Present Value Tests of the Current Account with

Durables Consumption

Talan B. _I�scan�

Department of EconomicsDalhousie University

Halifax, Nova Scotia, Canada B3H 3J5E-mail: tiscan@is.dal.ca

15 June 1999

Abstract

The present value tests of intertemporal model of the current account usually assumethat all goods are traded and that aggregate consumption decisions can be closely ap-proximated by a random walk process. This paper extends these models by explicitlyintroducing durables and nontraded goods into an intertemporal model of the currentaccount, and tests the model using Canadian data. Since aggregate consumption ex-penditures on durables do not exhibit random walk behaviour even when the aggregateconsumer has a quadratic utility function, the model that includes durables makes pre-dictions that di�er from those of the basic approach. When nontraded goods are alsoincorporated into the model, the most appropriate income variable becomes output netof nontraded production. These implications are examined using present value tests. Theresults suggest that introduction of both durables and nontraded goods improves uponthe model with (traded) nondurables only. This seems to be due to the combination ofdurables and nontraded goods, as durables alone do not su�ciently re�ne the basic model.

Key words: Current account; Durables; Traded and Nontraded Goods; Canada.

JEL Classi�cation: F32, F41.

�An earlier version of this paper was presented at the 1999 CEA Meetings. I wish to thank Elton

Fair�eld and James Gaisford for comments, and Nat�alia D��az-Insens�e for editorial suggestions.

All errors of interpretation are my own.

1 Introduction

From an intertemporal viewpoint, the current account is simply a manifestation of thesaving-consumption decisions at a national scale. It is therefore possible to think of anumber of analogies between the current account behaviour of individual countries and theconsumption-saving behaviour of individuals. For instance, according to a version of thepermanent income hypothesis, saving is merely a response to the expected changes in thelabour income earnings: an individual who anticipates a declining labour income adjustscurrent and future consumption by increasing current savings (Campbell 1987). Thisunderstanding of saving for the \rainy day" is also instructive once the current account isinterpreted as the saving of a country vis-�a-vis the rest of the world. By analogy, therefore,movements in the current account should re ect the expected changes in domestic income,net of investment and government spending. This view of the current account also makesthe prediction that there would be no change in current income when shocks to netoutput are expected to be permanent. In contrast, when shocks are temporary, thecurrent account would respond by the amount equal to the expected change in net outputappropriately discounted; i.e., only transitory disturbances would have an impact on thecurrent account.

All these implications of the basic intertemporal approach seem to concur well with theconventional understanding of adjustment in open economies to disturbances, and theyhave formed the basis of many studies on the current account; see, e.g., She�rin and Woo(1990), Otto (1992), Ghosh (1995), and Ag�enor et al. (1999). However, the empiricalsuccess of this intertemporal approach has been somewhat mixed. While there are anumber of industrialized countries for which intertemporal model appears to be a doinga \reasonable" job at �tting the data, for many countries the results are discouraging.

Figure 1 compares the actual Canadian current account series with those obtainedfrom a model inspired by Campbell (1987), developed in a di�erent context. From thisstandpoint, the basic intertemporal model of the Canadian current account either failsto closely track the actual series (annual data), or is biased (upward or downward inquarterly data depending on the real interest rate)|a conclusion also reached by She�rinand Woo (1990), Otto (1992), and Ghosh (1995) (see also Johnson 1986).1 Since thecurrent account tests of this variety are best suited for those small open economies whichare relatively free of capital controls and have access to international capital markets, andsince most economists would view Canada as a quintessential small open economy, suchevidence may call into question the relevance of an intertemporal approach to the currentaccount.

However, one important aspect of the present value tests of this intertemporal currentaccount model is their reliance on a rather special description of optimal consumption

1Conclusions based on more formal tests, which are presented in Appendix A, are consistent with theoverall inadequacy of the model in matching certain properties of the model and data.

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decisions. More speci�cally, existing present value tests of the current account adopt theview that the instantaneous utility function can be closely approximated by a quadraticfunction over traded nondurables, so that aggregate consumption follows a random walkprocess. For this reason, these tests are interpreted as joint tests of the degree of approx-imation for aggregate consumption behaviour and the rational expectations hypothesis.Such an approximation may, however, be questionable given that durables and semi-durables make up about 20 percent of total consumption expenditures in industrial coun-tries. And, expenditures on durables do not exhibit a random walk type behaviour evenwhen the aggregate consumer has a quadratic instantaneous utility function (Mankiw1982). This aspect of aggregate consumption is generally overlooked in empirical stud-ies on the current account.2 As a result, failure to �nd a \close" match between actualdata and data implied by the basic model does not constitute an outright rejection ofthe intertemporal approach to the current account, and the extent to which deviationsfrom the baseline permanent income hypothesis in uence the empirical performance ofthe intertemporal model remains an open issue.

Further, aggregate consumption consists of nontraded, as well as traded goods. Since,by de�nition, total expenditure on nontraded goods equals their domestic production, thecurrent account's response to permanent changes in income would primarily re ect theadjustment in the traded goods sector. In particular, the present value tests are basedon the idea that the current account conveys information about the expected changes indomestic disposable income, and thereby re ects adjustments in aggregate foreign saving.When all output is tradable, it is appropriate to view total output minus investment andgovernment expenditures as the relevant measure of domestic income. However, whensome goods are nontraded, their consumption and production are always identical, andthus, in the absence of strong substitution e�ects and complete asset markets, domesticincome from nontraded production cannot be readily transformed into foreign saving. Asa result, the use of domestic nontraded income for cross-country consumption smoothingpurposes may be considerably limited. This suggests that a more pertinent measureof income in an open economy model can be constructed by making an allowance fornontraded goods in net output, and modelling the e�ect of traded goods consumption onthe current account.

Of course, whether or not durables and nontraded goods matter for the current ac-count tests is ultimately an empirical question.3 This paper therefore examines the impactof these two extensions on the present value tests of the current account using Canadiandata from 1926 to 1997. Section 2 provides a tractable (linear) framework which allows to

2It should be emphasized that Campbell's (1987) paper, which preceded the open economy versions ofthe present value tests, analyzes nondurables and services consumption, and total consumption separately.Campbell, however, does not discuss in detail the implications of durability on consumption behaviour.

3In a cross-country time-series analysis of international consumption risk sharing, Lewis (1996) �ndsthe distinction between traded nondurables and other components of consumption to be quite important.

2

incorporate durables and nontraded goods into the baseline intertemporal open economymodel. Section 3 contains the main empirical �ndings of the paper. It �rst shows thatthe data exhibit certain stationarity properties which are required for the econometric es-timation of the model. The formal present value tests of the intertemporal model are alsoextended and presented in this section. The results suggest that augmenting the intertem-poral model by incorporating durables or nontraded goods alone may not be enough toimprove upon the baseline version. However, extending the model by both durables andnontraded goods appears to improve its empirical performance in Canadian data. There-fore, a combination of durables and nontraded goods consumption may account for themixed results obtained using the baseline model. Finally, this section also discusses therobustness of the results to alternative durables measures, the stability of the results insub-samples, and considers their validity when an allowance is made for a precautionarysaving motive. Section 4 concludes the paper.

2 A Framework for Current Account

In this section I present a framework that nests di�erent models of the current account.The �rst model does not discriminate between di�erent aspects of consumption such asdurability or tradability of goods and services. In this model aggregate consumption be-haves as described by Campbell (1987). The second model distinguishes between durablesand nondurables, and emphasizes their implications for the current account dynamics.The third model further decomposes consumption into traded durables and nondurables,and nontraded nondurables.

2.1 The Basic Model

The model considers a small open economy which faces a given world interest rate andhas no capital controls. A representative household, which also represents the nationaleconomy, maximizes the lifetime expected utility function

U = E0

"1Xt=0

�tu(t)

#; with 0 < � < 1;

where E0[�] denotes the expectations conditional upon the information available at time 0,and � is the subjective discount factor. Instantaneous utility u depends on nondurablesconsumption (C), and durables consumption (D) or, with some abuse of notation, u =u(C;D).

Assuming that all durables are traded, nondurables can further be expressed as acomposite of traded nondurables, CG, and nontraded nondurables, CS. The compositenondurables is determined by C = A(CG; CS), where A : R2

+ ! R+ is a homothetic

3

aggregator function. This assumption allows to solve the budget allocation problem intwo stages. In the �rst stage the household determines the total expenditures on durablesand nondurables, and, in the second stage, it allocates total expenditures on nondurablesbetween CG and CS. I will be more speci�c about the functional forms of u and A below(see sections 2.2{2.4).

The household can accumulate external assets B which evolve according to

B(t+ 1) = [1 + r(t)]B(t) +NO(t)� C(t)� CD(t)PD(t); t � 0;

where PD(t) is the purchase price of durables relative to the nondurable good whichis considered to be the numeraire in each period; B(t) is the stock of external assetsat the beginning of time period t; r(t) is the world interest rate measured in terms ofthe numeraire; NO denotes net output, de�ned as GDP minus the sum of investmentand government expenditures, all measured in terms of nondurables; and CD(t) is theexpenditure on durables. The evolution of the stock of durables is given by

D(t) = [1� �]D(t� 1) + CD(t); with 0 < � � 1;

where � is the depreciation rate.Maximization of the household's intertemporal utility function leads to the Euler equa-

tions that describe optimal intertemporal consumption decisions for t � 0

�[1 + r(t)]Et

"uC(t+ 1)

uC(t)

#= 1; (1)

PD(t)� �[1� �]Et

"PD(t+ 1)uC(t+ 1)

uC(t)

#=

uD(t)

uC(t): (2)

where uC, and uD denote the marginal intratemporal utility with respect to nondurableand durable goods, respectively. The left-hand side of equation (2) de�nes the user costof durables' services. These two allocation equations form the basis of the present valuetests that distinguish between alternative models of the current account.Discussion:1. The model only allows for a one-period bond, and thus assumes incomplete interna-tional securities markets. This is an important feature of all the present value tests of thecurrent account.2. In the model durables purchases are reversible and can be undertaken instantaneouslywithout incurring adjustment costs. Below, I will comment on the potential signi�canceof these issues on the interpretation of the model.

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2.2 The Baseline Model with Nondurables

In order to derive the existing tests of the intertemporal model of the current account,assume that: (i) all goods are traded [C(t) = CG(t) for all t], and nondurable [u(t) =u[C(t)] for all t]; (ii) the discount factor is equal to the inverse of the gross interest rate[� = 1=(1 + r) for all t]; and, (iii) u is quadratic in C. The quadratic utility function isspecial. However, the basic implication of this intertemporal model can also be obtainedby using a CARA instantaneous utility function (Ghosh and Ostry 1997). This extensionwill be discussed in section 3.5.

Using equation (1) together with assumptions (i){(iii) lead to the familiar expressionfor consumption

C(t) =

"rB(t) +

r

1 + r

1Xi=0

�1

1 + r

�iEt[NO(t+ i)]

#;

where 0 < � 1 is the factor of proportionality.This closed-form solution for consumption can be substituted into the \current ac-

count" as de�ned by CA(t) = rB(t)+NO(t)�(1= )C(t), to obtain the simple permanentincome hypothesis based version of the intertemporal model of the current account (see,e.g., She�rin and Woo 1990):4

CA(t) = �1Xi=1

�1

1 + r

�iEt[�NO(t+ i)]: (3)

This equation summarizes the basic idea of the intertemporal approach: the current ac-count acts as a milieu to smooth consumption and adjusts to future changes in net output.It also conforms with the commonly held view that a permanent shock to income leavesthe current account unchanged, and only temporary shocks a�ect the current account.5

Also note that the model based de�nition of the current account that appears on theleft-hand side of equation (3), di�ers from the usual de�nition of the current account usedin the balance of payments accounting when is di�erent from one.

2.3 Incorporating Durables

The baseline model of the current account is based on the premise that there is a compositenondurable good which is produced and consumed both domestically and internationally.

4Throughout the paper, for any variable X, �X(t) � X(t) �X(t � 1).5The generality of this statement depends on the extent to which temporary shocks to income are

uncorrelated worldwide, and economies di�er in size and initial endowments. Otherwise, since eacheconomy would respond to a temporary global shock symmetrically, the net impact of such a shock onthe current account would be zero.

5

If we relax this assumption, and postulate that u(t) is additively separable in C andD, andthat both goods enter the utility function in quadratic form; u = a0�(ac=2)C2�(1=2)D2,the �rst-order condition (2) becomes6

PD(t)� �[1� �]Et

"PD(t+ 1)C(t+ 1)

C(t)

#=

acD(t)

C(t):

Assuming that both the relative price of durables (PD), and the consumption basedreal interest rate in terms of the nondurables (r) are constant, the relationship betweendurable stock and nondurables consumption can be expressed as:

D(t)

C(t)=

"r + �

1 + r

# "PD

ac

#:

In this framework, it is well-known that both the stock of durables and consumptionof nondurables follow a random walk (Mankiw 1982):

C(t) = D"rB(t) +

r

1 + rEt

(1Xi=0

�1

1 + r

�iNO(t + i)

)+

PD[1� �]r

1 + r

!D(t � 1)

#;

where D � [ac(1 + r)2] =hac(1 + r)2 + (PD)2(r + �)2

i. Substituting this expression for

consumption into the current account equation yields (see Appendix B)

CA(t) = �1Xi=1

�1

1 + r

�iEt[�NO(t+ i)]� PD

1� �

1 + r

!�D(t): (4)

The main di�erence between this version of the current account model and equation (3)is that expectations about the innovations in net output can be inferred from two sources:(i) the current account, and (ii) an observable term which is proportional to net currentdurables consumption. In this formulation, the current account not only re ects revisionsabout future net output, but also contains a stock adjustment term. This new componenthas an important consequence: whereas in the standard model a permanent decrease innet output has no impact on the current account, in the speci�cation with durables itleads to a temporary current account surplus. This is due to fact that, after the realizationof the permanent decline in net output, households �nd themselves temporarily holding

6There are two main reasons for the quadratic and separable instantaneous utility function assumption.The most important reason is that it allows me to compare the results of the extended model with thoseof the baseline model. Since the main focus of the paper is to assess the empirical performance ofthe extended intertemporal model, this assumption will help to isolate the contribution of individualdepartures from the baseline version in a transparent way. Second, the model permits a closed formsolution.

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a high stock of durables. In response to that, they adjust their durables stock downwardby depleting the existing stock to levels that are optimal given the new net output. Thisleads to a decline in aggregate consumption spending and a temporary current accountsurplus. Similarly, a temporary decrease in net output leads to a smaller current accountde�cit because of the ability of the households to smooth their consumption through thestock of durables.7

The model also has implications for the volatility of the current account. This is relatedto the fact that consumption expenditures on durables ( ow) are muchmore variable thanthe stock of durables and nondurables consumption. To put this issue into context, writethe ratio of durables expenditures to replacement expenditures as

CD(t)

� �D(t � 1)=D(t)�D(t � 1)

� �D(t� 1)+ 1:

Suppose the depreciation rate � is about :18. Then a 1 percent increase in desired durablesstock leads to an 18 percent increase in durables expenditures, and the higher the averagedurability (that is, the lower the �), the higher the percentage change in expenditures.This can be compared with a 1 percent increase in desired nondurables consumption whichresults in only 1 percent increase in expenditures on nondurables.

Despite the fact that durables purchases impart an additional adjustment componentto the current account, the precise in uence of durables expenditures on the volatility ofthe current account depends on a host of factors. In the above model, these factors includethe preponderance of permanent versus temporary shocks (to net output) and their cor-relations with the determinants of durables expenditures. Other modelling choices, suchas adjustment costs and tradability, may also a�ect current account volatility in di�erentways. If some durables are nontraded (as in Matsuyama 1990), or durables purchasesare irreversible, then durable goods induced variability may dampen because such factorsmoderate the e�ects of unanticipated permanent income shocks on desired durables stock.In contrast, if some durables require �xed stock adjustment costs, households may bunchtheir durables expenditures, which leads to more variable current account dynamics.8

None of these modelling choices, of course, has been considered in the derivation of (4)as they lead to nonlinear environments and aggregate results are available only in veryspecial cases (Leahy and Zeira 1998).

7See Matsuyama (1990) for the e�ects of government expenditures on the current account with onetraded nondurable and one nontraded durable (residential housing), and Mansoorian (1998) for theimpact of terms of trade shocks on the current account with durables only. Although the speci�cs ofthese models di�er, they both show that a permanent negative net output shock may lead to a temporarycurrent account surplus|a result consistent with the above analysis.

8However, �xed adjustment cost models require sizeable aggregate shocks to generate signi�cantlymore variable current account behaviour; see e.g. De Gregorio et al. (1998).

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2.4 Incorporating Nontraded Goods

In the above analysis households form expectations about the future path of net aggre-gate output. Any temporary change in net output prompts them to trade o� currentsavings for future consumption. The di�erence between consumption and current outputpartly determines the current account which transfers income across time periods. Thisadjustment response assumes that all income changes can be traded across periods. How-ever, when nontraded, as well as traded goods are produced and consumed, aggregateoutput can no longer be viewed as entirely transferable over time to smooth consumptionbecause, by de�nition, nontraded goods consumption must be equal to its domestic pro-duction. Thus the current account implications of the model can be tested by modellingtraded goods consumption separately, which for this context implies that the current ac-count responds to temporary changes in domestic traded output net of investment andgovernment spending.

To see this, let P S be the price of nontraded services relative to traded nondurables.By construction, income from nontraded services P SY S is in every period equal to con-sumption spending on nontraded services; P SCS = P SY S . This results in the followingintertemporal budget constraint:

1Xi=0

�1

1 + r

�iEt

hCG(t+ i) + PD(t+ i)CD(t+ i)

i= [1 + r]B(t)

+1Xi=0

�1

1 + r

�iEt

hNOT (t+ i)

i;

where NOT � NO � P SCS.In the absence of strong relative price e�ects, and given the homotheticity assumption

on A(CG; CS) = C, consumption of nontraded services would be proportional to totalexpenditures on nondurables. Under the maintained assumption of quadratic utility, theproportionality modi�es the current account (expressed as a present discounted value ofexpected changes in net output and net durables purchases) as follows:

CA(t) = �1Xi=1

�1

1 + r

�iEt[�NOT (t+ i)]� PD

1 � �

1 + r

!�D(t): (5)

In sum, equations (4) and (5) modify the basic relationship between the current ac-count and present value of future changes in net output, by incorporating durables andnontraded goods, respectively. The next section addresses the empirical signi�cance ofthese di�erent measures of consumption for the Canadian current account behaviour.

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3 Empirical Results

The baseline intertemporal model of the current account in equation (3) is based on thepremise that changes in aggregate consumption can be represented by a random walk, andthat the current account only contains information about the households' expectationsconcerning future changes in net output. However, as mentioned in the Introduction, anddocumented in Appendix A, predictions made by this model are not always satis�ed in theCanadian current account. There may be a variety of reasons for the inadequacy of thisbasic model, including capital account restrictions, lack of a cointegrating relationshipbetween consumption and net output, and, as discussed above, issues surrounding thespeci�cation of consumption demand, such as durables versus nondurables, and tradedversus nontraded goods. In what follows these issues are discussed in detail. The readeris referred to the Data Appendix for the description of the data sources and variables.

3.1 Capital Mobility

The current account models presented in section 2 are only appropriate for those countrieswhich allow relatively free capital movements across national borders. Perfect capitalmobility ensures that domestic and world interest rates move in tandem, and that thesmall open economy takes the world interest rate as given. It is, therefore, important toassess the degree of capital mobility before testing the main implications of the model.While there does not appear to be a unique way of measuring the degree of capital mobility,existing studies tend to support the view that Canadian capital account has been relativelyfree over the period under consideration. For instance, using a macroeconomic variablesbased factor analysis Razin and Rose (1994, p.65) conclude that Canadian capital andcurrent accounts have been characterized by relatively high mobility. Shafer (1995, pp.139-42) reaches a similar conclusion using domestic and o�-shore interest rate di�erentials togauge capital controls.

As an additional check of the perfect capital mobility hypothesis, I used the test pro-posed by Shibata and Shintani (1998); see also Obstfeld (1995, p.34). The test involvesregressing �NO on �C, where C is aggregate consumption. The coe�cient estimateon �NO measures the degree of restrictions on capital mobility, with an estimate zerosuggesting no capital account restrictions. The GMM estimates of the degree of capi-tal mobility (not reported) using both the annual and quarterly data suggest that thehypothesis of perfect capital mobility cannot be rejected for Canada.9 Given that threeindependent tests of the capital mobility hypothesis point in the same direction, it seemssafe to proceed with testing the models' main premises using the Canadian data.

9All the results that are not reported in this paper are available upon request from the author.

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3.2 Cointegration Results

As emphasized by She�rin and Woo (1990, p.243), in the baseline model the currentaccount is stationary in levels despite the fact that consumption, interest income fromabroad and net output are all stationary in �rst di�erences. This is an example of acointegrating system in which the cointegrating relationship is given by the factor ofproportionality . Hence, by testing the stationarity of the current account, consumptionand net output, and estimating the cointegrating vector between the current account andnet output plus interest income from abroad, it is possible to assess whether the dataare consistent with these fundamental features of the intertemporal model. In addition,these cointegration tests provide some insight into the impact of di�erent measures ofconsumption on the results.

The unit root tests reported in Table 1 are encouraging in that Canadian �NO isdi�erence stationary, and CA is stationary in levels. To check for the stationarity ofconsumption, and estimate the cointegrating relationships between di�erent de�nitionsof C and NO, let � denote the total consumption divided by the particular measureof consumption. These consumption measures are: aggregate consumption C (� = 1),consumer durables and semi-durables CDSD (� = 4:05), and consumer nondurablesand services CNDS (� = 1:32).10 Table 1 shows that �C is also di�erence stationary.Together these unit root tests support the implication of the model that the currentaccount, which is a linear combination of �C(t)= and rB(t) + NO(t), is stationary inlevels [e.g., equation (3)].

I also estimated the cointegrating vector between NO plus interest payments fromabroad and consumption measured in the three measures de�ned above, namely C,CDSD, and CNDS. I used both Saikkonen's (1991) and Park's (1991) estimators forcointegrated regressors, and the results are very similar in both cases. The estimatesshown in Table 2 indicate that there is no compelling evidence against the null hypothesisof = 1 for any of the consumption measures. Further, since the three estimated coin-tegrating relationships are reasonably similar, it suggests that the long-run relationshipsbetween di�erent measures of consumption and NO plus interest income from abroadhave been stable.

In addition, I tested the existence of a cointegrating relationship between rB + NOand the three consumption measures. Notice that, in contrast to nondurables, the theorydoes not imply a cointegrating relationship between income and expenditures on durables.Overall, there is no evidence against cointegration in the aggregate data. However, whenconsumer durables and semi-durables, and nondurables and services are used as regres-

10These �'s are period averages: in the annual data the share of durables in total consumption is:117 (.036), durables and semi-durables is .246 (.029), and nondurables and services is :754 (:029), withstandard errors in parentheses. In the quarterly data the shares are, :133 (:011) for durables, :247 (.020)for durables and semi-durables, and :753 (:020). Since the shares are very similar in annual and quarterlydata, I used the annual averages for both estimates.

10

sors, the cointegrating relationship appears to weaken. For these consumption measures,Table 2 shows that the Park's H(p; q) test generally implies a strong rejection of thecointegrating relationship, and this is especially strong for the quarterly data. There-fore, the assumption of a long-run relationship between between aggregate consumptionand net output plus income from abroad seems to become less tenable for the individualcomponents of consumption. In any event, these cointegration results may be compatiblewith a range of models, and should not be viewed as direct evidence for the intertemporalmodel. Further, Elliott (1998) shows that these cointegration estimators can have largesize distortions when the variables have near roots, and tend to overreject the no cointe-gration restriction. The present value tests assess the implications of the intertemporalmodel more directly, and I now turn to the discussion of these tests.

3.3 Present Value Tests

The present value tests employed to examine the relationship between the current accountand expected changes in net output in a model of durables and nontraded goods is similarto those tests that treat all consumption as traded and nondurable. The only signi�cantnovelty in extending the tests to durables involves augmenting the system of forecastingequations from a two variable case, which only includes �NO and CA, to a three variableframework with �D. The main implication of the model for these forecasting equationsis that the current account and changes in durables help forecast future changes in netoutput, appropriately de�ned.

There are two ways to assess this implication of the model. First, one can estimatean unrestricted VAR, and test whether past values of CA and �D contain informationabout current �NO. This can be viewed as a \weak" implication of the model. Second,the restrictions implied by the intertemporal model can be imposed on the VAR. Theserestrictions yield the result that

R(t) � CA(t)��NO(t) � ��D(t) � [1 + r]CA(t� 1)

should be a purely expectation error, where � � (1� �)=(1+ r) (She�rin and Woo 1990).In other words, values of CA, �NO, and �D, that are included in the information, shouldhave no power in explaining R. These restrictions also allow to estimate the in-sampleforecasts of the CA that can be compared with actual series by various statistical methods.These tests thus encompass the \strong" implications of the model (see Appendix C).

Table 3 presents tests pertaining to these two (mutually consistent) interpretationsof the model. To check the sensitivity of the results to the particular interest rate used,I estimated the same speci�cations assuming r = :04 and r = :14.11 I also conditioned

11These choices follow She�rin and Woo (1990). Barro and Sala-i-Martin (1990, p.22) calculate theworld short-term real interest rates on government securities (such as Treasury bills) of major OECD

11

the R(t) equation upon two alternative information sets with (i) variables dated t � 1and earlier, and (ii) variables dated t � 2 and earlier. Note that the �rst informationset overlaps with some of the variables included in R(t), and therefore may be correlatedwith the expectations errors. In this context, the second information set may be a moreappropriate measure, and thus only these results are reported in Table 3.

First, consider the unrestricted VAR(2) results for the durables model only.12 Ac-cording to the estimates based on annual data the model performs poorly because �NOcoe�cients are jointly signi�cant despite the fact that the past values of CA and �Dhave already been accounted for in the speci�cation. However, the coe�cients on CA and�D have expected (negative) signs, and the coe�cients on �D are jointly signi�cant atthe 1 percent level. These suggest that an increase in the current account de�cit can beinterpreted as a (rational) forecast of an increase in net output (but the coe�cients onCA are not jointly signi�cant at levels below 5 percent). The results based on quarterlydata are mixed. While the sum of the coe�cients on the CA have the expected sign, thecoe�cients are estimated imprecisely|except in the case of �D.

In terms of the forecasting error equations (R), annual and quarterly data again pro-vide somewhat di�erent interpretations of the model. In the annual data forecastingerrors are correlated with �NO, whereas in the quarterly data they are correlated with�D. Also, these conclusions don't seem to be sensitive to the particular interest rateassumption. (The sensitivity of the results to di�erent depreciation rate assumptions ischecked below.)

Table 3 also reports the same tests for the extendedmodel with durables and nontradedgoods.13 The results emerging from the unrestricted and restricted VAR(2) analysis aresimilar to those of the previous model. Speci�cally, the past values of �NO are stillsigni�cant in predicting its future values, even after controlling for CA. Further, in thequarterly data, especially when r = :14, forecasting errors are correlated with the CA.

countries, and their estimate of average annual expected (realized) real interest rate is about 2 (1.8)percent from 1959 to 1989. They also report that in the U.S. realized real interest rates on assetscomparable to prime commercial paper averaged about 5 percent from 1920 to 1940. In light of theseestimates, for Canada the real interest rate assumption of 4 percent seems reasonable. However, all theseestimates apply to high grade borrowers, and it appears implausible to assume that a \representative"Canadian household had faced these same borrowing rates over this period. On the other hand, 14percent interest rate implies a relatively high spread, and the actual rate is likely to fall between thesetwo values.

12As discussed in Appendix A, based on AIC, VAR(1) and VAR(2) were statistically indistinguishable,and both models outperformed those with longer lags. Given that VAR(2) imposes a larger numberrestrictions on the behaviour of CA, this less parsimonious (or more demanding) model is presentedbelow. Results based on VAR(1) speci�cation are similar and are not reported.

13In the absence of more detailed and consistent aggregate time series data, this paper uses servicesas a measure of nontraded goods consumption. Given this potential concern regarding nontraded data,the following results may be used to evaluate whether services consumption is su�ciently di�erent froma �ner measurement of nontraded goods to substantially change the basic conclusions of this paper.

12

However, consistent with the implications of the model, in the annual data, past �NO andCA are not correlated with the expectations errors, while, inconsistent with the model,past �D are correlated.

These tests so far suggest that extending the baseline model to include durables andnontraded goods generate results that are somewhat consistent with the predictions of themodel. For instance, if one (arbitrarily) considers the combination of r = :14 and annualdata, the data comfortably satis�es the main restrictions implied by the extended model(Table 3, last two columns).14 In addition, Figure 2, which graphs the in-sample forecastsand actual current account data, exhibits the progression of the �t of the intertemporalmodel as the nontraded goods are incorporated into the analysis.

Of course, whether or not these constitute genuine improvements over the baselinemodel remains an open issue, especially since the unrestricted VAR analysis provides verylittle formal guidance in choosing between alternative model speci�cations. It is howeverpossible to check whether extending the baseline model improves the performance of therestricted VAR, in terms of matching certain statistical properties of the actual data.Speci�cally, as in Campbell (1987), one can compare the moments and correlations of theactual CA with those of the in-sample forecasts obtained from the VAR(2) model withall the theoretical restrictions imposed. In the current context, this method provides atransparent and convenient comparison of alternative speci�cations.

Table 4 compares the standard deviations of and the correlations between actual andforecasted CA obtained from four di�erent models: the baseline model, the model thatintroduces durability, the model that accounts for nontraded services but ignores durabil-ity issues, and the extended model with durables and nontraded goods.15 Two importantresults of Table 4 stand out. First, the interest rate has considerable impact on the in-terpretation of the results: in all cases a higher interest rate signi�cantly reduces thestandard deviation of the in-sample forecasts. It does not, however, appear to a�ect thecorrelations in any substantial way. Second, compared to the baseline model in-sampleforecasts from the model with durables and nontraded goods have standard deviationsthat are closer to actual data, except in the case of quarterly data with r = :14. Over-all, in terms of standard deviations, this model never performs signi�cantly worse thanthe baseline model. In terms of correlations between actual CA and in-sample forecasts,based on annual data, the model with durables and nontraded goods has one of the high-est correlations. However, the baseline model fares much better as far as the quarterly

14Alternatively, the fact that, for annual data the model requires a high real interest rate to pass therestrictions may be viewed as an important shortcoming. In fact, this is the case whether the entire sampleor post-WWII data are used. Irreversibility of durables and �xed costs of adjustment which reduce thesensitivity of durables purchases to interest rate changes therefore appear as plausible explanations. Notehowever that in the quarterly data high interest rates are not needed.

15The intermediate model that incorporates nontraded services is essentially the baseline model withNO

T instead of NO used in the VAR analysis. The summary statistics of this speci�cation are providedfor comparison purposes only, and the remaining tests are not reported.

13

correlations are concerned.16

Those speci�cations that ignore either tradability or durability also reveal some inter-esting insights. If only durability is incorporated into the analysis, its in-sample forecastsare outperformed by at least one model in any given speci�cation. Despite its successin matching correlations with actual CA, the mere incorporation of nontraded goods ap-pears to impart too little variability to in-sample forecasts. In contrast, durability aloneimplies a much higher CA variability than present in actual data, and the introduction ofnontraded goods seems to remedy this aspect of the model. There is therefore a sense inwhich, in this data, the introduction of durables helps increase the variability of in-sampleforecasts but only after accounting for nontraded goods.

Although moment matching exercises of this variety may not be entirely satisfactoryfor model selection purposes, the empirical results may help interpret some of the existing�ndings in the literature. In particular, after conducting a similar analysis for a group of�ve industrialized countries including Canada, Gosh (1995) �nds evidence for the \excess"sensitivity of the current account to income. (Note however that Ghosh's data sources,variable de�nitions, and time period di�er from those used in the current analysis.) Inthe case of Canadian data, the results show that conclusions concerning sensitivity toincome depend not only on the real interest rate and data frequency, but also on theincorporation of both durability and nontraded goods into the analysis.

In sum, based on these correlations and standard deviations, Table 4 suggests thatincorporating durables and nontraded goods into the intertemporal model signi�cantlyimproves upon the baseline model. In particular, the improvement appears to arise froma combination of durables and nontraded goods, as durables or nontraded services bythemselves do not seem to su�ciently re�ne the baseline model.

3.4 Sensitivity Analysis

3.4.1 Alternative Measures of Durables Stock

The estimates reported above depend on a host of assumptions concerning the mea-surement of durables stock, such as the depreciation rate. To check the sensitivity ofthe conclusions to these factors, I �rst re-estimated the extended model with durablesand nontraded goods using the durables stock estimates published by Statistics Canada(\StatsCan") and compared them with those constructed by the perpetual inventorymethod with � = :18. Table 5 shows the correlations and standard deviations pertainingto actual and forecasted data. (Since the published series start only in 1961, the sampleperiod is shortened.) These statistics indicate that while the CA forecasts obtained withthe published durables stock data result in standard deviations that closely match those of

16Unfortunately, I have not been able to �nd a satisfactory explanation of the low correlations pertainingto the extended model's quarterly in-sample forecasts.

14

the actual CA, the correlations between the actual data and the same forecasts are ratherpoor. When these are compared with those correlations and standard deviations gener-ated using the computed durables stock, the forecasts based on the computed durablesseries have a much higher correlation with the actual CA.17

The period average depreciation rate also a�ects the durables stock calculations andin-sample forecasts of the CA substantially. I considered two alternative speci�cationswith � = :15 and :21, and re-estimated the model with durables and nontraded goods.The standard deviations and correlations that emerged from these speci�cations are alsopresented in Table 5. These statistics seem to indicate that the sensitivity of the resultsto the assumed depreciation rate diminish at higher interest rates. A comparison ofthese results with those of Table 3 also gives some hints about an ambitious \momentsmatching" strategy. In particular, if the sole objective is to match the standard deviationsof the (annual) actual and forecasted CA, and to achieve a high correlation between actualand forecasted values, the combination of r = :14 and � = :18 are the preferred valueswithin the narrow set of parameter choices considered in this paper.

3.4.2 Sub-sample Stability

The results presented so far seem to indicate that the extended model with durables andnontraded goods exhibits certain advantages over the baseline model|especially for theannual data. However, it may still be desirable to make a stronger case by demonstratingthe robustness of the results to the time horizon used in the analysis. To this end, I used a\rolling regression" analysis by progressively increasing the sample period, and, as above,examining certain statistical properties of the results. Although this does not constitutea conventional stability analysis in the sense of time invariant parameters or structuralshifts, it allows to detect the in uence of certain periods upon the results.

In order to carry out this analysis, I �rst estimated the baseline model and the modelincorporating durables and nontraded goods using the annual data from 1935 to 1946,after imposing all the implied restrictions of these models. From these estimates, for eachmodel I calculated the standard deviations of the in-sample forecasts and their correlationswith the actual CA, as well as their GMM standard errors. And, this exercise was repeatedby increasing the sample size by one year at a time.

The results of this rolling regression analysis are summarized in Figure 3, which reportsthe results for both r = :04 and :14. In the graphs, the standard deviations of the in-sample forecasts of the baseline and extended models are normalized by the correspondingstandard deviation of the actual data. (In order not to clutter the graphs, the standarderrors are not shown.)

17There is no simple interpretation of these results, and thus it is not possible to judge the quality ofthe two durables series based on these simple statistics. They are however indicative of the di�cultiesencountered in the empirical analysis of the current account models which allow for durables consumption.

15

Several aspects of the correlations graphed in Figures 3(a) and (b) are worth men-tioning. First, for both model forecasts the initial correlations with the actual CA areconsiderably low (even negative), but increase substantially after the second half of 1950s.Small sample sizes underlying these estimates may account for these low correlations. Itis also possible that the post-WWII data are \special" in the sense that, during the war,durables purchases were delayed, and thereby these correlations exhibit the consequencesof this timing by households. In this context, the somewhat higher correlations of themodel with durables during this initial period are suggestive|although, as mentionedearlier, timing of consumer durables purchases does not play a role in our linear model.

Another aspect of the Figures 3(a) and (b) is that, although the correlations obtainedfrom these models are relatively similar (especially after 1960), the advantage of thebaseline model only becomes evident when the later observations are included. It shouldalso be noted that the correlation of the baseline model drops dramatically in 1991 (arecession year in Canada). For the same year the deterioration in the extended model's�t is less pronounced, possibly re ecting the fact that durables complement �nancialassets in smoothing consumption.

Comparison of the standard deviations of the baseline and extended models shown inFigures 3(c) and (d) also suggest some interesting sub-sample dynamics. First, in bothcases initial relatively high standard deviations rapidly decline to their sample means,despite a temporary increase in implied volatility around the �rst oil shock. Second, interms of matching standard deviations, the model with durables and nontraded goods hasa better performance during the entire period. Thus, one could take comfort in the overallrobustness of the main results to alternative sample speci�cations, and the in uence of\outliers."

3.5 Precautionary Savings

The present value tests provide a very convenient structure to investigate the basic con-sumption smoothing implication of an intertemporal model. Further, these tests can beextended to environments in which uncertainty about future income may in uence thecurrent account dynamics in ways that are not captured by the above model. Speci�cally,when households exhibit preferences that can be represented by constant absolute or rel-ative risk aversion utility functions, there is usually a component to saving and currentaccount that re ects a preference to insure against low consumption streams, known asprecautionary motive. In contrast, households in the above model behave according to thecertainty equivalence principle, and thus consumption smoothing constitutes their onlysaving motive.

This model however can be extended to incorporate the precautionary motive. Forinstance, Ghosh and Ostry (1997) examine a speci�c case with a CARA utility function,and show that there is a linear relationship between the variance of the net output pro-cess and the precautionary saving component of the current account. In order to assess

16

the potential signi�cance of this saving motive for the current account, I followed themethodology followed by Ghosh and Ostry (pp.129-30), and estimated the current ac-count surplus that could be attributed to the precautionary motive. However, consistentwith their estimates for Canada, I found no evidence for signi�cant precautionary motivein the data.18 Thus, the results of this paper appear to be compatible with more generalspeci�cations within the class of linear current account models based on intertemporaloptimization.

4 Conclusion

This paper has incorporated durables and nontraded goods consumption into a simplemodel of the current account, and examined whether these novel properties help improvethe empirical performance of the model. The results suggest that introduction of bothdurables and nontraded goods into the intertemporal model leads to a signi�cant improve-ment over the baseline model with (traded) nondurables only|as judged by the models'ability to match certain properties of the (annual) data. Also, this improvement appearsto arise from a combination of durables and nontraded goods, as durables or nontradedgoods alone do not su�ciently re�ne the baseline model.

In testing the implications of a range of optimizing models of the current account,this paper used several present value tests in the spirit of Campbell (1987). One aspectof these tests is that they do not require the speci�cation of a particular data generatingprocess for net output. Given that net output process is compatible with a variety ofgeneral equilibrium models, there is no need to be more speci�c about the production,investment and government expenditure processes, and it su�ces to model consumptionalone. As such, they may not be appropriate in other contexts. For instance, in orderto study the current account response to di�erent productivity shocks in the G-7, Glickand Rogo� (1995) and _I�scan (forthcoming) explicitly model both the demand and supplysides of the economy. Johnson (1986, 1994) uses a similar model with a more elaborategovernment sector to assess the Ricardian equivalence for Canada.

Put di�erently, the present value tests only focus on the broad (or \weak") implica-tions of the intertemporal model. As a result, these tests do not provide any guidanceconcerning the potential weaknesses of the framework, such as nonseparabilities in util-ity between traded nondurables and other components of consumption, as well as leisure(Lewis 1996) or time varying real interest rate. However, the analysis of the Canadian cur-rent account has suggested that controlling for di�erent aspects of consumption demand

18Speci�cally, following Ghosh and Ostry's methodology (see their Table 2, column 2), I found themagnitude of the precautionary motive for the Canadian current account to be negative, both in theannual and quarterly data (not reported). Therefore, either the CARA model has certain weaknesses, orelse the precautionary saving motive is relatively unimportant for Canada|though Canada may not betypical in this respect.

17

may improve the performance of any intertemporal model of the current account.

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De Gregorio, Jos�e, Pablo E. Guidotti, and Carlos A. V�egh. \In ation stabilization andthe consumption of durable goods," Economic Journal 108 (January 1998): 105-31.

Elliott, Graham. \On the robustness of cointegration methods when regressors almosthave unit roots," Econometrica 66 (January 1998): 149-58.

Ghosh, Atish R. \International capital mobility amongst the major industrial countries:Too little or too much?" Economic Journal 105 (January 1995): 107-28.

Ghosh, Atish R., and Jonathan D. Ostry. \Macroeconomic uncertainty, precautionarysaving, and the current account," Journal of Monetary Economics 40 (September1997): 121-39.

Glick, Reuven, and Kenneth Rogo�. \Global versus country-speci�c productivity shocksand the current account," Journal of Monetary Economics 35 (February 1995): 159-92.

_I�scan, Talan B. \The terms of trade, productivity growth, and the current account,"Journal of Monetary Economics, forthcoming.

Johnson, David. \Ricardian equivalence: Assessing the evidence for Canada." In De�cit

Reduction: What Pain, What Gain? Ed. by W.R.B. Robson, and W.M. Scarth.C.D. Howe Institute, Ottawa, pp. 81-118.

Johnson, David. \Consumption, permanent income, and �nancial wealth in Canada: Em-pirical evidence on the intertemporal approach to the current account," Canadian

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Econometrics 54 (October-December 1992): 159-78.

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Lewis, Karen K. \What can explain the apparent lack of international consumption risksharing?" Journal of Political Economy 104 (April 1996): 267-297.

Mankiw, N. Gregory. \Hall's consumption hypothesis and durable goods," Journal of

Monetary Economics 10 (November 1982): 417-25.

18

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Matsuyama, Kiminori. \Residential investment and the current account," Journal of

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Obstfeld, Maurice. \Are industrial-country consumption risks globally diversi�ed?" InCapital Mobility: The Impact on Consumption, Investment and Growth, ed. by L.Liederman, and A. Razin. Cambridge: Cambridge University Press, 1994, pp. 13-44.

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book of Statistics, ed. by G.S. Maddala, C.R. Rao, and H.D. Vinod. Elsevier SciencePublishers, 1993, pp. 455-488.

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Rates, and Monetary Policy in the World Economy, ed. by S. Edwards. Cambridge:Cambridge University Press, 1995, pp. 119-56.

She�rin, Steven M., and Wing Thye Woo. \Present value tests for an intertemporal modelof the current account," Journal of International Economics 29 (November 1990):237-53.

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Data Appendix

All data are from Statistics Canada's CANSIM database, and were retrieved in November1998. In what follows, the numbers in parentheses refer to the corresponding CANSIMmatrix numbers. Annual data are from 1926 to 1995, quarterly data are annualized andseasonally adjusted from 1961:1 to 1997:2. All variables are measured in real per capita

19

terms (thousands of 1986 dollars).19 Nominal variables are de ated by the de ator basedon expenditure on goods and services (D11012/D14443 for annual and D14817/D20464for quarterly data), and divided by total population (D31248 for annual and D22166 forquarterly data) to obtain per capita data. (As an alternative, I also experimented withGDP de ator based real variables, but due to the high correlation coe�cient betweenthese two de ators (:979), the results did not seem to be a�ected by this.)

Net output|Annual data: GDP (D11011) minus government spending [expenditures(D11017) + investment (D11018) + changes in inventories (D11022)] � business invest-ment (D11023) and changes in business inventories (D11027). Quarterly data: GDP(D14840) minus government spending [expenditures (D14822) + investment (D14823) +changes in inventories (D14824)] � business investment (D14825) and changes in businessinventories (D14830).

Current Account|GDP + investment income from abroad (D58041 for annual andD59041 for quarterly data) � government spending � private investment and changes inprivate inventories.20

Consumption|Annual data: Durable goods (D11013), semi-durable goods (D11014),non-durable goods (D11015), and services (D11016), expenditure based. Quarterly data:Durable goods (D14818), semi-durable goods (D14819), non-durable goods (D14820), andservices (D14821), expenditure based.

Durables Stock|Both annual and quarterly series were constructed using the durablesstock equation given in the text. Three di�erent parameterizations of the depreciation ratewere used; 15, 18, and 21 percent at annualized rates. Throughout the paper \durables"refers to series calculated using both durables and semi-durables since o�cial de�nition ofsemi-durables includes items, such as furnishings, which are typically considered durablein economic studies.21 Since there was no initial stock estimate for 1926, the �rst nineyears of the annual durables stock data were dropped to reduce the sensitivity of theresults to the choice of initial observation. For the quarterly data, the initial observationis the beginning of 1961 durable stock calculated from the annual estimates.

An alternative method is to use the annual estimates of private and unincorporatedbusiness consumer durables published by Statistics Canada, National Balance Sheet Ac-

counts. The latter series also includes some semi-durables, such as recreational materialwith service life below three years, and uses a perpetual inventory method with deprecia-

19The annual and quarterly data end in di�erent periods because Statistics Canada no longer publishesthese data in constant 1986 prices. More recent series are based on constant 1992 prices, but start onlyin 1961. To ensure consistency, I did not attempt to convert 1996 quarterly data into annual �gures.

20This current account measure is suggested and also used by She�rin and Woo (1990).21In terms of simple descriptive statistics, the durables expenditure is more volatile: in annual data,

standard deviations of expenditures on durables and semi-durables are, respectively, :559 (:211) and :276(:072), standard errors in parentheses (statistics for quarterly data are similar). Also, these two seriesexhibit high correlation, :963 (:025).

20

tion and discards. These data are available in current and constant 1986 prices but onlyfor the period from 1961 to 1992. Unfortunately, the durables expenditure and deprecia-tion data underlying these series cannot be recovered using publicly available information.When expenditure on consumer durables alone is used to reconstruct these series, the im-plied annual depreciation rate gradually increases from 14 to 22 percent over this period,rendering 18 percent a reasonable mid-point choice. When expenditures on both durablesand semi-durables are used, the implied depreciation rate is much higher. An attemptto estimate historical durables stock data by going \backwards" using either of these de-preciation rates quickly failed because of implied negative durables stock.22 In light ofthese data problems, I checked the robustness of the results using both the computed and\StatsCan" measures.

Appendix A: The Current Account Tests of the Baseline Model

Since the methodology is fairly standard, I omit the details which can be found in Camp-bell (1987), and She�rin and Woo (1990). The test of the intertemporal model of thecurrent account when changes in aggregate consumption follows a random walk postu-lates that the current account (CA) be stationary in levels and the net output (NO)be stationary in �rst-di�erences. Table 1 reports, for both annual and quarterly data,the unit root and stationarity test statistics for CA, NO, as well as total consumptionC, consumption of durables and semi-durables (\durables" CDSD), and consumption ofnon-durables and services (\non-durables" CNDS). While in their cross-country studiesboth She�rin and Woo, and Shibata and Shintani (1998) could not reject the null of non-stationarity for the Canadian CA, in the annual CA data both Dickey-Fuller (�ct) andPerron-Phillips (zct) tests reject the unit root hypothesis at the 10 percent level. Also,consistent with the model (and earlier studies), the null of unit root cannot be rejectedfor the annual NO. Further, based on the LM test statistic proposed by Kwiatkowski etal. (1992), the null of stationarity around a constant and time trend cannot be rejectedfor the CA and �NO. The only qualitative di�erence between the annual and quarterlydata occurs in the case of �ct test-statistic for the CA. In this case, the null of unit rootcannot be rejected at conventional levels of signi�cance. However, the LM test statisticdoes not provide evidence against the nulls of stationarity of CA around a constant, anda constant and trend. Note also that the null of stationarity of �NO around a constantor a constant and time trend cannot be rejected at even 1 percent. In sum, there is nostatistical evidence against the stationarity of the CA and �NO, which suggests that thetests proposed by Campbell can be safely extended to these data.

Campbell's tests, when applied to an intertemporal model of the current account,consist of assessing the signi�cance of the CA in forecasting the changes in NO, which isa measure of income at a national scale. CA and �NO regressions, and the tests of the

22The discussion in Johnson (1994, p.118) points out to similar di�culties.

21

intertemporal model based on the random walk property of consumption are performed forboth annual and quarterly data. For model speci�cation purposes, Akaike and Schwartzinformation criteria were used for appropriate lag selection. Based on these criteria,models with one and two lags were essentially indistinguishable, and models with largerlags had much higher values. Another consideration for model speci�cation is that, asthe number of lags in the VAR decreases the number of restrictions implied by the modeldecrease by a multiple of two. As discussed by Campbell (1987, p. 1267) a VAR(1)has very few distinguishing features for the simple permanent-income hypothesis, as itonly entails two cross-equation restrictions. This therefore constitutes a weak test forthe model. Hence, in what follows I only present the estimation results of VAR(2), andresults of VAR(1) are available upon request from the author.

Table 6 presents the estimation results of the CA and �NO regressions from a VARmodel with two lags, VAR(2). The �rst implication of the model is that the sum of thecoe�cients on the CA in the VAR equation explaining �NO are negative (and signif-icant). This is not the case for both annual and quarterly data. Also, the hypothesisthat CA does not cause �NO, in the sense of Granger, can only be rejected at the 4.1percent level or higher. Second, the model predicts that coe�cient estimates in columns[3]{[6] are individually and jointly insigni�cant. The dependent variable in these regres-sion speci�cations is essentially an expectation error at t or t + 1|under the null ofrational expectations and quadratic utility function, and should be uncorrelated with anyinformation available at t � 1. This implication of the model is also rejected for �NOin both annual and quarterly data, and for two parameterizations of r. Especially, the�nding that past changes in NO help predict future �NO, even after controlling for theCA, indicates that the CA systematically fails to anticipate the changes in NO. Third,the overall �t of the model, as summarized by the standard deviations of and correla-tions between forecasted and actual values of CA, is sensitive to data frequency and thereal interest rate assumption: while annual data indicate excess sensitivity of the CA tochanges in NO, quarterly data with r = :14 provides the opposite interpretation.

In sum, an intertemporal model of small open economy based only on the tradednondurable goods consumption appears to do an unsatisfactory job in providing a gooddescription of the current account dynamics.

Appendix B: Derivation of the CA with Durables

In the presence of durables the current account can be expressed as

CA(t) = rB(t) +NO(t)� DC(t) +(PD)2

ac

r + �

1 + r

!2

C(t)� PD[D(t)� [1� �]D(t� 1)]:

22

Using the expression in the text for C(t) gives

CA(t) = �

1Xi=1

�1

1 + r

�iEt[�NO(t+ i)]�

PD[1� �]r

1 + rD(t� 1) + PD[1� �]D(t� 1)

+

"(PD)2

ac

# "r + �

1 + r

#2C(t)� PDD(t)

= �

1Xi=1

�1

1 + r

�iEt[�NO(t+ i)] + PD

"1 � �

1 + rD(t� 1)

#� PDD(t)

+ PD

r + �

1 + r

!D(t)

= �

1Xi=1

�1

1 + r

�iEt[�NO(t+ i)] + PD

1� �

1 + r

!D(t� 1)� PD

1� �

1 + r

!D(t);

where the second equality uses the relationship between durables and nondurables con-sumption.

Appendix C: Restrictions Implied by the Extended Model

Although the results reported in the text are from a VAR system with 2 lags, it is nota-tionally less burdensome to carry out the argument for VAR(1). The extension to VAR(2)is relatively straightforward.

Write the 3 variable VAR system as:

264 �NO(t)

CA(t)�D�D(t)

375 =

264 a11 a12 a13a21 a22 a23a31 a32 a33

375264 �NO(t� 1)

CA(t� 1)�D�D(t � 1)

375 :

Alternatively, in a concise form Xt = A � Xt�1 where X 0 = [�NO;CA;�D�D]. Takingexpectations gives, EtXt+i = Ai �Xt. Thus, forecasts of �NO can be expressed as

Et�NO(t+ i) = h0Ai �Xt; with h0 = [1; 0; 0]:

Similarly, the current account and the change in durables can be written as

CA(t) = g0Xt

�D�D(t) = m0Xt;

23

where g0 = [0; 1; 0], and m0 = [0; 0; 1]. In terms of equation (4),

g0Xt = �1Xi=1

�1

1 + r

�ih0AiXt �m0Xt:

Convergence of the present value of net output changes implies that

g0�I �

�1

1 + r

�A�= h0

�1

1 + r

�A�m0

�I �

�1

1 + r

�A�:

Working out the algebra for these restrictions implies that a21 = a11 � a31, a22 =a12 � a32 + (1 + r), and a23 = a13 � a33 + (1 + r). Thus, one empirical strategy involves�rst estimating

�NO(t) = a11�NO(t� 1) + a12CA(t� 1) + a13�D�D(t � 1)

�D�D(t) = a31�NO(t� 1) + a32CA(t� 1) + a33�D�D(t � 1);

and then computing the in-sample forecasts of the current account, CAf yields

CAf(t) = a21�NO(t) + a22CA(t) + a23�D�D(t)

= (a11 � a31)�NO(t) + [a12 � a32 + (1 + r)]CA(t)

+ [a13 � a33 + (1 + r)]�D�D(t):

These constitute the VAR based in-sample forecasts of the CA with the restrictions ofthe intertemporal model with durables imposed.

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Table 1

Unit Root and Stationarity Tests

Variable �c �ct zc zct LMc LMct

Annual data: 1926-1995CA �0:956 �3:412 �11:858 �28:289 0:785 0:067NOa 1:644 �2:232 0:878 �5:118 0:465 0:095C 0:533 �2:873 0:569 �5:303 1:060 0:232CDSD �0:567 �2:707 �0:735 �12:405 1:057 0:100CNDS 0:959 �2:748 0:905 �3:288 1:209 0:294

Quarterly data: 1961:1-1997:2CA �2:034 �1:917 �21:513 �23:695 0:367 0:082NOa �1:188 �1:884 �0:873 �6:483 0:161 0:048C �1:134 �2:048 �0:750 �2:163 2:956 0:435CDSD �1:650 �2:040 �2:945 �4:458 1:513 0:306CNDS �1:045 �2:173 �0:353 �1:108 1:416 0:187

Notes: �c and �ct are t-test statistics on the lagged variable in the augmented Dickey-Fullerregression equation with constant, and constant and time trend, respectively. Asymptotic 10percent critical values are �2:57 with constant, and �3:13 with constant and trend. zc and zctare formed from the test statistic which is the number of observations times the coe�cient onthe lagged variable in the augmented Dickey-Fuller regression. Asymptotic 10 percent criticalvalues are �11:2 with constant, and �18:2 with constant and trend. LMc and LMct are theKwiatkowski et al. (1992) test for stationarity with constant, and constant and trend, respec-tively. Asymptotic 10 (5) percent critical values are 0:347 (0:463) with constant, and 0:119(0:146) with constant and trend. Long-run covariance matrices are estimated using Bartlettkernel, with lag truncation parameters selected using the method suggested by Newey and West(1994).a For the LMc and LMct tests the �rst-di�erence of NO is used.

25

Table 2

Cointegrating Regression Results

Independent variable = rB(t) +NO(t)

[1] [2] [3] [4] [5] [6]Variable SCR CCR ADF t-stat. H(0; 1) H(1; 2) H(1; 3)

Annual data: 1926-1995C 0.943 0.950 �3:145 0.065 0.170 2.962

(0.005) (0.007) (10%) (0.799) (0.680) (0.227)CDSD 0.930 0.942 �1:040 0.948 51.373 50.329

(0.010) (0.030) (0.330) (0.000) (0.000)CNDS 0.930 0.946 �2:276 6.493 9.957 7.660

(0.008) (0.012) (0.011) (0.002) (0.022)

Quarterly data: 1961:1-1997:2C 0.957 0.959 �2:277 9.254 2.347 4.341

(0.007) (0.007) (0.002) (0.125) (0.114)CDSD 0.980 1.081 �1:797 387.726 0.659 3.881

(0.008) (0.055) (0.000) (0.417) (0.144)CNDS 0.932 0.943 �2:323 0.964 5.024 11.001

(0.004) (0.009) (0.326) (0.025) (0.003)

Notes: SCR is Saikkonen's (1991) estimator for cointegrated regressors, and CCR is Park's(1992) estimator for cointegrated regressors. ADF t-stat. is the augmented Dickey-Fuller teststatistic for the null of no cointegration. H(p; q) is Park's test statistic for the null-hypothesisthat the variables are cointegrated, where p and q are the orders of the time polynomial in the�tted regression. In cols. 1 and 2 standard errors are in parentheses, in col. 3 asymptotic levelsof signi�cance, and in cols. 4{6 p-values. Lag truncation parameters are selected using themethod suggested by Newey and West (1994).

26

Table 3

Current Account Regressions with Durables and Nontraded Goods

r = :04 r = :14

Variable �NOt Rt+1 �NOTt Rt+1 �NOt Rt+1 �NOT

t Rt+1

Annual data: 1935-1995�NOt�iy; 0:365 �0:744 0:375 �0:352 0:365 �0:746 0:375 �0:392i = 1; 2 (0:173) (0:349) (0:219) (0:491) (0:173) (0:338) (0.219) (0:457)

CAt�i ; �0:133 0:027 �0:114 0:019 �0:133 0:065 �0:114 �0:394i = 1; 2 (0:087) (0:141) (0:082) (0:116) (0:087) (0:135) (0.082) (0.394)

��Dt�i ; �0:699 �0:501 �0:854 �0:614 �0:766 �0:425 �0:936 �0:529i = 1; 2 (0:249) (0:615) (0:176) (0:393) (0:273) (0:666) (0.193) (0.421)

�R2 0.128 -0.286 0.167 -0.269 0:128 �0:249 0:167 �0:195

Quarterly data: 1961:1-1997:2�NOt�iy; �0:288 �0:043 �0:272 0:139 �0:288 �0:034 �0:272 0:123i = 1; 2 (0:189) (0:196) (0:159) (0:145) (0:189) (0:187) (0.160) (0:148)

CAt�i ; �0:046 �0:005 �0:039 �0:050 �0:046 �0:098 �0:039 �0:143i = 1; 2 (0:043) (0:038) (0:043) (0:033) (0:043) (0:035) (0.044) (0.031)

��Dt�i ; 0:451 �1:283 0:247 �1:172 0:495 �1:304 0:271 �1:167i = 1; 2 (0:245) (0:299) (0:201) (0:179) (0:269) (0:292) (0.215) (0.191)

�R2 0.032 0.184 0.012 0.217 0:032 0:243 0:012 0:278

Notes: Standard errors reported in parentheses are calculated using the method suggestedby Newey and West (1994). Constant terms are omitted in cols. 1, 3, 5 and 7. Rt+1 �

CAt ��NOt � ��Dt � (1 + r)CAt�1, (similarly for �NOT). The reported estimation resultsare for sums of regression coe�cients. � � (1� �)=(1 + r) with � = :18.y �NOT for the model with nontraded goods.

27

Table 4

Correlations and Standard Deviations of Actual and In-Sample

Forecasts of Canadian Current Account

r = :04 r = :14Variable � Corr. � Corr.

Annual data: 1935-1995Actual 0.307 - 0.307 -

(0.041) (0.041)Baseline 1.134 0.890 0.476 0.832

(0.147) (0.036) (0.076) (0.066)Durables 1.073 0.844 0.538 0.823

(0.154) (0.063) (0.067) (0.081)Nondurables 0.437 0.923 0.191 0.835and nontraded (0.047) (0.022) (0.019) (0.068)

Durables 0.500 0.915 0.284 0.907and nontraded (0.066) (0.025) (0.029) (0.033)

Quarterly data: 1961:1-1997:2Actual 0.282 - 0.282 -

(0.024) (0.024)Baseline 0.351 0.997 0.158 0.997

(0.029) (0.001) (0.014) (0.001)Durables 0.423 0.356 0.235 0.416

(0.103) (0.271) (0.063) (0.261)Nondurables 0.162 0.997 0.078 0.985and nontraded (0.014) (0.001) (0.006) (0.003)

Durables 0.231 0.254 0.142 0.300and nontraded (0.051) (0.274) (0.031) (0.262)

Notes: � is standard deviation, and \Corr." is the correlation coe�cient between the actualand in-sample forecasts of CA. Standard errors of the correlations and standard deviations arecomputed numerically using GMM as suggested by Ogaki (1993, sec.8.4). � = :18 when durablesare used.

28

Table 5

Sensitivity Analysis|Annual Data

r = :04 r = :14Variable � Corr. � Corr.

Actual (1961-1992) 0.259 - 0.259 -(0.027) (0.028)

Computed, � = :18 0.429 0.801 0.208 0.739(0.074) (0.053) (0.028) (0.088)

StatsCan, � = :18 0.258 0.006 0.219 0.012(0.061) (0.515) (0.052) (0.530)

Actual (1935-1995) 0.307 - 0.307 -(0.045) (0.042)

Computed, � = :15 0.481 0.892 0.283 0.892(0.067) (0.036) (0.029) (0.044)

Computed, � = :21 0.514 0.927 0.283 0.914(0.066) (0.067) (0.029) (0.028)

Notes: � is standard deviation, and \Corr." is the correlation coe�cient between the actualCA and its in-sample forecasts from the model with durables and nontraded goods. Standarderrors of the correlations and standard deviations are computed numerically using GMM assuggested by Ogaki (1993, sec.8.4). \Computed" series follow the methodology described inthe Data Appendix, and \StatsCan" series are from Statistics Canada, National Balance Sheet

Accounts.

29

Table 6

Current Account and Net Output Regressions

[1] [2] [3] [4] [5] [6]Variable �NOt CAt Rt (.04) Rt (.14) Rt+1 (.04) Rt+1 (.14)

Annual data: 1926-1995�NOt�i ; i = 1; 2 0:337 �0:226 �0:741 �0:741 0:421 �0:394

(0:135) (0:118) (0:102) (0:102) (0:117) (0:148)CAt�i ; i = 1; 2 �0:072 0:857 �0:003 �0:103 0:098 0:007

(0:121) (0:061) (0:051) (0:051) (0:055) (0:060)

�R2 0.100 0.666 0.154 0.205 �0:151 �0:118

CA Granger causes �NO at 4.1% level in column [1].

�NO Granger causes CA at 21.5% level in column [2].

r = :04: �(CA) = :295 (:041), �(CA) = 1:070 (:135), corr(CA; CA) = :868 (:040).

r = :14: �(CA) = :464 (:055) corr(CA; CA) = :802 (:068).

Quarterly data: 1961:1-1997:2�NOt�i ; i = 1; 2 �0:134 0:005 �0:142 �0:142 �0:319 �0:303

(0:144) (0:153) (0:080) (0:080) (0:117) (0:119)CAt�i ; i = 1; 2 �0:045 0:847 0:007 �0:093 �0:004 �0:098

(0:045) (0:009) (0:030) (0:030) (0:033) (0:031)

�R2 0.012 0.703 -0.068 0.080 �0:021 0:091

CA Granger causes �NO at 62.3% level in column [1].

�NO Granger causes CA at 27.7% level in column [2].

r = :04: �(CA) = :282 (:023), �(CA) = :351 (:029), corr(CA; CA) = :997 (:001).

r = :14: �(CA) = :158 (:014) and corr(CA; CA) = :997 (:001).

Notes: Standard errors reported in parentheses are calculated using the method suggested byNewey and West (1994). Constant terms are omitted in cols. 1 and 2. Rt (r) � CAt��NOt�

(1+r)CAt�1. The reported estimation results are for sums of regression coe�cients. �(X), and�(X) are, respectively, the standard deviations of the in-sample forecasts and actual values ofX , and \corr" is the correlation coe�cient. Standard errors of the correlations and standarddeviations are computed numerically using GMM as suggested by Ogaki (1993, sec.8.4).

30

Figure 1.| Actual and In-Sample Forecasts of the Current Account|Baseline Model

Figure 2.| Actual and In-Sample Forecasts of the Current Account|ExtendedModels

Figure 3.| Correlations and Standard Deviations from Rolling Regressions

31