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The dynamic-optimizing approach to import demand: a structural model
Economics Letters 74 (2002) 265–270 www.elsevier.com / locate / econbase
The dynamic-optimizing approach to import demand: a structural model Xinpeng Xu a,b , * a
Department of Business Studies, Hong Kong Polytechnic University, Hong Kong, Hong Kong b Australia Japan Research Centre, Asia Pacific School of Economics and Management, the Australian National University, Canberra, Australia Received 8 March 2000; accepted 24 July 2001
Abstract The conventional import demand equations are generally regarded as static. And its empirical specifications are often criticized as ad hoc. This paper derives a tractable structural import demand equation from the dynamic-optimizing intertemporal approach. 2002 Elsevier Science B.V. All rights reserved. Keywords: Import demand; Intertemporal optimization JEL classification: D90; F41
1. Introduction The behavior of foreign trade flows has been the subject of extensive investigation during the last decades (Orcutt, 1950, Woodland, 1982 and Ceglowski, 1991). One of the many reasons for this ongoing interest is that the price and income elasticity of international trade is at the heart of the international transmission mechanism of various shocks. Most of the theoretical models have relied on the conventional import demand equation (in the case of imports), derived from either the imperfect substitute model or perfect substitute model (Goldstein and Kahn, 1985). Although these models can be derived from well-established consumer demand or production theory, they suffer from several drawbacks. First, they are partial and static in nature and therefore, lack intertemporal elements. In particular, the current income variable is typically used without any justification from intertemporal optimization theory. Second, the empirical implementation is somewhat ad hoc. Typically a log-linear
* Tel.: 1852-2766-7139; fax: 1852-2765-0611. E-mail address: [email protected] (X. Xu). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 01 )00538-9
2002 Elsevier Science B.V. All rights reserved.
X. Xu / Economics Letters 74 (2002) 265 – 270
266
relationship is assumed but its inconsistency with consumer demand theory has long been well known.1 Recent research has attempted to apply modern intertemporal approaches to trade flow analysis and to make use of the time series estimation techniques to tackle nonstationary time series problems. For example, Clarida (1994) and Senhadji (1998) employ a two-good version of rational-expectation permanent-income model to derive a structural econometric equation to estimate the parameters of the demand for imported nondurable consumer goods. Reinhart (1995) derives directly an import demand equation from the representative agent’s T-period budget constraints. Although this subset of literature has advanced the analysis of the behavior of foreign trade flows, there are severe limitations. For example, in Clarida (1994) and Senhadji’s (1998) model, output is assumed to be stationary and follows an AR(1) process. This is clearly inconsistent with the usual observation that output is nonstationary but its first difference is. The other drawback is that the investment and government sector is not built into the model and this might change the estimation result substantially.2 Reinhart’s model (1995), deriving directly an import demand equation from the representative agent’s T-period budget constraints, does not incorporate the agent’s intertemporal and intratemporal decision making. Her empirical estimation also uses a current income variable to approximate permanent income which may not be a reasonable estimation strategy. This paper aims to advance this literature by deriving a structural import demand equation using an intertemporal optimization approach (Obstfeld and Rugoff, 1996). Unlike the earlier literature, it takes into account both a growing economy (rather than an endowment economy) and investment and government activity. We are able to derive an import demand function that is close to the conventional one but is more flexible. The result is also in sharp contrast with that of Senhadji (1998). The rest of the paper will be devoted to the derivation of the structural model.
2. Preference, production and technology In an economy with uncertainty, the representative Home agent maximizes the von Neumann– Morgenstern expected lifetime utility,
HO `
Vt 5 Et
s 5t
(1 1 d )
t2s
U(Cs )
J
(1)
where U(Cs ) 5 Cs 2 (a 0 / 2)C 2s . where E is the expectations operator,3 (1 1 d )21 is the subjective discount rate, Cs is an index of consumption of Home and Foreign commodity bundles at time s. Denote period-t consumption of good Z by CZ , s , we assume the composite Home good is of the form 4 a 21 b Cs 5 (1 2 a )21 Ms C 12 Ns C 12 H,s 1 (1 2 b ) F,s
1
(2)
See Basman et al. (1973) for a formal proof. As it is shown later in this paper, the exclusion of investment and government sector may lead to use of wrong ‘activity variable’, as in the case of Senhadji (1998). 3 Et X is the expected value of random variable X conditional on all information available up to and including time t. 4 This form is closely related to constant elasticity of substitution (CES) but more general. 2
X. Xu / Economics Letters 74 (2002) 265 – 270
267
where the composite consumption good is the composite of Home good and Foreign good with Mt and Nt being random, trend-stationary shocks to consumption.5 More specifically, Mt 5 e a 0 1b 0 t 1 yM,t
and Nt 5 e a 1 1b 1 t 11 yN,t
(3)
where a i and b i (i50,1) are constants, and t is time trend and may carry the economic meaning of ‘habit persistance’. We choose Home good as the numeraire, i.e., PH 51. PF is then the relative price of Foreign good in terms of Home good. The representative Home agent does not foresee perfectly the random economic events that can affect his / her consumption and investment decisions. The uncertainty mainly emanates from the random productivity shocks, A t , which leads to random output for each period. Output is simply given by the production function Yt 5 A t F(Kt )
(4)
where A t is a random variable that follows an AR(1) process, with unconditional mean A¯ and an unconditional variance s 2 /(1 2 m ) 2 A t11 2 A¯ 5 m (A t 2 A¯ ) 1 et 11 , et | (0,s )
(5)
where 0# m #1 and et11 is a serially uncorrelated shock with Et et 11 5 0. 3. Budget constraint The accumulation of capital stock is governed by Kt11 5 Kt 1 It
(6)
A unit of capital is created from a unit of the consumption good. One simplification for this is that the relative price of capital goods in terms of consumption always equals 1. Savings can flow into capital as wells as foreign assets, B. The Home good can either be consumed domestically or exported. Both the government and private sectors can trade riskless bonds freely in the world capital market at gross interest rate r measured in terms of total consumption C. We simplify by assuming government spending is financed by non-distortionary taxes so that Richardian equivalence holds. This assumption enables us to integrate the government’s budget constraint into the representative Home agent’s budget constraint. The one-period intertemporal budget constraint therefore is given by Bt11 2 Bt 5 rBt 1 A t F(Kt ) 2 Kt11 1 Kt 2 Gt 2 (CH,t 1 PF CF,t )
(7)
where Ct 5CH , t 1PF CF , t . The same budget constraint as under certainty holds for each period since we are assuming that the 5
This follows Clarida (1994) and Senhadji (1998).
X. Xu / Economics Letters 74 (2002) 265 – 270
268
world interest rate is constant at r. The only implicit difference is that the budget constraint under uncertainty involves random variables such as output. The transversality condition is given by lim (1 1 r)2T Bt1T 11 5 0
(8)
T →`
The T-period intertemporal budget constraint, after imposing the above transversality condition, can be derived by iterative method,
O(1 1 r) `
O(1 1 r) `
t 2s
s5t
Cs 5 (1 1 r)B 1
s5t
t 2s
(Ys 2 Is 2 Gs )
(9)
4. First-order conditions The following first-order conditions for the representative Home agent can be solved using Pontryagin’s Maximum Principle. U 9(Cs ) 5 (1 1 r)b Es hU 9(Cs11 )j
(10)
U 9(Cs ) 5 Es h[1 1 A s11 F9(Ks11 )] b hU 9(Cs11 )j
(11)
9 (Cs ) 5 l U H,s
(12)
U 9F,s (Cs ) 5 lPF
(13)
Eq. (10) is obtained by combining date s and s11 first order condition with respect to the composite Home good Cs . It has the familiar interpretation that the representative agent smoothes expected marginal utility. Substituting the isoelastic form of the utility as set out in Eq. (1) into Eq. (10),6 we obtain Es Ct11 5 Ct
(14)
This implies that consumption follows a martingale, an important property that is first derived from the linear-quadratic permanent income model (Hall, 1978). It follows clearly that the representative Home agent will prefer consumption smoothing. Eq. (11) is obtained by differentiating the Hamiltonian with respect to Kt11 . If we assume that investment is determined according to certainty-equivalence principle,7 the expected marginal product of capital in period t11 would be r and this equation would be the same as Eq. (10).
6
In order to constrain consumption to follow a trendless long-run path, we specify that (11r)b 51, although this restriction could easily be relaxed. 7 People make decisions under stochastic environment by acting as if future stochastic variables were sure to turn out equal to their conditional mean.
X. Xu / Economics Letters 74 (2002) 265 – 270
269
Eqs. (12) and (13) are first-order conditions with respect to Home good and Foreign good, respectively, where l is the shadow value of Home composite good. Substituting Eqs. (3) and (11) into (12) and taking logs yields the following C˜ F,t 5 h 1 v t 1 ab 21 C˜ H,t 2 b 21 P˜ F 1 j t
(15)
21 21 21 where h 5 (a 1 2 a 01 )b , √ 5 (b 1 2 b 0 )b , j t 5 b (nM,t 2 nN,t )and X˜ denotes the log of variable X. In this model, CH , t 5GDPt 2It 2Gt 2EXt , where EXt is exports. Eq. (15) can be written as 21 21 C˜ F,t 5 h 1 v t 1 ab [log(GDPt 2 It 2 Gt 2 EXt )] 2 b P˜ F 1 j t
(16)
Thus, our simple intertemporal general equilibrium model provides an import demand equation that is close to the standard import demand function except that there is a trend term that captures any trend-stationary shocks to consumption and that the correct activity variable is ‘national cash flow’ 8 (GDPt 2It 2Gt 2EXt ) rather than GDPt . This therefore offers a theoretical foundation for the conventional import demand equation. Our Eq. (15) also suggests that a ‘national cash flow’ variable, relative prices and a time trend are necessary and sufficient to define the long-run behavior of imports. This would argue against the inclusion of any other variables in an ad hoc manner, for example, the current income variable, or supply side variables. The inclusion of investment and the government sector also produce an ‘activity variable’ that is different from the ‘activity variable’(GDP minus exports) as suggested by Senhadji (1998). Our import demand equation is more general and flexible than others (for example, the conventional ad hoc import demand equation and that of Reinhart (1995), Clarida (1994) and Senhadji (1998)) in that time trend term can be empirically tested and no restrictions are placed as to the income and price elasticities.9
5. Conclusion The behavior of foreign trade flows has long been the focus of theoretical and empirical investigation in international economics. The conventional import demand equations are generally regarded as static. And its empirical specifications are often criticized as ad hoc. This paper derives a tractable structural import demand equation from the dynamic-optimizing intertemporal approach. Our structural import demand equation is close to the conventional one and therefore provides theoretical foundation for the estimation of an import demand equation. Our structural import demand equation is more general and flexible and has many implications for empirical testing.
8
A similar term is referred to as national cash flow by Ghosh (1995), net output by Sheffrin and Woo (1990), and net private noninterest cash flow by Obstfeld and Rogoff (1994). See also Cashin and McDermott (1998). 9 In Reinhart (1995), the income and price elasticities are imposed to be one and minus one, respectively, due to the Cobb–Douglas utility function assumption.
270
X. Xu / Economics Letters 74 (2002) 265 – 270
Acknowledgements I wish to thank Professor Peter Drysdale for his insightful comments and suggestions.
References Basman, R.L., Battalio, R.C., Kagel, J.H., 1973. Comment on R.P. Byron’s ‘The restricted Aitken estimation of sets of demand relations’. Econometrica 41, 365–370. Cashin, P., McDermott, C.J., 1998. Are Australia’s current account deficits excessive? Economic Record 74, 346–361. Ceglowski, J., 1991. Intertemporal substitution in import demand. Journal of International Money and Finance 10, 118–130. Clarida, R.H., 1994. Cointegration, aggregate consumption, and the demand for imports: a structural econometric investigation. American Economic Review 84, 298–308. Ghosh, A.R., 1995. International capital mobility amongst the major industrialised countries: too little or too much? Economic Journal 105, 107–128. Goldstein, M., Kahn, M., 1985. Income and price effect in foreign trade. In: Ronald, J., Kennen, P. (Eds.), Handbook of International Economics. North-Holland, Amsterdam, pp. 1042–1099. Hall, R., 1978. Stochastic implications of the life cycle-permanent income hypothesis: theory and evidence. Journal of Political Economy 86, 517–523. Obstfeld, M., Rogoff, K., 1994. In: The intertemporal approach to the capital account. NBER Working Paper No. 4893. National Bureau of Economic Research, Cambridge, MA. Obstfeld, M., Rogoff, K., 1996. In: Foundations of International Economics. MIT Press, Cambridge, MA. Orcutt, G., 1950. Measurement of price elasticities in international trade. Review of Economics and Statistics 32, 117–132. Reinhart, C.M., 1995. Devaluation, relative prices, and international trade. IMF Staff Papers 42, 290–312. Senhadji, A., 1998. Time series analysis of structural import demand equations: a cross-country analysis. IMF Staff Papers 45, 236–268. Sheffrin, S.M., Woo, W.T., 1990. Present value tests of an intertemporal model of the current account. Journal of International Economics 29, 237–253. Woodland, A.D., 1982. In: International Trade and Resource Allocation. North-Holland, Amsterdam.
The dynamic-optimizing approach to import demand: a structural model Xinpeng Xu a,b , * a
Department of Business Studies, Hong Kong Polytechnic University, Hong Kong, Hong Kong b Australia Japan Research Centre, Asia Pacific School of Economics and Management, the Australian National University, Canberra, Australia Received 8 March 2000; accepted 24 July 2001
Abstract The conventional import demand equations are generally regarded as static. And its empirical specifications are often criticized as ad hoc. This paper derives a tractable structural import demand equation from the dynamic-optimizing intertemporal approach. 2002 Elsevier Science B.V. All rights reserved. Keywords: Import demand; Intertemporal optimization JEL classification: D90; F41
1. Introduction The behavior of foreign trade flows has been the subject of extensive investigation during the last decades (Orcutt, 1950, Woodland, 1982 and Ceglowski, 1991). One of the many reasons for this ongoing interest is that the price and income elasticity of international trade is at the heart of the international transmission mechanism of various shocks. Most of the theoretical models have relied on the conventional import demand equation (in the case of imports), derived from either the imperfect substitute model or perfect substitute model (Goldstein and Kahn, 1985). Although these models can be derived from well-established consumer demand or production theory, they suffer from several drawbacks. First, they are partial and static in nature and therefore, lack intertemporal elements. In particular, the current income variable is typically used without any justification from intertemporal optimization theory. Second, the empirical implementation is somewhat ad hoc. Typically a log-linear
* Tel.: 1852-2766-7139; fax: 1852-2765-0611. E-mail address: [email protected] (X. Xu). 0165-1765 / 02 / $ – see front matter PII: S0165-1765( 01 )00538-9
2002 Elsevier Science B.V. All rights reserved.
X. Xu / Economics Letters 74 (2002) 265 – 270
266
relationship is assumed but its inconsistency with consumer demand theory has long been well known.1 Recent research has attempted to apply modern intertemporal approaches to trade flow analysis and to make use of the time series estimation techniques to tackle nonstationary time series problems. For example, Clarida (1994) and Senhadji (1998) employ a two-good version of rational-expectation permanent-income model to derive a structural econometric equation to estimate the parameters of the demand for imported nondurable consumer goods. Reinhart (1995) derives directly an import demand equation from the representative agent’s T-period budget constraints. Although this subset of literature has advanced the analysis of the behavior of foreign trade flows, there are severe limitations. For example, in Clarida (1994) and Senhadji’s (1998) model, output is assumed to be stationary and follows an AR(1) process. This is clearly inconsistent with the usual observation that output is nonstationary but its first difference is. The other drawback is that the investment and government sector is not built into the model and this might change the estimation result substantially.2 Reinhart’s model (1995), deriving directly an import demand equation from the representative agent’s T-period budget constraints, does not incorporate the agent’s intertemporal and intratemporal decision making. Her empirical estimation also uses a current income variable to approximate permanent income which may not be a reasonable estimation strategy. This paper aims to advance this literature by deriving a structural import demand equation using an intertemporal optimization approach (Obstfeld and Rugoff, 1996). Unlike the earlier literature, it takes into account both a growing economy (rather than an endowment economy) and investment and government activity. We are able to derive an import demand function that is close to the conventional one but is more flexible. The result is also in sharp contrast with that of Senhadji (1998). The rest of the paper will be devoted to the derivation of the structural model.
2. Preference, production and technology In an economy with uncertainty, the representative Home agent maximizes the von Neumann– Morgenstern expected lifetime utility,
HO `
Vt 5 Et
s 5t
(1 1 d )
t2s
U(Cs )
J
(1)
where U(Cs ) 5 Cs 2 (a 0 / 2)C 2s . where E is the expectations operator,3 (1 1 d )21 is the subjective discount rate, Cs is an index of consumption of Home and Foreign commodity bundles at time s. Denote period-t consumption of good Z by CZ , s , we assume the composite Home good is of the form 4 a 21 b Cs 5 (1 2 a )21 Ms C 12 Ns C 12 H,s 1 (1 2 b ) F,s
1
(2)
See Basman et al. (1973) for a formal proof. As it is shown later in this paper, the exclusion of investment and government sector may lead to use of wrong ‘activity variable’, as in the case of Senhadji (1998). 3 Et X is the expected value of random variable X conditional on all information available up to and including time t. 4 This form is closely related to constant elasticity of substitution (CES) but more general. 2
X. Xu / Economics Letters 74 (2002) 265 – 270
267
where the composite consumption good is the composite of Home good and Foreign good with Mt and Nt being random, trend-stationary shocks to consumption.5 More specifically, Mt 5 e a 0 1b 0 t 1 yM,t
and Nt 5 e a 1 1b 1 t 11 yN,t
(3)
where a i and b i (i50,1) are constants, and t is time trend and may carry the economic meaning of ‘habit persistance’. We choose Home good as the numeraire, i.e., PH 51. PF is then the relative price of Foreign good in terms of Home good. The representative Home agent does not foresee perfectly the random economic events that can affect his / her consumption and investment decisions. The uncertainty mainly emanates from the random productivity shocks, A t , which leads to random output for each period. Output is simply given by the production function Yt 5 A t F(Kt )
(4)
where A t is a random variable that follows an AR(1) process, with unconditional mean A¯ and an unconditional variance s 2 /(1 2 m ) 2 A t11 2 A¯ 5 m (A t 2 A¯ ) 1 et 11 , et | (0,s )
(5)
where 0# m #1 and et11 is a serially uncorrelated shock with Et et 11 5 0. 3. Budget constraint The accumulation of capital stock is governed by Kt11 5 Kt 1 It
(6)
A unit of capital is created from a unit of the consumption good. One simplification for this is that the relative price of capital goods in terms of consumption always equals 1. Savings can flow into capital as wells as foreign assets, B. The Home good can either be consumed domestically or exported. Both the government and private sectors can trade riskless bonds freely in the world capital market at gross interest rate r measured in terms of total consumption C. We simplify by assuming government spending is financed by non-distortionary taxes so that Richardian equivalence holds. This assumption enables us to integrate the government’s budget constraint into the representative Home agent’s budget constraint. The one-period intertemporal budget constraint therefore is given by Bt11 2 Bt 5 rBt 1 A t F(Kt ) 2 Kt11 1 Kt 2 Gt 2 (CH,t 1 PF CF,t )
(7)
where Ct 5CH , t 1PF CF , t . The same budget constraint as under certainty holds for each period since we are assuming that the 5
This follows Clarida (1994) and Senhadji (1998).
X. Xu / Economics Letters 74 (2002) 265 – 270
268
world interest rate is constant at r. The only implicit difference is that the budget constraint under uncertainty involves random variables such as output. The transversality condition is given by lim (1 1 r)2T Bt1T 11 5 0
(8)
T →`
The T-period intertemporal budget constraint, after imposing the above transversality condition, can be derived by iterative method,
O(1 1 r) `
O(1 1 r) `
t 2s
s5t
Cs 5 (1 1 r)B 1
s5t
t 2s
(Ys 2 Is 2 Gs )
(9)
4. First-order conditions The following first-order conditions for the representative Home agent can be solved using Pontryagin’s Maximum Principle. U 9(Cs ) 5 (1 1 r)b Es hU 9(Cs11 )j
(10)
U 9(Cs ) 5 Es h[1 1 A s11 F9(Ks11 )] b hU 9(Cs11 )j
(11)
9 (Cs ) 5 l U H,s
(12)
U 9F,s (Cs ) 5 lPF
(13)
Eq. (10) is obtained by combining date s and s11 first order condition with respect to the composite Home good Cs . It has the familiar interpretation that the representative agent smoothes expected marginal utility. Substituting the isoelastic form of the utility as set out in Eq. (1) into Eq. (10),6 we obtain Es Ct11 5 Ct
(14)
This implies that consumption follows a martingale, an important property that is first derived from the linear-quadratic permanent income model (Hall, 1978). It follows clearly that the representative Home agent will prefer consumption smoothing. Eq. (11) is obtained by differentiating the Hamiltonian with respect to Kt11 . If we assume that investment is determined according to certainty-equivalence principle,7 the expected marginal product of capital in period t11 would be r and this equation would be the same as Eq. (10).
6
In order to constrain consumption to follow a trendless long-run path, we specify that (11r)b 51, although this restriction could easily be relaxed. 7 People make decisions under stochastic environment by acting as if future stochastic variables were sure to turn out equal to their conditional mean.
X. Xu / Economics Letters 74 (2002) 265 – 270
269
Eqs. (12) and (13) are first-order conditions with respect to Home good and Foreign good, respectively, where l is the shadow value of Home composite good. Substituting Eqs. (3) and (11) into (12) and taking logs yields the following C˜ F,t 5 h 1 v t 1 ab 21 C˜ H,t 2 b 21 P˜ F 1 j t
(15)
21 21 21 where h 5 (a 1 2 a 01 )b , √ 5 (b 1 2 b 0 )b , j t 5 b (nM,t 2 nN,t )and X˜ denotes the log of variable X. In this model, CH , t 5GDPt 2It 2Gt 2EXt , where EXt is exports. Eq. (15) can be written as 21 21 C˜ F,t 5 h 1 v t 1 ab [log(GDPt 2 It 2 Gt 2 EXt )] 2 b P˜ F 1 j t
(16)
Thus, our simple intertemporal general equilibrium model provides an import demand equation that is close to the standard import demand function except that there is a trend term that captures any trend-stationary shocks to consumption and that the correct activity variable is ‘national cash flow’ 8 (GDPt 2It 2Gt 2EXt ) rather than GDPt . This therefore offers a theoretical foundation for the conventional import demand equation. Our Eq. (15) also suggests that a ‘national cash flow’ variable, relative prices and a time trend are necessary and sufficient to define the long-run behavior of imports. This would argue against the inclusion of any other variables in an ad hoc manner, for example, the current income variable, or supply side variables. The inclusion of investment and the government sector also produce an ‘activity variable’ that is different from the ‘activity variable’(GDP minus exports) as suggested by Senhadji (1998). Our import demand equation is more general and flexible than others (for example, the conventional ad hoc import demand equation and that of Reinhart (1995), Clarida (1994) and Senhadji (1998)) in that time trend term can be empirically tested and no restrictions are placed as to the income and price elasticities.9
5. Conclusion The behavior of foreign trade flows has long been the focus of theoretical and empirical investigation in international economics. The conventional import demand equations are generally regarded as static. And its empirical specifications are often criticized as ad hoc. This paper derives a tractable structural import demand equation from the dynamic-optimizing intertemporal approach. Our structural import demand equation is close to the conventional one and therefore provides theoretical foundation for the estimation of an import demand equation. Our structural import demand equation is more general and flexible and has many implications for empirical testing.
8
A similar term is referred to as national cash flow by Ghosh (1995), net output by Sheffrin and Woo (1990), and net private noninterest cash flow by Obstfeld and Rogoff (1994). See also Cashin and McDermott (1998). 9 In Reinhart (1995), the income and price elasticities are imposed to be one and minus one, respectively, due to the Cobb–Douglas utility function assumption.
270
X. Xu / Economics Letters 74 (2002) 265 – 270
Acknowledgements I wish to thank Professor Peter Drysdale for his insightful comments and suggestions.
References Basman, R.L., Battalio, R.C., Kagel, J.H., 1973. Comment on R.P. Byron’s ‘The restricted Aitken estimation of sets of demand relations’. Econometrica 41, 365–370. Cashin, P., McDermott, C.J., 1998. Are Australia’s current account deficits excessive? Economic Record 74, 346–361. Ceglowski, J., 1991. Intertemporal substitution in import demand. Journal of International Money and Finance 10, 118–130. Clarida, R.H., 1994. Cointegration, aggregate consumption, and the demand for imports: a structural econometric investigation. American Economic Review 84, 298–308. Ghosh, A.R., 1995. International capital mobility amongst the major industrialised countries: too little or too much? Economic Journal 105, 107–128. Goldstein, M., Kahn, M., 1985. Income and price effect in foreign trade. In: Ronald, J., Kennen, P. (Eds.), Handbook of International Economics. North-Holland, Amsterdam, pp. 1042–1099. Hall, R., 1978. Stochastic implications of the life cycle-permanent income hypothesis: theory and evidence. Journal of Political Economy 86, 517–523. Obstfeld, M., Rogoff, K., 1994. In: The intertemporal approach to the capital account. NBER Working Paper No. 4893. National Bureau of Economic Research, Cambridge, MA. Obstfeld, M., Rogoff, K., 1996. In: Foundations of International Economics. MIT Press, Cambridge, MA. Orcutt, G., 1950. Measurement of price elasticities in international trade. Review of Economics and Statistics 32, 117–132. Reinhart, C.M., 1995. Devaluation, relative prices, and international trade. IMF Staff Papers 42, 290–312. Senhadji, A., 1998. Time series analysis of structural import demand equations: a cross-country analysis. IMF Staff Papers 45, 236–268. Sheffrin, S.M., Woo, W.T., 1990. Present value tests of an intertemporal model of the current account. Journal of International Economics 29, 237–253. Woodland, A.D., 1982. In: International Trade and Resource Allocation. North-Holland, Amsterdam.