CAHIERS ECO & MATHS

98.25

ASYMMETRIC SHOCKS AND MONETARY UNION

Martine CARRE

Fabrice COLLARD

MAD
# Asymmetric shocks and monetary union

Martine Carré*

CREST - MAD université de Paris I

Fabrice Collard†

CNRS-Cepremap

First draft: July 1997

This draft: November 1997

<footnote>*Address: MAD, Université Paris I, 106-112 Bd de l'Hopital, F-75013 Paris, France. Email: carrem@univ-paris1.fr</footnote>

<footnote>†Address: Cepremap, 142 rue du Chevaleret, F-75013 Paris, France. Email fabrice.collard@cepremap.cnrs.fr</footnote>

<footnote>Part of this research was undertaken as the second author benefited from the postdoctoral fellowship of the department of economics, université catholique de Louvain, Belgium. We are thankful to A. d'Autume, P. Beaudry, F. Bec, F. Dufour, J.O. Hairault, P. Monfort, F. Portier, F. Postel-Vinay and J.M. Tallon. We also thank all participants to AFSE 97 congress, MAD and Cepremap seminars. All mistakes and insufficiencies are ours.</footnote>
— Abstract —

This article intends to study the potential benefit of moving from a flexible exchange rate regime to a monetary union. To this end, we develop a two countries intertemporal general equilibrium model. We extend the Obstfeld and Rogoff [1995a] specification by introducing both physical capital accumulation and nominal rigidities through price adjustment costs within a monopolistic competition framework. We show that instituting a monetary union allows to reduce the wealth gaps between countries following asymmetric technology and fiscal shocks, whenever their persistence is high enough. We then establish that as nominal rigidities increase, the gain from implementing a monetary union decreases in the presence of asymmetric technology shocks, whereas it increases in the presence of fiscal shocks.

**Keywords:** Asymmetrical shocks, Exchange rate regimes, Monetary union

**JEL Class.:** F41, F42

— Résumé —

Nous proposons un modèle d'équilibre général intertemporel en économie ouverte dans lequel les entreprises sont en concurrence monopolistique sur le marché des biens. La présence de coûts d'ajustement sur les prix introduit une rigidité dans les deux économies. Nous évaluons les effets de chocs budgétaires et technologiques asymétriques sur le comportement des deux économies. Nous montrons ensuite que le passage à la monnaie unique permet de stabiliser les écarts de richesse entre les deux économies, et est donc profitable, dès lors que la persistance des chocs est suffisamment marquée. Nous établissons alors que lorsque le degré de rigidité nominale augmente, le gain au passage à la monnaie unique décroît dans le cas de chocs technologiques asymétriques, tandis qu'il augmente dans le cas de chocs budgétaires.

**Mots clefs :** Chocs asymétriques, régimes de changes, union monétaire

**JEL Class.** : F41, F42
# Introduction

The creation of a Monetary Union in Europe is usually considered as the ultimate phase of European economic and financial integration. Instituting a common currency in such an integrated area seems optimal in the sense of McKinnon [1963], for a common currency eliminates the risk induced by volatile exchange rates in international trading. Too high a volatility would indeed distort the terms of trade among countries.

On the other hand, exchange rates flexibility allows for a quicker adjustment of relative prices after asymmetric shocks when labor is not mobile, when wages are rigid or when fiscal policies are not coordinated. One is thus led back to conclude, along the lines of Mundell [1961] and more generally according to the literature on optimal currency areas, that the predominance of symmetric shocks is a prerequisite for instituting a common currency.

However the origin of the shock is equally important, independently of the degree of nominal rigidity in the economies concerned by the Monetary Union. Identifying the source of the shocks (demand vs. supply shocks) is as important as assessing their nature (symmetric vs. asymmetric shocks) for the analysis of the desirability of instituting a common currency. This has been underlined by Buiter [1997] in a simple model à la Dornbusch in which nominal interest rates and foreign prices are exogenous. This model is consequently exposed to the usual criticisms addressed to this approach, namely the lack of micro-economic foundations on the one hand, and the neglect of wealth effects (due to trade surplus) in the determination of exchange rates on the other hand. Finally, Buiter [1997] deals with a small open economy (in which, however, the demand for exports is a decreasing function), whereas we believe that feed-backs among countries might be important (especially if one thinks of the future European Monetary Union, in which countries such as Germany and France can hardly be seen as negligible for the rest of the Union).

In this paper, we address the issue of the consequences of the loss of exchange rate flexibility in a richer model. We study the impact on real variables of asymmetric shocks, either fiscal or technological, in two different institutional settings, namely flexible exchange rates and common currency. The study is based on a two-country micro-founded intertemporal model, in which market imperfections and nominal rigidities are introduced. Such a comparison has, to our knowledge, never been made in a dynamic framework. Taking into account wealth effects reveals some interesting and new arguments in the debate
about the desirability of a monetary union. In particular, we show in this model that not only the nature and the source of shocks matter, but that the degree of persistence also plays an important role when contemplating the creation of a monetary union.

The setup we develop is an extension of Obstfeld and Rogoff [1995a]. It is a deterministic model with monopolistic competition à la Blanchard and Kiyotaki [1987]. The specification of Obstfeld and Rogoff [1995a] is extended to allow for capital accumulation<fnref n="1" />. Introducing capital accumulation allows for a better understanding of the dynamics of the trade balance (see Backus, Kehoe and Kydland [1994]). We also enrich Obstfeld and Rogoff [1995a] model by considering a smooth price adjustment. Indeed, they assumed that the price of goods is fixed one period in advance and can fully adjust during the subsequent period. We consider a less extreme adjustment process and introduce a nominal rigidity through quadratic adjustment costs on goods prices (see e.g. Hairault and Portier [1993]).

We propose an evaluation of the implementation of a monetary union in terms of wealth distribution between countries. Our framework incorporates current account effects into exchange rates dynamics. Integrating exchange rate dynamics and the current account yields a new perspective on both. For example, asymmetric shocks affect in this model the international distribution of wealth through current account effects. We then choose an index that focuses on the cross-country wealth distribution. Further, this index can lead to an interpretation in terms of real convergence of European countries.

One should note at the outset that our analysis does not allow for uncertainty except for an initial unexpected shock. One alternative would have been to study a stochastic model and focus on the volatility of aggregates. This could be done in a complete market setting. However, as argued in Obstfeld and Rogoff [1995b], international capital markets are far from the frictionless, full information, complete market ideal. Factors inhibiting complete international capital markets include sovereign default risk, difficulties in insuring national government spending shocks, moral hazard problems and so on. Besides, the assumption of perfect international risk pooling precludes discussions on wealth re-distributions between countries. Thus, a natural extension would be to introduce market incompleteness. However, such a model raises interesting and difficult questions, especially

<footnote n="1">¹Kollmann [1996] and Betts and Devereux [1996], who also investigate the effects of sticky prices in two-countries models, do not take capital accumulation into account. Chari, Kehoe and McGrattan [1996] also have capital accumulation and nominal rigidities but of a different type since price stickiness in their model is due to price contracts. Beaudry and Devereux [1995] develop a two country model, in which the price stickiness is endogenous and relies on the indeterminacy of equilibrium without price setting. More fundamentally, these two models differ from this one in the respect that they assume perfect international risk pooling.</footnote>
as to how the “no Ponzi scheme” condition should be written. The formal solution to this problem, derived in Hernandez and Santos [1996], is in our sense, difficult to implement with actual numerical methods.

Hence, we chose to study in the line of Obstfeld and Rogoff [1995a], a deterministic model with an initial unanticipated shock, which, while being tractable, mimics certain features of incomplete markets models, namely the impossibility to pool risk across countries.

We establish that a common currency reduces wealth differences between the two countries and is therefore beneficial if the shocks are sufficiently persistent. As nominal rigidities are more stringent the gain there is to implement a common currency decreases in presence of asymmetric technological shocks, whereas it increases in presence of fiscal shocks. It may then be worth studying the different sources and degrees of persistence of shocks in European economies in order to evaluate the real costs of implementing European Monetary Union.

The paper proceeds as follows. The setup of the model is developed in a first section. A second section is devoted to the calibration of the model. In a third section we study the impact of non-anticipated asymmetric shocks on the dynamics of some aggregates in both institutional settings, thus allowing for a comparison between the flexible exchange rates regime and the common currency regime. The performance of the different regimes in terms of their ability to reduce wealth gaps between the two countries are assessed in a fourth section. Section five concludes.

# 1 The model

The economy is comprised of a continuum of agents split between two countries. Domestic agents are indexed by $z \in [0, n)$, while foreign agents<fnref n="2" /> are indexed by $z \in [n, 1]$. There is a continuum of goods.

## 1.1 The households

Domestic and foreign households are identical and infinitely lived. Each domestic household $z$ maximizes the following utility function:

$$U_{j,t} = \sum_{s=t}^{\infty} \beta^{s-t} [\log c_{j,s} + \eta \log(1 - h_{j,s})] \quad (1)$$

<footnote n="2">²Throughout the paper, foreign variables are starred.</footnote>
where $\beta \in (0, 1)$ is the discount factor, $h_{j,t}$ represents hours worked during period $t$ and $c_{j,t}$ is the bundle consumed by $j$ at time $t$:

$$c_{j,t} = \left[ \int_{0}^{1} c_{j,t}(z)^{(\theta-1)/\theta} dz \right]^{\theta/(\theta-1)} \quad \forall j \text{ with } \theta > 1$$

where $c_{j,t}(z)$ denotes consumption of good $z$.

The only tradable asset is a bond, whose holding is denoted $f_{j,t}$. This bond is traded on perfectly integrated financial markets and yields an interest rate $r_t$. Household $j$ gets at time $t$ a labor income $w_t h_{j,t}$ and, as the owner domestic firms perceives their profits $\Pi_{j,t} = \int_0^n \Pi_t(z)/ndz$.

We therefore assume that domestic agents are the sole owners of domestic firms, and symmetrically that foreign agents are the sole owners of foreign firms. This assumption rules out the possibility of a mutualization of risk across households of different nationalities.

Finally, household $j$ pays a lump-sum tax $T_{j,t}$. His budget constraint can thus be written, at time $t$:

$$f_{j,t+1} \leq (1+r_t)f_{j,t} + w_t h_{j,t} + \Pi_{j,t} - c_{j,t} - T_{j,t} \quad (2)$$

## 1.2 Public spending

The government spends $g_t$ in consumption goods at time $t$. The composition of this bundle is taken to be the same as the bundle consumed by households, preventing composition effects à la Gali [1994]. Thus, let:

$$g_t = \left[ \int_{0}^{1} g(z)^{\frac{\theta-1}{\theta}} dz \right]^{\frac{\theta}{\theta-1}}$$

Since Ricardian equivalence holds in this model, we can assume without loss of generality that there is no public debt. The government budget constraint is hence simply:

$$g_t = T_t \quad (3)$$

The foreign government budget constraint is identical.

## 1.3 Firms

Each domestic firm $z \in [0, n]$ produces a good $z$ with a constant returns technology:

$$y_t(z) = A_t k_{z,t}^{\alpha} h_{z,t}^{1-\alpha} \quad (4)$$
where $k_{z,t}$ and $h_{z,t}$ are respectively the capital stock of firm $z$ and hours worked in that firm at time $t$. $A_t$ is a technological factor common to all domestic firms. The technology in the foreign country is identical.

Firms interact strategically, determining the price and the quantity of the good they produce taking aggregate output and aggregate demand as given. Firms are therefore in a situation of monopolistic competition à la Blanchard and Kiyotaki [1987].

Following Hairault and Portier [1993], we assume that it is costly for firms to change their price, thus introducing a nominal rigidity. The cost of adjustment is given by<fnref n="3" />:

$$ca_{z,t} = \frac{\phi}{2} \left( \frac{p_t(z)}{p_{t-1}(z)} - 1 \right)^2 \quad (5)$$

We thus assume that only deviations of the growth rate of prices from its value at the steady state are costly. $\phi$ is a constant parameter.

We assume that firms' adjustment costs are expressed in terms of a bundle of goods, assumed to be the same as the bundle consumed by households and government:

$$ca_{z,t}(j) = \left( \frac{p_t(j)}{p_t} \right)^{-\theta} ca_{z,t}$$

where $ca_{z,t}(j)$ is consumption of good $j$, which is induced by the price stickiness.

Capital is a composite good, whose composition is the same as the consumption bundle. Hence, in order to avoid composition effects, we assume that investment $i_{z,t}$ has the same structure as the consumption index. The accumulation process can be written:

$$k_{z,t+1} = (1 - \delta)k_{z,t} + i_{z,t} \quad (6)$$

where $i_{z,t} = \left[ \int_{0}^{1} i_{z,t}(j)^{(\theta-1)/\theta} dj \right]^{\theta/(\theta-1)}$ and $\delta$ is the capital depreciation rate.

We assume that there exists a quadratic adjustment cost on capital accumulation. More precisely, to modify their capital level by an amount $k_{z,t+1} - (1 - \delta)k_{z,t} = i_{z,t}$, firms have to pay an installation cost given by $ci_t = \frac{\kappa}{2} \frac{i_{z,t}^2}{k_{z,t}}$. These costs are expressed in terms of the usual bundle of goods. Hence, faster capital adjustment leads to a smaller net product. As a result, a positive domestic productivity shock will raise, in the short run, the marginal value of domestic capital above the real interest rate since adjustment costs will prevent investment from being high enough. Notice that installation costs depend

<footnote n="3">³Note that implicit in (5) is that we consider a zero inflation in steady state.</footnote>
negatively on the stock of capital already installed. This implies that large firms will bear
a lower cost than small firms for a given investment.

The presence of adjustment costs on prices and capital makes the problem of the firm
explicitly dynamic. It solves the following problem:

$$
\max V_{z,0} = \sum_{t=0}^{\infty} \rho_t p_t \pi_{z,t} \quad (7)
$$

$$
\text{s.t.} \quad y_t(z) \le y_t^d(z) \qquad (8)
$$

$$
k_{z,t+1} = (1 - \delta)k_{z,t} + i_{z,t} \quad (9)
$$

where $p_t \pi_t(z) = p_t(z)y_t(z) - p_t w_t h_{z,t} - p_t i_{z,t} - p_t \frac{\kappa}{2} \frac{i_{z,t}^2}{k_{z,t}} - p_t c a_{z,t}$.

$y_t^d(z)$ represents demand to firm $z$ and $\rho_t = (1+r_t)^{-1}$ is the discount rate. The Lagrange multipliers respectively associated to constraints (8) and (9) are denoted : $\mu_t$ and $Q_t$. The demand faced by firm $z$ is given by:

$$
y_t^d(z) = \left( \frac{p_t(z)}{p_t} \right)^{-\theta} y_t^{dw} \quad (10)
$$

where $y_t^{dw}$ denotes aggregate world demand, i.e.:

$$
y_t^{dw} = c_t^w + i_t^w + g_t^w + ca_t^w + ci_t^w \quad (11)
$$

The superscript $w$ refers to “world variables”, i.e. the weighted sum of domestic and foreign aggregates.<fnref n="4" />

1.4 Money

There exists many ways to introduce money within a general equilibrium framework depending on the function of money we want to put emphasis on: unit of account, medium of exchange or store of value. In this paper, money is not taken as a store of value.<fnref n="5" /> Money is considered through its role as medium of exchange and unit of account. The demand for money therefore reduces to a quantitative equation<fnref n="6" />:

$M_t = p_t(h)y_t$

<footnote n="4">⁴These aggregates are defined in the symmetric case by equation (14).</footnote>

<footnote n="5">⁵Households cannot transfer money balances from a period to another. Thus, money does not appear in the budget constraints because we assume that at the beginning of each period households sell their endowments to the central bank, then they trade in asset and currency markets, and at the end of each period they sell their money holdings back to the central banks in exchange for consumption goods. See Magill and Quinzii [1992] and Neumeyer [1997].</footnote>

<footnote n="6">⁶This equation is written in a symmetric equilibrium that will be defined later on.</footnote>
The demand for money is thus governed by the level of nominal transactions and consequently depends only on the price level and on the product.

Note that Obstfeld and Rogoff [1995a] introduced money differently, putting it directly in the household's utility function. In their setup, money demand therefore depends on the consumption bundle and not on the product. The main difference between these two specifications is, according to Helpman and Razin [1984], the role played by money in international transactions. Our modeling assumes that goods are paid using the money of the seller's country. In most developed countries, international trade is indeed labelled in the money of the exporting country. This specification has been studied by Helpman [1981], Lucas [1982], and Persson [1984]. Under this assumption the exchange rate depends not only on consumption levels in the two economies, but also on their investment. The latter being rather volatile, this leads to a stronger response of exchange rates to a non-anticipated shock.

Finally, money supply in each country follows the simple rule:

$$M_{t+1} = \tau M_t$$

where $\tau$ is the exogenous growth rate of money.

## 1.5 The purchasing power parity hypothesis

We assume that goods are freely exchanged worldwide, without transaction nor transportation costs. Each good has therefore a unique price. Let $e_t$ denote the nominal exchange rate, $p_t(z)$ the price of good $z$ in the domestic currency and $p_t^*(z)$ the price of that same good in the foreign currency. The following relationship between domestic and foreign prices is thus assumed to hold for all $t$:

$$p_t(z) = e_t p_t^*(z)$$

excluding deviations from the law of unique price.

Domestic and foreign agents having identical preferences, the relation above extends to price indices:

$$p_t = e_t p_t^* \qquad (12)$$

It is worth pointing out that the purchasing power parity will not hold for production indices. Hence, the terms of trade will be modified by asymmetric shocks.

We will exclude in the sequel asymmetric shocks on preferences, for they would lead to a violation of equation (12), which would render the model intractable.
## 1.6 Equilibrium

We focus on the symmetric equilibrium, at which all producers of a given country have the same strategy. In particular, all domestic (resp. foreign) producers fix the same price in the domestic (resp. foreign) economy. Let $p_t(h)$ be the price, in domestic currency, of a typical domestic good, $p_t^*(f)$ the price in foreign currency of a typical foreign good, and $p_t(f)$ the price of a typical foreign good in domestic currency. Each domestic (resp. foreign) firm produces $y_t$ (resp. $y_t^*$).

At the symmetric equilibrium, the consumption price index is therefore equal to:

$$p_t = \left[ np_t(h)^{1-\theta} + (1-n)[e_t p_t^*(f)]^{1-\theta} \right]^{\frac{1}{1-\theta}} \quad (13)$$

Aggregate demands are defined as follows:

$$x_t^w = nx_t + (1-n)x_t^* \quad \text{where } x \in \{c, i, g, ca, ci\} \quad (14)$$

Market clearing conditions on the good market in the two economies imply<fnref n="7" />:

$$y_t(p_t(h))^\theta = y_t^*(p_t(f))^\theta \quad (15)$$

Market clearing on the market for bonds is given by:

$$n f_t + (1 - n) f_t^* = 0 \quad (16)$$

and market clearing on the domestic labor market yields:

$$\frac{\eta}{1 - h_t} = \lambda_t (1 - \alpha) (p(h)_t - \mu_t) \frac{y_t}{h_t} \quad (17)$$

Equilibrium on the foreign labor market entails a similar condition.

Finally, the budget constraint of the domestic consumer (equation (2)) leads to the following relationship:

$$\beta \frac{\lambda_{t+1}}{\lambda_t} f_{t+1} = f_t + \frac{p_t(h)}{p_t} y_t - c_t - i_t - g_t - \frac{\kappa i_t^2}{2 k_t} - \frac{\phi}{2} \left( \frac{p_t(h)}{p_{t-1}(h)} - 1 \right)^2 \quad (18)$$

An equilibrium is therefore a price sequence $\{p_t(h), p_t^*(f), w_t, w_t^*, r_t, e_t\}_{t=0}^\infty$, and a sequence $\{c_t, c_t^*, y_t, y_t^*, k_{t+1}, k_{t+1}^*, f_{t+1}, h_t, h_t^*\}_{t=0}^\infty$ such that this last sequence is an optimal solution to agents' problems given the price sequence, and markets clear.

<footnote n="7">⁷with $p_t(f) = e_t p_t^*(f)$.</footnote>
## 1.7 A single currency model

Our model can easily be adapted to describe an economy with a single currency. Indeed, the quantitative equation writes as:

$$M_t^w = np_t(h)y_t + (1-n)p_t(f)y_t^*$$

whereas money supply is given by:

$$M_{t+1}^w = \tau^w M_t^w$$

This immediately yields a unit exchange rate, so that:

$$p_t = p_t^*$$

## 2 Calibration

The dynamic system describing the general equilibrium of this economy does not have an analytical solution. We thus log-linearize it around a deterministic steady state, and solve the resulting linear system using the method described in Farmer [1993]. As this approach is essentially numerical, we need a calibration of the deep parameters of the model that the present section describes.

We assume that the economies we are considering are symmetric. The model is calibrated for a benchmark European economy, namely the French economy, relying heavily on the work of Hairault and Portier [1993]. We assume, without loss of generality, that the economies display neither growth nor inflation in the steady state.

The labor share in output is set to its mean value on French national account, 54%. The markup rate is arbitrarily set to 0.225, value used by Hairault and Portier [1993]<fnref n="8" />. Knowing that at the steady state, the markup rate, $\omega$, is given by

$$\omega = \frac{1}{\theta - 1}$$

we deduce that $\theta = 5.4444$. Then, $\alpha$ is set such that the labor share in output equals its empirical counterpart.

$\delta$, the depreciation rate for physical capital is set such that the annual depreciation is 5%. The parameter $\kappa$, ruling the capital adjustment cost, is set such that the marginal

<footnote n="8">⁸Hairault and Portier [1993] argue that the French economy is less competitive than the US economy for which the markup is 0.197 according to Morrison [1994].</footnote>
adjustment cost of capital represents 0.15% of the marginal cost of investment (see e.g. Fairise [1995]).

$\phi$, the parameter determining the degree of nominal rigidities, is arbitrarily set to 0.1. This implies that the price adjustment costs is 0.007% of output when $p_t(h)$ displays a 1% deviation from the steady state. This value is given only for benchmark considerations, and we will undertake a sensitivity analysis in order to assess the sensitivity of our results to nominal rigidities.

<table><caption>Table 1: Model's parameters</caption><thead><tr><th>α</th><th>θ</th><th>δ</th><th>κ</th><th>φ</th><th>h</th><th>β</th><th>η</th></tr></thead><tbody><tr><td>0.3385</td><td>5.4444</td><td>0.0125</td><td>0.1200</td><td>0.1000</td><td>0.2000</td><td>0.9900</td><td>3.2712</td></tr></tbody></table>

Note: parameters are the same in the two economies.

$\eta$ is such that an individual devotes 20% of its total time endowment to productive activities. $\beta$, the discount factor, is set to 0.99.

In this article, we are considering persistent but transitory unanticipated modification on initial conditions for technology, and government expenditures. The degree of persistence of these shocks are set according to the RBC literature. The perturbation will thus be of the sort:

$$x_t = \rho_x x_{t-1}$$

where the degrees of persistence are given in table (2).

<table><caption>Table 2: Persistence</caption><thead><tr><th>ρ<sub>a</sub></th><th>ρ<sub>a*</sub></th><th>ρ<sub>g</sub></th><th>ρ<sub>g*</sub></th></tr></thead><tbody><tr><td>0.95</td><td>0.95</td><td>0.98</td><td>0.98</td></tr></tbody></table>

They correspond to what is usually found in the literature. Nevertheless, we will study the implications of a modification of the degree of persistence when we address the question of moving to EMU. It is also worth noting that shocks are strictly asymmetric, insofar as domestic and foreign shocks are uncorrelated. This assumption can easily be relaxed, and does not alter our conclusions.
# 3 Asymmetric shocks and aggregate dynamics

This section is devoted to the analysis of the aggregate dynamics of the two economies after an unanticipated shock affecting technology (A) and government expenditures (G). We successively study the cases of a flexible exchange rate economy and a monetary union. Shocks occur in the domestic economy.

## 3.1 Flexible exchange rate

### 3.1.1 A domestic technology shocks

The instantaneous effect of a technology shock is positive on both domestic output, real interest rate and real wage rate. The rise in output implies a positive wealth effect. Households expect a persistent gain in terms of wealth, and thus increase their level of consumption above its steady state value. This mechanism is partially countered by an intertemporal substitution effect transiting through real interest rate dynamics, that leads households to increase their savings.

In the short run, foreign output rises above its steady state value. Two main assumptions can explain this result: (i) the lack of risk sharing between countries and (ii) the existence of imperfections on the good market. We thus find Baxter and Crucini's result, according to which the outputs of the two countries are positively correlated during the first periods of adjustment after a shock. These authors show that, in a model where goods are perfect substitutes, the structure of financial markets matters and alters the labor supply behavior. When financial markets are incomplete, the foreign country responds to technology shocks by increasing its labor supply. Thus, the wage rate in the foreign economy increases with complete markets whereas it decreases with incomplete markets. These results are magnified by imperfect competition on the good market. Since firms have a market power on the good market, they charge a price greater than the marginal cost. Thus a positive technology shock will translate into a slowdown in the general price index and a rise in the markup, since productivity gains are not entirely passed on production prices. This behavior tends to smooth the relative slowdown in the price of the domestic good and to lower the modification of the structure of demand in favor of domestic goods. Finally, the less substitutable the goods are, the more the decrease in prices of domestic goods can lead to an increase in demand for foreign goods. Said differently, the more complementary the goods produced are in the two economies, the more symmetric will be the implications of asymmetric shocks in the two economies.
<figure><img src="image_1.png" /><figcaption>Figure 1: Impulse response function : technology shock</figcaption></figure>
The rise in domestic output leads to an appreciation of the exchange rate that softens the slowdown in the domestic relative prices, which is due to the decrease in domestic production prices. This competitiveness effect gets the upper hand on the appreciation of the exchange rate in so far as terms of trade, $p_t(h)/p_t(f)$, deteriorate. Furthermore, the model generates a *J* curve: trade balance deteriorates in the short run because of investment dynamics. In the model, as in the data, investment fluctuations are volatile enough to render absorption more volatile than output and generate a negative correlation between net exports and output in the short-run. As time goes on, investment becomes less profitable and the current deficit translates into surplus.

The wealth transfer between countries affects the level of the steady state of the economy. In the long run, domestic households lower their labor supply, domestic output decreases, terms of trade improve and exchange rate depreciates.

### 3.1.2 A domestic government expenditures shock

A rise in government expenditures yields, ceteris paribus, an instantaneous increase in demand. As prices are rigid in the short-run, output temporarily increases above its steady-state value. This effect is reinforced by the standard wealth effect implied by a higher lump-sum tax. Since government levies higher taxes, domestic households have to increase their labor supply in order to maintain their wealth. Thus, as physical capital is predetermined, domestic output increases. The decrease in domestic consumption is lower than the rise in government expenditures. Nevertheless, the rise in output cannot offset the impact on higher lump sum taxes on domestic consumption.

As the interest rate increases, foreign households lower their current consumption and supply more labor because of the standard intertemporal substitution effect. Contrary to the domestic economy, the negative wealth effect does not affect the foreign economy, and thus domestic output increases more than foreign output.

The results generated by our model mainly differ from Obstfeld and Rogoff [1995a] in their implications for the exchange rate. In Obstfeld and Rogoff [1995a], money enters the utility function directly. Demand for money then positively depends on the level of domestic consumption, and negatively on real interest rate. Thus, a decrease in domestic consumption leads to a decrease in demand for domestic money, which therefore depreciates. In our model, the demand for money is given by the so-called quantitative equation $M = py$. Then after a positive government expenditures shock, the rise in domestic and foreign output leads to an increase in domestic and foreign money. As domestic output
<figure><img src="image_2.png" /><figcaption>Figure 2: Impulse response function : government shock</figcaption></figure>
increases by more than foreign output, domestic currency appreciates and domestic prices decrease more than foreign prices. Chang and Lai [1997] also show how sensitive the response of exchange rate is with respect to the specification of demand for money.

Two counteracting effects determine the evolution of the terms of trade. On the one hand, the relative rise in domestic output deteriorates terms of trade. This phenomenon was already mentioned by Obstfeld and Rogoff [1995a]. On the other hand, the appreciation of the exchange rate tends to improve the terms of trade and thus acts in the opposite direction. In our model, and for the calibration we use, the former effect gets the upper hand.

Finally, the temporary rise in government expenditures creates a trade deficit for the domestic economy. Indeed, as domestic output increases by less than government expenditures, a transitory shock on government expenditures alters the structure of world wealth. This phenomenon plays in favor of the foreign households. Thus, in the long run, domestic households consume less and supply more labor.

## 3.2 EMU

This section is devoted to the analysis of qualitative dynamics of the economy under the assumption that it is a part of the EMU. Contrary to the flexible exchange rate case, this latter cannot smooth fluctuations in the terms of trade.

### 3.2.1 A domestic technology shock

The behavior of the domestic economy following a technology shock is qualitatively the same as the one observed in the flexible exchange rate case. However, it is worth noting that on a purely quantitative point of view, consumption is less responsive in the EMU than in the flexible exchange rate case. On the other hand, investment, hours worked and output are more responsive. This can be explained in the light of the evolution of the terms of trade. Indeed, the exchange rate stabilizing mechanism does not intervene anymore. Terms of trade thus deteriorate more than previously. Households can then take less advantage of the positive wealth effect triggered by a positive technology shock. They therefore increase their labor supply and respond less in terms of consumption. The response of output is then magnified.

The wealth effect does not seem to be too sensitive to the exchange rate regime. The model still generates a *J* curve, but the deterioration of trade balance is less persistent. Indeed, the exchange rate does not transmit its own persistence any longer. A rise in
<figure><img src="image_3.png" /><figcaption>Figure 3: Impulse response function : technology shock</figcaption></figure>
productivity in the domestic economy leads, in the long run, to an international shift of
wealth in favor of domestic households. They thus reduce their labor supply. Output
diminishes.

3.2.2 A domestic government expenditures shock

As in the technology shock case, the main qualitative dynamic properties of the economies
remains the same as in the flexible exchange rate case, at the exception of foreign and do-
mestic investment and of the terms of trade. A rise in government expenditures provokes
an increase in domestic investment whereas foreign investment responds negatively and
more sharply. Indeed, as the exchange rate is fixed, it dampen soften the effect of the de-
crease of domestic prices anymore. Terms of trade deteriorate. The price-competitiveness
effect is then beneficial to the domestic country. Thus, output increases more in the EMU
than in the flexible exchange rate regime, and domestic investment rises.

<figure><img src="image_4.png" /><figcaption>Figure 4: Impulse response function : government shock</figcaption></figure>
# 4 Wealth gaps and exchange rate regimes

This section proposes an evaluation of the different exchange rate regimes hinging on their ability to reduce the wealth gap between the two economies after an asymmetric shock. We first show that an analysis of world-wide aggregate variables dynamics is not sufficient to discriminate between the two regimes. We then define an index accounting for wealth gaps and allowing for a comparison between the implications of both exchange rate regime. A third section proposes the results.

## 4.1 Aggregate wealth and exchange rate regimes

The preceding section has demonstrated the importance of exchange rate regimes on aggregate dynamics in each country. It then seems natural to extend this analysis at the global level in order to evaluate the impact of implementing EMU on global aggregate dynamics.

<figure><img src="image_5.png" /><figcaption>Figure 5: $IRF_u(C^W)-IRF_f(C^W)$</figcaption></figure>

But, as shown in figure (5), EMU does not affect the level of aggregate variables at the global level neither during the adjustment process nor in the long-run. The level of equilibrium world aggregate consumption is not affected by a change in exchange rate regime. Only the cross-country wealth distribution is modified as the previous analysis has shown.

We therefore have to define an index accounting for a modification in cross-country wealth distribution following a shock. This may shed light on the debate on the real convergence between the European economies, insofar as we evaluate the effects of implementing the monetary union in terms of wealth distribution. Further, implementing a monetary union is usually perceived as an opportunity to mutualize risks. Monetary union
indeed introduces an insurance mechanism allowing to smooth the wealth gap following an asymmetric shock. We thus propose an index accounting for such wealth gaps and allowing for a comparison between the implications of both exchange rate regime<fnref n="9" />.

## 4.2 Definition

The index his based on the analysis of wealth gaps through Lagrange multipliers attached to households' budget constraints, which represent the marginal utility of wealth. The perfect mobility of capital implies

$$ \frac{\lambda_t}{\beta\lambda_{t+1}} = \frac{\lambda_t^*}{\beta\lambda_{t+1}^*} $$

thus:

$$ \lambda_t = \Lambda\lambda_t^* $$

As underlined in the dynamic analysis, any asymmetric transitory shock translates into a disequilibrium in current accounts and a permanent wealth transfer between the two economies, which is accounted for by the multipliers $\lambda_t$ and $\lambda_t^*$ – or identically by the two consumption levels<fnref n="10" /> $c_t$ and $c_t^*$. We thus propose the following index<fnref n="11" />:

$$ \mathcal{E} = \frac{|c_{f,t} - c_{f,t}^*|}{|c_{u,t} - c_{u,t}^*|} $$

Whenever $\mathcal{E}$ is greater than one, monetary union leads to lower wealth gaps than in the flexible exchange rate economy after an unexpected asymmetric change in economic environment. Remark first that this index does not depend on the size of the shock<fnref n="12" />. Further, as the two economies are perfectly symmetric, it does not depend on the location of the shock.

## 4.3 Results

Figure (6) proposes an evaluation of this criterion with regards to the level of nominal rigidity, $\phi$.

It first appears that whatever the shock and the level of nominal rigidity, implementing the monetary union allows to reduce wealth gaps between the two economies. This result

<footnote n="9">⁹It is worth noting that this index does not hinge on any welfare criterion, in so far as our modeling of moving to monetary union does not imply any change in the steady state.</footnote>

<footnote n="10">¹⁰See Appendix B.</footnote>

<footnote n="11">¹¹$c_{f,t}$ and $c_{u,t}$ respectively denote consumption in the flexible exchange rate economy and in the monetary union.</footnote>

<footnote n="12">¹²See appendix B.</footnote>
<figure><img src="image_6.png" /><figcaption>Figure 6: Nominal Rigidity</figcaption></figure>

mainly relies on the dynamics of terms of trade, which effect relies on two mechanisms: a
wealth effect and an intertemporal substitution effect.

In the case of a domestic positive change in technology, terms of trade deteriorate in the very short run. This, all things being equal, reduces the increase in households' wealth. This thus limits the increase in consumption. This effect is reinforced by an intertemporal substitution mechanism, attached to better terms of trade in the long run. Households thus postpone consumption. As the two effects act in the same direction, lowering the magnitude of the response of terms of trade after a technology change corresponds to reduce the impacts of these two effects and thus increase the gap between consumptions<fnref n="13" />. Exchange rate flexibility precisely plays this role in our model. Implementing the monetary union, by forbidding any change in exchange rate, allows for an adjustment of terms of trade and thus contributes to the reduction of consumption gaps, and thus wealth gaps.

Consider now an unexpected increase domestic public expenditures. Terms of trade deteriorate and magnify the lowering of domestic consumption due to the standard negative wealth effect. Nevertheless, the magnitude of this deterioration remains lower in the short run than in the long run. The intertemporal substitution effect thus smoothes the decrease in domestic consumption. Exchange rate flexibility, by smoothing the profile of the dynamics of terms of trade, lower this effect and increases the gap between consumption in the two economies, for the calibration we consider. Thus, implementing monetary union allows to reduce this gap.

A second remark concerns the level of $\mathcal{E}$ depending the “shock” we consider. If the

<footnote n="13">¹³It is worth noting that we focus on wealth gaps (identically consumtion gaps) between countries. An analysis in terms of activity levels would lead to different results.</footnote>
wealth gap is quite high for a change in the level of technology (ranging from 39% to 50%), it is much lower when public expenditures are affected (between 5% and 6.5%). Indeed, the quantitative effects of changes in technology highly vary when we pass from a flexible exchange rate framework to a monetary union, whereas those of changes in public expenditures do not vary that much between the two setup. This can be understood recalling that changes in technology directly affect the determination of relative prices in the model while changes in public expenditures only affect the environment through the negative wealth effect they imply. Thus relative prices are only indirectly affected in the latter case.

A third remark concerns the impact of the degree of nominal rigidity on the level of wealth gaps. Whatever the shock we consider, domestic prices diminish by more than foreign prices do. Nevertheless the higher the degree of nominal rigidity is, the less terms of trade deteriorate in the short run, whatever the exchange rate regime we consider. This reinforces the intertemporal substitution effect in the case of a change in public expenditures, but lowers it for a variation in technological environment. We thus understood that a rise in the level of nominal rigidity diminishes $\mathcal{E}$ in the case of a technology shock. The gain associated with monetary union is thus lower when prices are rigid. The reverse is true for changes public expenditures, for our calibration.

The preceding discussion shows how important is the role played by wealth and substitution effects. As these fundamentally depend on the persistence of shocks, we propose, in figure (7), a sensitivity analysis of the wealth gap as a function of the degree of persistence.

<figure><img src="image_7.png" /><figcaption>Figure 7: Persistence</figcaption></figure>

It appears that a high degree of persistence is needed to justify the implementation of
EMU. The explanation of such a phenomenon is found in the implications of persistence on the mechanisms affecting the dynamics of the model. Indeed, as persistence is low, intertemporal substitution effects dominate the dynamics. The role of long run effects is thus reinforced, as shown in table (3).

<table><caption>Table 3: Short-run and long-run multipliers of terms of trade</caption><thead><tr><th rowspan="2"></th><th rowspan="2">Pers.</th><th colspan="3">Flex. Exch. Rates</th><th colspan="3">EMU</th></tr><tr><th>SR</th><th>LR</th><th>LR-SR</th><th>SR</th><th>LR</th><th>LR-SR</th></tr></thead><tbody><tr><td rowspan="5">ΔA</td><td>ρ = 0.5</td><td>-0.2955</td><td>0.0383</td><td>0.3338</td><td>-0.3190</td><td>0.0060</td><td>0.3250</td></tr><tr><td>ρ = 0.8</td><td>-0.2900</td><td>0.0502</td><td>0.3402</td><td>-0.3145</td><td>0.0161</td><td>0.3306</td></tr><tr><td>ρ = 0.95</td><td>-0.2651</td><td>0.0922</td><td>0.3573</td><td>-0.2912</td><td>0.0621</td><td>0.3533</td></tr><tr><td>ρ = 0.98</td><td>-0.2405</td><td>0.1493</td><td>0.3898</td><td>-0.2577</td><td>0.1275</td><td>0.3852</td></tr><tr><td>ρ = 0.99</td><td>-0.2120</td><td>0.2060</td><td>0.4180</td><td>-0.2241</td><td>0.1928</td><td>0.4169</td></tr><tr><td rowspan="5">ΔG</td><td>ρ = 0.5</td><td>-0.37E-3</td><td>-0.74E-3</td><td>-0.0004</td><td>-0.36E-3</td><td>-0.71E-3</td><td>-0.0004</td></tr><tr><td>ρ = 0.8</td><td>-0.0009</td><td>-0.0018</td><td>-0.0009</td><td>-0.0009</td><td>-0.0017</td><td>-0.0008</td></tr><tr><td>ρ = 0.95</td><td>-0.0032</td><td>-0.0063</td><td>-0.0031</td><td>-0.0031</td><td>-0.0060</td><td>-0.0029</td></tr><tr><td>ρ = 0.98</td><td>-0.0063</td><td>-0.0126</td><td>-0.0063</td><td>-0.0062</td><td>-0.0120</td><td>-0.0058</td></tr><tr><td>ρ = 0.99</td><td>-0.0092</td><td>-0.0189</td><td>-0.0097</td><td>-0.0092</td><td>-0.0179</td><td>-0.0087</td></tr></tbody></table>

Note: SR Short-Run, LR Long-Run

First of all, let us recall that the impact of terms of trade on consumption mainly relies on two mechanisms: wealth and intertemporal substitution effects. The higher the degree of persistence is, the more the wealth effect dominates the dynamics.

In the case of a technology shock, whatever the horizon and the degree of persistence we consider, terms of trade deteriorate more within the EMU regime than in flexible exchange rates regime. Thus the wealth effect always intervenes in favor of EMU. On the contrary, the intertemporal substitution always intervenes in favor of flexible exchange rate. As $ρ$ increases, the wealth effect dominates in adjustment dynamics, therefore implementing EMU allows to reduce the wealth gap between the two countries. A similar reasoning holds in the case of a public expenditures shock.

# 5 Concluding remarks

We proposed an intertemporal general equilibrium model of an open economy, in which we introduce nominal rigidities, via prices adjustment costs. We studied the implications of both technology and government expenditures shocks on aggregate dynamics in a flexible exchange rate regime as well as in a EMU.
The analysis of wealth gaps in each exchange rate regime allows us to characterize two important properties of our model:

(i) Implementing EMU reduces the wealth gap when the degree of persistence is high enough, which corresponds to the situation in European countries.

(ii) The wealth gap decreases as the degree of nominal rigidities increases when only technology shocks are considered, but increases when we restrict ourselves to government expenditures shocks.

The decision to implement EMU is thus conditional on the status and the persistence of shocks. It may then be worth studying the different sources of fluctuations in European economies in order to evaluate the costs of moving to EMU.

It is also worth noting that our results were established under the purchasing power parity (PPP) hypothesis. Changes in exchange rate are then totally reverberated on the level of international relative prices. But, recent studies (See e.g. Chari et al. [1996], Betts and Devereux [1996]) have stressed the need to abandon the PPP hypothesis to explain the degree of exchange rates volatility. Indeed, after the seminal papers by Krugman [1987] and Dornbusch [1987], the pricing-to-market hypothesis has widely been analyzed. It may be worth considering our results within this framework in so far as export prices are no more affected by changes in the exchange rate.
# APPENDIX

## A Individuals optimal behavior

### A.1 Households

The first order conditions defining the household's optimal behavior are:

$$ \frac{1}{c_{j,t}} = \lambda_t \quad (1) $$

$$ \frac{1}{c_{j,t}} = \beta(1 + r_t) \frac{1}{c_{j,t+1}} \quad (2) $$

$$ \frac{\eta}{1 - h_{j,t}} = \lambda_t w_t \quad (3) $$

where $\lambda_t$ is the Lagrange multiplier attached to the intertemporal budget constraint (2). Equation (1) is the Frischian demand for consumption. Equation (2) characterizes the standard consumption-saving arbitrage, thus accounting for the household's behavior in-tertemporal. Finally, equation (3) defines the optimal labor supply behavior. There is an analogous system in the foreign economy. Thus the capital perfect mobility hypothesis implies

$$ \frac{\lambda_{j,t+1}^*}{\lambda_{j,t}^*} = \frac{\lambda_{j,t+1}}{\lambda_{j,t}} \quad (4) $$

Finally, we impose the no-Ponzi game condition

$$ \lim_{\tau \to +\infty} [\beta^{t+\tau} \lambda_{j,t+\tau} f_{j,t+\tau}] = 0 \quad (5) $$

### A.2 Firms

The first order conditions associated the profit maximization of an entrepreneur z are:

$$ p_t w_t = (1 - \alpha) \frac{y_{z,t}}{h_{z,t}} (p_t(z) - \mu_{z,t}) \quad (6) $$

$$ Q_{z,t} = p_t \left(1 + \kappa \frac{i_{z,t}}{k_{z,t}}\right) \quad (7) $$

$$ Q_{z,t} = \frac{1}{1+r_t} \left[ \alpha(p_{t+1}(z) - \mu_{z,t+1}) \frac{y_{z,t+1}}{k_{z,t+1}} + p_{t+1} \frac{\kappa}{2} \left( \frac{i_{z,t+1}}{k_{z,t+1}} \right)^2 + (1-\delta) Q_{z,t+1} \right] \quad (8) $$
$$ y_{z,t} = \theta \mu_{z,t} \frac{y_{z,t}}{p_t(z)} + \phi \frac{p_t}{p_{t-1}(z)} \left( \frac{p_t(z)}{p_{t-1}(z)} - 1 \right) \\ - \phi \frac{1}{1+r_t} \frac{p_{t+1}}{p_{t+1}(z)} \left( \frac{p_{t+1}(z)}{p_t(z)} \right)^2 \left( \frac{p_{t+1}(z)}{p_t(z)} - 1 \right) \quad (9) $$

Equation (6) defines the optimal labor demand for the firm, whereas (7) characterizes her optimal investment behavior as a function of Tobin's Q, which law of motion is given by (8). Finally, equation (9) is the optimal pricing behavior of the firm. As shown by this relationship, this behavior is dynamic, so will be the markup:

$$ p_t(z) = (1 + \nu_t(z))C_{m,t}(z) $$

where $C_{m,t}(z)$ denotes the marginal costs of the firm, given in our model by $C_{m,t}(z) = p_t(z) - \mu_{z,t}$.

When prices are perfectly flexible, the markup remains constant along the business cycle, the supply curve is thus vertical. Any rise in demand, through a monetary expansion for instance, will translate in an increase in inflation rate, while both the level of output and markup will remain unchanged.

On the contrary, when prices are rigid, the supply curve is increasing with regard to prices. The higher the degree of nominal rigidities is — i.e. the higher prices adjustment costs are — and the lower the slope of the supply curve will be. A demand shock will thus affect real aggregates, and especially output. The markup is no more constant, and decreases. When a positive technology shock occurs, prices decrease and markup rises, since productivity gains are not entirely reported on production prices.

Finally, we impose the transversality conditions

$$ \lim_{\tau \to \infty} \left[ \frac{\rho_{t+\tau+1}}{\rho_{t+\tau}} Q_{z,t+\tau+1}(z) k_{z,t+\tau} \right] = 0 \quad (10) $$

$$ \lim_{\tau \to \infty} \left[ \frac{\rho_{t+\tau+1}}{\rho_{t+\tau}} \frac{\partial V_{z,t+\tau+1}}{\partial p_{t+\tau}(z)} p_{t+\tau}(z) \right] = 0 \quad (11) $$
# B The wealth gap index

Let recall that the wealth gap index is given by

$$ \mathcal{E} = \frac{|c_{f,t} - c_{f,t}^*|}{|c_{u,t} - c_{u,t}^*|} $$

The log-linearization of the model implies a strict proportionality of the response of consumption to any alteration of the economic environment: $c_{f,t} = \kappa_{f\epsilon}\epsilon_t$. $\kappa_f$ denotes the proportionality factor to the shock $\epsilon$ for the domestic economy, and $\epsilon_t$ denotes the shock. Similarly, we can define $\kappa_{f\epsilon}^*$, $\kappa_{u\epsilon}$ and $\kappa_{u\epsilon}^*$. Thus:

$$ \mathcal{E} = \frac{|\kappa_{f\epsilon}\epsilon_t - \kappa_{f\epsilon}^*\epsilon_t|}{|\kappa_{u\epsilon}\epsilon_t - \kappa_{u\epsilon}^*\epsilon_t|} = \frac{|\kappa_{f\epsilon} - \kappa_{f\epsilon}^*|}{|\kappa_{u\epsilon} - \kappa_{u\epsilon}^*|} \frac{|\epsilon_t|}{|\epsilon_t|} = \frac{|\kappa_{f\epsilon} - \kappa_{f\epsilon}^*|}{|\kappa_{u\epsilon} - \kappa_{u\epsilon}^*|} $$

As the two economies are strictly symmetric, $\kappa_{f\epsilon} = \kappa_{f\epsilon}^*$ and $\kappa_{f\epsilon}^* = \kappa_{f\epsilon}$. where $\kappa_{f\epsilon}^*$ and $\kappa_{f\epsilon}^*$ denote the elasticity of foreign consumption (resp. domestic) to a given shock in the foreign economy.

$$ \mathcal{E} = \frac{|\kappa_{f\epsilon} - \kappa_{f\epsilon}^*|}{|\kappa_{u\epsilon} - \kappa_{u\epsilon}^*|} = \frac{|\kappa_{f\epsilon}^* - \kappa_{f\epsilon}^*|}{|\kappa_{u\epsilon}^* - \kappa_{u\epsilon}^*|} $$

The wealth gap index is thus independent on the location of the shock.

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