Twin Deficits and Inflation Dynamics in a Mundell-Fleming-Tobin Framework

Transcription

1 Twin Deficits and Inflation Dynamics in a Mundell-Fleming-Tobin Framework Peter Flaschel, Bielefeld University, Bielefeld, Germany Gang Gong, Tsinghua University, Beijing, China Christian R. Proaño, IMK Düsseldorf, Düsseldorf, Germany Willi Semmler, New School University, New York, USA August 5, 2006 Abstract In this aer we consider a small oen economy of the Mundell-Fleming-Tobin tye. We study its accumulation laws of government and foreign debt (or surluses) and coule these dynamics with a standard Phillis curve aroach for such an economy. The resulting dynamical system and the equilibrium relationshis on which it is based are rather comlex and allow for a variety of monetary and exchange rate regimes and stability results. We study in this aer in articular the case of an interest and exchange rate eg and a regime with erfectly flexible exchange rates and given money suly. In both case we get stable adjustment rocesses of the considered twin deficits or surluses only under very restrictive assumtions on the behavioral equations of the model and various tye of instability results otherwise, to be investigated in more detail in future research. Keywords: Mundell-Fleming-Tobin model, twin deficits or surluses, rice level dynamics, (in-)stability, case studies. JEL classifications: E31, E32, E37, E52. 1

2 Contents 1 Introduction 3 2 The general framework Budget equations and saving/financing decisions Real Disosable Income and Wealth Exressions Temorary equilibrium: Outut, interest and exchange rate determination Dynamics and the steady state of the economy Local stability analysis Real twin deficit accumulation and inflation dynamics Caital account and inflation dynamics under interest and exchange rate egs Assumtions The model Steady state determination Stability analysis Twin deficit or surlus accumulation Overshooting exchange rates and inflation dynamics for erfectly flexible exchange rate regimes Equilibrium conditions Dynamics and steady state determination Dornbusch (1976) exchange rate dynamics Caital account and budget deficit dynamics Conclusions 27 6 Aendix: Notation 29 2

3 1 Introduction Over the last decade, the unrecedented increase in the internal and external imbalances of two of the largest economies in the world, the U.S. and China, has raised serious concerns about the dangers of such macroeconomic imbalances for the stability of the world economy. Nevertheless, a correction of these imbalances by means of a significant readjustment concerning the U.S. dollar is not very robable in the near future, due to the reluctance to deal with this issue not only of both governments but also because many other countries do not make stes into this direction. In this light, national wage rice adjustments as well as foreign asset in- and outflows have become even more imortant as macroeconomic adjustment mechanisms to these imbalances. In view of such develoments, we consider in this aer in a Mundell-Fleming-Tobin framework the dynamics of government deficits or surluses as well the direction of foreign assets accumulation, here for a small oen economy, when financial assets are assumed to be imerfect substitutes (where therefore the UIP condition does not hold) and where inflation dynamic is driven by an oen-economy Phillis curve. We moreover assume, as in Rødseth (2000, that domestic bonds are non-tradables, i.e., the accumulation of foreign assets by the domestic economy can only occur through surluses in the current account and not via balanced exchanges of domestic against foreign assets on the international caital markets. International caital movements of this sort will be added in Asada, Flaschel, Groh and Proaño (2006) and will then be investigated with resect to the differences this imlies comared to the case of non-tradable domestic bonds (where asset reallocations are confined to the stocks held domestically). Concerning the goods markets in the domestic economy, we introduce a Keynesian demand constraint in lace of the assumtion of Say s law in Flaschel (2006) where the world market delivered or consumed everything not resent or not needed in the domestic economy. This will be done by adding an exort function (and now also an investment function) to the descrition of aggregate goods demand in the domestic economy. Finally, we will now assume regressive exchange rate exectations formation in lace of rational exectations which, on the one hand, hels to avoid the questionable jum variable technique of the rational exectations school (in order to get stability by assumtion in an otherwise unstable saddleoint environment) and which, on the other hand, allows for maximum stability of the considered dynamics (since only fundamentalist and thus in rincile only converging exectations revisions are allowed for). This simlifying assumtion will be helful for the central objective of the aer which is to focus on the fundamental destabilizing forces contained in the two accumulation equations for internal and external deficits or surluses, caused by the government budget equation and the evolution of the current account of the considered economy. We thus allow, comared to Flaschel (2006), for underutilized labor and caital due to insufficient effective demand on the goods market, 1 as they can result from Keynesian consumtion and investment demand, augmented by a net exort schedule in this oen economy, and the goods market equilibrium condition based on these aggregate demand functions. We consider on this basis a Keynesian aroach to the business cycle in the real art of the model (based on an IS curve that equates savings to investment). Due 1 and of course also overutilized labor and caital deending on the state of aggregate demand. 3

4 to our use of a standard oen economy money wage Phillis curve, this real cycle is accomanied by labor market driven inflation or deflation dynamics which in combination with the caital account and government budget dynamics of the tye considered in Flaschel (2006) rovides a dynamic model that goes significantly beyond standard Mundell-Fleming tye aroaches. Finally, since we are now considering exorts and imorts simultaneously we are of course now using a two commodity (but single small country) aroach in contrast to the aer of Flaschel (2006), where rimarily only one commodity cases were considered. Desite the intrinsic government budget and caital account dynamics of the model, we have also a rich set of feedback channels resent in it: Hicksian disosable income effects, Pigou rice level effects, Keynes rice level effects, the Mundell-Tobin effect of inflationary exectations in both the consumtion and the investment function, Dornbusch exchange rate effects, ortfolio effects, and the stated stock-flow interactions. The interaction of these effects allows for a variety of (in-)stability results, too numerous in order to allow their investigation in a single aer of this model tye. We therefore concentrate in this aer on basic studies of a regime with egged interest as well as exchange rate and contrast this situation with a regime where the exchange rate is erfectly flexible and the money suly a given magnitude, under the control of the Central Bank of the domestic economy. In the next section we derive the model of this aer and the stock-flow interaction that characterize its intrinsically generated dynamics (which includes also a Phillis curve aroach to inflation dynamics), calculate the steady state osition of the dynamics and erform some reliminary stability considerations. Section 3 investigates the case of an interest rate eg couled with an exchange rate eg and derives stability as well as instability results for such a monetary regime. In section 4 we do the same for the regime of erfectly flexible (overshooting) exchange rates and a given money suly. Section 5 concludes. 2 The general framework As oint of dearture of our theoretical analysis we emloy a standard small oen economy Mundell-Fleming-Tobin model, as discussed in detail in Rødseth (2000, Ch.6). On this basis our urose is to analyze rigorously the stock-flow dynamics that are generated by the caital account in the balance of ayments (with resect to the foreign bond accumulation by rivate households) and by the government budget constraint (with resect to their domestic bond holdings), when these dynamics are linked (and interact) with macroeconomic activity levels through rice level adjustments they imly. 2.1 Budget equations and saving/financing decisions We start with the budget equations of the three relevant sectors, households, the government and the central bank. With resect to firms, we assume that all of their income is transferred to the household sector and that households then rovide the credit needed 4

5 to allow them to finance their investment exenditures (which is by and large the same as the assumtion of a direct investment decision by the household sector). Concerning the Central Bank (CB) we note that it may change its government bond holdings by means of an oen market olicy db c = dm, and similarly its foreign bond holdings through df c = dm, without influencing the flow budget equations to be discussed below, since all interest income from these bond holdings is transferred back to the government sector which therefore only has to ay interest on the bonds B held by the rivate sector. The domestic bond holdings of the CB can therefore be neglected in the following and an additional indexation of the magnitude that is held by the household sector can thus be avoided. The budget restrictions for the three sectors of the domestic economy are given by: (Y T ) + rb + er F C + I + Ṁ + Ḃ + e F (1) T + er F c + Ḃ + Ṁ G + rb (2) Ṁ B c (3) We denote here by B, F the domestic and foreign bonds held by the household sector and by F c the foreign assets held by the central bank (its currency reserves, that can only be changed by oen market oerations on the domestic market for foreign assets, we assume, as in Flaschel (2006), that domestic bonds are non-tradables). We use r for the nominal rate of interest and e for the nominal exchange rate and index by foreign set variables, which are obviously not under the control of the domestic economy. All other symbols are fairly standard and thus need no exlanation here. We stress again that domestic and foreign interest incomes of the CB are transferred to the government sector so that the central bank can only change its asset osition by rinting new money. In the normal course of events it will channel this money into the economy by buying of domestic government bonds as shown in the third budget equation, but it can also rearrange its ortfolio of domestic and foreign bonds (not considered exlicitly here) by oen market oerations on the domestic financial markets (as already considered above). These budget equations imly for the evolution of domestic and foreign bonds held by the rivate sector of the domestic economy: Ḃ = rb + (G T ) er F c Ṁ (4) ef = ef = (Y C G I) + er F (5) These equations show the nominal evolution of government debt imlied by its budget constraint and of the countries foreign debt (or foreign surlus) osition as imlied by the balance of ayments (which due to the situation assumed to hold for the budget equations of the three sectors of our economy is here always balanced, indeendently of the exchange rate and monetary regime that is to be investigated). 2 Considering the given situation of a balanced balance of ayments (without the intervention of the CB) from the viewoint of savings we can write: S = (Y T ) + rb + er F C = I + Ṁ + Ḃ + e F 2 This is due to assumtion that the new issue of money and domestic government bonds is always voluntarily absorbed by rivate households. 5

6 S g = T + er F c rb G = Ḃ Ṁ which gives for the total savings S of the economy (NX net exorts): S = Y C G + er (F + F c ) = NX + er F = I + e F = I + e F, F = F + F c This is again the formulation of the fact that the balance of ayments must be balanced in the considered situation without any further adjustment rocesses, based on the assumtion that the issue of new money Ṁ and new government bonds Ḃ is in fact always acceted by the household sector (as it is imlicitly made in the above formulation of the three budget equations of our economy). 2.2 Real Disosable Income and Wealth Exressions Concerning the real disosable incomes of the rivate and ublic sectors in the domestic economy, in analogy to the conventional Hicksian definition of rivate disosable income which is defined as the level of income which when consumed just reserves the current level of wealth of the considered sector we first define and rearrange this concet for the aggregate government sector (including the foreign interest income of the central bank) and rovide thereafter these concets as a recaitulation for the sector of rivate households (cf. Flaschel (2006) in this regard). Since the rate of inflation ˆ = ṗ/ 3 is a variable in the following comletion of the model we will use this exression here already in the definition of the real rates of interest to be emloyed in the calculation of real disosable incomes of the aggregate government sector Yg a and of rivate households Y. By definition, the aggregate real income of the government sector Yg a is comosed of the tax and interest rate ayments and receits of the government lus the inflation and caital gains on government debt and central bank reserves, Yg a := T rb + er F c + ˆ M + B + (ê ˆ) ef c. After some maniulations, we can exress the aggregate real income of the government sector as Y a g = T + r M + ξ M + B where real aggregate government wealth is defined as + ρ W a g, (6) W a g := (M + B) + ef c (M + B) = + ef c = W g + W c, (7) where ξ = r + ê r, ρ = r + ê ˆ, and ρ e = r + ɛ(e) ˆ reresent the actual risk remium on foreign bonds, the actual real rate on return on foreign bonds and finally the exected one (with ɛ(e) a regressive exectations mechanism for examle). Note that the third term in eq. (6) can be ignored if the uncovered interest rate arity condition is assumed to hold. This is however only ossible if international trade in domestic and foreign bonds is allowed for as in Asada, Flaschel, Proaño and Semmler (2006) where 3 We use in this text ˆx to denote the growth rate of a variable x. 6

7 this condition is considered as a limit case to imerfect substitutability of internationally traded bonds. Concerning the Hicksian real disosable income of the rivate sector, it is defined as or, after some maniulations, Y = Y T + (r + ê ˆ) ef + (r ˆ)B ˆM, Y = Y T + ρ (W W a g ) ξ M + B r M (8) where the actual wealth of the rivate sector is defined as the difference between the wealth of the whole economy W and the aggregate wealth of the government sector Wg a, i.e. W = M + B + ef = W Wg a. (9) From the calculations of disosable income of households and the government, we finally in sum get: Y = Y Yg a + ρ W or Y + Yg a = Y + ρ W as a relationshi between the country s total disosable income, its domestic roduct and the real interest on domestically held foreign bonds. 2.3 Temorary equilibrium: Outut, interest and exchange rate determination Having described the budget restrictions and disosable income equations of the different sectors in the domestic economy, we follow again Rødseth (2000) in his descrition of the temorary equilibrium relationshis on the goods and the asset markets, which are given by: Y IS = C(Y, W W a g, ρ, ρ e ) + I(Y, ρ, ρ e ) + G + NX(, η, Y ) (10) M/ LM = m d (Y, r), m d Y > 0, m d r < 0 (11) W F F = ef/ = e(f d + F d c )/ = f d (ξ e, W W a g ) + ef d c /, (12) f d ξ e > 0, f d W (0, 1) B/ = W f d (ξ e, W ) m d (Y, r), ξ e = r + ɛ(e) r (13) with ρ = r ˆ and ρ e = r +ɛ(e) ˆ reresenting the real domestic interest rate and the exected real return on foreign bonds resectively. While eq. (10) reresents an IS-curve of an advanced traditional tye, 4 the money market equilibrium, the standard textbook LM relationshi, is described by eq. (11), where money demand is as usual assumed to 4 The comonent in the net exort function stands for the variables that determine the domestic absortion in terms of consumtion and investment demand. 7

8 deend ositively on the level of outut and negatively on the domestic interest rate. Eq. (12), the FF-curve, which reresents the equilibrium on the market for foreign bonds (foreign exchange), is determined rimarily by the reaction of rivate household with resect to the risk remium ξ and the marginal wealth effect fw d in foreign (and domestic) bond demand, as in Rødseth (2000), with F = F d + Fc d. Concerning the market for domestic bonds, it is always cleared, by Walras s Law of Stocks, when the money market and the market for foreign bonds are in equilibrium. These equations are to be solved (by means of the imlicit function theorem) for the variables considered as statically endogenous (deending on the monetary and exchange rate regimes that are assumed) and to be inserted into the laws of motion of, B and F in order to obtain an autonomous system of ordinary differential equations, describing domestic rice level dynamic, the dynamic of the government budget constraint, and of the foreign osition of the domestic economy. Of course, the definitions of Y, ρ, ρ e, η have also to be inserted to achieve this end. Note that the variables M, B, F, r, e may become olicy arameters deending on the monetary and exchange regime that is under consideration. 5 Concerning the interest rate, by alying the imlicit function theorem to eq. (11) and assuming that money demand is based on the full emloyment outut level Ȳ, we get for its level in its reduced form reresentation the formula: r = r(, M, Ȳ ) with r 1 > 0, r 2 < 0, r 3 > 0. The theory of the nominal rate of interest is thus the standard or even textbook one of Keynesian macroeconomics and closely related to the working of the so-called Keyneseffect whereby money wage decreases stimulate the economy when they imly rice level changes in the same direction and on this basis lower interest rate which then work on consumtion and investment via the real rate of interest. Concerning the nominal exchange rate, inserting the above equation into eq. (12) which describes the equilibrium in the market for foreign bonds, gives us an equation in the endogenous variables e and and thus rovides us with a theory of the nominal exchange rate in its deendence on dynamically endogenous stock variables B, F and the rice level. F = f d (r + ɛ(e) r(, M, Ȳ ), M + B + ef )/e (14) We recall that f1 d, f2 d > 0 is assumed to hold and that we have ɛ (e) < 0 due to the assumtion of a regressive formation of exectations of exchange rate de- or areciation. In the case of a erfectly flexible exchange rate e where M, F c are given magnitudes that are under the control of the CB, and F = F +F c is also assumed to be a given magnitude, we obtain by means of the imlicit function theorem the following exressions for the 5 In the case of a flexible exchange rate regime and a given money suly we will for examle get jums in the variables e, η, W, Wg a when there is a shock in money suly occurring. 8

9 artial derivatives with resect to the dynamically endogenous variables: e e(1 f2 d ) = < 0 F F (1 f2 d ) f1 d ɛ e B = f d 2 F (1 f d 2 ) f d 1 ɛ > 0 e = f d f1 d r 1 f2 d W = ef (1 f2 d )/ f1 d r 1 f2 d F (1 f2 d ) f1 d ɛ M+B F (1 f d 2 ) f d 1 ɛ < 0 with 0 < f2 d < 1 (the ortfolio choice condition). We note that the last artial derivative is negative if the degree of caital mobility with resect to the risk remium is chosen sufficiently high (which is what we do in the following). The signs of the artial derivatives shown above will also aly to the real exchange rate in the lace of the nominal one, due to its definition η = e()/. Note finally that the first two artial derivatives will aroach zero if caital mobility aroaches infinity and that in this case the limit of the artial derivative with resect to is simly given by r 1 /ɛ. The result e < 0 reflects the message of the Dornbusch (1976) model, according to which an increase in the domestic interest rate (caused by shrinking real balances) leads to higher dereciation gains exectations which in a regressive exectations environment demands for a decrease, an areciation of the nominal exchange rate. Since the dynamic behavior of rices enters in the IS-equilibrium condition through the real interest rate, we already define here the law of motion for the rice level, which is determined, under the assumtion of constant marku-ricing, by a standard, exectations augmented, oen-economy Phillis curve 6 ˆ = β w (Y Ȳ ) + γ ˆ + (1 γ)(π + ɛ(e)) = β w (Y Ȳ )/(1 γ) + ɛ(e), γ (0, 1) (15) where the outut ga Y Ȳ measures the demand ressure on the labor market. Note that this form of a Phillis curve derives from an exectations augmented one where the cost ressure item (concerning the consumer rice index) is initially given by a weighted average of domestic and imort rice inflation of the form: γ ˆ + (1 γ)(π + ɛ(e)) and where myoic erfect foresight is assumed with regard to the evolution of the domestic inflation rate. By inserting the oen-economy Phillis curve equation in the IS equilibrium equation described by eq. (10), we can calculate the following signs of the artial derivatives, which for the case where the seed of adjustment of money wages β w is chosen sufficiently low, are: Y F > 0, Y B > 0, Y < 0 This holds again only in the case where in addition caital mobility is assumed as sufficiently high. We leave the lengthy calculations of the involved artial derivatives here to the reader and only state that increasing wealth of rivate households with resect to domestic and foreign bond holdings stimulate economic activity, while and increasing rice level will reduce economic activity through various channels in the model, in 6 See Rødseth (2000, Ch.6) for its motivation. 9

10 articular through real wealth effects in consumtion demand, but also through interest rate increases and real exchange rate decreases. In the case where caital mobility is nearly erfect (fξ d ) and wages nearly rigid with resect to demand ressure (β w 0) we may summarize the comarative static roerties as far as the dynamically endogenous variables are concerned aroximately as follows: r = r(), r > 0, e = e(), e < 0, Y (F, B, ), Y 1 > 0, Y 2 > 0, Y 3 < Dynamics and the steady state of the economy Our dynamical reresentation of the Mundell-Fleming-Tobin model in its general form (with F c a given magnitude in the considered exchange rate regime and with = 1 for simlicity), 7 exressed in nominal terms, consists of the following differential equations F = r (F + F c ) + NX(, η, Y )/η, η = e, = 1 (16) Ḃ = rb + G T er F c (17) to be couled with the law of motion for the rice level : ṗ = [β w (Y Ȳ )/(1 γ) + ɛ(e)] (18) and with the descrition of the temorary equilibrium given by eq. (10)-(12) and the definitions of rivate wealth and real disosable income discussed in the revious section. In order to allow for a sequential determination of the steady state values of this dynamical system, we roceed as follows. We assume (and shall later on rove) that the steady state value r o of r is given by r, i.e., we have ξ = 0 in the steady state. Due to the Phillis curve we furthermore know that Y = Y o must hold true. The given quantity of money M then allows to determine the steady state value of as o = M/m d (Y o, r ). Setting Ḃ = 0 furthermore gives a simle ositive relationshi between B o and e o, which reresent the equilibrium in the domestic bond market. The FFB-curve imlies on this basis: F o F F B = o f d (0, M + B o(e o ) + e o F o o ) = o f d (0, M o + T G r + e o(f o + F c ) o ), which defines a ositive relationshi between e o and F o, as the figure 1 (where we use linear curves for reasons of simlicity). From F = 0, the equilibrium in the foreign currency bond market, we furthermore get r F o + o NX(, e o / o, Y ) = 0, 7 Such an aroach is further justified through the observation that the dynamics of the nominal stock magnitude B is involved in the above considered real dynamics as long as ξ 0 holds true which shows that the real dynamics is then in fact a hybrid as far as the distinction between real and nominal variables is concerned. 10

11 that is, a negative relationshi between e o and F o, reresented in figure 1 by the FB curve. If we assume that M+B o is nonnegative (comare figure 1), we have a nonnegative demand for foreign bonds at e o = 0 and thus a nonnegative value of F o associated with it. In the case of linearity (which need not hold in the large) we will then get an intersection of the F = 0 and the F F B curve in the ositive half lane of the (F, e) sace which gives us ositive steady state values of both F and e (since one can assume that there is a ositive value e where NX = 0 holds). Under the stated conditions we thus have that the rivate agents of the domestic economy will hold a ositive amount of foreign bonds in the steady state and that net exorts must therefore be negative in the steady state due to a value of the exchange rate that is below the one that balances the trade balance. In the general situation where both curves in figure 1 are nonlinear, one must show that the F = 0 curve is not to flat in view of the intersection of the F F B curve with the vertical axis and both curves are not aroaching + for finite values of the nominal exchange rate. F F = 0 FFB M, T G F o d M T G o f (0, + ) * r o e o M, Y NX = 0 e NX > 0 Figure 1: Steady State Stock Equilibrium (B o > 0). Figure 1 shows on the basis of the above the determination of the steady state values of both the nominal exchange rate and the value of foreign debt held domestically, and also indicates how these values can be influenced by fiscal and monetary olicy in articular. It shows that fiscal consolidation will make the currency stronger and increase the amount of foreign $-denominated debt held domestically. The latter effect is also roduced by a monetary exansion, whose effect on the value of e may however be ambiguous, deending on the cometitiveness of the considered economy, i.e., on the elasticity of the net exort function with resect to the real exchange rate at the steady state of the economy. Note that at this steady state we have a negative trade account 11

12 and a ositive interest rate account and of course a balanced caital account in the balance of ayments. Insecting the IS curve on the basis of what has been determined so far shows however that no endogenous variable is then left that allows for IS-equilibrium at the full emloyment level Y and the foreign interest rate r. We therefore now adjust the values T, G such that T G remains unchanged (that is without imact on the left hand side of the government budget constraint) until also the IS-curve asses through the determined steady state values. This holds if G, T are on the basis of a given value for G T determined by: Y = C(Y T + r e o F o / o + r B o / o, r, r ) + G o + NX(, e o / o, Y ) if I = 0 holds in the steady state (see below). Note here also that B o / o is given by (T G)/r + η o F c need not be ositive and in fact must be negative in the case of a value of T G that is sufficiently negative. This is due to the fact that interest ayments rb o are ositive in the steady state in the case of a ositive value of government debt, imlying that real government income T + e o F c / o must be sufficiently high relative to G to allow for the given interest obligation of the government (since there is no issue of new government debt in the steady state). Note also that we assume the behavioral functions and arameters of the model to be such that disosable income Y is ositive at the steady state. Note finally that our regressive exectation function for exchange rate de- or areciations is always assumed to fulfill ɛ(e o ) = 0 in the steady state (is assumed to be asymtotically rational) and is therefore shifting with the steady state solution for e o. We have determined in advance the steady state values for, r, Y, ρ, ρ and then simultaneously the steady state values for e, η, F, B basically from stock equilibrium conditions. We have so far not mentioned the caital stock K here whose growth rate is to be determined by Y/K. The model s dynamics are in fact treated without any consideration of the law of motion of the caital stock. We justify this here by assuming as further consistency condition that 0 = I(Y, r, r ) holds in the steady state. The caital stock will then converge to a certain finite value which is of no imortance in the model as it has been formulated so far (since we have constant marku ricing by firms, i.e., rices do not react to demand ressure on the market for goods). Measuring this demand ressure by way of Y/K for examle would suggest that this term should enter the investment function in the lace of just Y. The dynamics of the caital stock would then feed back into the goods market and become interdeendent with the rest of the dynamics, even if rices do not react to such a demand ressure term. We now consider some features of the 3D MFT dynamics of this aer close to the steady state as determined in the receding subsection by means of the Jacobian matrix of the dynamics calculated at the steady state osition of the economy. 2.5 Local stability analysis In the resently considered olicy regime we will here first of all derive a situation where the steady state of the model is surrounded by centrifugal forces (is reelling). This 12

13 case will then be contrasted with a situation where an attracting steady state is given. The calculations needed to show these two results will show that there exists indeed a multilicity of situations where either stability or instability may revail around the steady state. The conclusions will be that emirical and numerical methods are needed in order to get a more comlete icture of the stock-flow dynamics of the considered oen MFT economy and that it is likely that olicy must be more active than it is currently assumed (in articular with resect to the government budget) to enforce convergent behavior around the steady state of such a small oen economy. Inserting the functions obtained from our short-term comarative static analysis into the laws of motion for the variables F, B, gives rise to the following eigen-feedbacks of the considered state variables (if Y F is used in exlicit form in the first artial derivative): F = r NX Y NX Y (1 C Y ) ) C W > 0, F 1 C Y I Y NX Y 1 C Y I Y NX Y if 1 C Y I Y > 0 and C W sufficiently small Ḃ B = r > 0 ˆ = ɛ (e)e () > 0 We thus have in such a situation that the trace of the Jacobian of the dynamics at the steady state is ositive (as is the determinant). The three state variables taken in isolation are therefore subject to reelling forces as far as their own steady state osition is concerned: J = + ± 0 + ± with in fact all eigenvalues of this Jacobian being real and ositive and thus destabilizing. Even if one assumes that the first of the above artial derivatives is negative, by allowing a high wealth effect on consumtion C W, and furthermore that the second artial derivative (in the diagonal of J) is sufficiently low (i.e., if the accumulation of foreign and domestic bonds is not by itself subject to strong destabilizing forces), we get for the considered Jacobian aroximately still the following sign structure: J = ± 0 0 ± due to the assumed nearly erfect caital mobility. High caital mobility is therefore roblematic for the stability of the balance of ayments adjustment rocess, the evolution of the government debt and for the dynamic rice level of the considered small oen MFT tye economy. There are some forces, by contrast that aear to be stabilizing, but more detailed analysis is in fact needed in order to get clear-cut results on local asymtotic stability and thus local convergence towards the steady state. Such stability issues will be aroached in the next sections by means of two basic scenarios in the case of fixed as well as flexible exchange rate regimes. 13

14 2.6 Real twin deficit accumulation and inflation dynamics In order to highlight the role of rice level adjustments, as well as the comlications they imly for the theoretical modelling of the dynamics of the economy, we now reformulate the model in real terms, with the evolution of the real aggregate wealth of the economy and the government sector instead of the law of motions for F and B. On this basis we show in articular that the aggregate wealth of the government sector Wg a is in its time rate of change as in the case of the rivate sector determined by deducting from its real disosable income the real consumtion of this sector. This then rovides us with a simle law of motion for real aggregate wealth of the government sector, besides the one we have determined for the total (foreign) wealth of the domestic economy in Flaschel (2006), to be reconsidered below. These two laws describe on the one hand the evolution of surluses or deficits in the government sector and the evolution of current account surluses or deficits, and thus in articular allow the joint treatment of the issue of twin deficits in an oen economy with a government sector, but not yet with real caital accumulation and economic growth. For the time rate of change of the aggregate wealth of the government, we get from eq. (7): Ẇ a g = (Ṁ + Ḃ) + ėf c ṗ (M + B) + ef c = (G + rb T r ef c ) + êef c = T r B + ˆM + B Ẇ a g = Y a g + (r + ê ˆ) ef c G = ρ W a g + r M + ξ M + B ˆ (M + B) + ef c G which finally gives + T G (19) as the law of motion for the real aggregate wealth or debt that characterizes the government sector as a whole. Since this debt osition is no longer constant, as in Flaschel (2006), we adjust next from this text, but in a self-contained way, the equation for the evolution of total wealth W of the economy to this case and then consider again rivate disosable income Y and rivate wealth W in its interaction with the evolution of aggregate government debt and the foreign osition of the economy. Note that we assume goods market equilibrium Y C I G = NX in the following derivations. Concerning the aggregate (foreign) wealth of the domestic economy, we start defining it as or in growth rates W := W + W g + W c = ef, with F = F + F c Ŵ = ê + ˆF ˆ or Ẇ = êw + e F ˆW (20) 14

15 Making use of eq. (5), we obtain Ẇ = êw + (Y C G I) + er F ˆW = (ê ˆ)W + r ef + Y C G I, or alternatively, Ẇ = (r + ê ˆ)W + Y C G I = ρ W + Y C G I, ρ = r + ê ˆ In the following we set foreign inflation equal to zero (π = 0), 8 and assume given olicy arameters (M, T, G). Inserting the behavioral equations given by eqs. (10) - (12), we obtain, together with the law of motion for the rice level described by eq. (15), the following 3D dynamical system 9 Ẇ = ρ W + Y C(Y, W W a g, ρ, ρ e ) I(Y, ρ, ρ e ) G (21) = ρ W + NX(, η, Y ) (22) Ẇg a = ρ Wg a + ξ M + B + r M + T G (23) ˆ = β w (Y Ȳ )/(1 γ) + ɛ(e), γ (0, 1). (24) Note that we assume myoic erfect foresight with resect to inflation on the market for goods, but allow for errors in exchange rate exectations here. Note also that actual laws of motions are to be based on actual rates of changes in the exchange rate e, but that we have to use the exected dereciation rate inside behavioral relationshis. We have assumed above following Rødseth (2000, Ch.6) that total rivate consumtion of domestic and foreign goods deends (ositively) on disosable income, rivate wealth and (negatively) on the real rate of returns exected for the two tyes of bonds considered in this aer, but not on the real exchange rate η = e / that characterizes this small oen economy, and similarly that total net investment deends (ositively) on domestic economic activity and (negatively) on the same real rates of return of bonds. The real exchange rate η = e / only enters the goods market equilibrium condition only via exorts by way of an exort function of the tye X = X(η, Y ). Note again that the above laws of motion for W, Wg a are actual laws of motion based on actual rates of return and thus actual changes in the exchange rate, while some arguments in the consumtion function and the investment function are exected ones (relying on our use of a regressive exectations scheme later on) and have thus to be characterized by an index e for exected. Furthermore, we have assumed myoic erfect foresight with resect to the inflation dynamics and thus do distinguish there between exected and actual inflation rates, with the former to be used in the behavioral relationshis later on while the latter aly to the actual laws of motion for the considered wealth variables. The distinction between actual and erceived rates of return will become imortant when exchange rate dynamics is considered later on (in our reresentation of 8 and consider of course all foreign variables as given for the small oen economy. 9 Note that due to the assumed goods market equilibrium Y C I G can always be relaced by N X if this is convenient for certain calculations of the model s imlications. 15

16 the Dornbusch model in a MFT aroach to financial markets). Note finally that we may extend the consumtion function of Rødseth (2000, Ch.6) later on, if we want to distinguish between the consumtion of the domestic and the foreign commodity and thus have to include then the real exchange rate into the consumtion function exlicitly. Note also that nothing has been said yet about which of the standard regimes od the MFT oen economy is actually revailing in the considered economy. the choice of which will determine later on which variable of the model have to be considered as endogenous and which ones as exogenous. 3 Caital account and inflation dynamics under interest and exchange rate egs We are now going to consider the dynamic imlications of a articular regime among the ones that are economically ossible in the considered MFT framework. We here follow Rødseth (2000, ch. 6.6) and choose a case where in fact the asset markets are sent into the background of the model, a case which therefore solely studies the interactions of the IS-curve with a conventional tye of Phillis curve and the dynamics of the caital account. The conventional tye of IS-PC analysis (without an LM-curve) is therefore here augmented by the change in foreign assets resulting from the excess of domestic savings over domestic investment (or v.v.). The case considered in this section may be alicable after some modifications to an economic situation as reresented by the Chinese economy (at least for certain time eriods of this economy). 3.1 Assumtions The assumtions we emloy in order to derive this secial case from our general framework are the following ones: 1.) Given Y,, r : The small oen economy assumtions 2.) r = r : An interest rate eg by the central bank (via an accommodating monetary olicy) 3.) ē = const (= 1) : A fixed exchange rate via an endogenous suly of dollar denominated bonds by the central bank (which is never exhausted) 4.) W a g : A tax olicy of the government that kees the aggregate wealth of the government fixed 5.) consumtion goods are imort commodities and never rationed in this resect 6.) ω : The real wage is fixed by a conventional tye of marku ricing 7.) ρ n f : The normal rate of return of firms is fixed (since the real wage is a given magnitude) and set equal to r for simlicity 16

17 8.) Y = y K, L d = Y/x : Fixed roortions in roduction (y, x caital and labor roductivity, resectively) 9.) K = const : The caacity effect of investment is ignored. Potential outut Y (= 1) is therefore a given magnitude 10.) Ȳ = x L(= 1) : A given level of the full emloyment outut On the basis of these assumtions we get that the real rates of interest are equalized for the domestic economy: ρ = r + ê ˆ = r ˆ = ρ. Furthermore, the risk remium ξ is zero in the considered situation. Finally, due to the assumed tax olicy we have for the disosable income in the household sector: Y = Y + ρ W G. Private wealth W is given by W Wg a in the considered situation. 3.2 The model We define again the real exchange rate by η = (e )/, i.e., the amount of domestic goods that are exchanged for one unit of the foreign good. This rate reduces to 1/ due to the above normalization assumtions. Households directly buy investment goods for their firms and use only the normal rate of rofit in order to judge their erformance, which is a given magnitude here due to the above assumtions (normal outut times the rofit share). We moreover need only consider one real rate, the rate ρ, in the following formulation of the consumtion decisions (for domestic and foreign goods) and the investment decisions of the household sector now. Note that we now distinguish imorted from domestic goods in domestic consumtion demand and include an of the real exchange rate on this substructure of total rivate consumtion now. C 1 = C 1 (Y, W, ρ, η) : consumtion demand for the domestic good C 2 = C 2 (Y, W, ρ, η) : consumtion demand for the foreign good C = C 1 (Y, W, ρ, η) + C 2 (Y, W, ρ, η)/η : total consumtion I = I(Y, ρ) : investment demand, for domestic goods solely On this basis the goods market equilibrium or the IS-curve of the model is given by: C(Y, W, ρ, η) + I(Y, ρ) + G + NX( ) = Y where net exorts are based on a standard exort function and imort demand as determined by C 2. Imorts can be suressed in this equation by reformulating it as follows Y = C 1 (Y + ρw G, W W a g, ρ, η) + I(Y, ρ) + G + X(Y, η), η = 1/, ρ = r ˆ. We have here assumed that exorts X deend as usually on foreign outut and the real exchange rate. We note that we have to add the law of motion for K : K = I(Y, r 1 1 γ β w(y 1)) for a comlete treatment of the dynamics of this examle of a small oen economy. Since however the analysis without such caacity effects of investment is already comlicated 17

18 enough we do not go into such an extended dynamic analysis here. Furthermore, we may also return to an endogenous treatment of the variable Wg a which would increase the comlexity of the analysis further, desite the simle framework that is here chosen (where ortfolio choice does not matter for the analysis of the dynamics of the real art of the model, T, G given magnitudes): ˆ = β w (Y 1)/(1 γ) Ẇ a g = (r ˆ)W a g + r m d (Y, r ) + T G, Ẇ = (r ˆ)W + X(Y, 1/) C 2 ( Y + (r ˆ)(W W a g ) r m d (Y, r ) T, W W a g, r ˆ, 1/ ) /. This extension would again allow for the discussion of the occurrence of twin deficits and other situations of domestic and foreign debt / surluses. 3.3 Steady state determination For reasons of simlicity we here return however to the situation where aggregate government wealth (basically the government deficit) stays constant in time (by choosing T aroriately) and thus investigate now the steady state solution and the dynamics of the following system: ˆ = 1 1 γ β w(y (, W ) 1) Ẇ = (r ˆ)W + X(Y, 1/) C 2 (Y (, W ) + (r ˆ)W G, W W a g, (r ˆ), 1/)/ where the roerties of the IS-equilibrium are characterized by the standard artial derivatives we have discussed above. With resect to the steady state solution of this dynamical system we assume that the government ursues in addition to its tax olicy a constant government exenditure olicy that is aimed at fixing the steady state value of exorts at the level X. This imlies that the steady state value of the rice level, o, is to be determined from X = X(Y, 1/ o ). Assuming that this equation has a (uniquely determined) ositive solution for o we then can obtain the steady state value of W from the labor market equilibrium equation 1 = Ȳ = Y ( o, W o ). The solution of this equation may be ositive or negative and is again uniquely determined, since the right hand side of this equation is strictly increasing in W o. The level of government exenditure G that allows for this solution rocedure, finally, is then given by 0 = r W o + X C 2 (Ȳ + r W o G, W o W a g, r, 1/ o )/ o In this equation, this exenditure level is adjusted such that net imorts are equal to the foreign interest income of domestic residents, i.e. an excess of imorts over exorts is needed in the case of a ositive foreign bond holdings in the domestic economy in the steady state. Note that the above is also based on the assumtion that I(Ȳ, r ) = 0 holds in the steady state, since there must be a stationary caital stock in the steady state of the model. 18

19 3.4 Stability analysis Due to our simlifying assumtion on the goods-market equilibrium equation Y = Y (, W ) which guarantee that rice level increases reduce economic activity and thus rovide a check to further inflationary tendencies and which induce economic activity to increase with dollar denominated wealth due to its effects on consumtion we have a straightforward sign structure in the artial derivatives of the first law of motion. The second law of motion is however much more difficult to handle. Its artial derivative with resect to W is much more involved than the one in Flaschel (2006) and given by (due to ˆ o = 0): Ẇ W = Y r (1 η o C 2Y ) η o C 2Y W η oc 2W + ˆ W [(η o C 2Y 1)W o + η o C 2ρ ] where we have denoted by ˆ W the artial derivative of the first law of motion with resect to W. We have now considerably more terms in the feedback of foreign debt on its time rate of change than was the case in Flaschel (2006) for the there considered erfectly oen economy. These additional terms seem to rovide more suort for a negative feedback chain comared to Flaschel (2006) (if the assumtions on Y (, W ) hold true) where we simly had that this artial feedback mechanism became ositive (destabilizing) when wealth effects in consumtion are sufficiently weak. The remaining artial derivative for local stability analysis is given by Ẇ = ((η oc 2Y 1)W o + η o C 2ρ )ˆ η o C 2Y Y + (C 2 + η o C 2η X η )/ 2 ). The first two exressions in this equation are ositive in sign while the last term in brackets the quantitative reaction of net imorts to rice level changes via the real exchange rate channel is generally assumed as being negative (η = (e )/ = 1/). For the Jacobian J we thus in sum get as sign structure: J = ( ˆ Ẇ The easiest case for a stability result is ˆ W Ẇ W ) = ( + ± ± ). J = ( ˆ Ẇ ˆ W Ẇ W ) ( + = ), i.e., the case where interest effects do not dominate the caital account adjustment rocess and where the normal reaction of the trade balance (based on the so-called Marshall-Learner conditions) dominates the income, wealth and interest rate effects generated by the general form of a consumtion function used in this aer and Flaschel (2006). The steady state is in this case obviously locally asymtotically stable (since trace J < 0, det J > 0). Grahically, we get in this situation the hase diagram shown in the following figure: 19

20 W ˆ = 0 W = 0 Figure 2: the secial examle of stable inflation and caital account dynamics. In view of this figure we must however kee in mind the very restrictive assumtions we have made with resect to the IS-curve and its relacement by the evolution of the state variables of the dynamics, the reaction of the balance of ayments and the dynamics of the caital account and also on the reaction of foreign bond accumulation with resect to rice level changes. It is therefore by no means clear how dominant the case of stable rice level and caital account dynamics are in the set of all ossible stability scenarios even in the secial case of a MFT economy here under consideration. In the case of divergence the question is of course what mechanisms in the rivate sector may then kee the dynamics bounded or what olicy actions are needed to ensure this. The deicted dynamical imlications are by and large of the tye considered in Rødseth (2000, Ch.6.6), though our consumtion and investment functions differ to some extent from the ones used by Rødseth. Note that Rødseth (2000, Ch.6.6) is using the negative of W in order to characterize the international credit or debt osition of the domestic economy. Rødseth (2000, Ch.6.6) also considers a variety of further issues for this case of a stable steady state of the Mundell-Fleming regime with an interest and ab exchange rate eg. The reader is referenced to this analysis for further asects of this stable monetary and exchange rate regime. By contrast, the worst case scenario (for instability) is given by the situation ) ( ) + J = =, + + ( ˆ Ẇ ˆ W Ẇ W in which case the steady state clearly is of saddleoint tye. This situation is deicted in figure 3. 20

21 W ˆ = 0 W = 0 Figure 3: the case of centrifugal inflation and caital account dynamics. Advocates of the jum variable technique will not be able to aly this technique here under consideration, since both the rice level and the foreign osition W of the economy are redetermined variables here (desite myoic erfect foresight as far as domestic inflation rates are concerned). The solution to the instability shown in figure 3 can thus not be found in an ad hoc imosition of aroriate jums in the rice level, but must be found through the consideration of rivate sector or ublic olicy behavioral changes when the economy has dearted too much from its steady state osition. We consider this a descritively relevant aroach to observed instabilities in the adjustment of the balance of ayments in articular. 3.5 Twin deficit or surlus accumulation In order to highlight the imortant role of the rice dynamics for the stability of the system, as discussed above, we now set foreign inflation equal to zero (π = 0) and assume also constant rice levels for the domestic economy ( = = 1 for notational simlicity). We assume given olicy arameters (M, T, G). Inserting the behavioral equations given by eqs. (10) - (12), we obtain in the resently considered case the 2D dynamical system 10 Ẇ = r W + Y C(Y, W W a g, r ) I(Y, r ) G = r W + NX( ) (25) Ẇ a g = r W a g + r M + T G, (26) 10 Note that due to the assumed goods market equilibrium Y C I G can always be relaced by NX(Y, Y, e) if this is convenient for certain calculations of the model s imlications. 21