ifdp · October 31, 1988

The Dynamics of Uncertainty or the Uncertainty of Dynamics: Stochastic J-Curves

Abstract

This paper characterizes the statistical distribution of the response of the U.S. trade account to a dollar depreciation. To accomplish this task, the paper builds and estimates an econometric model of U.S. bilateral trade. Given an exchange-rate shock, this distribution is generated empirically by stochastically simulating this model using random drawings for both innovations and trade elasticities. The paper finds that the distribution of trade-account responses is not stationary, that its variance is directly related to the size of the exchange-rate shock, that the dominant source of uncertainty lies with imports' price elasticities, and that the dispersion of these responses is more pronounced in the short run than in the long run. Based on these properties, the analysis applies Chebychev's inequality to the sample of trade-account responses and finds that hysteresis in price elasticities has a low probability of accounting for the persistence of the U.S. trade deficit.

International Finance Discussion Papers Number 335

November 1988

THE DYNAMICS OF UNCERTAINTY OR THE UNCERTAINTY OF DYNAMICS: STOCHASTIC J-CURVES

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publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.

Abstract This paper characterizes the statistical distribution of the response of the US trade account to a dollar depreciation. To accomplish this task, the paper builds and estimates an econometric model of US bilateral trade. Given an exchange-rate shock, this distribution is generated empirically by stochastically simulating this model using random drawings for both innovations and trade elasticities. The paper finds that the distribution of trade-account responses is not stationary, that its variance is directly related to the size of the exchange-rate shock, that the dominant source of uncertainty lies with imports’ price elasticities, and that the dispersion of these responses is more pronounced in the short run than in the long run. Based on these properties, the analysis applies Chebychev’s inequality to the sample of trade-account responses and finds that hysteresis in price elasticities has a low probability of accounting for the persistence of the US trade deficit.

These findings have two practical implications. First, forecasts of trade-account responses to exchange-rate shocks should include the associated confidence intervals. Uncertainty in these responses is potentially large and omitting the corresponding confidence intervals is analogous to omitting standard errors of regression estimates. Second, deriving confidence intervals needs to recognize that parameter estimates are random variables and

that they contribute, quite significantly in this application, to the width of

these intervals.

The Dynamics of Uncertainty or The Uncertainty of Dynamics: Stochastic J-curves Jaime Marquez!

1. Introduction Recognizing that estimated trade elasticities are random variables means that the response of the trade account to a depreciation is a random variable. Very little, however, is known about the distribution of this response. What are the time profiles of the associated mean and variance? Are these moments systematically related to exchange-rate shocks? How wide are the confidence intervals of trade-account responses to alternative exchange rate developments? What are the main determinants of these confidence intervals? Are import responses more uncertain than export responses?

Although these questions are central for developing and implementing trade policies, judging the predictive accuracy of trade-account forecasts, and evaluating the role of speculation in stabilizing foreign exchange markets, they cannot be addressed using the available literature. Existing analyses treat estimated trade elasticities as though they were known with

certainty, a treatment that undermines their usefulness in addressing

I want to thank David Gordon for encouragement and many suggestions. I have also benefited from comments by F. Gerard Adams, Neil Ericsson, William Helkie, David Howard, Lawrence Klein, Edward Leamer, Nathaniel Leff, and Adrian Pagan. The empirical tests are performed with the GIVE computer software developed by David Hendry and installed into TROLL by Ralph Tryon. Earlier versions of this paper have been presented in seminars at the Federal Reserve Board, the U.S. Department of Agriculture, the 1988 meetings of the Society for Economic Dynamics and Control, and the Departments of Economics of University of Iowa and University of Illinois at Champaign. I am responsible for any remaining errors. This paper represents the views of the author and should not be interpreted as reflecting the views of the Board of Governors of the Federal Reserve System or other members of its staff.

practical questions in which uncertainty plays a central role.

Deriving the distribution of trade-account responses would be a relatively straightforward task if the relation between exchange rates and trade were linear and static. This task is considerably more difficult when this relation is nonlinear and dynamic, two features of trade relations supported by 30 years of empirical research. To take these features into account, the paper relies on stochastic simulations of a nonlinear, dynamic model explaining US bilateral trade. Given an exchange rate shock, this model is repeatedly simulated with random drawings of both innovations and elasticity estimates. As a group, these simulations constitute a random sample of trade-account responses to an exchange-rate shock. Based on this sample, the analysis computes time series for both the mean and the variance, examines their time-series properties, and constructs confidence intervals for dynamic paths. The distinguishing feature of these confidence intervals is that the width in any period is influenced by the dispersion of trade-account responses in all periods.

The analysis begins in section 2 with the estimation of income and price elasticities for US bilateral trade with Canada, Germany, Japan, the United Kingdom, other industrial countries, OPEC, and non-OPEC developing countries.

To evaluate the reliability of these estimates, the paper tests both the

Empirical analyses of the effects of changes in exchange rates on the trade account include Clark (1974), Wilson and Takacs (1980), Krugman and Baldwin (1987), Bryant and Holtham (1987), Helkie and Hooper (1987), Hooper and Mann (1987), Hooper (1988), and Meade (1988); see Dornbusch (1975) and Levin (1980) for theoretical analyses of trade-account responses to exchange-rate changes. See Williamsom (1972), Driskill and McCafferty (1980), and Levin (1983) for the relation between trade-account responses and the role of speculation in foreign exchange markets. Finally, see Krugman (1988) and United States Library of Congress (1988) for a survey of the policy issues associated with the trade imbalance of the United States. These papers, however, do not examine the statistical properties of the response of the trade account to changes in exchange rates.

properties of the error term and the choice of dynamic specification. Section 3 describes both the design of the sample and the construction of confidence intervals; section 4 presents the empirical results. Section 5 examines the sensitivity of these confidence intervals to both the source of uncertainty and the horizon over which they are constructed.

According to the results, the distribution of trade-account responses is ‘not stationary, its variance is directly related to the size of the exchange rate shocks, the dominant source of uncertainty lies with imports’ price elasticities, and the dispersion of trade-account responses is greater in the short run than in the long run. Section 6 examines the implications of uncertainty in trade elasticities for the persistence of the US trade deficit. Based on Chebychev’s inequality, the analysis finds that "hysteresis" in price elasticities is not a likely explanation for this persistence. Finally,

section 7 concludes the paper by pointing out its main implications and

limitations.

2. The Behavior of US International Trade Flows 2.1 Econometric Formulation The analysis assumes that bilateral imports of country k (the United States)

from country s behave according to the imperfect-substitute model (Goldstein

and Khan, 1985):

= P _ P (1) nM, ot OKs + ae + M4, (inY,, InYy ) + Z.a@ 1

473ksj ks tj

+ Y.a 1

j74ksj Peqis,t-j + %Sks tes t-1 + est?

where Mes = volume of imports of country k from country s,

Yy = real income of country k,

YP potential real income of country k, Pi, = ‘relative price for imports of country k from country s, Pea|s = relative price for imports of country k from country q, *3k55 7 $30 + 3:13 + bsoi for j~-0,...,j;,

2 2 ks j = $40 + $41) + $4.j , for jn0,...,54,

2 “knst ~ NCO, 3 EU ct es t-h) - 0 Vh.

Reliance on bilateral trade flows allows for differences in both income and price elasticities across US trading partners and avoids constraining the cross-price elasticity to zero.> To explain bilateral imports of country s from country k, the analysis uses (1) with the subscripts k and s replaced by s and k, respectively.*

According to (1), the response of imports to income has two components: a secular effect, measured by the parameter a> and a cyclical effect captured by the parameter ao The own-price elasticity is a, and the cross-price

elasticity is a, The choice of a logarithmic formulation is based on the

Box-Cox tests reported in Marquez (1988). Finally, (1) assumes homogeneity of

Previous bilateral trade models include Branson (1968), Houthakker and Magee (1969), Armington (1969), Hickman and Lau (1973), and Marwah (1976). For more recent work, see Cushman (1988), Thursby and Thursby (1987), and

Haynes et al. (1986). See Goldstein and Khan (1985) and Magee (1975) for surveys of the literature.

Differences in reporting practices across countries, shipment delays, and CIF/FOB differentials introduce a discrepancy between the value of exports of country k to country s and the value of imports of country s from country k.

See Marquez (1988, section 4) for details on how to take into account these measurement problems.

degree zero in prices.”

The reliability of (1) depends on three factors: the properties of the disturbance term, the choice of dynamic specification, and the sensitivity of the estimates to alternative estimation methods .° The paper applies the Jarque-Bera statistic (Jarque and Bera, 1980) to test normality and the ARCH statistic (Engle, 1982) to test homoskedasticity. For serial independence, “the analysis applies an F-test to the hypothesis that all the coefficients of an AR(4) for the residual are equal to zero. To test the choice of dynamic specification, the paper performs two F-tests. The first test involves estimating (1) with and without the Almon restrictions. The second test involves estimating both (1) and an "unrestricted" dynamic specification that eliminates the Almon restrictions and includes all predetermined variables

lagged one period. For both F-tests, equation (1) is the null hypothesis.’

5 Note that (1) does not allow for uncertainty of exchange rates as a separate variable. In other words, the paper focuses on the uncertainty of exchange-rate effects and not on the effects of exchange-rate uncertainty. Hooper and Kohlhagen (1978) and Thursby and Thursby (1985) suggest that this uncertainty has no measurable effect on US bilateral trade. More recently, Cushman (1988) finds that exchange-rate uncertainty affects certain US bilateral trade flows. Though statistically significant, Cushman’s estimates need not be economically significant because they are several orders of magnitude smaller than the associated own-price elasticities. Equation (1) also excludes expectations of exchange rates as a separate argument. Although important for certain applications (Driskill and McCafferty, 1980), Wilson and Takacs (1980, figure 6, p. 21) find that such an inclusion is of no empirical relevance for the United States. Finally, equation (1) does not show seasonal dummies for notational convenience.

6 The reliability of (1) also depends on the constancy of the parameter estimates. Given that the focus is on the effects of parameter uncertainty, the paper does not present stability tests to save space. Marquez (1988) presents both Chow tests and Brown-Durbin-Evans tests for parameter stability.

The paper relies on a 99 percent significance level for statistical inferences because j, and j, are empirically determined. Equation (1) also assumes that the speed of adjustment, once estimated, is fixed; Husted and Kollintzas (1984) allow a variable speed of adjustment. For equation (1), however, Brown-Durbin-Evans tests for parameter stability suggest a fixed speed of adjustment (See Marquez, 1988, appendix B, figure B17).

Appendix A examines the robustness of (1) using a Band Spectrum estimator

(Engle, 1974).

2.2 Estimation Results

Estimating (1) involves testing whether the conditioning variables (income, prices, and exchange rates) are super exogenous with respect to trade elasticities and examining whether the import-supply import-demand system is recursive. After finding support for both of these propositions, the paper

applies ordinary least squares to (1) using quarterly data for 1973Q1- 198592.°

Based on their Monte Carlo distributions, the long-run income elasticities for bilateral trade (table 1) vary between 0.5 and 4.11, and are generally twice as large as their standard errors. The associated aggregate income elasticities are 2.27 for imports and 1.52 for exports.” The estimated own-price elasticities range from -0.45 to -1.70, but they have relatively large standard errors, a finding that strengthens the case for

quantifying the uncertainty in the response of the US trade account to changes

Appendix B describes and presents the data. Testing for super exogeneity (Engle, Hendry, and Richard, 1983) asks whether treating prices and income as exogenous variables entails a significant loss of information for the trade elasticities. This task involves applying sequential Chow tests to both the conditional model (equation (1)) and the marginal processes (the exogenous variables). The latter are modeled as function of lagged policy variables (Marquez 1988, appendix B). The conditional processes exhibit parameter stability whereas the marginal processes do not, which implies that there is no loss of information by treating the conditioning variables as exogenous. To examine recursiveness, Marquez (1988, appendix B) estimates an export (relative) price equation for each bilateral trade equation. In 12 out of 14 cases, the coefficient of the volume of bilateral imports in this price equation is not significantly different from zero; the residual of each price equation is uncorrelated with the residual of the associated bilateral trade

equation. Marquez (1988, appendix C) reports the complete specification for the equations in this paper.

A one-tail test suggests that US imports have a greater income elasticity than US exports, a result first noted by Houthakker and Magee (1969).

Table 1 6a Income and Price Elasticities of US Bilateral Trade Flows Long-Run Estimates and Test Statistics 1973Q1-1985Q2

Elasticities Error Properties ° Dynamic Specification . a _SER_

Trade Trading

Flow Partner Income Std Err Price Std Err _J.B. _AR(4) ARCH Almon URDS

Imports Canada 1.87. 0.3 -0.80 0.3 0.12 0.00 0.19 0.33 0.82 0.95 0.05 Germany 2.90 0.7 -1.70 0.8 0.18 O.78 0.26 0.93 0.89 0.93 0.08 Japan 3.56 1.0 -1.13 0.6 0.24 0.96 0.64 heated 0.80 0.97 0.07 UK 4 2.67 0.7 -0.34 0.4 0.62 0.57 0.45 iaiaied 0.16 0.90 0.09 ROECD 2.51 0.5 -1.17 0.4 0.40 0.49 0.93 . 0.58 0.76 0.95 0.06 LDCs 5 3.04 1.0 “0.45 0.3 0.08 0.31 0.58 0.61 0.68 0.98 0.05 OPEC 6 1.11 0.7 -1.29 0.8 0.26 0.20 0.32 0.43 0.33 0.93 0.14 Aggregate 2.27 0.3 -0.92 0.2

Exports Canada 7 2.01 0.3 -0.99 0.3 0.35 0.30 0.87 0.78 0.89 0.93 0.04 Germany 1.95 0.3 -0.89 0.3 0.50 0.15 0.50 coheed 0.87 0.89 0.06 Japan 0.79 0.3 -0.72 0.4 0.62 0.63 0.74 0.76 0.55 0.88 0.06 UK 4,11 1.3 -0.88 0.6 0.77. 0.49 0.23 0.49 0.72 0.86 0.08 ROECD 2.32 0.6 -0.72 0. 0.56 0.30 0.44 ooo" 0.73 0.87 0.05 LDCs 0.54 0.2 -1.45 1.2 0.57. 0.60 0.43 ated 0.63 0.95 0.05 OPEC. 0.96 0.3 -0.52 0.3 0.26 0.55 0.09 0.86 0.91 0.89 0.06 Aggregate 1.52 0.2 ~0.99

The long-run income and own-price elasticities associated with (1) are =a sro, ) and s s s

1k € =Za /(1-e@ ), respectively. The paper generates the probability distributions for both n and € using ks j 3ksj 5ks ks Ks

the Monte-Carlo procedure of Krinsky and Robb (1986). Entries for the elasticities are the median (left colum) and the scaled median deviation (right colum) of their Monte-Carlo distributions.

These distributions are generated

assuming that @ (L)~ N(@ (L), & ) and substituting the associated jth drawing « (j=1...4000) into n and € . ks ks ks ks ks ks

The reliability of this procedure requires that ag < 1, an assumption supported by the empirical evidence (Marquez 1988, table 6).

2 The table shows the probability of rejecting the associated null hypothesis. Entries under J.B. belong to the

test for normality; entries under AR(4) belong to the test of serial independence; entries under ARCH correspond to the test for homoskedasticity.

The table shows the probability of rejecting the associated null hypothesis. Entries under Almon belong to the test for the Almon lags; entries under URDS correspond to the test for an unrestricted dynamic specification.

4 ROECD stands for Rest of OECD countries.

Cyclical income elasticity. an nn 22 The aggregate income elasticity for imports, n , isn = 298 » , with var(n ) =298 o , where s

s s

*Vs is the mean of the share of nominal imports of country k from country s in total imports of country k;

“2

"\s = square of the scaled median absolute deviation of the elasticity for imports of country k from country s. The

aggregate income elasticity for exports is constructed analogously.

This equation includes a dummy variable equal 1 for 1977Q3 and zero otherwise.

in exchange rates. 1° The own-price elasticities for aggregate trade are at least twice as large as their standard errors and satisfy the Marshall-Lerner condition.

The results from the statistical tests (table 1) support the elasticity estimates associated with (1). The data are consistent with the assumptions of normality and homoskedasticity in all of the trade equations; the F-test for serial correlation supports the assumption of serial independence for the residuals in 13 out of 14 cases. For the nine equations in which they are used, the Almon restrictions are supported by the data. Finally, the F-test comparing (1) against an unrestricted dynamic specification supports the lag structure of (1) for all of the equations. On the whole, the failure to reject either the conditions for classical inference or the dynamic

specification of (1) are reassuring.

3. Statistical Analysis of J-Curve Uncertainty

3.1 Model Formulation

Based on the elasticity estimates, the analysis assembles the trade equations into a model of the U.S. trade account. The endogenous variables are the bilateral trade flows (14 equations), nominal exports, nominal imports, and

the nominal trade account. The exogenous vaiiables are income levels (actual

10 : Houthakker and Magee (1969), Morgan (1970), Addler (1970), and Cushman

(1988) also report relatively large standard errors for price elasticities. 11 .

The estimates of (1) are also very close to both the Band Spectrum estimates and the estimates of Houthakker and Magee (1969) (appendix A).

and potential), nominal exchange rates, and price levels.)

The simulated response of the trade account to an exogenous change in

the exchange rate can be expressed as

J. = Lh yj fa, — M,)/de ]de

j,t-h°-“j,t-h’ where x. and M. are nominal exports and nominal imports, respectively; e. is the dollar price of country j's currency, and for simplicity, the analysis -assumes that dese = A for all j and t. The J-curve associated with \ is * JT rares| Recognizing that the simulated response of exports and imports to

exchange-rate changes depends on estimated elasticities and residuals, both of

A which are random variables, means that J. is a random variable:

A A

(2) J, = J,la(L), a, al, where a(L) is the vector of parameter estimates for all of the bilateral trade equations and u, is the lxm vector of estimated residuals associated with these equations. Note that 5, is nonlinear and that its dynamics are embedded in the lag distribution of the parameter estimates, a(L).

Given that 5, is nonlinear in its arguments, knowledge of the distributions of both a(L) and u is not sufficient to estimate the associated moments. To bypass this difficulty, the paper applies an exchange rate shock to the trade model, which is repeatedly simulated by randomly drawing values for both the residuals and the parameter estimates. Taken together, these simulations constitute a random sample of J-curves which the analysis uses to

study the associated statistical properties.

12 Trade flows with centrally planned economies account for less than five percent of US trade and are taken as exogenous. Marquez (1988) applies residual-based stochastic simulations to this model to both compute Mean Absolute Percentage Errors and estimate regressions of the actual on the (mean

of) predicted values. The results (Marquez, 1988, table 13) indicate a fairly tight fit of the data.

3.2 Sample Space

Following Brown and Mariano (1984), the analysis takes the ith drawing of u_,

t ui; as “ -5 * . = =1,..., N; t=1l,..., T; p,q=l,..., m, (3) us Tu log Poqtill i=l, N; t=l P.q where 6 is the Kronecker delta, 9 . is an IN(O,1) variable, N is the Pq pqti

number of drawings, and T is the simulation horizon. Reliance on (3) ensures

that both the original and the alternative residuals have the same

distribution. }3 Given the uncertainty in the dynamics of price elasticities (see table

1), the analysis draws random values for the own-price elasticities, 31, (L)

and O34 (L) Vs, and for the speeds of adjustment, G15 and Oe ok Vs.

drawing of these parameters is generated using Fair's approach (Fair, 1986):

The ith

(4) a,(L) = a(L) +P I"9,, i-1,...,N

where a(L) ~ N[@(L), 2], P is a Cholesky decomposition of = (PP’ = 5), ?; is a vector of standard normal variables, and I" is a perforated identity matrix (zeroes along the main diagonal except in the positions corresponding to the

own-price elasticities and the speeds of adjustment) . 14 Reliance on (4)

13 Bootstrapping does not require prior knowledge of the distribution of

residuals. But recall that the data support the normality assumption for the residuals of (1) (table 1). The process of generating random numbers from the normal distribution uses two seeds. The first seed is the replication number and the second seed is twice the drawing of a standard normal with seed one. This procedure allows for different seeds across both equations and time periods. Fair (1986) reviews alternative procedures for evaluating model performance with stochastic simulations.

By applying the Cholesky decomposition to the entire covariance matrix, the paper allows the random drawings of price elasticities and speeds of adjustment to be influenced by the uncertainty in all of the coefficients estimates. Also, the independence between the estimator of the variance of the residuals and the estimator of @ justifies shocking both the residuals and the parameter estimates.

ensures that the distributions of both the original and the randomly generated

estimates are the same (Fair, 1986).

Given (3) and (4), the value of J. generated by the ith drawing of

residuals and parameters is A

Jeg = J[a@,(L),

Ue A] = JQ), t=1,...,T; i=1,...,N, T

and Ji=(J, 5) 407

}

ti denotes the ith J-curve for i=l,...,N. The sample mean and

. A N A A variance associated with (Je) gey are, respectively, BO) = U5I,,0Q)/N and

A A

g,Q) = HJ...) - BA} /(N-1) for t=l1,...,T.

3.3 Confidence Intervals

The construction of confidence intervals for J-curves needs to recognize that the unit of observation is a dynamic path--that is, the whole J-curve--and that these paths differ in many respects: extreme values, adjustment delays, variability over time, and present discounted values. Instead of trying to

aggregate these attributes into a single measure, the paper determines the

frequency of J-curves enclosed by a confidence interval of width nd?

Rim, A) = (HO) Fe oO) E

Consequently, constructing a y-percent confidence interval involves finding a

x such that y percent of the sample of J-curves belong to g, +6

To determine the frequency of J-curves associated with a given x, the

paper defines

1 : ; : P ° If the focus were on a given attribute of the J-curve, for example its

minimum value, then the computation of a distribution for this attribute would follow standard methods.

16 Note that & depends on \ because exchange-rate shocks interact with parameter shocks. Intuitively, the larger the coefficient shock the larger the associated effect on the trade response induced by a given exchange-rate shock, an interaction that affects the dynamic path of trade responses and

thus the probability of finding a given J-curve inside a dynamic confidence interval.

1 if J, «€ B(n, r) (5) o,(m, A) =

0 otherwise

According to (5), the ith J-curve belongs to a confidence interval of width x if all of the observations of this curve fall within this interval. In other words, o, (nm, A)=0 even if the ith J-curve exits R(x, A) for one period (i.e., one quarter). +’ This requirement ensures that R(n, A) is not a sequence of static confidence intervals for trade-account responses.

Based on (5), the relative frequency of J-curves belonging to Bln, 4) is [D5 ¥; (* d)/N] = O(n, A). By systematically changing x, the | analysis finds the band width consistent with a given probability yj: v(m, A) = 7. The confidence interval associated with this n, is (BQ) ¥ , o,0))t_, . Note that the estimation of x, as given by (5), implies that the width of B(n, A) in any period depends on the dispersion of trade-account responses in all periods. Consequently, B(n, A) and n are

sensitive to both the horizon over which ¥; is calculated--t and T--and the

A A source of uncertainty--a(L) and u; section 5 examines this sensitivity.

4. Empirical Results

Given an exchange rate shock, the analysis performs 100 drawings of both residuals and elasticity estimates (N=100). For each drawing, the model is simulated from 1976Q2 to 1985Q2 (T=37), a horizon that allows the dynamics of

the model to be operative 18 Because the results might be sensitive to Xr, the

Because a one-quarter exit from &(m, \) might be considered an insignificant departure, the analysis has also considered confidence interval allowing for a one-quarter departure. The results, available on request,

indicate that allowing one exit from R(m, ) lowers the value of x consistent with a given y. ,

1 8 The US trade account in 1976Q2 recorded a deficit of $10 billion.

analysis considers four cases: no exchange rate shock (A=1.00), 10 percent depreciation (A=1.10), 25 percent depreciation (A=1.25), and 50 percent depreciation (A=1.50).29 These shocks are applied at once and maintained throughout the simulation horizon. For \=1.00, BQ) is the sample mean of the model's prediction error of the trade account at time t and 0,02) is the standard error of this prediction error.

Inspection of the sample moments (table 2) reveals that an exogenous depreciation of the dollar induces a quick, strong, and volatile response in the trade account. For example, the mean improvement has swings as high as $20 billion at annual rates, and after 37 quarters, reaches $29 billion for A=1.10 and $103 billion for A’=1.50. That the mean response is highly uncertain is evident from the coefficient of variation of BQ). For example, 0, (2) represents more than 10 percent of the mean response for A=1.50 and this percentage is higher for the other exchange rate shocks. Finally, the dispersion of trade-account responses increases with the size of the exchange rate shock. Specifically, an increase in X from 1.25 to 1.50 raises 2,02) in each period by an average of 46 percent.~° Given B.A) and 0,00), the analysis uses (5) to construct confidence

intervals for each value of ». Based on the results (table 3), the

probability of finding a J-curve inside a confidence interval is zero for x

19 The analysis uses the same drawings of residuals and coefficients for the four exchange rate shocks (see Fair, 1988).

20 The analysis uses the data of table 2 to examine the time-series properties A A

of g,Q). The results, available on request, reveal that a0) follows a

stationary AR(1) process exhibiting parameters that are constant and innovations that are normal, serially independent, and homoskedastic; for A

A=1.00, a Dickey-Fuller test suggests that a0) follows a random-walk.

Table 2 12a

US Trade Account Responses to Exchange Rates Shocks Sample Mean and Standard Deviation (USS Billions, annual rates) Alternative Exchange Rate Shocks

~ a

Sample Mean : u()) Sample Standard Deviation : o()) Simulation 2 EEE Periods A=1.00 A=1.10 A#1,25 A=1.50 A=1.00 A=1.10 A=1.25 A=1.50 1 -0.225 -8.774 -17.135 -31.629 2.963 4.368 6.766 11.134 2 0.181 -2.454 -9.669 -21.780 3.086 4.228 6.525 11.019 3 0.335 -3.876 -8.674 -17.246. 3.160 3.934 5.928 9.737 4 0.045 8.852 5.863 -0.365 3.578 4.390 6.431 10.750 5 0.024 7.364 7.738 8.274 3.912 4.714 6.806 11.016 6 0.306 4.639 7.586 12.771 3.828 4.635 6.550 10.354 7 0.385 18.068 24.562 35.706 3.501 4,519 6.522 9.996 8 0.102 25.828 34.300 48.924 3.986 4.606 6.124 8.765 9 -0.014 18.697 30.204 49.989 4.849 5.534 7.337 10.713 10 -0.102 13.491 26.064 47.817 5.263 5.998 7.553 10.537 11 0.016 10.040 26.185 53.929 5.519 6.817 8.886 12.683 12 -0.112 10.845 29.312 61.104 5.698 7.204 9.200 12.631 13 -0.262 22.527 43.935 80.770 6.326 7.794 9.922 13.582 14 -0.505 14.926 36.163 72.823 6.530 8.121 10.326 14.149 15 -0.35 14.209 38.131 79.276 6.447 8.047 10.468 14.727 16 -0.425 12.524 37.842 81.196 7.182 8.638 11.023 15.202 17 -0.382 7.471 35.132 82.583 7.668 8.961 11.370 15.652 18 -0.266 -7.663 19.433 66.019 6.926 8.929 11.428 15.808 19 0.31 7.581 37.329 88.487 7.133 9.013 11.489 15.933 20 0.727 8.132 38.104 89.542 7.680 9.375 11.902 16.380 21 0.85 14.163 44.930 97.936 7.752 9.203 11.740 16.319 22 0.916 7.445 35.670 84.518 7.616 9.107 11.581 16.002 23 0.628 20.162 49.632 100.587 7.489 8.617 11.143 15.724 24 0.503 16.387 44.584 93.550 7.277 8.624 11.131 15.692 25 0.759 6.798 35.196 84.577 6.483 7.937 10.460 15.017 26 0.689 22.418 47.678 91.647 6.581 7.797 10.066 14.255 27 0.347 17.332 43.738 89.760 5.438 7.042 9.417 13.823 28 0.42 3.768 29.360 73.954 5.207 6.757 9.127 13.568 29 0.62 22.158 49.074 95.889 5.481 6.865 9.303 13.866 30 0.486 22.490 47.248 90.424 5.870 6.961 9.206 13.628 31 0.438 26.670 53.084 99.016 6.210 6.999 9.196 13.833 32 0.356 35.188 60.984 105.808 6.146 6.513 8.796 13.618 33 0.273 27.401 54.795 102.362 6.542 7.028 9.397 14.613 34 0.463 39.722 64.984 108.760 7.719 7.281 9.225 14.028 35 0.448 7.281 33.793 79.523 7.066 6.878 8.485 13.280 36 0.296 8.757 34.066 77.745 8.099 7.075 8.342 12.926 37 -0.394 29.474 56.665 103.488 8.928 8.022 9.227 13.982

ner

Notes: For each exchange rate shock, there are 100 stochastic simulations with random draws for coefficients and residuals; for each draw, the simulation horizon is 1976Q2-1985Q2. The sample size is 100 for each period. The value of indicates the exchange rate shock in percentage terms: \=1.50 means a 50 percent exchange rate shock.

Table 3

US Trade Account Response to Exchange Rate Shocks

Dynamic Confidence Intervals

Alternative Band Widths (”) and Exchange Rate Shocks (\)

Percentage of J-curves in -Bands

Band Width n A=1.00

a UREN

0.1 0. 0.2 0. 0.3 0. 0.4 0. 0.5 0. 0.6 QO. 0.7 0. 0.8 1. 0.9 2. 1.0 7. 1.1 13. 1.2 18. 1.3 22. 1.4 31. 1.5 34. 1.6 45. 1.7 48. 1.8 60. 1.9 69. 2.0 73. 2.1 79. 2.2 85. 2.3 86. 2.4 87. 2.5 89. 2.6 90. 2.7 91. 2.8 96. 2.9 97. 3.0 98. 3.1 98. 3.2 98. 3.3 99. 3.4 99. 3.5 99. 3.6 99. 3.7 100. 3.8 100. 3.9 100. 4.0 100.

Notes: For each exchange rate shock, there are 100 stochastic simulations with random draws of both coefficients and residuals; for each draw, the simulation horizon is 1976Q2-1985Q2. The value of » indicates the exchange rate shock in percentage terms; A=1.5 means a 50 percent exchange rate shock.

A=1.10

12. 20. 27. 32. 38.

45. 54. 62. 69. 73.

77. 81. 86. 87. 90.

91. 94. 95. 96. 96.

99. 99. 100. 100. 100.

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A=1.25

uw NO Oo

16. 26. 31. 37.

41. 46. 56. 62. 69.

73. 78. 80. 85. 91.

95. 97. 97. 98. 98.

99. 99. 100. 100. 100.

100. 100. 100. 100. 100.

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A=1.50

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Nn oO FP OO

12. 18. 19. 22. 29.

36. 45. 52. 62. 66.

75. 78. 81. 84. 88.

94. 96. 97. 99. 99.

99. 99. 99.

100.

100. 100. 100. 100. 100.

12b

less than 0.8; for m greater than 3.3, this probability is one. For other values of a, the evidence reveals a direct and monotone association between (a, A) and a, although the rate of change of this association does not exhibit a systematic pattern. The value of wm consistent with a 95 percent confidence interval, mgy,, varies between 2.6 for A=1.25 and 2.8 for A=1.10, a narrow range of variation.“!

Based on the band widths of table 3, figure 1 presents the 95 percent confidence interval for a 50 percent depreciation (mg, = 2.7). Inspection of the evidence reveals several conclusions. First, the range of trade-account responses increases initially because of the cumulative effect of model uncertainty. This increase levels off after four years and ranges between $70 billion and $140 billion after 37 quarters. Second, the bias associated with

deterministic simulations changes sign, lacks any obvious systematic pattern,

and could be as large as $30 billion. 72 Third, the delay in meeting the

Marshall-Lerner condition ranges between 2 and 8 quarters .77 Finally, to

assess the sensitivity of this interval to the source of uncertainty, figure 1

a1 If the band-width for one period is derived using the dispersion of trade-

account responses of that period only, then the value of a consistent: with a 95 percent static confidence interval is 2. Thus the application of static

confidence intervals to a dynamic process is likely to underestimate the band width. The downward bias in the present application is 27 percent (0.7/2.6).

22 In terms of the notation of this paper, the simulated value of the trade-

account for the deterministic case is J. = J[a(L), u,, A]

23 Goldstein and Khan (1985, p. 1077) report delays of 4 quarters in meeting the Marshall-Lerner condition, which is the delay associated with the mean response for a 50 percent depreciation (table 2). Based on the sample of J-curves, the mean delay varies from 5.4 quarters for \=1.10 to 3.1 quarters for \A=1.25 with a standard error that ranges from 4.4 quarters for \’=1.10 to 1.0 quarter for \=1.50. Note that the delay in meeting the Marshall-Lerner condition is the result of the partial-equilibrium nature of this model. Dornbusch (1975) examines the response of the trade account to a depreciation allowing for fiscal policies and one of the key findings is that the trade account need not deteriorate as a result of a depreciation.

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also presents confidence intervals when only parameter uncertainty is allowed

24 The evidence reveals that

and when only residual uncertainty is allowed. parameter uncertainty dominates the uncertainty in the J-curve but that

residual uncertainty determines the volatility in the J-curve.

5. Sensitivity Analysis

5.1 The Trade-Channels of Uncertainty

To isolate the channels through which uncertainty in coefficient and residuals operate, the analysis decomposes a. (2) into the variances of ‘export and import

responses:

= + 1 xt + mt Oxmt , A

where o,, = Var[y, Yj (OX, /dey ey Al/ var (J) ,

w+ var (Jp, Yj COM /8e5 ep Al/ Var(J.), and mn is the covariance between export and import responses (Olin = 0). The results for a 50 percent depreciation (figure 2) suggest several conclusions. First, uncertainty in imports’ price elasticities, on accounts for more than 70 percent of the variance of the trade account response to the depreciation. Second, the importance of on diminishes considerably when the residuals are the only source of uncertainty. Finally, export and import responses have a negative covariance in periods where the dollar exhibits rapid changes, such

as in 1978 and 1984.

5.2 The Dynamics of Uncertainty Dynamic confidence intervals are time dependent because changes in the horizon

over which they are constructed influence " Furthermore, as figure 1

24 The paper computes separate band widths for each of these two additional cases.

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suggests, ame is also sensitive to the source of uncertainty. To examine these dependencies, the analysis re-calculates the frequency distribution of Jcurves using two alternative horizons: 1976Q2-1979Q1 (the first 12 quarters) and 1982Q3-1985Q2 (the last 12 quarters), and three forms of uncertainty: residual uncertainty, coefficient uncertainty, and both residual and coefficient uncertainty. 7°

To standardize the measure of dispersion of trade-account responses across these six cases, the analysis relies on the coefficient of variation

associated with a 95 percent confidence interval:

A A

CV. 9s = Nos FO) /4.Q). The numerator of CVg, gives the dispersion of trade-account responses associated with a 95 percent confidence interval 7° By scaling the numerator relative to bes CV gs measures the dispersion of trade-account responses per dollar of mean response. Note that CVg, might be negative because b might be negative, but the sign of this ratio does not affect its interpretation: Larger values indicate greater dispersion than smaller values.

Inspection of the evidence for a 50 percent depreciation (table 4) suggests three conclusions. First, CV,, is greater in the short run than in the long run, a pattern robust to the source of uncertainty. For example, when uncertainty in the coefficients is allowed, a one-dollar improvement in the mean of the trade account is associated with at least one dollar

dispersion in the short run but with only 30-40 cents in the long run. This

finding suggests that the properties of the adjustment process of this model

25 All of the simulations start in 1976Q2 and end in 1985Q2.

Note that the analysis computes ™ ys for each of these six cases.

l5a Table 4 US Trade Account Responses to a 50 Percent Depreciation

95 Percent Coefficient of Variation!

Alternative Horizons and Sources of Uncertainty“

CVy5 = %yg(A=1.50) / p(A=1.50)

Source > Coefficients Residuals Coefficients and Residuals Horizon ~ First 12 Last 12 First 12 Last 12 | First 12 Last 12 (Mg5=2.7) (mg ,=2.3) (mo57%2.6) (my5=2.8) (%o5=2.6) (g5=2.3) Periods Quarters uarters Quarters Quarters Quarters Quarters 1 -1.14 0.39 -0.09 0.10 -0.92 0.36 2 -1.31 0.37 -0.14 0.06 -1.32 0.35 3 -1.72 0.35 -0.07 0.12 -1.47 0.42 4 -1.96 0.37 11.28 0.08 -76.61 0.33 5 -21.84 0.38 0.48 0.06 3.46 0.35 6 3.21 0.38 0.28 0.05 2.11 0.32 7 1.67 0.39 0.16 0.05 0.73 0.30 8 1.15 0.38 0.18 0.03 0.47 0.33 9 0.87 0.40 0.1 0.06 0.56 0.30 10 0.73 0.33 0.08 0.10 0.57 0.38 11 0.64 0.34 0.07 0.08 0.61 0.38 12 0.55 0.36 0.04 0.11 0.54 0.31

For each period, an entry represents the dispersion of trade-account responses per dollar of mean response for a 95 percent confidence interval. Multiplying each of these entries by 2 gives the width of this interval per dollar of mean response.

2 The first 12 quarters correspond to the period 1976Q2-1979Q1 and the last 12

quarters correspond to the period 1982Q3-1985Q2. All of the simulations start in 1976Q2 and end in 1985Q2. The data for the case of shocks to both coefficients and residuals are in table 2. The data for the other cases are available on request.

P 27 are subject to greater uncertainty than the properties of its steady state.

Second, CVg, reaches a maximum after 4 or 5 periods and declines steadily afterwards. This maximum value for CVg, occurs when the mean of the tradeaccount response changes from negative to positive because, at that time, , is very close to zero. For example, if only uncertainty in the coefficients is allowed, CV,, reaches $76 during the crossing date, a result confirmed by figure 1. Finally, coefficient uncertainty has the largest effect on CVg,--

that is, treating estimated trade elasticities as though they were known with

certainty amounts to ignoring the most important source of uncertainty.

6. Implications for Trade Deficit Persistence

That the persistence in the US trade deficit might stem from changes in price elasticities--"hysteresis"--is intuitively clear. As Baldwin (1988) and Krugman and Baldwin (1987) point out, large swings in exchange rates might affect trade elasticities through entry and exit of firms into domestic markets with a corresponding flattening of the J-curve. What is missing from the literature is an estimate of the probability associated with this

flattening.

To this end, this paper relies on Chebychev's inequality which, under

the assumption that the distribution of J-curves is symmetric, “° equals (6) prob(J, < J. ds (1/2n.),

27 ‘ . This empirical finding corroborates Levin's theoretical analysis of J-

curves (Levin, 1980). By providing small perturbations to the price elasticities, Levin (1980, figure 2, p. 364) produces J-curves that exhibit

very dissimilar responses in the short-run but that converge to a unique longrun equilibrium.

28 . A A A The paper finds that [median(J, 5 (A)) - B.O)]/e,.Q) is not significantlv i

different from one.

where Jy = BLO) - m,o,.(A) is the J-curve associated with hysteresis and « is a constant a time t.

For simplicity, the analysis considers two alternative cases for ie The first case assumes that hysteresis induces a permanent violation of the Marsha]ll-Lerner condition, which precludes any improvement in the trade

account. To implement this case, the analysis sets.

| Ros for t = 1976Q2 Ke =

[Hy - min(p, - Rog a) 1/0, for t = 1976Q3-1985Q2

Intuitively, gh is equal to the lower bound of the 95 percent confidence band for the first quarter and to the minimum of this lower bound for the remaining 36 quarters .2? For a 50 percent exchange rate shock (x,,=2.7), the upper bound on the probability of finding a trade-account response below gh (left panel of figure 3) starts at 6 percent, diminishes to less than 5 percent after two quarters, and does not exceed 5 percent afterwards.

The second case assumes that hysteresis produces an additional delay in meeting, the Marshall-Lerner condition, which is modeled as a downward shift in the path of Me To highlight the nonlinearities of (6), the paper considers two shifts: $20 billion and $40 billion, which involves setting i= 20/0, and

= 40/0, Vt, respectively. Although the probability of a $20 billion fall

in the mean of the J-curve (right panel of figure 3) could be as high as 35

percent, doubling the value of «x cuts this probability to less than 10

29 Note that min(p, - Mog 7,)<0. A permanent violation of the Marshall-

Lerner is also consistent with alternative paths for x,, which might be

t’ generated using the data of tables 2 and 3.

Figure 3 US Trade Account Responses to a SO % Depreciation Chebychev’'s Probability Bounds for Hysteresis in US Trade

Soil

— Trade Account Responses 140 Trade Account Responses

Mean - $20 bill

Mean of 100 draws

Persistent Deficit

Chebychev Probability Bound Prob, Chebychev Probability Bound Prob

O35 0.35

O3 Os

Q2s Q2s

Q2 a2

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aoso oso 1976 ‘ 1979 1962 1988 ° 1976 _ 1979 1962 1938S

CASE 1 CASE 2

percent. Note that these probabilities start at zero, reach a global maximum after 6 years, and then decline afterwards.

Taken as a whole, these low probabilities do not deny the existence of a persistent trade deficit. Rather, they indicate that hysteresis in price elasticities is not the most likely source of this persistence, a finding

conjectured by both Baldwin (1988) and Krugman and Baldwin (1987).

7. Conclusions

This paper characterizes the distribution of trade-account responses to exchange-rate shocks for the United States. To accomplish this task, the paper builds and estimates an econometric model of US bilateral trade. Given an exchange-rate shock, this distribution is generated empirically by stochastically simulating this model with random drawings for both innovations and trade elasticities. The paper finds that the distribution of tradeaccount ‘esponses is not stationary, that its variance is directly related to the size of the exchange-rate shock, that the dominant source of uncertainty lies with imports’ price elasticities, that the dispersion of these responses is more pronounced in the short run than in the long run, and that hysteresis in price elasticities has a low probability of accounting for the persistence of the US trade deficit.

that they contribute, quite significantly in this application, to the width of

these intervals.

This study and its conclusions are subject to several limitatiors, many of which arise because it is the first analysis that quantifies the uncertainty of the J-curve for the United States. First, there is no allowance for the response of income and trade prices to changes in exchange rates. Although there is evidence that these variables might be taken as exogenous for parameter estimation, they are not necessarily exogenous in model simulations. Current work is underway to derive the distribution of trade-account responses without conditioning on the exogeneity of prices and income.

Second, the results are conditioned on exchange rate shocks that take place exogenously with no modeling of the effects of uncertainty of exchange rates on the trade equations. Allowing for the effects of uncertainty is likely to increase the uncertainty of the effects. Fourth, because the Jcurve is a partial equilibrium construct, the sample of J-curves generated in this paper is model dependent. Replication of this analysis with other models will determine how important is this dependency. Finally, although the number of drawings is not small, it is conceivable that outliers for either the coefficients or the residuals have not been taken into account.

Eliminating these limitations will, no doubt, affect the conclusions of the paper, but will also strengthen its main point: That trade responses are

random variables and that very little is known about their distribution.

Appendix A: Sensitivity Analysis To evaluate the sensitivity of the estimates to alternative estimation

methods, the paper applies Engle's Band Spectrum estimator (Engle, 1974) to

(Al) TM st ~ Bo + Pres Pee + Bos Myce + Past Pegist + Yest:

By estimating elasticities across spectral frequencies, the paper recognizes the criticism by Haynes and Stone (1983) that the time-series of income should not be decomposed into potential and deviations from potential. °° Because of space considerations, the paper presents the estimates of (Al) with a spectral band of [9, 0.125) only, which encloses frequency components that take at least two years to complete a cycle.

A comparison of the estimates of (1) and (Al) (table Al) reveals that the OLS and the Band Spectrum estimates for the income elasticity are very close. The price elasticities, though similar, are less robust to the estimation method, a finding that reinforces the interest in determining the associated implications for trade deficit responses to exchange-rate changes .°+ Finally, table Al presents the elasticity estimates of Houthakker and Magee (1969) to provide a well-known and independent basis for

comparisons. Inspection of the evidence points to strong similarities among

the three sets of parameter estimates.

30 Equation (Al) differs from the formulation of Haynes and Stone (1983) in

three respects: it includes an intercept, allows for cross-price effects, and assumes homogeneity of degree zero in prices.

31 Note that the Band Spectrum price elasticity for OPEC is not significantly different from zero, which is contrast to the OLS results. One probable explanation is that the Band Spectrum estimator identifies not an import demand schedule but an oil export supply schedule. A zero price elasticity would then be consistent with the non-renewable nature of oil.

20a

Table Al Income and Price Elasticities of US Bilateral Trade Flows Band Spectrum Estimates and Alternative Studies

1 2 3 OLS —____Band Spectrum +s: Houthakker-Magee _ Trade Trading Flow _Partner_ Income. § _Qwn-Price Income __ _Own-Price_ Income Own-Price Elast Std Elast Std Elast Std Elast Std Elast Elast Err Err Err Err Imports Canada 1.87 0.3 -0.80 0.3 1.45 0.2 -1.01 0.2 1.94% -0,92 Germany 2.90 0.7 -1.70 0.8 1.86 0.5 -0.48 0.6 2.77% -4,64* Japan 3.56 1.0 -1.13 0.6 3.68 0.4 -0.81 0.4 3.52* -1.51 UK 2.67 0.7 -0.34 0.4 2.76 0.4 -0.84 0.2 1.85* -2.46 OECD 2.51 0.5 -1.17 0.4 2.09 0.3 ~-0.88 0.2 LDCs 3.04 1.0 -0.45 0.3 3.39 0.3 -0.50 0.2 OPEC 1.11 0.7 -1.29 0.8 -2.10 2.0 -0.00 0.4 Exports Canada 2.01 0.3 -0.99 0.3 1.33 0.2 -0.13 0.3 1.13* -1.45 Germany 1.95 0.3 -0.89 0.3 1.66 0.3 -1.16 0.3 1.95* -2,39* Japan 0.79 0.3 -0.72 0.4 0.81 0.2 0.04 0.3 1.10* -0.41 UK 4.11 1.3 -0.88 0.6 3.11 0.9 -0.74 0.2 2.58* -1.69* OECD 2.32 0.6 -0.72 0.4 2.33 0.5 -0.61 0.2 LDCs 0.54 0.2 -1.45 1.2 0.52 0.1 -0.66 0.5 OPEC 0.96 0.3 -0.52 0.3 0.82 0.3 -0.90 0.2

Notes 1 Source: Table 1. 2 Band Spectrum estimates of equation (Al) for a frequency band of [0, 0.125). 3; * denotes

3 Source: Houthakker and Magee (1969), table 4; the price elasticity corresponds to Ps

statistical significant.

Appendix B : The Data

Bl. Definitions

All of the series indicated below are maintained in the databank of the Federal Reserve Board's MultiCountry Model. Data sources appear as underlined abbreviations and are described in section B.2.

411 data for trade flows are in billions of U.S. dollars, quarterly at annual rates. To estimate the volume of imports, the analysis deflates the dollar value of imports by the associated dollar import price:

Ms = MKSV / e.P. ,

where MKSV = goods imports of country i from country s (FOB), DOT .

e = U.S. dollar exchange rate index ($U.S./local currency) with 1972=1; MDL: quarterly average of series Canada (SXMBCD), Germany (SXMBDM), Japan (SCDBJY), and U.K. (SXDBUKP).

P = multilateral export unit value of country s in local currency with 1972=1; MDL: for Japan (JXPRICE75Q/value in 1972) and the United States (XTOUV72Q); Canada (BOC, D50501*100/D40587); U.K. (BOE, CGTOQU8080 0-); Germany

(DBB, XU0110). For Industrial and developing countries:

C79) P= I, (e PP) ps where s<i,1. The weights are

s Ss‘ ps ps

historical means of exports of each member of the group in total exports of that group. The data for exports and export prices come from the IFS. See Marquez (1988, section 2.3 for a listing of the countries). For OPEC, P. is the oil market price as reported by the IEA. Note that the export price of LDCs, OPEC, and other industrial countries is expressed in US dollar. Thus, under the

assumption that these prices remain constant in their

currencies, P(fx), a dollar depreciation raises their

prices denominated in dollars, P($), because P’($)=P(fx) e($/fx), where e($/fx) is the bilateral dollar exchange rate, which by assumption is increasing in value.

Data for the relative price of imports of country k (the United States)

from country s, Pus? are constructed as

Pes = ©, (1+1) Po /P yy: where Pik = US GNP Deflator: NIA Table 7.1, line 1. T = ad-valorem tariff rate constructed as the share of tariff

receipts (US Treasury, Monthly Bulletin) in tot:al US

imports. Data for the relative price of imports of country s from country k, P ok? are constructed as P ok = Py/e Pig) where P = GNP Deflator of sth country with 1972=1:

ys Canada: Nominal GNP divided by real GNP, CSR Table 1.2, series

D40551 and D40593. Germany: Nominal GNP divided by real GNP, (DIW). Japan: Nominal GNP constructed from components, BOJ, divided by real GNP (BOJ). U.K.: Nominal GNP, ET Table 2, divided by real GNP (ET). In view of data difficulties, the paper assumes that the GNP/GDP deflator for the Rest of OECD, Non-OPEC LDCs, and OPEC is their export price.>*“ Real income (Y) for Canada, Germany, Japan, the United Kingdom, and the United States is defined as real GNP/GDP measured in local currency:

Canada: CSR series D40593.

Germany: constructed from components, DIW.

32 Thus exports of the United States to OPEC, for example, use OPEC’s export

price as a proxy for OPEC's GNP price deflator.

Japan: constructed from components, BOJ. U.K.: real GDP, ET, Table 4. U.S.: NIA Table 1.2, line 1.

For both industrial and developing countries, real income is measured as a geometric meen of industrial production for selected countries. Finally, in view of data difficulties, the paper assumes that OPEC's income equals OPEC's real exports.

Data om potential output for Canada, Germany, Japan, the United Kingdom, and the United States are generated using Cobb-Douglas production functions. These functions include labor, capital, oil, and imports as inputs, and the associated parameters are estimated econometrically.>?? Data for potential output of LDGs and the bloc of industrial countries are generated as a trend of actual output.

Data for the relative price for imports of country k from country q (the

country competing with country s in exporting goods to country k) are

constructed as

®@ P = [I P) PlyP_,, kq|s [Mm tenPD yk

where @, is the share of the pth country (p¥k,s) in world exports. The aggregation of export prices of various countries into a single index makes two important: assumptions: first, imports of country k from country s are strongly separable from country k’s imports from countries other than s;

second, the elasticity of substitution among imports from countries other than

33 The estimates range from four to 14 percent for the share of capital; from

60 to 80 percent for the share of labor; from four to seven percent for the share of oil; and from eight to 18 percent for the share of imports. See Edison, H., J. Marquez, and R. Tryon, 1986, The structure and properties of the FRB MultiCountry Model, International Finance Discussion Papers, No. 293 (Federal Reserve Board, Washington D.C.).

s is one. These assumptions are needed to avoid the multicollinearity problem

that arises when third-country prices are considered individually in (1).

B2. Sources

le] [)

lex] t=

les} (an

a \@p) Ee

j=] oo oo

\~] I Ew

Bank of Canada. Bank of England. Bank of Japan.

Canadian Statistical Review, published quarterly by Statistics Canada.

Deutsche Bundesbank.

“Lange Reihen der vierteljahrlichen volkswirtschaftlichen Gesamtrechnung fur die Bundesrepublik Deutschland", published quarterly by Deutsches Institute fur Wirtschaftsforshung, Berlin.

Direction of Trade Statistics, published monthly by the International Monetary Fund.

Economic Trends, published monthly by U.K. Central Statistical Office. International Energy Agency.

International Financial Statistics, published by the International Monetary Fund.

Macro Data Library of the Federal Reserve Board of Governors.

National Income Accounts in Survey of Current Business, published monthly by U.S. Department of Commerce, Bureau of Economic Analysis.

B.3 Data Series The data appear after the references.

References

Addler, F., 1970, The relationship between the income and price elasticities of demand for United States exports, Review of Economics and Statistics, 52, 313-319.

Armington, P., 1969, Adjustment of trade balances: Some experiments with a model of trade among many countries, IMF Staff Papers, 27, 488-526.

‘Baldwin, R., 1988, Hysteresis in import prices: The beachhead effect, American Economic Review, 78, 773-785.

Branson, W., 1968, A disaggregated model of the U.S. trade balance, Staff Economic Studies, No. 44 (Federal Reserve Board, Washington D.C.)

Brown, B. and R. Mariano, 1984, Residual-based procedures for prediction and estimation in a nonlinear simultaneous model, Econometrica, 52, 321- 344.

Bryant, R and G. Holtham, 1987, The US external deficit: Diagnosis, prognosis, and cure, Brookings Discussion Papers No. 55 (The Brookings Institution, Washington D.C.).

Clark, P., 1974, The effects of recent exchange rate changes on the US Trade Balance, in P. Clark, D. Logue, and R. Sweeney (eds.), The effects of exchange rate adjustments (US Department of Treasury, Washington, DC).

Cushman, D., 1988, U.S. Bilateral Trade Flows and Exchange Risk During the Floating Period, Journal of International Economics, 24, 317-330.

Driskill, R., and S. McCafferty, 1980, Speculation, rational expectations, and stability of the foreign exchange market, Journal of International Economics, 10, 91-102.

Dornbusch, R., 1975, Exchange rates and fiscal policy in a popular model of international trade, American Economic Review, 65, 859-871.

Engle, R., 1974, Band spectrum regression, International Economic Review, 15, 1-11.

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Reserve Board, Washington D.C.).

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

HDrPrPrwonrrwonr FWNHRrP F WNP FWNPRP F WNP FWNHP FYWNPPFWNKPFWNRP FSF WNP FWNP FWND

CEI

goo 9090 097090 9000000009090 F990 fC Oooo eo oo oOo oO oO oO DO OC OC OH HP OCC OOO rh Be Rr BP DOO OO RP HP HPO

- 987715 00274 00772 00181 . 993502 . 990759 - 986868 - 990848 .01097 . 02622 .01007 00458 - 992158 - 969452 . 961066 -97359 -995481 - 01186 .0135

- 998875 - 962332 -941236 - 926072 . 899197 . 889939 . 878868 . 866382 - 840634 . 835061 - 855534 849241 . 843186 851065 - 846483 - 85501 . 836773 . 830061 - 826524 -817811 - 831385 - 819533 - 796198 . 792793 804449 . 807067 - 804604 - 803575 - 799939 - 789235 - 766475 754045 . 751329 . 731895 + 723352

CGNP

102. 105. 105. 107. 111. 112. 113. 116. 117. 117. 116. 117. 117. 117. 11g. 120. 124. 126. 125. 125. 126. 127. 128. 129. 130. 131. 133. 134. 135. 136. 137. 137. 138. 137. 137. 139. 142. 144, 142. 141. 138. 136. 135. 134. 137. 139. 142. 144, 145. 146, 149. 150. 152. 153.

458 116 666 694 532 045 065 055 701 109 991 13 205 785 141 371 272 371 628 972 816 299 483 621 763 931 602 228 941 327 452 662 62 251 557 846 819 242 781 668 452 949 995 74 478 905 462 33 8 871 26 528 04 257

CGNPPOT

114. 281 - 167 -002 +343 665 .195 -721 415 254 .205 .032 - 852 «125 .14

. 568 .772 . 767 .271 -313 .123 -403 -574 12

- 904 -475 .255 36

+942 042 947 .975 . 996 -678 . 308 -637 594 465 . 196 .156 .192 -091 977 -011 047 .131 -997 -726 .99

.215 -924 -799 . 109

373

CPGNP

0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 1. 1. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2. 2.

2. 2. 2. 2.

981705 989798 00376 02367 0459 0745 10177 14277 18834 24254 2882 31499 34189 36969 41295 44908 47734 51879 53991 57533 59812 6303 65382 68231 70497 73048 76674 79957 83709 90803 96222 01618 06473 12935 17806 23209 29877 33965 40363 47206 54399 59031 65215 71314 72059 75053 79455 78824 81095 84931 84296 86208 90114 9288

CPXGUV

0.98665 0.993149 1.00048 1.01971 1.05835 1.10901 1.16909 1.24423 1.389 1.50165 1.57108 1.61401 1.63243 1.65518 1.6986 1.70864 1.69007 1.69111 1.70798 1.70529 1.76782 1.78803 1.85285 1.86263 1.91023 1.92287 2.00372 2.07351 2.20581 2.31236 2.48015 2.57917 2.75295 2.72894 2.79675 2.86184 2.98977 2.88111 2.96072 3.01858 3.01659 2.91904 2.98104 3.04041 2.97536 2.9069 2.98006 2.92645 2.95287 3.00063 2.9969 2.97237 3.05737 3.03151

EEI

1.03842

0.977856 0.945136 0.966872 1.01169

0.991219 0.951122 0.911908 0.959131 0.940138 0.931581 0.955972 0.929742 . 85157

- 817223 - 798709 - 721857 . 706303 - 6602

-685271 -68735

. 693907 - 725096 .770759 - 733893 .772479 . 793231 - 806107 - 832137 . 893195 - 862566 - 901352 - 914147 952453 - 954533 + 923464 - 830538 . 735213 - 753046 . 737811 -711421 - 689829 - 65956

611897 -621614 -60342

- 588106 - 573911 - 558197 - 519531 - 486943 - 446038 . 502897

oo oO

oo oo°0°o;970

eo oo ~~ 2 ~~ = 2 oo

EGNP

54. 55. 55. 57. 60. 60. 60. 59. 58. 59. 61. 60. 59. 59. 58. 60. 61. 61. 61. 62. 61. 62. 62. 63. 63. 64. 64. 64, 63. 66. 66. 66. 64. 63. 64, 63. 64, 63. 62. 64, - 2955 64. 63. 65. 66. 65. 67. 67. 67. 67.

927 6471 8277 3543 7701 2397 6978 7597 5996 899 0565 25 5532 6448 6641 2204 4269 0565 8076 7818 7185 0695 338 6697 2864 9124 1678 7627 6839 4196 4944 0634 9111 9381 44 8232 0994 1393 827 1316

1097 7497 1795 6105 7679 0287 3771 8532 3074

-6558 68. 69. 70.

5152 2572 1166

76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

DPE WNHR FEF WNP fF WNP fF WNP FWONHPFP FSF WNP FWON PF WNHPHP FWN PF WNP fF WNP fF WNP SF WN

EGNPPOT

58 58 58 58 60 60

59.

60 61

61.

61 62 61 61 61

62.

63 63 63 63 65

64,

64 65 66 66 66 67 68 68

68.

68 69

69.

69 69

70.

70 69 70 71 71 71 71 72 72 72 72 74 75 75 76 77 76

3354 .3578 -2278 - 7993 1579 .0712 819

- 2079 -0665 196

4222 0861 -6898 . 8693 - 5306 381

.5715 2416 .0578 +7451 -0517 881

8474 - 5821 -7012 - 837

- 6225 -5155 - 9216 4413 261

- 6706 - 5608 402

-1617 - 7087 768

- 3546 . 9766 4054 .7519 . 1927 . 1096 . 2357 .2128 - 4062 4725 .7391 . 3798 0634 4389 -0255 - 5927 -6175

EPGNP

FPP PF FWY W WHY WWW WWNwwnwwowwnnNNNNNNNNNNP PPP PrP Be RPP PP PP PP PPP Ooo

- 967247 -987797 - 01082 03413 05295 0585 .0776 - 13126 - 16403 21171 - 29336 .37195 - 48654 - 57626 - 65273 - 71224 «75975 -8151

85841

-91947 - 9935

03307 - 08894 . 13986 24952 . 26989 34286 . 39002 - 46618 5457

- 64967 . 75923 - 90786 03881 -17504 . 27993 34031 - 39567 - 46399 . 50018 . 53225 - 64862 -69583 - 75781 - 80174 - 82843 - 89547 -94817 99238 .02903 05151 -11214 . 21368 . 23283

EPXGUV

0.972319 0.986159 1.0173 1.02422 1.06574 1.09689 1.14533 1.20069 1.30104 1.41177 1.48097 1.55017 1.67474 1.71626 1.78893 1.85813 1.93426 2.03806 2.15917 2.2872 2.38062 2.47059 2.53633 2.57439 2.67474 2.6955 2.76125 2.80969 2.90311 2.97578 3.0692 3.17993 3.32872 3.46713 3.52595 3.51557 3.60208 3.70934 3.83045 3.92042 3.95502 3.95848 4.05536 4.11765 4.25606 4.3218 4.391 4.43599 4.54671 4.64706 4.74395 4.88927 5.06574 5.0346

EUPCOMP

0.983526 1.00213 1.00571 1.00734 1.08344 1.17655 1.29569 1.29319 1.34349 1.51805 1.53014 1.5864 1.67497 1.65783 1.56579 1.53694 1.53832 1.51968 1.55127 1.5831 1.62636 1.65759 1.70049 1.77641 1.8882 1.94352 2.05401 2.1569 2.21376 2.23234 2.39488 2.42375 2.53891 2.5811 2.67847 2.64594 2.59295 2.40046 2.28164 2.43279 2.3632 2.31604 2.22503 2.20398 2.21424 2.17022 2.09117 2.02039 2.02218 2.00821 1.90955 1.84328 1.76471 1.87529

GEI

POPP PPP PHP BPP RPP BPP RP BP BP BP BP PPP PP RP RP PRP PRP PRP PRP RP RP RP RP PP PRP PRP PP PPP OP RPO

9974

00414 00257 - 995423 06453 -16777 33153 - 25219 -17528 + 27355 - 22168 - 26708 36453 - 35361 - 24895 + 22752 - 23839 - 24595 - 25992 - 32395 - 33046 34938 . 38193 -43516 - 53619 - 53514 - 58895 7021 - 71823 - 68187 . 75615 . 807

- 79853 . 76127 . 79605 67031 . 53069 -40154 .31265 .41909 . 35919 - 34063 - 28388 .2753 . 32358 . 28352

2061

. 19068 . 18136 . 17623

.09206 -04341 . 979715 .0324

GGNP

807. 816. 826. 842. 854. 859. 862. 867. 869. 865. 865. 855. 839. 843. 856. 867. 884. 897. 901. 914. 916. 916. 925. 935. 941, 949, 960. 968. 973. 994. 1001. 1009. 1019. 1008. 1007. 1004. 1007. 1007. 1010. 1012. 1001. 1002. 1000. 995. 1001. 1020. 1017. 1029. 1046. 1036. 1051. 1061. 1053. 1076.

782 073 3 898 505 493 998 538 71 457 425 74 156 979 106 018 75 591 674 617 393 347 542 371 383 725 115 366 651 477 63 62 66 38 85 51 41 22 66 42 98 23 48 248 67 4 41 63 34 9

GGNPPOT

NA NA NA 891. 899. 914. 926. 934. 935. 940. 942. 946. 949, 956. 959. 960. 965. 976. 987. 995. 998. 1008. 1016. 1023. 1031. 1042. 1054. 1064. 1071. 1082. 1096. 1107. 1115. 1124. 1131. 1137. 1142. 1146. 1154. 1158. 1164, 1175. 1183. 1186. 1189. 1199. 1208. 1214. 1216. 1230. 1242. 1251. 1258. 1265.

325 517 501 186 455 51

811 583 746 74

886 044 778 365 346 468 314 832 98

59 81 33 06 79 26 12 19 59

91 88

78 14

24 46 45 97

99 79 35 56 29 97 96

GPGNP

PRPPPP RPP RPP RP RP PP PP PRP Pep PPP PP PP RP Pe PPP PP PPP PPP PPP PP PP PPP PP oO Oo

- 9765 - 995352 .01004 .0181 .03985 . 05699 .07254 . 0903 . 10064 . 13308 .15245 .17353 . 1962 . 20301 .21157 . 22668 - 23162 24475 . 26333 - 25836 27731 - 2961 - 29532 .31789 - 33055 + 34451 . 36221 . 36659 - 38045 . 39092 . 41198 - 42826 - 43961 - 47048 . 47882 - 48857 - 50211 - 51887 - 53959 - 56018 - 57245 . 58814 - 60794 -61411 . 62976 -64295 .65616 - 66374 66546 67573 -68277 - 69692 69827 . 70831

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

NrPPFwWNH PrP fF WNP FF WNP F WNP FUN P EF WNHeE EP WONHE WNP KUNBFPEUWYNHBPEFWNHEPE ER WONHP EWN E

GPXGUV

0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 1. 1. 1. 1. 1. 1. 1. 1. 1, 1. 1. 1. 1. 1. 1. 1. 1, 1. 1. 1. 1. 1.

985468 994165 00835 01201 03307 03902 04634 06969 13331 2038 25644 27383 31136 3196 32326 32647 34844 35934 38115 39097 40951 4106 40351 39697 40787 41005 41932 43295 45531 47276 50493 53765 59708 62434 65051 67396 70122 72412 75957 76611 78956 81082 83045 82991 83209 83536 83154 85444 87407 87135 92042 94059 97495 98803

GUPCOMP

0.979358 1.00268 1.00687 1.0093 1.06467 1.12897 1.18886 1.23193 1.3371 1.48805 1.51809 1.56306 1.61355 1.59402 1.56068 1.55775 1.56284 1.54687 1.59164 1.59511 1.64457 1.68242 1.72828 1.79402 1.88096 1.94427 2.05383 2.0846 2. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

14493

. 21787 . 36636 . 34666 .49355 . 58983 . 68869 . 72646 . 78522 .64168 . 53955 .66121 60451 .51565 .44707 .44056 41364 . 40807 .39413 . 29036 . 29622 .27849 . 19291 .1502

. 08637 .18615

IGNPTRD

4 4 4 4 4 4 4 4 4 4 4

4 4 4 4 4 4 4 4

4 4 4 4 4 4

4 4 4

ee ee ee ee ae ae ae Sa Se a Ss

. 30799 . 31633 - 32467 . 33301 -34135 - 34969 . 35804 - 36638 «37472 . 38306 .3914 39974 -40808 41643 -42477 43311 -44145 - 44979 - 45813 - 46647 -47481 - 48316 -4915 - 49984 . 50818 - 51652 - 52486 - 5332 - 54154 - 54988 . 55823 - 56657 - 57491 - 58325 -59159 - 59993 -60827 -61661 -62496 - 6333 -64164 -64998 - 65832 - 66666 -675

- 68334 -69169 - 70003 - 70837 - 71671 + 72505 - 73339 74173 - 75007

IPXGUV

0.974572 0.988639 1.00748 1.0293 1.10663 1.20373 1.33175 1.3314 1.36489 1.53823 1.59479 1.66024 1.79634 1.80351 1.69093 1.68307 1.65292 1.65567 1.70125 1.75456 1.80028 1.82527 1.85477 1.88594 1.98024 2.01455 2.11519 2.20558 2.29111 2.34309 2.51958 2.6197 2.73257 2.76835 2.85426 2.76226 2.62991 2.48847 2.42079 2.55665 2.50084 2.44839 2.34857 2.31055 2.36046 2.27851 2.20597 2.21367 2.25126 2.26574 2.13797 2.07069 1.98503 2.08386

EXUVI

NPN UW OD @

PN UN

101.5

101. 103. 104, 107. 110. 111. 112. 115. 116. 120. 123. 125. 126. 129. 131. 135. 138. 142, 142.

“NF @ ©

one NN

JEI

0.988028 0.99894 1.00651 1.00651 1.08471 1.14411 1.1432 1.10289 1.0444 1.08289 1.01924 1.01046 1.0344 1.03652 1.01682 0.998636 1.00287 1.0134 1.04219 1.03214 1.06222 1.10167 1.13891 1.22867 1.27519 1.37433 1.5735 1.59108 1.50391 1.39187 1.38529 1.27335 1.24538 1.30809 1.37921 1.44043 1.47388 1.3788 1.30827 1.35095 1.29602 1.24151 1.17022 1.17703 1.28571 1.27594 1.24971 1.29453 1.31406 1.31943 1.24473 1.23118 1.17769 1.20814

JGNP

8.92726E+)4 9.05671E+)4 9.28057E+)4 9.52824E+4 9. 96226E+1)4 1.0087 8E+1)5 1.00829E+1)5 1.01129E+)5 9.82154E+H)4 9.98238E+4 1.00926E+1)5 1.00447E+05 9.94691 E+04 1.01467E+05 1.02501E+05 1.03891E+05 1.05660E+05 1.06926E+05 1.08198E+05 1. 08669E+(5 1.11543E+05 1.12677E+C5 1.13422E+05 1.14773E+C'5 1.17017E+C'5 1.17909E+C5 1.19269E+C5 1.21269E+C 5 1.23000E+C5 1.24729E+05 1.26162E+05 1.27739E+05 1.29538E+05 1.30313E+05 1.31612E+05 1.33188E+05 1.34658E+05 1.36139E+05 1.37233E+05 1.37097E+05 1.37981E+05 1.40402E+05 1.40675E+05 1.42465E+05 1.42660E+05 1.43978E+05 1.46173E+05 1.48686E+05 1.50892E+05 1.53770E+05 1.55127E+05 1.58553E+05 1.58863E+05 1.61856E+05

JGNPPOT

-04434E+05 .05188E+05 . O6906E+05 -08795E+05 .08859E+05 . O9595E+05 -10241E+05 . 11088E+05 .11008E+05 .12076E+05 - 14000E+05 - 15036E+05 - 16392E+05 . 16915E+05 . 19168E+05 - 20475E+05 -21838E+05 . 22989E+05 - 24997E+05 .25841E+05 - 27449E+05 -29186E+05 .30507E+05 - 32689E+05 -34211E+05 -35434E+05 .37337E+05 - 38600E+05 .39071E+05 - 40389E+05 -41809E+05 -43047E+05 -45164E+05 -45559E+05 - 47598E+05 - 49504E+05 -51278E+05 -51657E+05 .53319E+05 - 55693E+05 -58185E+05 -58517E+05 -60720E+05 -62867E+05 -64587E+05 -65467E+05 .68790E+05 -69841E+05 -71523E+05 -71225E+05

PpPpPpPPPP RPP PP Re Pe PP PP Pe PPP PP Pee PPP PP BPP BP PEP PP EEE PEE

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

NHNepP fF wWONP fF WNHP F WHR fF WHR fF WNP fF WNP F WHF F WHEY fF WNP fF WH HP F WH eH fF WH KP FWD PB

JPGNP

0.974543 0.990068 1.01097 1.02431 1.04969 1.08321 1.12636 1.18706 1.25567 1.31806 1.36301 1.40249 1.42304 1.44084 1.45622 1.47649 1.50027 1.53248 1.55847 1.57325 1.59597 1.61705 1.63934 1.66169 1.67736 1.69836 1.7176 1.72278 1.73147 1.7435 1.74708 1.74769 1.75184 1.78802 1.81644 1.8247 1.83151 1.83304 1.84737 1.85668 1.86655 1.87487 1.89474 1.87935 1.89362 1.89744 1.89097 1.87903 1.88649 1.89618 1.8968 1.89488 1.90771 1.90857

JPXGUV

0.968726 0.990084 1.00992 1.03127 1.01754 1.01907 1.10297 1.19146 1.37452 1.4569 1.55912 1.61709 1.56674 1.53013 1.5225 1.5286 1.50114 1.49352 1.50114 1.55301 1.52555 1.51487 1.50114 1.47521 1.45538 1.52555 1.40808 1.38825 1.45995 1.56064 1.62319 1.69336 1.77879 1.79252 1.73761 1.72235 1.74828 1.79558 1.83219 1.87185 1.88558 1.93593 1.90705 1.88973 1.76502 1.75117 1.75635 1.56064 1.55149 1.53623 1.56369 1.56217 1.582 1.59268

LGNPTRD

3.56191 3.59141 3.62091 3.65041 3.67991 3.7094

3.7389

3.7684

3.7979

3.8274

3.8569

3.88639 3.91589 3.94539 3.97489 4.00439 4.03389 4.06339 4.09288 4.12238 4.15188 4.18138 4.21088 4.24038 4.26987 4.29937 4.32887 4.35837 4.38787 4.41737 4.44687 4.47636 4.50586 4.53536 4.56486 4.59436 4.62386 4.65336 4.68285 4.71235 4.74185 4.77135 4.80085 4.83035 4.85985 4.88934 4.91884 4.94834 4.97784 5.00734 5.03684 5.06633 5.09583 5.12533

LPXGUV

0.976578 0.998956 0.995375 1.02909 1.15829 1.27674 1.38475 1.46084 1.69327 1.84305 1.84455 1.8538 1.90631 1.82694 1.71446 1.72311 1.76876 1.84693 1.92153 2.01671 2.11458 2.27868 2.1835 2.12741 2.19215 2.18201 2.24198 2.32612 2.42757 2.54125 2.66149 2.73281 2.92824 2.96792 3.02104 3.05415 2.973 2.91302 2.788 2.80083 2.77577 2.69909 2.65403 2.62629 2.60242 2.58243 2.57914 2.61913 2.69909 2.72057 2.60421 2.51499 2.46009 2.43384

MCU_ERR

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.005671 0.044485 -0.026913 -0.019874 -0.000728 0.024817 -0.021712 -0.019753 0.075444 0.025459 -0.067723 -0.001863 0.029971 -0.030166 0.029265 0.050378 0.02694 0.015676 -0.03029 0.033529 -0.000599 0.01151 0.027604 -0.000343 -0.039207 -0.033549 0.015398 -0.071555 0.009925 0.008153 0.036601 -0.002723 0.080903 0.022258 0.046888 -0.050132 -0.017104 -0.039885

MCUV

12. 15. 13. 15. 16. 1g. 16. 20. 21. 24. 22. 26. 23. 27. 23. 27. 27. 31. 26. 29. 29. 34. 27. 30. 29. 38. 31. 37. 39. 44. 40. - 5552 44, 48. 39. 48. 48. 55. 46. 48. 43. 46. 40. 39, 43. 51. 47. 52. 57. 63. 55.

8324 6056 018 9884 4336 4016 2408 5764 44 852 6368 3272 7936 1748 3212 2352 6512 168 4112 7932 6972 2616 7376 7732 3692 1224 0036 4436 7548 1792 3816

4136 4336 8008 6376 3156 784

3304 5576 0916 698

1236 5736 3176 4776 0152 698

258

3696 9868

- 6972 37. 64.

2628 896

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

MEU_ERR

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

ooo°0o;°o

-059257 -0. .011827 001273 -047643 - 022324 -011737 148746 .178114 048795 016126 - 008615 . 105495 . 109375 . 147568 000003 144465 . 15655

-054465 . 022107 - 102414 -00704

-057505 - 024309 - 059757 - 056952 005484 - 026774 .012998 002546 .073918 061392 - 032263 007881 .027649

072815

0.078211 0.048215

-017531

MEUV

2416 ~7544 4804 3176 .748

. 8852 -66

. 5868 - 7652 - 4968 -9444 - 9004 - 8884 - 26

6388 . 1296 - 4684 3836 - 266

- 8224 6.6828 6.9452 6.338

5.8276 8.2348 8.2716 7.6688 8.5376 8.7748 9.236

11.0984 11.7092 14.614

16.1128 12.8628 12.8856 12.5052 12.6064 11.9552 11.878 11.904

12.746

11.0224 11.038 11.9864 12.2688 10.62

10.9552 12.0136 12.7892 11.99

13.3472 14.4648 13.8344

wo wn ND WwW

AAanananwr WVU WN FHF Fw Ww

MGU_ERR

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA 0.083202 0.015427 0.013371 0.146974 -0.063793 0.056874 0.000001 0.036399 ~0.122243 -0.025277 -0.087637 0.044148 -0.031008 -0.096678 -0.047755 0.036261 0.108296 0.074988 0.050665 -0.036749 0.006893 0.019034 0.003595 0.00944 -0.019879 0.084116 0.016202 -0.018022 0.002738 -0.046151 0.01551 -0.068405 ~0.011757 -0.026821 0.030013 -0.045893 0.051002 0.024789

MGUV

3.72 3.208 2.98 3.6 4.276 4.448 4.588 5.068 5.156 5.516 5.216 5.748 5.96 5.992 5.196 5.996 6.9 6.536 6.16 8.388 7.188 7.776 4.428 7.7084 7.6652 8.5948 7.92 10.7232 10.6156 10.3312 10.2552 13.1212 15.1296 14.7196 13.2828 13.514 13.5296 12.85 11.0648 13.0024 12.104 12.6956 10.5896 11.1732 11.3468 10.998 10.2952 10.8432 11.522 11.0436 10.3512 10.9188 11.1468 11.0676

MJU_ERR

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.020031 0.009499 0.056108 -0.026536 0.016773 -0.061151 -0.053887 -0.077491 -0.001452 -0.035136 0.062806 -0.039971 0.010191 -0.06025 0.036158 -0.016035 0.017969 0.072829 -0.028429 -0.006083 0.023533 ~0.084621 0.033527 0.08251 -0.063165 0.008844 0.008016 -0.03922 -0.009537 0.071234 0.04135 0.043361 0.017226 0.038441 0.048369 -0.017458 0.025839 0.041534

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

MJUV

5.7492 5.6524 5.6812 6.34 7.6896 9.4304 9.2924 10.6984 11,5196 13.478 12.0388

13.6876

12.6176 11.85

11.1384 10.8652 10.9748 11.8192 12.3276 12.3484 12.9932 12.9228 12.0836 11.9096 13.05

14.1824 15.788

16.6948 18.584

19.7536 21.1292 21.7856 23.1204 25.7572 24.278

25.1112 26.2784 24.8596 23.6268 26.334

24.284

25.284

24.1196 23.0528 22.5632 24.9724 24.9948 26.6476 26 . 9628 26.9236 26.9704 26.6896 27.0708 26.8164

MUC_ERR

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.026504 0.051576 0.104825 0.020162 0.01718 0.042488 -0.028332 0.031285 -0.009371 -0.01507 ~0.052351 -0.034268 ~0.017353 -0.052719 -0.055256 -0.034034 -0.002683 -0.113791 -0.090755 0.022504 -0.079024 -0.055926 -0.06214 -0.035478 -0.046624 -0.04198 0.055164 -0.033968 -0.004251 -0.023904 -0.000917 -0.018148 0.068069 0.064253 0.089332 0.046371 0.058043 0.055252

MUCV

14.984 16.716 13.956 17.5 18.424 20.268 16.548 19.8 20.828 24.66 23.16 26.44 21.328 23.336 21.588 24.756 24.8036 28.9936 27.4416 29.0292 28.7848 32.76 28.4856 33.4452 31.9544 36.4468 32.31 37.876 37.7296 39.34 36.552 42.26 44.0664 40.1368 37.5096 46.3072 45.44 48.9244 44,5384 48.4032 45.0788 49.1424 46.448 46.4976 48.892 54.2524 49.7508 57.2884 64.946 69.6132 64.1832 68.9019 68.1112 73.748

MUE_ERR NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA -0.002774 -0.011577 -0.093024 -0.068325 0.022429 -0.057164 ~0.061742 -0.079541 0.109175 0.020369 -0.118756 -0.064724 -0 03296 0.036832 -0.099081 0.110739 0.010479 -0.100795 0.043716 0.001307 0.023152 0.060713 0.131471 -0.116735 -0.040129 0.030839 0.019698 0.154688 -0.138411 0.055692 0.090011 0.07842 0.05827 -0 0602 0.079282 0.02434 -0.11742 0.048581

MUEV

ow wn © W

rR Bp OO MOMAAVNODUHUHUH Ph FHSS OOK EEE OEY

.06

-624 -692 -824 -832

.732 544 .568 .356

. 876

- 664

-108

- 2524 . 5756 - 6288 «7456 -0248 - 5748 814

- 468

-5112 . 3368 - 882

. 9828 9244 - 526

8244 7744 9728 -9204 -604

10. 11. 13. 15. 12. 11. 13. 14. 15. 11. 13. 14, 12. 14. 14, 15. 15. 13. 15.

6016 8016 65 6004 2104 478 146 2204 32 1376 1772 678 6072 2916 752 7216 412 392 7984

MUG_ERR

. 022667 .031055 - 032738 009812 .073336 014118 . 039673

0.025884

095159 .039855 -015177 .081676 - 154646 -07536

005289 004991

0.004879 0.058698 0.013448

080499 045109 .036627 026421 .018336 . 062293 .059977 .069513 -010651 -044141 - 048338 044268 .015134 .069983 .097427 .090743 .066958 .134247 .015099

MUGV

- 436

. 388 -672 244 «752 -492 -148 24

724 46

- 684 - 356 - 068 - 892 -6332 - 9804 -6364 -638 . 5872 . 58 -006 -6308 2776 - 2628 - 5724 . 1876 -2136 . 3908 -6316 . 2592 . 1872 - 522 -8212 . 9996 . 384 .1572 462 -6672 . 3836 .594 . 9264 .1072 -2272 . 1928 . 7636 . 7332 468 4512 .0352 . 286 .1148 . 1268

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

DPEFWNBPEFWNREP EF WNPEFWNFFWONPE WNP EWN EF WNP FE WNP EWN HPF WN PF WNH PF WON

MUI_ERR

-048351 01546 002426 00983 . 02233

0.002541

.028073 .041215 .056651

0.029645

.015051 . 032248 . 065623 - 045817 0.055706

0.014198

t oo

oooooeo0oo0o99e°9o

.010805 006406 077083 .016519 000681 034061 006929 043288 008199 072671 . 080018 . 035869 . 060863 021249 058112 . 118364 096952 . 06649 . 138967 .093085 .057333 .007993

MUIV

10. 11. 11. 13. 13. 15. 14, 16. 13. 12. 12. 13. 13. 14. 14, 15. 16. 17. 17. 18. 21. 23. 23. 23. 23. 27. 26. 28. 29. 29. 26. 29. 29. 31. 30. 33. 30. 32. 31. 29. 30. 33. 32. 32. 43. 41. 48. 42. 47. 51.

oon o

.052 . 892 .392

748 112 88 704 636 976 7732 434 7632 67 2572 1396 522 2328 3852 2912 0884 9644 6508 1148 3384 734 9636

7992 2004 9852 5108 5104 062

3512 156

4272 722

3436 1416 638

7124 0512 7156 6684 1697 1953 1925

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

MUJ_ERR

. 105276 062634 054996 022324 .072191 049315 004272 .061273 .067365 036415 . 043256 050928 050673 .019906 .045143 . 021086 002574 - 038232 048874 . 018342 004238

0.010882 0.009311

.078213 012455 .033093 .021857 087364 .018055 .06251

069407 070364

0.047548

015481 -08831 - 119467 083471 - 025522

MUJV

- 864

9.184

10. 10. -748 10. 10. 10. 10. 12. 14. 15. 13. 11. 11. 12. 15. 16. 17. 18. 17. 19. 21. 22. 24. 27. 27. 26. 26. 28. 28. 29. 30. 34. 33. 33. 36. 39. 40. 42. 42. 40. 40. 35. 39. 41. 42. 50. 54. 59. 68. 58. 69. 73.

152 196

192 68 372 332 756 996 216 688 36 832 464 1176 7324 842 0212 218 9536 0044 6352 9396 0264 4752 4452 1816 7284 5176 2644 77 0488 458 6192 5812 9656 7008 3692 3524 8776 702 7932 3676 56 9936 3148 9672 348 7956 3744 4908 6504

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

MUL_ERR

03942

. 027262 . 002657 000678 .021916 047642 .03509

-010199

0.020848 0.030149

021657 -017209 .053658 .019067 017447

0.015322

011102 . 009337 -096575 .01415 .028961 .016902 .021758

0.023521

. 059876 .00895

032925 + 041523 034251 069444 004126 . 003606 089825 .051397 .090489 . 035682 . 040037 007742

MULV

11. 11. 12. 12. 14. 15. 16. 18. 23. 26. 27. 26. 23. 23. 25. 25. 27. 28. 30. 32. 35. 37. 36. 36. 40. 42. 44, 45. 47. 51. 56. 60. 66. 66. 63. 65. 69. 69. 70. 71. 67. 68. 73. 70, 70. 78. 81. 82. 96. 90. 100. 90. 94, 92.

968 78

304 94

768 78

264 508 104 948 388 784 968

664 772 284 984 804 372 848 192 388 94

448 416 088 784 696 232 28

008 86

812 208 192 14

976 436 796 72

052 808 332 116 028 46

876 508 856

136 436 3

“MUO_ERR

- 057305 . 192.231 012752 -018175

- 192216 . 0081189 .015:766 - 007374 . 105176

- 012762 . 039835 - 026734

0.049481

025491 044693 - 016521 -030977 .012514 -162172 03314 - 050575 015101 . 184312 05639 . 038313 - 2415927 21358 0616

. 143605

0.08104 0.32:2183

04718 . 113857 . 14.2563 051192 +153275 - 315837 084554

MUOV

Oorw ww Nn Dd N

On WE FH WHUWH WW DW WF WWWW WWW WF wWWNH NP RP RP PP PP eb

664 456 644 064 452 984 -924 .352 356 384 .588 .136 .58

.904

.124

. 0884 . 8708 842

. 3352 .918

. 8772 .1976 .114

4316 9624 -6104 - 7692 -0408 458

4496 . 2304 . 2752 . 0624 -4048 . 9956 - 3932 . 5348 - 8804 6052 . 3084 . 986

7464 844

- 9096 . 5452 - 7952 4024 - 9332 -9552 +412

- 5816 . 7832 - 6248

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

DPF WHR FWNHKHP fFWNHHRP fF WNP SF WNP FWNHFH FSF WN HY SF WNP SF WH PF WNP SF WNP F WNP fF WN

MUTV

56.4 58.2 57.332 63.556 67.612 73.332 71.972 81.516 90.608 ‘10.828 113.904 116.708 ‘05.152 98.132 01.488 08.896 19.964 129.064 137.144 142.684 154.472 161.8 160.28 165.504 ‘176.408 185.98 187.208 194.76 195.632 215.964 228.736 249.008 265.656 260.64 243.86 258.8 272.028 279.28 266.992

275.124

257.588 252.916 262.816 246.208 242.848 265.424 277.832 293.416 331.668 338.136 363.076 331.804 350.076 368.856

MUZV

1.37197 1.47199 1.73596 1.71995 1.86398 2.11197 2.39599 2.51996 2.53996 2.81195 2.99597 2.564 2.48398 2.29596 2.53598 2.80399 3.0116 3.49323 4.186 3.87283 3.83403 4.72285 4.86243 5.03802 5.46046 6.23767 7.18164 6.75087 6.19524 7.17406 8.14244 8.47765 7.56081 7.83749 9.05524 7.88423 8.30264 8.56123 9.86356 10.0108 8.9155 9.96201 11.5375 9.59204 10.8545 11.5266 13.7528 14.4816 15.5027 16.4447 20.0595 15.9422 18.5525 18.4148

OPOIL72

. 979766 - 979766 0181 - 02236 . 1033 . 1885 - 28647 . 2066 . 83919 . 79233 . 83067 . 75399 -60916 - 59638 - 57508 . 00532 .00958 . 00958 .0181 .0181 - 42705 - 43557 - 54207 . 53355 . 52077 . 51225 . 50373 - 49947 . 87433 . 27582 - 57934 .0319 +2343 +9542 - 5208 -8914 - 8797 -7561 4835 6752 14.5091 14.2194 14.3088 14.2833 13.2396 12.2556 12.2343 * 12.2343 12.2556 12.2599 12.2556 12.1704 12.0341 11.9744

On UUW UWUUW WU WW UU WW WHn WN & & F&F F&F FN KP YP RP PP Oo 8

PPP PRP PP Pe fF F&F FW WN DN OO :

ROWIPEEC

80.9688 82.9617 83.559 85.876 86.7518 88.5842 91.2871 91.7751 94.1375 94.1943 94.0609 89.2997 85.8343 84.7829 83.9154 87.6059 89.8081 91.6555 93.0286 93.2438 94.1059 92.1925 90.1362 91.9063 92.0993 93.562 93.9249 96.7526 95.6006 97.3759 100.239 100.768 103.038 100.208 98.2397 98.4724 98.4373 98.9745 98.4569 98.7499 97.5367 97.5165 95.4826 94.7468 95.7302 96.9368 97.0314 98.163 99.9973 100.1 101.194 101.067 102.336 102.159

ROWIPLDC

39. 42. 42. 44. 47. 46. 48. 51. 51. 52. 51. 50. 51. 55. 57. 59. 62. 65. 66. 67. 67. 73. 73.

3305 3418 7905 6428 5726 9021 5465 0885 6272 4268 1529 4687 0623 6901 2805 8033 1799 4341 6722 4348 4126 1592 9653

. 0996 79. 87. 89. 90. 91. 95. 95. 97. 96. 99.

100.

103.

102.

109.

110.

108.

110.

108.

109.

114.

117.

119.

121.

127.

128.

127.

131.

0598 0308 6917 8242 8921 2991 7121 9031 7177 4797 262 163 887 319 938 997 022 346 564 046 137 367 947 513 705 186 559 644 847 156

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

HNrPer WNP FF WNP FEF WNP FWONP PF WNP EF WNP EF WNP EF WNPRP EF WNKP PR WONHP SE WNKREWNHHERWNE

UFPXFIW

31109

- 46626 - 50076 -63071 -68888 - 78974 . 75267 - 71605 - 55496 4513

- 60235 . 53914 - 48232 -41134 40135 - 4188

- 38919 + 32425 - 26108 - 26682 - 25089 - 15836 - 10406 -03017 . 13672

UGNP

- 980799 1183. -00108 00834 . 00846 07741 .15957 - 26116 -27074 . 33488 . 5045

- 52428 - 58183 -67739 . 66368 - 59495 - 58444 -60299 -60121 -64651 - 68382 .72797 - 76225 - 80478 . 86982 . 98153 . 02226 -12496 - 20889 - 27043

0 1 1206. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 2 2 2 2 2. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

1218. 1241. 1269. 1273. 1272. 1282. 1277. 1279. 1262. 1252. 1228. 1240. 1262. 1278. 1303. 1310. 1315. 1328. 1345. 1367. 1394. 1391. 1403. 1447, 1459. 1478. 1478. 1478, 1490. 1486. 1502. 1467. 1468. 1487. 1516. 1511. 1517. 1496. 1473. 1477. 1465. 1468. 1480. 1515. 1536. 1563. 1600. 1620. 1630. 1636. 1648. 1658.

69 94

46 93 7

86 87 12 47 88 1

79 07 59 47 44 78 66 15 82 67

96 22 18

91 15 97 93 51 32 29 96 81

05 76

04 48 42 05 57 67 68 63

UGNPPOT

1221.78 1235.11 1246. 1255.83 1275.88 1291.08 1303.19 1316.61 1330.96 1330.01 1349. 1356.5 1364.69 1364.54 1375.23 1383.32 1403.93 1419.61 1438.77 1451.02 1472.37 1488.78 1501.67 1517.14 1536.03 1554.22 1569.89 1584.28 1607.65 1608.26 1625.29 1635.39 1652.53 1652.18 1658.05 1660.95 1683.16 1690.23 1694.5 1702.15 1711.44 1720.54 1735.15 1739.53 1737.35 1747.45 1777.63 1785.51 1799.37 1818.83 1837.01 1842.64 1860.83 1864.1

UGPCOMP

0.979537 1.00276 1.00679 1.00911 1.06423 1.12846 1.18801 1.23121 1.33664 1.4876 1.5179 1.56281 1.61359 1.59423 1.56128 1.55872 1.56414 1.54818 1.59277 1.59573 1.6452 1.68262 1.72846 1.7932 1.88016 1.94138 2.05043 2.08137 2.14265 2.21693 2.36601 2.34762 2.49558 2.59066 2.68991 2.72697 2.78556 2.64186 2.5404 2.66176 2.60546 2.51572 2.44885 2.44289 2.41515 2.40951 2.39626 2.29351 2.29915 2.28127 2.1959 2.15307 2.08958 2.18894

UJPCOMP

0.988605 1.00502 1.00571 0.999062 1.069 1.15751 1.26124 1.25699 1.30375 1.4815 1.50381 1.56527 1.69624 1.68969 1.61045 1.60371 1.63597 1.63075 1.67405. 1.71094 1.76437 1.79366 1.83677 1.88879 2.0241 1.99871 2.09634 2.20891 2.29525 2.35803 2.54134 2.62399 2.78161 2.81105 2.93072 2.84709 2.76285 2.5812 2.46919 2.62669 2.57089 2.50846 2.47269 2.46179 2.4694 2.4417 2.36784 2.34522 2.34618 2.32874 2.232 2.16629 2.08754 2.21062

UPGNP

0.985476 0.991931 1.00484 1.01775 1.03281 1.05433 1.07585 1.10167 1.11673 1.1404 1.17913 1.2114 1.24153 1.26089 1.28886 1.31253 1.32759 1.34481 1.36417 1.38784 1.41151 1.43948 1.4567 1.48252 1.50403 1.54061 1.56858 1.60086 1.63744 1.67402 1.70844 1.74287 1.77945 1.82033 1.86121 1.91501 1.9645 1.99677 2.04196 2.08069 2.11296 2.13878 2.16891 2.18827 2.20549 2.2227 2.24206 2.26788 2.2937 2.31092 2.33028 2.34965 2.37116 2.39053

UPXGUV

0 0 0 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1. 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2

2. 2. 2.

- 984326 994701 -997494 02348 .07028 -1271 19471 27747 - 36256 - 40976 - 4889 -57271 -64678 -60709 - 60737 -6245 64781 - 66821 -68139 + 71424 - 73733 . 75798 . 75262 . 7569

- 79607 - 85396 - 87683

93664

01445 - 11353 . 16614 - 20436 .27251 - 30872 . 38331 46432 - 52614 - 52615 . 5303

- 54226 -5575

+ 54943 - 52017 - 49645 - 49627 - 49903 - 51247 - 54895 - 56034 - 58083 . 54521

51053 48095 46672

UTARIFF

1.06007 1.05773 1.05877 1.05808 1.05572 1.05325 1.05252 1.04955 1.0474 1.04632 1.04916 1.04672 1.04728 1.05146 1.05267 1.05352 1.04991 1.05153 1.052 1.04779 1.04885 1.0493 1.0549 1.04774 1.0487 1. 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

05347

- 05567 - 05332 -05029 05065 .05

- 04538 - 03946 -04153 04483 -0423

-0413

04447 . 04923 - 04804 - 04606 -04535 - 04634 - 04704 -03525 - 04497 - 04694 .04225 - 03956 04345 1. 1. 1. 1.

04663 04321 04181 04082

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 7 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

YDPrwWONP PF WNP fF WNKFPPKWONKP KF WNHK SF WNP FWONP KF WNP PF WNP SF WNP fF WNH PE fF WNP fF WN

UTRADE

-8.22801 -9.43199 10.408 -8.14799 -5. ~3.056 ~3.06 2.07201 0.472 -9.67599 -20.408 -8.34 3.72 8.76001 -0.807999 5.28 -10.424 -10.24 27.356 20.52 -36.312 ~34.512 -43.784 -42.772 -52.476 -37 .692 -45.964 -33.176 -31.128 -37.984 ~49.728 -42.488 ~53.492. -34.2119 -31.86 -26 .2638 33.0798 ~36.236 -46.3559 -42.784 -36.3319 -24.804 -61.8599 -47 .436 -42.546 -63.4078 -84.312 -87.14 -116.516 -118.528 -149.972 -108.112 -125.488 -151.568

xOTV

29.739 29.739 29.739 29.739 43.513 43.513 43.513 43.513 120.012 120.012 120.012 120.012 115.372 115.372 115.372 115.372 139.716 139.716 139.716 139.716 154.848 154.848 154.848 154.848 152.227 152.227 152.227 152.227 214.538 214.538 214.538 214.538 301.246 301.246 301.246 301.246 271.748 271.748 271.748 271.748 216.099 216.099 216.099 216.099 187.108 187.108 187.108 187.108 179.676 179.676 179.676 179.676 157.02 157.02

XUC_ERR

NA NA NA NA 0.01787 0.03636 0.008905 0.012155 0.062697 -0.003644 0.001659 0.049103 0.042917 -0.01042 0.027377 0.038342 -0.010416 -0.034886 -0.04381 -0.045928 -0.010804 -0.052209 0.015366 -0.059208 0.017516 0.005283 0.007257 -0.05634 -0.019678 -0.027881 0.001836 -0.004448 0.033117 -0.037527 -0.038551 -0.025167 0.010388 0.002603 -0.009324 0.015981 0.043947 0.021443

xUCV

11. 13. 11. 13. 13. 16. 13. 16. 17.

20 18

22. 20. 23. 20. 23. 22. 26. 22. 24. 25.

28 22 26 24

30.

26 31 31 34 31 35

34.

37 32 36 38 45

37. 36.

36.

32 31 35 39 36 41 45 50 44

45.

46 52

236 22

424

796 296 336 988 876 . 896 696 26

112 336 372 216 896 72

626 .0872 - 9236 - 5156 - 8604 876 1444 -6064 4248 - 6604 . 2968 -0012

.1744 . 7508 -756 - 8928 . 0308 53 804 -6128 792 . 5596 . 9168 .6116 . 9732 -3528 .0388 .3772 . 6932 . 1864 84

- 9296 . 8388

SEE

SESSESES

XUE_ERR

. 087264 -002481 009215 - 06281

.073699 -015806 -016107 - 115713 . 113825 .033572 .116949 044762 . 240085 - 193529 009957 039157 -047498 006878 .107831 - 029373 - 140049 . 16738

065969 045853 -009158 -013029 - 02225

- 089279 . 000659 - 015083 010715 - 006344 - 061372 043788 . 078426 017423 .017409 - 126399

XUEV

2.856 2.4 2.456 -928 .192 488 32

- 256 - 336 -616 184 .16 456 224 - 108 -312 - 504 724 «744 224 6172 . 2292 . 706 . 2508 6964 - 5964 - 282 - 9008 . 1872 -9904 - 4508 -9104 -9464 - 7348 -82 2784 - 2936 424 -936 . 1028 - 8824 - 3364 - 5052 8548 0684 . 8756 . 7812 - 7596 - 7888 -0412 -122 - 8864 - 6688 -016

SM On OODUADWN WU HS PF PF kf FFU UN SF S&F FF WwW wD

PRPPPrPP eB PP PRPPPPPPPPrP PPB w PWN NNHRFPOCWHOrFPHOrP OPP WWNHOKNH OO O

XUG_ERR

NA NA

BEESSSSESS SS SSE

0.004167 0.022965 -0.019519 0.051304 0.025362 0.042607 0.460327 -0.041544 -0.021607 -0.103331 0.111897 -0.077336 -0.084533 -0.060803 -0.087579 -0.096465 -0.08777 -0.060998 -0.127538 -0.088326 -0.055788 -0.016644 0.026654 -0.066908 0.008122 -0.092223 -0.064157 -0.033462 -0.089395 ~0.016149 -0.013081 -0.011269 -0.004966 -0.011631 -0.030829 0.034215 0.061758 0.002349

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

Ne fF WNP fF WHR fF WNP FF WNP FF WNH PP fF WNP F WNP FF WNP F WNP KF WNP F WNP FSF WNP fF WD BP

XUGV

PP PPP rR COMO OO OF Pe

ON N DWN AAMUUWUAAAN KF UUWWH FFU W FU WNW SF WWW WN DN DN

of09 0 O7OO DW ODD DW GB O

. 856 - 768 - 504 .128 . 284 - 692 +552 496 .12

. 196 . 232 . 396

-752 - 536 . 788 -628 264 . 868 .16

. 0064 - 4684

5196

- 9596

+224 -27 194 .1768 -912

- 9824 - 9204 - 5656 . 9656 - 3876 -9168 - 4504 . 5572 . 182 . 3268 . 5648 . 326 -9476 74 -8476 . 5012 . 8588 6676 -9272 4004

3404

974 -074

XUI_ERR

-0.037534 0.058846 -0.033806 0.052209 -0.09005 -0.006019 0.021981 -0.094856 -0.103007 0.036106 0.00708 0.005592 -0.020908 0.013155 -0.031755 0.074596 0.041218 0.024395 -0.035703 -0.045208 0.029181 0.024337 0.072216 0.052356 -0.027518 0.088245 0.021441 -0.006915 0.041305 -0.067329 0.008119 -0.04077 0.017043 -0.082741 0.054492 -0.032649 0.024062 -0.060398

XUIV

.928 . 56 14

. 116 -756 044 412 .976 -324 -104 -472 . 184 - 496 -948 .38

- 804 . 588 - 3288 6132 . 592 . 2372 4248 - 4196 - 4124 . 5696 - 0904 - 0656 -1516 . 83

. 9968 - 7928 - 9016 - 9924 - 9616 B44 .25 -0372 4144 - 9236 . 1084 . 9396 - 4516 - 6816 +2216 -1972 - 6364 -5772 -0712 4152 - 9952 . 1588 5444 3944 32

XUJ_ERR

NA NA NA NA NA NA NA NA NA

NA NA NA NA NA NA -0.006313 0.033866 -0.012198 -0.019036 -0.000092 -0.023093 -0.047902 0.01258 -0.064641 0.042857 -0.017524 0.038879 0.046094 0.006389 0.007143 -0.037831 -0.003602 -0.014124 -0.01772 -0.044775 -0.008488 0.004094 0.013771 -0.014617 0.017761 -0.017792 -0.025755 0.04181 -0.015765 0.018153 0.04843 0.026723 ~0.026436 0.059851 -0.020224 0.020802 0.062912 -0.042033

XUJV

4.82 4.544 4.64 5.856 7.484 8.176 8.3 9.292

10.8

10.392

10.056

11.468

10.472 9.308 9.168 9.312 9.352 9.9712

10.4308

10.844

11.1652

10.3104 9.8632

10.7896

10.5136

12.1012

13.33

15.5952

16,8012

16.3204

18.3536

18.9124

19.9448

20.9196

20.6076

21.688

22.5956

20.5524

20.6892

23.4548

21.4144

20.4552

20.30/6

21.6872

19.2228

20.8392

22.6756

24.7396

22.7792

23.5592

23.3284

24.6328

25.0092

21.1912

XUL_ERR

.041755 .028049 .002808 084404 .07609 001507 006054 - 085524 -031725 037202

0.012261

004382 048027 011043 -027991 072654 -017487 035672 - 030897 051412 - 002787 -010098 -046141 01043

025823 - 036357 -064718 -079523 038427 -028551 007152 . 035237 - 061328 .020212 075557 - 037092

0.044713

.014395

XULV

12. 12. 12. 14, 15. 18. 20. 23. 26. 29. 29. 30. 32. 31. 29. 31. 30. 31. 31. 30. 29. 32. 33. 32. 33. 39. 41. -6012 «7484 -356 6428 . 8972 6384 - 3688 - 5076 2184 -8271 - 7631 . 2283 - 8844 - 6372 - 9028 . 1856 -6188 . 1948 -11

3356 42

8472 054 . 1308 .7572 . 7188 -6444

768 664

364 62 136 308 832 616 964 52 892 532 816 624 952 138 311€ 2648 218 0004 8564 358 301€ 21 3384 112

NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA NA

XUO_ERR

00406 .030394 006583

0.072945

-064616 - 062389 006464 .026765

0.086423 0.096127

t 4 4 oo o0c:9o

008447 007104 144094 . 108793 031114 . 068941 - 023252 - 016536 - 015612 - 062403 068423 046284 .008085 .018591 142764 - 053396 . 089862 .071023 -040857 047396 .017116 053746 -017568 099724 - 022587 024116 . 008309 . 128166

72 72 72 72 73 73 73 73 74 74 74 74 75 75 75 75 76 76 76 76 77 77 77 77 78 78 78 78 79 79 79 79 80 80 80 80 81 81 81 81 82 82 82 82 83 83 83 83 84 84 84 84 85 85

NPPRFWONPFP SF WNP RE WNP PF WNHEP FEF WNP EF WNHP SF WNHP SF WNP SF WN SF WNHP SF WN SF WNP FON

‘XUOV

2.64 2.652 2.296 2.932 3.22 3.26 3.24 4.04 4.488 5.876 6.5 8.748 9.324 10.28 10.492 11.384 10.6804 12.0652 12.012 13.908 12.1732 14.232 13.644 13.8812 14.4348 17.1712 15.9896 16.4612 13.586 14.2696 14.7064 15.3168 15.0344 16.8568 17.4476 18.4444 19.4492 21.6376 20.584 21.2584 22.0048 22.7812 21.8024 21.8 17.6 16.7944 15.9524 15.33 14.2888 13.646 13.4356 14.0872 12.6348 11.6364

XUTV

48.172 48.768 46.924 55.408 62.612 70.276 68.912 83.588 91.08 101.152 93.496 108.368 108.872 106.892 100.68 114.176 109.54 118.824 109.788 122.164 118.16 127.288 116.496 122.732 123.932 148.288 141.244 161.584 164.504 177.98 179.008 206.52 212.164 226.428 212. 232.536 238.948 243.044 220.636 232.34 221.256 228.112 200.956 198.772 200.3 202.016 193.52 206.276 215.152 219.608 213.104 223.692 224.588 217.288

XUZV

1.06797 0.959969 1.30793 1.65996 2.25996 3.18398 3.44398 3.708 2.52 3.10798 1.83597 3.26001 2.77997 3.22798 4. 6.40798 4.75359 5.43921 3.81522 4.43799 4.33444 4.67962 3.06202 3.62124 4.5072 7.89041 5.05039 5.07364 5.74963 8.47445 8.90685 10.598 6.78724 7.84648 7.05688 9.51328 8.93571 7.77132 7.18768 9.54527 10.4381 8.82806 5.58807 6.72525 6.66525 6.83965 6.34403 9.05803 7.98805 8.69201 8.34165 10.6036 9.25843 7.56724

MNEMONIC ]

CEI CGNP CGNPPOT CPGNP CPXGUV EEI EGNP EGNPPOT EPGNP EPXGUV EUPCOMP GEI GGNP GGNPPOT GPGNP GPXGUV GUPCOMP IGNPTRD IPXGUV EXUVI JEI JGNP JGNPPOT JPGNP JPXGUV LGNPTRD LPXGUV MCU_ERR MCUV MEU_ERR MEUV MGU_ERR MGUV MJU_ERR MJUV MUC_ERR MUCV MUE_ERR MUEV MUG_ERR MUGV MUI_ERR MUIV MUJ_ERR MUJV MUL_ERR MULV MUO_ERR MUOV MUTV MUZV OPOIL72

ALPHABETICAL LIST OF VARIABLES FOR MODEL

DEFINITION

US-CANADA EXCHANGE RATE (USS$/C$)--INDEX 1972 CANADIAN REAL GNP--DOMESTIC CURRENCY--1972 CANADAIA POTENTIAL OUTPUT--DOMESTIC CURRENCY--1972 CANADIAN GNP DEFLATOR--DOMESTIC CURRENCY--1972 CANADIAN EXPORT UNIT VALUE--DOMESTIC CURRENCY~--1972 US-UK EXCHANGE RATE (US$/POUND)--INDEX 1972 BRITISH REAL GNP--DOMESTIC CURRENCY--1972

BRITISH POTENTIAL OUTPUT--DOMESTIC CURRENCY--1972 BRITISH GNP DEFLATOR--DOMESTIC CURRENCY--1972 BRITISH EXPORT UNIT VALUE--DOMESTIC CURRENCY--1972 THIRD COUNTRY PRICE FOR UK-US TRADE

US-GERMANY EXCHANGE RATE (US$/DM)--INDEX 1972 GERMAN REAL GNP--DOMESTIC CURRENCY--1972

GERMAN POTENTIAL OUTPUT--DOMESTIC CURRENCY--1972 GERMAN GNP DEFLATOR--DOMESTIC CURRENCY--1972 GERMAN EXPORT UNIT VALUE--DOMESTIC CURRENCY--1972 THIRD COUNTRY PRICE FOR GERMAN-US TRADE

LOG OF OTHER OECD TREND OUTPUT--DOMESTIC CURRENCY--1972 OTHER OECD EXPORT UNIT VALUE--DOMESTIC CURRENCY-~-1972 NON-OIL UNIT VALUE FOR THE UK--1972=1

US-JAPAN EXCHANGE RATE (USS/YEN)--INDEX 1972 JAPANESE REAL GNP--DOMESTIC CURRENCY--1972 JAPANESE POTENTIAL OUTPUT--DOMESTIC CURRENCY--1972 JAPANESE GNP DEFLATOR--DOMESTIC CURRENCY--1972 JAPANESE EXPORT UNIT VALUE--DOMESTIC CURRENCY--1972 LOG OF LDCS TREND OUTPUT--DOMESTIC CURRENCY--1972 LDCS EXPORT UNIT VALUE--DOMESTIC CURRENCY--1972 RESIDUAL IN MCUV EQUATION

CANADIAN IMPORTS FROM US (8)

RESIDUAL IN MEUV EQUATION

UK IMPORTS FROM US--NOMINAL $

RESIDUAL IN MGUV EQUATION

GERMAN IMPORTS FROM THE US --NOMINAL $

RESIDUAL IN MJUV EQUATION

IMPORTS OF JAPAN FROM THE US --NOMINAL $

RESIDUAL IN MUCV EQUATION

IMPORTS OF THE US FROM CANADA --NOMINAL $

RESIDUAL IN MUEV EQUATION

IMPORTS OF THE US FROM THE UK --NOMINAL $

RESIDUAL IN MUGV EQUATION

IMPORTS OF THE US FROM GERMANY --NOMINAL $ RESIDUAL IN MUIV EQUATION

IMPORTS OF THE US FROM OTHER OECD--NOMINAL $ RESIDUAL IN MUJV EQUATION

IMPORTS OF THE US FROM JAPAN --NOMINAL $

RESIDUAL IN MULV EQUATION

IMPORTS OF THE US FROM LDCS --NOMINAL $ RESIDUAL IN MUOV EQUATION

IMPORTS OF THE US FROM OPEC --NOMINAL $

TOTAL IMPORTS OF THE US --NOMINAL $

US IMPORTS FROM THE RESIDUAL REGION--NOMINAL $ NOMINAL OIL PRICE INDEX FOR OPEC--1972=1

ROWIPEE> ROWIPLD= UFPXFTW UGNP UGNPPOT UGPCOMP UJPCOMP UPGNP UPXGUV UTARIFF UTRADE XOTV XUC_ERR xUCV XUE_ERR XUEV XUG_ERR xUGV XUI_ERR XUIV XUJ_ERR xXUIV XUL_ERR XULV XUO_ERR xuoV XUTV XUZV

OTHER OECD REAL GNP

LDCS REAL GNP

US FOREIGN IMPORT PRICES

US REAL GNP--DOMESTIC CURRENCY--1972

US POTENTIAL OUTPUT--DOMESTIC CURRENCY--1972 THIRD COUNTRY PRICE FOR US-GERMAN TRADE THIRD COUNTRY PRICE FOR US-JAPAN TRADE

US GNP DEFLATOR--DOMESTIC CURRENCY--1972

US EXPORT UNIT VALUE--DOMESTIC CURRENCY--1972 MULTILATERAL US TARIFF--INDEX 1972=1

US TRADE BALANCE

TOTAL EXPORTS OF OPEC -- NOMINAL S$

RESIDUAL IN XUCV EQUATION

EXPORTS OF THE US TO CANADA --NOMINAL S$ RESIDUAL IN XUEV EQUATION

EXPORTS OF THE US TO THE UK --NOMINAL S$ RESIDUAL IN XUGV EQUATION

EXPORTS OF THE US TO GERMANY --NOMINAL S$ RESIDUAL IN XUIV EQUATION

EXPORTS OF THE UNITED STATES TO OTHER OECD --NOMINAL S RESIDUAL IN XUJV EQUATION

EXPORTS OF THE US TO JAPAN ~-NOMINAL S$ RESIDUAL IN XULV EQUATION

EXPORTS OF THE US TO LDCS -- NOMINAL $ RESIDUAI, IN XUOV EQUATION

EXPORTS OF THE US TO OPEC -- NOMINAL S$

TOTAL EXPORTS OF THE US --NOMINAL S$

US EXPORTS TO THE RESIDUAL REGION--NOMINAL $

IFDP

NUMBER

335

334

332

331

330

329

328

327

326

325

324

323

International Finance Discussion Papers

TITLES 1988

The Dynamics of Uncertainty or The Uncertainty of Dynamics: Stochastic J-Curves

Devaluation, Exchange Controls, and Black Markets for Foreign Exchange in Developing Countries

International Banking Facilities

Panic, Liquidity and the Lender of Last Resort: A Strategic Analysis

Real Interest Rates During the Disinflation Process in Developing Countries

International Comparisons of Labor Costs in Manufacturing

Interactions Between Domestic and Foreign Investment

The Timing of Consumer Arrivals in Edgeworth’s Duopoly Model

Competition by Choice

The Determinants of the Growth of Multinational Banking Organizations: 1972-86

Econometric Modeling of Consumers’ Expenditure in Venezuela

Income and Price Elasticities of Foreign Trade Flows: Econometric Estimation and Analysis of the US Trade Deficit

Money, Interest, and Capital ina Cash-in-Advance Economy

AUTHOR (s)

Jaime Marquez

Steven B. Kamin

Sydney J. Key Henry S. Terrell

R. Glen Donaldson

Steven B. Kamin David F. Spizelman

Peter Hooper Kathryn A. Larin

Guy V.G. Stevens Robert E. Lipsey

Marc Dudey

Mare Dudey Robert S. Doaner Henry S. Terrell Julia Campos

Neil R. Ericsson

Jaime Marquez

Wilbur John Coleman II

Please address requests for copies to International Finance Discussion Papers, Division of International Finance, Stop 24, Board of Governors of the Federal Reserve System, Washington, D.C. 20551.

IFDP NUMBE,

317

316

315

314

313

312

311

310

309

308

International Finance Discussion Papers

TITLES 1987

The Simultaneous Equations Model with Generalized Autoregressive Conditional Heteroskedasticity: The SEM-GARCH Model

Adjustment Costs and International Trade Dynamics

The Capital Flight "Problem"

Modeling Investment Income and Other Services in the U.S. International Transactions Accounts

Improving the Forecast Accuracy of Provisional Data: An Application of the Kalman Filter to Retail Sales Estimates

Monte Carlo Methodology and the Finite Sample Properties of Statistics for Testing Nested and Non-Nested Hypotheses

The U.S. External Deficit: Its Causes and Persistence

Debt Conversions: Economic Issues for Heavily Indebted Developing Countries

Exchange Rate Regimes and Macroeconomic Stabilization in a Developing Country

Monetary Policy in Taiwan, China

The Pricing of Forward Exchange Rates Realignment of the Yen-Dollar Exchange Rate: Aspects of the Adjustment Process in Japan : ; The Effect of Multilateral Trade Clearinghouses on the Demand for

International Reserves

Protection and Retaliation: the Rules of the Game

Changing

International Duopoly with Tariffs

AUTHOR(s )

Richard Harmon

Joseph E. Gagnon

David B. Gordon Ross Levine

William Helkie Lois Stekler

B. Dianne Pauls

Neil R. Ericsson

Peter Hooper Catherine L. Mann

Lewis S. Alexander

David H. Howard

Robert F. Emery Ross Levine

Bonnie E. Loopesko Robert E. Johnson

Ellen E. Meade

Catherine L. Mann

Eric O’N. Fisher Charles A. Wilson

Cite this document

APA

Jaime Marquez (1988). The Dynamics of Uncertainty or the Uncertainty of Dynamics: Stochastic J-Curves (IFDP 1988-335). Board of Governors of the Federal Reserve System, International Finance Discussion Papers. https://whenthefedspeaks.com/doc/ifdp_1988-335

BibTeX

@techreport{wtfs_ifdp_1988_335,
  author = {Jaime Marquez},
  title = {The Dynamics of Uncertainty or the Uncertainty of Dynamics: Stochastic J-Curves},
  type = {International Finance Discussion Papers},
  number = {1988-335},
  institution = {Board of Governors of the Federal Reserve System},
  year = {1988},
  url = {https://whenthefedspeaks.com/doc/ifdp_1988-335},
  abstract = {This paper characterizes the statistical distribution of the response of the U.S. trade account to a dollar depreciation. To accomplish this task, the paper builds and estimates an econometric model of U.S. bilateral trade. Given an exchange-rate shock, this distribution is generated empirically by stochastically simulating this model using random drawings for both innovations and trade elasticities. The paper finds that the distribution of trade-account responses is not stationary, that its variance is directly related to the size of the exchange-rate shock, that the dominant source of uncertainty lies with imports' price elasticities, and that the dispersion of these responses is more pronounced in the short run than in the long run. Based on these properties, the analysis applies Chebychev's inequality to the sample of trade-account responses and finds that hysteresis in price elasticities has a low probability of accounting for the persistence of the U.S. trade deficit.},
}