The Constancy of Illusions or the Illusion of Constancies: Income and Price Elasticities for U.S. Imports, 1890-1992

International Finance Discussion Papers Number 475

July 1994

The Constancy of Illusions or the Illusion of Constancies: Income and Price Elasticities for U.S. Imports, 1890-1992

Jaime Marquez

NOTE: International Finance Discussion Papers are preliminary materials circulated to stimulate discussion and critical comment. Reference 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(other than an acknowledgment that the writer has had access to unpublished material) should be cleared with the author or authors.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 Virtually all we know about the behavior of U.S. imports rests on studies estimating income and price elasticities with postwar data. But anyone examining the evolution of U.S. trade cannot avoid asking whether the postwar period provides enough information to characterize that behavior. From 1890 to 1940, the United States became an increasingly closed economy and experienced the most pronounced fluctuations in income and prices of this century. Is our current understanding of the behavior of U.S. imports consistent with those features of the U.S. economy? Being consistent with the distant past might not appear as relevant for forecasting, but the literature ignoring that past offers a range of elasticity estimates wide enough to suggest that the role of income and prices in determining imports is not known with any precision. This paper offers the first analysis of that role using data since 1890. Estimating the elasticities of the most popular model in the literature with 1890-1992 data, I find that income and frices do not affect imports whereas the opposite conclusion arises with postwar data. The difference in results stems from differences in the time-series properties of the data in the two samples. As an alternative, I consider several models consistent with both optimization and the time-series properties of the data. These models predict substantial secular changes in income and price elasticities and confirm “he importance of optimization for characterizing the behavior of U.S. imports. What is new about the results is that only through optimization can one recognize the implications of the

evolution of U.S. trade for estimating elasticities.

The Constancy of Illusions or the Illusion of Constancies: Income and Price Elasticities for U.S. Imports, 1890-1992

Jaime Marquez! Virtually all we know about the behavior of U.S. imports rests on studies estimating income and price elasticities with postwar data. But anyone examining the evolution of U.S. trade cannot avoid asking whether that period provides enough information for characterizing that behavior. From 1890 to 1940, the United States became an increasingly closed economy and experienced the most pronounced fluctuations in income and prices of this century. Are existing explanations of the behavior of U.S. imports consistent with those features of the U.S. economy? Being consistent with the distant past might seem irrelevant for practical applications, but the literature ignoring that past offers a large range of estimates suggesting that the role of income and prices in determining imports is not known with any precision. This paper examines that role using data since 1890 and offers three new findings.

First, the treatment of elasticities as constant parameters, even if valid for each study considered individually, is not valid when all studies are considered as a whole: As a collection, existing elasticity estimates are systematically influenced by the switch from fixed to floating exchange rates, even if the estimates from individual studies were constant. This paradox stems from the use of estimation samples covering short and non-overlapping periods that cannot detect secular changes in elasticities. Thus agreeing on a characterization of U.S. imports requires the longest span of data available. Second, when the sample includes the longest span of data, the estimates from the widely used log-linear formulation are effectively zero whereas the Opposite conclusion arises with postwar data alone. Di‘ferences in the time-series Properties of the data in the two samples account for this finding: the postwar sample exhibits cointegration among imports, expenditures, and relative prices

whereas the full sample does not exhibit this property. Third, only models resting on optimizing

1 The author is a staff economist in the Division of International Finance. I have benefited from comments by William Barnett, David Bowman, Clive Granger, William Helkie, Dale Henderson, David Hendry, Jon Faust, Cathy Mann, William Melick, and seminar participants of our workshop series. The calculations use the following software: Limdep 5.0, PC-GIVE 7.0, and PC-FIML. I am grateful to David Hendry for allowing the use of a preliminary release of PC-FIML. The views expressed in this paper are the author's and should not be interpreted as reflecting those of the Board of Governors of the Federal Reserve System or other members of its staff.

behavior can incorporate both the evolution of U.S. trade and the properties of the associated timeseries. The estimated income and price elasticities from these models fluctuate in response tc changes in the composition of expenditures; models that ignore this response overstate the sensitivity of U.S.

imports to changes in income and prices.

2. Second Thoughts

Most econometric analyses of U.S. imports treat income and price elasticities as constant pare meters (Marquez, 1992). This assumption would be useful if the dispersion of estimates were small. But a survey of fifty years of econometric work (appendix A) reveals an unsettling dispersion of elzsticities that range from -0.5 to -4.8 for price and from 0.8 to 4.0 for income (figure 1). In addition, the estimates contradict economic theory which predicts that if income and price elasticities are constant, then they must equal one and minus one (Deaton and Muellbauer, 1980b, p. 17).

The dispersion of estimates shown in figure 1 might arise from differences in modeling assumptions and sample periods. To quantify the relative importance of these possibilities, I model the elasticity estimates with a fixed-effect model in which the dependent variable is the ith study's elasticity estimate and the explanatory variables are the associated modeling assumptions (shown in appendix A): (1) & = Q + o,Fixed + o,No-homogeneity + o,Annual + o,Static + o.Shiller + @.IV + Oil + u, , where €, = Long-run elasticity estimate of the ith study.

Fixed = Dummy variable equal to one if exchange rates are fixed in the sample.

No-homogeneity = Dummy variable equal to one if price homogeneity is absent.

Annual = Dummy variable equal to one if the sample's frequency of observation is annual.

Static = Dummy variable equal to one if the estimates abstract from delayed adjustments.

Shiller = Dummy variable equal to one if dynamic adjustments follow a Shiller lag.

IV = Dummy variable equal to one if the estimation method recognizes simultaneity.

Oil = Dummy variable equal to one if imports include oil.

Figure 1: Income and Price Elasticities for U.S. Imports

selected studies

Incorne Elasticity / Total imports

-

1920 1945 1970 The honzontal line represents range of the study

Income Elasticity / Non-oil Imports

4.75 4.5

4.25

3.75 3.5

3.25

2.75 2.5

2.25

1.75

1.5

1.25

0.75

0.5

0.25

0 1949 196C 1971 1982 1993

The hori::ontal line represents the estimation range of the study

Price Elasticity / Total Imports

1920

Price Elasticity / Non-oil Imports

1949

1960

1970

1971

1982

2.25

1.75 1.6

1.25

0.75 0.5

0.25

0 1993

u, = White noise disturbance.

Extending the list of explanatory variables is possible but would exhaust the degrees of freedom. The parameter , is the prototype elasticity for studies that (1) use data for the period of floating exchange rates, (2) assume price homogeneity, (3) employ either semi-annual or quarterly data, (4) allow for lagged responses that do not involve Shiller lags, (5) apply ordinary least squares, and (6) exclude oil from the measure of imports.’ The other parameters in (1) measure the extent to which alternative modeling assumptions change the prototype elasticity. For example, if @, is significantly different from zero then elasticity estimates based on data for the period of fixed exchange rates differ from the estimates based on data for the floating exchange-rate period.

I estimate the parameters of (1) using data from 33 studies listed in appendix A, the estimation method is weighted least squares where the weights equal the inverse of the estimated standard errors of the long-run elasticity estimates. The prototype estimates are 2.04 for income and -1.22 for prices (table 1). These estimates are not sensitive to either frequency of observation or estimation method but are sensitive to the treatment of price-homogeneity, the specification of dynamic adjustments, and the exchange-rate system.’ Specifically, the estimate of ©, in (1) is negative and significant which means that the estimated price elasticities based on data for the period of floating exchange rates are lower (in absolute terms) than the estimates based on data for the period of fixed exchange rates; estimated income elasticities exhibit the opposite pattern.

This finding indicates that even if the assumed constancy of elasticities were correct for each study considered individually, it is not correet when all studies are considered as a whole. This

paradox stems, as figure 1 suggests, from the use of small samples with a minimal of overlap; not one

2 The Shiller lag is singled out even though only one study (Wilson and Takacs, 1979) used this technique because the elasticity estimates appear to be outliers.

> Several studies that report ordinary least squares (OLS) results note that in preliminary testing, simultaneous-equation estimation yields nearly the same results as OLS estimation--see, for example, Geraci and Prewo (1982) and Helkie and Hooper (1988).

3a

Table 1 Estimation Results from Fixed-Effect Model of Trade Elasticities

€, = Oy + O, Fixed + &, No-homogeneity + a, Annual + a, Static + a, Shiller + oO, IV + a, Oil + u,

Dep. Variable > Income Elasticity Price Elasticity

[Noshomegeneiy | 009 | 036 | 074 aos | 0.10 | 070 “186

R2

€, = Estimate of the long-run elasticity of the ith study.

Fixed = Dummy variable equal to one if exchange rates are fixed in the estimation sample. No-homogeneity = Dummy variable equal to one if price homogeneity is absent.

Annual = Dummy variable equal to one if the sample's frequency of observation is annual. Static = Dummy variable equal to one if the estimation abstracts from delayed adjustments. Shiller = Dummy variable equal to one if dynamic adjustments are modeled with Shiller lags. IV = Dummy variable equal to one if the estimation method recognizes simultaneity.

Oil = Dummy variable equal to one if imports include oil.

study covers the postwar period as whole, much less the whole evolution of U.S. trade. Short and discontinuous samples do not have enough information for detecting parameter instability arising from secular forces. Equation (1), however, effectively combines all of these sub-samples and uncovers the instability concealed by sample selection. Overall, the results suggest that a necessary condition for achieving consensus on the role of income and prices in determining U.S. imports is the use of the

longest span of data available.

3. Hidden History Inspecting the evolution of U.S. openness since 1890 reveals several features pertinent for characterizing the behavior of U.S. imports (figure 2). First, the United States became an increasingly closed economy during the prewar period with the share of imports in expenditures declining from eight percent to two percent; this pattern stands in sharp contrast to the experience of the postwar period. Second, the volatility of expenditures and relative prices during the prewar period dwarfs that of the postwar period; neither the oil-price shocks nor the exchange-rate fluctuations of 1970-80 induced changes in relative prices comparable to those occurring in the beginning of this century. Finally, the U.S. population has been aging with the share of the population of at least sixty-five years of age increasing from 3.8 percent in 1890 to 12.2 percent in 1992 (figure B1, appendix B). Aging might affect preferences with a corresponding effect on purchases.*

Given these data, I use OLS to estimate the parameters of a widely used log-linear formulation

assuming imperfect substitutability between domestic and foreign products:

(2) B,(L)In(m") = By + By(L)In(y’,) + Bs(L)IN(p "im /P'a)»

“ Branson (1980), Dornbusch and Fischer (1986), and Lipsey (1994) document the evolution of U.S. openness but do not quantify the role of income and prices in explaining U.S. imports. Appendix B discusses the construction of the series, displays the evolution of their components, and reports the associated data sources. Real expenditures equal real GNP plus real imports of goods and services minus real exports of goods and services. The relative price of imports equals the ratio between the non-oil tariff-adjusted price of non-oil imports and the GNP deflator.

Figure 2:

4a

Imports, Relative Prices, and Expenditures

United States, 1890-1992

Percent

Non-oil Imports 19878

, Expenditure Share ,

Per Capita Level

ie) 1890

1900 1910 1920 1930 1940 1950 1960 1970 1980

Relative Price Percent

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980

Per Capita Domestic Expenditures 19875

1890 1900 191C 1920 1930 1940 1950 1960 1970 1980 1990

0 1990

50 1990

Per Capita Non-—oil Imports — Growth Rate

Percent

2000

1800

1600

1400

1200

1000

800

600

400

200

4 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

Relative Price — Growth Rate Percent 300

250

200

150

100

3 1990

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980

Per Capita Domestic Expenditures — Growth Rate Percent

20000 25

18300 20 16600 14900 13200 5 11500 0

9800 5

8100

6400 15

4700 20

3000

25 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

where B,(L) is a polynomial in the lag operator L (i > 0) and the symbol "*" denotes variables demographically scaled.° Because these variables are not observable, I follow Pollak and Wales (1992, pp. 76-78) and express them as m’, = ma,*, y’, = y,a,°, and p', = p,ae for i=m,d, where m, is percapita imports; a, is the share of U.S. population of at least sixty-five years of age; Py is the price of non-oil imports adjusted by non-oil tariffs; pg is the price of domestic products; y, is per-capita real domestic expenditure, and & is the demographic-scaling parameter. Given these assumptions, (2) becomes (3) B,(L)In(m,) = By + By(L)In(y,) + ByL)In(pyy /Pa) + &(B, (L) - By(L)) In(a). The long-run elasticities are B,(1)/B,(1) for income and B,(1)/B,(1) for prices; if B,(1) = 0 then imports lack a steady state; I include three dummy variables in (3) to control for world-war disruptions.® Based on 1890-1992 data, the long-run elasticity estimates of (3) lack statistical s:gnificance and are, relative to existing studies, extraordinarily large (table 2).’ Moreover, the estimated coefficient for the lagged dependent variable is nearly one and the magnitude of the other coefficient estimates suggests that the equation can be re-written in logarithmic differences. Overall. this formulation indicates that imports do not have a steady state. Starting the estimation period in 1960, however, reverses these findings: long-run elasticities are significantly different from zero, the coefficient for the lagged dependent variable is far from one, and the estimates replicate those found in the literature (which violate the theoretical benchmarks); population aging, as modeled here, plays no

role in determining U.S. imports.

> The logarithmic formulation is the most common specification for modeling U.S. imports (see Goldstein and Khan 1985 and Marquez 1992); for demographic scaling see Pollak and Wales (1982).

6 Using several test statistics, I cannot reject the hypothesis that the variables in (3) are integrated of order one which means that the regression is balanced; appendix C documents these results. Note that (3) is an unrestricted Autoregressive Distributed Lag and its long-run parameters are identical to those given by the Error- Correction formulation (see Banerjee et al., 1993, section 2.5).

7 To select the lag structure, I begin with a formulation having four lags for imports, income, relative prices and test for zero restrictions at each lag length.

6

The difference in results in the two samples is not due to heteroskedasticity, serial correlation in the residuals, or failure to meet the functional-form test.’ Rather, the difference in results stems from differences in the time-series properties of the data in the two samples. For 1890-1992 data, the Engle-Granger cointegration test (Engle and Granger, 1987) indicates that these variables do not have a long-run relation among themselves--that they are not cointegrated--whereas estimates using 1960- 1992 data reverse this finding; Clarida (1994) also finds cointegration for postwar data. Thus the results suggest that (2) has a long-run relation if the estimates do not use data covering a long run.

The cointegration results of table 2 treat, however, income and prices as given and I examine the importance of this treatment with Johansen's technique (Johansen, 1988). This technique uses the reduced form. of a dynamic, simultaneous system for imports, expenditures, and relative prices:

(4) Ax, = 9 + T, Ax,, +..4 T; Ax,; + Tx,, + 6D, + u, ,

where x, is a 3x1 vector with the three variables of interest; D is a vector of exogenous variables; T is a 3x3 matrix of coefficients; and u, is a 3x1 vector of serially independent and jointly normal disturbances. The exogenous variables included in (4) are the war dummies and the share of population of 65 years of age and older; statistical tests for these data reveal that four years accounts for delayed zdjustments.

Johansen shows that the rank of I’ gives the number of cointegrating relations--that is, the number of equations for which a long-run formulation exists. To determine the rank of I, Johansen estimates T° with a maximum likelihood method, computes the associated eigenvalues, and shows that the rank of I’ equals the number of non-zero eigenvalues. Johansen and Juselius (1989) offer a statistic to test whether the ith eigenvalue is zero (A(i),,,,) and another statistic to test whether the sum of r eigenvalues is zero (A(r) ace). Based on 1890-1992 data, both statistics indicate that the rank of T is

8 J test homoskedasticity using Engle's ARCH test (Engle,1982). I test serial independence by

applying an F-test to the hypothesis that all the coefficients of an AR(4) for the residual are zero. The test for

functional form uses Ramsey's statistic. These tests are implemented and documented in Doornik and Hendry (1992).

5a Table 2

Sensitivity of Income and Price Elasticities to Sampie Period:Log-inear Formulation

inom) = B, + Sinon ys + Boing e Baya) +t SycltD + BaP) + PuiMay + Samia)

| | 1890-1992 900.1992 | 960-1992 ee MC ec ce

LR Income Bastcty| 1669 | 02 | 2632] 7.475] ee ee ee ee CS ee ser | ors] | cos} seria ndependencee | ors | | ot | Homostedastciy’ | 043 | | | skewness | os | | excess Kunosis’ | 2.05 | | on | | |

| |

Functional Form

: . f

Notes: m is per-capita, real non-oil imports; y is per-capita, real domestic expenditures; p is the ratio of the tariff-adjusted non-oil import price to the GNP deflator. The regression includes three dummy variables for three war years: 1918, 1942, and 1946.

“Significance level for rejecting the hypothesis that residuals are serially independent.

Significance level for rejecting the hypothesis that residuals are homoskedastic.

“Skewness of the empirical distribution of the residuals; this entry is zero for a normal distribution. “Excess Kurtosis of the empirical distribution of the residuals; this entry is zero in normal distributions. *Significance level for rejecting the choice of functional form using the RESET test statistic. ‘Engle-Granger test of cointegration: a ** denotes significant at the 1 percent level.

zero (table 3): the procedure cannot identify a single long-run relation among the logarithms of imports, price, and expenditures just as found in table 2.

Table 3 Cointegration Tests for Imports, Relative Prices, and Expenditures: United States, 1890-1992

log-differences Null Hypothesis 1 Mr) race Mr) race Rank > 1 7.15 Rank 2 2 17.15**

Note: A "**" denotes statistical significance at the one percent level. Both Mi)max ANd Mr)erace include ar adjustment for degrees of freedom equal to the product of the number of variables and the number of lags. The critical values for M(i)max are 21, 14.1, and 3.8; the critical values for A(7)srace are 29.7, 15.4, and 3.8.

This failure to find cointegration does not involve, however, a rejection of the imperfect substitute model embodied in (2). Indeed, the solution to the first-order conditions for optimization relates changes in purchases to changes in income and relative prices suggesting that changes in these variables should be cointegrated. Cointegration results for differenced data support this theoretical prediction (table 3) and suggest that modeling U.S. imports in terms of expenditures and relative prices

should use data in first differences. The remaining question is how.

4. Model. Formulation and Results

I assume that individuals determine their spending on domestic and foreign products, d and m respectively, by maximizing a utility function u(d,m) subject to p,m’ +p’ = p'yy. Differentiating the first order conditions for maximizing any utility function and solving the associated system for quantities in terms of prices yields

(5) wdIn(m’) = wdin(y") + 2din(p’), > ™%<O0,

where w, is the share of imports in expenditures; , is the marginal response of spending on imports

to changes in expenditures; 7, is the compensated (Slutsky), own-price effect, and p’, = (Pm /P'a)-” Equation (5) explains how much of the change in the nominal import share stems from changes in import volume. In the absence of further restrictions, however, (5) cannot be rejected by ‘he data and thus is not suitable for empirical work. One way of bypassing this limitation involves assuming that Li, and 7, are constant, which gives the Rotterdam model:

(6) w,din(m’,) = pdin(y’,) + ndIn(p’) + uy

where u, is the disturbance induced by the assumed constancy of 4 and x. The Rotterdam model is appealing because it is linear in the parameters and, with the exception of integrability, it satisfies the properties of consumer demand theory globally.'° Treating | and m as autonomous, however, amounts to approximating (5) and the quality of this approximation depends on the assumed constancy of and m (Barnett, 1984; Byron 1984); I evaluate this assumption through parameter-constancy tests.

An alternative to the assumed constancy of and 7 involves approximating the utility function with a specific formulation and finding the exact solution to the optimization problem. The Almost Ideal model of Deaton and Muellbauer (1980a) follows this approach and the corresponding solution is (7) dw, = Sdin(y’,) + ydin(p’) + uy,

i]

which explains the change in the nominal import share.'! Equation (7) is appealing becatise it rests on

a specific utility function, is linear in the parameters, and satisfies integrability; this model, however, meets the concavity requirement only locally.

The income elasticities are s/w, for the Rotterdam model and (1+6/w, ) for the A)most Ideal

? Expenditures shares are invariant to demographic scaling. For the derivation of equaticn (5) see Barten (1964), Theil (1965), and Barnett (1979); see Kohli (1991) for an approach that uses cost minimization by firms.

10 A necessary condition for the Rotterdam model to meet the integrability condition is the presence of cointegration among the levels of imports, expenditures, and prices. (As noted before, the logarithms of these variables are not cointegrated.) I apply the Johansen technique and find that there is one cointegration vector which suggests the existence of a relation in the levels of these variables.

11 The solution of the Almost Ideal System is w, = 5In(y’,) + yin(p’,) but this formulation fails cointegration tests. Thus I use equation (17) of Deaton and Muellbauer (1980a, p.317).

model; the compensated own-price elasticities are m/w, for the Rotterdam and (-1+w,+ ¥/w,) for the Almost Ideal model. These expressions underscore that elasticities from optimizing models respond to changes in the composition of expenditures; these elasticities will be constant if either w, is constant, which contradicts the data, or if parameter changes offset exactly changes in w,, which I test.

Expressing (6)-(7) in terms of observables yields (8) Rotterdam: w,,Aln(m,) = pAIn(y,) + tAln(p,) - EuAln(a,) + Ew, Aln(a,) + u, ,

(9) Almost Ideal: Aw, = dAln(y,) + yAln(p,) - d€Aln(a,) + u,, ,

where the us2 of w,, instead of w, reflects the switch from infinitesimal changes to discrete differences (Theil 1971, p.371) and the variables are expressed in logarithmic differences as suggested by the cointegration evidence of table 3 above. Demographic scaling induces both overidentifying restrictions and lagged effects in the Rotterdam model but not in the Almost Ideal formulation.

For estimation, I include in (8)-(9) the war dummies and an intercept.” Finding a statistically significant intercept means that imports change even if income, prices, and population's age profile were unchanged, a sign of misspecification. Based on 1890-1992 data, the estimated income and price effects are significant and the intercept is insignificant (table 4). The residuals do not show autocorrelation or heteroskedasticity but their distribution is more concentrated than the normal distribution; the Engle-Granger test cannot reject the hypothesis that the variables in (8)-(9) are cointegrated. Only the Almost Ideal model fails the functional-form test suggesting that explaining nominal shares involves additional terms.

I examine parameter constancy with three formulations of the Chow test: a sequence of F-tests for the hypothesis that the one-period ahead forecast error is zero (17); a sequence of F-tests for the

12 T use an Augmented Dickey-Fuller to test whether w, ,AIn(m,) is stationary and the corresponding statistic is -4..)9 suggesting that it is; the ADF regression has a constant, a trend, and four lags.

13. To examine the validity of the overidentifying restriction in the Rotterdam model, I re-estimate (8) with nonlinear least squares. The estimates (t-stats) are 0.0652 (9.37) for p, -0.0147 (-3.38) for 7, and 0.261 (0.9) for €; the standard error of the regression is 0.0039. Thus the main implication of imposing the overidentifyir g restriction is that population appears to have no role.

9a

Table 4 Income and Price Effects for U.S. Imports, 1890-1992 Alternative Models

Variables Rotterdam:w,, Aln(m,) |fAlmost Ideal: Aln(w,)

Intercept x 100 -0.0124 0.0196 (0.53) (-0.32)

Alnty,) 0.0679 0.0678 0.0134 0.0132 (10.29) (10.38) (2.10) (2.09)

Aln(p,) . -0.0160 03 0.0393 (-3.7% (-3.67) 9, (9.52)

0.0313 0.0206 72) (0.75) sar es

Notes: m is per-capita, seal non-oil imports; y is per-capita, real domestic expenditures; p is ihe ratio of ihe tariff-adjusted non-oli import price to the GNP deflator. The regression includes three dummy variables for three war years: 1918, 1942, and 1946.

“Significance level for rerecung the hypothesis that residuals are serially independent.

Significance level for rejecting the hypothesis that residuals are homoskedastic.

“Skewness of the empirical distribution of the residuals; this entry is zero for a normal distribution. “Excess Kurtosis of the empirical distribution of the residuals; this entry is zero in normal disiributions. “Significance level for rejecting the choice of functional form with the RESET test statistic. ‘Engle-Granger test of cointegration: a * denotes significant at the 5% level; ** means 1% level.

Figure 3: Parameter-Constancy Tests, 1909-1992 9b

(a) (b) Rotterdam (e) (£) belsters— MHS — GEE reype rt 14 ead

“es isas 196s esses 1945 82 45) 965 1985 1925 1945 1965 1985 1925 1945 1965 1985 Nd CHORs=__ ‘SX crits... Nt Clos: Sx crits... ab Ag | Ay 6 bk rl py ® ty / | | Legend: Ar) va 4 | aes I “ / | ! NN tf ” ~~ . | / A (a) 95% band for one-step ahead residuals , ! (b) Chow test: one-step ahead Q OnE Jeera Danae en (c) Chow test: s-step ahead, forecast horizon declines 1925 19451968 i988 1525 194519651985 (d) Chow test: s-step ahead, forecast horizon increases (c) (d) (e) 95% band for income coefficient (f) 95% band for price coefficient (a) (b) : (e) £ Resi$tep=___ it HOds=_ SX erit=. Almost Ideal PCype= em £2N.Le $20.02.. hs eed O2r ; 4} 054+ oe oo et sal — t —™ b 1925 sai NS 1965 1925 1945 19651985 Us iss 196s ses ses d9as 19651985

MS CHOMs=__ss«5% enitt= Nf CHOWs=___s 5% eerit=

aseeenterstenseneenesete mesueeascsnesmmmammgnenmeneseeses [crea rceetereerecnsereseennennnenmenssses

Le

r) eae en (c) 1925 1945 1965 1985 (a) 1945 1965 1985

10

hypothesis that the out-of-sample forecast errors are jointly equal to zero where the forecast horizon decreases from N to 1 (NJ); and a sequence of F-tests for the hypothesis that the out-of-sample forecast errors are jointly equal to zero where the forecast horizon increases from 1 to N (N17). I perform these tests over 1909-92 by applying recursive least squares to (8)-(9); this method also gives a sequence of parameter estimates and associated standard errors.* Based on these tests, the two models exhibit a remarkable degree of parameter constancy (figure 3).'°

The 95 percent confidence intervals for the elasticity estimates implied by these models reveals several features of interest (figure 4). First, income elasticities are positive, significant, and fluctuate over time; own-price elasticities are significant, fluctuate over time, and with the exception of the Almost Ideal model, are negative. This model violates the negativity condition from 1930 to 1970 and

I treat this evidence as an argument to not use it here. Second, fluctuations in the income and price

elasticities of the Rotterdam model replicate the timing of instability in elasticity estimates reported previously:

The results reveal significant upward shifts in estimates of both income and price elasticities of U.S. non-oil imports during the early 1960s, followed by significant downward shifts in those estimates during the early 1970's. [Hooper, 1978, p.3]

Previous investigations of imports had suggested evidence of structural change in the mid-1960s on the basis of split samples but without an unambiguous dating as to when the change may have occurred. We used a series of tests that permitted the data to indicate the presence of structural change. Our results give some support to the earlier findings that change occurred in the mid- to late 1960s. [Stern, Baum, and Green, 1979, p.191]

This paper provides strong evidence that parameter change occurred in US import demand during the shift to flexible exchange rates and the first oil-price shock. [Ziets and Pemberton, 1993, p. 664)

14 T reserve eighteen observations to serve as initial conditions. Thus for the first sub-period (1891- 1909), the value of N is 83; for the second sub-sample (1891-1910), the value of N is 82, and so on.

1S To examine whether income and prices can be taken as given, I implement the superexogeneity test of Engle, Hendry, and Richard (1983). This procedure involves testing parameter constancy for the equations explaining income and relative prices in terms of exogenous variables. I use government purchases and currency in circulation, both in real and per-capita terms, as instruments and reject the hypothesis of parameter constancy in the equations for income and relative prices. This result, combined with the finding of parameter constancy in

(8) and (9), suggests that treating income and prices as exogenous generates no loss of information for estimating the parameters of these two equations.

10a

Figure 4: 95% Confidence Bands for Income and Price Elasticities United States, 1890-1992

Income Elasticity / Rottardam Modei

cians Rotterdam \og—linear

+e y ’ ’ i - PMNs eX mh PN ed 7 \ ' 7 Mev gt aw ¥ vo NN eA Ne vous parte Ny One vay ‘ Varly t i \ a\n . ew MN wrt . vk '

1890 1900 1910 1820 1930 1940 1950 1960 1970 1980 1990

Income Elasticity / Almost Ideal Model

INN a a fet EN

rv [——

ave

1890 1900 1910 1820 1930 1940 1950 1960 1970 1980 1990

Price Elasticity / Rotterdam Model

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

Price Elasticity / Almost Ideal Model

0.5

lo+

0.5

1.5

1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

11

But fluctuations in the elasticities from the Rotterdam model arise from optimization and not from unspecified structural changes.

Third, the elasticity estimates of the log-linear model overstate the sensitivity of U.S. imports to changes in income and prices relative to the estimates from the Rotterdam model. For 1992, the income elasticity of the log-linear model is 2.6 versus 0.8 for the Rotterdam model; price elasticities also differ substantially but the large standard error for the estimate of the log-linear model makes the difference statistically insignificant. Overall, these results confirm the importance of optimization for characterizing the behavior of U.S. imports. What is new about the results is that only through

optimization can one recognize the evolution of U.S. trade for estimating elasticities.’

5. Conclusion

Treating elasticities as constant parameters and estimating them with sub-samples of the postwar period are two features unifying fifty years of econometric work on US. imports. These two features, however, do not provide an adequate understanding of the role of income and prices in determining these imports: the dispersion of elasticities is substantial and the estimates are unstable. A necessary condition for reaching an agreement on the determinants of U.S. imports is the use of all the data available. Otherwise, fluctuations in elasticities arising from the use of different sub-samples precludes arriving at a definitive view of the role of income and prices in determining these imports. Bu: when all the data available are used to estimate the parameters of the popular log-linear model, the results misrepresent the role of income and prices because that model does not treat adequately the time-series

properties of the data.

*® To examine the role of tradeables and non-tradeables, I respecify the Rotterdam model as

(8) W,.,Aln(m,) = pAln(y,) + 1,Aln (p,, /py) + An (p, IP) - 5uAln(a,) + Ew, ,Aln(a,) + u,, ,

where p,, is the price of domestically produced goods and P,, 1s the price of domestically rendered services; data for these prices are not available prior to 1930. The estimated compensated, own-price effect (x,) is -0.0143, which is close to the estimate reported in table 4 and confirms the low substitutability between foreign and domestic tradeables. This conclusion ignores, however, the difference between single-equation and system estimation with cross-equation restrictions; further work is thus required to verify this result.

12

As an alternative, I estimate the parameters of formulations that use all the data available, recognize the associated time-series properties, and rest on optimization. Recognizing the evolution of the U.S. eccnomy need not be central to estimating income and price effects if the associated estimates are used for short-term forecasting. This practice, however, confuses understanding with predicting, contributes to the large dispersion of estimates found in the literature, and leaves unanswered a key

question: If 2lasticities are constant why are they reestimated so often?

13

Appendix A: Chronology of Elasticity Estimates for Selected Studies of U.S. Imports

This appendix lists papers reporting econometric estimates of trade elasticities for single-equation models of U.S. aggregate import demand. By design, the appendix excludes studies examining the structure of U.'5. trade on the basis of factor content or using non-parametric methods; papers reporting econometric estimates “or relatively small components of U.S. imports are not included in this survey. Stern et al. (1976), Thursby and Thursby (1984), Goldstein and Khan (1985), Kohli (1991), and Marquez (1992) provide reviews of the literature that are not limited by these considerations. Table Al shows the studies used in this paper and their main characteristics which are listed below.

Estimator: ILS: Indirect Least Squares NLS: Nonlinear Least Squares OLS: Ordinary Least Squares

Price Behavior: Exogenous: Prices are taken as given for estimation. Endogenous: Prices are not taken as given for estimation.

Dynamic Structure: DL: Distributed lags. ECM: Error-correction model. Koyck: Lagged dependent variable is the only lag. PDL: Polynomial distributed lag. RL: Rational lag. Shiller: Shiller lags. Static: No allowance for lags.

Homogeneity: Yes: Estimating equation maintains homogeneity of degree zero in prices. No: In the absence of homogeneity, the price elasticity corresponds to the estimated coefficient on the foreign-price, whether or not it is combined with an exchange-rate term.

Price Data: Multilateral: Price data do not differentiate across trading partners. Bilateral: Price data differentiate across trading partners.

Data Frequency: A: Annual; Q: Quarterly; S: Semi-annual.

Trade Data: Total: Measure of imports includes oil imports. Non-oil: Measure of imports excludes oil imports.

Author's aggregation of individual elasticities using trade shares.

1 Author's imputation of standard error. If the study does not report standard errors but indicates that the elasticities are significant, then I impute a t-statistic of 2. If the study does not give a sense of how significant are the elasticities, then I impute a t- Statistic of one.

13a

Table Al Chronology of Elasticity Estimates: Selected Studies for the United States

Study Estimator/

Price

Dynamic Price Data/ Structure/ Frequency; Behavior Homogeneity] Sample

Chang (1946,table 4) | OLS/Exog. | Statis/Yes Multilateral/ | Total A;1924-38

Krause (1962,table 3) | OLS/Exog. | Static/Yes Cross-sec./ Nonoil A;1947-58

Kreinin (1967,table 3) | OLS/Exog. | DL/Yes Multilateral/ | Total A; 1954-64

Hein (1968,pp.709) OLS/Exog. | DL/Yes Multilateral/ | Total A;1951-65

Houthakker and OLS/Exog. | Static/Yes Multilateral/ | Total

Magee (1969, table 1) A;1951-66

Magee (197°,pp. 8-9) | OLS/Exog. | Static/Yes Bilateral/ Nonoil A;1951-69

Taplin (1973, tables 1-| OLS/Exog. | Static/Yes Multilateral/ | Total

2) A;1953-70

Clark (1974,pp.220-8) | OLS/Exog. | PDL/Yes Multilateral/ | Nonoil Q;1963-73

Miller and Fratiani OLS/Exog. | Koyck/Yes | Multilateral/ | Total (1974, table 1) Q;1956-72 Ahluwalia and ILS/Endog. | DL/No Multilateral/ Hernandez-Cata (1975, Q;1960-73 table 1)

Khan and Ross (1975,} OLS/Exog. | Static/Yes Multilateral/ | Total table 1) S;1960-72 Hooper (1975, table 2)} OLS/Exog. | DL/Yes Multilateral/ | Nonoil Q;1956-75 Murray and Ginman | OLS/Exog. | Static/No Multilateral/ | Total (1976, table :2) Q;1961-68 Khan and Ress (1977,] OLS/Exog | Koyck/Yes | Multilateral/ | Total table 2) Q;1960-72 Deppler and Ripley OLS/Exog. | DL/Yes Multilateral/ (1978, tables 11, 13, S;1964-76 14, and 16) Hooper (1978, table 3)} OLS/Exog. | Static/Yes Multilateral/ | Nonoil Q;1955-77 | Wilson and Takacs OLS/Exog. | Shiller/No Multilateral/ | Nonoil | (1979, table 6) Q;1957-71

eee

Trade Elasticity Estimates Data

Income (t-stat)| Price (t-stat)

1.27 (1.001) -0.97 (-1.00i)

1.00 (1.003) -1.98 (-4.13)

1.27 (16.3) -1.11 (-6.94)

1.21 (7.56) -0.62 (-3.10)

1.51 (12.1) | -0.54 (-1.60) 1.54 (1.001) | -1.26 (-1.00i)

1.81 (2.001) -1.05 (-2.00i)

2.79 (51.2)* | -3.72 (-7.40)*

1.96 (2.001) | -0.73 (-1.00i)

-1.65 (-5.64)

Nonoil | 1.33 (14.77)

1.91 (4.87) -1.00 (-1.90)

1.06 (2.00) -0.54 (-5.32)

0.96 (3.80) -1.05 (-1.60)

1.42 (5.68) -2.16 (-2.00)

Nonoil

1.39 (2.24)*

2.03 (10.65)

-1.04 (-3.90)

4.08 (8.66) | -4.78 (-1.00) |

13b

Table Al (continued) Chronology of Elasticity Estimates: Selected Studies for the United States

Dynamic Price Data/_ | Trade Elasticity Estimates

Structure/ Frequency; Data "

Homogeneity] Sample Income (t-stat) | Price (t-stat)

DL/Yes Multilateral/ | Nonoil | 3.08 (27.00) S;1962-77

DL/No Multilateral/ | Total 1.12 (3.24) Q;1953-76

Static/Yes Multilateral/ | Total 2.52 (6.37) A;1950-73

Koyck/Yes Bilateral/ Total 1.53 (10.2) Q;1958-74

Static/No Multilateral/ | Total 1.83 (9.42) -0.61 (-3.16) Q;1955-79

PDL/No Multilateral/ | Nonoil | 2.01 (2.001) -2.53(-2.001) Q;1970-80

PDL/Yes Multilateral/ | Nonoil | 2.11 (5.30) -1.15 (-10.0) Q;1969-84

DL/Yes Multilateral/ | Total 2.44 (2.001) Q;1973-87

Koyck/Yes Multilateral/ | Total 1.07 (4.60) Q;1958-83

DL/Yes Multilateral/ | Nonoil | 1.31 (2.98) A;1971-86

PDL/No Multilateral/ | Total 2.50 (9.07) Q;1967-87

PDL/Yes Multilateral/ | Nonoil | 0.73 (3.00) -1.47 (-14.3) S;1976-90

RL/Yes Multilateral/ | Total 1.94 (4.97) -0.92 (-4.80) Q;1973-85

PDL/Yes Multilateral/ | Nonoil | 2.56 (3.00) Q3;1975-89

ECM-DL/ Multilateral/ | Nonoil | 2.48 (40.9)

Yes Q;1976-90

ECM-DL/ Multilateral/ | Nonoil | 2.15 (1.001)

Yes Q;1968-90

Study Estimator/ Price

Behavior

Lawrence (1978, table | OLS/Exog. -1.52 (-4.70)

Stern, Baum, and Green (1979, table 2)

OLS/Exog. -2.18 '-3.41)

i ma

Goldstein, Khan, and Officer (1980, table 3)

OLS/Exog.

-0.68 ‘-3.30)

Geraci and Prewo OLS/Exog. (1982, table 1)

-1.23 (-2.20)

Haynes and Stone (1983, table 1)

OLS/Exog.

Warner and Kreinin (1983, table 2)

OLS/Exog.

Helkie and Hooper (1988, table 4)

OLS/Exog.

Cline (1989, table 4A.3)

OLS/Exog. -1.36 (-1.00i)

Deyak, Sawyer, and Sprinkle (1989, table 1)

Krugman (1989, table | OLS/Exog. 3)

OLS/Exog. -0.29 (-1.00)

-0.93 (-3.10)

Moffet (1989, table 5)| OLS/Exog. -0.69 (-7.40)

| Hi wa

Lawrence (1990, table | OLS/Exog.

Marquez (1990, table | OLS/Exog. 2)

Blecker (1992, table A-1)

OLS/Exog. -0.97 (-2.00)

Zietz and Pemberton | OLS/Exog. (1993, table 5)

-1.14 (-15.5)

Clarida (1994, p.306) | NLS/Exog. -0.95 (-1.00i)

14

Appendix B: Data Sources

The main data sources are the Survey of Current Business (Survey) and the Historical Statistics of the United States: Colonial Time to 1970 (Historical Statistics) assembled by the Bureau of Economic Analysis of the U.S. Department of Commerce; alternative sources are explicitly indicated whenever they are used. The Bureau of Economic Analysis offers data over 1929-92 with "real" variables expressed in 1987 prices. For the period 1890-1928, the Historical Statistics offers a comparable database but uses a different base year to deflate nominal magnitudes. ‘Thus to obtain data for the 1890-1928 period in 1987 prices, I extrapolate backwards the series from the Survzy using the growth rates of the series of the Historical Statistics.” Data Series

Figure B1 shows annual data for the level of U.S. real GNP, population, per-capita GNP, and the growth rates cf these variables since 1890.'* According to the data, the expansion of GNP has been largely susiained and the volatility in the growth rate of GNP declined considerably in the postwar period; the iargest one-vear decline in GNP occurs in 1946 because of the cutback in defense spending. Total U.S. population shows aise a sustained expansion."” Easterlin (1980) argues that fluctuations in the growth rate of population up ‘Go 1940 arose from changes in the immigration rate; since 1°40, changes in the growth rate of population stem from changes in the fertility rate induced by changes in the ability of a given cohort to provide comparable living standards to their offsprings. The figure also shows that the share of population with at least 65 years of age remained largely unchanged at 4 percent from 1890 to 1920 and increased steadily to reach 12 percent by 1992.

Figure B2 shows the evolution of the defiators for GNP and non-oil imports, the tariff rate, and the relative price oF imports since 1890. The data reveal substantia! price instability from 1890 to 1940 including the deflationary pressures of the 1930s. Since 1973, increases in the GNP deflator have been interrupted by the recessions of }980 anc 1990. Up to 1945, non-oil imnport prices show fluctuations as large as those of the GNP defiator especially during che WWI period. The decline in import prices in 1920 is the largest decline over the fast century. Finally, figure B2 shows thie evolution of the totai and non-oil tariff rate since 1890. 1 measure these rates as the ratic between the jeve! of duties and nominal merchandise imports excluding tariffs. The tariff

rate shows wide swings prior to 1944 and while BI has a bref chronology of the main pieces of tariff legislation.

"7 Romer (1989) reports estimates of U.S. real GNP (and its deflator) for the period 1869-1929 in 1982

prices; thus d fferences in the choice of base year are still present. Nevertheless, the correlation between the

series that I use and those reported by Romer, for 1890-1929, are 0.994 for real GNP and 0.998 for the GNP deflator.

18 {use GNP as a measure of income instead of GDP because data for GDP are not readily available

for the 19th century and the early part of the 20th century.

19 The data on population include Armed Forces overseas. Data for population including Armed

Forces prior to 1930 are not available except for 1917-19 which appear in footnote 1 of page 8 of Historical Statistics. J adjust the growth rate to include Armed Forces overseas for 1917-19.

14a

Figure B1: GNP and Population United States, 1890-1992

Gross National Product (billions) Gross National Product — Growth Rate 1987$ Perceni 6000 25 5400 20 4800 15 4200 10 3600 5 + 3000 0 2400 5 1806 10 1200 16 600 20 0 26 1890 1900 1910 1920 1930 1940 1950 1960 1870 1980 1990 1890 1800 1910 1920 1930 1940 1950 1960 1970 1980 1990 Population Growth mographics Percent Demograp Millions Percent 270 3 Population 248 2.7 226 2.4 204

Sos

24 182 NY 1.8 160 1.5 138 1.2

116 94 0.6 72 0.3 0 50 fe) 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 1890 1900 1910 1920 1930 1940 1950 1960 1970 1{180 1990 Per Capita GNP Per Capita GNP — Growth Rate 1987$ Percent 24000 25 21900 20 iv 19800 15 17700 10 15600 5 + 13500 0 11400 5 9300 10 A 7200 15 V 5100 20

3000 25 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 1890 1900 1910 1920 1930 1940 1950 1960 1970 ~980 1990

14b

Figure B2: Import and Domestic Prices United States, 1890-1992

Import and Dom»stic Prices growth rates Percent Percent 140 —-— Non-oil Imports 126 Non-oil Imports —— — —GNP Deflator ° ———— GNP Deflator

0 1890 1900 19°0 1920 1930 1940 1950 1960 1970 1980 1990 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

Average Tarit Fiate growth rate of tariff rate Percent Percent 40

110 ——_—_——— relative to merchandise imports

. . . 88 ae relative to non—oil merch. imports 35

66 30 44 25 22 20 15 22 44 10 66 5 88 0 110 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990 Import Price(1 tariff rate)/GNP Price growth rate of relative price Percent Percent 300 40 250 30 20 WW 200 10 150 + 0 100 10 r S50 20

0 30 1890 1900 1310 1920 1930 1940 1950 1960 1970 1980 1990 1890 1900 1910 1920 1930 1940 1950 1960 1970 1980 1990

15

Sources

1. Real GNP in 1987 Prices: 1929-1992: Survey December 1992, table 2. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 224, series F-3.

2. Total Resident Population: 1929-1992: Survey, table 2.1. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 8, series A-7.

3. Merchandise Imports, Current Prices: 1929-1992: Survey, table 4.1. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 889, series U-219.

4, Merchandise Imports, 1987 Prices: 1929-1992: Survey, table 4.2. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 893, series U-237.

5. Imports of Petroleum and Petroleum Products, Current Prices:

1965-1992: Survey, table 3.B-U.S. Merchandise Trade.

1908-1964: Backward extrapolation using growth rates from Historical Statistics, p. 900, series U-316. 1890-1907: Volume of oil imports are negligible (Historical Statistics, series M-140) and set to zero.

6. Imports of Petroleum and Petroleum Products, 1987 Prices: Imports of Petroleum and Products in current prices (#5) deflated by the associated price index (#1!) below).

7. Non-oil Imports, Current Prices: Difference between total imports in current prices (#3) and oil imports in current prices (#5).

8. Non-oil Imports, 1987 Prices: Difference between total imports in 1987 prices (#4) and oil imports in 1987 prices (#6).

9. GNP Deflator: 1929-1992: Ratio between nominal and real GNP; for data on nominal GNP: Survey December 1992, table 1. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 224, series F-5.

10. Oil-import Price Deflator:

1967-1992: Ratio between current-price and 1987-price data for fuel imports (BOP basis) from the U.S. Commerce Department, Merchandise Trade Statistical Release.

1947-1966: Grows at the rate of the U.S. domestic price of oil (Producer Price Index Press Release, Bureau of Labor Statistics).

1890-1946: Grows at the rate of the price of domestic petroleum production ($/barrel): Historical Statistics, p. 593, series M-139.

11. Non-oil Import Price Deflator: Ratio of non-oil imports in current prices (#7) to non-oil imports in 1987 prices (#8).

12. Custom Duties: 1929-1992: Survey, table 3.2. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 1105, series Y-344.

13. Export of Goods and Services in Current Prices: 1929-1992: Survey December 1992, table 1.

16

1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 891, series U-225 (index of export volume) times U-226 (index of export price).

14. Export of Goods and Services in 1987 Prices: 1929-1992: Survey December 1992, table 2.

1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 891, series U-225 (index of export volume).

15. Import of Goods and Services in Current Prices: 1929-1992: Survey December 1992, table |. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 890, series U-219.

16. Import oj Goods and Services in 1987 Prices: 1929-1992: Survey December 1992, table 2. 1890-1928: Backward extrapolation using growth rates from Historical Statistics, p. 893, series U-237.

17. Domestic Expenditures in Current Prices:

GNP in 1987 prices (#1) times GNP deflator (#9) + Imports of Goods and Services in current prices (#15) - Exports of Goods and Services in current prices (#13).

18. Domestic Expenditures in 1987 Prices:

GNP in 1987 prices (#1) + Imports of Goods and Services in 1987 prices (#16) - Exports of Goods and Services in 1987 prices (#14).

19. Price Deflator for Domestic Expenditures: Ratio between Domestic Expenditures in current prices (#17) and 1987 prices (#18).

20. Population Age:

1988-1992: Statistical Abstract of the United States, 1993, U.S. Department of Commerce, Bureau of the Census, p. 14 (table 14) and p. 33 (table 35).

1900-1987: Liesner (1989), table US.9 p. 92-93.

1890-1899: Linear interpolation using the 1890 and 1900 values reported in Liesner (1989).

21. Price of Domestic Tradeables:

1947-1992: Fiatio of current and constant price expenditure on domestic goods: Survey, table 1.3 (current prices) and table 1.4 (constant prices). 1930-1946: Backward extrapolation using growth rates from Historical Statistics, p. 198, series E-16.

22. Price of Domestic Non-Tradeables:

1947-1992: Ratio of current and constant price expenditure on domestic services: Survey, table 1.3 (current prices) and table 1.4 (constant prices).

1930-1946: Backward extrapolation using growth rates from Historical Statistics, p. 198, series E-17.

23. Governrent Purchases in Current Prices:

1929-1992: Survey, table 1.1.

1890-1928: Backward extrapolation using growth rates from Liesner (1989), table US.1, p. 74.

Real government purchases equal nominal government purchases (#23) deflated by the GNP deflator (#9).

24. Currency in Circulation: 1959-1992: Board of Governors of the Federal Reserve System, Weekly Statistical Release, table 4. 1890-1958: Historical Statistics, p. 992, series X-410.

Table B1: Chronology of U.S. Legislation on External Tariffs 16a

. the maximum rate is 24% {p. 370)

: CTLs j ety og Hoo ner ones 2

S72 Tariff rates are jowered by 10%, but raised again in 1875 (p. 370) |

McKinley Act raises the level of tariff rates to 50% (p. 371)

Tariff rates are raised to almost 60%, except tor raw materials and semifinished products (p. 371)

Underwood-Simmons bill lowers tariff rates and increases the list of items exempt from tariffs. The average tariff rate is 25%.

Emergency Tariff Act (p. 662).

Fordney-McCumber Act raises average tariff rate to 33% (p. 663).

Hawley-Smoot Act raises average tariff rate to 40% (p. 663).

Congress gives the President authority to negotiate tariffs p. 663).

President's power to negotiate tariffs is expanded (p. 663).

Creation of the GATT (p. 665).

Trade Expansion Act gives power to the President to lower tariffs (p. 665).

Nixon Administration announces a 10% surcharge on dutiable imports (p. 662).

Source: Robertson (1973); page numbers refer to this publication.

17

Appendix C: Order of Integration I apply the procedure of Dickey and Pantula (1987) to determine the order of integration of the logarithms of per-capita, real domestic expenditures, y, ; per-capita, real non-oil imports, m, ; and the tariff-adjusted relative price, p, , using annual observations for 1890-1992. This procedure tests sequentially the hypotheses of multiple unit-roots, single unit-root, and stationarity while removing the assumption of at most one unit-root maintained by the Dickey-Fuller test. Sequential Testing for Multiple Unit Roots I assume tat a given variable z, evolves over time according to (C1) Z = W+ YT + (Py + PrdZ1 - (PiPrZ2 + & » where | is a drift parameter; Y is a deterministic-trend parameter; both p, and Pp, are the roots of the dynamic

process; T denotes time; and e, is a white-noise disturbance.”

Re-arranging (C1) gives

(C2) A’2z,= + yT + O,Az,, + 02%, +e,

where ©, == (P,P. - 1) and a, = (Pp, -1)(P, -1). If z, has two unit roots (Pp, = Pp, = 1), then a = O, = 0. If z, has one unit root (p, = 1, p) < 1) then a, < 0; @ = 0. Noting that a, = 0 in both the null and the alternative hypotheses, Dickey and Pantula propose a two-step testing strategy. The first step sets ©, = 0, applies least squares to A’z,= w+ YI + a, Az,, + e, and tests the null hypothesis of two unit roots (a, = 0) versus the alternative of only one unit root (a, < 0). If the null hypothesis is rejected, then the order of the series is at most one. The second step applies least squares to A’z, = 1 + YT + a, Az,, + 2, + €, and tests the null hypothesis of one unit root (&, = 0) versus the alternative of stationarity (Q, < 0).

Test Results

The estimates of 0, are negative and significantly less than zero for all three series (table C1). Thus the data reject the hypothesis of two unit roots for the three series and suggest that their order of integration is at most one. The estimates of &, are not significantly different from zero for imports and relative prices -- that is, these two variables are integrated of order one. For domestic expenditures, however, the estimate of ©, is significantly less than zero which suggests that this series is stationary. Finding that the logarithm of per-capita U.S. domestic expenditures in real terms is stationary contradicts the generally accepted view that the main U.S. economic aggregates are non-stationary (Stock and Watson, 1988). Previous findings, however, normally exclude from their samples the WWII period and do not use the Dickey-Pantula sequential procedure adopted here.

Excluding 1941-1946 from the sample gives estimates of , from the first step that are negative and significan‘ly less than zero for all three series (table C1) which suggests the absence of multiple unit roots; the estimates of a, are not significantly different from zero which suggests that the associated series are nonstationary. Thus, abstracting from the period 1941-1946, the data for the logarithms of per-capita domestic

expenditure, per-capita non-oil imports, and relative prices are integrated of order 1.

20 Equation (C1) extends section 4.5.1 of Banerjee et al. (1993) by adding both a drift and a deterministic trend to the process explaining z.

Table C1 l7a Test Results for Order of Integration for Imports, Expenditures, and Relative Prices: United States, 1890-1992

In(m)

In) 40" in) 047

Step 2

Pa [als [oo

Step 1 Step 2

ra l= [oo inn) aus | a oso || iny) ino)

Notes:

The critical values for the full sample are -3.73 (T=100) and -3.66 (asymptotic); for the sub-samples, the critical values are -3.8 (T=50) and -3.66 (Banerjee et al., 1993, p.103, c-block of table 4.2). An ertry with * means that the data reject the associated null hypothesis. The estimation samples allow for lags.

Step 1: Estimate A’z, = O +0, Az,, +0, Time +e, Test Hy: two unit roots (, =0) versus H,: one unit root (Q, < 0)

Step 2: Estimate A’z, = %) + O, Az,, + ©z,, + &, Time + e, Test Hy: one unit root (@, = 0) versus H,: stationarity (a, < 0)

18

To assess the robustness of these conclusions, I report the results from the Augmented Dickey-Fuller (ADF) formulation: (C3) Az,=+yT+ a,Az,, +... + Az, + Bz, + &. The ADF »rocedure applies least squares to (C3) and tests the null hypothesis that B=0. If B is not significantly different from zero, then z, has a unit root. Al of the estimated t-statistics for B are above the ADF critical value (-3.73) which suggests that the data cannot reject the hypothesis that B = 0 (table C2).

Table C2 Augmented Dickey-Fuller Test, 1890-1992

Variables In(y) In(p) 2.16

Several conclusions emerge from these tests. First, the data for the logarithms of the series used in this analysis

appear to de non-stationary. Nevertheless, the inclusion of the WWII period in the estimation sample induces stationarity in the data for the logarithm of domestic expenditure because of the magnitude of the 1946 contraction in real GNP. Second, the unambiguous support to non-stationarity provided by the ADF test results stands in contrast to the evidence from the Dickey-Pantula procedure. As noted by Banerjee et al. (1993), the choice of test statistic matters for establishing the order of integration. From the standpoint of this paper, I will

treat the order of integration of these series as being equal to one.

19

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Dickey, David and Sastry Pantula, "Determining the Order of Differencing in Autoregressive Process," Journal of Business and Economic Statistics, 5, 1987, 455-461.

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Engle, Robert, "Autoregressive Conditional Heteroscedasticity, with Estimates of the Variance of United Kiigdom Inflations," Econometrica, 50, 1982, 987-1008.

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Engle, Robert and Clive Granger, "Cointegration and Error Correction: Representation, Estimation, and Testing," Econometrica, 51, 1987, 251-276.

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22

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IFDP Number

475

474

473

472

47}

470

469

468

467

466

465

464 463

23

International Finance Discussion Papers

The Constancy of Illusions or the Illusion of Constancies: Income and Price Elasticities for U.S. Imports, 1890-1992

The Dollar as an Official Reserve Currency under EMU

Inflation Targeting in the 1990s: The Experiences of New Zealand, Canada, and the United Kingdom

International Capital Mobility in the 1990s

The Effect of Changes in Reserve Requirements on Investment and GNP

International Economic Implications of the End of the Soviet Union

International Dimension Of European Monetary Union:

Implications For The Dollar

European Monetary Arrangements: Implications for the Dollar, Exchange Rate Variability and Credibility

Fiscal Policy Coordination and Flexibility Under European Monetary Union: Implications for Macroeconomic Stabilization

The Federal Funds Rate and the Implementation of Monetary Policy: Estimating the Federal Reserve’s Reaction Function

Understanding the Empirical Literature on Purchasing Power Parity: The Post-Bretton Woods Era

Inflation, Inflation Risk, and Stock Returns

Are Apparent Productive Spillovers a Figment of Specification Error?

Author(s)

Jaime Marquez

Michael P. Leahy John Ammer Richard T. Freeman Maurice Obstfeld

Prakash Loungani Mark Rush

William L. Helkie David H. Howard Jaime Marquez

Karen H. Johnson

Hali J. Edison Linda S. Kole

Jay H. Bryson

Allan D. Brunner

Hali J. Edison Joseph E. Gagnon William R. Melick

John Ammer

Susanto Basu John S. Fernald

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 Number

462

461

460

459

458

457

456

455

454

453

452

451]

450 449

24

International Finance Discussion Papers

When do long-run identifying restrictions give reliable results?

1993 Fluctuating Confidence and Stock-Market Returns

Dollarization in Argentina

Union Behavior, Industry Rents, and Optimal Policies

A Comparison of Some Basic Monetary Policy Regimes:

Implications of Different Degrees of Instrument Adjustment and Wage Persistence

Cointegration, Seasonality, Encompassing, and the Demand for Money in the United Kingdom Exchange Rates, Prices, and External Adjustment

in the United States and Japan

Political and Economic Consequences of Alternative Privatization Strategies

Is There a World Real Interest Rate?

Macroeconomic Stabilization Through Monetary and Fiscal Policy Coordination Implications for Monetary Union

Long-term Banking Relationships in General Equilibrium

The Role of Fiscal Policy in an Incomplete Markets Framework

Internal Funds and the Investment Function

Measuring International Economic Linkage with Stock Data

Author(s)

Jon Faust Eric M. Leeper

Alexander David Steven B. Kamin

Neil R. Ericsson Phillip Swagel

Dale W. Henderson Warwick J. McKibbin

Neil R. Ericsson David F. Hendry Hong-Anh Tran

Peter Hooper Jaime Marquez

Catherine L. Mann Stefanie Lenway Derek Utter

Joseph E. Gagnon Mark D. Unferth

Jay H. Bryson

Michael S. Gibson

Charles P. Thomas

Guy V.G. Stevens

John Ammer Jianping Mei