Clarida-

American Economic Association Cointegration, Aggregate Consumption, and the Demand for Imports: A Structural Econometric Investigation Author(s): Richard H. Clarida Source: The American Economic Review, Vol. 84, No. 1 (Mar., 1994), pp. 298-308 Published by: American Economic Association Stable URL: http://www.jstor.org/stable/2117985 Accessed: 10-09-2017 06:08 UTC JSTOR is a not-for-profit service that helps scholars, researchers, and students discover, use, and build upon a wide range of content in a trusted digital archive. We use information technology and tools to increase productivity and facilitate new forms of scholarship. For more information about JSTOR, please contact support@jstor.org. Your use of the JSTOR archive indicates your acceptance of the Terms & Conditions of Use, available at http://about.jstor.org/terms American Economic Association is collaborating with JSTOR to digitize, preserve and extend access to The American Economic Review This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms Cointegration, Aggregate Consumption, and the Demand for Imports: A Structural Econometric Investigation By RICHARD H. CLARIDA* Employing a two-good version of the rational-expectations permanent-income model, this paper derives a structural econometric equation that can be used to estimate the parameters of the demand for imported nondurable consumer goods. With strongly separable, addilog preferences (see Hendrik Houthakker, 1960), the log of the demand for imported goods is shown to be linear in the log of the relative price of imports, the log of the consumption of domestically produced varieties, and the log of an unobservable shock to tastes. The rational-expectations permanent-income hypothesis in conjunction with the addilogpreference structure implies that the log of the demand for domestic goods is the correct "activity" variable on the right-hand side of the import demand equation. This is because log consumption of domestic goods is a noisy proxy for the unobservable log of the forward-looking index of permanent income, the marginal utility of wealth. In quarterly U.S. data, it is not possible to reject the hypothesis that log consumption of domestic nondurable goods is nonstationary in levels but is stationary in first differences. From this fact, my model implies that, in the open-economy macroeconomic equilibrium, the demand for domestic nondurable goods and the demand for foreign nondurable goods share a stochastic trend and that this trend may in fact be identified with the log marginal utility of wealth. According to the theory, log imports, log domestic goods, and the log relative price of imports will be cointegrated if the equilibrium relative price of imports contains a stochastic supply trend that is not cointegrated with the log utility index of permanent income. If these three variables are cointegrated, the import demand equation's structural parameters-the elasticities of marginal utility with respect to foreign-goods consumption (-q) and home-goods consump- tion (a)- are exactly identified by the co- integrating vector. The data decisively reject the null hypoth- esis that imports, the relative price of imports, and the consumption of home goods are not cointegrated. To correct for simultaneous-equations bias, I employ the nonlinear least-squares technique recently proposed by Peter Phillips and Mico Lore* Department of Economics, Columbia University, tan (1991) to estimate the parameters of the New York, NY 10027, and The National Bureau of Economic Research. This paper was completed during structural import demand equation. my stay as a Visiting Scholar at the Federal Reserve The results of the empirical work may be Bank of New York. I thank Richard Davis, Akbar summarized as follows. The price elasticity Akhtar, Charles Pigott, Bruce Kasman, Susan Hickok, of import demand is estimated to average Juann Hung, and seminar participants at the Federal Reserve Bank of New York; Mike Gavin, Ricardo -0.95 during the sample. Given the preciCaballero, Jordi Gali, and seminar participants at sion of the estimate, it is not possible to Columbia University; Peter Hooper, William Helkie, reject the null hypothesis of a unitary price Jaime Marquez, Dale Henderson, and seminar particielasticity, thus putting the estimate in the pants at the Federal Reserve Board of Governors; Bill range of earlier empirical studies (William Branson, Ken Rogoff, and seminar participants at the 1991 NBER Summer Institute; two referees of this Branson, 1972; Morris Goldstein and journal; and seminar participants at Princeton, Chicago, Mohsin Kahn, 1985; William Helkie and Wisconsin, the IMF, Virginia, New York University, Peter Hooper, 1986; WIlliam Cline, 1989). Georgetown, Syracuse, and UC-Davis for their comThe elasticity of import demand with rements and suggestions. All remaining confusions are my doing. spect to an increase in real spending is 298 This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms VOL.84 NO. 1 CLARIDA: COINTEGRATION, CONSUMPTION, AND IMPORT DEMAND 299 estimated to average 2.15 during the sample, roughly the same as reported by Helkie and Hooper (1986), somewhat smaller than reported by Cline (1989), and somewhat larger than the average of the many studies surveyed by Goldstein and Kahn (1985). In the context of my theoretical specification, the Marshallian price elasticity of import demand is not constant, but in fact converges to -1 as the share of total spending on imports rises, while the elasticity of import demand with respect to an increase in real spending is not constant but in fact declines over time as the share of spending on imports rises. The paper ends with some concluding remarks. I. The Model I begin by deriving the demand for nondurable foreign goods, FJ, from a standard rational-expectations permanent-income I shall assume that u is an addilog utility function (see Houthakker, 1960). (6) u(Ht,Ft)=DtHt-a(1-a) + BtFt'-q(1 - where Bt and Dt are random, trend-stationary shocks to preferences.1 Using (6), (4a) and (4b) are easily solved for the opti- mal consumption of domestic and foreign goods as a function of At and Pt: (7a) Ht = Ak - l/aDJI/a (7b) Ft = At- 1 I1Pt- 1 I1B 1/q. Letting lowercase letters denote logs, one sees that (8) ftt=bt /1-q(117q)pt-(11-q)logkAt. model. Letting P, denote the price of imports in terms of domestic goods, H, the consumption of domestic nondurable goods, Along the optimal path, the log of the de- At assets, yt labor income, and rt the real mand for imported consumer goods is linear interest rate, the representative household in the log of the relative price of imports selects {Ht, Ft, At + 1}, t = O, . . ., T, so as to and the log of the marginal utility of wealth, solve the forward-looking utility index of permanent income implied by theory where T (1) max E [ (1+6) tu(Ht;Ft) t =O0 A(At; yt; Pt; rt; G( yt+1,,yt+,,* * ; Pt+, Pt+29 . ..; rt+,, rt+2 * - * )) subject to (2) Ht+PtFt+At+,=(l+rt)At+yt (3) AT?O. with G the joint probability distribution over the entire future time path of labor income, import prices, and real interest rates. If, given the assumption of addilog preferences, data were available on logAt, this Assuming an interior utility solution, the first-order index of permanent income would be conditions are given by the proper "activity" variable to include on the right-hand side of the import demand equation. Such data are not available. How(4a) UH =At (4b) UF = AtPt (5) At = (1 + 6) Et[At+1(l + rt+l)] where At is the Lagrange multiplier on the accumulation constraint (2). IThe addilog utility function has been estimated in a number of previous studies of consumer demand and intertemporal substitution, including Angus Deaton (1974), Jeffrey Miron (1986), Laurence Ball (1990), and Janet Ceglowski (1991). In what follows I will discuss the recent contributions of Masao Ogaki (1988, 1992) and Ogaki and Joon Park (1989). This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms 300 THE AMERICAN ECONOMIC REVIEW MARCH 1994 ever, using the fact that ((9) 9) ~Hta /q1 = k t- I/D 1 /q one may express the demand for imported consumer goods as ( 10) ftt=yt - (1q)pt + (a1-)ht +et where yt (bo + b1t - do- d1t)/ is the linearly deterministic component of the log shocks to preferences divided by 77 and (11) et = (bt - bo - b1t)177 - (dt - do - d1t)/lq. (12) of the model, in an open-economy macroeconomic equilibrium in which the log consumption of domestically produced nondurables is an integrated I(1) process, the demand for forgein nondurable goods and the demand for domestic nondurable goods should share a stochastic trend. This stochastic trend may in fact be identified with the log marginal utility of wealth. While the theory implies that the log con- sumption of home goods, ht and foreign goods, ft, share a stochastic trend, these two variables are not necessarily cointegrated (Robert Engle and Clive Granger, 1987). In fact, as is revealed by equation (10), if the equilibrium relative price of imports contains a stochastic supply trend that Thus, if the model is true, log consumption is not cointegrated with logAt, the model of domestically produced goods may be used implies that ft and ht are not cointegrated. as a noisy proxy for the unobserved log Rather, the model implies that ft. ht, and marginal utility of wealth.2 Pt are cointegrated so long as the preferA well-known property of the standard ence shocks are trend-stationary.3 Furtherpermanent-income model with a constant more, by the results of James Stock and Mark Watson (1988), the existence of two real interest rate is that At, the utility index of permanent income, follows a martingale common stochastic trends among three I(1) (Robert Hall, 1978). Taking logs of both variables implies that there exists a unique sides of (7a) and using (8) one obtains (at least up to a scale factor) cointegrating vector. In the context of my model, if two common stochastic trends are found to be (12) ht =dt/a -(1/a)logAt. present in the data, these trends may be As I show below in Table 1, with quarterly identified with the log marginal utility of U.S. data it is not possible to reject the wealth, logAt, and a permanent shock to hypothesis that log consumption of domesthe supply schedule for imported nontic nondurable goods is nonstationary in levdurable goods. The unique cointegrating els but is stationary in first differences. It vector is [1,1/7, -a/77]' as defined by equation (10). follows from (12), and the assumption that dt is stationary, that logAt is also nonsta- tionary in levels but stationary in first differences. According to equations (8) and 3In prior (but independent) work Ogaki (1988, 1992) and Ogaki and Park (1989) also exploit the fact that, if the equilibrium consumption paths of different goods 2I allow for a trend in the cointegrating relationship are each I(1), the assumption of addilog preferences for two reasons: first, for comparability with the vast (and stationary preference shocks) implies a cointegraempirical literature devoted to estimating ad hoc import demand equations; second, to capture the influence of what are certain to be omitted variables such as improvements in product quality and the accumulation of knowledge about the characteristics of imported varieties of consumer goods (Robert Feenstra, 1992). A nonlinear trend would probably be preferable on theoretical grounds, but the bulk of the available research on cointegration has focused on cointegrating relationships about a deterministic linear trend. tion restriction across the consumption of different goods and the relative prices of these goods. These authors show that cointegration methods can be used to estimate the parameters of the addilog utility function, and they apply their approach to estimating the "long-run intertemporal elasticity of substitution" and the "Engel's Law" relationship in U.S. data. Ogaki and Park (1989) also explore the conditions under which the addilog utility function (which is not homothetic) can be aggregated across heterogenous consumers. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms VOL. 84 NO. 1 CLARIDA:COINTEGRATION, CONSUMPTION,ANDIMPORTDEMAND 301 It follows that, in a cointegrating regres- By using data on imports of foreign con- sion of f, on p, and ht, the utility parame-sumer goods instead of data on consumption ters qi and a (the elasticities of marginal utility with respect to foreign and home goods) are just identified. In Section IV, of imported goods, I introduce measurement error. Letting the measurement errors zt and ut be defined by after presenting estimates of a and -q, I shall use (7) and these estimates to obtain estimates of the Marshallian price elasticity of import demand holding constant real ex- (15) Mt= t +zt (16) h' =h +Ut penditure C = H + PF, ECf pc, as well as of substitute to a change in real spending, f C;p' holding equation to be estimated: the elasticity of import demand with respect for ft constant import prices. II. The Data The National Income and Product Accounts (NIPA) provide quarterly, seasonally adjusted nominal and 1982-dollar data on nondurable consumer-goods imports, Mt, beginning with 1967:1. The NIPA do not provide data for the spending on or consumption of domestically produced consumer goods, but of course they do provide quarterly, seasonally adjusted nominal and 1982-dollar data on nondurables consumption. My measurement of H, is defined as (13) Ht = (Et - PFtMt)/PHt (17) mt =yt - (1)p,+(a/n)ht+vt (18) vt = et + zt - (al-q)ut. The stationarity of preference shocks et is assumed. In the working-paper version of this paper (Clarida, 1991), I examine the conditions under which one would expect the measurement errors zt and ut to be stationary. If zt and ut are stationary, the model implies that mt, pt, and h't are coin- tegrated and that the parameters of interest can be recovered from the cointegrating vector [1, 1/' , - a / . III. Testing for Unit Roots and Common Trends where Et is the NIPA definition of quarter-tI begin by reporting the results obtained consumption of nondurable goods valued in current dollars, PFt is the NIPA deflator for nondurable consumer-goods imports, and from a Dickey-Fuller test of the hypothesis that each of the series mt, Pt, and h't pos- sesses a unit root. The alternative hypotheis that these series are stationary about a PHt is the producer price index (PPI) sis for deterministic trend. This test is just a t test nondurable consumer goods. A constant, or that the coefficient , is equal to zero in the even random but stationary, markup of the following regression: unobservable deflator for home goods over the PPI for home goods could be incorporated without changing the thrust of the (19) Axt=AO+Ait+pxt_i+PiAxt-i argument. It follows that (14) Ht' = Ht + Pt(Ft -Mt) + .. +ppAxtP + Ext, The results of these tests are reported in where P, = PFt /PHt, Ht is the 1982-dollar value of quarter-t consumption of domestic nondurable goods, Ht' is the 1982-dollar value of measured quarter-t consumption of domestic goods, and Ft is the 1982-dollar value of quarter-t consumption of imported nondurable goods. Table 1, with critical values from Wayne Fuller (1976) and are easily summarized. The analysis cannot reject at even the 10percent level the null hypothesis of a unit root in any of the three variables, mt, pt, or th'. With no strong evidence against the null This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms and 302 THE AMERICAN ECONOMIC REVIEW MARCH 1994 TABLE 1-TESTING FOR UNIT ROOTS I then regress changes in the estimated residuals, AEpht on one lagged level of the Dickey-Fuller Regression: Axt = /LO + /L1t +fXt_1 + pAxt-1 + xt residual and lagged changes: Variable Estimated /8 t ratio Mt Pt ht --0.0958 - 0.0555 --0.0417 Fuller -2.080 - (1976) (21) AEpht = 6oEpht-1 + P1AEpht-1 1.461 -1.860 Critical Values + + Pp A8pht-p + epht (from his table - 3.12 at the 10-percent level - 3.41 at the 5-percent level - 3.96 at the 1-percent level The test is just a t test on the coefficient 60; the appropriate critical values are those reported in Engle and Byung Yoo (1987) since Notes: The sample is 1968:2-1990:2. Variables are as defined in the text. All three equations were reestithe cointegrating regression has a constant mated with four, three, and two lags of Axt, and the term. I also run the test allowing for the lag length for calculating the t test was chosen as recommended by John Campbell and Pierre Perron alternative that pt and h't are stationary the 10-percent level. Ouliaris (1990). As can be seen from the (1991). Using this approach, the null hypothesis of a about a deterministic trend, obtaining critical values from Peter Phillips and Sam unit root in ht, mt, or pt was never rejected at even results in Table 2, pt and h't do not appear to be cointegrated according to the hypothesis of a unit root in mt, Pt, or h' , IGranger-Engle test: the t ratios fall well turn next to an investigation of the number below the level that would be required to of stochastic trends that are present among reject the null hypothesis of no cointegrathe three variables in the system. tion at even the 10-percent level. Stock and Watson (1988) demonstrate Recall that if Pt is driven in part by a that any system of m I(1) variables has a stochastic supply trend that is not cointecommon-trends representation, and that in grated with log At, one should not expect mt a system composed of m I(1) variables beand h't to be cointegrated. Table 2 also ing driven by n < m common trends, the reports the results of tests that mt and h't number of linearly independent cointegratare not cointegrated, again both excluding ing vectors must equal m - n. It follows as well as allowing for the presence of a immediately from Stock and Watson's result time trend. As can be seen from Table 2, mt that if there exists one common trend among and h't do not appear to be cointegrated according to the Granger-Engle test. For m variables, then all m(m -1)/2 possible pairs of these variables must be cointecompleteness, Table 2 also reports the regrated. Of course, if there exist n = m - 1 sults of tests that mt and pt share a comcommon trends among m variables, the mon trend. Again, these variables do not cointegrating vector is unique up to scale. appear to be cointegrated. Recall from Table 1 that the hypothesis These findings are consistent with the of a unit root in the relative price of imports prediction of the model that two common cannot be rejected. Consider the hypothesis stochastic trends, one identified with the log that the relative price of imports and log At, marginal utility of wealth, logAt, and the the utility index of permanent income, are other identified with supply shocks to the not cointegrated, as would be the case if the relative price of imports, pt, are driving the relative price of imports is driven in part by nonstationary components of the system's a stochastic supply-shock trend. Following three variables, mt, pt, and h's. If in fact Engle and Granger (1987) I test the null there are two common trends present among hypothesis that pt and h't are not cointe[mt, Pt, ht], these three variables will be grated by running the regression (20) Pt=/lo+ 3ht+ pht cointegrated, and the cointegrating vector will be unique-up to a multiplicative scale factor. It follows that the parameters of This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms 8. VOL.84 NO. 1 CLARIDA: COINTEGRATION, CONSUMPTION, AND IMPORTDEMAND 303 TABLE 2-TESTING FOR A COMMON TREND If it is found that, in the regression A. Cointegrating Regression: Xt = A0 + Alt + Pyt + exyt (23) AEmph't (S8lEmph't-1 + P1A Empht- 1 Dickey-Fuller Regression: + + Pp A Empht -p + ;t Asxyt = 8lExyt-, + pA xyt-l + exyt Variables Estimated 81 t ratio [mt, h] -0.1508 -2.2500 [mt,pt] -0.1240 -2.5230 [pt, ht] - 0.0543 -1.4414 61 is significantly negative, the OLS esti- mates of [1, 1/nq, - a/77]' given by [1, - 1 92 I2]' are consistent, despite the fact that v, is correlated with pt and h't and is also likely to be serially correlated. Phillips and Ouliaris (1989) Asymptotic Recent research, as summarized in the Critical Values (from their table HIc): survey by Campbell and Perron (1991), has -3.51 at the 10-percent level documented that, with the sample sizes -3.80 at the 5-percent level available for macroeconomic time-series re- -4.36 at the 1-percent level B. Cointegrating Regression: xt = AO + PYt + 8xyt Variables Estimated So t ratio search, the OLS estimate of the cointegrating vector can be severely biased. Furthermore, it is not possible to test hypotheses about the parameters of the cointegrating vector when these are estimated by OLS (Campbell and Perron, 1991 p. 56). Fortunately, both Stock and Watson (1988) and Phillips and Loretan (1991) have discovered tractable methods for obtaining asymptotiEngel and Yoo (1987) Critical cally Values full-information maximum-likelihood (from their table 2) for a Sample of estimates of 100: the cointegrating vector. For - 3.03 at the 10-percent level this reason, I will rely on the cointegrating - 3.37 at the 5-percent level regression primarily for its estimates of 8mph't - 4.07 at the 1-percent level and AEmpht, which are needed to test the null hypothesis of no cointegration among Notes: For part A, the sample is 1968:2-1990:2; for part B, the sample is 1968:2-1990:2. The data are m t pt, and h't. [mt,ht] - 0.0382 - 1.2857 [m1,pt] 0.0492 -1.5287 [pt, ht] -0.0488 - 1.6545 defined in the text. All regressions were estimated with four, three, and two lags of AEXYo and the lag length for calculating the t test was chosen as recommended by Campbell and Perron (1991). IV. Cointegration, Consumption, and the Demand for Imports: Empirical Results The results of the Engle and Granger interest, a and 77, can be recovered from the unique cointegrating vector defined by equation (17), [1/ 1/ n -,- a / -/]'. In light of the results reported in Table 2, a rejection of the null hypothesis of no cointegration (1987) test of the null hypothesis that mt, pt, and h't are not cointegrated are presented in Table 3A. The critical values are those reported in Phillips and Ouliaris (1990) since both a constant and a linear among mt, pt, and h't is evidence in favortime trend are included in (22), the cointe- of the model. grating regression. It is seen that the esti- Engle and Granger (1987) suggest estimating [1,1/7, - a/77]' directly from the first-stage ordinary least-squares (OLS) re- dard error of 0.0863 and a t ratio of - 4.774. Under the null hypothesis that AEmpht is a gression: random walk, the estimated 61 is significant mated value of 51 is -0.4119 with a stan- at the 1-percent level using the Phillips- (22) Mt Ao +Alt+ 3lpt + 32h't + Emph't Ouliaris critical values. In light of the results reported in Table 2, I conclude that the data are consistent with the prediction of the model that two This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms 304 THE AMERICAN ECONOMIC REVIEW MARCH 1994 TABLE 3-TESTING FOR COINTEGRATION A. Cointegrating Regression: mt = u0 + A1t +1Pt +p2h' +8 mph't, Dickey-Fuller Regression: A -mph't = l-mph't-1 + ;t Estimated 81 t ratio -0.4119 - 3.84 at the 10-percent level - 4.16 at the 5-percent level - 4.65 at the 1-percent level B. Augmented Dickey-Fuller regression: A Emph't = l Emph't-1 + P 1 A Emph't-1 + + P4 A-cmph't-4 + ;t C. OLS estimates of the parameters: Coefficient Estimated value (SE) Al -6.4105 (0.1661) 0.0170 (0.0004) -0.9577 (0.0684) 2 brought about by a jump in bt would be positively correlated with pt and thus negatively correlated with - pt. One would also expect the structural preference shock, dt to be positively correlated with ht. It follows that et= (bt - dt)/77 - Yt/77 -4.7740 Phillips and Ouliaris (1989) Critical Values (from their table Mc): ALO positively correlated with pt. That is, a transitory rise in consumption of foreign goods 2.3258 (0.1386) Notes: For part B, the lag length used to calculate the t statistic for 81 was chosen as recommended by Campbell and Perron (1991). For part C, the R2 is 0.979892; the Durbin-Watson statistic is 0.8107. The sample is is likely to be negatively correlated with the regressors in equation (22). Phillips and Loretan (1991) propose a parametric procedure for estimating the cointegrating vector in an equation in which the variables are in fact known to be cointegrated. The Phillips and Loretan approach tackles the simultaneity problem by including lagged and led values of the change in the regressors. The approach deals with the autocorrelation in the residuals by including lagged values of the stationary deviation from the cointegrating relationship. Phillips and Loretan (1991) prove that the estimates of the cointegrating vector obtained from this approach are asymptotically efficient. They also show that standard t and likelihood-ratio statistics can be used to test hypotheses about the parameters of the cointegrating vector. Let yt denote the vector [1, t, pt, h]' and let ,B denote the vector [,0, , /31 1 2]* The Phillips-Loretan equation is given by 1967:2-1990:2. Variables are defined in the text. (24) mt = IB'yt + p(mt_1 -Pyt_1) stochastic trends and thus one cointegrating vector describe the data. The OLS estimate j=T of the cointegrating vector is [1, 0.96, - 2.33]. j=T + E Apt -j + VjAhtj + Emt 1=-i-~~~~~ti t j-T j-Tf This implies an OLS estimate of -q, minus the elasticity of marginal utility with respect to the consumption of foreign goods, of The ,B vector, p, and the < 'S and yj's are estimated by nonlinear least squares 77OLS = 1.04 and an OLS estimate of a,(NLS). mi- The implied estimates of , and p nus the elasticity of marginal utility with along with standard errors are reported in respect to the consumption of home goods, Table 4. As shown in Table 4, the NLS estimate is of aOLS = 2.37. quite similar to the OLS estimate of the As discussed above, if vt is correlated cointegrating vector. The NLS estimate of with the regressors pt and h', OLS estimates of the cointegrating vector can be the cointegrating vector is [1,0.94, -2.21]. biased in small samples. One would expect This implies an NLS estimate of -q, minus the elasticity of marginal utility with respect the structural-preference shock, bt to be This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms VOL.84 NO. 1 CLARIDA: COINTEGRATION, CONSUMPTION, AND IMPORTDEMAND 305 TABLE 4-PHILLIPS AND LORETAN (1991) NONLINEAR LEAST SQUARES Phillips-Loretan equation with A = P /P1 PP2h: j=1 where s is the share of spending that falls on domestic goods. Substituting for log A in (8), one obtains the expression for the Marshallian price elasticity: Mt =P,'Y,=+ p(Mt_l- 1 Yt-l) + E fji\Pt-i j=-1 (26) Ef,P; c (4[ ( 7)+(1s)] ( f P' ( n )7 (7s /a) + (1 -s)] 1=1 + E PjAht_j + mt, Since the estimate of 77, 2NLS j= -1 ceeds 1, the estimated Marshallian elasticity Nonlinear Least-Squares Estimates of O: must, in absolute value, exceed 1/ NLS = Coefficient Estimated value (SE) ,u o -6.2096 (0.3289) 0.0164 (0.0008) P1 -0.9404 (0.1366) 82 p 2.2062 (0.2721) 0.5085 (0.1136) Implied Elasticities: Elasticity Estimated value ef, cf, p; C C;p -0.95 2.15 Notes: The elasticities are derived in the. text; see equations (36) and (39). The Phillips-Loretan equation was estimated with up to r = 3 leads and lags and with up to two lags of the equilibrium error with no significant difference in the results. 0.94. In the sample, 1- s (the share of total nondurables spending that falls on imports) rises from 0.01 in 1967 to 0.04 in 1990. Using the estimate of aNLS = 2.27, it can be determined that, in this sample, the Marshallian price elasticity of the demand for imports falls in the following range: (27) 0.94 < f,p;C < 0.95. I now derive an expression for the elasticity of import demand with respect to an increase in real expenditure, holding constant the relative price of imports. From (8) and (12), one sees that the source of such a permanent rise in real spending must be a permanent decline in the marginal utility of wealth. Using (7) it is straightforward to show that s 1 -s to the consumption of foreign goods, of (28) d log C =-a + d log A. 17NLS = 1.05 and an NLS estimate of a, mi- nus the elasticity of marginal utility with respect to the consumption of home goods, Substituting for log A and differentiating with respect to log C, one obtains of aNLS = 2.27. I now use these NLS estimates of -q and a to construct estimates of the familiar Marshallian price elasticity and the expenditure elasticity of the demand for imports. If total real expenditure C = H + PF is to remain constant in the face of an increase in the relative price of foreign goods, (7) can be used to show that (25) (77-1)(1-s)dlogP/77 = [s/a +(1-s)/'7]dlogA (29) efC;P( a S+(a)q)(1 j s) Thus, since aNLS exceeds ?JNLS, the elasticity of import demand with respect to a rise in real expenditure is bounded above by 2.21, the NLS estimate of P2. Using the fact that 1- s rises from 0.01 to 0.04 in the sample, one obtains (30) 2.11 < Ef,C;p < 2.18. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms 306 THE AMERICAN ECONOMIC REVIEW MARCH 1994 These elasticity estimates are firmly in the range of those reported in the many studies surveyed by Goldstein and Kahn (1985) and those reported by Helkie and Hooper (1986) and Cline (1989). However, the Marshallian price elasticity and the expenditure elasticity are not constant if, as in the case in the present sample, the share of spending that falls on imports is changing over time. It is easily verified that, as the share of spending on imports (1 - s) rises over time, the permanent-expenditure elasticity must decline over time from 2.21 to 1.00, while the Marshallian price elasticity must rise (in absolute value) over time from -0.94 to - 1.00. Jaime Marquez (1991) has recently emphasized the importance of allowing for time-varying elasticities in empirical trade models. One message of this paper is that, at least for nondurable consumer goods, it is possible to interpret the traditional import demand equation as a cointegrating regression. The striking similarity between the OLS and Phillips-Loretan estimates suggests that the simultaneous-equation bias is not large. A second message of this paper is that the permanent-income theory, along with the empirically testable restriction that the log relative price of imports and the log marginal utility of wealth are not cointegrated, predicts that the cointegrating vec- permanent-income model to derive a structural econometric specification of the demand for imported consumer goods. With strongly separable, addilog preferences, the log of the demand for foreign goods is shown to be linear in the log of the relative price of imports, the log of the demand for domestic goods, and the log of an unobservable shock to tastes. The rational-expectations permanent-income hypothesis in conjunction with the addilog preference structure implies that the log of the demand for domestic goods is the correct "activity" variable on the right-hand side of the import demand equation. This is because consumption of domestic goods is a noisy proxy for the unobservable log utility index of permanent income, the marginal utility of wealth. The model implies that log consumer- goods imports, the log price of imports, and log consumption of domestically produced varieties are cointegrated and that the cointegrating vector is unique. Using the approach of Engle and Granger (1987) I was able to reject decisively the null hypothesis that imports, the relative price of imports, and the consumption of home goods are not cointegrated. The estimation technique proposed by Phillips and Loretan (1991) was employed to estimate the parameters of the structural import demand equation. The long-run price tor for [ft, pt, h,] is unique and that estimates of this vector can be used to identify elasticity of import demand was estimated the parameters of the household utility to average -0.95. The elasticity of import function. An expenditure elasticity in excess demand with respect to a permanent inof unity is consistent with the theory when crease in real spending was estimated to the concavity of the subutility function for average 2.15, roughly the same as reported home goods exceeds the concavity of the by Helkie and Hooper (1986), somewhat subutility function for foreign goods. My smaller than reported by Cline (1989), and estimate is that the elasticity of the marginal somewhat larger than the average of the utility of home-goods consumption, a, is a many studies surveyed recently by Goldstein bit more than twice the elasticity of the and Kahn (1985). In the context of the optimarginal utility of foreign-goods consumpmization problem of the representative tion. household, the Marshallian price elasticity of import demand is not constant, but in V. Concluding Remarks fact converges to -1 as the share of total spending on imports rises, while the elasticAbstracting from such complications as ity of import demand with respect to a liquidity constraints and life-cycle aggregapermanent increase in real spending contion (Clarida, 1990, 1991), this paper has verges to 1 as the share of spending on employed a simple rational-expectations imports rises. An advantage of my utility- This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms VOL. 84 NO. 1 CLARIDA: COINTEGRATION, CONSUMPTION, AND IMPORTDEMAND 307 based, cointegration approach is that, by recovering consistent estimates of the utility parameters via Phillips-Loretan nonlinear least squares, one is able to estimate the permanent-income elasticity of import demand without having to specify a proxy for permanent income or having to estimate a time-series model for actual income (as in This means that if utility is given by (6'), the cointegration approach discussed in Ogaki (1992) and Ogaki and Park (1989) and derived independently here can be used to estimate the addilog parameters 77 and a; it cannot be used to recover the parameter a. REFERENCES Steven Sheffrin and Wing Woo [1990]). Masao Ogaki (1992) and Ogaki and Joon Park (1989) point out that it is possible to recover estimates of the addilog utility pa- Ball, Laurence. "Intertemporal Substitution and Constraints on Labor Supply: Evidence from Panel Data." Economic Inquiry, October 1990, 28(4), pp. 706-24. Branson, William. "The Trade Effects of the 1971 Currency Realignments." Brookings rameters from the cointegrating vector if Papers on Economic Activity, 1972, (1), APPENDIX utility in each period is given by: pp. 15-69. Campbell, John and Perron, Pierre. "What Macroeconomists Should Know About Unit Roots," in Olivier Jean Blanchard and Stanley Fischer, eds., NBER macroe+ BtFt [1- 71) conomics annual 1991. Cambridge, MA: MIT Press, pp. 72-96. where v is a concave transformation of the Ceglowski, Janet. " Intertemporal Substitution addilog utility function. In this case, ht is no in Import Demand." Joumal of Intemalonger the simple noisy proxy for log At thattional Money and Finance, March 1991, it is in the absence of said concave transfor10(1), pp. 118-30. mation. For example, if Clarida, Richard. "International Lending and Borrowing in a Stochastic Stationary Equilibrium." Intemational Economic Rev(u) = 1a)-u- 'U (6') v(u(Ht,Ft)) = V(D,Ht?[1-a]_1 then (12') ht=dt/a - (1/ a) (logkAt + af log ut) and (8') ft = bt /7t - (1/Y7)pt view, August 1990, 31(3), pp. 543-57. . "Aggregate Stochastic Implications of the Life-Cycle Hypothesis." Quarterly Journal of Economics, August 1991, 106(3), pp. 851-69. . "Cointegration, Aggregate Consumption, and the Demand for Imports: A Structural Econometric Investigation." National Bureau of Economic Research (Cambridge, MA) Working Paper No. 3812, August 1991. Cline, William. United States extemal adjustment and the world economy. Washington, and ht remains a noisy proxy for the correct DC: Institute for Internal Economics, 1989. "activity" variable on the right-hand side of the import demand equation (8'), (log At +Deaton, Angus. "The Analysis of Consumer a- log ut). Substituting (12') into (8') one Demand in the United Kingdom, 1900-1970," Econometrica, March 1974, sees that the cointegrating equation is un42(2), pp. 341-67. changed: Engle, Robert and Granger, Clive. "Cointegration and Error Correction: Representation, Estimation, and Testing." Econo- - 1/77(logkAt + af log ut) This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms 308 THE AMERICAN ECONOMIC REVIEW MARCH 1994 metrica, March 1987, 55(2), pp. 251-76. ior of U.S. Imports." Federal Reserve Engle, Robert and Yoo, Byung. "Forecasting Board, Discussion Paper No. 396, Wash- and Testing in Co-integrated System." Journal of Econometrics, May 1987, 35(1), pp. 143-59. Feenstra, Robert. "New Product Varieties and Measures of International Prices." Mimeo, University of California-Davis, August 1992. Fuller, Wayne. Introduction to statistical time series. New York: Wiley, 1976. Goldstein, Morris and Kahn, Mohsin. "Income and Price Effect in Foreign Trade," in Ronald Jones and Peter Kennen, eds. Handbook of international economics, Amsterdam: North-Holland, 1985, pp. 1042-99. ington, DC, May 1991. Miron, Jeffrey. "Seasonal Fluctuations and the Life-Cycle Permanent Income Model of Consumption." Joumal of Political Economy, December 1986, 94(6), pp. 1258-79. Ogaki, Masao. "Learning About Preferences from Time Trends." Ph.D. dissertation, Hall, Robert. "Stochastic Implications of the Life Cycle-Permanent Income Hypothesis: Theory and Evidence," Journal of Po- litical Economy, December 1978, 86(6), pp. 517-23. Helkie, William and Hooper, Peter. "An Empirical Analysis of the External Deficit, 1980-86," in Robert Bryant, Gerald Holtham, and Peter Hooper eds., External deficits and the dollar. Washington, DC: Brookings Institution, 1986, pp. 10-56. Houthakker, Hendrik. "Additive Preferences." Econometrica, January 1960, 28(1), pp. 62-87. Marquez, Jaime. "The Econometrics of Elasticities or the Elasticities of Econometrics: An Empirical Analysis of the Behav- University of Chicago, 1988. . "Engel's Law and Cointegration." Journal of Political Economy, October 1992, 100(5), pp. 1027-46. Ogaki, Masao and Park, Joon. "A Cointegration Approach to Estimating Preference Parameters." Mimeo, University of Rochester, December 1989. Phillips, Peter and Loretan, Mico. "Estimating Long-Run Economic Equilibria." Review of Economic Studies, May 1991, 58(3), pp. 407-36. Phillips, Peter and Ouliaris, Sam. "Asymptotic Properties of Residual Based Tests for Cointegration." Econometrica, January 1990, 58(1), pp. 165-93. Sheffrin, Steven and Woo, Wing. "Present Value Tests of an Intertemporal Model of the Current Account." Journal of International Economics, November 1990, 29(3-4), pp. 237-53. Stock, James and Watson, Mark. "Testing for Common Trends." Journal of the American Statistical Association, December 1988, 83(404), pp. 1097-1107. This content downloaded from 129.78.56.160 on Sun, 10 Sep 2017 06:08:53 UTC All use subject to http://about.jstor.org/terms