An intertemporal model of the real exchange rate, stock market, and international debt dynamics: policy simulations


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1 This page may be remove to conceal the ientities of the authors An intertemporal moel of the real exchange rate, stock market, an international ebt ynamics: policy simulations Saziye Gazioglu an W. Davi McCauslan 1 Department of Economics, University of Abereen, Ewar Wright Builing, Ol Abereen, AB24 3QY. Tel: 44 (0) /0 Fax: 44 (0) J. E. Lit. Nos.: E60, F40, G15, 60 Key wors: stock market, international ebt, the real exchange rate Abstract This paper evelops an open economy intertemporal optimising moel that seeks to analyse the effect of bill finance government expeniture on several key financial markets. The main results suggest that an increase in bill finance government expeniture leas to a rise in net international ebt, a fall in omestic the real exchange rate an a fall in the stock market value. Furthermore, ue to the presence of nonlinearities in the moel, reversing the eficit financing policy oesn t restore the initial net international creit, high stock market value state. Instea, the country fins itself stuck in an international ebt an low stock market value trap. Copyright: Department of Economics, University of Abereen E286 11/03/ :48 PM 1 Comments receive on an earlier version of the paper presente at Louisiana State University an Bilkent University are gratefully acknowlege; all remaining errors are our own.
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3 An Intertemporal Moel of The real exchange rate, Stock Market, an International Debt Dynamics J. E. Lit. Nos.: E60, F40, G15, 60 Key wors: stock market, international ebt, the real exchange rate Abstract This paper evelops an open economy intertemporal optimising moel that seeks to analyse the effect of bill finance government expeniture on several key financial markets. The main results suggest that an increase in bill finance government expeniture leas to a rise in net international ebt, a fall in omestic the real exchange rate an a fall in the stock market value. Furthermore, ue to the presence of nonlinearities in the moel, reversing the eficit financing policy oesn t restore the initial net international creit, high stock market value state. Instea, the country fins itself stuck in an international ebt an low stock market value trap.
4 1 Introuction Our motivation in this paper is to explore the effect on international ebt of wiening the portfolio choice to inclue shares as well as government bills. Bill financing the buget eficit, through portfolio reallocations, affects the real exchange rate an net international ebt. Implicitly, there is a transfer of ebt from being omestic to being international. Evience from eveloping countries seems to confirm this mechanism. Our results show that an increase in bill finance government expeniture leas to a rise in net international ebt, an, ue to the presence of nonlinearities in the moel, reversing the eficit financing policy oesn t restore the initial state of net international creit, but rather, the country fins itself stuck in an international ebt trap. This paper constructs an open economy intertemporal optimising moel that extens the approach evelope by Obstfel an Rogoff (1995) by consiering the ynamics of the real exchange rate in a Ramsey (1928) type continuoustime framework. Karayalcen (1996) aopts this approach with ajustment costs of investment with free international mobility of capital an instantaneous mobility of ownership claims to capital stocks. In this paper we evelop this approach to inclue the real exchange rate, stock market prices an ebt ynamics, with nonlinearities in international ebt. The moel is base aroun the behaviour of representative utility maximising agents in an environment characterise by a number of intertemporal stockflow constraints. On the firm sie, we consier the behaviour of a representative profit maximising perfectly competitive firm subject to a stanar neoclassical prouction function. Some units of output are use to augment the capital stock  the quantity of such capital investment is etermine optimally by investing up until the point where the cost of investment exactly matches the real return. Interestingly, the approach evelope here gives a strong microfounations justification for the use of the arbitrage conitions that result from this technique in new macro moels. Our key innovation is the integration of the ynamics of the real exchange rate, net international ebt an the stock market. Although the moel evelope in this paper is intrinsically Ricarian, the aition of the analysis of the stock market allows us to make a brige between the firm an the financial sector (this link is formally represente by the combine constraint in equation ( 10)). Since shares an government bills are substitutes, the
5 issue of bills has ynamic effects in the stock market, as well as on net international ebt an omestic the real exchange rate. We fully integrate the ynamics of the real exchange rate with the ynamics of net international ebt, an uniquely, the stock market. Although Obstfel an Rogoff (1995) o eal with the ynamics of the stock market, for the first time in the literature we integrate these with the ynamics of net international ebt an the real exchange rate. Finally, a very important prouct of the use of our non linear framework is that we can capture hysteresis effects in the stock market, the real exchange rate an net international ebt ynamics. In view of the importance attache to the control of buget eficits in contemporary policy making ebates, this paper seeks to analyse the effects of changes in such eficit expeniture on other key financial markets, such as the stock market. Although there may be a short term incentive to run large eficits, we investigate the possibility that there exists unforeseen long run consequences to this course of action. In section two we evelop the moel. In section three we begin our policy analysis. Section four presents our finings an our simulation results. Concluing comments are offere in section five.
6 2 The Moel We consier first the behaviour of firms, then of househols, before proceeing to solve the moel. 2.1 Firms We assume there are a large number of perfectly competitive firms with constant returns to scale, each earning zero long run profit. Each firm prouces both nontrae goos (goos for omestic consumption) an trae goos (goos for export). The price of nontrae goos is normalise to unity, an so therefore, ue to purchasing power parity, the real exchange rate etermines the price of trae goos. At each point in time they employ the given stocks of labour an capital, pay them their marginal prouct, an sell the resulting output. The representative firm s constraint is therefore Y WN X D K & ( 1) which states that the revenue of the firm, Y, which is equal to the revenue from trae an nontrae goos, is ivie between payment to labour, WN, ivien payments, X D, an physical capital augmentation, K & I. This profit maximising, perfectly competitive firm operates subject to a stanar neoclassical prouction function of the form given by ( K N ) Y Zq, ( 2) where Z is an exogenous constant an q 0, q < 0, q > 0, q < 0. Part of the firm s K > KK N NN output is use to augment the physical capital stock. The quantity of investment is etermine optimally by investing up until the point where the real return exactly equals the cost of investing, erive in equation ata! Başvuru kaynağı bulunamaı. of the appenix an repeate here for convenience Zq K R ( 3)
7 This is simply the conition that the marginal prouct of capital is equal to the real return on capital. We also assume a perfectly competitive labour market, which, given the prouction function above combine with equation ( 1) gives us the equilibrium conition that the marginal prouct of labour is equal to the real wage Zq N W ( 4) Finally, the objective of the firm is to maximise a profit function of the form e β π t 0 [ Y ( K, N ) I[ 1 k] ]t ( 5) where k are the installation costs of investment. Solving this maximisation problem yiels the optimal capital investment level I K& as shown in equation ata! Başvuru kaynağı bulunamaı. in the appenix. 2.2 ousehols Representative omestic agents maximise time separable utility functions of the form max U U 0 { A() t G() t } βt [ A() t G() t ] e t ( 6) where A represents omestic aggregate consumption inex (as in Rogoff an Obstfel, 1996), an G net government spening, subject to the following three constraints 2. We eal with each in turn. Firstly, the government buget constraint & & B B B& f f C R B R B C G ( 7) 2 A full symbols list is provie in Appenix F.
8 The issue of omestic bills, B, & to omestic resients, B &, an foreign resients, B & f, finances government expeniture net of tax revenue, G, an the cost of ebt servicing, f R B R B C, where C is the real exchange rate efine as the price of one unit of foreign currency. Thus, the issue of bills involves an intertemporal transfer from the future to the present. We stress that we o not in this paper seek to moel how the government comes to this ecision of bill finance visàvis alternative financing methos; rather our focus is on the effects of this metho once it has been chosen, an the mechanism by which it affects the real exchange rate an net international ebt. As in Obstfel an Rogoff (1995), Ricarian Equivalence is a feature of this moel. owever, Ricarian Equivalence oes not imply the same thing for omestic an foreign resients, since omestic resients know that bon financing increases their future tax liabilities, but the same thing cannot be sai for foreign resients. This opens up a channel for fiscal policy to be effective. Seconly, the stock market constraint, following Obstfel an Rogoff (1995), X& X & X D ( 8) states 3 that a change in the proportion ( X ) of the value of omestic firms 4 that omestic iniviuals own (in other wors, shares: the value of omestic claims to the entire future profits of omestic firms, ), X&, is equal to the omestic proportion of the change in the stock market valuation of these shares, X &, plus their proportion of iviens, X. Thirly an lastly, the balance of payments constraint C& & Π 1 C 1 f f R B C R F T f ( R ) ( 9) states that the net accumulation of foreign assets 5 by omestic agents, &, can only be accumulate by running a trae surplus, T, ajuste accoringly to take account of the net 3 See Obstfel an Rogoff (1996, p.100) for a iscrete time formulation. 4 We assume that there are a large number of homogenous perfectly competitive omestic firms proucing goos for both omestic an foreign consumption. 5 Net international ebt,, is efine in Appenix A.
9 f f income from holing these net asset stocks, R F R B C an real net profit repatriation 6, Π, efine as the foreign owne share of omestic iviens minus the omestic owne share of foreign iviens 7, plus any capital gain form holing foreign money in terms of foreign goos. ence, consumption is affecte by the income from foreign asset holings an the repayments on ebt. Thus, the existence of the balance of payments constraint stresses the intertemporal choice being mae by consumers to transfer their consumption intertemporally, by both omestic an international mechanisms. Combining equations ( 8) through ( 9) yiels the aggregate constraint B& Y R X& C& f F f f f f f ( & D ) X ( & D ) X C& 1 C A G I R f ( 1 R ) B R B f C ( 10) In essence, therefore, the right han sie of the constraint represents net omestic income (factor earnings, net interest from asset holings, return on shares) minus consumption (private, government an investment), reflecte by the saving (net wealth accumulation) on the left han sie. 6 f f ( )( ) Π 1 X D C X D 7 It is important to note that both countries are large  agents in both countries hol each others assets.
10 2.3 Equilibrium Conitions Maximising 8 ( 6) subject to ( 10) yiels the familiar Euler equations, which can be combine to yiel the extene Blanchar (1981) arbitrage conition R & D ( 11) Finally, we have the stanar uncovere interest parity conition 9 C 1 C & e & ( 12) C 1 R 1 C 1 R f From equation ( 9), since T C > 0 (the MarshallLerner conition: a epreciation improves the trae balance), T > 0 (wealth effects: a rise in international ebt is a rise in foreign wealth which improves exports an a fall in omestic wealth which reuces imports, hence improving the trae balance), T > 0 (since the value of omestic firms reflects their relative prouctivity, rises in the stock market valuation of omestic firms tens to be associate with an improving trae balance) an T G < 0 (increases in government spening worsen the trae balance), an assuming profit repatriation effects are small relative to trae effects, therefore, from equation ( 9), & C < 0, & < 0 10, & < 0 an & G > 0 From equation ( 11), & R D ( C,,, G), since D C > 0 (rise in omestic the real exchange rate improves omestic profits an hence iviens), D < 0 (increases in net international ebt, through wealth effects, aversely affect omestic profitability 11 ), D > 0 8 The working is shown in Appenix B, an follows Obstfel an Rogoff (1996) an Barro an SalaiMartin (1995). 9 We o not go into the erivation of this, since it is well known that it may also be erive from optimising behaviour: inee UIP is an arbitrage conition equating the forwar price of foreign assets (bills an shares) with the spot exchange rate minus the iscounte value of the interest foregone by holing foreign assets. We assume the perfect foresight approximation to rational expectations. Thus, c is the only jump variable in the moel. Instantaneous ajustment of the real exchange rate captures the effect of price ajustment. 10 See Roberts an McCauslan (1998) for further comments regaring the sign of &. 11 We make the stanar assumption that the greatest proportion of omestic prouction is for the omestic market.
11 (the stock market valuation of firms is in effect the valuation of the entire future profit stream an is hence positively relate to iviens) 12 an D G < 0 (increase government spening ecreases iviens because the issue of government bills implies epresse future consumption, which firms respon to by reucing current iviens), therefore & C < 0, & > 0, & < 0 13 an & G > 0. Finally, from equation ( 11) 14, R C > 0, R < 0, R > 0 an R G < 0. ence, from equation ( 12) 15, & C C > 0, & C < 0, & C > 0 an & C G < 0. Equations ( 9), ( 11) an ( 12) therefore capture the ynamics of the whole system, an, given the iscussion above, may be summarise 16 in matrix form by C& C& & & & & C C C C& & & C& & & C C& & & G G G [ G] ( 13) where the signs of the elements of the matrix are, from the iscussion above: C & C > 0, C & < 0, &C > 0 an C & G < 0; C & < 0, & < 0 17, & < 0 an & G > 0; & C < 0, & > 0, & < 0 an & G > 0. We now have all the tools in place necessary to procee to the policy analysis conucte in the next section. 12 A change in this stock market valuation is assume not to affect internally generate physical capital augmentation. 13 From equation ( 11), & R D. We assume initially that R < D, implying the stock market return ominates the return on net government borrowing, therefore & < We have obtaine above the signs of the partial erivatives of D, hence, R & D C,,, G, from equation ( 11). 15 The partial erivatives for R f will, of course, have the opposite signs to those given for R. 16 Although portfolio shares ynamically ajust to flow isequilibrium, they are, of course, constant in long run equilibrium, hence X & 0. Furthermore, following Obstfel an Rogoff (1996), in orer to concentrate on the ynamics of omestic net international ebt, the real exchange rate an the stock market, we assume B & 0 an & f See Roberts an McCauslan (1998) for further comments regaring the sign of &.
12 3 Policy Analysis Following Kawai (1985), we can ecompose the ynamic system represente by equation ( 13) into three ynamic subsystems represente in equations ( 14) through ( 16), where variables are reefine in terms of eviations about long run equilibrium. The precise efinitions of the matrix coefficients are given in Appenix C. Note that C is the jump variable in this moel in accorance with the perfect foresight approximation to rational expectations, which is the stanar assumption employe in the literature in these moels. [ ] g h c w w w w h c ω ω & & ( 14) [ ] g h v x x x x h v χ χ & & ( 15) [ ] g v c z z z z v c ζ ζ & & ( 16) The ynamics of these three subsystems are illustrate in Figure 1 below, which shows the effect of a rise in bill finance government expeniture (g ). Appenix D gives the erivations of their ynamic properties an Appenix E the slopes an shifts of the respective stationary loci.
13 v v 45 &v 0 &c 0 c &h 0 &v 0 &h 0 h &c 0 Figure 1 Effect of rise in government eficit (the loci corresponing to the initial equilibria are represente by ashe lines) Long Run Effects We now consier the long run effects of an unanticipate rise in billfinance government expeniture, represente by a rise in the parameter g. In the bottom right quarant we illustrate the international ebt an the real exchange rate (ch) ynamics. A rise in g shifts both stationary loci leftwars (the original loci are enote by ashe lines) resulting in a long run rise in net international ebt (h ) an fall in the omestic real exchange rate (c ). The intuition behin these results is clear. Firstly there is the irect effect that an issue of government ebt will partly be hel by foreigners an therefore constitutes by efinition part of net international ebt. In aition, there is also an inirect effect. The issue of omestic
14 bills generates a rise in the return on omestic bills (R ) an fall in the return on foreign bills (R f ). This excess of the omestic over the foreign return generates a capital inflow (foreign resients purchasing omestic bills). This leas to a balance of payments surplus. Balance is restore by a fall in the real exchange rate (c ), which reuces the trae balance, an in turn, results in a rise in net international ebt (h ). In summary, therefore, the omestic real exchange rate falls an net international ebt rises. In the bottom left quarant we illustrate the international ebt an stock market (hv) ynamics. A rise in g shifts both stationary loci rightwars resulting in a long run rise in net international ebt (h ) an a long run fall in the stock market value (v ). We have given above some intuition as to the route through which net international ebt rises, so all that remains is to explain the effect on stock market value. A fall in the omestic real exchange rate an a fall in omestic wealth (rise in net international ebt) reuce the stock market value of future omestic profits. In the top right quarant we illustrate the stock market an the real exchange rate (cv) ynamics. A rise in g shifts both stationary loci leftwars, resulting in a long run fall in the stock market value (v ) an fall in omestic the real exchange rate (c ). We have alreay provie some intuition behin these results above. The top left quarant is a merely a pictorial evice. Short Run Ajustment Finally, uring the ajustment of the system, we note that R f > R. From UIP this implies the expectation of a rise in the omestic real exchange rate. The only way these expectations can be consistent with the long run equilibrium fall in omestic the real exchange rate is through the omestic real exchange rate initially falling by more than the require long run fall an then ajusting upwars. In other wors, there is the real exchange rate overshooting. An alternative way of looking at this overshooting phenomena is in terms of the short run ivergence between the returns on the ifferent assets. We show in Appenix D that the ajustment in the top right an bottom right quarants is characterise by salepath behaviour towars long run equilibrium. This reflects the fact that both quarants contain the jump variable c (as alreay note in footnote 9, c is the
15 only jump variable in the moel). On the other han, ajustment in the bottom left quarant is characterise by stable cyclical behaviour towars long run equilibrium (as shown in Appenix D). Thus we now have the basic moel in place, which assumes away the existence of nonlinearities. We now procee to relax these assumptions an analyse the policy consequences of the inherent nonlinearities in the moel. We aress this issue in the next section. 4 The Irreversible Effects of Deficit Spening In this section we relax some of the coefficient sign assumptions mae in the previous section, an, in oing so, amit the possibility of multiple equilibria. It is well known in the hysteresis literature 18 that it is large changes that may lea to policy irreversibility in nonlinear moels such as this one, where large is efine to be a change beyon the critical value that triggers the loss of an equilibrium point. A large unanticipate rise in the (billfinance) government eficit may lea to a loss of the net international creit/high stock market value equilibrium, an a structural shift to the net international ebt/low stock market equilibrium. This is represente by a shift from E 0 to E 1 on Figure There are a large number of references on hysteresis an irreversibility, inee the issues are covere toay by most goo avance textbooks. ysteresis is efine here in the mathematical sense of true remanence (rather than mere persistence). ysteresis thus refers to a situation where an effect remains, even after its original cause has been remove. arian (1979) is an early example of the application of this technique of analysis. Cross (1993) gives an overview of the more methoological founations of hysteresis together with a list of more recent applications.
16 v &c 0 45 v 0 &v 0 E 0 v &h 0 v 0 E 0 v 2 v 1 v 2 v 1 h 0 E 1 E 2 c c 1 c 0 c 2 &h 0 E 0 &v 0 E 2 E E 1 1 h h 2 h 1 E 2 &c 0 Figure 2 Effect of rise in government eficit: hysteresis (the loci corresponing to the initial equilibria are represente by ashe lines) ( h, v, c show eviations aroun the long run equilibrium values of,, C, respectively, as shown in the appenix) The shapes of the loci in Figure 2 are easily verifie by appealing to the Intermeiate alue Theorem as shown below. Proposition 1 We have establishe in the text that T > 0 & R T > 0 or & R T < 0
17 These imply that & is nonlinear (see Lemma 1 below) Lemma 1 Uner Proposition 1, there exists multiple locally stable steay state equilibria if the following conitions are satisfie lim F T & lim B C T & & > 0 where F, B C are the upper an lower bouns to. See Roberts an McCauslan (1999) for simulations using CobbDouglas functional forms that satisfy these conitions. The first two conitions state that the slope of & in the, & space tens to minus infinity at both the upper an lower bouns. The thir conition states that if there exists a region between these bouns in which & > 0, then the Intermeiate alue Theorem implies that the shape of the locus shown in Figure 2. Roberts an McCauslan (1999) use the CobbDouglas form which satisfies these three conitions & φ α 1 θ β { A( F ) C B( D C ) C } r, where the term in curly brackets is the trae balance (exports minus imports, where exports an imports are etermine by wealth an the real exchange rate an the parameters A an B ) an the term outsie the brackets is the ebt repayment term. The lower an upper bouns are foun by setting exports an imports to zero respectively. The fact that T > 0 confirms that there is only a single minimum, an hence only a single region over which & > 0. Proof: Since & is continuous in, Lemma 1 follows from the Intermeiate alue Theorem, noting Figure 2. Proposition 2 We have establishe in the text that D > 0, D N > 0 & R D < 0 or & R D > 0, & D < 0 N N
18 These imply that 1. & is nonlinear (see Lemma 1 below) Lemma 2 Uner Proposition 2, there exists multiple locally stable steay state equilibria if the following conitions are satisfie lim J D & lim P D & & > 0 Proof: Since (, N, R) & is continuous in, Lemma 1 follows from the Intermeiate alue Theorem, noting Figure 1an Figure 2 an Figure 3 below. The first two conitions state that the slope of & in the &, space tens to minus infinity at both the upper an lower bouns. The thir conition states that if there exists a region between these bouns in which & > 0, then the Intermeiate alue Theorem implies that the shape of the locus shown in Figures 13. Below we provie a simple plausible example of a ivien function that satisfies the sufficient conitions for the existence of multiple steay state equilibria liste in Lemma 2. We conuct simulations using CobbDouglas forms that satisfy the conitions given in Lemma 2. Suppose D ( C,, G), takes the form φ α γ η µ ε ( J ) C M ( P ) C D L ( 17) where the first term represents revenue an the secon term represents costs, uner the simplifying assumption that all profits are reistribute to shareholers in the form of iviens. L is a portmanteau coefficient representing all other factors etermining revenue (an here specifically representing the net revenue effect of government spening), M is a
19 portmanteau coefficient representing all other factors etermining costs, P an J are upper an lower bouns to stock market value (which are foun by setting revenues an costs to zero respectively), an 0 < (, η) < 1 φ reflect the properties of iminishing marginal revenues an marginal costs. We assume the plausible parameter value of (, η, α, µ, γ, ε ) 0.9, J 1 R 0.04, φ P an equilibrium values of C an of unity. The results are robust with respect to changes aroun these main values. A rise in G is represente by a fall in the exogenous portmanteau coefficient L (since we establishe earlier that D < 0 through a Ricarian Equivalence effect ecreasing current consumption an G hence firm revenue. A fall in L from to results in the three equilibria ( 0.785, 0, 0.785) being reuce to a single equilibrium (.991) 0 as shown on Figure 3. & J P ( & 0) 1 ( & 0) 0 Figure 3 Now consier an unanticipate cut in bill finance government expeniture which reuces the eficit to its former level. This oes not lea to the restoration of the initial equilibrium, but rather to the locally proximate equilibrium E 2 in figure 2, also characterise by net international ebt/low stock market value. 19 This may mimic to some egree the experience of eveloping countries, who, in trying to grow too quickly by eficit spening, en up in a far worse position, when the hysteresis an irreversibility costs of such spening are finally reveale. 19 Note that equilibrium E 2 has a higher level of the real exchange rate an lower commoity prices than equilibrium E 0. igher the real exchange rate may, when consiere in isolation, be esirable ; however, in combination with net international ebt an low stock market value, it is somewhat less esirable.
20 The European policy implications of this analysis are that, although in the short term there may be an incentive for the iniviual member country to overborrow in avance of the imposition of bining criteria, there are amaging long run consequences. The country may inee fin itself unable to escape from a position of net international ebt an low growth (low stock market value) espite cutting its eficit (reversing its policy). This has long run consequences for the economic performance of the eventual Union as a whole. 5 Conclusions This paper looks at the effects of bill finance government eficit expeniture, where bills are hel by both omestic an foreign resients. The issue of bills affects the ynamics of the stock market. In the short run the real returns on these ifferent assets iverges: there is overshooting of the omestic real exchange rate. In the long run, we show that an increase in bill finance government eficit expeniture leas to a fall in the omestic real exchange rate, a rise in net international ebt, a eterioration of the omestic trae balance an a fall in the stock market value. Furthermore, ue to nonlinearities in the ynamic equations for international ebt an stock market value, hysteresis effects are present in the moel. This implies that a reversal of a eficit financing policy oes not lea to a restoration of the initial state: in other wors, the country gets stuck in a low stock market value an international ebt trap. This has been shown both analytically an simulate using plausible parameter values. This result has obvious relevance to eveloping countries an aitionally shoul provie a note of caution to countries running loose fiscal policies.
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