Estimating Pass-Through: Structure and Stability

Board of Governors of the Federal Reserve System International Finance Discussion Papers Number 387

September 1990

Estimating Pass-Through: Structure and Stability

William R. Melick

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publications to International Finance Discussion Papers (other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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 estimates the pass-through relationship between exchange rates and import prices for the United States using recursive techniques across a variety of specifications to examine structural and coefficient stability in a systematic fashion. Results of estimations:

1) indicate that pass-through at the macroeconomic level is a complicated amalgamation of disparate industrial structures that involves more than one long-run equilibrium relationship between the variables of interest, and 2) call into question the prevailing wisdom that foreign firms changed their pricing behavior in light of the large appreciation in the exchange

value of the dollar in the early 1980s.

Estimating Pass-Through: Structure and Stability

William R. Melick!

Two issues have dominated studies of the "pass-through" of exchange rate changes into aggregate dollar import prices: the size of the pass-through coefficient (both in the short-run and the long-run) and the stability of the pass-through relationship. In this paper the pass-through relationship is estimated using recursive techniques across a variety of econometric specifications to examine structural and coefficient stability in a systematic fashion. This approach allows for a careful analysis of the stability issue, and it also provides estimates of the size of the pass-through coefficient. The main conclusions of the paper are: (1) pass-through at the macroeconomic level is a complicated amalgamation of disparate industrial structures that involves more than one long-run equilibrium relationship between the variables of interest, and (2), claims of changes in the aggregate behavior of foreign firms in response to the large dollar appreciation in the early 1980s may be unfounded.

The paper begins with a presentation of three simple theoretical models of pass-through. The second section presents the results of

estimating the pass-through relationship using the Johansen (1990)

1. The author is a staff economist in the Division of International Finance. 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. I especially thank Peter Hooper and Catherine Mann both for helpful comments and the generous provision of their data set. I also thank Marc Dudey, Hali Edison, Neil Ericsson, Dale Henderson, David Hendry, David Howard, Eric Leeper, Ellen Meade, Andrew Rose, Charles Thomas, Charles Whiteman, and participants in the International Finance Division's Monday Workshop series. Elizabeth Vrankovich provided valuable research assistance.

procedure, a vector auto-regressive (VAR) approach that allows for non-stationary variables. The results from the simpler single-equation Engle-Granger (1987) (E-G) procedure are presented in the third section. The E-G results allow for a close comparison with a re-estimation of a more traditional specification, found in the fourth section. Conclusions

are presented in the fifth section.

I. Simple Models of Pass-Through

A variety of models of the pricing behavior of foreign firms in the U.S. market have been specified, including, among many others, Hooper and Mann (1989) (henceforth H-M), Baldwin (1988), and Dornbusch (1987). These models focus only on costs, exchange rates, and prices, ignoring income and other variables that would be present in a reduced form solution to a supply and demand formulation. A general specification, using variables typically found in the literature can be written as

(1) PM = £(ER, PD, CF, CD)

where

PM = the price of imports measured in dollars

ER = the exchange rate, foreign currency per dollar

PD = competing domestic prices, in dollars

CF = foreign unit costs, measured in foreign currency

CD = domestic unit costs, measured in dollars Three simple theoretical models illustrate the variety of long-run relationships that might exist between the variables found in (1).

Consider first a competitive specification. In such a world free entry and exit and goods arbitrage would produce three long-run relationships: in each country the rate of return (profits divided by

total costs) should yield zero economic profit, and purchasing power

parity. These three conditions can be written as

PD d (2) gpalte PM*ER f (3) “Geos ilter PM (4) pp 71

where xf and xt are the rates of return in the foreign and domestic countries that ensure zero economic profits. If these two rates of return were equal, (2) and (3) would imply, using (4) to eliminate PM and PD,

(5) CF = ER*CD In such a world, a change in the exchange rate, in the long-run, would have no effect on import prices. Rather, the relative number of foreign firms would change as movements in the exchange rate altered the cost competitiveness of foreign firms.

Alternatively, one could use any of a wide variety of imperfectly competitive models. For example, consider a domestic firm and a foreign, both Nash price competitors, selling two differentiated products. Linear demand curves (f for foreign and d for domestic) for each of the firms are given by

(6) Qe = - a,PM + b, PD ay: by >0

(7) Qa + b, PM - ayPD ao) by > 0 Profits for the two firms would then be given by

(8) I, = (- a,PM + b, PD) (PM*ER - CF)

(9) I,- ( bo PM - a PD) (PD - CD). Differentiating (8) and (9) with respect to PM and PD (assuming that unit costs do not depend on output), setting the derivatives equal to zero, and

solving for PM and PD yields”

2. An assumption about the functional form of the total cost function

for each firm, TC, = g,(Q.), would eliminate CF and CD from the solutions i i**i for PD and PM.

-4-

2a b,CD CF (10) PM= 7a a = b,! 7 + SR J 1°72 °1°2 2a, bo CF (11) PD = TI OS Ct acd j. 4a, ay-b,b, 2ER 2

The pass-through coefficient for this model is found by differentiating (10) with respect to ER, which when expressed as an

elasticity yields

-2a,a aPM ER 72898) cr (12) 3ER*PM 7 4a,a,-b,b, PM*ER?

Using (10) to substitute for PM on the right-hand side reduces the expression to

(13) gPM ER -1

aER PM ER*CD_ | 5 2a, *CF

Polar cases for (13) can be considered. Setting ay equal to infinity (the foreign firm is a price-taker) yields the pass-through coefficient of -1, exchange rate changes are fully offset. Setting ay equal to zero (demand for the foreign firm's product is unaffected by the price it charges) results in a pass-through coefficient of zero. The H-M mark-up model is a second imperfectly competitive

formulation. The mark-up of price over cost is given by

| (14) PM = age The mark-up, A, is variable and responds to the difference between

competing domestic prices and foreign costs in dollars, as well as to

changes in foreign capacity utilization (CU). This can be written as

PD_.a B,.CF = ‘* ad (15) PM = [ (CF/ER? (CU)" }*ER - Again polar cases can be considered. Setting a@ equal to 1 and B# equal to zero transforms (15) into the purchasing power parity condition found in

(4) of the perfectly competitive model. Exchange rates have no effect on

import prices. Setting a and 8 equal to zero yields complete pass-through as exchange rate changes are entirely offset.

These three simple models suggest the wide variety of long-run relationships that might be expected to hold between the five variables in (1). The point to be taken from this discussion is that any econometric work should proceed in as general a fashion as possible, allowing for the possibility of several unique relationships among the variables in the

data set.

II. Johansen Procedure

The Johansen (1990) procedure is extremely general and therefore meets the estimation requirements outlined above. It is also allows for, but does not require, non-stationary variables integrated of order one.? This is an important consideration given the data considered here (see Charts 1-5, and Appendix III below). The procedure analyzes the relationship among p I(1) or I(0) variables using the following VAR system

(16) AX. = TAX. 4 +... + Py Ake. (e-1) - TX, + pt oD, + EL» where XxX. is a (p,l) vector of observations on the p variables at time t. dD. is a (p,3) matrix of centered, seasonal, dummy variables‘, wisa (p,1) vector of constant terms for each equation. The matrices Tr; and II are (p,p) matrices of coefficients, and « is a (p,1) vector of error terms.

The matrix II captures the long-run relationships between the p variables, and there are three possibilities for it

1. Rank of Il = p, vector process X is stationary. "3. A stationary variable is said to be integrated of order zero, denoted I(0). A non-stationary variable that is rendered stationary by first

differences is I(1). 4. A centered, seasonal dummy variable sums to zero over a year’s time.

2. Rank of I = 0, M1 is the null matrix, AX is stationary. 3. Rank of Il = r < p, there are r linear combinations of X that are stationary, i.e. that are co-integrated.

In the Johansen procedure, the rank of fl is determined by calculating its p eigenvalues and determining if they are different than zero ina statistical sense.” The number of non-zero eigenvalues provides an estimate of r, the number of co-integrating vectors. If O<r<p, then II can be decomposed into two (p,r) matrices a and 8 such that

(17) TI = af’.

It is important to emphasize that these matrices are not unique. Appendix I gives a simple example to clarify these ideas. The matrix 8 consists of the r (p,l) co-integrating vectors® while a, termed the loadings by Johansen, are the coefficients on the co-integrating vector(s) in each of the p equations.

Johansen provides two tests for determining the number of co-integrating vectors. The first is an unconditional test of the form Ho: r < i, while the second is a conditional test of the form Ho: r=i|r=j, j>i. Johansen also develops procedures to test linear restrictions imposed across the coefficients of a and 8, and to test the restriction that the constant terms yp can be incorporated into f, the co-integrating vectors.

The quarterly data set found in H-M, augmented with the domestic cost variable CD, was used in all estimations in this paper (see Appendix

II). The data set contains 62 observations, beginning in first quarter of

1973 (73:1) and ending in the second quarter of 1988 (88:2). Charts 1-5

3. The procedure actually considers a transformation of Il that restricts all the eigenvalues to be real numbers between 0 and 1.

6. Under certain restrictions the constant terms in (2) can be incorporated in the co-integrating vectors, yielding co-integrating vectors of dimension (p+1,1l).

plot the natural logarithms of the five variables (lower case letters denote variables expressed as natural logarithms). In order to implement the Johansen procedure one must choose a value for k, the number of lags in (16). Unfortunately the procedure can be sensitive to the choice of k./

Table 1 presents the results of analyzing the 5 variable system of pm, er, cf. pd, and cd (the variables found in the competitive model), setting k = 2, 3, and 4 to address the sensitivity question. °® The top half of Table 1 presents the estimated eigenvalues and the conditional and unconditional hypothesis tests on the value of r, the number of co-integrating vectors. Starred values indicate a rejection of the null hypothesis shown on the left-hand side of the table at the 5% significance level. It seems clear that the procedure is identifying two co-integrating vectors among these variables. Although not shown in Table 1, a test of the restrictions involved in including a constant term in the co-integrating vector(s) was rejected for all values of k.

The two significant co-integrating vectors, the estimate of 8, are given in the table, with the coefficient on pm normalized to equal -1l in both vectors. Economic explanations of the coefficients in these vectors is difficult at best: the procedure cannot uniquely identify co-integrating vectors since any linear combination of co-integrating vectors is also a valid co-integrating vector. Interpretation must be

guided by an underlying theoretical model, a task complicated by the

7. This is true for other data sets than that considered here. Using the data in Johansen and Juselius and setting k=3 rather than k=2 reverses.some of their conclusions (e.g. money and income homogeneity in Denmark would have been rejected).

8. The Johansen procedure was coded in GAUSS. The program was checked by replicating to the fourth digit the results of Johansen and Juselius.

Ho: Ho: Ho: Ho: Ho:

Ho: Ho: Ho: Ho: Ho:

RAA RA IA IA IA IA JA OrRrNWS

2

- 8-

Table 1

K, Longest lag in Johansen VAR

3

4

Eigenvalues

0.047 0.065 0.265 0.468 0.492

0.057 0.144 0.267 0.454 0.641

Unconditional Hypothesis Tests, Trace

375 .525

395 810"

2.839 6.808

25.004,

62.201, 102.208

3.390 12.416 30.427, 65.493

124.858

Conditional Hypothesis Tests, Maximum Eigenvalue

375 150 306"

*

894

*

084

2.839 3.969 18.196, 37.198)

40.007

3.390 9.025 18.011, 35.066,

59.365

Beta, assuming r = 2

-1.000 0.935 5.511

-2.877

-2.089

-1.000 -0.700 1.217 -0.715 0.463

-1.000 -1.000 -0.591 -0.446 -0.301 1.018 1.433 -0.004 -0.280 -0.146

-1.000 -1.000 -0.615 -0.522 -0.694 0.809 1.795 0.020 -0.244 0.061

Hypothesis Tests of Restrictions Across Rows of B

“Bi3 = Bio * * 6.516 18.607 38.080 Bis = ~(B;17Bi oth 0.937 20.014 22.896" “Bs 3 Z Bs 9 and Bis (Bay Bs otBiy) 22.837" 42.439 59.760" Bi5 = 9 4.426 3.935 4.893

. Denotes statistically different from zero at the 5 % signifigance level.

competing models. Therefore, the implications of each of the three models will be analyzed in turn.

Data generated in a competitive world would yield three co-integrating vectors corresponding to equations (2)-(4) However, the Johansen procedure would only be able to identify arbitrary linear combinations of the three vectors. Re-writing equations (2)-(4) in logarithmic form yields

(18) pd - cd = In(1tr4) = x4

(19) pm + er - cf = In(1trt) = xf

(20) pm - pd = 0 An arbitrary linear combination of these relationships would be written as

pm 0 f -1 -

1 -o-X er ‘| 0 -1 0 -0 (21) cf Tr 0 + o 1 + A 0 j= fo pd 1 0 1 T+X cd -1 0 0 -T constant rt rf 0 -rrteort.,

What is clear from the right-hand side of (21) is that even if the data were generated in a competitive world, one would not expect to find a zero coefficient on er in a co-integrating vector. The only testable restrictions on the co-integrating vectors are those that can be applied across all the co-integrating vectors, or put another way, the only testable restrictions are those that hold for an arbitrary linear combination of the co-integrating vectors. For the competitive model under consideration, two restrictions can be placed across the five rows of the right-hand side of (21). Denoting an element of a co-integrating vector by Bi; (i=column,j=row as in Johansen and Juselius and the opposite

of standard matrix notation) the restrictions implicit in (21) can be

written as

- 10 -

(22) -Bi3 ~ Bip

(23) Bis = -(By1-Bi2*B in): Tests of each of these restrictions are presented at the bottom of Table 1, along with a joint test of the two restrictions. In all cases but one the restrictions are overwhelmingly rejected.

Alternatively, the data might be generated in a non-competitive

world described by (10) and (11), which for simplicity can be written as

CF

(24) PM = ¢CD + XER CF

(25) PD = Her + «CD.

As above, an arbitrary linear combination of these vectors would be given

by: Cc - PM -1 0 -T CF/ER K Bb TKtOp PD T 0 + a -1 = -0 cD ¢ K Toton

Unlike the competitive case, no restrictions can be imposed on the rows of the linear combination of the co-integrating vectors. In this formulation the data are expressed in levels, and CF and ER do not enter independently in any of the co-integrating vectors. The system of PM, CF/ER, CF, PD, CD and constant was estimated to generate the restriction that the

coefficient on CF be equal to zero in all co-integrating vectors. Table 2 presents results for this system, and the restriction that the coefficient

on CF is equal to zero is rejected for lag lengths 3 and 4 but not 2.

-ll- Table 2 K, Longest lag in Johansen VAR

2 3 4

Eigenvalues

0.0052 0.0006 0.0019 0.1031 0.0737 0.0874 0.2741 0.2656 0.2229 0.3099 0.3970 0.3636 0.4383 0.4644 0.5906

Unconditional Hypothesis Tests, Trace

Ho: x4 0.314 0.036 0.111 Ho: x3 6.843 4.556 5.418 Ho: r<2 26.065 22.772, 20.044, Ho: rs 48.319, 52.611, 46.261, Ho: r<0 82.928 89.444 98.065

Conditional Hypothesis Tests, Maximum Eigenvalue

Ho: r=4|r=5 0.314 0.036 0.111 Ho: r=3j}r=4 6.530 4.520 5.307 Ho: r=2|r=3 19.221 18.215 14.627 Ho: r=1[r=2 22.254 29.840, 26.216, Ho: r=0|r=1 34.609 36.833 51.804

—_______sts—“(—é‘~iettA, assuming r= 200

PM -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 CF/ER -30.051 61.825 68.805 50.707 65.227 54.211 PD -0.983 0.659 2.073 0.498 2.122 0.248 cD -1.482 -0.091 -0.354 -0.226 -0.296 -0.014 CF 3.106 -0.318 -1.534 0.034 -1.579 0.083

Hypothesis Tests of Restrictions Across Rows of 8

Bis = 0

a eer rr ey

3.796 17.116" 35.988"

* Denotes statistically different from zero at the 5 % signifigance level.

2

-12-

Table 3

3

K, Longest lag in Johansen VAR

4

Eigenvalues

0.048 0.169 0.330 0.361

0.056 0.080 0.422 0.452

0.065 0.111 0.377 0.655

Unconditional Hypothesis Tests, Trace

Ho: r <3 2.927 3.412 3.915 Ho: xr<2 13.999, 8.306, 10.721, Ho: r<l 38.048, 40.643, 38.166, Ho: xr <0 64.906 76.169 99.947 Conditional Hypothesis Tests, Maximum Eigenvalue Ho: r=3|r=4 2.927 3.412 3.915 Ho: r=2|r=3 11.073, 4.894, 6.806 Ho: r=1|r=2 24.049 32.337, 27.444. Ho: r=0O|r=1 26.858 35.526 61.781 Beta, assuming r = 2 a b b a b a pm -1.000 -1.000 -1.000 -1.000 -1.000 -1.000 er -0.607 -0.660 -0.615 -0.548 -0.574 -0.577 cf 0.715 -0.526 -0. 868 0.517 -0.315 0.726 pd 0.177 1.401 1.735 0.378 1.193 0.172 constant 3.257 3.672 3.501 2.966 3.219 3.081 Hypothesis Tests of Restrictions Across Rows of b3 - -b, 6.789" 20.748" 43.600" by, = by-b, 6.977" 17.704" 37.536" b - “by and b, = b,-by 27.509" 43.304" 69.259" *Denotes

level.

statistically different from zero at the 5 % signifigance

-13-

As a final possibility, the H-M model, (15), expressed in logarithms is given by” (26) pm = -(l-a)er + (l-a)cf + apd,

yielding the co-integrating vector

pm -1 er -(l-a) cf T l-a pd a

Two restrictions can be placed on this vector,

(27) By = -By

(28) By, = Bo-B,-

Moreover, this system can be nested within the five variable competitive system, the restriction that cd equals zero allowing the simplification to the four variable system. This restriction is never rejected (see the bottom of Table 1) and results for the four variable are presented in Table 3,10 Again it appears that the system possesses two co-integrating vectors, rather than the one vector suggested by the H-M model. As shown at the bottom of the table, the restrictions in (27) and (28) are soundly rejected.

None of the models seems to stand-up to the scrutiny of the data, not a surprising result given the simplicity of the models and the aggregate nature of the data. Across the data set, firms in industries probably range from near perfect competitors to near monopolists. Such a disparity of industrial structures, when aggregated, might well be

expected to yield a pass-through coefficient somewhere between zero and

9. The capacity utilization variable used by H-M is ignored here, as it never entered significantly in any of their results.

10. In contrast to the first two systems, for the H-M system the constant terms can be incorporated into the co-integrating vectors for any value of k.

-14-

one as well as more than one co-integrating relationship. This suggests that more fruitful studies of pass-through are probably best conducted at the industry level, where known market structures can be brought to bear on the problem (e.g. Knetter (1989)). It is interesting to note that the indication of two co-integrating vectors is robust across specifications. Additionally, in Table 3, regardless of the value of k, one of the vectors yields coefficients close to the typical pass-through results obtained using single-equation methods (see Sections III and IV below). Averaging

the three vectors labeled "a" in Table 3 yields the vector

pm -1.00 er -.58 cf .65 pd .24

constant 3.10 The coefficients indicate that, in the long-run, firms pass-through approximately 60 percent of a change in either exchange rates or costs. The coefficient on pd suggests that they react very little to a change in competing domestic firms’ prices.

Some researchers have formulated models of hysteresis in import prices, occasionally testing the models by looking for instability in estimated pass-through equations (e.g. Baldwin). A similar exercise can be conducted here, by estimating the Johansen procedure recursively. Such estimation generated the break-point Chow tests for each equation of (14)

found in Charts 6-91 Only the equation for pd exhibits any instability,

11. Let RSS. stand for the residual sum of squares for an estimation whose sample ends at time t. Let RSS, equal the residual sum of squares over the entire sample. The break-point Chow test used throughout this

. Study compares RSS, to RSS,,, correcting for different degrees of freedom.

A series of Chow tésts is Created in a recursive estimation as t moves

(Footnote continues on next page)

- 15 -

and at that only for one time period. Chart 10 plots the average of the coefficients on er from the two co-integrating vectors in Table 3 as sample size increases, setting k=3. Somewhat surprisingly, given the stability results for the individual equations, this average has been far from constant over time, although perhaps it has been in a statistical sense if its standard errors were large enough. The results on stability are mixed, but indications of instability do not appear to be related to exchange rate changes. This is in contrast to the results of earlier work (e.g. Baldwin, Piggot and Reinhart, Mastropasqua and Vona, and in some cases H-M). However, given the different estimation techniques, it is difficult to compare the results presented here with previous work. The next section will focus on single-equation estimations using the variables in the H-M specification to facilitate comparisons with previous work.

The switch to simpler methods is not without costs, as these methods only allow for the identification of a single co-integrating vector. Given the fairly consistent finding of two co-integrating vectors, the

single-equation results might well be an over-simplification.

III. E-G Procedure An alternative estimation strategy to attempt to identify a co-integrating vector among these potentially I(1) variables is the E-G

two-step procedure. However, the E-G procedure is not without its

(Footnote continued from previous page)

towards T. The final point plotted compares RSS, to RSS. The graph plots this series of Chow tests, each divided by its appropriate 5% critical value. Thus, points that lie above 1.0 are periods for which the null hypothesis of a constant structure are rejected.

- 16 -

drawbacks. Unlike the Johansen procedure, the E-G procedure allows for only one co-integrating vector, and each variable in the system must be I(1) and not 1(0). 12 In order to allow for comparisons to earlier work, the four

variable system of H-M was estimated using the E-G technique. The first stage estimation yielded (29) pm, = 2.531 - .586 er, + -652 cf + .405 pd, - .003 trend

R? = .997, o = .0127780, DW = 1.194

RSS = .0093068484 for 5 variables and 62 observations (73:1-88:2). This equation corresponds to (26). The signs of the coefficients are as expected, dollar prices fall with an appreciation of the dollar, rise with an increase in foreign costs, and rise with an increase in the price of competing goods. The coefficients suggest that 60 percent of an exchange rate change is passed through to import prices, with a similar movement in response to a change in costs. Only 40 percent of a change in domestic prices is reflected in a change in import prices. Comparing (29) to (26) gives three estimates of a from the H-M model, respectively they are .413, -630, and .544. As noted above, these coefficients are quite close to the average of the vectors labelled "a" in Table 3.

To test if the residuals from (29) were I(0), an augmented

Dickey-Fuller test (ADF) was run resulting in (t-ratios in parentheses,

significance levels in brackets)

12. A vector consisting of one I(0) variable is trivially a co-integrating vector. Therefore, since the E-G procedure can only identify one co-integrating vector it is important not to mistakenly include 1(0) variables that will confound this identification. Appendix III presents common unit root tests as well as the alternative trend stationary test proposed by DeJong, Nankervis, Savin, and Whiteman (1989) (DNSW) for each variable. As is often the case, it is impossible for almost all of the variables to determine whether or not the variable is I(0) or I(1).

-17-

(30) Au. = .0003 - .605 ued

(.18) (¢-5.01) R? = .299, o = .0114881, DW = 1.874 RSS = .0077865429 for 2 variables and 61 observations (73:2-88:2). The t-statistic is above the critical value of 4.67 found in MacKinnon (1990), indicating that a unit root hypothesis is rejected for these

residuals.

A general to simple approach was used to derive the specification for the second-stage error-correction equation. The steps taken from this general model to arrive at the final specification are shown in Table 4. Across the table, sample size is constant at 57 observations, 74:2-88:2. For each of the steps all the coefficients and their t-ratios are shown, along with a battery of diagnostic tests conducted at each step. 4 A star denotes the rejection of the null hypothesis that the particular problem is absent. Also shown at the bottom of Table 4 are the F-tests of the restrictions imposed in moving from the general to the final specification. The final specification was re-estimated over a slightly longer period, since the sample size was kept constant in moving from general to simple in Table 4, yielding (31) Spm, = - .003 + .165 Apm, 4 - .247 der, + . 885 Apd, - .384 uy

(-1.09) (2.01) (-5.45) (7.60) (-5.61)

+ .003Q1 + .005Q2 - .001Q3

(.93) (1.47) (-.24)

Ro = .830, o = .0084469, F(7,52) = 36.26 [ .0000], DW = 2.104

RSS = .0037101985 for 8 variables and 60 observations (73:3-88:2).

13. An LM test of serial correlation through the fourth lag on the residuals of (30) was insignificant.

14. The regressions were run in David Hendry’s package PC-Give, where all these tests are calculated and displayed.

Constant -.008

Alpm i 225 -.01

Aipm 2 018

Alpm 13 252

Alpm 4 -.118

Aler, -.295

Aler,_ : .057

Aler, 5 .053

Aler 3 102

Aler 4 .008

Alco, 118

Alco, 1 .056

Alco, , -.073

Alco. , -.046

Alco, 4 .092

Alpd, 856

Alpd,_ 1 -.105

Alp, . -.057

Alpd, .254

Alpd,_ 4 -.253

u tt -.526

Qi .009

Q2 .010

Q3 .003

Re

Oo

DW

RSS

LM,AR(4)

ARCH(4)

J-B

LM, het.

RESET2

RESET3

RESET4

General to Intermediate General to Simple Intermediate to.Simple

LM, AR(4): LM test for serial correlation from lags 1 to 4

ARCH(4): Engle’s test for autoregressive conditional heteroskedasticity from lags 1 to 4. J-B: Jarque Bera test for normality

LM test for heteroskedasticity

LM, het.: RESETi

General

.899 .007830 1.839 .002054 3.20° 07

831

na 2.734 1.801 1.219

-2.05 1.31

1.65 -.83 -4.86 .48 51 1.12 07 .76 34 -.41 -.28 52 3.51 -.30 -.17 .80 -.92

-2.83

1.54 2.16 .60

18

TABLE 4

Intermediate

-.005 2.13 186 2.04 -045 47 175 1.91 -.144 -1.87 -.263 6.05 953 8.08 -.384 5.22 005 1.72 007 2.30 002 60

869

007619

1797

002670

44

31

926

1.1371

4091"

2.107

1768

F-tests of Model Simplification

F(13,33)=.76

Denotes statistically different than zero at the 5 % level of signifigance

Test Descriptions

RESET test of adding the second through ith powers ot y to the regression

Simple

-.004 -1.79 .208 2.61

-.251 -§.85

905 8.13

-.400 -§.62

.005 1.58 005 1.78 .001 .39

855 007755 1.880 002947 1.11 33 192 1.2059 2.803 1.509 1.058

F(16,33)=.90 F(3,46)=1.59

- 19 -

Given the interest in parameter stability generated by the hysteresis hypothesis, (31) was estimated recursively, generating Charts 11-13. Chart 11 plots the break-point Chow test for equation (31). Chart 12 plots the error-correction coefficient (the coefficient on a) from (31) along with its standard errors, and Chart 13 does the same for the coefficient on Aer. As is quite obvious, this specification does not exhibit stability problems at any point in time. Ignoring the difficulties in moving from the Johansen procedure to single-equation methods, these results call into question the conclusion that foreign firms began to behave in a different manner when the dollar began its long appreciation.

The question remains, given the finding of two co-integrating vectors by the Johansen procedure, whether the E-G procedure was an appropriate simplification. Further light can be cast on this problem by re-estimating (29) four times, using each of the four variables in turn as the dependent variable. The resulting four estimates of a single co-integrating vector can then compared by dividing each vector by a constant such that the coefficient on pm is set equal to -1 (i.e. moved to the left-hand side). The four estimates of the single co-integrating

vector are

Dependent Variable

Variable pm er cf pd pm -1.000 -1.000 -1.000 -1.000 er - .586 - .663 - .660 -.477 cf 652 .734 1.241 -.214 pd .405 . 330 -.133 1.246 constant 2.531 2.720 2.680 2.112

These results are not encouraging, particularly with respect to cf and pd,

which switch sign across the different dependent variables. It is

- 20 -

interesting how the coefficients from the vector that treats pd as the dependent variable correspond fairly closely to the coefficients from the vectors labelled b in Table 3. The sensitivity to the choice of

normalization re-enforces the presumption of two co-integrating vectors.

IV. Traditional Specification

Further light can be shed on the stability of the pass-through relationship by comparing the E-G results to previous work. An estimated equation from H-M will be used as a representative specification. This equation is fairly typical of previous work in its use of PDLs and AR(1)

corrections!>. They estimated the following equation 7 3 8 (32) pm=b, + 2b, + 2 b, cf. + pit 3P Sti + byocu

er, . 0 i-0 itl t-i =0 i+9 2

R° = .999, o = .0067023, DW = 1.768

RSS = .0018417 for 22 variables and 53 observations (75:2-88:2).

with the coefficients and standard errors

Estimate T-Ratio Estimate T-Ratio bo 3.2395 11.668 bio .16535 2.1005 bj -.21657 -8.077 b13 .79902 3.8538 by - .14935 -15.808 bi, .067019 4922 b3 - .095155 -8.227 bis -.077009 -1.0278 b, - .053993 -3.1109 big -.16633 -3.6853 be - .025859 -1.4626 bj -.20093 -4.4736 be -.010755 - .84742 big -.18083 -3.9537

15. The purpose of the H-M paper was to "update" the pass-through analysis, hence they chose a PDL, AR(1) specification to facilitate comparison to previous work. Only their most general specification will be considered here (their equation (12), as the restrictions imposed by

two other equations are rejected. Baldwin's equations are similar, he corrects for MA(4) errors.

- 21 -

b, - .0086791 - .82027 big -.10602 -3.1618 bs - .019632 -.74058 bog .023504 1.3437 by 071963 89686 boi -20774 3.6981 bio .12132 2.3037 boo -.0066744 -.109 bi .15245 2.6393 rho -42026 3.3718

The equation is corrected for first order serial correlation, and the distributed lags on cf and er are estimated as second-order PDLs. The distributed lag on pd places no constraint on the contemporaneous coefficient and a second-order PDL on the remaining coefficients.

Recursive estimation of (32) generated Charts 14-16. Chart 14 plots the break-point Chow tests for structural stability, while Charts 15 and 16 plot the short-run and long-run pass through coefficients as well as their standard errors. Chart 14 indicates structural instability when comparing periods through 1981 with later periods. Charts 15 and 16 indicate an approximately 50 percent reduction in absolute size of both the short-run and long-run elasticities during 1981. This instability is “not unique to the H-M equation, as H-M state "On balance, the literature seems to support structural breaks in both the import price equation and the pass-through coefficient in the early 1980s. Our own results on this point are mixed.» 16 Previous work has attributed such shifts to changes in foreign firm behavior due to the large appreciation of the dollar that began in roughly 1981.

It is surprising that the H-M equation shows problems with structural breaks, while (31) doesn’t, Changes in the correlations between the explanatory variables in (31) and (32) can be used to pinpoint

the cause of the instability in (32). To this end, correlations for these

16. Hooper and Mann p. 320. See also Piggot and Reinhart, Baldwin, and Mastropasqua and Vona (1988).

- 22 -

two sets of variables were calculated over the periods 75:2-80:4 and 82:1- 88:2. The biggest change in correlation over the two periods was between the PDL, serial correlation corrected pd in (32) and Apd from (31). This change in correlation suggests that the use of the PDL and the correction for serial correlation perhaps obscured the fundamental change that took place in domestic prices around 1981, muting the influence of domestic prices on import prices. The change is probably the result of the change in monetary policy operations begun in October 1979. This misspecification, brought about by inappropriate data transformations, !’ is a likely cause of the instability exhibited by (32), rather than a change in behavior of economic agents in response to the large dollar appreciation. 18 Unfortunately, the appropriate alternative specification

is still not clear given the troubling instability of the Johansen

procedure.

V. Conclusions

This paper makes two points. First, pass-through at the macroeconomic level is a complicated amalgamation of disparate industrial structures that involves more than one long-run equilibrium relationship between the variables of interest. The data are inconsistent with the three over-simplified models considered here. Efforts to relate the pass-through coefficient to parameters from a theoretical model are best done at as disaggregated a level as possible. Second, claims of changes in the aggregate behavior of economic agents in light of the large dollar

appreciation appear to be unfounded.

17. Tests of the common factor restriction imposed by the serial correlation correction in equation (30) fail. 18. H-M are careful not to make this claim.

References

Baldwin, Richard E. 1988. "Hysteresis in Import Prices: the Beachhead Effect." American Economic Review 78:773-85.

DeJong, David, J.C. Nankervis, N.E. Savin, and C.H. Whiteman. 1989. "Integration Versus Trend-stationarity in Macroeconomic Time Series." University of Iowa Department of Economics Working Paper No. 89-31 (December) .

Dornbusch, Rudiger. 1987. "Exchange Rates and Prices." American Economic Review 77:93-106.

Engle, Robert, and C.W.J. Granger. 1987. "Co-integration and Error Correction: Representation, Estimation, and Testing." Econometrica 55:251-76.

Hendry, David F. 1989. PC-Give An Interactive Econometric Modelling System. Institute of Economics and Statistics University of Oxford.

Hooper, Peter, and C.L. Mann. 1989. "Exchange Rate Pass-through in the

1980s: The Case of U.S. Manufactures." Brookings Papers on Economic Activity 1:1989,

Johansen, Soren 1990. "Estimation and Hypothesis Testing of Co-integration Vectors in Gaussian Vector Autoregressive Models." Econometrica forthcoming.

Johansen, Soren, and K. Juselius. 1990 "Maximum Likelihood Estimation and Inference on Co-integration - With Applications to the Demand for Money." Oxford Bulletin of Economics and Statistics 52:169-210.

Knetter, Michael M. 1989. "Exchange Rate Pass-Through: An Industrial Organization Approach." Working Paper No. 89-16, Department of Economics, Dartmouth College.

MacKinnon, James G. 1990. "Critical Values for Cointegration Tests." Discussion Paper No. 90-4, Department of Economics, University of California, San Diego.

Mastropasqua, Cristina, and Stefano Vona. 1988 "The U.S. Current Account Imbalance and the Dollar: The Issue of the Exchange Rate Pass-through." Banca d'Italia (December) .

Piggott, Charles, and Vince Reinhart. 1985. "The Strong Dollar and U.S. Inflation." FRB of New York Quarterly Review 10:23-29.

- 24 -

APPENDIX I - Simple Example

Consider the relationship between the price of crude oil (C), heating oil (H), and gasoline (G). One might conjecture that the price of crude oil follows a random walk, and that in the long-run the prices of heating oil and gasoline move one-for-one with the price of crude oil. This system would possess two co-integrating vectors, subtracting H from C, and G from C (or equivalently G from H) would generate two I(0) combinations of I(1)

variables. Such a system might have the following dynamic representation

CLT Ce-1 + ae

HL = -07C. 4 + -03C, 5 + -SH. 4 + 4H oo + €o,

GC. = 146, 4 + .06C. 4 + 36.4 + 5G. 9 + ea)

This can be written as AX. = PAX. 4 + M9 + Eee AC, |° 0 0 ea | 0 oO Ofic., cr 4H = j.07 -.5 0 j OAL ; + 1 -.1 0 Ho + feo, AG, |.14 0 -.7 [ace | 2 0 -.2)/6. 5] e344

a B' II r “~ . 0 0 -l1 1 0 Ha 0 -.1 0) -1 0 lj-e 1 ) 0 -.2 2 2

L

- 25 -

However, II could also be decomposed as

fo B' II 0 0 -1.5 2 -.5 0 0 0 -.1 -.1 5 -1 .5 |= |].1 -.1 0 -.4 -.8 .2 0 -.2

generating a very different looking estimate of 8. Normalizing the two estimates of £ so that the first coefficient in each column equals -1 (as

in the text) would give

- -1 -1 -1 -1 1 0 and 1.33 2 0 1 -.33 -1

In this system, the only restriction that can be imposed across the rows

of both columns of £ is b3 - ~ (bj +b,).

- 26 -

Appendix II - Data

The following brief data descriptions are for the most part taken

directly from H-M:

PM =

PD =

Fixed-weighted average (using 1982 imports share weights) of import prices for capital goods, automotive products, consumer goods, and industrial supplies excluding petroleum and products.

Weighted average of producer price indexes for various manufacturing sectors weighted by shares in U.S. imports.

CD = Weighted average of manufacturing unit labor costs and

the producer price index for crude materials for further processing.

The foreign variables were constructed using nine countries that comprise

approximately

ER =

CF =

CU =

75 percent of non-oil manufactured imports .!?

Weighted average of foreign exchange rates, using variable current-import-share weights.

Variable current-import-share weighted average of individual country costs. For each country a weighted average of

unit labor compensation in manufacturing and price indexes for raw material and energy inputs into manufacturing was constructed. The weights used were .65 for labor and .35 for materials and energy.

Weighted average of foreign capacity utilization rates using variable current-import-share weights.

19. The countries were Canada, United Kingdom, West Germany, France,

Italy, Japan,

Korea, Taiwan, and Mexico.

- 27 -

APPENDIX III - Stationarity Tests

Table A.1 presents six stationarity tests (corresponding to the six columns) for each variable and its first difference. Test statistics

for six null hypotheses concerning the parameter 19 from the regression

t n - j-1 i . (A.1) X Yo + yt + 9X p41 + 73207 + fan i*$ 5 (x, M%e-4-1)

are presented, where x is the natural logarithm of the variable of interest (e.g. pm = 1n(PM)). The familiar Dickey-Fuller (DF) and augmented Dickey-Fuller (ADF) tests of the null hypothesis Yor1 are displayed in columns 1, 2, 4, and 5. As an alternative, the DeJong, Nankervis, Savin, and Whiteman (1989) (DNSW) test of the null hypothesis

You-95 is displayed in column 3, and an augmented DNSW (ADNSW) test is

shown in column 6.29 Below each test statistic is an LM test of serial

correlation up to the fourth order in the residuals of (A.1).

20. The DNSW paper does not present an augmented test although they do note that most macroeconomic time series display positive serial correlation that invalidates the test they propose. I constructed the ADNSW test in order to make inference in the presence of positive serial correlation. Critical values for this test were obtained by Monte Carlo methods using 5000 repetitions and 10 values of rho (0.0 through .9) for the model

Xe 7 Z,, z= 992,04 + Use Us Our + te

One-sided critical values obtained for the values of rho were C7] 0.0 1 .2 3 4 5 6 7 8 9 OGD critical value -.72 -.73 -.73° -.73 -.72 -.73 -.70 -.64 -,47 +.38

The critical value reported in the table was that for @=.3, the @ that fit most closely the six series used in the pass-through analysis.

- 28 -

Table A.1 DF DF NSDW ADF ADF ANSDW n=-0 n=-0 n=0 n=1 n=1 n=l 170,750,171 1370,1422 147-95 747947370 74-1 1370: Wwrl yn-95

Ho: Youl Ygul ¥9™-95 Youl Youl 197: 95 Hot Mth PTT pm * * T-stat -4.894 3,405 613 -1.718 -2.085 -1.413 LM-sig __.000 “000 “000 “821 927 878 er * * T-stat -.973 - 542 1.122 -1.501 -1.148 -.161 LM-sig .023 "014 "054 _736 679 "752 co * * * T-stat -5.381 -2.426 -.152 -2.910 -2.229 -1.272 IM-sig .024 "012 "002 "108 "193 “061 cu * T-stat -2.426 -1.920 - 693 -3.472 -3.373 -2.947 LM-sig _.000 “000 -000 -870 876 (926 pd * * T-stat -6.560 -1.037 652 -2.307 -1.641 -1.664 LM-sig 000 "000 "000 "719 "700 686 cd * * T-stat 4.897 -0.763 745 -3.092 -0.648 0.101 LM-sig _.001 "002 “000 “003 “004 "001 Apm * * T-stat -3.807 -3.763 -3.458 -2.652 -2.673 -2.672 IM-sig _. 861 "886 033 399 “424 "007 Aer T-stat -5.255" -5.319" -4.974 -4.112" -4.218" -3.814 LM-sig _—-. 871 "885 "590 663 "788 “442 Aco T-stat -4.091" -4.804" 4.570 -3.305" -3.792* — -3.413 IM-sig .081 378 “017 "184 "394 007 Acu T-stat -3.757" -3.796" -3.371 -3.807" -3,889" -3.517 IM-sig .428 "189 “015 568 "161 024 Apd T-stat -2.498 -3.090 -2.572 -2.500 -3.441 -2.996 IM-sig .591 "694 "108 "866 "580 “000 Acd T-stat -5.053 -6.300 -5 860 -3.301 -3.812 -3.339 IM-sig .000 -007 “000 “000 “001 “000

EEE

*statistically different from zero at the 5% signifigance level

- 29 -

Significant serial correlation makes inference impossible using the DF and DNSW tests for the levels of the variables. For the augmented tests the troubling but common result is that: 1) the ADF tests cannot reject the difference stationary (I(1)) hypothesis (with the exceptions of cf and cu when 170) and 2) the ADNSW test cannot reject the trend stationary (I(0)) hypothesis. 24 Tests based on the differences of the variables indicate that with the possible exception of pd and cd, none of the variables needs to be differenced more than once to be rendered stationary (i.e. none appear to be I(2)). In sum, no firm conclusion regarding the stationarity of the univariate process for each variable can be reached. However, this result is not as troubling as might first appear. The issue to be examined here is the process for pm conditional on the remaining variables. Keeping this in mind, the results in Table 1 indicate the importance of flexible estimation strategies, such as the

Johansen procedure, that allow for I(1) variables.

21. Although the ADF(1) tests for cd continue to display significant serial correlation, the residuals for an ADF(5) do not and the difference stationary hypothesis cannot be rejected for the ADF(5). However, augmenting the DNSW test with as many as six lags was not successful in eliminating the serial correlation.

"73-1 76-1 79-1 82-1 85-1

Chart 2

“73-1 76-1 79-1 82-1 85-1 88-1

Chart 3

TH 761 79-1 82-1 85-1

Chart 4

Chart 5 cd

48

47

46

45

44

43

4.2

41

79-3 80-3 81-3 82-3 83-3 84-3 85-3 86-3 87-3 Last Period in Estimation

- 33 -

Chart 7 Break-Point Chow, er in VAR eq. (16)

82-3 83-3 84-3 85-3 86-3 87-3

Last Period in Estimation

Chart 8 - Break-Point Chow, cf in VAR eq. (16)

82-3 83-3 84-3 85-3 86-3 87-3

Last Period in Estimation

- 34 -

Chart 9 Break-Point Chow, pd in VAR eq. (16)

79-3 80-3 81-3 82-3 83-3 84-3 85-3 86-3 87-3 Last Period in Estimation

Chart 10 Coefficient on LER, Average

79-1 80-1 81-1 82-1 83-1 84-1 85-1 86-1 87-1 88-1 Last Period in Estimation

- 35 -

Chart 11 Break-Point Chow, eq. (31)

80-4 81-4 82-4 83-4

- 84-4 85-4 86-4 87-4 Last Period in Estimation

Chart 12 Coefficient on ECM +/- 2 S.E. eq. (31)

06

0.4

0.2

80-4 81-4 82-4 83-4 Last Period in Estimation

84-4 85-4 86-4 87-4

- 36 -

Chart 13 Coefficient on er +/- 2 S.E. eq.(31)-

0.6

04

0.2

-1 78-4 79-4 80-4 81-4 82-4 83-4 Last Period in Estimation

84-4 85-4 86-4 87-4

Chart 14 Break-Point Chow, eq. (32)

0 78-4 79-4 80-4 81-4 82-4 83-4 Last Period in Estimation

84-4 85-4 86-4 87-4

- 37 .-

S-R Coefficient on er eq. (32)

0.6 0.4

0.2

4 va

Last Period in *eoimation

L-R Coefficient’ on er, eq. (32)

Last Period in Estimation

IFDP NUMBER

387

385

384

383

382

381

380

378

377

374

373

372

- 38 -

International Finance Discussion Papers TITLES 1990 Estimating Pass-through: Structure and Stability Evidence

International Capital Mobility: from Long-Term Currency Swaps

Is National Treatment Still Viable? U.S. Policy in Theory and Practice

Three-Factor General Equilibrium Models: A Dual, Geometric Approach

Modeling the Demand for Narrow Money in the United Kingdom and the United States

The Term Structure of Interest Rates in the Onshore Markets of the United States, Germany, and Japan

Financial Structure and Economic Development

Foreign Currency Operations: An Annotated Bibliography

The Global Economic Implications of German Unification

Computers and the Trade Deficit: The Case of the Falling Prices

Evaluating the Predictive Performance of Trade-Account Models

Towards the Next Generation of Newly Industrializing Economies: The Roles for Macroeconomic Policy and the Manufacturing Sector

The Dynamics of Interest Rate and Tax Rules in a Stochastic Model

Stock Markets, Growth, and Policy Prospects for Sustained Improvement in U.S. External Balance: Structural Change versus

Policy Change

International Financial Markets and the U.S. External Imbalance

—_o

Please address requests for co

AUTHOR(s)

William R. Melick Helen Popper Sydney J. Key Douglas A. Irwin David F. Hendry

Neil R. Ericsson

Helen Popper

Ross Levine

Hali J. Edison Lewis S. Alexander Joseph E. Gagnon Ellen E. Meade Jaime Marquez

Neil R. Ericsson

Catherine L. Mann

Eric M. Leeper Ross Levine

Catherine L. Mann

Deborah Danker Peter Hooper

pies to International Finance Discussion

Papers, Division of International Finance, Stop 24, Board of Governors of the

Federal Reserve System, Washington, D.C.

20551.

IFDP NUMBER

371

370

369

368

367

366

365

364

363

362

361

360

359

358

357

356

355

- 39 -

International Finance Discussion Papers

TITLES

1989

Why Hasn't Trade Grown Faster Than Income? Inter-Industry Trade Over the Past Century

Contractionary Devaluation with Black Markets for Foreign Exchange

Exchange Rate Variability and the Level of International Trade

A Substitute for the Capital Stock Variable in Investment Functions

An Empirical Assessment of Non-Linearities In Models of Exchange Rate Determination

Equilibrium in a Production Economy with an Income Tax

Tariffs and the Macroeconomy: from the USA

Evidence

European Integration, Exchange Rate Management, and Monetary Reform: A Review of the Major Issues

Savings Rates and Output Variability in Industrial Countries

Determinants of Japanese Direct Investment in U.S. Manufacturing Industries

The U.S. and U.K. Activities of Japanese Banks: 1980-1988

Policy Rules, Information, and Fiscal Effects in a "Ricardian" Model

A Forward-Looking Multicountry Model: Mx3

Implications for Future U.S. Net Investment Payments of Growing U.S Net International Indebtedness

U.S. Policy on the Problems of International Debt

International Economic Policy: The Role of Exchange Rates

An Econometric Analysis of UK Money Demand in Monetary Trends in the United States and the United Kingdom by Milton Friedman and Anna J. Schwartz

AUTHOR(s

Joseph E. Gagnon Andrew K. Rose Steven B. Kamin Joseph E. Gagnon

Guy V.G. Stevens

Richard A. Meese Andrew K. Rose

Wilbur John Coleman 17

Andrew K. Rose Jonathan D. Ostry

Garry J. Schinasi

Garry J. Schinasi Joseph E. Gagnon

Catherine L. Mann Henry S. Terrell Robert S. Dohner

Barbara R. Lowrey

Eric M. Leeper Joseph E. Gagnon Lois E. Stekler William L. Helkie Edwin M. Truman

Edwin M. Truman

David F. Hendry Neil R. Ericsson