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Estimating Elasticities for U.S. Trade in Services

Jaime Marquez*

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. References in publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors. Recent IFDPs are available on the Web at http://www.federalreserve.gov/pubs/ifdp/. This paper can be downloaded without charge from the Social Science Research Network electronic library at http://www.ssrn.com/.

Abstract:

Explanations of the persistent deficit in U.S. net exports of goods rest on macroeconomic developments and an asymmetry in elasticities: the income elasticity for imports being larger than the income elasticity for exports. Such macroeconomic developments are not applicable to the equally persistent surplus in U.S. net exports of services unless the income elasticities for services exhibit the reversed asymmetry. There have been surprisingly few attempts to demonstrate the existence of this reversed asymmetry, a task that I undertake here. Specifically, I estimate income and price elasticities for U.S. trade in services and evaluate the importance of simultaneity and aggregation biases. The analysis reveals two findings. First, the income elasticity for U.S. exports of services is significantly greater than the income elasticity for U.S. imports of services. Second, disaggregation is the most important aspect of econometric design in this area.

Keywords: U.S. service trade, external imbalances, income elasticity, price elasticity, general-to-specific, automated specification.

JEL classification: C52, C63, C87, F17, F32


1  Introduction and Conclusion

Explanations of the persistent deficit in U.S. net exports of goods rest on macroeconomic developments and an asymmetry in elasticities: the income elasticity for imports being larger than the income elasticity for exports.1 Those explanations cannot, however, account for the equally persistent surplus in net exports of services unless the elasticities for service trade exhibit the reversed asymmetry: the income elasticity for exports being larger than the income elasticity for imports. This reversed asymmetry is central to reconciling macroeconomic developments with the divergence of U.S. external balances (figure 1) but there have been surprisingly few attempts to document its existence.2 Finding out whether this reversed asymmetry is supported by the data is what I do here.

Interest in estimating elasticities for trade in services extends beyond questions of external imbalances. Indeed, services and goods differ in nature and thus the available elasticity estimates for trade in goods need not be relevant for understanding the behavior of trade in services.3 For example, the production and delivery of services coincide and thus previous work characterizing dynamic adjustments for trade in goods need not extend to trade in services. Further, the scope for differentiation in services is greater than in goods (e.g., insurance policies versus oil), a feature that enhances the scope for price discrimination in services. Econometrically, differentiation means that data disaggregation and price endogeneity are relevant for estimating elasticities for trade in services.

Accordingly, I estimate income and price elasticities for exports and imports of four categories: travel, fares, transportation, and other private services. To assess aggregation biases, I compare these elasticities to the ones associated with aggregate services. I assess simultaneity biases by comparing estimates from three estimation methods: ordinary least squares, instrumental variables, and full information maximum likelihood. For modeling dynamic adjustments, I implement a General-to-Specific strategy based on the automated search algorithm developed by Krolzig and Hendry (2001). A key feature of their algorithm is that it adjusts the significance levels of statistical tests to recognize the joint nature of model specification and parameter estimation.

Two conclusions emerge from this investigation. First, the income elasticity for U.S. exports of services is significantly greater than the income elasticity for U.S. imports of services. This reversed asymmetry means that one can reconcile macroeconomic developments with the divergence in U.S. external balances. Second, disaggregation is central to this reversed asymmetry: No disaggregation means no reversed elasticity asymmetry, regardless of estimation method and specification technique.


2  External Balances and Trade Elasticities

The framework currently used to explain external imbalances assumes that foreign and domestic products are imperfect substitutes and that income and real exchange rates are the proximate determinants of international trade. With these assumptions, net exports of goods, NXg, are expressed as

\begin{displaymath} NX_t^g =X_t^g (Y_t^\ast ,Q_t )-M_t^g (Y_t ,Q_t ) \end{displaymath} (1)

where X$ ^{g }$ denotes exports of goods; Y* denotes foreign real income; Q denotes the real effective value of the dollar; Mg denotes imports of goods; and Y denotes U.S. real income. To quantify the importance of these variables on net exports, the change of NX$ _{t}^{g }$ is expressed in terms of trade elasticities and growth rates:

\begin{displaymath} dNX_t^g =X_{t-1}^g \cdot (\eta _x^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t^\ast +\varepsilon _x^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Q}} _t )-M_{t-1}^g \cdot (\eta _m^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t +\varepsilon _m^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Q}} _t ) \end{displaymath} (2)

where the symbol 'hat' stands for growth rate, \begin{displaymath} \eta _x^g \end{displaymath} is the income elasticity for exports, \begin{displaymath} \varepsilon _x^g \end{displaymath} is the price elasticity of exports, \begin{displaymath} \eta _m^g \end{displaymath} is the income elasticity for imports, and \begin{displaymath} \varepsilon _m^g \end{displaymath} is the price elasticity for imports.

One can simplify equation (2) further by recognizing two properties of the data. First, since 1970, the average rate of change of the real effective value of the dollar has been close to zero (figure 1) and thus I set \begin{displaymath} \hat {Q}_t =0 \end{displaymath}. Second, prior to 1976, net exports of goods were balanced meaning that \begin{displaymath} X_{t-1}^g =M_{t-1}^g \end{displaymath} . 4 With these properties, equation (2) becomes

\begin{displaymath} dNX_t^g =X_{t-1}^g \cdot \left[ {\left( {\eta _x^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t^\ast -\eta _m^g \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t } \right)} \right] \end{displaymath} (3)

Equation (3) has implications for the pattern of income elasticities. Specifically, as figure 1 shows, growth in the rest of the world has been, on average, quite close to that of the United States.5 Thus reconciling \begin{displaymath} \hat {Y}_t^\ast \approx \hat {Y}_t \end{displaymath} with dNXg < 0 implies that \begin{displaymath} \eta _x^g \end{displaymath} < \begin{displaymath} \eta _m^g \end{displaymath}, an asymmetry with ample empirical support.6

Though coherent, this framework cannot account for the persistent surplus in net exports of services. Indeed, if one uses real income and real exchange rates to explain services, then the change in net exports of services, \begin{displaymath} dNX^s>0 \end{displaymath}, can be written as

\begin{displaymath} dNX_t^s =X_{t-1}^s \cdot \left[ {\left( {\eta _x \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t^\ast -\eta _m \cdot \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t } \right)} \right] \end{displaymath} (4)

where Xs denotes exports of services; ηx is the income elasticity for exports of services; and ηm is the income elasticity for imports of services. Thus reconciling \begin{displaymath} \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t^\ast \approx \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\frown$}}\over {Y}} _t \end{displaymath} with dNXs > 0 implies that $ \eta_{x }>\eta_{m}$. The question I address is whether the data support this reversed asymmetry.


3  Econometric Design

The empirical formulation rests on the imperfect substitute model in which movements in the logarithm of trade are explained in terms of movements in the logarithms of income and relative prices.7 To allow for delayed responses, induced perhaps by service contracts, I use an autoregressive distributed lag formulation.

3.1  Specification

The specification for exports of the ith type of services is

\begin{displaymath} (1-\theta _{1i} (L))\ln x_{it} =\theta _{0i} +\theta _{2i} (L)\ln \left( {\frac{P_{xit} }{P_t^\ast }} \right)+\theta _{3i} (L)\ln Y_t^\ast +u_{xit} ,u_{xit} \sim IN(0,\sigma _{xi}^2 ) \end{displaymath} (5)

where xi denotes real exports of services of the ith category; Pxi denotes the dollar export price of the ith category of services; P* denotes the foreign price deflator expressed in U.S. dollars; \begin{displaymath} \theta _{ki} (L)=\sum\limits_{j=0}^{\ell _x } {\theta _{kij} L^j} \end{displaymath} (k > 0) where L is the lag operator. The long-run income elasticity is

\begin{displaymath} \eta _{xi} =\frac{\theta _{3i} (1)}{1-\theta _{1i} (1)}>0 \end{displaymath} (6)

and the long-run price elasticity is \begin{displaymath} \varepsilon _{xi} =\frac{\theta _{2i} (1)}{1-\theta _{1i} (1)}<0 \end{displaymath} .

Having estimated the long-run elasticities across export categories, I aggregate them into an elasticity for aggregate exports. For the income elasticity, the aggregate is

\begin{displaymath} \eta _{xt}^d =\sum\limits_i {\mu _{it} \cdot \eta _{xi} } \end{displaymath} (7)

where ηit is the export share of the ith type of service exports and the superscript 'd ' denotes an aggregate elasticity based on disaggregated equations; I construct a comparable aggregate for the price elasticities.

As an alternative to equation (7), I estimate elasticities for aggregate exports as such:

\begin{displaymath} (1-\theta _1 (L))\ln x_t =\theta _0 +\theta _2 (L)\ln \left( {\frac{P_{xt} }{P_t^\ast }} \right)+\theta _3 (L)\ln Y_t^\ast +u_{xt} ,u_{xt} \sim IN(0,\sigma _x^2 ) \end{displaymath} (8)

where x denotes aggregate exports of services in real terms, Pxt denotes the dollar export price of aggregate services, and \begin{displaymath} \theta _i (L)=\sum\limits_{j=0}^{\ell _x } {\theta _{ij} L^j} ,(i>0) \end{displaymath}. The long-run income elasticity is

\begin{displaymath} \eta _x^a =\frac{\theta _3 (1)}{1-\theta _1 (1)}>0 \end{displaymath} (9)

and the associated long-run price elasticity is \begin{displaymath} \varepsilon _x^a =\frac{\theta _{2i} (1)}{1-\theta _{1i} (1)}<0 \end{displaymath} ; the superscript 'a ' denotes an aggregate elasticity based on an aggregate equation. With two alternative estimates of the aggregate income elasticity, I assess the importance of aggregation bias by testing whether \begin{displaymath} \eta _x^a \end{displaymath} is significantly different from \begin{displaymath} \eta _x^d \end{displaymath} ; I apply the same test to the price elasticities.

The specification for imports of the ith type of services is

\begin{displaymath} (1-\phi _{1i} (L))\ln m_{it} =\phi _{0i} +\phi _{2i} (L)\ln \left( {\frac{P_{mit} }{P_t }} \right)+\phi _{3i} (L)\ln Y_t +u_{mit} ,u_{mit} \sim IN(0,\sigma _{mi}^2 ) \end{displaymath} (10)

where mi denotes real imports of the ith type of service; Pmi denotes the dollar import price of services; P denotes the U.S. GDP deflator; \begin{displaymath} \phi _{ki} (L)=\sum\limits_{j=0}^{\ell _m } {\phi _{kij} L^j} (k>0) \end{displaymath}. The long-run income elasticity is

\begin{displaymath} \eta _{mi} =\frac{\phi _{3i} (1)}{1-\phi _{1i} (1)}>0 \end{displaymath} (11)

and the long-run price elasticity is \begin{displaymath} \varepsilon _{mi} =\frac{\phi _{2i} (1)}{1-\phi _{1i} (1)}<0 \end{displaymath} . The aggregate of the income elasticities is

\begin{displaymath} \eta _{mt}^d =\sum\limits_i {\omega _{it} \cdot \eta _{mi} } \end{displaymath} (12)

where ωit is the import share of the ith type of service imports; I construct a comparable aggregate for the price elasticities.

The corresponding specification for aggregate imports of services is

\begin{displaymath} (1-\phi _1 (L))\ln m_t =\phi _0 +\phi _2 (L)\ln \left( {\frac{P_{mt} }{P_t }} \right)+\phi _3 (L)\ln Y_t +u_{mt} ,u_{mt} \sim IN(0,\sigma _m^2 ) \end{displaymath} (13)

where m represents aggregate imports of services in real terms; Pmt denotes the dollar import price of aggregate services; and φi(L) is a polynomial in the lag operator L. The long-run income elasticity of aggregate imports is

\begin{displaymath} \eta _m^a =\frac{\phi _3 (1)}{1-\phi _1 (1)}>0 \end{displaymath} (14)

and the long-run price elasticity is \begin{displaymath} \varepsilon _m^a =\frac{\phi _2 (1)}{1-\phi _2 (1)}<0 \end{displaymath} . Again, I assess the magnitude of the aggregation bias in the estimated income elasticity by testing whether \begin{displaymath} \eta _m^a \end{displaymath} is significantly different from \begin{displaymath} \eta _{mt}^d \end{displaymath} ; I apply the same test to the aggregate of price elasticities.

3.2  Estimation: Automated specification

The automated-specification algorithm developed by Hendry and Krolzig (2001) offers three advantages relative to implementing a General-to-Specific strategy interactively.8 First, their algorithm considers all of the statistically valid specifications. Second, the algorithm adjusts the significance levels for statistical tests to recognize the joint nature of model specification and parameter estimation. Finally, each step in the process of automated search can be replicated at once.

The algorithm combines least squares with a selection strategy that is implemented in four stages:9

  1. Estimate the parameters of a general formulation -- equation (5) for example -- and test for congruency (white-noise residuals).


  2. Implement multiple "simplification paths" simultaneously. One simplification path could get started by excluding the least significant variable whereas another simplification path could get initiated by excluding a block of variables that are jointly insignificant.


  3. Test whether the specification from a simplification path is congruent. If it is, then implement another round of simplifications and re-test for congruency; continue this process until the specification violates congruency. In that case, the algorithm selects the immediately prior specification and labels it Final model.


  4. Collect the Final models from all simplification paths and apply encompassing tests to them. The specification that encompasses all others becomes the Specific model. If there is no single encompassing model, then the algorithm forms a "union" model using the variables from all of the Final models and re-starts the specification search from step (2). If this strategy fails to yield a single Specific model, then the algorithm applies three information criteria (Akaike, Schwarz, and Hannan-Quinn) to the Final models and selects the one that minimizes all these criteria; that model becomes the Specific model.10 Otherwise, the algorithm fails to find a Specific model.

I implement these steps following two automated strategies. In the first one, labeled Liberal, the cost of excluding a relevant variable is deemed higher than the cost of retaining an irrelevant variable; thus the algorithm errs on the side of retaining additional variables in the specification. In the second one, labeled Conservative, the cost of including irrelevant variables is deemed higher than the cost of excluding relevant variables; thus the algorithm errs on the side of excluding relevant variables.

3.3 Data Sources and Definitions

I disaggregate data for services into their four components: travel, fares, transportation, and other private services.11 Data for travel exports are receipts from foreign residents on food, lodging, recreation, gifts, and local transportation; travel imports are payments to foreign residents on the same groupings. Data for fare exports are expenditures by foreign travelers to U.S. carriers; fare imports are payments by U.S. residents to foreign carriers and foreign cruise operators. Data for transportation exports are receipts from foreign residents on freight services for ocean, air, rail (Canada and Mexico); data for transportation imports are expenses by shippers in foreign ports and payments to foreign residents for vessel charters, aircraft rentals, and freight-car rentals. Data for exports of other private services are receipts for education, financial services, insurance, telecommunications, business, and other.12 Data for imports of other private services are payments by U.S. residents to foreign residents on the same six categories.

I measure the relative import price of the ith category as \begin{displaymath} \frac{P_{mit} }{P_t } \end{displaymath} where Pmi is the chain weighted price index for imports of the ith category and P is the chain weighted price for GDP; the data come from the BEA. I measure the relative price of exports of the ith category as \begin{displaymath} \frac{P_{xit} }{P_t^\ast } \end{displaymath} where Pxit is BEA's chain weighted export price index for the ith category of services, and P* is the foreign deflator in dollars. I measure this deflator as

\begin{displaymath} P_t^\ast =\prod\limits_j {(P_{jt} \cdot E_{\$ /j,t} )^{\gamma _{jt} },\sum\limits_j {\gamma _{jt} =1} } \end{displaymath} (15)

where E$/j is the nominal, bilateral rate of the dollar against the jth currency; Pj is the deflator for the jth country in local currency; γjt is the time-varying share of country j in U.S. bilateral exports of services to 36 countries.13

I measure U.S. GDP with BEA's chain weighted measure of GDP in constant prices; I measure foreign real GDP as

\begin{displaymath} Y_t^\ast =\prod\limits_j {Y_{jt} ^{\gamma _{jt} },\sum\limits_j {\gamma _{jt} =1} } \end{displaymath} (16)

where Yj is an index of the real GDP of the jth country.

For disaggregation to matter, relative prices should exhibit different trends and trade shares should change in relative importance. Figure 2 shows that these conditions are met for U.S. trade in services. For example, the relative price for imports of other private services declines steadily whereas the relative prices for imports of fares rises steadily. Further, travel exports had, until 1996, the largest share of total exports of services, exceeding 30 percent. Since then, exports of other private services have become the category with the largest share: nearly 45 percent in 2001. The counterpart to this increase is the decline in the export share of other transportation services: from 20 percent to 10 percent.


4  Estimation Results

Using quarterly observations from 1987 to 2001, I obtain elasticity estimates for the general and specific formulations (liberal and conservative). To address the question of how "general is the general model," I use alternative general models that differ solely in their lag lengths: 4, 6, and 8 quarters. For each specification, I test for congruency (residuals exhibiting normality, serial independence, and homoskedasticity). To explore the role of estimation methods, I use ordinary least squares (OLS), instrumental variables (IV), and Johansen's

full information maximum likelihood (FIML) procedure.14

Table 1 reports OLS and IV estimates for selected specifications.15 Specifically, for each estimator and search strategy, I select the estimates from the congruent specification with the smallest standard error of the regression; the appendix reports detailed results for each specification.16 The results reveal three findings of interest. First, estimated elasticities vary greatly across types of services. For example, the IV estimates of the income elasticity for imports range from 0.4 (significant) for transportation to 2.5 (significant) for other private services; the corresponding price elasticities range from zero for transportation to -2.1 (significant) for other private services; the dispersion of estimates across categories is robust to changes in econometric design. Second, for a given service category, the estimated income elasticity is robust to changes in econometric design. This robustness extends to the income elasticity of aggregate imports but not to the income elasticity of aggregate exports. Third, with the exception of travel services, estimated price elasticities are quite sensitive to changes in econometric design. For travel, the price elasticity for exports ranges from -0.7 to -0.8, both significant; the price elasticity for travel imports ranges from -1.3 to -1.5, both significant.

4.1 Gains from Automation

A complete assessment of the gains from pursuing automated specification involves replicating previous work not based on automation, a task that is beyond this paper. Nevertheless, an interesting question is whether the absence of automation yields an empirical model that is consistent with theory. In the context of this paper, the question is whether the estimates from the general specification are consistent with the predictions from the imperfect-substitute model. For aggregate exports, the IV estimates of the general model exhibit an income elasticity of zero whereas estimation based on automated search yields an income elasticity greater than one (table 1). For exports of other private services, the only instances of negative price elasticities involve automated search: without it, the results would not support the imperfect substitute model.

Estimates for travel appear, however, invariant to the use of automation. Specifically, as shown in table A-10 of the appendix, the long-run income elasticity for travel imports is 1.1 whereas the associated long-run price elasticity varies from -1.3 to -1.5, a narrow range. One possible explanation for this seemingly irrelevant role of automation is my focus on long-run elasticities at the expense of other properties such as the nature of dynamic adjustments. To this end, I study how the elasticities' cumulative lag distributions change in response to a change in the specification strategy. An elasticity's cumulative lag distribution is the ratio between the value the elasticity takes q quarters into an adjustment process and the value this elasticity takes in the long run.17 A ratio of two after q quarters, for example, indicates that the elasticity estimate after q quarters is twice as large as the value it will have in the long run.

Figure 3 shows the cumulative lag distributions for travel imports when the general model has eight lags.18 The results reveal that, in the absence of automated search, the dynamic adjustment has large and frequent oscillations. For example, the cumulative lag distribution for the income elasticity has a value of 2.5 after five quarters followed by a value of 0.2 after eight quarters. Such large oscillations are, however, dampened considerably using automated specification. The figure also reveals that reliance on automated search shortens the adjustment delay. For example, the estimates from the general formulation suggest that reaching the long-run income elasticity takes more than 40 quarters whereas the estimated delay from a conservative search strategy is ten quarters.

Overall, relying on a general model with no (automated) simplification has two drawbacks for explaining trade in services. First, the elasticity estimates do not support the imperfect-substitute model. Second, the dynamic adjustment for travel imports is implausibly slow.

4.2  Gains from Full Information Estimation

Table 2 compares the FIML estimates to those of table 1.19 From an econometric standpoint, the most significant result is that the difference between IV and OLS estimates is negligible when compared to the difference between IV and FIML estimates. In other words, just using IV estimation suggests that simultaneity biases are small when they are not. From an economic standpoint, the most important result is that the FIML estimates for the income elasticities of aggregate equations do not exhibit a reversed asymmetry: 1.3 for exports and 1.6 for imports. This finding implies that either the imperfect-substitute model is inconsistent with the surplus in net exports of services or that aggregation biases conceal a reversed asymmetry in income elasticities.

4.3  Gains from Disaggregation

Table 2 suggests that aggregation biases could indeed be concealing a reversed asymmetry in income elasticities: the estimates for disaggregated exports are generally greater than the corresponding income elasticities for imports.20 To explore this possibility further, figure 4 displays the 95 percent confidence bands for the income elasticity based on the disaggregated estimates (\begin{displaymath} \eta _{xt}^d \end{displaymath} , \begin{displaymath} \eta _{mt}^d \end{displaymath}) and based on the aggregate estimates (\begin{displaymath} \eta _x^a \end{displaymath} , \begin{displaymath} \eta _m^a \end{displaymath}). The most important finding is that, based on the disaggregate estimates, the income elasticity for aggregate exports is significantly higher than the income elasticity for aggregate imports. Furthermore, the existence and statistical significance of this reversed asymmetry are not sensitive to the estimation method. For example, the FIML estimates of \begin{displaymath} \eta _{xt}^d \end{displaymath} and \begin{displaymath} \eta _{mt}^d \end{displaymath} are 2.5 and 1.1, respectively, quite comparable to the reversed asymmetry for the OLS and IV estimates. The second important finding is that the elasticity estimates based on the aggregate equation do not exhibit such a reversal, regardless of estimation method. In other words, estimating the parameters of equations for aggregate service yields empirical models that, though supported by tests of statistical adequacy, cannot reconcile macroeconomic developments with the divergence in U.S. external balances. Overall, then, disaggregation is central to accounting for the divergence in the U.S. external balances with the imperfect substitute model.


References

Bryant, R., G. Holtham, and P. Hooper, 1988, External deficits and the Dollar, Washington, DC: Brookings Institution.

Burger, A. (ed.), 1989, U.S. Trade deficit: Causes, Consequences, and Cures, Boston, MA: Kluwer Academic Press.

Deardorff, A., S. Hymans, R. Stern, and C. Xiang, 2001, "Forecasting U.S. Trade in Services," in R. Stern, ed., Services in the International Economy: Measurement and Modeling, Sector and Country Studies, and Issues in the WTO Services Negotiations, Ann Arbor: University of Michigan Press.

Goldstein, M. and M. Khan, 1985, "Income and Price Effects in Foreign Trade," in R. Jones and P. Kenen (eds.), Handbook of International Economics, Amsterdam: North-Holland.

Granger, C. and D. H. Hendry, 2004, "A Dialogue Concerning a New Instrument for Econometric Modeling," Econometric Theory, forthcoming.

Hendry, D. F. and J. Doornik, 1999, Empirical Econometric Modelling Using PcGive, London: Timberlake.

Hendry, D. F. and H. Krolzig, 2001, Automatic Econometric Model Selection Using PcGets, London: Timberlake.

Hendry, D. F. and H. Krolzig, 2003, "New Developments in Automatic General-to-specific Modeling," in B. Stigum (ed.), Econometrics and the Philosophy of Economics, Princeton: Princeton University Press.

Houthakker, H. and S. Magee, 1969, "Income and Price Elasticities in World Trade," Review of Economics and Statistics, 51, 111-125.

Johansen, S., 1988, "Statistical Analysis of Cointegration Vectors," Journal of Economic Dynamics & Control, 12, 231-254.

Kimura, F. and H. Lee, 2004, "The Gravity Equation in International Trade in Services," Kangwon National University, mimeo.

Mann, C., 1999, Is the U.S. Trade deficit Sustainable? Washington DC: Institute for International Economics.

Mann, C., 2004, "The US Current Account, New Economy Services, and Implications for Sustainability," Review of International Economics, 12, 262-276.

Marquez, J., 2002, Estimating Trade Elasticities, Dordrecht: Kluwer Academic Publishers.

Mirza, D. and G. Nicoletti, 2004, "Is there Something Special About Trade in Services?" OECD, mimeo.

Phillips, P., 2004, "Automated Discovery in Econometrics," Cowles Foundation Discussion Paper No. 1469, New Haven, Yale University.

Reeve, T., 2001, "Trade in Services," Federal Reserve Board, mimeo.

van Welsum, D., 2003, "International Trade in Services: Issues and Concepts," Birkbeck College London, mimeo.



Figure 1:  U.S. External Balances, Incomes, and the Real Exchange Rate

Figure 1 has three panels. For each panel, the horizontal axis depicts time (increasing from left to right) and the vertical axis depicts values for one, or more, variable of interest (increasing from bottom to top). The top left panel two lines the first of which shows a steady rise in net exports of services; the second line indicates a declining net exports of goods and services. The top right panel shows the change in the real exchange rate; there is no trend. The bottom left panel has two lines: one for foreign GDP and another for U.S. GDP. Foreign GDP is rising faster than U.S. GDP.

GDP Growth Rates

Statistic
Foreign
U.S.
Sample Mean
3.4
3.2
Standard Deviation of Sample Mean*
0.12
0.37

* Standard Deviation of growth rate / Sqrt (Sample size).


Figure 2:  Relative Prices and Trade Shares for U.S. Trade in Services

Figure 2 has four panels. For each panel, the horizontal axis depicts time (increasing from left to right) and the vertical axis depicts values for one, or more, variable of interest (increasing from bottom to top). The top left panel has five lines representing the relative price of exports for the four types of services and their aggregate; these relative prices decline through 1995 and rise thereafter. The top right panel has five lines representing the relative price of imports for the four types of services and their aggregate; some of these relative prices decline over time whereas others increase. The bottom left panel shows four lines four the shares of exports of services in total exports of services; some shares rise (other private services) whereas other shares decline (other transportation). The bottom right panel shows four lines four the shares of imports of services in total imports of services; some shares rise (other private services) whereas other shares decline (other transportation).


Figure 3:  Cumulative Lag Distributions for OLS Elasticities of Travel Imports - 8 lags

Figure 3 shows the cumulative lag distributions for the case of eight lags. The figure has six panels arranged in two rows: three panels in the top and three panels in the bottom; each panel has a single line. For each panel, the horizontal axis depicts time (increasing from left to right) and the vertical axis depicts values for one, or more, variable of interest (increasing from bottom to top). The panels in the top show the evolution of the cumulative lag distribution of the income elasticity as the numbers of periods increase; the panels in the top show the evolution of the cumulative lag distribution of the price elasticity as the numbers of periods increase.


Figure 4:  Income Elasticity for Aggregate Services-Sensitivity to Estimation Method

Figure 4 has six panels arranged in three rows with two panels each. For each panel, the horizontal axis depicts time (increasing from left to right) and the vertical axis depicts values for one, or more, variable of interest (increasing from bottom to top). Each panel shows the confidence bands for aggregate income elasticity of imports. Each panel has the confidence intervals for the aggregate income elasticities based on disaggregated equations and based on the aggregate equation. The top left panel has the results for exports with FIML; the top right has the results for imports with FIML. The middle left panel has the results for exports with IV; the middle right has the results for imports with IV. The bottom left panel has the results for exports with OLS; the top right has the results for imports with OLS.



Table 1:  Long-run Elasticities for Trade in Services Sensitivity to Single-Equation Estimation Method Selected Specificationsa - Panel A:  Income Elasticity

Category
Exports: OLS: Generalb
Exports: OLS: Specificc
Exports: IV: General
Exports: IV: Specific
Imports: OLS: General
Imports: OLS: Specific
Imports: IV: General
Imports: IV: Specific
Other Private
3.23*
3.12*
3.26*
3.20*
2.26
1.54*
2.18
1.50*
Fares
0.40
0.59
0.10
0.00
2.12*
2.36*
2.12*
2.47*
Transportation
0.92*
0.99*
1.12*
0.86*
0.73
0.65*
0.73*
0.36*
Travel
1.48*
1.30*
1.12*
1.32*
1.07*
1.08*
1.09*
1.09*
Aggregate Trade
1.29*
1.67*
0.00
1.69*
1.47*
1.37*
1.37*
1.36*

Table 1:  Long-run Elasticities for Trade in Services Sensitivity to Single-Equation Estimation Method Selected Specificationsa - Panel B:  Price Elasticity

Category
Exports: OLS: General
Exports: OLS: Specific
Exports: IV: General
Exports: IV: Specific
Imports: OLS: General
Imports: OLS: Specific
Imports: IV: General
Imports: IV: Specific
Other Private +0.48 -1.08* +0.35 -1.14* -1.31 -2.18* -1.06 -2.10*
Fares -1.07 +0.01 -2.02* +0.32 -0.62* -1.37* -0.62 -1.53*
Transportation -0.12 -0.17* -0.06 -0.09* +0.80 -0.53* +0.80 0.00
Travel -0.68* -0.76* -0.81* -0.77* -1.40* -1.26* -1.43* -1.29*
Aggregate Trade -0.50 -0.26* -1.12* -0.27* -1.10* -1.60* -1.62* -1.57*

a  Selection criteria: For the General formulation, with either OLS or IV, there are three candidates that differ in the number of lags; I report the estimates for the specification that is both congruent and has the lowest standard error of the regression. For the Specific formulation, there are six candidates for each estimation method: 3 alternative initial lags and two search strategies. Of these, I report the estimates associated with the specification that is both congruent and has the lowest standard error of the regression.
b  General: General Unrestricted Model; there is no search.
c  Specific: Outcome of the automated specification algorithm.

Table 2:  Long-run Income and Price Elasticities for Exports and Imports of Services - 1987-2001: Alternative Estimation Methods - Selected Formulations** (Standard errors)

Category
Exports:
Income
Exports:
Price
Exports:
Estimation Method
Exports:
Search Algorithm
Imports:
Income
Imports:
Price
Imports:
Estimation Method
Imports:
Search Algorithm
Aggregate
1.33*
(0.13)
-0.37
(0.20)
FIML
NA
1.55*
(0.62)
-0.92*
(0.16)
FIML
NA
Aggregate
1.69*
(0.03)
-0.27*
(0.02)
IV
Liberal
1.36*
(0.04)
-1.57*
(0.07)
IV
Liberal
Aggregate
1.67*
(0.04)
-0.26*
(0.02)
OLS
Liberal
1.37*
(0.03)
-1.60*
(0.05)
OLS
Conservative
Other Private
1.79*
(0.65)
-1.52*
(0.32)
FIML
NA
1.73*
(0.10)
-2.51*
(0.19)
FIML
NA
Other Private
3.20*
(0.51)
-1.14*
(0.26)
IV
Liberal
1.50*
(0.06)
-2.11*
(0.11)
IV
Conservative
Other Private
3.12*
(0.52)
-1.08*
(0.26)
OLS
Liberal
1.54*
(0.08)
-2.18*
(0.15)
OLS
Liberal
Fares
1.11*
(0.21)
-1.43*
(0.58)
FIML
NA
2.11*
(0.09)
-0.92*
(0.20)
FIML
NA
Fares
0.10
(0.84)
-2.02*
(1.12)
IV
None
2.47*
(0.17)
-1.53*
(0.34)
IV
Liberal
Fares
0.59
(0.61)
0.01
(0.30)
OLS
Liberal
2.36*
(0.13)
-1.37*
(0.29)
OLS
Liberal
Transportation
0.95*
(0.27)
-0.53*
(0.36)
FIML
NA
0.91*
(0.07)
-0.14
(0.16)
FIML
NA
Transportation
0.86*
(0.86)
-0.09*
(0.04)
IV
Liberal
0.36*
(0.01)
0.00
-
IV
Liberal
Transportation
0.99*
(0.10)
-0.17*
(0.05)
OLS
Liberal
0.65*
(0.10)
-0.53*
(0.19)
OLS
Conservative
Travel
1.57*
(0.17)
-0.79*
(0.19)
FIML
NA
1.04*
(0.03)
-1.56*
(0.10)
FIML
NA
Travel
1.32*
(0.12)
-0.77*
(0.15)
IV
Conservative
1.09*
(0.05)
-1.43*
(0.16)
IV
None
Travel
1.30*
(0.09)
-0.76*
(0.12)
OLS
Conservative
1.08*
(0.02)
-1.26*
(0.04)
OLS
Liberal

NA: not applicable.
** Selection: Lowest SER among functional forms that satisfy congruence.
* Statistically significant at the 5 percent level.



Appendix:  Detailed Estimation Results

In this appendix I report the details of the estimation results. To organize the presentation, I focus on three questions: What are the consequences of a change in the search strategy given the estimation method? What are the effects of a change in the estimation method given the search strategy? Finally, what happens to the estimates in response to a change in lag-length given estimation method and search strategy?

A  Aggregate Services

Exports: The estimates suggest that aggregate service exports are income elastic and price inelastic (figure A1, top panel; table A1). However, differences in initial lag lengths, in estimation method, and in search strategies translate into different point estimates in most instances. For example, IV estimation using 8 lags and no search suggests that the income elasticity is zero whereas relying on automated search yields an income elasticity of 1.7.

Imports: The estimates suggest that aggregate service imports are income elastic and price elastic (figure A1, bottom panel; table A2). The OLS estimates are not sensitive to changes in the number of lags and are, in general, unaffected by the adoption of an automated strategy. In contrast, the IV estimates are quite sensitive to lag length: general formulations with more than four lags yield positive price elasticities.

Figure A1:  Income and Price Elasticities for Aggregate Exports and Imports of Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Figure A1 reports the values of income and price elasticities for aggregate services. The figure has two panels: one in the top for exports and one in the bottom for imports. For each panel, the horizontal axis depicts six groups of econometric configurations. An econometric configuration consists of choice of the number of lags, a choice of estimator, and a choice of search strategy. From left to right, the configurations are First: Eight lags, OLS, no-search, liberal search, conservative search. Second: Eight lags, IV, no-search, liberal search, conservative search. Third: Six lags, OLS, no-search, liberal search, conservative search. Fourth: Six lags, IV, no-search, liberal search, conservative search. Fifth: Four lags, OLS, no-search, liberal search, conservative search. Sixth: Four lags, IV, no-search, liberal search, conservative search. The vertical axis depicts the value of income and price elasticities. For the top panel, the income elasticity ranges from zero to 2.8; the price elasticity ranges from +0.6 to -1.2. For the bottom panel, the income elasticity ranges from zero to three; the price elasticity ranges from +4.5 to -1.5.

AR:  Autoregressive Specification.
GUM:  General Unrestricted Model.
Lib:  Liberal specification strategy.
Con:  Conservative specification strategy.

Table A1:  Long-run Income and Price Elasticities for Exports of Aggregate Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Lags Method
Income
Own-Price
JB
AR
ARCH
SER-GUM (%)
SER-Spec (%)
Par-GUM
Par-Spec
Max Lag in Spec
8OLS & GUM
0.99
-0.70
Y
Y
Y
1.50
1.50
28
28
8
8OLS & Lib. Search
1.67*
-0.26*
Y
Y
Y
1.50
1.32
28
7
6
8OLS & Con. Search
1.74*
-0.29*
Y
Y
Y
1.50
1.51
28
4
6
8IV & GUM
0.00
-1.12
Y
Y
Y
1.51
1.51
28
28
8
8IV & Lib. Search
1.69*
-1.27*
Y
Y
Y
1.51
1.37
28
5
6
8IV & Con. Search
1.74*
-0.29*
Y
Y
Y
1.51
1.50
28
4
6
6OLS & GUM
1.29*
-0.50
Y
Y
Y
1.35
1.35
22
22
6
6OLS & Lib. Search
1.67*
-0.26*
Y
Y
Y
1.35
1.32
22
7
6
6OLS & Con. Search
1.69*
-0.27*
Y
Y
Y
1.35
1.38
22
5
6
6IV & GUM
3.01
-0.06
Y
Y
Y
2.89
2.89
22
22
6
6IV & Lib. Search
0.00e
+0.61*
Y
Y
Y
2.89
2.44
22
5
6
6IV & Con. Search
0.00e
+0.59*
Y
Y
Y
2.89
2.46
22
4
1
4OLS & GUM
1.67*
-0.26*
Y
Y
Y
1.59
1.59
16
16
4
4OLS & Lib. Search
1.74*
-0.29*
Y
Y
Y
1.59
1.50
16
5
4
4OLS & Con. Search
1.76*
-0.30*
Y
Y
Y
1.59
1.53
16
4
4
4IV & GUM
0.20
-0.34
Y
Y
Y
2.29
2.29
16
16
4
4IV & Lib. Search
1.76*
-0.30*
Y
Y
Y
2.29
1.59
16
4
3
4IV & Con. Search
1.77*
-0.30*
Y
Y
Y
2.29
1.69
16
4
1

FIML

Statistic
VAR lags:
8
VAR lags:
6
VAR lags:
4
VAR lags:
2
Income Elasticity
1.81*
3.14*
1.33*
1.67*
Own-Price Elasticity
-0.17
+0.56
-0.37
-0.23
Loading Coefficient
-0.20
+0.05
-0.188
-0.28*
No. Cointegration vectors
2
2
1
0
JB
Y
Y
Y
Y
AR
Y
Y
Y
Y
ARCH
Na
Y
Y
Y

* Statistically significant at the 5 percent level
JB: Jarque-Bera test for normality
AR: Test of Serial independence for the residuals
ARCH: Test of constant
GUM: General Unrestricted Model
SER-GUM: Standard error of the regression associated with the General Unrestricted Model
SER-Spec: Standard error of the regression associated with the Specific Model
Par-GUM: Number of parameters in the General Unrestricted Model
Par-Spec: Number of parameters estimated in the Specific Model
Max-Lag in Spec: Maximum lag-length in the Specific Model
Y: One cannot reject the associated null hypothesis
N: One cannot accept the associated null hypothesis
e: Automated specification excludes this variable
Na: Not Applicable because of insufficient degrees of freedom.

Table A2:  Long-run Income and Price Elasticities for Imports of Aggregate Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Lags Method
Income
Own-Price
JB
AR
ARCH
SER-GUM (%)
SER-Spec (%)
Par-GUM
Par-Spec
Max Lag in Spec
8 OLS & GUM
1.72*
-0.15
Y
Y
Y
1.96
1.96
28
28
8
8 OLS & Lib. Search
1.36*
-1.58*
Y
Y
Y
1.96
1.74
28
28
6
8 OLS & Con. Search
1.37*
-1.60*
Y
Y
Y
1.96
1.75
28
28
3
8 IV & GUM
2.92
+4.64
Y
N
Y
2.50
2.50
28
28
8
8 IV & Lib. Search
1.78*
0.00e
Y
N
Y
2.50
1.90
28
28
6
8 IV & Con. Search
0.00e
0.00e
Y
N
Y
2.50
2.29
28
28
1
6 OLS & GUM
1.49*
-0.99
Y
N
Y
1.83
1.83
22
22
6
6 OLS & Lib. Search
1.40*
-1.65*
Y
N
Y
1.83
1.79
22
22
5
6 OLS & Con. Search
1.40*
-1.65*
Y
Y
Y
1.83
1.79
22
22
5
6 IV & GUM
2.18
+1.71
Y
N
Y
2.72
2.72
22
22
6
6 IV & Lib. Search
1.78*
0.00e
Y
N
Y
2.72
1.90
22
22
6
6 IV & Con. Search
1.78*
0.00e
Y
N
Y
2.72
1.90
22
22
6
4 OLS & GUM
1.47*
-1.10*
Y
Y
Y
1.75
1.75
16
16
4
4 OLS & Lib. Search
1.37*
-1.60*
Y
Y
Y
1.75
1.68
16
16
4
4 OLS & Con. Search
1.37*
-1.60*
Y
Y
Y
1.75
1.75
16
16
3
4 IV & GUM
1.32*
-1.62
Y
Y
Y
1.77
1.77
16
16
4
4 IV & Lib. Search
1.36*
-1.57*
Y
Y
Y
1.77
1.66
16
16
4
4 IV & Con. Search
1.76*
0.00e
Y
Y
Y
1.77
1.84
16
16
3

FIML

Statistic
VAR lags:
8
VAR lags:
6
VAR lags:
4
VAR lags:
2
Income Elasticity
3.14*
3.47*
2.07*
1.55*
Own-Price Elasticity
+5.25*
+6.96*
+1.23
-0.92*
Loading Coefficient
-0.22*
-0.13*
-0.35*
-0.27*
No. Cointegration vectors
0
0
1
1
JB
Y
Y
Y
Y
AR
Y
Y
Y
N
ARCH
Na
Y
Y
Y

* Statistically significant at the 5 percent level
JB: Jarque-Bera test for normality
AR: Test of Serial independence for the residuals
ARCH: Test of constant
GUM: General Unrestricted Model
SER-GUM: Standard error of the regression associated with the General Unrestricted Model
SER-Spec: Standard error of the regression associated with the Specific Model
Par-GUM: Number of parameters in the General Unrestricted Model
Par-Spec: Number of parameters estimated in the Specific Model
Max-Lag in Spec: Maximum lag-length in the Specific Model
Y: One cannot reject the associated null hypothesis
N: One cannot accept the associated null hypothesis
e: Automated specification excludes this variable
Na: Not Applicable because of insufficient degrees of freedom.

B  Other Private

Exports: Automated search matters in every instance except OLS with eight lags (figure A2, top panel; table A3). Specifically, the only instances of negative price elasticities involve combining instrumental variables and automated search: without these two features, the results do not support the conventional imperfect substitute model. Finally, the choice of search strategy matters a lot. Specifically, there are three instances in which the best-fitting model is an autoregressive formulation; each of these instances stems from relying on a conservative search strategy.

Imports: Automated search matters for every configuration of estimation method and lag length; the choice of automated specification strategy is less relevant (figure A2 bottom; table A4). For example, the IV estimate of the price elasticity with 8 lags and no search is positive whereas reliance on automated search yields a negative price elasticity. Simultaneity also matters: price elasticities based on OLS are much smaller (in absolute value) than the corresponding IV estimates.

Figure A2:  Long-run Income and Price Elasticities for Exports and Imports of Other Private Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Figure A2 reports the values of income and price elasticities for other private services. The figure has two panels: one in the top for exports and one in the bottom for imports. For each panel, the horizontal axis depicts six groups of econometric configurations. An econometric configuration consists of choice of the number of lags, a choice of estimator, and a choice of search strategy. From left to right, the configurations are First: Eight lags, OLS, no-search, liberal search, conservative search. Second: Eight lags, IV, no-search, liberal search, conservative search. Third: Six lags, OLS, no-search, liberal search, conservative search. Fourth: Six lags, IV, no-search, liberal search, conservative search. Fifth: Four lags, OLS, no-search, liberal search, conservative search. Sixth: Four lags, IV, no-search, liberal search, conservative search. The vertical axis depicts the value of income and price elasticities. For the top panel, the income elasticity ranges from zero to 8; the price elasticity ranges from +0.6 to -1.5. For the bottom panel, the income elasticity ranges from zero to five; the price elasticity ranges from +2 to -4.

AR:  Autoregressive Specification
GUM:  General Unrestricted Model
Lib:  Liberal specification strategy
Con:  Conservative specification strategy

Table A3:  Long-run Income and Price Elasticities for Exports of Other Private Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Lags Method
Income
Own-Price
JB
AR
ARCH
SER-GUM (%)
SER-Spec (%)
Par-GUM
Par-Spec
Max Lag in Spec
8 OLS & GUM
3.18*
+0.49
Y
Y
Y
1.76
1.76
27
27
8
8 OLS & Lib. Search
3.28*
+0.47*
Y
Y
Y
1.76
1.54
27
10
6
8 OLS & Con. Search
3.25*
+0.46*
Y
Y
Y
1.76
1.78
27
5
5
8 IV & GUM
3.60
-1.12
Y
Y
Y
2.37
2.37
27
27
8
8 IV & Lib. Search
4.48
-1.73
Y
Y
Y
2.37
1.87
27
9
7
8 IV & Con. Search
0.00e
0.00e
Y
Y
Y
2.37
1.98
27
1
1
6 OLS & GUM
3.23*
+0.48
Y
Y
Y
1.64
1.64
21
21
6
6 OLS & Lib. Search
3.12*
-1.08*
Y
Y
Y
1.64
1.47
21
11
6
6 OLS & Con. Search
8.50
0.00e
Y
Y
Y
1.64
1.69
21
6
5
6 IV & GUM
3.26*
+0.35
Y
Y
Y
1.86
1.86
21
21
6
6 IV & Lib. Search
3.20*
-1.14*
Y
Y
Y
1.86
1.53
21
11
6
6 IV & Con. Search
6.03
0.00e
Y
Y
Y
1.86
1.69
21
6
5
4 OLS & GUM
3.23*
+0.54*
Y
Y
Y
1.84
1.84
15
15
4
4 OLS & Lib. Search
3.25*
+0.48*
Y
Y
Y
1.84
1.74
15
7
4
4 OLS & Con. Search
0.00e
0.00e
Y
Y
Y
1.84
1.98
15
1
1
4 IV & GUM
3.27*
+0.49*
Y
Y
Y
2.32
2.32
15
15
4
4 IV & Lib. Search
3.22*
+0.48*
Y
Y
Y
2.32
1.93
15
5
1
4 IV & Con. Search
0.00e
0.00e
Y
Y
Y
2.32
1.98
15
1
1

FIML

Statistic
VAR lags:
8
VAR lags:
6
VAR lags:
4
VAR lags:
2
Income Elasticity
4.09*
3.79*
2.57*
0.68
Own-Price Elasticity
-1.72
-1.52*
-0.75*
+0.35
Loading Coefficient
0.01
0.01
-0.03*
0.00
No. Cointegration vectors
2
1
0
0
JB
Y
Y
Y
Y
AR
Y
Y
Y
Y
ARCH
Na
Y
Y
Y

* Statistically significant at the 5 percent level
JB: Jarque-Bera test for normality
AR: Test of Serial independence for the residuals
ARCH: Test of constant
GUM: General Unrestricted Model
SER-GUM: Standard error of the regression associated with the General Unrestricted Model
SER-Spec: Standard error of the regression associated with the Specific Model
Par-GUM: Number of parameters in the General Unrestricted Model
Par-Spec: Number of parameters estimated in the Specific Model
Max-Lag in Spec: Maximum lag-length in the Specific Model
Y: One cannot reject the associated null hypothesis
N: One cannot accept the associated null hypothesis
e: Automated specification excludes this variable
Na: Not Applicable because of insufficient degrees of freedom.

Table A4:  Long-run Income and Price Elasticities for Imports of Other Private Services - 1987-2001: Alternative Estimation Methods and Automated Specification Algorithms

Lags Method
Income
Own-Price
JB
AR
ARCH
SER-GUM (%)
SER-Spec (%)
Par-GUM
Par-Spec
Max Lag in Spec
8 OLS & GUM
5.00*
-0.97
Y
Y
Y
4.89
4.89
28
28
8
8 OLS & Lib. Search
0.00e
-3.94*
Y
Y
Y
4.89
4.26
28
7
8
8 OLS & Con. Search
0.00e
-3.94*
N
N
Y
4.89
4.26
28
7
8
8 IV & GUM
4.63*
+2.01
Y
Y
Y
5.15
5.15
28
28
8
8 IV & Lib. Search
1.39*
-1.91*
Y
Y
Y
5.15
4.10
28
7
8
8 IV & Con. Search
1.39*
-1.91*
Y
Y
Y
5.15
4.10
28
7
8
6 OLS & GUM
2.26
-1.31
Y
Y
Y
4.79
4.79
22
22
6
6 OLS & Lib. Search
1.54*
-2.18*
Y
Y
Y
4.79
4.10
22
6
3
6 OLS & Con. Search
3.10*
0.00e
N
Y
Y
4.79
4.32
22
4
2
6 IV & GUM
2.97
-0.46
Y
Y
Y
4.86
4.86
22
22
6
6 IV & Lib. Search
1.50*
-2.11*
Y
Y
Y
4.86
4.30
22
7
2
6 IV & Con. Search
3.10
0.00e
Y
Y
Y
4.86
4.32
22
4<