.34% of the 463,289 total observations in the panel, recalling that a time-series for a country-pair ends in 2006 if no PTA is formed or in the year a PTA enters into force (see footnote 3). From these data, we can create a variable representing the "Time-to-PTA event," as done in duration analysis. Our focus will then be to find the economic, political, and historical determinants that explain the "Time-to-PTA event," meaning the timing of the formation of a new agreement or an enlargement of an existing PTA agreement. (7)

Our goal in this paper is to predict the duration (in years) before a country-pair entered a PTA (through formation or enlargement) using a duration model with a parsimonious set of time-invariant and time-varying variables. This contrasts with the goal of BB, Magee (2003), Egger and Larch (2008, henceforth EL), Chen and Joshi (2010), and Baldwin and Jaimovich (2012) who focused on explaining which country-pairs had a PTA in a given year. The econometric framework employed there was the qualitative choice model of McFadden (1975, 1976). In BB, the probability of a PTA was linked heuristically to an underlying latent variable, denoted [DELTA][U.sub.ij] here. In that study's context, [DELTA][U.sub.ij] represented the difference in utility levels from an action (formation of a PTA), where

(1) [DELTA][U.sub.ij] = [x.sub.ij][beta] + [e.sub.ij],

and [x.sub.ij] denoted a vector of explanatory variables (economic characteristics) of country-pair ij including a constant, [beta] was a vector of parameters, and error term [e.sub.ij] was assumed to be independent of [x.sub.ij] and to have a standard normal distribution. In the context of BB's model, [DELTA][U.sub.ij] = min([DELTA][U.sub.i], [DELTA][U.sub.j]), where [DELTA][U.sub.i] ([DELTA][U.sub.j]) denoted the change in utility for the representative consumer in i (j); both countries' representative consumers needed to benefit from a PTA for their governments to form one. (8) The latent variable [DELTA][U.sub.ij] was assumed to generate the binary indicator variable of PTA membership, [PTA.sub.ij], which was unity if two countries had a PTA and zero otherwise. The response probability for a PTA, P, was then:

(2) P ([PTA.sub.ij] = 1) = P ([DELTA][U.sub.ij] > 0) = G ([x.sub.ij][beta]),

where G(*) was the standard normal cumulative distribution function, which ensured that P([PTA.sub.ij] = 1) was between 0 and 1. This literature has assumed that P([PTA.sub.ij] = 1) > 0.5 "indicated" [DELTA][U.sub.ij] > 0 and P([PTA.sub.ij] = 1) [less than or equal to] 0.5 indicated [DELTA][U.sub.ij] [less than or equal to] 0.

Rather than focusing on the static explanation of PTAs in a cross-section of data in a given year, this paper aims at examining the determinants of the timing of PTA events using duration analysis. Duration models fall within the class of limited dependent variable models in general and censored regression models in particular (cf., Wooldridge 2010). Duration analysis has been used increasingly in the economics literature since 1980. The most common application is in labor economics evaluating empirically the determinants of the length of a spell of unemployment of an individual, cf., Heckman and Singer (1984) and Kiefer (1988). There is only a small number of studies which have applied this framework in international trade. (9)

For the research question of this paper, two issues have to be addressed. First, we have to rationalize an empirical model of timing of PTAs in the absence of time-invariant and time-varying economic covariates. Second, we have to allude to how the hazard rate interacts with fundamental economic variables that are known to shift a country-pair's probability of forming an agreement at any point in time. We address these issues separately below. (10)

B. Economic Motivation for a Discrete-Time Duration Model

In this section, we discuss a simple economic motivation for a discrete-time duration model for analyzing time-to-PTA events. Suppose that, at the country-pair ij level in any year t, each of two governments choose between two states, entering a bilateral PTA or not. The decision of interest is the duration of years [T.sub.ij] after which governments i and j will adopt a bilateral PTA. Data on elapsed time since some fixed year until the inception of a PTA are only available by year. Hence, we cannot portray time-to-PTA events by a continuous process econometrically, but need to resort to a discrete-time representation.

In the No-PTA state and year t, assume the governments of i and j receive utility [U.sub.ij'] (t) associated with bilateral trade flows. These governments may receive the possibility in any year t to form a PTA. From that, they would realize cum-PTA utility (associated with cum-PTA trade flows) drawn from a continuous distribution with density f([U.sub.ij](t)) at a constant rate g in every year t. The probability of realizing the benefits [U.sub.ij](t) from concluding a PTA (and the associated trade flows) after T years is gT. Suppose that the possibility to conclude PTAs is drawn independently of f([U.sub.ij](t)), and governments know the density function f(*) but not the utility [U.sub.ij](t) from a given PTA. Moreover, suppose for simplicity that reservation utility [U.sub.ij'](t) from staying outside of a PTA is independent of the change in trade flows induced by the conclusion of the PTA, while the change in utility through PTA formation is a function of the change in trade flows but not of the functional form f(*). Upon receiving the possibility to conclude a PTA at random intervals, governments then decide about when to form a PTA. The decision about when to enter a PTA will depend on the comparison of the expected gains from PTA membership as captured by [U.sub.ij](t) with the reservation gains captured by [U.sub.ij'](t). Accordingly, the probability that a PTA is acceptable can be written as:

(3) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

Country-pair ij's transition rate from No-PTA to PTA in year 1 is reflected in the product of the constant rate at which PTAs become possible in any year (g) and the probability that they are acceptable in year t, [P.sub.ij](t). This transition rate is the probability of leaving the No-PTA state in t given that governments i and j did not conclude a PTA until then, and it may be referred to as the hazard rate for the distribution of duration until PTA formation:

(4) [[lambda].sub.ij](t) = P([T.sub.ij] = t | [T.sub.ij] [greater than or equal to] t) = g [P.sub.ij](t),

where [T.sub.ij] is the survival time out of PTA status of country-pair ij.

There are several possible distributions for modeling the hazard rate, [[lambda].sub.ij](t). For a discrete-time multivariate model as the one proposed here, the complementary log-log distribution is a common choice (see Jenkins 1995, 2005). In comparison to other distributions, this specification has the advantage of allowing for time-varying covariates--an essential element of our study discussed in the next section. Figure 1 suggests that, apart from the covariates in vector [x.sub.ijt], we may want to allow for a general time trend in a specification of time-to-PTA events. The latter can be easily done with the complementary log-log distribution when specifying [[lambda].sub.ij](t) as:

(5) [[lambda].sub.ij](t) = 1 - exp [-exp ([x.sub.ijt][beta] + [[gamma].sub.t])],

where [x.sub.ijt][beta] = [[beta].sub.0] + [[beta].sub.1] [x.sub.1,ijt] + [[beta].sub.2][x.sub.2,ijt] + ... + [[beta].sub.K][x.sub.K,ijt] and [[gamma].sub.t] captures the general time trend.

We model the general time trend as [[gamma].sub.t] = r ln(t), which implies that the shape of the hazard monotonically increases if r > 0, decreases if r < 0, or is constant if r = 0 (see Jenkins 2005). If concluding PTAs becomes generally easier as time marches on, we would expect r > 0.

Figure 2 illustrates the relationship between the hazard rate and time t with a complementary log-log distribution function. The slope of the hazard rate depends on the coefficient of the general time trend r as well as the explanatory variables. Consistent with estimates reported later on for the data underlying this study, we assume that r = 0.61 in Figure 2. (11) If other explanatory variables do not matter and the hazard rate [[lambda].sub.ij](t) of leaving the initial No-PTA state increases with larger t, we obtain a functional relationship as shown by the continuous concave locus labeled "Time trend only" in Figure 2 with [[lambda].sub.ij](t) = 1 - exp[-exp(0.61 ln(t))]. One may think of many factors underlying a rising hazard rate with time per se. For instance, falling tariffs due to multilateral trade liberalization under the General Agreement on Tariffs and Trade (GATT) or WTO may have had an influence; in fact, we examine this later empirically in Section VI. Alternatively, generally declining political costs of political and economic cooperation after World War II could be mentioned here.

Beyond a trend (and multilateralism's possible effect), the timing of PTAs is likely influenced by economic, historical, and political factors. Clearly, variables that have been found to increase the probability of concluding a PTA in previous research will lead to a reduction of the time-to-PTA events with processes as specified in Equations (3) and (5). The reason is that everything that influences the net utility gain of country-pair ij from participating in a PTA in any year t will also raise the hazard rate [[lambda].sub.ij](t). Hence, obvious candidate variables in [x.sub.ijt] to predict (in- and out-of-sample) a substantive share of the 1,560 PTA events underlying Figure 1 are the determinants of PTA memberships in a cross-section of data in BB. For instance, having a common land border (a time-invariant variable) or two countries being jointly economically larger (a time-variant variable) are strong partial predictors of PTA membership in a cross-section. Either of these factors raises the probability that a PTA is acceptable, [P.sub.ij](t), ceteris paribus. Hence, either of these factors should raise the hazard rate [[lambda].sub.ij](t). However, time-invariant and time-variant elements in [x.sub.ijt] affect the hazard rate in functionally different ways. This is illustrated by the two broken loci in Figure 2. For the locus labeled "Including positive time-invariant regressor," we added 0.52 to the time trend so that [[lambda].sub.ij](t)= 1 -exp[-exp(0.52 + 0.61 ln(t))]. (12) For the locus labeled "Including positive timevariant regressor," we added 0.10[[epsilon].sub.ijt] to the time trend, where [[epsilon].sub.ijt] is drawn randomly from a normal distribution with mean and standard deviation of one. Then, [[lambda].sub.ij](t) = 1 - exp [-exp(0.13[[epsilon].sub.ijt] + 0.61 ln(t))]. (13) As can be seen from Figure 2, there is a tendency for both time-invariant and time-variant shifters of [P.sub.ij](t) to raise the hazard rate. However, time-variant shifters of [P.sub.ij](t) render the hazard rate a potentially non-monotonic function of time, which is not the case for time-invariant shifters.

III. FACTORS SHIFTING THE PROBABILITIES OF PTAs

A. Economic Factors

The purpose of this section is to identify economic variables that potentially "shift" the hazard rate, [[lambda].sub.ij](t), in any year t, thus increasing or decreasing the likelihood that a PTA occurs sooner. (14) In the spirit of the extant literature, we consider determinants of the probability of PTAs suggested in recent studies by BB, EL, and Baldwin and Jaimovich (2012), as such variables are expected to alter in any period t the latent variable [U.sub.ij](t) defined earlier. (15)

Notice that the time-to-PTA-event structure addressed in the previous section makes both the theoretical and the empirical approach in this paper fundamentally different from the ones in BB, EL, Chen and Joshi (2010), and Baldwin and Jaimovich (2012). These papers provided only a static motivation for PTA formation. Hence, conditional on observable (economic and/or political) time-specific and time-invariant determinants, PTA membership was explained in the cross-section pertaining to a specific time period. However, duration, time-to-event, or survival models as the one outlined in the previous section are inherently dynamic, since the selection into PTA membership changes conditional on the time elapsed (see Wooldridge 2010, chapter 22, Section IV.B for a discussion of the dynamic nature of duration models). However, the present approach shares with the earlier work that there are time-specific fundamental (economic, political and/or historical) drivers of PTA formation that are at play and inform the otherwise dynamic process.

Figure 3 illustrates the interplay between dynamic model aspects and shifters of the probability of becoming a PTA member. It takes the information associated with Figure 1 and combines the Time-to-PTA event data with three particular economic characteristics associated with the members of PTAs relative to those of nonmembers. One economic characteristic is the "proximity" of PTA members relative to nonmembers. We measure this using the average distance between the economic centers of members of PTAs relative to the average distance between economic centers of nonmembers. A second economic characteristic is the average economic size of PTA members relative to that of nonmembers; economic size is measured using countries' gross domestic products (GDPs). The third economic characteristic is the average difference between country-pairs' GDPs for PTA members relative to that of nonmembers.

Figure 3 illustrates several profoundly systematic relationships between distance, economic size, economic similarity, and the timing of PTA events. (16) The bottom line indicates two phenomena. The earliest PTA events (1958-1961) were between members whose average distance between members relative to nonmembers was the smallest. As time passed, the average distance between members relative to nonmembers rose systematically. This line suggests that PTAs formed or enlarged sooner among closer countries. The middle line indicates two phenomena related to economic size and PTA-event timing. The earliest PTA events were also between countries whose average economic size was the largest relative to nonmembers. Then, as time passed, the average relative economic size of members declined. This line suggests that PTAs formed or enlarged sooner among economically larger countries. The top line indicates two phenomena related to economic size similarity and PTA-event timing. The earliest PTA events were also among countries with very similar GDP sizes. As time passed, the degree of size similarity declined in general. This line suggests that PTAs formed or enlarged sooner among countries with more similar economic sizes.

BB provided theoretical motivations for the relationships between a country-pair's bilateral proximity, remoteness, economic size, economic similarity, and relative factor endowments for influencing the probability of a PTA, based upon a Krugman-type model of trade. Two countries' governments want to liberalize their bilateral trade through a PTA if they are less distant from each other but more distant from the rest of the world (ROW), if they are larger but more similarly sized economically, and have sufficiently different relative factor endowments.

Drawing on the domino theory in Baldwin (1995), EL enriched the BB framework by examining the role of other country-pairs' PTAs for influencing the likelihood of a PTA of a given country-pair. EL showed that, given a PTA forms, outsiders will lose in utility due to trade diversion. This creates, under some conditions, an incentive for them to join an existing PTA, or under alternative conditions form a new PTA. We introduce four new variables inspired by EL's approach to capture the influences of existing agreements on new or enlarged PTAs. First, we include the log distance of a pair of countries to the "nearest PTA" (DISTPTA). Intuitively, the closer are two countries to an existing PTA, the greater is the trade diversion they have incurred from that PTA. This implies a greater economic incentive to form/enlarge a PTA because of the potentially offsetting trade creation. Hence, DISTPTA is expected to be negatively related to the hazard rate. Second, a country-pair's utility is influenced by the "degree of regionalism" (or "competitive liberalization") in the ROW. The greater the number of PTAs in the ROW, the more trade diversion and loss of utility a country-pair experiences. We include a variable measuring the "degree of regionalism" in the ROW for every pair which is a spatially weighted average of all the PTAs that countries i and j face in ROW, denoted WPTA. WPTA is expected to be positively related to the hazard rate. Third, the variable DISTPTA influences--in the terminology of Baldwin (1995)--the "demand for membership" of outsiders into an existing PTA or a new PTA. However, in Baldwin (1995), the "supply of membership" was purposely assumed to be infinitely elastic. In reality, PTA membership is also constrained potentially by existing members; that is, supply of membership may have finite elasticity. In a theoretical model, we are able to show that the likelihood of a PTA between a country-pair may at first increase with the number of members in the "nearest PTA" but eventually may be constrained by the number of members in it, as some members of the existing agreement suffer sufficient trade diversion from other existing members as a result of a potential new entrant that these "marginally worse-off' members prevent entry. This suggests a quadratic relationship between the number of members in the nearest PTA and the hazard rate. We capture this new influence with a variable NPTA (and its squared value, SQNPTA), which is the actual number of members of the nearest existing PTA (and the square of that number). We expect NPTA (SQNPTA) to be positively (negatively) related to the hazard rate. These four variables, alongside the seven variables motivated by BB, suggest 11 economic covariates to be included in our duration analysis. (17)

B. Political and Historical Factors

In reality, political and historical factors matter. We employ several other control variables as shifters of the hazard rate as had been used in earlier work. The Polity 2 index is a well-known measure of political freedom in a country; we employ DPolity2 as a measure of the disparity in this index between country-pairs. We expect that a wider difference in two countries' degrees of political freedom will tend to reduce the likelihood of PTA formation. In an alternative specification, we also consider measures of differences of sub-indices of the Polity index: differences in political regimes of two countries (democracy and autocracy scores, DDEMOC and DAUTOC, respectively), differences in the party competition in the parliament (DPARCOMP) and in the political competition in government (DPOLCOMP). Earlier work has provided evidence that PTAs are less likely to form between countries with dissimilar political systems.

We also consider historical factors that have surfaced in the literature as determinants of PTAs. There are two variables related to the length and recency of wars between two countries (CUMDURAT and DIFFYEAR, respectively). The length of wars between a country-pair (CUMDURAT) is likely to have a negative effect on the hazard rate, but the number of years since the last war (DIFFYEAR) is likely to have a positive effect on the hazard rate. Earlier work has provided evidence that PTAs are less likely to form between countries that have had long war history and recent wars (see Egger, Egger, and Greenaway 2008, and EL).

IV. DATA

A. Data on PTAs and Associated Variables

The data set for the timing-of-PTA events was compiled for the period 1950-2006 using information from notifications to the WTO, the CIA World Fact Book, and individual web pages of countries.

The information on the timing of PTA membership of country-pair ij at time t (the dependent variable) as well as on four explanatory variables--[WPTA.sub.ij,t-5] (the inverse-distance-weighted PTA membership of other pairs than ij at time t - 5), [DISTPTA.sub.ij,t-5] (the minimum distance of i and j to a PTA at time t - 5) and [NPTA.sub.ij,t-5] as well as [SQNPTA.sub.ij,t-5] (the number of members in the nearest PTA to ij at time t - 5 and its squared value)--are based on the information on all PTAs notified to the WTO in conjunction with information on the geographic location of countries i and j (see also EL).

B. Data on Geography and Associated Variables

Geographic information is based on the CIA World Fact Book. Beyond [WPTA.sub.ij,t-5] and [DISTPTA.sub.ij,t-5], such information is used to construct three time-invariant, geographical variables which are supposed to capture whether two countries are "natural" trading partners or not. [DIST.sub.ij] is the (natural) logarithm of the great circle distance between the capitals of countries i and j (based on the great circle distance between their economic centers), [BORDER.sub.ij] indicates whether two countries share a common land border (=1) or not (=0), and [REMOTE.sub.ij] measures a country-pairs' remoteness from the ROW. The latter variable is the interaction of an indicator variable of 1 (0) for two countries on the same (on a different) continent, [DCONT.sub.ij], and a measure of "remoteness":

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

C. Data on Country Size, Relative Factor Endowments, and Associated Variables

Countries' economic sizes are measured using real GDPs from Maddison (2003). [GDPSUM.sub.ij,t] is the log of the sum of two countries' real GDPs. [GDPSIM.sub.ij,t] is the log of the similarity of two countries' RGDPs, where "similarity" is measured (as traditionally) using the product of country i's share of both countries' real GDPs with country j's share. In order to generate variables which run up through 2006, we extrapolate the information on real GDPs from Maddison with the one on real GDPs from the World Development Indicators (2009).

Apart from GDPs, we use data from Maddison (2003) on population to construct absolute differences between two countries' log real per-capita income and its squared value, PCYDIFFA and SQPCYDIFF. As with real GDP, we extrapolate the information on population from Maddison (2003) with the one from the World Development Indicators (2009) to obtain data series that run up through 2006.

D. Data on Political and Historical Variables

We employ seven different covariates that relate to political and historical conflict factors driving PTA formation and membership. The two historical conflict variables capture the war history between two countries. DIFFYEAR measures the period elapsed since two countries i and j last saw a period of war, and CUMDURAT measures the cumulative number of days of war since 1945 (the data source is the International Institute for Strategic Studies' Armed Conflict Database, https://acd.iiss.org/). Other political variables are based on Marshall, Gurr, and Jaggers' (2013) Polity IV database, and all measure absolute differences in political characteristics between two countries i and j at time t. DPolity2 is an overall index of differences in political freedom. A higher Polity2 index means more political freedom, and a larger value of DPolity2 measures a bigger discrepancy in such freedom among two countries. As an alternative to DPolity2, we employ four sub-indices thereof which are again formulated as absolute differences in the scores of i and j at t: two countries' democracy and autocracy scores (DDEMOC, DAUTOC); the political party competition in parliament score (DPARCOMP); and the political competition in government score (DPOLCOMP).

Descriptive statistics for all variables are provided in Table 1. It is important to note that the sample size falls by about 28% from 463,289 to 335,450 (or 340,726) once we include political variables. Consequently, pseudo-[R.sup.2] values will not be directly comparable for specifications due to the sample differences. Hence, we will report results with and without the political variables. (18)

Table 2 provides a list of the 146 countries included in the sample, together with each country's number of PTA partners. It is interesting to note that several countries in Latin America--notably, Chile and Mexico--have pursued a large number of bilateral PTA agreements. By contrast, the United States has only five PTA partners; however, one reason for the low number of the United States' PTAs is the cut-off of the sample in 2006.

V. EMPIRICAL RESULTS

We discuss the main empirical results as follows. First, we discuss the empirical results for a time trend only and then include the geographic controls, economic controls, and other PTA "interdependence" determinants. Next, we address the sensitivity of the results by adding the historical and political variables. We then account for unobserved heterogeneity using fixed effects for all the specifications.

Table 3 provides the results from estimating the determinants of the instantaneous probability of leaving the initial state (No-PTA) in the interval [t, t + dt) given survival up until time T (i.e., the hazard rate), based upon Equation (5). Specification 1 provides the results of estimating the hazard rate on the time trend alone. We find evidence of positive duration dependence. In the absence of economic, historical, and political covariates, this result suggests that the longer a country-pair has had no PTA, the higher the probability in any period t that it will enter a PTA. This could be attributable to the trend effects of "multilateralism" (which we address later) or even trend movements in economic, political or historical variables. The very low [R.sup.2] for this variable suggests there is room to improve explanation of the determinants of the timing of PTA events, which we now examine.

We next turn to Specifications 2 through 4 in Table 3 including the geographic, economic, historical, and political variables. An important result to especially note in Specifications 2 through 4 is the substantive change in the coefficient estimate for "Time-to-PTA event" (i.e., the time elapsed since 1950) and its z-statistic as compared to Specification 1. This indicates that time per se (reflecting the dynamic mechanism behind PTA formation and enlargement) is implicitly picking up the effect of time-varying covariates in Specification 1.

Specifications 2 through 4 confirm our expectation about the relationship between geography and the hazard rate suggested by our earlier discussion (and the underlying theoretical framework). A lower distance (DIST) between two countries i and j, sharing a common land border (BORDER), and a larger distance from the ROW (REMOTE) raise the likelihood for a pair ij to form or join the same PTA sooner. Specifications 2-4 also confirm that countries with larger and more similar economic sizes (GDPSUM and GDPSIM, respectively) appear to have larger gains from forming a PTA or joining the same PTA sooner. With regard to relative factor endowments proxied by PCYDIFF, larger relative factor endowment differences tend to enhance the likelihood of a PTA forming or enlarging sooner. Moreover, the negative coefficient estimate for SQPCYDIFF implies that this effect diminishes with the degree of per capita income differences, similar to results in BB.

Moreover, the results of Specifications 2 through 4 in Table 3 suggest that "existing PTAs," or "interdependence" in EL's terms (or "contagion" in terms of Baldwin and Jaimovich 2012), plays an influential role in the timing of PTA events. In line with expectations, the farther a country-pair is from its nearest other PTA (i.e., the larger is DISTPTA) the smaller are the potential gains from a PTA between two countries that is concluded sooner rather than later. The results also confirm that the probability of forming/enlarging a PTA earlier in time rises with the "degree of regionalism (or competitive liberalization)" in the ROW at that time, measured by WPTA. Specifications 2 through 4 also add the number of members in the nearest PTA of the pair linearly and quadratically (NPTA, SQNPTA). Consistent with our theoretical conjectures, we find a positive effect for the linear term of the number of members in the nearest PTA and a negative one for the quadratic term in the duration analysis. (19)

Specifications 3 and 4 also control for political and historical factors determining the hazard rate, beyond the geography, economic, and interdependence fundamentals. In both specifications, we control for the period elapsed since two countries i and j last saw a period of war (DIFFYEAR), and for the cumulative number of days of war since 1945 (CUMDURAT). In both specifications DIFFYEAR and CMDURAT are not significantly different from zero. However, we note, in particular, that the variable DIFFYEAR is highly collinear with the variable "Time-to-PTA event." Specification 3 includes one compact measure of the absolute difference in political freedom between two countries, captured by the difference in Polity IV scores (DPolity2). This measure is higher the larger is the average difference in two countries' political freedom. The results suggest that countries with more similar political systems and degrees of freedom tend to enter PTAs earlier than others. In contrast, Specification 4 use sub-indices behind the Polity IV index and condition on absolute differences of two countries' democracy and autocracy scores (DDEMOC, DAUTOC), as well as for the absolute differences in political party competition in parliament (DPARCOMP) and the political competition in government (DPOLCOMP). This specification suggests that the political variables are all relevant. Countries with different degrees of democracy (autocracy) tend to enter PTAs earlier (later) than ones with similar degrees. A greater similarity (dissimilarity) in party competition in parliament (political competition in government) tends to lead to an earlier entry in PTAs. In comparing pseudo-[R.sup.2] values, please note, as Table 1 suggests, that due to data constraints the sample sizes differ somewhat across specifications, with Specifications 3 and 4 having smaller sample sizes. Also, the sample size is about 5,000 observations larger when the Polity IV sub-indices are used in Specification 4, rather than the summary measure in Specification 3.

Specifications 5 through 7 add parameterized pairwise fixed effects to Specifications 2 through 4, respectively. The purpose is to see whether the results in Specifications 2 through 4 are biased by unobserved heterogeneity. The range of possible omitted variables is vast. In order to allow for a set of unobserved effects which may be correlated with [x.sub.ij](i), we consider introducing fixed country-pair effects. However, the introduction of fixed effects in a non-linear function is not a trivial endeavor, since the number of incidental parameters is increasing with sample size. Chamberlain (1980) shows that, for a fixed time dimension, maximum likelihood estimates of p will be inconsistent as the number of cross-sectional observations goes to infinity. Chamberlain (1980) provides an approach that eliminates the incidental parameters problem. Essentially, the unobserved effects can be eliminated by an appropriate differencing transformation. Chamberlain (1980) suggests including averages of all time-varying explanatory variables along with the original variables in the empirical models (see also Wooldridge 2010).

Specifications 5 through 7 report the results using the Chamberlain-Wooldridge-type model. For brevity, we do not report coefficient estimates for fixed effects; moreover, recall that DIST and BORDER are time-invariant (and so are not demeaned). First, unsurprisingly the pseudo-[R.sup.2]'s increase, from 23-27% to 35-38%. Second, Specifications 5-7 reveal that most of the coefficient estimates maintain the same qualitative effects as found in the previous specification. In particular, PTA economic determinants DIST, BORDER, REMOTE, GDPSUM, GDPSIM, PCYDIFF, SQPCYDIFF, DISTPTA, and WPTA all retain their expected coefficient signs and their coefficient estimates are statistically significant. However, NPTA and SQNPTA change signs unexpectedly; this could be attributable to multicollinearity. Third, the large change in quantitative values of the coefficient estimates should not come as a surprise. The new coefficient estimates are based upon only time variation of the variables; the coefficient estimates for DIST and BORDER are unchanged because only those two variables are not time-demeaned. (20)

In qualitative terms, virtually all of the coefficient estimates of the political and historical variables are unaffected, though most change in quantitative terms because of the time-demeaning nature of the fixed effects. Note that DIFFYEAR's coefficient estimate turns positive when including the fixed effects in Specification 7 (compare Specifications 4 and 7), but remains economically and statistically insignificant. Also, CUMDURAT turns statistically significant; however, the coefficient estimates are not economically different from zero. (21) However, we need to bear in mind that CUMDURAT is relatively time-invariant and the difference in the parameter on it from Specifications 3 and 4 to 6 and 7, respectively, may flow from multicollinearity with the pairwise fixed effects. Even though the pseudo-[R.sup.2] of the models rises if we add fixed effects, Specifications 2 through 4 appear to work reasonably well (when remembering the large amount of zeros in the dependent variable). Moreover, two advantages of Specifications 2 through 4 relative to 5 through 7 are that: (1) fixed effects cannot be estimated precisely in duration models, and (2) they are unknown whenever predictions are supposed to be made out-of-sample (i.e., high-level assumptions have to be made regarding their changes).

VI. PREDICTIVE ANALYSIS

In this section, we examine the ability of the model to predict the actual year of the formation (or enlargement) of a PTA between each pair of countries, as well as for various "windows" leading up to PTA events. The section has four parts. The first part addresses the in-sample and out-of-sample predictive power of the model using the main specifications presented in Section V. The second part evaluates the predictive power of the model after accounting for multilateralism, but using a much smaller sample (due to data availability of multilateralism variables). The third part examines the predictive power of the model for the time-to-PTA events of the CUSFTA, the NAFTA, and the European Community's formation and subsequent enlargements. The fourth part examines whether the model's ten most likely time-to-PTA events in the post-sample period (2007-2013) have actually occurred as predicted.

A. Predicting the Actual Years of PTA Formation or Enlargements

In this section, we examine the predicted timings--in particular, even the predicted year--of all PTA events. Because predicting the specific year is a demanding objective, we also consider predicting an event within time "windows" of up to 10 years prior to the event. It is important to again contrast our duration analysis with previous analyses predicting the existence of a PTA in a given year. In the latter studies, predictions can occur in the years prior to the PTA's entry into force, in the year of the PTA's entry into force, or in the years following the PTA's entry into force. By contrast, our analysis can only predict the actual year of the PTA's entry into force, or a designated window leading up to that year. Hence, predictions from our analysis cannot be compared to previous non-duration-analysis-based predictions.

Table 4 provides a summary of the accuracy for predicting the timing of each bilateral PTA event using Specifications 1 through 7 from Table 3. It is important to note that our preferred specifications for predicting events are Specifications 2 through 4 for the reasons mentioned at the end of the previous subsection. In order to map the continuous linear index behind the hazard rate or the hazard rate itself into discrete event predictions, we must utilize a cut-off probability. Various methods to select endogenously the cut-off exist, including Sensitivity-Specificity analysis (see Baier, Bergstrand, and Mariutto 2014) or a quadratic loss function akin to Matthew's Correlation Coefficient (see Bergstrand and Egger 2013). In the latter approach used here, the cut-off probability which distinguishes zeros from ones for the predicted PTA indicator is chosen so as to minimize the associated loss function which trades off correct and incorrect unitary and zero predictions (notice that the cut-off probability will not be at 50%, since the PTA indicator data in panel form contain numerous zeros relative to the ones).

Table 4 is organized horizontally in seven blocs (referring to Specifications 1 through 7) and vertically in four blocs. The bloc at the top represents the base case directly associated with Specifications 1-7 as reported in Table 3. The other three blocs are based on parameter estimates akin but not identical to the ones in Table 3 (we suppress presenting these parameter estimates for the sake of brevity). The results from the second bloc are based on Specifications 1 -7 from Table 3 that are rerun only using data from 1970 (rather than from 1950) onwards. This set of results tells us how much of the explanatory and predictive power is due to letting the process run from a time period which is relatively distant in time from most of the PTA events in the data. The third bloc of results runs Specifications 1-7 using data from 1950 to only 2000 (rather than 2006), but predicting events out-of-sample for the years 2001-2006. The last bloc of results runs Specifications 1-7 using data from 1950 to only 1989 (rather than 2006), but predicting events out-of-sample for the years 1990 through 2006. The last two blocs are meant to assess generally the out-of-sample prediction quality of the models near-term versus long-term, respectively.

With regard to the benchmark model predictions at the top of Table 4, we see that Specifications 1-4 predict various percentages of all 1,560 events covered within the year or up to ten years prior to the event. About 13-26% of the events are predicted within the same year that they had occurred. Among the four specifications, Specification 3 performs relatively best. It predicts 26% of the events within the same year that the actual PTA membership occurred, 30% in the same year or up to 1 year prior to actual PTA membership, and 33% within the same year or up to 2 years prior to actual PTA membership, respectively. In comparison, Specification 1 only predicts 13% of the events within the same year that the actual PTA membership occurred, 23% in the same year or up to 1 year prior to actual PTA membership, and 28% within the same year or up to 2 years prior to PTA membership, respectively.

Not surprisingly, Specifications 5 to 7, which include parameterized fixed country-pair effects, perform even better in predicting PTA membership events. These specifications predict 69-72% of the events within 10 years prior to actual PTA membership. Among those, Specification 5 works best for the 10-year window and Specification 6 works best for a window of up to 3 years, explaining 39% of the events within the same year that the actual PTA membership occurred, 46% in the same year or up to 1 year prior to actual PTA membership, and 52% within the same year or up to 2 years prior to the actual event. In the subsequent discussion, we mainly focus on Specifications 2 to 4 since they will turn out to outperform Specifications 5 to 7 in terms of out-of-sample predictions and also exclude fixed effects (which complicates out-of-sample predicting).

In the second vertical bloc, using data from 1970 rather than from 1950 onwards leads to a better predictive performance for all specifications. This is intuitive, since the density of PTA events is relatively much higher during the more recent decades of the data than in the first ones. However, there is not a material difference in predictive power between the two blocs.

With regard to out-of-sample predictions of PTA events in the third bloc, Specification 3 tends to work best. Note that in the third bloc we only forecast events in the 6 years after the end of the estimation sample in 2000 (2001 through 2006) and we forecast the years with relatively many PTA events. We predict 66% of the events within the same year that the actual PTA membership occurred, 69% in the same year or up to 1 year prior to actual PTA membership, 73% of all 284 events within the same year or up to 2 years prior to the actual event, and 82% of all 284 actual PTA events in 2001-2006 within up to 5 years prior to their occurrence. This near-term out-of-sample performance of Specification 3 dominates the predictions of Specification 1, which uses only the time trend. No other study has provided out-of-sample predictions of PTA timings. These results suggest a strong predictive power of our model relative to the simple time trend near term.

However, a different outcome results for long-term forecasting of PTA events, shown in the fourth vertical bloc. Estimating the models from 1950 through 1989 and then predicting all events that had occurred between 1990 and 2006, Specification 3 predicts only 24% of the events within the same year that the actual PTA membership occurred, 27% in the same year or up to 1 year prior to actual PTA membership, and 35% within the same year or up to 10 years prior to the actual event. Not surprisingly, the previous vertical bloc in Table 4 shows a much better performance of Specification 3 to predict PTA events than in the last vertical bloc. The reasons are that, in contrast to the fourth bloc, in the third bloc we only forecast events in the 6 years after the end of the estimation sample in 2000 (2001 through 2006) and we forecast the years with relatively many PTA events. Although the predictive power is lower than previously, note that our model still outperforms out-of-sample the model with only a time trend (Specification 1) when forecasting the specific year of the event or a window up to 3 years preceding the event. Yet, for windows of up to 4, 5, or 10 years prior to the event, the model with only a time trend has better predictive power. Note, however, that the model itself is only estimated using data through 1989, and consequently includes only one-third of the events as in the entire sample (523 events for the fourth bloc versus 1,276 events for the third bloc). (22)

In sum, even relatively parsimonious specifications without fixed effects perform quite well in predicting PTA events in- or out-of-sample, as long as the estimates are based on data with a sufficient number of PTA events and if the out-of-sample forecast period is not too long.

B. Robustness to Multilateralism's Effects

As mentioned earlier, the time trend in the econometric model could likely capture overall trends in multilateral liberalization. The influence of multilateralism on PTA formation in terms of empirical work started with Mansfield and Reinhardt (2003). The focus of that study--and subsequent empirical studies--has been on four variables related to the influence of multilateralism potentially explaining PTA formations. Baldwin and Jaimovich (2012) incorporated these four variables in their predictions of PTAs. Gradeva and Jaimovich (2014) reexamined the original Mansfield and Reinhardt (2003) findings, focusing largely on the robustness of the original four Mansfield-Reinhardt multilateralism variables.

The first of the four variables is WTOMEMBERS, the number of contracting parties to the GATTAVTO (in the previous period). The argument is that an increasing number of parties reduces each party's leverage over the progress and path of multilateral liberalization, making it more difficult to conclude such rounds. Country-pairs may provide an alternative means for countries to pursue trade liberalization to avoid adverse implications of slow multilateral liberalization, that is, more PTAs. Hence, WTOMEMBERS is expected to have a positive impact on the hazard rate of PTA events.

The second variable is MTNROUND, a dummy variable indicating if a GATT or WTO multilateral trade negotiation (MTN) round is in place in the current year (1), or not (0). The expected sign on this variable is ambiguous due to two alternative views. One view is that countries' governments may believe they can increase their bargaining power in a current MTN round if they form PTAs; this suggests a positive impact of MTNROUND on the hazard rate. A second view is that PTAs and multilateral liberalizations are complements, cf., Freund (2000). Hence, if a MTN round has been completed (hence, the dummy is zero), the likelihood of a PTA is higher; this suggests a negative impact of MTNROUND on the hazard rate. Baldwin and Jaimovich (2012) found a negative but statistically insignificant effect of MTNROUND on the probability of a PTA. However, Gradeva and Jaimovich (2014) found a negative and statistically significant effect, if the sample was constrained to 1980-2007. Moreover, Fugazza and Robert-Nicoud (2011) show that the frequency in which the United States grants immediate duty-free access to PTA

partners is larger for goods in which multilateral tariffs have had the largest cuts. Based on these various considerations, we expect a negative coefficient estimate.

The third variable is DISPUTE3rdPARTY, a dummy variable indicating if either i or j is a complainant or defendant in a new GATT/WTO dispute with a third party in the previous year (1), or not (0). The argument is that a country that has entered a dispute with a third party may have an incentive to form a PTA to gain leverage in the dispute. Hence, DISPUTE3rdPARTY is likely to have a positive impact on the hazard rate.

The fourth variable is LOST3rdPARTY, a dummy variable indicating if either i or j lost a GATT/WTO dispute with a third party 3 years prior (1), or not (0). The argument is that a country that recently lost a dispute is at risk for securing market access through the multilateral system. This may encourage incentives to form PTAs. Hence, LOST3rdPARTY is likely to be positively related to the hazard rate.

Consequently, we re-estimated our models above to add these four multilateralism variables to see if our results change materially, both in terms of model explanatory power as well as predictive power. However, we note one important restriction associated with this robustness analysis, and therefore present the associated results separately. Due to data availability, the overlap in data on the multilateralism variables from Gradeva and Jaimovich (2014) and our data set is narrow. As noted above, in our Specifications (3) and (4) without fixed effects ((6) and (7) with fixed effects), the sample size is either 335,450 observations (for Specifications (3) and (6)) or 340,726 observations (for Specifications (4) and (7)). Adding the multilateralism variables reduces our sample size to only 141,096 or 141,523 observations, respectively. The reason is that the data set in Gradeva and Jaimovich (2014) has considerably fewer observations than ours in the first 30 years of their sample (1948-1978). Thus, while we consider it worthwhile to see the sensitivity of the earlier regression results and predictions to including multilateralism variables, the results are not directly comparable due to the difference in samples.

Table 5 provides the empirical results for Specifications (3), (4), (6), and (7) now including the multilateralism variables; these are labeled accordingly Specifications (3A), (4A), (6A), and (7A), respectively. Several points are worth noting; for brevity we compare first Specification (3) in Table 3 to Specification (3A) in Table 5. First, the coefficient estimates for the four multilateralism variables are all statistically significant. Moreover, three of the four coefficient estimates' signs are as expected; only LOST3rdPARTY has a coefficient estimate sign different from the expectation. Second, we note that the coefficient estimate for the time trend now becomes trivially small, though still statistically significant. This result is consistent with our earlier conjecture that the time trend may be reflecting overall trends in multilateral trade liberalization. Third, despite the presence of the multilateralism variables causing the time trend's effect to become trivially small, their presence has little effect on the other variables' coefficient estimates in Specification (3). The coefficient estimates for the three geography and the four economic size and similarity and relative factor endowments variables are qualitatively the same. However, coefficient estimates for DISTPTA, NPTA, and SQNTA change sign. Yet, one must keep in mind that the sample is considerably different from that in the main empirical specifications, which could also explain the changes. Fourth, the changes just discussed largely carry over to the other specification comparisons, and so for brevity are not discussed.

Table 6 provides the predictions for Specifications (3A), (4A), (6A), and (7A), similar to those for comparable specifications in Table 4. The main point to note is that for Specifications (3A) and (4A) the predictive power of the model is enhanced somewhat using specifications incorporating the multilateralism variables. However, once again a caveat for any comparison is the different samples used, and hence the results are effectively not comparable. For Table 6, the results are influenced by a shorter sample for a period with a higher density of PTAs and that consequently influences the predictive power of the model.

C. Predictions of CUSFTA, NAFTA, and the European Union's Formation and Enlargements

Two of the most well-known PTAs are the NAFTA--following in the footsteps of the CUSFTA--and the European Union (EU), which began as the EEC in 1958. Since we have data going back to 1950, it would be useful to know how well our model, in retrospect, predicted the timing of these events. As apparent by now, our model explains and predicts bilateral events. So an additional evaluation of the successfulness of the model is determining the clustering of the bilateral events around the plurilateral events.

We divide our analysis here into three parts. First, we examine the prediction of the original CUSFTA, which began in 1989. This constitutes the prediction of one (bilateral) event. Second, we examine the prediction of NAFTA in 1994. In this case, we are predicting two events: a Mexico-Canada event and a Mexico-U.S. event. Third, we examine the predictions associated with the formation of the EU and its subsequent enlargements. Thus, the first 10 events are the bilateral pairings among Belgium (which, for data reasons, includes Luxembourg; see earlier), the Netherlands, Germany, France, and Italy, which comprise the original EEC membership. We will then discuss the predictive power of the model for each of the seven subsequent enlargements of the EU. (23)

Table 7 will be helpful in organizing the discussion. First, we discuss CUSFTA. While CUSFTA officially began in 1989, it is important to note that the foundation for CUSFTA was in the Canadian-United States Automobile Trade Agreement, which was signed in 1965 to facilitate free Canadian-U.S. trade in autos and auto parts. Going further back historically, during the Great Depression of the 1930s following the isolationism of the world economy with rampant tariff escalation, Canada and the United States started reducing tariffs under a bilateral agreement. However, the post-World War II environment of multilateral liberalization dominated the 1950s, 1960s, and 1970s, so that little attention was given in Canada and the United States to a bilateral free trade agreement. The imbalance in macroeconomic policies of the 1980s along with expansion of the EEC provided impetus so that CUSFTA discussions began in 1985 and concluded with CUSFTA entering into force in 1989. Our model predicted CUSFTA in 1976, which we note is halfway between the start of the Canada-U.S. Auto Pact and CUSFTA's year of entry into force.

Second, we discuss NAFTA. Just as the path to NAFTA began with CUSFTA, the path to NAFTA started earlier between Mexico and the United States than between Mexico and Canada. The 1980s saw structural economic reforms beginning in Mexico. In 1985, the United States signed with Mexico the Understanding on Subsidies and Countervailing Duties, a substitute for Mexican participation in the subsidies code of the GATT. In 1987, Mexico and the United States signed the Framework of Principles and Procedures for Consultation Regarding Trade and Investment Relations, which established an agenda for bilateral trade and investment negotiations. In 1989, the two countries signed an Understanding Regarding Trade and Investment Facilitation Talks. Thus, while Mexican-U.S. bilateral liberalization initiatives lagged behind Canadian-U.S. initiatives, the former started as early as 1985. In Table 7, the 1/2 (meaning "1 out of 2") refers to Mexico-United States; our model predicts the Mexican-U.S. PTA starting as early as 1978. By contrast, Canadian-Mexican agreements arose more slowly, with ten minor accords signed in 1990. Our model predicted the Canadian-Mexican PTA in 1994--the year it actually went into force. Moreover, it is interesting to note that the year that the model predicted both a Mexican-U.S. PTA and a Mexican-Canadian PTA was 1994 (i.e., 2/2 in 1994 in Table 7), the year NAFTA actually began.

Our third part---which is more extensive than the first two parts combined--is an analysis of the (in-sample) predictive ability of the model for the formation of the EU (termed in 1958 the EEC) and its seven subsequent enlargements. (24) Table 7 reports comprehensively the predictions of the model (in column 2) and the actual formation years (in column 3). A detailed analysis of every row is beyond the scope of this paper due to the eight rounds of activity; however, we will summarize the key implications using the last row of data for each of the eight rounds (the formation and seven enlargements). We begin with the formation of the EU; the Treaty of Rome went into effect in 1958. As noted above, Belgium represents Belgium and Luxembourg; hence, we have five original EEC countries and ten non-direction country-pairs (10 = [5 x 4]/2). As shown in Table 7, our model predicts six of the ten original EU country-pairs in 1958, the actual year of entry into force. Based upon economic size, proximity, political similarity, and the interdependence variables in our model, it is likely that the other four pairs would have been predicted for later years, but the data set's construction precludes that as discussed earlier. It is also possible that our historical conflict variables' influence contributed to predicting the other four country-pairs PTA events later.

We now discuss each of the seven enlargements. The first enlargement in 1973 added Denmark, Ireland, and the United Kingdom. Five of the 15 bilateral events were predicted in 1973. Likely because of (West) Germany's economic size, three of these five pairs were Germany with the three new EU partners. Once again, based upon economic size, proximity, political similarity, and the interdependence variables in our model, it is likely that the other ten pairs would have been predicted for later years, but the data set's construction precludes that. Also, it is possible again that our historical conflict variables' influence contributed to predicting the other ten country-pairs PTA events later. The second enlargement in 1981 added Greece. The model predicted all eight country-pair events for Greece with the other eight members starting in 1978, only 3 years prior to the events. The third enlargement added Spain and Portugal in 1986. Although a few of these 18 (18 = 9 x 2) bilateral events were predicted in earlier years, all 18 bilateral events were predicted beginning in 1978, 8 years prior to the event. The fourth enlargement added three new members--Austria, Finland, and Sweden--in 1995. As shown in Table 7, all 33 PTA events (33 = 11 x 3) were predicted beginning in 1983 about 12 years before the events.

The fifth and sixth enlargements were all quite large in terms of numbers of new members. Actually, ten new members joined the EU in 2004. However, due to data constraints, our model was only able to make predictions for eight of these new members: Czech Republic, Estonia, Hungary, Latvia, Lithuania, Poland, Slovakia, and Slovenia. With 14 countries in our model as of the fourth enlargement in 1995, this allows 112 predictions (112 = 14 x 8). Our model predicted all 112 events starting in 1994, about 10 years prior to the 2004 enlargement. Year 2007 saw the sixth enlargement by adding Bulgaria and Romania. These 36 PTA events were predicted starting in 1994 also, about 13 years prior to their inclusion. The seventh enlargement in 2013 to add Croatia was predicted in 1990.

Although the precise timing of the bilateral PTA events by actual year is difficult, we note two important results. First, not only the formation of the EU--but also five of the seven enlargements--were predicted within a 10-year window of the actual events (as summarized above). The fifth and seventh enlargements were predicted 12-13 years before the events occurred. It is feasible that politics played an influential role in the actual timing of the events. A second interesting result is the sequencing of the enlargements. The second enlargement was predicted no later than the third enlargement. The third enlargement was predicted before the fourth enlargement. The fourth enlargement was predicted before the fifth enlargement. The fifth enlargement was predicted no later than the six enlargement. Thus, the model generally explains well the sequencing of the EU's enlargements.

While the discussion above has focused on in-sample predictions of particular PTA events that occurred during the sample, it would be interesting to see whether the model--based upon data from 1950 to 2006--predicts the most likely post-2006 out-of-sample PTA events. This is the subject of the next section.

D. Evaluating Realizations of the Model's Ten Most Likely Post-Sample Time-to-PTA Events

The main sample of the paper spanned the period 1950-2006. In this section, we consider the predictive analysis of the model for the post-2006 period--2007-2013--using actual values of right-hand-side variables. In particular, we focus on the ten most likely PTA events predicted post-sample by the model, comparing their predicted year of PTA formation with the actual status of PTA formation--either entered into force, proposed, or not yet considered.

Table 8 will be helpful in organizing the discussion. The first column of Table 8 lists the country-pairs for which a PTA was most likely to be formed in the post-sample period 2007-2013, ranked by highest to lowest probabilities. (25) The second column lists the probability associated with the PTA event. The third column lists the year predicted for the event. The fourth column specifies a year associated with an entry-into-force of an agreement, a year associated with a significant development in a proposed agreement, or the reporting of no PTA or proposed PTA.

For these ten most likely PTA events, seven of the ten pairs have PTAs entered into force or proposed; there is no reported activity for only three of the most likely events. The last column of Table 8 provides details about pairs with proposed agreements or actual PTA formations. We discuss the ten pairs in three groupings: implemented agreements, proposed agreements, and absence of agreements. First, three of the ten country-pairs with post-sample predicted PTA events formed PTAs in the post-sample period. The China-Pakistan PTA went into force in 2007, and was predicted by the model for 2011. The EU formed a PTA with South Korea in 2011. Italy and Spain were both predicted by the model to form PTAs with South Korea in 2011.

The second group of country-pairs is those with predicted PTAs but only a proposal is in place, not an actual agreement. There are four country-pairs in this group. First, Egypt and South Africa had a probability of 0.705 of forming a PTA in 2011. In an October 2008 summit followed by another June 2011 summit, the African Free Trade Zone (AFTZ) was proposed. Comprised of 26 countries that span three major existing PTAs--the East African Community (EAC), the Southern African Development Community (SADC), and the Common Market for Eastern and Southern Africa (COMESA)--the AFTZ would create a free trade area that goes from Cairo to Cape Town. Interestingly, the AFTZ would actually implement the dream of Cecil Rhodes in the 1890s of free trade spanning Egypt to South Africa. The AFTZ is expected to be operational in 2018 and progress suggests this is feasible. Second, we have the special case of Libya and Chad. The model predicted a PTA in 2009. The table lists that the two countries were both founding members of the Community of Sahel-Saharan States (CEN-SAD) in 1998, which exists and has a goal of becoming an economic union. However, most observers consider that the FTA signed has not been "effective." Consequently, we consider the 1998 CES-SAD agreement as a proposed agreement. Third, our model predicted an Italy-Pakistan PTA in 2010. The EU instituted in 2009 a 5-year Engagement Plan to extend its current one-way GSP treatment to Pakistan to an FTA. Fourth, our model predicted an Egypt-Gabon PTA in 2011. There was a proposal in 2012 that the AFTZ, proposed during October 2008 and June 2011 summits, be extended from the EAC, SADC, and COMESA to include the Economic Community of Central African States (ECCAS), which would then unite Egypt and Gabon in a PTA.

The third group of country-pairs is those with no planned or existing PTA. This group includes Australia-Egypt, Pakistan-Saudi Arabia, and Pakistan-United Arab Emirates. VII.

VII. CONCLUSION

Despite the proliferation of PTAs in the last 60 years, there have been only 1,560 bilateral formations/enlargements among 10,518 pairings of 146 countries from 1950 to 2006. We used an econometric duration analysis to determine the economic, political, and historical factors explaining the instantaneous probability at a particular year of leaving the initial state of "No-PTA" to form or enter a PTA (given survival of the state No-PTA up until that period). We found that geography, economic size and similarity, relative factor endowments, interdependence (or contagion) in PTA formation, and political and historical factors had statistically significant effects on the timing of country-pairs' PTA "events." Moreover, the coefficient estimates for the variables are consistent with relationships suggested by an underlying theoretical model, suggesting the PTA events are occurring sooner when the net welfare gains for the countries' consumers are higher.

When estimating a specification on all 1,560 PTAs over the period 1950 through 2006, the preferred parsimonious specification (without fixed effects) explains 26%, 46%, and 57% of the PTA events within 1, 5, and 10 years, respectively, up until the actual occurrence of those PTAs within the sample and estimation period. Estimating such a specification for the years 1950 through 2000, the model explains out-of-sample 66% of the events within the same year that the actual PTA membership occurred in 2001 through 2006, 69% in the same year or up to 1 year prior to actual PTA membership, and 82% within 10 years up until the actual occurrence of all 284 PTAs. The model largely explains in-sample the formations of the Canadian-U.S. FTA, NAFTA, and the EU's formation and subsequent enlargements. Moreover, for seven of the ten most likely post-2006 out-of-sample PTA events, either a PTA formed during the period 2007-2013 or one has been proposed.

The results suggest not only that the path of regionalism over time in terms of country-pairs has been one consistent with welfare-maximizing behavior of countries' governments, but that there is a feasible "road map" for policy makers for the evolution of PTAs in the world economy. While most observers might agree that overall multilateral liberalization would be the most preferred policy for the world economy in principle, in the absence of such progress the path of regionalism has likely been a beneficial one.

doi: 10.1111/ecin.12241

ABBREVIATIONS

AFTZ: African Free Trade Zone

BB: Baier and Bergstrand (2004)

COMESA: Common Market for Eastern and Southern Africa

CUs: Customs Unions

CUSFTA: Canada-United States Free Trade Agreement

EAC: East African Community

ECCAS: Economic Community of Central African States

EEC: European Economic Community

EL: Egger and Larch (2008)

EU: European Union

FTAs: Free Trade Agreements

GATT: General Agreement on Tariffs and Trade

GDPs: Gross Domestic Products

MTN: Multilateral Trade Negotiation

NAFTA: North American Free Trade Agreement

PTAs: Preferential Trade Agreements

ROW: Rest of the World

SADC: Southern African Development Community

WTO: World Trade Organization

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SUPPORTING INFORMATION

Additional Supporting Information may be found in the online version of this article:

Appendix S1. Theoretical supplement

(1.) Egger and Larch (2008) and Baldwin and Jaimovich (2012) examined the influence on the probabilities of PTAs of existing nearby agreements in a previous period using spatial econometrics, providing broad empirical support for potential trade diversion inducing nonmembers to either join existing PTAs (supporting Baldwin's domino theory) or form new ones. A similar analysis motivated by network formation was undertaken by Chen and Joshi (2010). However, these studies did not examine the effects of existing PTAs on the timing of new PTAs and enlargements, which we examine.

(2.) Baldwin and Jaimovich (2012) used duration analysis in one robustness analysis of their model. Liu (2008, 2010) used a duration analysis, but excluded interdependence controls. Also, neither of these studies focused on the role of time and all of them omitted in-sample and out-of-sample predictions.

(3.) As will be discussed later, the potential number of observations is 599,526, given the number of country-pairs and years. However, we construct our sample such that--once a country-pair forms a PTA in a particular year--subsequent years are excluded. For instance, Germany and France entered (into force) the European Economic Community in 1958; consequently, years 1959-2006 are excluded for Germany-France. This reduces our number of observations from 599,526 to 463,289. Subsequent data constraints will reduce it further for some empirical specifications.

(4.) The cumulative number of all PTA events corresponds to the number of country-pairs in the sample which liberalized trade preferentially since 1950. We had to amend the data to capture agreements not included in the WTO data base. For instance, most of the members of the former communist bloc were engaged in agreements outside the WTO (or, prior to the foundation of the WTO, the General Agreement on Tariffs and Trade, GATT). Note that an event requires that explanatory variables employed in the subsequent empirical analysis are not missing for a country-pair. Accordingly, the memberships associated with this figure are the same ones used in estimation later. Figure 1 presents these cumulative events as a percentage of 10,518 country-pairs covered.

(5.) Higher levels of economic integration, such as common markets and economic unions, are also included; for instance, Germany and France--members of the Eurozone--are considered in the WTO listing as a customs union (CU). One-way preferential trade agreements, such as Generalized System of Preferences (GSP) agreements, are excluded.

(6.) For instance, the 10 events in 1958 correspond to the formation of the EEC in that year. The corresponding number of memberships is 10, because Belgium and Luxembourg are counted as a single country (as often done in economic studies), so that there are 5 founding members and the number of unique dyads is 5(5 - 1)/2.

(7.) Figure 1 illustrates three apparent "waves of regionalism" since 1950. The first wave (beginning in 1958) was initiated by the formation of the European Economic Community (EEC) and then the European Free Trade Agreement (EFTA). The second wave (beginning in 1973) included several enlargements of the EEC and the introduction of several new PTAs. The third wave (beginning in 1989) included the formations of the Canada-United States FTA, NAFTA, MERCOSUR, and numerous bilateral agreements.

(8.) Side (or compensation) payments were ruled out.

(9.) Joyce (2005) and Conway (2007) studied determinants of the lengths of spells of IMF programs. Besedes (2008), Besedes and Prusa (2006a, 2006b), Fugazza and Molina (2009), Nitsch (2009), and Hess and Persson (2010) all have studied the determinants of bilateral trade-flow durations. Only two other studies have examined determinants of the timing of PTA events, namely Liu (2008, 2010). However. Liu (2008) focused on the marginal effects of political economy determinants of PTA timings (specifically, income-inequality's interactive effects with relative capital-labor endowment ratios) to test a "median-voter" model of PTA timing versus a "lobbying" model. That study's finding in favor of the median-voter model provides support for our economic determinants of the timing of PTA approach and our alternative focus on domino effects, competitive liberalization, and PTA interdependence. Liu (2010) extends Liu (2008) by testing competing predictions of the median voter model versus the lobbying model. However, Liu (2008, 2010) omitted controls for "interdependence," did not provide any predicted probabilities of time-to-PTA events, and did not provide any out-of-sample predictions, all of which are goals of the present paper.

(10.) The vast number of pairs of countries that form PTAs in our sample (1,560 events) do so permanently; our sample includes only 48 events of pairs ending agreements. By contrast, the labor economics duration literature on unemployment spells and the international economics literature on IMF program spells deal with macroeconomic policies/ environments, where entering and exiting spells of unemployment or programs, respectively, is frequent. Due to the insignificant number of PTA exits, we do not address the latter events in this study.

(11.) This result is consistent with a time trend parameter of 0.61 in Specification 2 in Table 3 below.

(12.) A parameter on common borders of 0.52 is also consistent with Specification 2 in Table 3 below.

(13.) A parameter of 0.13 is, for example, consistent with the coefficient on two countries' joint economic size in Specification 2 in Table 3 below. However, we do not draw [[epsilon].sub.ijt] from a normal distribution with mean and variance as of two countries' joint economic size for reasons of illustration.

(14.) In short, period t economic variables influence [P.sub.ij](t) in the equation [[lambda].sub.ij](t) = g[P.sub.ij](t), because [P.sub.ij](t) is a function of period t utility, [U.sub.ij](t).

(15.) We provide in an online Theoretical Supplement (Appendix SI) a one-sector Krugman-type general equilibrium model to account for sequencing of PTA events to motivate all the economic factors below (except relative factor endowments).

(16.) "Similarity" is measured (as traditionally) using the product of country i's share of both countries' real GDPs with country j's share.

(17.) As noted earlier, all of these economic variables (with the exception of relative factor endowments) are shown to influence the sequencing of PTA events in our theoretical model in the Online Theoretical Supplement. Note that DISTPTA, WPTA, NPTA and SQNPTA all account for various channels through which other PTAs influence the formation of subsequent PTAs (i.e., interdependence). Other papers that have distinguished sources of interdependence include Chen and Joshi (2010), Baldwin and Jaimovich (2012), and Baier, Bergstrand, and Mariutto (2014); the latter paper details distinctions among these three papers and EL. Also, Deltas, Desmet, and Facchini (2012) provide evidence of the effects of the nature of PTA interdependencies on bilateral trade flows.

(18.) The last four variables in Table 1 (multilateralism variables) will be discussed later in Section VI; they are included here for convenience.

(19.) In the context of the "domino theory" in Baldwin (1995), an increase in the number of members of the nearest PTA causes a rise in demand for membership of non-members in this agreement, tending to increase the hazard rate for ij. However, Baldwin's domino theory assumes an infinitely elastic supply of membership by a PTA. As the number of members of a PTA increases, there are incumbent members whose utility falls when a new member is added, especially the members of the PTA most distant from the core. Every time a new member is added, the utility from the PTA of the (marginal) "worse-off' member declines. It can be shown in our simple Krugman-like model (in the Theoretical Supplement) that at some point the marginal worse-off member's utility declines from new members, dampening the average utility gain of members in the PTA. This finite-elasticity-of-membership supply implies theoretically a quadratic relationship between the number of members of the nearest PTA (NPTA) and the hazard rate for pair ij. See our Theoretical Supplement for an illustration of this argument.

(20.) For instance, typical gravity equations of international trade have similar differences for GDP variables' coefficient estimates if variables are time-demeaned.

(21.) A possible reason for this positive correlation might be that countries with a higher probability of war (a longer war history) have higher opportunity costs from a war the larger are the trade gains, making PTA formation more likely (see Martin, Mayer, and Thoenig 2012).

(22.) Note that with out-of-sample predictions a decision has to be made with regard to the values assumed for covariates determining the time-to-PTA events. Moreover, with parameterized fixed country-pair effects, one has to decide whether to keep those effects fixed outside of the sample period and, if not, how to adjust them. In Table 4, we use the covariates as they are observed even outside of the sample period. However, it should be noted that keeping them fixed at the end of the estimation sample period does not have a substantive impact on the predictions. The reason appears to be that the covariates determine well the cross-sectional variation in hazard-rate base levels, and the time trend predicts well the cross-sectional heterogeneity in the timing-to-PTA events relative to the end of the sample period. For instance, let us compare the results for a model that is the same as Specification 3 in Table 4 for the out-of-sample predictions from 1990 to 2006 for the PTA events in those years, but keeping the covariates constant at their 1989 levels and only letting time change. In this setting, the specification predicts up to 43% (47%) of the 1,037 PTA events between 1990 and 2006 in the same year or up to 5 (10) years prior to the actual events. The corresponding number in Table 4, where the covariates change as observed in the out-of-sample period, is 35% (35%) for the same precision window.

(23.) For all these predictions, we used Specification 4 from Table 3; similar results were obtained using Specification 3.

(24.) The name of the EU has evolved over time. For tractability, we will use EU for the original EEC as well as for subsequent names.

(25.) Predictions were enabled by use of actual values of countries' GDPs and other time-varying right-hand-side variables for the period 2007-2013 using Specification 3; similar results were obtained using Specification 4.

JEFFREY H. BERGSTRAND, PETER EGGER and MARIO LARCH *

* The authors gratefully acknowledge numerous valuable comments from the editor, Bruce Blonigen, three anonymous reviewers, Richard Baldwin, Mathias Thoenig, and several other participants at the conference "Empirical Determinants of Regionalism," The Graduate Institute of International and Development Studies, Geneva, the 25th Annual Congress of the European Economic Association, 2010, Glasgow, and the 12th Gottingen Workshop "Internationale Wirtschaftsbeziehungen", 2010, Gottingen.

Bergstrand: Professor, Department of Finance, Mendoza College of Business, University of Notre Dame, Notre Dame, IN 46556, Phone 1 574-261-1071, Fax 1 574-6315255, E-mail bergstrand. 1@nd.edu

Egger: Professor, Chair of Applied Economics, ETH Zurich, 8092 Zurich, Switzerland. Phone 41-44-632-4108, E-mail egger@kof.ethz.ch

Larch: Professor, Chair of Empirical Economics, University of Bayreuth, 95447, Bayreuth, Germany. Phone 49-92155-6240, E-mail mario.larch@uni-bayreuth.de

TABLE 1
Descriptive Statistics

Variable        Obs      Mean       SD     Minimum   Maximum

Dep. var.     463,289      0.02     0.15         0         1
TIME          463,289      2.96     0.94      0.00      4.04
PTA           463,289      0.00     0.06         0         1
YEAR          463,289   1979.04    16.65      1950      2006
Geography
DIST          463,289      8.71     0.73      4.09      9.89
BORDER        463,289      0.02     0.13      0.00      1.00
REMOTE        463,289      1.91     3.59      0.00      9.70
Size and relative factor endowments
GDPSUM        463,289     11.16     1.67      4.74     16.63
GDPSIM        463,289     -1.97     1.37     -9.92     -0.69
PCYDIFF       463,289     -1.25     0.89     -4.66      0.00
SQPCYDIFF     463,289     -2.36     2.90    -21.69      0.00
PTA determinants
DISTPTA       463,289      3.44     1.81      0.17     15.21
WPTA          463,289      0.05     0.06      0.00      0.43
NPTA          463,289     10.80     3.97      7.19     18.90
SQNPTA        463,289    132.34   100.16     51.70    357.27
Historical
DIFFYEAR      463,289      0.13     2.17         0       107
CUMDURAT      463,289      5.96   172.33         0    15,389
Political
DPolity2      335,450      8.12     6.49         0        20
DDEMOC        340,726     10.65    21.94         0        98
DAUTOC        340,726     10.06    21.93         0        98
DPARCOMP      340,726      8.06    22.03         0        93
DPOLCOMP      340,726     10.30    22.28         0        98
Multilateralism
WTO Members   165,962    103.98    31.02        34       147
MTN Round     172,974      0.59     0.49         0         1
Dispute 3rd   165,962      0.39     0.49         0         1
Loss 3rd      152,011      0.26     0.44         0         1

TABLE 2
Countries and Numbers of PTAs per Country, 1950-2006

Country                  Number

Afghanistan                 9
Albania                     7
Algeria                    38
Angola                     16
Argentina                  40
Armenia                    11
Australia                   3
Austria                    27
Azerbaijan                 15
Bahrain                     5
Bangladesh                 45
Belarus                    10
Belgium                    23
Benin                      44
Bolivia                    40
Bosnia-Herzegovina          5
Brazil                     42
Bulgaria                   28
Burkina Faso                7
Burundi                    15
Cambodia                    9
Cameroun                   43
Canada                      4
Cape Verde                  0
Central African Rep.        5
Chad                        5
Chile                      68
Colombia                   40
Comoros                    15
Costa Rica                  1
Cote d'Ivoire               7
Croatia                    18
Cuba                        7
Czech Republic             22
Denmark                    25
Djibouti                   15
Dominican Republic          0
Ecuador                    40
Egypt                      70
El Salvador                 2
Equatorial Guinea           5
Estonia                    26
Finland                    29
France                     26
Gabon                       5
Georgia                    11
Germany                    25
Ghana                      38
Greece                     26
Guatemala                   0
Guinea                      0
Guinea-Bissau              44
Haiti                       2
Honduras                    0
Hong Kong                   0
Hungary                    26
India                      41
Indonesia                  41
Iran                       46
Iraq                       38
Ireland                    27
Israel                     30
Italy                      28
Jamaica                     2
Japan                       2
Jordan                     11
Kazakhstan                 15
Kenya                      15
Kuwait                      5
Kyrgyzstan                 15
Laos                       13
Latvia                     29
Lebanon                     0
Liberia                     0
Libya                      49
Lithuania                  29
Macedonia                  12
Madagascar                 15
Malawi                     16
Malaysia                   41
Mali                        7
Mauritania                  0
Mauritius                  16
Mexico                     53
Mongolia                    7
Morocco                    46
Mozambique                 50
Myanmar                    41
Nepal                       4
Netherlands                32
New Zealand                 2
Nicaragua                  38
Niger                       7
Nigeria                    38
Norway                     35
Oman                        5
Pakistan                   50
Panama                      1
Paraguay                   19
People's Rep. of China     13
Peru                       42
Philippines                45
Poland                     31
Portugal                   32
Qatar                       5
Republic of Korea          44
Republic of Moldova        17
Republic of the Congo       5
Romania                    54
Russia                      9
Rwanda                     15
Sao Tome and Principe       0
Saudi Arabia                5
Senegal                     7
Sierra Leone                0
Singapore                  46
Slovakia                   28
Slovenia                   31
Somalia                     0
South Africa                5
Spain                      26
Sri Lanka                  41
Sudan                      49
Sweden                     34
Switzerland                35
Syria                       0
Tadjikistan                15
Tanzania                   50
Thailand                   42
The Gambia                  0
Togo                        7
Trinidad and Tobago        40
Tunisia                    44
Turkey                     31
Turkmenistan               15
Uganda                     15
Ukraine                     9
United Arab Emirates        5
United Kingdom             26
United States               5
Uruguay                    19
Uzbekistan                 15
Venezuela                  40
Vietnam                    48
Yemen                       0
Zambia                     15

TABLE 3
Economic Determinants of Hazard Rates for Country-Pairs (a)

Explanatory              Theory    Spec. 1      Spec. 2      Spec. 3
Variables

Time-to-PTA event          +       2.05 ***     0.61 ***    0.53 ***
                                   (74.56)      (33.53)      (27.75)
Geography
DIST                       -                   -0.15 ***    -0.16 ***
                                                (-8.66)      (-8.64)
BORDER                     +                    0.52 ***    0.53 ***
                                                 (6.99)      (6.69)
REMOTE                     +                    0.01 **       0.004
                                                 (2.07)      (0.99)
Size and relative factor endowments
GDPSUM                     +                    0.13 ***    0.15 ***
                                                (17.12)      (17.60)
GDPSIM                     +                    0.16 ***    0.18 ***
                                                (18.36)      (17.32)
PCYDIFF                    +                    0.26 ***    0.27 ***
                                                 (7.44)      (7.34)
SQPCYDIFF                  -                   -0.08 ***    -0.08 ***
                                                (-7.50)      (-7.64)
PTA determinants
DISTPTA                    -                   -0.17 ***    -0.15 ***
                                                (-13.81)    (-11.78)
WPTA                       +                    5.25 ***    5.66 ***
                                                (42.00)      (42.52)
NPTA                       +                    0.41 ***    0.27 ***
                                                (10.40)      (6.55)
SQNPTA                     -                   -0.004 ***     0.00
                                                (-2.71)      (0.26)
Political and historical
DPolity2                   -                                -0.01 ***
                                                             (-7.51)
DDEMOC                     -

DAUTOC                     -

DPARCOMP                   -

DPOLCOMP                   -

DIFFYEAR                   +                                 -0.002
                                                             (-0.60)
CUMDURAT                   -                                  -0.00
                                                             (-0.62)
Constant                          -10.82 ***   -10.51 ***   -9.33 ***
                                  (-106.25)     (-34.54)    (-28.55)
Pseudo-[R.sup.2]                     0.11         0.27        0.24
Number of observations             463,289      463,289      335,450
Log-likelihood (model)             -44,840      -36,521      -32,939

Explanatory               Spec. 4      Spec. 5     Spec. 6
Variables

Time-to-PTA event         0.54 ***    1.74 ***    1.57 ***
                          (28.90)      (33.14)     (28.01)
Geography
DIST                     -0.16 ***    -0.25 ***   -0.25 ***
                          (-8.79)     (-13.92)    (-13.32)
BORDER                    0.51 ***    0.49 ***    0.49 ***
                           (6.50)      (6.42)      (6.03)
REMOTE                    0.01 **     12.92 ***   11.83 ***
                           (2.29)      (12.15)     (10.22)
Size and relative factor endowments
GDPSUM                    0.10 ***    2.16 ***    2.24 ***
                          (12.14)      (58.86)     (56.70)
GDPSIM                    0.14 ***    0.80 ***    0.81 ***
                          (14.22)      (32.09)     (30.51)
PCYDIFF                   0.28 ***    0.40 ***    0.38 ***
                           (7.92)      (8.24)      (7.43)
SQPCYDIFF                -0.08 ***    -0.14 ***   -0.12 ***
                          (-7.40)      (-9.79)     (-8.25)
PTA determinants
DISTPTA                  -0.17 ***    -0.67 ***   -0.65 ***
                          (-13.84)    (-22.35)    (-20.72)
WPTA                      5.39 ***    14.68 ***   14.91 ***
                          (41.08)      (71.48)     (68.58)
NPTA                      0.34 ***    -0.16 ***   -0.20 ***
                           (8.41)      (-3.30)     (-3.85)
SQNPTA                     -0.002      0.003 *    0.004 **
                          (-1.46)      (1.83)      (2.32)
Political and historical
DPolity2                                          -0.03 ***
                                                  (-11.90)
DDEMOC                   0.032 ***
                           (6.38)
DAUTOC                   -0.03 ***
                          (-6.47)
DPARCOMP                  0.05 ***
                           (9.25)
DPOLCOMP                 -0.06 ***
                          (-7.71)
DIFFYEAR                   -0.001                   0.001
                          (-0.33)                  (0.18)
CUMDURAT                   -0.00                  0.00 ***
                          (-0.67)                  (2.60)
Constant                 -9.21 ***      -1.56       1.75
                          (-28.52)     (-1.44)     (1.54)
Pseudo-[R.sup.2]            0.23        0.38        0.35
Number of observations    340,726      463,289     335,450
Log-likelihood (model)    -34,151      -31.019     -27,978

Explanatory               Spec. 7
Variables

Time-to-PTA event         1.71 ***
                          (30.11)
Geography
DIST                     -0.27 ***
                          (-14.44)
BORDER                    0.44 ***
                           (5.48)
REMOTE                   10.42 ***
                           (9.02)
Size and relative factor endowments
GDPSUM                    2.31 ***
                          (57.89)
GDPSIM                    0.77 ***
                          (28.06)
PCYDIFF                   0.40 ***
                           (7.73)
SQPCYDIFF                -0.11 ***
                          (-7.72)
PTA determinants
DISTPTA                  -0.72 ***
                          (-23.13)
WPTA                     14.40 ***
                          (66.37)
NPTA                     -0.24 ***
                          (-4.72)
SQNPTA                   0.005 ***
                           (2.83)
Political and historical
DPolity2

DDEMOC                    0.07 ***
                          (11.11)
DAUTOC                   -0.06 ***
                          (-8.40)
DPARCOMP                  0.10 ***
                          (14.08)
DPOLCOMP                 -0.12 ***
                          (-14.73)
DIFFYEAR                   0.003
                           (0.46)
CUMDURAT                  0.00 **
                           (2.40)
Constant                    1.66
                           (1.48)
Pseudo-[R.sup.2]            0.36
Number of observations    340,726
Log-likelihood (model)    -28,813

Notes: There are 463,289 observations, 10,518 country-pairs and
1,560 events in specifications (1), (2), and (5); 335,450
observations, 9,920 country-pairs, and 1,511 events in
specifications (3) and (6); and 340,726 observations, 9,925 country-
pairs, and 1,516 events in specifications (4) and (7). The
likelihood value of the constant only model is -50,207. The p value
of the likelihood ratio statistics on the model is 0.

(a) z-statistics in parentheses.

* p < 0.10, ** p <0.05, *** p < 0.01.

TABLE 4
Predicting the Timing of the PTA Events Covered (a)

                                     Specification 1   Specification 2

                                               %                 %
                                             of all            of all
                                              PTA               PTA
Predicted Events                    Number   Events   Number   Events

Base case
  Total number PTA events           1,560      100    1,560      100
    In the same year as the event     209       13      320       21
      occurred
    In the same year as the event     353       23      384       25
      occurred or up to 1 year
      prior to that
    In the same year as the event     431       28      416       27
      occurred or up to 2 years
      prior to that
    In the same year as the event     531       34      541       35
      occurred or up to 3 years
      prior to that
    In the same year as the event     546       35      551       35
      occurred or up to 4 years
      prior to that
    In the same year as the event     678       43      640       41
      occurred or up to 5 years
      prior to that
    In the same year as the event     853       55      752       48
      occurred or up to 10 years
      prior to that
Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100    1,517      100
    In the same year as the event     209       14      337       22
      occurred
    In the same year as the event     353       23      394       26
      occurred or up to 1 year
      prior to that
    In the same year as the event     431       28      424       28
      occurred or up to 2 years
      prior to that
    In the same year as the event     531       35      550       36
      occurred or up to 3 years
      prior to that
    In the same year as the event     546       36      569       38
      occurred or up to 4 years
      prior to that
    In the same year as the event     678       45      647       43
      occurred or up to 5 years
      prior to that
    In the same year as the event     853       56      762       50
      occurred or up to 10 years
      prior to that
Regression only run on data up to 2000 and out-of-sample predictions
for 2001 to 2006
  Total number PTA events             284      100      284      100
    In the same year as the event       9        3      175       62
      occurred
    In the same year as the event      15        5      183       64
      occurred or up to 1 year
      prior to that
    In the same year as the event      42       15      194       68
      occurred or up to 2 years
      prior to that
    In the same year as the event      95       33      207       73
      occurred or up to 3 years
      prior to that
    In the same year as the event     109       38      217       76
      occurred or up to 4 years
      prior to that
    In the same year as the event     112       39      218       77
      occurred or up to 5 years
      prior to that
Regression only run on data up to 1989 and out-of-sample predictions
for 1990 to 2006
  Total number PTA events           1,037      100    1,037      100
    In the same year as the event     144       14      231       22
      occurred
    In the same year as the event     222       21      263       25
      occurred or up to 1 year
      prior to that
    In the same year as the event     322       31      316       30
      occurred or up to 2 years
      prior to that
    In the same year as the event     337       32      331       32
      occurred or up to 3 years
      prior to that
    In the same year as the event     469       45      346       33
      occurred or up to 4 years
      prior to that
    In the same year as the event     474       46      346       33
      occurred or up to 5 years
      prior to that
    In the same year as the event     653       63      346       33
      occurred or up to 10 years
      prior to that

                                     Specification 3   Specification 4

                                               %                 %
                                             of all            of all
                                              PTA               PTA
Predicted Events                    Number   Events   Number   Events

Base case
  Total number PTA events           1,560      100    1,560      100
    In the same year as the event     402       26      379       24
      occurred
    In the same year as the event     468       30      434       28
      occurred or up to 1 year
      prior to that
    In the same year as the event     517       33      477       31
      occurred or up to 2 years
      prior to that
    In the same year as the event     635       41      600       38
      occurred or up to 3 years
      prior to that
    In the same year as the event     646       41      616       39
      occurred or up to 4 years
      prior to that
    In the same year as the event     710       46      679       44
      occurred or up to 5 years
      prior to that
    In the same year as the event     891       57      857       55
      occurred or up to 10 years
      prior to that
Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100    1,517      100
    In the same year as the event     408       27      373       25
      occurred
    In the same year as the event     477       31      435       29
      occurred or up to 1 year
      prior to that
    In the same year as the event     526       35      478       32
      occurred or up to 2 years
      prior to that
    In the same year as the event     643       42      607       40
      occurred or up to 3 years
      prior to that
    In the same year as the event     655       43      625       41
      occurred or up to 4 years
      prior to that
    In the same year as the event     731       48      692       46
      occurred or up to 5 years
      prior to that
    In the same year as the event     918       61      871       57
      occurred or up to 10 years
      prior to that
Regression only run on data up to 2000 and out-of-sample predictions
for 2001 to 2006
  Total number PTA events             284      100      284      100
    In the same year as the event     188       66      178       63
      occurred
    In the same year as the event     196       69      185       65
      occurred or up to 1 year
      prior to that
    In the same year as the event     208       73      198       70
      occurred or up to 2 years
      prior to that
    In the same year as the event     222       78      217       76
      occurred or up to 3 years
      prior to that
    In the same year as the event     232       82      227       80
      occurred or up to 4 years
      prior to that
    In the same year as the event     232       82      228       80
      occurred or up to 5 years
      prior to that
Regression only run on data up to 1989 and out-of-sample predictions
for 1990 to 2006
  Total number PTA events           1,037      100    1.037      100
    In the same year as the event     244       24      251       24
      occurred
    In the same year as the event     277       27      274       26
      occurred or up to 1 year
      prior to that
    In the same year as the event     333       32      328       32
      occurred or up to 2 years
      prior to that
    In the same year as the event     349       34      342       33
      occurred or up to 3 years
      prior to that
    In the same year as the event     366       35      355       34
      occurred or up to 4 years
      prior to that
    In the same year as the event     366       35      355       34
      occurred or up to 5 years
      prior to that
    In the same year as the event     366       35      355       34
      occurred or up to 10 years
      prior to that

                                     Specification 5   Specification 6

                                               %                 %
                                             of all            of all
                                              PTA               PTA
Predicted Events                    Number   Events   Number   Events

Base case
  Total number PTA events           1,560      100    1,560      100
    In the same year as the event     551       35      616       39
      occurred
    In the same year as the event     651       42      713       46
      occurred or up to 1 year
      prior to that
    In the same year as the event     744       48      818       52
      occurred or up to 2 years
      prior to that
    In the same year as the event     840       54      901       58
      occurred or up to 3 years
      prior to that
    In the same year as the event     900       58      950       61
      occurred or up to 4 years
      prior to that
    In the same year as the event     971       62      991       64
      occurred or up to 5 years
      prior to that
    In the same year as the event   1,121       72    1,084       69
      occurred or up to 10 years
      prior to that
Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100    1,517      100
    In the same year as the event     742       49      769       51
      occurred
    In the same year as the event     855       56      883       58
      occurred or up to 1 year
      prior to that
    In the same year as the event     916       60      940       62
      occurred or up to 2 years
      prior to that
    In the same year as the event     995       66    1,033       68
      occurred or up to 3 years
      prior to that
    In the same year as the event   1,021       67    1.067       70
      occurred or up to 4 years
      prior to that
    In the same year as the event   1,062       70    1.111       73
      occurred or up to 5 years
      prior to that
    In the same year as the event   1, 102      73    1, 156      76
      occurred or up to 10 years
      prior to that
Regression only run on data up to 2000 and out-of-sample predictions
for 2001 to 2006
  Total number PTA events             284      100      284      100
    In the same year as the event      97       34      122       43
      occurred
    In the same year as the event      98       35      123       43
      occurred or up to 1 year
      prior to that
    In the same year as the event     106       37      131       46
      occurred or up to 2 years
      prior to that
    In the same year as the event     107       38      132       46
      occurred or up to 3 years
      prior to that
    In the same year as the event     108       38      133       47
      occurred or up to 4 years
      prior to that
    In the same year as the event     108       38      133       47
      occurred or up to 5 years
      prior to that
Regression only run on data up to 1989 and out-of-sample predictions
for 1990 to 2006
  Total number PTA events           1,037      100    1,037      100
    In the same year as the event     282       27      314       30
      occurred
    In the same year as the event     317       31      343       33
      occurred or up to 1 year
      prior to that
    In the same year as the event     337       32      361       35
      occurred or up to 2 years
      prior to that
    In the same year as the event     338       33      361       35
      occurred or up to 3 years
      prior to that
    In the same year as the event     338       33      361       35
      occurred or up to 4 years
      prior to that
    In the same year as the event     338       33      361       35
      occurred or up to 5 years
      prior to that
    In the same year as the event     338       33      361       35
      occurred or up to 10 years
      prior to that

                                     Specification 7

                                               %
                                             of all
                                              PTA
Predicted Events                    Number   Events

Base case
  Total number PTA events           1,560      100
    In the same year as the event     601       39
      occurred
    In the same year as the event     690       44
      occurred or up to 1 year
      prior to that
    In the same year as the event     783       50
      occurred or up to 2 years
      prior to that
    In the same year as the event     868       56
      occurred or up to 3 years
      prior to that
    In the same year as the event     924       59
      occurred or up to 4 years
      prior to that
    In the same year as the event     968       62
      occurred or up to 5 years
      prior to that
    In the same year as the event   1,076       69
      occurred or up to 10 years
      prior to that
Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100
    In the same year as the event     731       48
      occurred
    In the same year as the event     843       56
      occurred or up to 1 year
      prior to that
    In the same year as the event     912       60
      occurred or up to 2 years
      prior to that
    In the same year as the event     997       66
      occurred or up to 3 years
      prior to that
    In the same year as the event   1,060       70
      occurred or up to 4 years
      prior to that
    In the same year as the event   1, 106      73
      occurred or up to 5 years
      prior to that
    In the same year as the event   1. 168      77
      occurred or up to 10 years
      prior to that
Regression only run on data up to 2000 and out-of-sample predictions
for 2001 to 2006
  Total number PTA events             284      100
    In the same year as the event     131       46
      occurred
    In the same year as the event     132       46
      occurred or up to 1 year
      prior to that
    In the same year as the event     140       49
      occurred or up to 2 years
      prior to that
    In the same year as the event     141       50
      occurred or up to 3 years
      prior to that
    In the same year as the event     142       50
      occurred or up to 4 years
      prior to that
    In the same year as the event     142       50
      occurred or up to 5 years
      prior to that
Regression only run on data up to 1989 and out-of-sample predictions
for 1990 to 2006
  Total number PTA events           1,037      100
    In the same year as the event     302       29
      occurred
    In the same year as the event     331       32
      occurred or up to 1 year
      prior to that
    In the same year as the event     347       33
      occurred or up to 2 years
      prior to that
    In the same year as the event     347       33
      occurred or up to 3 years
      prior to that
    In the same year as the event     347       33
      occurred or up to 4 years
      prior to that
    In the same year as the event     347       33
      occurred or up to 5 years
      prior to that
    In the same year as the event     347       33
      occurred or up to 10 years
      prior to that

(a) Underlying cut-off values minimize a quadratic loss function of
predicting binary events by the complementary log-log model. For the
base case, the cut-off for specification 1 is 0.038, for
specifications 2, 3, and 4 it is 0.009, for specification 5 it is
0.023, for specifications 6 it is 0.035, and for specification 7 it
is 0.033. For the predictions using data from 1970 onwards only, the
cut-off for specification 1 is 0.039, the cut-off for specification
2 is 0.011, for specifications 3 and 4 it is 0.01, for specification
5 it is 0.054, for specification 6 it is 0.056, and for
specification 7 it is 0.051. For the predictions using data up to
2000, the cut-off for specification 1 is 0.006, for specifications 2
and 3 it is 0.011, for specification 4 it is 0.009, for
specification 5 it is 0.09, for specification 6 it is 0.08, and for
specification 7 it is 0.086. For the predictions using data up to
1989, the cut-off for specification 1 is 0.002, for specifications 2
and 3 it is 0.014, for specification 4 it is 0.016, for
specification 5 it is 0.041, for specification 6 it is 0.056, and
for specification 7 it is 0.063.

TABLE 5
Multilateralism Determinants of Hazard Rates for Country-Pairs (a)

Explanatory variables    Theory   Spec. 3A      Spec. 4A

Time-to-PTA event          +        -0.08 ***     -0.09 ***
                                   (-2.70)       (-2.84)
Geography
DIST                       -        -0.06 ***     -0.07 ***
                                   (-2.60)       (-2.73)
BORDER                     +         0.64 ***      0.62 ***
                                    (5.51)        (5.42)
REMOTE                     +         0.03 ***      0.03 ***
                                    (5.30)        (5.66)
Size and relative factor endowments
GDPSUM                     +         0.06 ***      0.05 ***
                                    (4.93)        (3.79)
GDPSIM                     +         0.09 ***      0.08 ***
                                    (6.34)        (5.47)
PCYDIFF                    +         0.17 ***      0.20 ***
                                    (3.71)        (4.41)
SQPCYDIFF                  -        -0.05 ***     -0.07 ***
                                   (-3.41)       (-4.97)
PTA determinants
DISTPTA                    -         0.14 ***      0.15 ***
                                   (10.71)       (11.03)
WPTA                       +         2.68 ***      2.64 ***
                                   (15.95)       (15.84)
NPTA                       +        -8.00 ***     -8.10 ***
                                  (-56.04)      (-56.80)
SQNPTA                     -         0.23 ***      0.23 ***
                                   (52.47)       (53.25)
Political and historical
DPolity2                   -        -0.003
                                   (-1.11)
DDEMOC                     -                      -0.01 *
                                                 (-1.88)
DAUTOC                     -                       0.04 ***
                                                  (4.70)
DPARCOMP                   -                       0.006
                                                  (0.78)
DPOLCOMP                   -                      -0.03 ***
                                                 (-3.80)
DIFFYEAR                   +        -0.008 *      -0.007 *
                                   (-1.78)       (-1.72)
CUMDURAT                   -        -0.00 *       -0.00 *
                                   (-1.75)       (-1.75)
Multilateralism
WTO Members                +         0.43 ***      0.44 ***
                                   (70.78)       (71.38)
MTN Round                  -        -1.14 ***     -1.17 ***
                                  (-11.75)      (-12.11)
Dispute 3rd Party          +         0.19 ***      0.21 ***
                                    (5.51)        (6.30)
Lost 3rd Party             +        -0.17 ***     -0.18 ***
                                   (-4.87)       (-5.11)
Constant                             7.58 ***      8.01 ***
                                   (14.68)       (15.57)
Pseudo-[R.sup.2]                     0.44          0.44
Number of observations            141,096       141,523
Log-likelihood (model)            -14,730       -14,816

Explanatory variables    Spec. 6A      Spec. 7A

Time-to-PTA event          -1.30 ***     -1.26 ***
                          (-9.19)       (-8.99)
Geography
DIST                       -0.11 ***     -0.11 ***
                          (-4.19)       (-4.23)
BORDER                      0.65 ***      0.60 ***
                           (5.51)        (5.10)
REMOTE                      3.38 *        3.78 **
                           (2.21)        (2.48)
Size and relative factor endowments
GDPSUM                      0.93 ***      0.84 ***
                          (13.57)       (12.05)
GDPSIM                      0.64 ***      0.55 ***
                          (11.28)        (9.66)
PCYDIFF                     0.15 **       0.18 ***
                           (2.14)        (2.67)
SQPCYDIFF                  -0.02         -0.04 **
                          (-0.89)       (-1.98)
PTA determinants
DISTPTA                     0.17 ***      0.19 ***
                           (4.35)        (4.99)
WPTA                       10.33 ***     10.24 ***
                          (32.99)       (32.86)
NPTA                       -5.85 ***     -5.94 ***
                         (-40.03)      (-40.60)
SQNPTA                      0.14 ***      0.15 ***
                          (31.84)       (32.37)
Political and historical
DPolity2                   -0.02 ***
                          (-5.42)
DDEMOC                                    0.003
                                         (0.37)
DAUTOC                                   -0.003
                                        (-0.26)
DPARCOMP                                  0.05 ***
                                         (5.89)
DPOLCOMP                                 -0.06 ***
                                        (-5.69)
DIFFYEAR                    0.002         0.003
                           (0.15)        (0.24)
CUMDURAT                   -0.00         -0.00
                          (-0.11)       (-0.05)
Multilateralism
WTO Members                 0.43 ***      0.43 ***
                          (65.86)       (66.27)
MTN Round                  -0.72 ***     -0.75 ***
                          (-7.28)       (-7.64)
Dispute 3rd Party           0.15 ***      0.15 ***
                           (3.71)        (3.82)
Lost 3rd Party             -0.19 ***     -0.21 ***
                          (-4.11)       (-4.70)
Constant                   62.57 ***     62.45 ***
                          (40.78)       (40.64)
Pseudo-[R.sup.2]            0.49          0.49
Number of observations   141,096       141,523
Log-likelihood (model)   -13,427       -13,536

(a) z-statistics in parentheses. There are 141,096 observations,
6,625 country-pairs and 894 events in specification (3 A) and (6A),
and 141,523 observations, 6,625 country-pairs and 894 events in
specifications (4A) and (7A).

* p< 0.10, ** p <0.05, *** p < 0.01.

TABLE 6
Predicting the Timing of the PTA Events Covered with
Multilateralism (a)

                                    Specification 3A  Specification 4A

                                               %                 %
                                             of all            of all
                                              PTA               PTA
Predicted Events                    Number   Events   Number   Events

Base case
  Total number PTA events           1,560      100    1,560      100
    In the same year as the event     702       45      706       45
      occurred
    In the same year as the event     715       46      720       46
      occurred or up to 1 year
      prior to that
    In the same year as the event     757       49      748       48
      occurred or up to 2 years
      prior to that
    In the same year as the event     802       51      800       51
      occurred or up to 3 years
      prior to that
    In the same year as the event     823       53      807       52
      occurred or up to 4 years
      prior to that
    In the same year as the event     901       58      902       58
      occurred or up to 5 years
      prior to that
    In the same year as the event     995       64    1,022       66
      occurred or up to 10 years
      prior to that

Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100    1,517      100
    In the same year as the           746       49      746       49
      event occurred
    In the same year as the           761       50      759       50
      event occurred or up to 1
      year prior to that
    In the same year as the           781       51      779       51
      event occurred or up to 2
      years prior to that
    In the same year as the           825       54      823       54
      event occurred or up to 3
      years prior to that
    In the same year as the           857       56      855       56
      event occurred or up to 4
      years prior to that
    In the same year as the           905       60      903       60
      event occurred or up to 5
      years prior to that
    In the same year as the           993       65      991       65
      event occurred or up to 10
      years prior to that

Regression only run on data up to 2000 and out-of-sample
    predictions for 2001 to 2006
  Total number PTA events             284      100      284      100
    In the same year as the           153       54       45       16
      event occurred
    In the same year as the           171       60       60       21
      event occurred or up to 1
      year prior to that
    In the same year as the           213       75       96       34
      event occurred or up to 2
      years prior to that
    In the same year as the           257       90      276       97
      event occurred or up to 3
      years prior to that
    In the same year as the           258       91      279       98
      event occurred or up to 4
      years prior to that
    In the same year as the           260       92      282       99
      event occurred or up to 5
      years prior to that

Regression only run on data up to 1989 and out-of-sample
    predictions for 1990 to 2006
  Total number PTA events           1,037      100    1,037      100
    In the same year as the           498       48      482       46
      event occurred
    In the same year as the           512       49      504       49
      event occurred or up to 1
      year prior to that
    In the same year as the           538       52      532       51
      event occurred or up to 2
      years prior to that
    In the same year as the           539       52      573       55
      event occurred or up to 3
      years prior to that
    In the same year as the           539       52      579       56
      event occurred or up to 4
      years prior to that
    In the same year as the           539       52      628       61
      event occurred or up to 5
      years prior to that
    In the same year as the           539       52      731       70
      event occurred or up to 10
      years prior to that

                                    Specification 6A   Specification 7A

                                               %                 %
                                             of all            of all
                                              PTA               PTA
Predicted Events                    Number   Events   Number   Events

Base case
  Total number PTA events           1,560      100    1,560      100
    In the same year as the event     856       55      845       54
      occurred
    In the same year as the event     880       56      870       56
      occurred or up to 1 year
      prior to that
    In the same year as the event     932       60      926       59
      occurred or up to 2 years
      prior to that
    In the same year as the event     953       61      965       62
      occurred or up to 3 years
      prior to that
    In the same year as the event     959       61      981       63
      occurred or up to 4 years
      prior to that
    In the same year as the event     975       63      999       64
      occurred or up to 5 years
      prior to that
    In the same year as the event     999       64    1,047       67
      occurred or up to 10 years
      prior to that

Predictions using data from 1970 onwards only
  Total number PTA events           1,517      100    1,517      100
    In the same year as the           843       56      838       55
      event occurred
    In the same year as the           872       57      865       57
      event occurred or up to 1
      year prior to that
    In the same year as the           887       58      879       58
      event occurred or up to 2
      years prior to that
    In the same year as the           948       62      937       62
      event occurred or up to 3
      years prior to that
    In the same year as the         1,068       70    1,065       70
      event occurred or up to 4
      years prior to that
    In the same year as the         1,092       72    1,086       72
      event occurred or up to 5
      years prior to that
    In the same year as the         1,129       74    1,124       74
      event occurred or up to 10
      years prior to that

Regression only run on data up to 2000 and out-of-sample
    predictions for 2001 to 2006
  Total number PTA events             284      100      284      100
    In the same year as the            87       31       58       20
      event occurred
    In the same year as the            90       32       64       23
      event occurred or up to 1
      year prior to that
    In the same year as the           100       35       88       31
      event occurred or up to 2
      years prior to that
    In the same year as the           102       36      121       43
      event occurred or up to 3
      years prior to that
    In the same year as the           103       36      122       43
      event occurred or up to 4
      years prior to that
    In the same year as the           103       36      122       43
      event occurred or up to 5
      years prior to that

Regression only run on data up to 1989 and out-of-sample
    predictions for 1990 to 2006
  Total number PTA events           1,037      100    1,037      100
    In the same year as the           509       49      520       50
      event occurred
    In the same year as the           526       51      554       53
      event occurred or up to 1
      year prior to that
    In the same year as the           529       51      583       56
      event occurred or up to 2
      years prior to that
    In the same year as the           531       51      624       60
      event occurred or up to 3
      years prior to that
    In the same year as the           531       51      667       64
      event occurred or up to 4
      years prior to that
    In the same year as the           531       51      716       69
      event occurred or up to 5
      years prior to that
    In the same year as the           531       51      780       75
      event occurred or up to 10
      years prior to that

(a) Underlying cut-off values minimize a quadratic loss function of
predicting binary events by the complementary log-log model. For
the base case, the cut-off value for specification 3A is 0.002, for
specification 4A it is 0.001, for specification 6A it is 0.051, and
for specification 7A it is 0.033. For the predictions using data
from 1970 onwards only, the cut-off for specifications 3A and 4A is
0.001, and for specifications 6A and 7A it is 0.01. For the
predictions using data up to 2000, the cut-off for specification 3A
is 0.016, for specification 4A it is 0.001, for specification 6A it
is 0.097, and for specification 7A it is 0.015. For the predictions
using data up to 1989, the cut-off for specification 3A is 0.013,
for specification 4A it is 0.001, for specification 6A it is 0.066,
and for specification 7A it is 0.004.

TABLE 7
Prediction of CUSFTA, NAFTA, and EU
Formation and Enlargements

                                                Actual
Country              Predictions               Formation

CUSFTA
Canada-United        1/1 from 1976 to 1989       1989
  States
NAFTA
Canada-United        1/2 from 1978 to 1993
  States-Mexico      2/2 in 1994                 1994
EU
EU foundation        4/10 from 1950 to 1957
                     6/10 in 1958                1958
First EU             3/15 from 1950 to 1972
  enlargement        5/15 in 1973                1973
Second EU            1/8 from 1950 to 1977
  enlargement        8/8 from 1978 onwards       1981
Third EU             2/18 from 1950 to 1960
  enlargement        4/18 from 1961 to 1972
                     5/18 from 1973 to 1977
                     18/18 from 1978 onwards     1986
Fourth EU            3/33 from 1950 to 1959
  enlargement        4/33 in 1960
                     10/33 in 1961
                     13/33 from 1962 to 1975
                     14/33 in 1976
                     15/33 in 1977
                     30/33 in 1978
                     31/33 in 1979
                     32/33 in 1980
                     31/33 in 1981
                     32/33 in 1982
                     33/33 from 1983 onwards     1995
Fifth EU             54/112 in 1990
  enlargement
Note:                108/112 in 1991
We do not have       103/112 in 1992
  data for Cyprus    105/112 in 1993
  and Malta and      112/112 from 1994
  many data are        onwards
  missing before                                 2004
  1990.
Sixth EU             26/36 in 1990
  enlargement
Note:                35/36 in 1991
Data are missing     27/36 in 1992
  for Czech
Republic, Hungary,   32/36 in 1993
  Poland, and
Slovakia             36/36 from 1994 onwards     2007
Seventh EU           23/23 from 1990 onwards     2013
  enlargement

TABLE 8
Ten Highest Predictions for 2007-2013

                               Predictions
Country Pair     Probability    for Year

China-Pakistan      0.840         2011
Egypt-South         0.754         2011
  Africa
Australia-          0.724         2011
  Egypt
Libya-Chad          0.705         2009
Italy-South         0.701         2011
  Korea
Pakistan-Saudi      0.688         2011
Arabia
Spain-South         0.673         2011
  Korea
Italy-Pakistan      0.657         2010
United Arab         0.645         2011
Emirates-
  Pakistan
Egypt-Gabon         0.644         2011

Country Pair          Actual                     Details

China-Pakistan   2007               China-Pakistan FTA implemented
Egypt-South      Proposed in 2008   Oct 2008 and June 2011 Summits;
  Africa                            Proposed African Free Trade Zone
                                    (AFTZ) expected to be operational
                                    in 2018
Australia-       None               No agreement yet under
  Egypt                             consideration
Libya-Chad       Proposed in 1998   Community of Sahel-Saharan States
                                    (CEN-SAD); Founding members;
                                    Goal is to create an economic
                                    union; Not yet an effective free
                                    trade agreement
Italy-South      2011               EU-South Korea FTA implemented
  Korea
Pakistan-Saudi   None               No agreement yet under
Arabia                              consideration
Spain-South      2011               EU-South Korea FTA implemented
  Korea
Italy-Pakistan   Proposed in 2009   EU-Pakistan 5-year Engagement
                                    Plan instituted in 2009 to develop
                                    GSP treatment into a FTA
United Arab      None               No agreement yet under
Emirates-                           consideration
  Pakistan
Egypt-Gabon      Proposed in 2012   Proposed extension of proposed
                                    AFTZ to include Economic
                                    Community of Central African
                                    States (ECCAS)