1 No capital mobility

Transcription

1 University of British Columbia Department of Economics, International Finance (Econ 556) Prof. Amartya Lahiri Handout #7 1 1 No capital mobility In the previous lecture we studied the frictionless environment wherein the economy had access to perfectly competitive goods and bonds market. We saw in that analysis that with an endowment economy set-up and separable preferences between money and consumption, monetary policy had no real effects. This conclusion about monetary neutrality and superneutrality also carries over to environments where consumption and money are non-separable. Hence, the analysis thus far makes clear that in this intertemporally optimizing models without any additional frictions, it is not easy to get money to matter. In this lecture (and a few to follow) we shall investigate reasons why money can have real effects. In this lecture we study one such environment. In particular, we study an economy where there is no capital mobility. Consider the same model that we analyzed last time. In particular, consider a small open economy inhabited by a representative agent who maximizes lifetime welfare given by V = t=0 e βt [u(c t ) + v(m t )] dt (1) where m = M P denotes real money balances. In the following we shall assume that y t = ȳ for all t. As before, in this one good model with free goods mobility and the normalization of the 1 c Amartya Lahiri. Not to be copied, used, or revised without explicit permission from the copyright owner. 1

2 foreign currency price of the good to unity, we must have P = E. In a deviation from our previous assumption of perfect capital mobility, we now assume that the economy does not have access to any foreign capital markets at all. This assumption can reflect two potential scenarios. First, emerging economies often face restrictions on their capital market access. More importantly, after periods of financial market stress (widespread defaults etc.) developing countries are often shut out of international capital markets completely. Second, some governments at times voluntarily impose capital account restrictions themselves. This assumption is an extreme form of such a restriction. Since private agents can accumulate real balances over time, the flow budget constraint for the representative household is given by ṁ t = ȳ c t + g t π t m t The household maximizes welfare by choosing a path for c subject to the evolution equation for m. Hence, the control variable is c while the state variable is m. Setting up the Hamiltonian as described previously and following the previously described steps gives the necessary and suffi cient conditions for optimality: u (c t ) = λ t λ t = (β + π t ) λ t v (m t ) where λ is the co-state variable associated with m. 1.1 Government We assume that the government in this economy consists of a combined monetary and fiscal authority. The government prints money M, makes lump-sum transfers to the private sector g, and holds foreign bonds (foreign reserves) R. However, as opposed to the assumption 2

3 made in the previous lecture, we now assume that foreign reserves earn no interest. Hence, the government s flow constraint is given by Ṙ t = ṁ t + π t m t g t The wing of the government that holds foreign reserves is the central bank. bank s balance sheet identity is The central where d = D P R t + d t = m t is real domestic credit to the private sector. Time differentiating the central bank balance sheet identity gives Ṙ t = ṁ t d t Substituting this into the government s flow constraint gives the transfer policy for g : d t = g t π t m t 1.2 Flexible exchange rate equilibrium We start by studying the flexible exchange rate case. Under the pure flexible rates case the central bank refuses to buy or sell foreign currency. Hence, Ṙ = 0 and ṁ = d throughout. To simplify life, let us further assume that R = 0, i.e., the central bank does not have any reserves. This is just a normalization and can be relaxed though at the cost of some additional algebra. To complete the description of the government, we need to specify the nominal domestic credit rule. We assume that Ḋ t D t = µ D Hence, the growth rate of nominal domestic credit is assumed to be constant over time, i.e., µ t = µ D for all t. Since ṁ = d, we must have (µ t π t ) m t = (µ D π t ) d t 3

4 Since R = 0 the central bank balance sheet additionally implies that m = d. Substituting this in the previous equation above gives µ t = µ D for all t Hence, nominal money grows at the rate of nominal domestic growth. Now, the private flow budget constraint says that ṁ = ȳ c+g πm while the gvernment s flow constraint is Ṙ = ṁ + πm g. Combining the two gives Ṙ = ȳ c But since Ṙ = 0 under flexible exchange rates, we must have c t = ȳ for all t Hence, consumption is constant under flexible exchange rates. More generally, consumption equals output period by period under this exchange rate regime. Intuitively, the household may want to smooth out consumption but cannot as international capital markets are not available to it and the central bank refuses to sell foreign exchange for transactions on the current account under flexible rates. It is a rather sad situation, really! that How does the monetary side of the model work? The household s Euler equation dictates λ = (β + π) λ v (m) But, since c = ȳ is constant, λ must be constant as well. Hence, λ = 0. Combining the household s first order conditions then gives v (m) u (ȳ) = β + π t Since ṁ = µm πm by definition, and µ = µ D as we showed above, this reduces to the familiar differential equation ṁ m = β + µ D v (m) u (ȳ) This, as we showed in the previous lecture, is an unstable differential equation. Hence, m must jump to its steady state level instantaneously. 4

5 1.2.1 Unanticipated, permanent increase in µ D A permanent increase in the rate of domestic credit growth µ D will reduce the steady state m. As a result, on impact, P jumps up to put the system on the new steady state point. λ remains unchanged and so does consumption. Intuitively, the rise in the rate of growth of domestic credit raises the domestic inflation rate in the new steady state which induces a fall in desired steady state real money balances. The economy finds itself with surplus real money balances which it wants to get rid off. The increase in demand for foreign currency in order to buy the good causes an depreciation of the currency, i.e., E rises. Hence, P rises as well leaving consumption unchanged. Note that money is super-neutral here Unanticipated, one time, permanent increase in the level of D This is an increase in the level of money supply. However, this leaves the steady state m unchanged. Hence, M and P rise by the same proportion leaving real balances unchanged. The shock also leaves the rate of inflation unchanged. Money is neutral in this case since there is no effect on the real side of the economy. 1.3 Predetermined exchange rates We now study the case where the monetary authority chooses a predetermined path for the exchange rate. As we noted in the previous lecture, this case implies that money supply becomes endogenous; since the central bank chooses the exchange rate it stands ready to buy and sell as much foreign currency as people demand at the pre-announced exchange rate. We shall assume that g t = π t m t (2) Hence, d = 0 which, from the central bank balance sheet, implies that Ṙ t = ṁ t 5

6 Hence, international reserves and real money balances must move together. The assumed transfer policy makes the fiscal policy consistent with the exchange rate policy. The first-order conditions for the household are as before the household s problem is unchanged. But now the central bank has exogenously fixed the path of the nominal exchange rate. Hence, the rate of devaluation of the nominal exchange rate is given exogenously: Ė t E t = ε t = π t, E 0 given. We assume that the central bank announces a constant rate of devaluation, i.e., ε t = ε for all t d = 0 implies that the rate of growth of domestic credit must equal the rate of inflation (equivalently, the rate of devaluation) at all times, i.e., µ D = ε for all t. Combining the flow constraints of the private sector and the government yields the resource constraint for the economy: ṁ t = ȳ c t The first-order condition for optimal consumption can be used to solve for c as an implicit function of λ : c = ψ(λ), ψ < 0. The dynamic system for this economy can be represented by a system of two differential equations in λ and m: state: λ t = ( ) β + ε v (m t ) λ t λ t ṁ = ȳ ψ(λ t ) The system can be approximated by a first-order linear approximation around the steady λ β + ε ṁ ψ 0 v λ λ m m 6

7 In a local neighborhood of the steady state this system has two roots of opposite signs. This follows directly from the fact that the determinant of the Jacobian matrix of this system is ψ v < 0. Figure 1 shows the linearized system through a phase diagram in λ, m space. The λ = 0 locus is downward sloping while the ṁ = 0 locus is horizontal. Figure 1: Dynamic system λ. λ = 0. λ* m = 0 SS m* m Unanticipated, permanent increase in ε This reduces the steady state m. Households try to reduce their real money balances by raising their consumption above the endowment level. Hence, the economy runs a current account and trade account deficit during the adjustment. Note that this shock changes the rate of currency depreciation but does not change the level of the nominal exchange rate at the date of the shock, i.e., E does not jump. The process stops once m falls to its new steady state level. In the new steady state, consumption is unchanged because the endowment y remain unchanged. As is obvious, the response of the economy to an increase in the rate of devaluation is similar to the adjustment of the economy to an increase in the rate of growth of money supply. 7

8 1.3.2 Unanticipated, discrete devaluation This shock implies that there is an unanticipated increase in E on the date of the shock. Since the rate of devaluation remains unchanged, the nominal interest rate doesn t change. Hence, steady state real money balances remain unchanged. Given a nominal level of D, the rise in E reduces real money balances of the household. Since their steady real money balances are unchanged, this implies that households need to build up their real balances. Hence, consumption falls as the economy begins to run a current account and trade account surplus in order to increase m back towards its steady state level. There are three key contrasts to be drawn. First, in contrast with both the perfect capital mobility case, it is important to note that under predetermined exchange rates this model is neither neutral nor super-neutral. Second, in the previous case where the central bank was choosing the rate of money growth, an increase in the supply of nominal money (an increase in D) caused an instantaneous increase in E which allowed households to rebalance their desired real money holdings immediately. Hence, there were no real effects and money was neutral. Here, with predetermined exchange rates, the same adjustment could only happen if households could instantaneously increase their stock of nominal money balances. But they do not have any foreign assets to exchange for nominal balances. Hence, the economy has to run a sequence of current account surpluses in order to build up its stock of nominal money. Third, and related to the second point above, in contrast to the perfect capital mobility case, here agents cannot rebalance their money holdings by swapping foreign bonds at the pre-announced exchange rate. Hence, there are real effects of a discrete devaluation. 2 A digression on the great David Hume As the last two exercises make clear, the most fundamental idea behind the monetary approach to the balance of payments is that, under fixed or predetermined exchange rates, the 8

9 nominal money supply is endogenous. This idea goes back to David Hume. 2 As he put it in 1752 (almost 250 years ago): Suppose twenty billion were brought into Scotland..., how much would remain in the quarter of a century? Not a shilling more than we have at present. It goes to show that while Hume probably did not know how to solve an optimal control problem, he was a pretty good economist! 3 Cash-in-advance A popular monetary model is the cash-in-advance economy. Cash-in-advance models impose the assumption that money is held because agents need money balances for transactions purposes. The simplest statement of this is the assumption that m t αc t (3) This condition says that real money balances must be at least a fraction α of desired consumption. α < 1 would correspond to some consumption being possible through credit/barter transactions. A downside to the cash-in-advance assumption is that by assumption the velocity of money is held constant. How does the cash-in-advance economy behave? Consider, as before, a small open economy which can borrow and lend freely in perfectly competitive world capital markets at a constant real interest rate r, and can trade freely at the given world price. The economy consumes and produces a single good whose world price, in terms of the foreign currency, is constant and normalized to unity (P = 1). The law of one price implies that E = P. We assume that the household in this economy receives a constant endowment of the good every period. Hence, the flow constraint facing the household is ḃ = rb + y + g c ṁ πm 2 David Hume ( ) was a Scottish philosopher, historian, economist, and essayist. Interestingly, his most famous work was not on economics but on philosophy. 9

10 where we have suppressed time subscripts to economize on notation. Defining a = b + m, we can rewrite this constraint as ȧ = ra + y + g c im Combining this flow constraint with the cash-in-advance constraint that the household faces (equation (3)), we get: ȧ = ra + y + g c (1 + αi) (4) The revised constraint shows that the cash-in-advance constraint has the effect of raising the cost of consumption. Intuitively, households need to carry a a fraction α of their desired consumption in the form of real money balances. Since the carrying cost of money is the foregone nominal interest rate, this implies that the cost of consumption is no longer just the market price of the good (normalized to unity) but also the additional cost of holding adequate money balances, αi. The households maximizes lifetime welfare given by V = t=0 e βt u(c)dt subject to the flow constraint (4). The first-order conditions are u (c) = λ (1 + αi) λ = (β r) λ We continue to assume that β = r throughout. Hence, λ is constant over time. 3.1 Government We assume that the government holds interest bearing international reserves, prints money and makes lump-sum transfers. Its flow constraint is Ṙ = rr + ṁ + πm g. We assume that g = rr + πm 10

11 Hence, from the central bank balance sheet (R = m d), we must have d = 0 and Ṙ = ṁ. We also assume that the central bank announces a path for the nominal exchange rate. In particular, it picks a constant rate of devaluation of the domestic currency: 3.2 Equilibrium Ė t E t = ε. Combining the flow constraints of the private sector and the government gives f = rf + y c. (5) This is the same as before. Since all government revenues from money creation and foreign reserves are transferred back to the household, neither monetary conditions nor the composition of foreign bond holdings between the private sector and the central bank figure in the resource constraint/current account equation. A constant ε implies that the inflation rate is constant which, in turn, implies that the nominal interest rate is constant as well. A constant nominal interest rate along with a constant λ means that consumption is constant in this economy. From the resource constraint, one can solve for the constant level of consumption: c = rf 0 + y. 3.3 Permanent increase in ε A permanent increase in ε raises the nominal interest rate permanently. However, the increase is permanent and immediate. Hence, consumption must be constant over time. From equation (5) it is clear that aggregate resources for this economy are left unchanged. Hence, the constant level of consumption is unchanged. The increase in ε leaves the real side of the economy unchanged. The only effect is on the inflation rate which goes up. 11

12 3.4 Permanent increase in D A permanent increase in D raises nominal money supply in this economy. Since the nominal interest rate is unchanged, demand for real balances is unaffected. Households exchange their surplus nominal balances for foreign bonds at the pre-announced exchange rate. The only effect of this change is on the composition of foreign bond holding: b rises while R falls. It is easy to check that if the central bank chooses a rate of domestic credit growth instead, and allows the nominal exchange rate to float, the real outcomes of this economy would be similar to what we found here. In particular, money would be both neutral and super-neutral. 3.5 Temporary fall in ε A temporary fall in ε (expected to revert at date T ) implies that the nominal interest rate is low today but will be high in the future. You should verify that in this case, the economy would run a trade and current account deficit between 0 and T. In the long run, steady state consumption would be below the original consumption level as the economy would have to run a trade surplus in order to pay-off the interest burden of the additional debt that households acquired to finance their extra consumption during the period of the shock. 3.6 Endogenous labor-leisure Suppose instead of an endowment economy, this is a production economy with output being produced by labor: y t = f(n t ) where n (0, 1) denotes labor supply. Also, assume that now households derive utility from both consumption and leisure so that their instantaneous utility is given by u(c) + v(l) where l = 1 n denotes leisure. 12

13 It is straightforward to check that in this case the model is no longer super neutral. In particular, increases in either the rate of growth of money or the rate of devaluation (depending on which of these two the central bank is choosing) will have real effects through a reduction in labor supply and consumption. However, the model will continue to be neutral, i.e., changes in the level of money supply will have no real effects. 13