Savings, Investment and the Balance of Payments. Prof. George Alogoskoufis Fletcher School, University

Transcription

1 Savings, Investment and the Balance of Payments Prof. George Alogoskoufis Fletcher School, University

2 The Inter-temporal Approach The inter-temporal approach has as its stareng point the technological and market possibiliees of an economy to choose the opemal path of consumpeon over Eme. This approach is currently the dominant approach to internaeonal macroeconomics because of its theoreecal consistency as well as its compaebility with the experience of open economies. 2

3 A Two Period Economy without Capital We assume an economy which lasts for two periods, the present, period 1, and the future period 2. The inter-temporal approach can be generalized to an infinite number of periods, but the minimum number of periods is two. We will inieally assume that income is exogenous (manna from heaven) and there is no capital. Income for period 1 is y 1, and income for period 2 is y 2. 3

4 The OpEmal Choice of the ConsumpEon Path The representaeve household chooses the intertemporal path of its consumpeon, in order to maximize a uelity funceon which depends on consumpeon in the two periods. U=u(c 1 )+(1/(1+ρ))u(c 2 ) (1) u is the per period uelity funceon and ρ the pure rate of Eme preference of the representaeve household. 4

5 The Inter-temporal Budget Constraint of the RepresentaEve Household UElity is maximized subject to the inter-temporal budget constraint that the present value of household consumpeon is equal to the present value of its income. c 1 +(1/(1+r))c 2 =y 1 +(1/(1+r))y 2 (2) r is the real interest rate at which the household can borrow and lend between the two periods. 5

6 The RelaEonship Between ConsumpEon in the Two Periods The inter-temporal budget constraint can be re-wriyen as, c 2 = (1+r)( y 1 -c 1 ) +y 2 (3) In the second and last period of its life the representaeve household consumes all its income, plus its savings from the first period. 6

7 First Order CondiEons for the MaximizaEon of Inter-temporal UElity (1/(1+ρ))(u (c 2 )/u (c 1 ))=1/(1+r) (4) The marginal rate of subsetueon between present and future consumpeon is equated to the relaeve price of future and current consumpeon. The consumer cannot thus improve its lifeeme uelity by further subsetueng present for future consumpeon (Euler equaeon). 7

8 ImplicaEons of the First Order CondiEon for ConsumpEon in the Two Periods u (c 2 )/u (c 1 )=(1+ρ)/(1+r) (5) If the real interest rate is higher than the pure rate of Eme preference, then consumpeon in the second period is greater than consumpeon in the first period (the marginal uelity is smaller), as the rate of return on savings exceeds the pure rate of Eme preference. The opposite happens if the real interest rate is lower than the pure rate of Eme preference. 8

9 ConsumpEon Smoothing c 2 =c 1 if and only if r=ρ (6a) c 2 >c 1 if and only if r>ρ (6b) c 2 <c 1 if and only if r<ρ (6c) 9

10 The Benefits from Financial Openness 10

11 Financial Autarky and the Autarkic Real Interest Rate If this economy cannot borrow and lend internaeonally, i.e. in a regime of financial autarky, consumpeon in each period must be equal to the income of the period. There is no possibility of deviaeon of consumpeon from domesec income and there is no possibility of inter-temporal trade with the rest of the world. The Euler equaeon for consumpeon must be saesfied at a real interest rate r A which makes consumpeon in each period equal to income in each period. This is determined by the condieon, u (y 2 )/u (y 1 )=(1+ρ)/(1+r A ) (5 ) This equilibrium is depicted in point A. The autarkic real interest rate is the slope of the indifference curve that passes through point A. 11

12 The Benefits of Inter-temporal Trade If this economy cannot borrow and lend internaeonally, i.e. is in a regime of financial autarky, consumpeon in each period must be equal to the income of the period. There is no possibility of deviaeon of consumpeon from domesec income and there is no possibility of inter-temporal trade with the rest of the world. The country's parecipaeon in the internaeonal economy, i.e. financial openness, can increase its prosperity, as it allows consumers to choose their consumpeon based on the constraint that the present value of income is equal to the present value of consumpeon, rather than the much Eghter constraint which obliges them to consume all of their income in every period. As long as the internaeonal real interest rate differs from the autarkic real interest rate there are benefits from inter-temporal trade. The case depicted in the Diagram is the case where the internaeonal real interest rate is lower than the autarkic real interest rate. 12

13 The Current Account under Financial Openness CA 1 =F=Y 1 -C 1 CA 2 =Y 2 +rf-c 2 =Y 2 +r(y 1 -C 1 )-C 2 =-(Y 1 -C 1 )=-CA 1 The inter-temporal budget constraint implies that the current account of the second period will be equal to the opposite of the current account of the first period. 13

14 The Inter-Temporal EvoluEon of the Current Account If the first period aggregate consumpeon is higher than the first period income, and there is a current account deficit. In the second period, the opposite should happen. There must be a current account surplus in order to pay the internaeonal bond holders who lent the country in the first period. If the first period consumpeon was lower than first period income, and there is a current account surplus invested in internaeonal bonds, in the second period consumpeon will be greater than income, there will be a current account deficit, as the country will consume more than its current income, selling its internaeonal bonds, and consuming the proceeds. 14

15 The Advantages of the Intertemporal Approach A central advantage of the inter-temporal approach to external balance is that it forces us to monitor the intertemporal effects of external imbalances, through the intertemporal budget constraint. Current deficits must be converted into future surpluses and vice versa if the country is to respect its inter-temporal budget constraint. In an economy with a large number of periods, the current external debt should be equal to the present value of future surpluses in the trade balance. 15

16 GeneralizaEons of the Basic Model Even in an economy with capital and domesec investment, opening up to internaeonal capital markets improves naeonal welfare. The main prediceon that present current account deficits must be followed by future current account suprluses, also remains. The same happens in an economy that lasts for many periods. 16

17 ProducEon and External Balance in a Two Period Economy with Capital We again assume a two period economy. Income is produced according to a neoclassical produceon funceon, with constant returns to scale. This takes the form, Y = F(K, L) In the beginning of period 1, each household has inieal capital k 1, and each household supplies one unit of labor in every period. We assume L idenecal households. Thus, if follows that K 1 =Lk 1, K 2 =Lk 2, and, Y 1 = F(K 1, L) Y 2 = F(K 2, L) Defining I 1 as investment in period 1 and I 2 as investment in period 2, it follows that, K 2 = (1 δ )K 1 + I 1 I 2 = (1 δ )K 2 = (1 δ )((1 δ )K 1 I ) 1 17

18 The Balance of Payments, ConsumpEon and Investment in the Two Period Economy with Capital The current account in periods 1 and 2 is defined by, CA 1 = F 2 = Y 1 C 1 I 1 CA 2 = F 2 = Y 2 + rf 2 C 2 I 2 The representaeve household selects consumpeon and investment in the first period in order to maximize the uelity funceon, under the constraint, U = u(c 1 ) ρ u(c 2 ) C 1 + I 1 + C 2 (1 δ )((1 δ )K 1 + I ) 1 1+ r = F(K 1, L) + F((1 δ )K 1 + I 1, L) 1+ r 18

19 The DeterminaEon of ConsumpEon and Investment From the first order condieons for consumpeon and investment, it follows that, F K (K 2 ) δ = F K ((1 δ )K 1 + I 1 ) δ = r 1 u (C 2 ) 1+ ρ u (C 1 ) = 1 1+ r Investment in the first period is selected so as the net marginal product of capital in the second period is equal to the real interest rate. Households must be indifferent between inveseng in domesec capital or internaeonal bonds. Aggregate consumpeon and savings is selected so as to saesfy the usual Euler equaeon for consumpeon. 19

20 Financial Openness and the Independence of NaEonal Savings and DomesEc Investment A crucial characterisec that results from the first order condieons is that in a small open economy, which takes the world real interest rate as given, investment and the capital stock are independent of consumer preferences. A country that can borrow abroad at an interest rate r would never want to ignore investment opportuniees that yield more than r. To put it differently, aggregate investment is independent of naeonal savings, because the country can borrow freely from the rest of the world. This feature is due to specific assumpeon which we have made. First, that the economy is small and does not affect the internaeonal interest rate. A sizable (large) economy would affect the real internaeonal interest rate because it would affect the internaeonal balance of savings and investment. Second, we assume that the economy produces an internaeonally tradable commodity. If the economy produces and internaeonally non-tradable goods, the result does not follow. Thirdly, we have assumed that internaeonal capital markets operate without imperfeceons that can limit the countries' access to them. When there are factors such as the risk of bankruptcy, limieng access to internaeonal capital markets, naeonal savings affect domesec investment. 20

21 Financial Autarky, and the Equality of Savings with Investment In the two periods economy with capital, there may be savings and investment, even if the economy is not parecipaeng in the internaeonal capital markets. However, unlike the open economy in a closed economy (financial autarky) domesec investment must equal naeonal savings. This addieonal restriceon, which does not apply to an open economy, reduces welfare, and is the main reason why the parecipaeon of a country in internaeonal capital markets turns out to be in its favor. The difference from the economy without capital is that now there is an inter-temporal produceon possibility froneer, or inter-temporal transformaeon curve, which shows the technological possibiliees of a financially autarkic economy to turn consumpeon in period 1 into consumpeon in period 2. This feature does not exist in the autarkic economy without capital, because domesec savings cannot be converted to future produceon and consumpeon, as there is no investment in this case. 21

22 The Inter-Temporal TransformaEon Curve in a Two Period Economy with Capital The Inter-Temporal TransformaEon Curve is defined by, C 2 = F [(1 δ )K 1 + F(K 1 ) C 1 ]+ (1 δ )((1 δ )K 1 + F(K 1 ) C ) 1 It describes the maximum second period consumpeon, for given first period consumpeon, and a given inieal capital stock. Its slope is given by, dc 2 dc 1 = [1 δ + F K (K 2 )] = [1 δ + F K ((1 δ )K 1 + F(K 1 ) C 1 )] For C 1 =0 and for C 2 =0 it holds that, C 2 = F [(1 δ )K 1 + F(K 1 )]+ (1 δ )((1 δ )K 1 + F(K 1 )) C 1 = F(K 1 ) + (1 δ )K 1 22

23 The Benefits of Financial Openness in a Two Period Economy with Capital 23

24 Aggregate ProducEon and ConsumpEon under Financial Autarky Point Α is the equilibrium in a closed (financially autarkic) economy. The inter-temporal transformaeon curve is tangent to the highest possible indifference curve. Their common slope at point A defines the domesec (autarkic) real interest rate r A. This equilibrium is efficient, and all the equilibrium condieons are saesfied. First, there is maximizaeon of produceon, and investment decisions are opemal, in the sense that the marginal product of capital in period 2 is equal to the real interest rate r A. Secondly, at point A the uelity of the representaeve household is maximized in the sense that the Euler condieon is saesfied for a real interest rate r A. Thirdly, there is equilibrium in the sense that the sum of consumpeon and investment is equal to total output and income. 24

25 Aggregate ProducEon and ConsumpEon under Financial Openness If the self-sufficient economy is integrated into the global economy, and can borrow and lend at the internaeonal real interest rate, the rate it will face is the internaeonal interest rate r. In the Diagram it is assumed that the internaeonal real interest rate is lower than the autarkic rate. The internaeonal real interest determines the slope of the straight line which is tangent to the inter temporal transformaeon curve at point B. The country can borrow and lend freely at this internaeonal real interest rate, which is why the slope is a straight line. The equilibrium of the open economy differs from the equilibrium under autarky. At the lower internaeonal real interest rate, aggregate output is determined at point B, where the slope of the inter-temporal transformaeon curve is - (1 + r), and consumpeon at point C on an indifference curve higher than in the equilibrium under financial autarky. Both investment and consumpeon of the first period is higher than in the case of autarky in this case. 25

26 The Benefits of Financial Openness ParEcipaEon in global financial markets enables the economy of our example to achieve a higher level of welfare. This is because of the difference between the autarkic real interest rate and the internaeonal real interest rate. When the internaeonal real interest rate is lower than the autarkic real interest rate, the economy finances more consumpeon and investment in the first period through a deficit on the current account. In the second period it repays its debts with a small decrease in consumpeon in period 2, relaeve to the increase of consumpeon in period 1, because the addieonal investment made in the first period has increased produceon in period 2. An increase in welfare would arise even if the internaeonal real interest rate was higher than the autarkic real interest rate. Then we would have a small decrease in consumpeon of the first period and a higher increase in consumpeon in the second period. The country would have a surplus in the current account of the first period, it would accumulate high yielding internaeonal bonds, and through their higher return would fund the increase in consumpeon in the second period. 26

27 Generalising the Inter-temporal Approach to the Balance of Payments to Many Periods The inter-temporal approach can be generalised from 2 periods to many periods. The limieng case is the case of a representaeve household economy with an infinite horizon (infinite number of periods). This is esseneally an applicaeon of Friedman s (1957) permanent income hypothesis. OpEmal consumpeon behavior implies surpluses in the current account when there are temporary posieve deviaeons of output from its permanent level, and deficits when there are temporary posieve deviaeons of investment or public expenditure from their permanent levels. 27

28 Key ProperEes of the Generalised Intertemporal Approach to the Balance of Payments If output is temporarily higher than than its permanent level, this does not lead to an increase in consumpeon in this model. Consequently, naeonal savings rise temporarily above investment, and the current account shows a temporary surplus, which leads to accumulaeon of assets (bonds) from the rest of the world. If public expenditure is temporarily higher than its permanent level, this does not affect private consumpeon. Consequently, naeonal savings are reduced below aggregate domesec investment, and the current account moves into deficit. The deficit leads to a de-cumulaeon of net foreign assets or an increase in external debt. Finally, if aggregate domesec investment is temporarily higher than its permanent level, this also leads to a deficit in the current account, because a temporary change in the investment does not affect permanent disposable income, private consumpeon and savings. Aggregate domesec investment temporarily rises above naeonal savings and the country moves into a current account deficit and de-cumulaeon of net foreign assets or an increase in external debt. 28

29 Conclusions from the Inter-Temporal Approach to External Balance We have demonstrated that parecipaeon in global capital markets enables an economy to achieve higher levels of welfare through increased opportuniees for inter-temporal trade. When the real interest rate under autarky differs from the internaeonal real interest rate, an economy can smooth the inter-temporal path of consumpeon more effecevely, achieving a higher level of welfare. In a mule-period representaeve household model, we have also argued that when real output and income are temporarily high, the economy experiences a current account surplus, as naeonal savings exceed domesec investment. On the other hand, when aggregate domesec investment, or real government expenditure, are temporarily high, the current account moves into deficit, as domesec investment exceed naeonal savings. These properees of the inter-temporal approach to the current account carry over to more general models, that allow for long run economic growth, the role of money and financial markets, wage and price rigidiees and other distoreons. 29