Public debt and exchange rate dynamics in the new open economy macroeconomics framework Céline Breton, Karine Gente

Abstract: This paper investigates as Ganelli (2004) the e¤ects of a debt-…nanced tax cut in a New Open Economy Macroeconomics setting (NOEM). Taking into account the net foreign assets dynamics in an overlapping generations setting instead of assuming as Ganelli a one-period convergence, the results are reversed. We show that the traditional Mundell-Fleming (MF) results could not emerge in a microfounded setting and recover the Redux Model results despite the departure from Ricardian Equivalence: a debt-…nanced tax cut leads to a monotonic depreciation of the nominal exchange rate in both short-run and long-run.

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1

Introduction

The new open economy framework based on the famous Redux model [Obstfeld and Rogo¤ (1995)] aims at reconciling keynesian approach with microfoundations. A large part of this literature is dedicated to put in relief the same mechanisms as in the MundellFleming model. Concerning …scal policy, the Mundell-Fleming model predicts an exchange rate appreciation after a debt …nanced tax cut. This kind of results cannot appear in the Redux Model (RM) since Ricardian Equivalence holds. Agents do not perceive the increase in debt as a rise in their net wealth. Then, a rise in public spending has the same e¤ects whatever the way chosen to …nance the policy. In a two-country setting, public spending are allocated between both domestic and foreign goods. Such an expansionary …scal policy leads to a deterioration of the current account which leads to a depreciation of the exchange rate. Introducing an overlapping generations structure in the RM, Ganelli (2004) shows that a debt …nanced tax cut appreciates the exchange rate at least in the short run. The intuition behind this result is that since Ricardian Equivalence fails a debt …nanced increase in government spending leads to a rise in private consumption. Then, the depreciating e¤ect of the Redux model is in the short run o¤set by what Ganelli calls a ”money demand e¤ect”: the rise in private consumption is followed by an increase in domestic money demand entailing an appreciation of the exchange rate. Nevertheless, Ganelli uses an overlapping generations structure and assumes "a price adjustment that implies that net foreign assets at the end of the …rst period are already equal to the new steady state level" as in the RM. This note shows that if we assume a slow adjustment convergence process typical of an OLG structure [Ghironi (2003)], then we can question Ganelli’s results. Indeed, despite a zero population growth a permanent public-debt shock impulse a long-run adjustment that overheads the period of price stickiness. Considering this progressive adjustment of NFA explicitly, we obtain opposite results: the permanent rise in public debt leads to a monotonic exchange rate appreciation like in the RM. The departure from Ricardian Equivalence fails to recover the traditional MF results. The paper proceeds as follows. Section 2 develops the model putting in relief the 2

necessity to consider NFA dynamics in the medium-run instead of a convergence in one period as assumed by Ganelli (2004). Section 3 investigates a debt …nanced tax-cut to show that the main results are reversed when we take into account NFA dynamics. Section 4 provides some conclusions.

2

The Model

We use strictly the same setting as Ganelli (2004) with nominal rigidities in the form of one period nominal stickiness in the domestic currency price of home goods and in the foreign currency price of foreign goods. There are two countries in the world. In each period, n individuals are born in the Home country and 1

n in the Foreign country. In

each period, every agent in the world faces a constant probability of death (1

q). There

is also a measure 1 of (in…nitely lived) …rms in the world, n of these are located in the domestic country, 1

n in the foreign country. Firms and agents’behavior is exactly the

same as equations (1)-(9) in Ganelli (2004) in the short-run. The short-run is the time during which prices are sticky. The distinction we introduce concern the medium-run. The medium-run starts two periods after the shock1 . To describe the medium-run dynamics, we add the following equations Vt+s+1

Vt+s =

pt+s (h) Yt+s Pt+s

Ct+s + rt+s Vt+s

Dt+s+1 = (1 + rt+s ) Dt+s Ht+s+1 =

1 + rt+s+1 Ht+s q

(2)

t+s

Wt+s t+s + Pt+s Pt+s

(1)

t+s

(3)

for s = 1:::T: Equation (1) gives NFA dynamics, where V denotes NFA of the domestic country, p (h) is the price set by a typical home …rm in a symmetric equilibrium across …rms, Yt+s is the domestic output, Ct+s the aggregated consumption, rt+s the real interest rate and Pt+s the consumer price index. This medium-run equation is not considered by Ganelli since he assumes that NFA reach their new long-run level only one period after 1

This is what Ganelli does not consider assuming that the economy reaches the new steady state two

periods after the shock.

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the shock. Equation (2) gives the dynamics of the public debt D assuming that public spending are zero and

is the lump-sum tax rate.

Let us assume to simplify that

= 0 that is we drop monetary considerations to

understand simply why NFA cannot converge to the steady state one period after the shock occurs. We know that consumption per capita is a function of total wealth CtP C =

1 q 1+

HtP C + (1 + rt ) VtP C + DtP C

and NFA are given by Vt+2

PC Vt+1 = Zt+1

PC where Zt+1 =

(4)

(1 + ) Ct+1 + r:Vt+1

pt+1 (h) wt+1 Yt+1 + (1 Pt+1 Pt+1

et the permanent level of the variable Xt be2 Let X +1 X et = 1 + r q X 1 + r s=t

q 1+r

Lt+1 )

s t

Xs

We can write human wealth as

PC Ht+1 =

and then equation (4) becomes PC Vt+2 Vt+1 = Zt+1 (1

1+r PC Zet+1 1+r q

q (1 + r)) Vt+1 (1

q )

et+1

1+r PC Zet+1 1+r q

(5)

PC et+1 + (1 + r) Dt+1

Since debt per capita is constant, higher debt service is paid by higher future taxes and then:

1+r e 1+r q t+1

PC = (1 + r) Dt+1 . NFA dynamics is simply given by PC Vt+2 = q (1 + r) Vt+1 + Zt+1

(1

q ) (1 + r) eP C Zt+1 1+r q

(6)

We can notice that in equation (6), after a tax-shock the net foreign assets do not converge to the long-run level in one period except if q = 1: In this case, we recover the in…nite horizon setting and the RM when r = (1 2

) = : At the opposite, in the general case we

We use the same methodology as Obstfeld and Rogo¤ (1996).

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consider (q < 1), temporary shocks are not transmitted across generations through the intergenerational transfer of assets3 . As a result, the consequences of a debt-…nanced tax cut will die out while new entrants arrive with zero assets. Then, NFA decrease monotonically and reach slowly their new steady-state level. The NFA dynamics a¤ect wealth, consumption and money demand and …nally the short-run exchange rate reaction to a permanent shock on public debt.

3

A permanent increase in public debt

We investigate as Ganelli (2004) the e¤ects of a debt-…nanced tax cut with long-run taxes ^ t+1 denotes a change adjusting to pay for the higher interests that is ^t+1 = rDt+1 > 0 if X in the variable Xt+1 around the steady state. Then, the level of per capita government debt increases permanently. In the short-run, equations are the same as Ganelli. Nevertheless, in the medium-run, we consider the progressive convergence process of NFA (equations (1), (2) and (3)) instead of the random walk assumed by Ganelli. Let us assume that a tax-cut makes public debt rise permanently to a level D: Then, the permanent change in debt a¤ects the permanent tax level ~ according to [(1 + r) = (1 + r long-run we have:

q)] e = (1 + r) D: In the short-run we have t+1

t

< ~ whereas in the

> ~: Since the tax cut increases human wealth, consumption in-

creases too in the short-run4 . In the medium-run, tax rate is higher reducing total wealth and consumption. The convergence is progressive since q < 1: This progressive convergence will a¤ect money demand and then short-run exchange rate reactions to a rise in public debt. We now consider the level of parameters collected in Table 1 to calibrate the e¤ects of a debt-…nanced tax cut on exchange rate and net foreign assets for di¤erent level of q: After a debt-…nanced tax cut, the level of per capita government debt increases permanently. We obtain long-run results identical to Ganelli’s ones, whereas the short-run ones 3

PC PC Indeed, even if Zt+1 = Z~t+1 NFA will not converge in one period whereas in the case where q = 1

and r = (1 ) = we would have Vt+2 = Vt+1 . 4 See appendix for simulations.

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are exactly the opposite. Table 1 collects the values of parameters used in the simulation. Table 1

= 1;

= 1;

= 0:96; = 2;

= 0:5;

= 0:2

Figure 1 depicts the progressive adjustment5 of NFA, human wealth, consumption and the nominal exchange rate after a permanent rise in public debt. A debt-…nanced tax cut increases net wealth of agents alive6 when the policy takes place but reduces net wealth of agents born after the tax cut because they only experiment the rise in taxes induced by a higher debt service. On one hand, as new agents enter the economy, the average net wealth changes even if there is no population growth since they did not bene…t from the tax cut. On the other hand, the positive e¤ect of the tax cut will die out as agents alive at the time of the policy leave the economy. The tax cut increases …rst human wealth and consumption creating a money demand e¤ect that creates a pressure for a nominal appreciation of the exchange rate. Indeed, money market equilibrium is given by 1 + it+1 P C MtS = Ct Pt it+1 with M S the money supply. Then, following the …rst period rise in consumption, the nominal interest rate it+1 increases to clear the money market through a rise in Et+2 =Et+1 : In Ganelli’s framework, Et+2 is the long-run level of the exchange rate. This means that Et+2 is systematically lower when the NFA adjustment is progressive. As a result, the change in Et+1 is obviously lower in this case and hence this appreciation pressure on the nominal exchange rate becomes completely o¤set by the current account e¤ect that exerts a depreciation pressure on the exchange rate. After the …rst period where consumption and human wealth start decreasing, the money demand e¤ect is reversed: the drop in domestic money demand tends to depreciate the exchange rate. As in Ganelli (2004) this money demand e¤ect is reinforced by a 5

We use as Ghironi (2003) the undetermined coe¢ cients method to simulate the dynamics. See

appendix 1 for details. 6 At the time the policy takes place, human weath increases and then decreases monotonically.

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"current account e¤ect7 " which tends to depreciate the exchange rate after the …rst period. Nevertheless, we obtain a monotonic depreciation for the exchange rate instead of a shortrun appreciation and a long-run depreciation as predicted by the MF model. Taking into account the NFA adjustment changes the short-run exchange rate reaction: where Ganelli concludes to a nominal appreciation, we obtain a nominal depreciation. Figure 1: NFA and Nominal Exchange Rate dynamics following a debt-…nanced tax rate

4

Conclusion

Ganelli’s work on the macroeconomic e¤ects of government debt uses an overlapping generations setting with zero population growth. In this setting a debt-…nanced tax cut increases human wealth of agents alive at the time of the policy. At the opposite, those who enter the economy after the tax face a higher tax on their labor income. Financial wealth and net foreign assets (NFA) adjust progressively to this kind of policy while the positive e¤ect disappear progressively as those who have bene…ted from the policy leave the economy and new entrants arrive. Taking into account explicitly the NFA adjustment 7

This is the terminology used by Ganelli (2004) to design the fact that the rise in consumption worsens

the current account and then creates a depreciation pressure on the nominal exchange rate.

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we show that Ganelli’s results are reversed. A debt-…nanced tax cut policy leads to a monotonic nominal depreciation of the exchange rate as in the Redux Model.

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APPENDIX

A

NFA Convergence

In the medium-run, NFA dynamics is given by Vt+2

PC Vt+1 = Zt+1

(7)

(1 + ) Ct+1 + r:Vt+1

pt+1 (h) wt+1 Yt+1 + (1 Lt+1 ) Pt+1 Pt+1 (1 + ) Ct+1 = (1 q ) HtP C + (1 + rt ) VtP C + DtP C PC Zt+1 =

Vt+2

PC Vt+1 = Zt+1 + r:Vt+1

(1

PC PC PC q ) Ht+1 + (1 + rt ) Vt+1 + Dt+1

et the permanent level of the variable Xt be8 Let X +1 X et = 1 + r q X 1 + r s=t

q 1+r

(8)

s t

Xs

We can write human wealth as

PC Ht+1 =

and then equation (7) becomes PC Vt+2 Vt+1 = Zt+1 (1

1+r PC Zet+1 1+r q

q (1 + r)) Vt+1 (1

et+1

1+r PC Zet+1 1+r q

q )

PC et+1 + (1 + r) Dt+1

Since debt per capita is constant, higher debt service is paid by higher future taxes and then:

1+r e 1+r q t+1

PC = (1 + r) Dt+1 . NFA dynamics is simply given by PC Vt+2 = q (1 + r) Vt+1 + Zt+1

(1

In the steady state we have V = 8

1

(1 q )(1+r) 1+r q

1

q (1 + r)

Z

q ) (1 + r) eP C Zt+1 1+r q PC

The same methodology is developed in Obstfeld and Rogo¤ (1996).

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(9)

B

Dynamics and the undetermined coe¢ cient methods

As Ghironi (2003), the dynamic system that describes the medium-run adjustment is made of equations (1) (2) (3). Exchange rate dynamics results from money demand equations and PPP. This dynamics system could be written as a function of the backward variables b t+1 Vbt+1 and D

Vbt+2 =

V;V :Vt+1

bt+1 = E

E;V :Vt+1

b t+1 = H

b

+

V;D :Dt+1

+

H;D :Dt+1

b

+

E;D :Dt+1

b

H;V :Vt+1

b t+2 = (1 + r D

Then we can identify the coe¢ cients

V;V ;

dynamics.

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b

b

b t+1 )D

V;D ;

b

H;V ;

H;D ;

E;V ;

E;D

to simulate the

Figure 2 depicts the dynamics that follow a debt-…nanced tax cut with q = 0:77:

Figure 2

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References [1] Ganelli G. (2004), The new open macroeconomics of government debt, Journal of International Economics, 53, 218-240. [2] Ghironi F. (2003), Macroeconomic interdependence under incomplete markets, Boston College Working Papers in Economics, 471. [3] Obstfeld M. and K. Rogo¤ (1995), Exchange rate dynamics redux, Journal of Political Economy, 103, 624-660. [4] Obstfeld M. and K. Rogo¤ (1996), Foundations of International Economics, Cambridge MA, MIT Press.

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