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Monetary policy in a small open economy with durable goods and differing cash-in-advance constraints
Economics Letters 107 (2010) 246–248
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e t
Monetary policy in a small open economy with durable goods and differing cash-in-advance constraints Arman Mansoorian a,⁎, Leo Michelis b a b
Department of Economics, York University, North York, ON, Canada, M3J 1P3 Department of Economics, Ryerson University, Toronto, ON, Canada, M5B 2K3
a r t i c l e
i n f o
Article history: Received 13 January 2009 Received in revised form 15 January 2010 Accepted 22 January 2010 Available online 1 February 2010
a b s t r a c t We consider the effects of inflation in a small open economy when expenditures on non-durables are more heavily financed with money than expenditures on durables. The distinctions between non-durables and durables, and asymmetric cash-in-advance constraints give rise to important dynamics. © 2010 Elsevier B.V. All rights reserved.
JEL classification: E22 E52 E58 Keywords: Inflation Cash Credit Durables Capital
1. Introduction The small open economy literature has identified several channels though which monetary policy can affect the economy. For example, Obstfeld (1981a,b) considers the effects of monetary policies for a small open economy with Uzawa (1968) preferences, whereby the rate of time preference is an increasing function of instantaneous utility, and with the money-in-utility specification of Sidrauski (1967). Mansoorian (1998) considers the effects of habits, as in Ryder and Heal (1973), in the money-in-utility framework. There, the rate of time preference is fixed, but instantaneous utility depends on habits, which are modelled as a weighted average of past levels of instantaneous utilities. Shi and Epstein (1993) developed a model in which the rate of time preference is an increasing function of habits. Mansoorian and Mohsin (2006) consider a setting with a fixed rate of time preference and no habits, but with endogenous labour and a cash-in-advance (CIA) constraint. In this paper we consider another channel through which monetary policy can affect the economy; the presence of durable goods, in conjunction with the assumption that the method of payment for ⁎ Corresponding author. Department of Economics, York University, 4700 Keele Street, North York, Ontario, M3J 1P3, Canada. Tel.: +1 416 736 5083; fax: +1 416 736 5987. E-mail address: [email protected] (A. Mansoorian). 0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2010.01.037
durable goods differs from that for non-durables; whereas the latter are financed primarily with cash, the former are partly financed with loans or credit.1 These are realistic assumptions to make. A significant proportion of aggregate consumption, in many countries, consists of expenditures on durable goods such as housing, automobiles, household appliances and home electronics. For example, in the US the division between durable and non-durable consumption expenditures is about 23 and 77% respectively.2 Borzekowski and Kiser (2006) provide some recent evidence on the different types of payments instruments used by US households, supporting the assumption that non-durables are often paid for with cash (currency, debit cards or checking accounts), while durables are paid for largely with credit.3
1 In a related literature Lucas and Stokey (1983, 1987) have introduced the distinction between cash and credit goods. In that literature credit goods, like leisure, do not require means of exchange and thus are not subject to the inflation tax discussed in this paper. 2 To arrive at these figures, we added an estimate of housing services to the US National Income and Product Accounts (NIPA) measure of durable goods. To estimate housing services, we assumed that the ratio of housing services to non-durable consumption is 0.20, which is roughly consistent with the average estimate in Fig. 1 of Piazzesi et al. (2007); see also Obstfeld and Rogoff (1996, p. 96). 3 According to the US Federal Reserve Board's 2004 Survey of Consumer Finances (CFS) about 90 % of total household credit is for housing and automobile expenditures; See Bucks et al. (2006), Table 12.
A. Mansoorian, L. Michelis / Economics Letters 107 (2010) 246–248
The rest of the paper is organized as follows. Section 2 presents the model. Section 3 analyzes the effects of an increase in the inflation rate. Section 4 concludes. 2. The model We consider a small open economy, with perfect capital mobility. There is one non-durable good that is internationally traded, and which has a fixed price P⁎ in terms of the foreign currency. The domestic currency price of this good is P = EP⁎, where E is the nominal exchange rate: the price of foreign currency in terms of the domestic currency. With P⁎ fixed, the rate of inflation is equal to the rate of depreciation of the domestic currency: πt = Ėt/Et. 4 The preferences of the representative agent are given by ∞ −θt
∫0 e
N D U ct ; ct dt;
ð1Þ
D where U(cN t , ct ) is a standard instantaneous utility function, θ is the rate of time preference, cN t is the consumption of non-durable goods and cD t is the consumption of the services of durable goods at time t. Following the empirical literature (see, e.g., Dunn and Singleton (1986), Eichenbaum et al. (1988), and Eichenbaum and Hansen D (1990)) the services of durable goods cD t is modelled as ct = υdt, where υ is the depreciation rate for the durable good, and dt is the stock of durables available at time t. Next, note dt can be expressed as t
υ(τ − t)
the non-depreciated stock at time t; that is, dt = ∫ e implies that the evolution of dt is given by d˙ t = qt −υdt :
qτdτ, which
−∞
ð2Þ
where qt represents the purchases of new durables at time t. All expenditures on non-durables are financed with money while only a fraction α of the expenditures on durables are financed with money, and the rest with credit. Hence, if mt is the representative agent's total real money holdings, then N
mt ≥ct + αqt :
ð3Þ
We assume the foreign currency price of the internationally traded bonds is fixed, as is the real rate of return on them, r. If bt is the representative agent's holdings of these bonds, then his total asset holdings at time t will be at = mt + bt. In order to concentrate on the importance of the asymmetry in the CIA constraints, in conjunction with the existence of durable goods, we abstract completely from endogenous output; output is fixed at y. Further, the representative agent receives real monetary transfers of magnitude τt from the government. Hence, his flow budget constraint is N a˙ t = rat + y + τt −ct −qt −ðr + πt Þmt ;
ð4Þ
The representative agent maximizes lifetime utility (1), subject to conditions (2)–(4), the initial conditions d0 and a0, and the standard no Ponzi game condition, taking the time paths of the inflation rate π and the transfers τ as given. Noting that in equilibrium mt = cN t + αqt, we can write the current value Hamiltonian H for this problem as N N H = U ct ; υdt + λt ðqt −υdt Þ + μt rat + y + τt −ct −qt −ðr + πt Þmt ;
4
This setting is motivated partly by Obstfeld (1981a,b), Sen and Turnovsky (1989a,b), and Turnovsky (1997, 2000), among others.
247
where λ is the shadow price of durables d, and μ the shadow price of assets a. The optimality conditions are HcN = U1 −ð1 + πt + rÞμ = 0;
ð5Þ
Hq = λ−μ ð1 + αðπt + r ÞÞ = 0;
ð6Þ
˙ −Ha + θμ ≡ ðθ−r Þμ = μ;
ð7Þ
˙ −Hd + θλ ≡ −υU2 + λðυ + θÞ = λ;
ð8Þ
along with the standard transversality conditions. Monetary policy is directed at keeping the inflation rate (that is, the rate of depreciation of the domestic currency) at a constant level π, by the appropriate choice of the transfers τ at any time.5 The government faces the flow budget constraint τt = ṁt + πmt, which says that it should finance its expenditures by seigniorage. Combining this budget constraint of the government with the flow budget constraint of the representative agent (4), we obtain the resource constraint of the economy (i.e., the current account): N b˙ t = rbt + y−ct −qt :
ð9Þ
3. The steady state and transitional effects of inflation Consider first the steady state effects of inflation. From Eqs. (5), (6) and (8), in the steady state the marginal rate of substitution of nondurables for durables is given by U1 U2
=
υ ½1 + π t + r : ðυ + θÞ½1 + αðπt + r Þ
ð10Þ
As long as α b 1 an increase in π will increase the right hand side of Eq. (10), requiring a substitution of durable for non-durable goods in the new steady state. Now consider the transitional dynamics of the model to the new steady state. To this end, first note the adjustment of the non-durables will have a relatively minor effect on the current account. Consider a special case of the model where all goods are non-durable (with cD = q). In that case, both cN and q jump to their new steady state levels on impact, and thus the net foreign assets b adjusts instantly to its new steady state level, with ḃ = 0 in Eq. (9). Next, consider the adjustment of the model with durables. From Eq. (2) the steady state level of new durables is q ̅=υd ̅. With d ̅ larger, q ̅ must also be larger in the new steady state. Further, as d ̅ is larger in the new steady state, dṫ must be positive along its adjustment path, which, from Eq. (2), implies that qtNq ̅. Hence, along the adjustment path the purchases of new durables qt must exceed the amount needed to replace total depreciation in the steady state. Thus, on impact, after the increase in the inflation rate qt increases by more than q ̅, and savings fall, bringing about a current account deficit; see Eq. (9). Finally, consider the case with symmetric CIA constraints in which both durables and non-durables can be purchased only with cash, so that α = 1 in Eq. (3). In that case, it is easy to see from Eq. (10), there will be no substitution between the two goods, and therefore no adjustment required of the stock of durables; there will be no dynamics. Hence, in order for the model to exhibit dynamics we need
5 This assumption is convenient for our purposes, because by making the inflation rate exogenous, it abstracts completely from the off-steady state effects, arising from endogenous inflation, as emphasized by Fischer (1979).
248
A. Mansoorian, L. Michelis / Economics Letters 107 (2010) 246–248
both the presence of durable goods and asymmetric CIA constraints on purchases of durables and non-durables. 4. Conclusions We have explored the effects of inflation in a small open economy with non-durable and durable goods, which are subject to asymmetric cash-in-advance constraints. This is another channel through which monetary policy can impinge on the small open economy which has not been given attention in the literature. Acknowledgments We would like to thank the Social Sciences and Humanities Research Council of Canada for the financial support. Also, the second author wishes to thank Ryerson University for the financial support through an RRC award. All the remaining errors are our own. References Borzekowski, R., Kiser, E.K., 2006. The choice at the checkout: quantifying demand across payment instruments. Working Paper. Board of Governors of the Federal Reserve System, Washington, DC. Bucks, B.K., Kennickell, A.B., Moore, K.B., 2006. Recent changes in U.S. family finances: evidence from the 2001 and 2004 survey of consumer finances. Federal Reserve Bulletin, pp. A1–A38. March. Dunn, K.B., Singleton, K.J., 1986. Modelling the term structure of interest rates under non-reparability utility and durability of goods. Journal of Financial Economics 17, 27–55. Eichenbaum, M.S., Hansen, L.P., 1990. Estimating models with intertemporal substitution using aggregate time series data. Journal of Business and Economic Statistics 8, 53–69.
Eichenbaum, M.S., Hansen, L.P., Singleton, K.J., 1988. A time series analysis of representative agent model of consumption and leisure choices under uncertainty. Quarterly Journal of Economics 103, 51–78. Fischer, S., 1979. Capital accumulation on the transition path in a monetary optimizing model. Econometrica 47, 1433–1439. Lucas Jr., R.E., Stokey, N., 1983. Optimal fiscal and monetary policy in an economy without capital. Journal of Monetary Economics 12, 55–93. Lucas Jr., R.E., Stokey, N., 1987. Money and interest in a cash-in-advance economy. Econometrica 55, 491–513. Mansoorian, A., 1998. On the macroeconomic policy implications of habit persistence. Journal of Money Credit and Banking 28, 119–129. Mansoorian, A., Mohsin, M., 2006. On the employment, investment and current account effects of inflation. Journal of International Economics 70, 296–313. Obstfeld, M., 1981a. Capital mobility and devaluation in an optimizing model with rational expectations. American Economic Review Papers and Proceedings, pp. 217–221. Obstfeld, M., 1981b. Macroeconomic policy, exchange rate dynamics and optimal accumulation. Journal of Political Economy 89, 1142–1161. Obstfeld, M., Rogoff, K., 1996. Foundations of International Macroeconomics. MIT Press, Cambridge, MA. Piazzesi, M., Schneider, M., Tuzel, S., 2007. Housing, inflation and asset pricing. Journal of Fianancial Economics 83, 531–569. Ryder, H.E., Heal, G.M., 1973. Optimal growth with intertemporally dependent preferences. Review of Economic Studies 40, 1–31. Sen, P., Turnovsky, S.J., 1989a. Deterioration of the terms of trade and capital accumulation: a re-examination of the Laursen–Metzler effect. Journal of International Economics 26, 227–250. Sen, P., Turnovsky, S.J., 1989b. Tariffs, capital accumulation and the current account in a small open economy. International Economic Review 30, 811–831. Shi, S., Epstein, L.G., 1993. Habits and time preference. International Economic Review 34, 61–84. Sidrauski, M., 1967. Inflation and economic growth. Journal of Political Economy 75, 796–810. Turnovsky, S.J., 1997. International Macroeconomic Dynamics. MIT Press, Cambridge, MA. Turnovsky, S.J., 2000. Methods of Macroeconomic Dynamics, second edition. MIT Press, Cambridge, MA. Uzawa, H., 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital and Growth: Papers in Honour of Sir John Hicks. Aldine Publishing Company, Chicago, Illinois.
Contents lists available at ScienceDirect
Economics Letters j o u r n a l h o m e p a g e : w w w. e l s ev i e r. c o m / l o c a t e / e c o l e t
Monetary policy in a small open economy with durable goods and differing cash-in-advance constraints Arman Mansoorian a,⁎, Leo Michelis b a b
Department of Economics, York University, North York, ON, Canada, M3J 1P3 Department of Economics, Ryerson University, Toronto, ON, Canada, M5B 2K3
a r t i c l e
i n f o
Article history: Received 13 January 2009 Received in revised form 15 January 2010 Accepted 22 January 2010 Available online 1 February 2010
a b s t r a c t We consider the effects of inflation in a small open economy when expenditures on non-durables are more heavily financed with money than expenditures on durables. The distinctions between non-durables and durables, and asymmetric cash-in-advance constraints give rise to important dynamics. © 2010 Elsevier B.V. All rights reserved.
JEL classification: E22 E52 E58 Keywords: Inflation Cash Credit Durables Capital
1. Introduction The small open economy literature has identified several channels though which monetary policy can affect the economy. For example, Obstfeld (1981a,b) considers the effects of monetary policies for a small open economy with Uzawa (1968) preferences, whereby the rate of time preference is an increasing function of instantaneous utility, and with the money-in-utility specification of Sidrauski (1967). Mansoorian (1998) considers the effects of habits, as in Ryder and Heal (1973), in the money-in-utility framework. There, the rate of time preference is fixed, but instantaneous utility depends on habits, which are modelled as a weighted average of past levels of instantaneous utilities. Shi and Epstein (1993) developed a model in which the rate of time preference is an increasing function of habits. Mansoorian and Mohsin (2006) consider a setting with a fixed rate of time preference and no habits, but with endogenous labour and a cash-in-advance (CIA) constraint. In this paper we consider another channel through which monetary policy can affect the economy; the presence of durable goods, in conjunction with the assumption that the method of payment for ⁎ Corresponding author. Department of Economics, York University, 4700 Keele Street, North York, Ontario, M3J 1P3, Canada. Tel.: +1 416 736 5083; fax: +1 416 736 5987. E-mail address: [email protected] (A. Mansoorian). 0165-1765/$ – see front matter © 2010 Elsevier B.V. All rights reserved. doi:10.1016/j.econlet.2010.01.037
durable goods differs from that for non-durables; whereas the latter are financed primarily with cash, the former are partly financed with loans or credit.1 These are realistic assumptions to make. A significant proportion of aggregate consumption, in many countries, consists of expenditures on durable goods such as housing, automobiles, household appliances and home electronics. For example, in the US the division between durable and non-durable consumption expenditures is about 23 and 77% respectively.2 Borzekowski and Kiser (2006) provide some recent evidence on the different types of payments instruments used by US households, supporting the assumption that non-durables are often paid for with cash (currency, debit cards or checking accounts), while durables are paid for largely with credit.3
1 In a related literature Lucas and Stokey (1983, 1987) have introduced the distinction between cash and credit goods. In that literature credit goods, like leisure, do not require means of exchange and thus are not subject to the inflation tax discussed in this paper. 2 To arrive at these figures, we added an estimate of housing services to the US National Income and Product Accounts (NIPA) measure of durable goods. To estimate housing services, we assumed that the ratio of housing services to non-durable consumption is 0.20, which is roughly consistent with the average estimate in Fig. 1 of Piazzesi et al. (2007); see also Obstfeld and Rogoff (1996, p. 96). 3 According to the US Federal Reserve Board's 2004 Survey of Consumer Finances (CFS) about 90 % of total household credit is for housing and automobile expenditures; See Bucks et al. (2006), Table 12.
A. Mansoorian, L. Michelis / Economics Letters 107 (2010) 246–248
The rest of the paper is organized as follows. Section 2 presents the model. Section 3 analyzes the effects of an increase in the inflation rate. Section 4 concludes. 2. The model We consider a small open economy, with perfect capital mobility. There is one non-durable good that is internationally traded, and which has a fixed price P⁎ in terms of the foreign currency. The domestic currency price of this good is P = EP⁎, where E is the nominal exchange rate: the price of foreign currency in terms of the domestic currency. With P⁎ fixed, the rate of inflation is equal to the rate of depreciation of the domestic currency: πt = Ėt/Et. 4 The preferences of the representative agent are given by ∞ −θt
∫0 e
N D U ct ; ct dt;
ð1Þ
D where U(cN t , ct ) is a standard instantaneous utility function, θ is the rate of time preference, cN t is the consumption of non-durable goods and cD t is the consumption of the services of durable goods at time t. Following the empirical literature (see, e.g., Dunn and Singleton (1986), Eichenbaum et al. (1988), and Eichenbaum and Hansen D (1990)) the services of durable goods cD t is modelled as ct = υdt, where υ is the depreciation rate for the durable good, and dt is the stock of durables available at time t. Next, note dt can be expressed as t
υ(τ − t)
the non-depreciated stock at time t; that is, dt = ∫ e implies that the evolution of dt is given by d˙ t = qt −υdt :
qτdτ, which
−∞
ð2Þ
where qt represents the purchases of new durables at time t. All expenditures on non-durables are financed with money while only a fraction α of the expenditures on durables are financed with money, and the rest with credit. Hence, if mt is the representative agent's total real money holdings, then N
mt ≥ct + αqt :
ð3Þ
We assume the foreign currency price of the internationally traded bonds is fixed, as is the real rate of return on them, r. If bt is the representative agent's holdings of these bonds, then his total asset holdings at time t will be at = mt + bt. In order to concentrate on the importance of the asymmetry in the CIA constraints, in conjunction with the existence of durable goods, we abstract completely from endogenous output; output is fixed at y. Further, the representative agent receives real monetary transfers of magnitude τt from the government. Hence, his flow budget constraint is N a˙ t = rat + y + τt −ct −qt −ðr + πt Þmt ;
ð4Þ
The representative agent maximizes lifetime utility (1), subject to conditions (2)–(4), the initial conditions d0 and a0, and the standard no Ponzi game condition, taking the time paths of the inflation rate π and the transfers τ as given. Noting that in equilibrium mt = cN t + αqt, we can write the current value Hamiltonian H for this problem as N N H = U ct ; υdt + λt ðqt −υdt Þ + μt rat + y + τt −ct −qt −ðr + πt Þmt ;
4
This setting is motivated partly by Obstfeld (1981a,b), Sen and Turnovsky (1989a,b), and Turnovsky (1997, 2000), among others.
247
where λ is the shadow price of durables d, and μ the shadow price of assets a. The optimality conditions are HcN = U1 −ð1 + πt + rÞμ = 0;
ð5Þ
Hq = λ−μ ð1 + αðπt + r ÞÞ = 0;
ð6Þ
˙ −Ha + θμ ≡ ðθ−r Þμ = μ;
ð7Þ
˙ −Hd + θλ ≡ −υU2 + λðυ + θÞ = λ;
ð8Þ
along with the standard transversality conditions. Monetary policy is directed at keeping the inflation rate (that is, the rate of depreciation of the domestic currency) at a constant level π, by the appropriate choice of the transfers τ at any time.5 The government faces the flow budget constraint τt = ṁt + πmt, which says that it should finance its expenditures by seigniorage. Combining this budget constraint of the government with the flow budget constraint of the representative agent (4), we obtain the resource constraint of the economy (i.e., the current account): N b˙ t = rbt + y−ct −qt :
ð9Þ
3. The steady state and transitional effects of inflation Consider first the steady state effects of inflation. From Eqs. (5), (6) and (8), in the steady state the marginal rate of substitution of nondurables for durables is given by U1 U2
=
υ ½1 + π t + r : ðυ + θÞ½1 + αðπt + r Þ
ð10Þ
As long as α b 1 an increase in π will increase the right hand side of Eq. (10), requiring a substitution of durable for non-durable goods in the new steady state. Now consider the transitional dynamics of the model to the new steady state. To this end, first note the adjustment of the non-durables will have a relatively minor effect on the current account. Consider a special case of the model where all goods are non-durable (with cD = q). In that case, both cN and q jump to their new steady state levels on impact, and thus the net foreign assets b adjusts instantly to its new steady state level, with ḃ = 0 in Eq. (9). Next, consider the adjustment of the model with durables. From Eq. (2) the steady state level of new durables is q ̅=υd ̅. With d ̅ larger, q ̅ must also be larger in the new steady state. Further, as d ̅ is larger in the new steady state, dṫ must be positive along its adjustment path, which, from Eq. (2), implies that qtNq ̅. Hence, along the adjustment path the purchases of new durables qt must exceed the amount needed to replace total depreciation in the steady state. Thus, on impact, after the increase in the inflation rate qt increases by more than q ̅, and savings fall, bringing about a current account deficit; see Eq. (9). Finally, consider the case with symmetric CIA constraints in which both durables and non-durables can be purchased only with cash, so that α = 1 in Eq. (3). In that case, it is easy to see from Eq. (10), there will be no substitution between the two goods, and therefore no adjustment required of the stock of durables; there will be no dynamics. Hence, in order for the model to exhibit dynamics we need
5 This assumption is convenient for our purposes, because by making the inflation rate exogenous, it abstracts completely from the off-steady state effects, arising from endogenous inflation, as emphasized by Fischer (1979).
248
A. Mansoorian, L. Michelis / Economics Letters 107 (2010) 246–248
both the presence of durable goods and asymmetric CIA constraints on purchases of durables and non-durables. 4. Conclusions We have explored the effects of inflation in a small open economy with non-durable and durable goods, which are subject to asymmetric cash-in-advance constraints. This is another channel through which monetary policy can impinge on the small open economy which has not been given attention in the literature. Acknowledgments We would like to thank the Social Sciences and Humanities Research Council of Canada for the financial support. Also, the second author wishes to thank Ryerson University for the financial support through an RRC award. All the remaining errors are our own. References Borzekowski, R., Kiser, E.K., 2006. The choice at the checkout: quantifying demand across payment instruments. Working Paper. Board of Governors of the Federal Reserve System, Washington, DC. Bucks, B.K., Kennickell, A.B., Moore, K.B., 2006. Recent changes in U.S. family finances: evidence from the 2001 and 2004 survey of consumer finances. Federal Reserve Bulletin, pp. A1–A38. March. Dunn, K.B., Singleton, K.J., 1986. Modelling the term structure of interest rates under non-reparability utility and durability of goods. Journal of Financial Economics 17, 27–55. Eichenbaum, M.S., Hansen, L.P., 1990. Estimating models with intertemporal substitution using aggregate time series data. Journal of Business and Economic Statistics 8, 53–69.
Eichenbaum, M.S., Hansen, L.P., Singleton, K.J., 1988. A time series analysis of representative agent model of consumption and leisure choices under uncertainty. Quarterly Journal of Economics 103, 51–78. Fischer, S., 1979. Capital accumulation on the transition path in a monetary optimizing model. Econometrica 47, 1433–1439. Lucas Jr., R.E., Stokey, N., 1983. Optimal fiscal and monetary policy in an economy without capital. Journal of Monetary Economics 12, 55–93. Lucas Jr., R.E., Stokey, N., 1987. Money and interest in a cash-in-advance economy. Econometrica 55, 491–513. Mansoorian, A., 1998. On the macroeconomic policy implications of habit persistence. Journal of Money Credit and Banking 28, 119–129. Mansoorian, A., Mohsin, M., 2006. On the employment, investment and current account effects of inflation. Journal of International Economics 70, 296–313. Obstfeld, M., 1981a. Capital mobility and devaluation in an optimizing model with rational expectations. American Economic Review Papers and Proceedings, pp. 217–221. Obstfeld, M., 1981b. Macroeconomic policy, exchange rate dynamics and optimal accumulation. Journal of Political Economy 89, 1142–1161. Obstfeld, M., Rogoff, K., 1996. Foundations of International Macroeconomics. MIT Press, Cambridge, MA. Piazzesi, M., Schneider, M., Tuzel, S., 2007. Housing, inflation and asset pricing. Journal of Fianancial Economics 83, 531–569. Ryder, H.E., Heal, G.M., 1973. Optimal growth with intertemporally dependent preferences. Review of Economic Studies 40, 1–31. Sen, P., Turnovsky, S.J., 1989a. Deterioration of the terms of trade and capital accumulation: a re-examination of the Laursen–Metzler effect. Journal of International Economics 26, 227–250. Sen, P., Turnovsky, S.J., 1989b. Tariffs, capital accumulation and the current account in a small open economy. International Economic Review 30, 811–831. Shi, S., Epstein, L.G., 1993. Habits and time preference. International Economic Review 34, 61–84. Sidrauski, M., 1967. Inflation and economic growth. Journal of Political Economy 75, 796–810. Turnovsky, S.J., 1997. International Macroeconomic Dynamics. MIT Press, Cambridge, MA. Turnovsky, S.J., 2000. Methods of Macroeconomic Dynamics, second edition. MIT Press, Cambridge, MA. Uzawa, H., 1968. Time preference, the consumption function, and optimal asset holdings. In: Wolfe, J.N. (Ed.), Value, Capital and Growth: Papers in Honour of Sir John Hicks. Aldine Publishing Company, Chicago, Illinois.