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Financial frictions and the choice of exchange rate regimes.

I. INTRODUCTION

This article provides a quantitative assessment of the role of financial frictions for the choice of exchange rate regimes in a two-country model. The standard new open economy model neglects the role that financial frictions can play for the international transmission of shocks and for the optimal choice of exchange rate regimes. However, several historical episodes, such as the global financial crises during the Gold Standard regime or the exchange rate crisis during the European Monetary System (EMS), have shown the dangers of a close association between financial instability and pegged exchange rates. In general, pegged exchange rates tend to reduce monetary policy flexibility, and those constraints become even more stringent when the domestic economy faces credit frictions. Nowadays, those issues have acquired policy relevance for the euro area as some accession countries entered a system of managed exchange rates with the euro zone, known as the ERM II Central Bank Agreement: (1) the relinquishing of part of their monetary policy flexibility might be a concern as some of those countries are still characterized by unstable financial markets.

To analyze the above-mentioned issues, I use an artificial two-country economy characterized by imperfect financial integration in the market for international securities and sticky prices in an imperfectly competitive framework. The introduction of sticky prices is particularly helpful for comparing different monetary arrangements. To this economy, otherwise similar to those analyzed in some of the recent open-economy-macro literature, (2) I add borrowing constraints on investment associated with balance sheet effects in both countries. (3) Doing so adds realism to the model and moves a step forward toward integrating the analysis of the domestic and the international transmission mechanisms. I simulate the calibrated economy under monetary and productivity shocks, and I compare three different exchange rate regimes--that is, hard pegs, managed exchange rates, and floating exchange rates. To evaluate the relative performance of the different regimes, I rely on the comparison of volatilities for the main macro variables and on a simple welfare metric.

I first consider shocks originated in the foreign country. In the absence of financial frictions, floating exchange rates deliver good stability properties under both productivity and monetary policy shocks. This result confirms Milton Friedman's (1953) case for flexible exchange rate: he argued that in presence of sticky prices, floating exchange rates deliver better insulation properties from foreign shocks as they allow relative prices to adjust faster. In presence of financial frictions, such insulating property is strengthened further. The intuition runs as follows. Under fixed or managed exchange rates, an external shock with devaluation pressures forces the monetary authority to raise interest rates with a consequent increase in the cost of loans. The presence of borrowing constraints on investment exacerbates the tightening effect. To highlight the impact of borrowing constraints on investment, I compare the dynamic properties of the economy with and without agency costs. Both the absolute value for the volatilities of the main macro variables (output, investment, inflation, consumption, asset prices, and return on capital) and the difference in the same volatilities between the two regimes are higher when credit frictions are introduced into the model. Fixed and managed exchange rate regimes also appear to steepen the typical trade-off between inflation and output volatility. This effect is shown by illustrating the fact that the sacrifice ratio (the output-inflation volatility ratio) raises when moving from floating to fixed exchange rate regimes and that such an increase is higher in presence of credit frictions.

I therefore test the robustness of the results by analyzing the model with financial frictions under domestic shocks and under symmetric

and correlated shocks. With domestic shocks, results are reversed so that pegged exchange rates tend to stabilize more than floating. Consider for instance a domestic productivity slowdown: the decrease in investment opportunities generates an increase in the interest rate and in the cost of loans. Under floating exchange rates, the amplifying effect of borrowing constraints deteriorates the financial conditions. On the contrary, under fixed or managed exchange rates, the monetary authority dampens the increase in the interest rate in order to stabilize the currency.

The insulating property of floating regimes is also weakened under symmetric and correlated shocks. The dynamics in the latter case is in fact the result of the combined effects of domestic and foreign shocks. When the two shocks are considered in combination, the effect of the domestic shock tends to prevail; hence, floating exchange rates become more destabilizing than fixed exchange rate.

This article is related to several strand of the literature. It is related to the literature analyzing the role of financial frictions for the transmission of shocks (4) as it aims at analyzing the role of real frictions, such as credit frictions, in the standard new open economy model. (5) Some recent contributions have analyzed the role of credit frictions, in the form of borrowing constraints to investment demand, for: (a) the choice of exchange rate regimes in small open economy models of emerging markets (6) and (b) the international transmission of shocks. (7) This article is also related to a strand of the literature that studies the role of other types of financial frictions for the choice of exchange rate regimes. In particular, Lahiri, Singh, and Vegh (2007) challenge the standard Mundell-Fleming prescription by showing that in presence of segmented asset markets, floating exchange rate regimes perform better than fixed exchange rates when shocks are real and vice versa when shocks originate in the money market. Differently than Lahiri, Singh, and Vegh (2007), in this article, I focus on credit frictions rather than asset market segmentation. In addition, the results in this article show that the relative performance of floating versus fixed exchange rates depends more on the correlation of shocks across countries than on the type of shocks considered (real vs. monetary).

The article is organized as follows. Section II presents the theoretical model. Section III reports quantitative results under idiosyncratic shocks, and Section IV reports quantitative results under symmetric or otherwise correlated shocks. Section V tests the robustness of the results under the assumptions that loans are denominated in foreign currency, Section VI reports results for a shocks to the uncovered interest rate parity, and Section VII report results for the sacrifice ratios. Section VIII concludes.

II. THE MODEL

There are two countries of equal size. In both economies, population is divided into two groups, workers and entrepreneurs, that account for a total measure of one. The workers are infinitely lived agents who choose consumption and leisure and invest in bank deposits and in international bonds. Workers also own the firms of a monopolistic sector, which sets prices facing adjustment costs and produces different varieties of final goods. Varieties are then assembled into final goods by a competitive production unit. Entrepreneurs are finitely lived agents who choose consumption, invest in capital that they rent to the production sector, and face idiosyncratic shocks on the return to capital investment. To finance capital, entrepreneurs use internal funds as well as external borrowing. Indeed, a financial intermediary collects funds from the workers--that is, the lenders--and after pooling resources provides loans to the entrepreneurs--that is, borrowers. As the loan contractual relationship is subject to an agency problem, the borrowers must pay a premium on external finance.

A. Workers' Behavior in The Home and Foreign Country

Workers are infinitely lived agents who consume, work, and hold nonmonetary assets in the form of bank deposits and in the form of international bonds. Workers' utility is increasing, concave, and separable over consumption and leisure. In what follows, I derive the maximization problem for the workers in the home region.

Workers' utility in each country is given by the following: (8)

(1) [E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t] [U ([C.sub.t]) - V([N.sub.t])]

where N denotes the number of hours worked by the representative agent, V is increasing, convex, and differentiable, and C is a Dixit-Stiglitz-Spence aggregator. Their budget constraint reads like this:

(2) [P.sub.t][C.sub.t] + [B.sup.*.sub.t] [e.sub.t] + [D.sub.t] [less than or equal to] [W.sub.t][N.sub.t] + [T.sub.t] + [[gamma].sub.t] + [R.sup.F.sub.t-1] [e.sub.t] [B.sup.*.sub.t-1] + [R.sup.n.sub.t-1] [D.sub.t-1]

where [W.sub.t][N.sub.t] is nominal labor income, [D.sub.t] is nominal deposits that pay [R.sub.t][D.sub.t] one period later, [B.sup.*.sub.t] is nominal internationally traded bonds that pay [R.sup.F.sub.t] [B.sup.*.sub.t], and e is the nominal exchange rate. [T.sub.t] are government transfers, and [[gamma].sub.t] are nominal profits from the monopolistic sector. The following optimality conditions hold:

(3) [U.sub.c,t] [W.sub.t]/[P.sub.t] = [V.sub.n,t]

(4) [U.sub.c,t] [beta] [R.sup.n.sub.t] [E.sub.t] {[U.sub.c,t+1] [P.sub.t]/ [P.sub.t+1]}

(5) [U.sub.c,t] [beta] [R.sup.n.sub.t] [E.sub.t] {[U.sub.c,t+1] [P.sub.t] [e.sub.t+1]/[P.sub.t+1] [e.sub.t]}

Equation (3) gives the optimal choice of labor supply. Equation (4) is the Euler condition with respect to home deposits. Equation (5) is the Euler condition with respect to the foreign security. We can now define consumer price index (CPI) inflation as [[pi].sub.t] = [P.sub.t]/ [P.sub.t+1].

Due to imperfect capital mobility and/or in order to capture the existence of intermediation costs in foreign asset markets, workers pay a spread between the interest rate on the foreign currency portfolio and the interest rate of the foreign country. This spread is proportional to the (real) value of the country's net foreign asset position:

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [zeta] > 0, [[zeta].sup.'] > 0. (9) Aggregating the budget constraints of the workers and substituting for Equation (6), we obtain the following law of motion for the accumulation of bonds:

(7) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

B. Demand Aggregation and Open Economy Relations

The final good X in the domestic country, which is linearly allocated to workers' and entrepreneurs' consumption (respectively, [C.sub.t] and [C.sup.e.sub.t]) and to investment, [I.sub.t], is obtained by assembling domestic and imported intermediate goods via the Armington aggregate production function:

(8) [X.sub.t] = [([(1-[gamma]).sup.1/[eta]] [X.sup.[eta]-1/[eta].sub.H,t] + [[gamma]).sup.1/[eta]] [X.sup.[eta]- 1/[eta].sub.F,t]).sup.[eta]/[eta]-1]

with [P.sub.t] [equivalent to] [[(1 - [gamma]) [P.sup.1-[eta].sub.H,t] + [gamma] [P.sup.1-[eta].sub.F,t]].sup.1/1- [eta]] being the corresponding price index and where 1] represents the elasticity between domestic and foreign goods.

We define [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] as the composite aggregates of domestic and imported intermediate goods, respectively, with [??] being the elasticity across different varieties and [P.sub.H,t] [equivalent to] [([[integral].sup.1.sub.0] [P.sub.H,t] [(i).sup.1-[??]] di).sup.[??]/[??]-1] and [P.sub.F,t] [equivalent to] [([[integral].sup.1.sub.0] [P.sub.F,t] [(i).sup.1-[??]] di).sup.[??]/[??]-1] being the respective price indices.

Optimal demands for domestic and foreign goods are given by:

(9) [X.sub.H,t] = (1-[gamma])[([P.sub.t]/[P.sub.H,t]).sup.[eta]] [X.sub.t]; [X.sub.F,t] = [gamma][([P.sub.t]/[P.sub.F,t]).sup.[eta]] [X.sub.t].

All the relations hold symmetrically for the foreign country.

For expositional convenience, we now express all aggregators as functions of inflation and the nominal exchange rate. Let us define the terms of trade as the relative price of imported goods:

(10) [S.sub.t] [equivalent to] [P.sub.F,t]/[P.sub.H,t]

The terms of trade can be related to the CPIPPI ratio as follows:

(11) [P.sub.t]/[P.sub.H,t] = [[(1 - [gamma] + [gamma] [S.sup.1- [eta].sub.t]].sup.1/1-[eta]] [equivalent to] g ([S.sub.t])

with [g.sup.']([S.sub.t]) > 0. An equivalent relation holds for the ratio d([S.sub.t]) = [P.sub.t]/[P.sub.F,t]. We can therefore express the demand functions for domestic and foreign goods as follows:

(12) [X.sub.H,t] = (1 - [gamma])[(g([S.sub.t])).sup.[eta]][X.sub.t]

(13) [X.sub.F,t] = [gamma][(d([S.sub.t])).sup.[eta]][X.sub.t].

Finally, we need to obtain the relation between terms of trade and nominal exchange rates, which reads as follows:

(14) [S.sub.t]/ [S.sub.t-1] = [[pi].sup.*.sub.F,t]/[[pi].sub.H,t] [e.sub.t]/[e.sub.t-1]

where [[pi].sub.H,t] = [P.sub.H,t]/[P.sub.H,t-1] and [[pi].sup.*.sub.H,t] = [P.sup.*.sub.H,t]/[P.sup.*.sub.H,t-1] respectively, the domestic and the foreign PPI inflation rate. Finally, we can relate the CPI inflation rate to the PPI:

(15) [[pi].sub.t] = [[pi].sub.H,t] g([S.sub.t])/g([S.sub.t-1])

(16) [[pi].sub.t] = [[pi].sub.F,t] d([S.sub.t])/d([S.sub.t-1])

C. Production Sectors in Home and Foreign Country

Here, I present the optimization problem for the domestic production sector. The one for the foreign production sector looks symmetric. Each domestic household owns an equal share of the intermediate goods-producing firms. Each of these firms assembles labor (supplied by the workers) and entrepreneurial capital to operate a constant return to scale production function for the variety i of the intermediate good:

(17) [Y.sub.t](i) = [A.sub.t]F([N.sub.t](i), [K.sub.t](i))

where [A.sub.t] is a productivity shifter common to all entrepreneurs. Each firm i has monopolistic power in the production of its own variety and therefore has leverage in setting the price. In so doing, it faces a quadratic cost equal to, [[??].sub.t](i) = [omega]p/]2 [([P.sub.H,t](i)/[P.sub.H,t-1](i) - 1).sup.2], with [omega]p measuring the degree of nominal price rigidity. The higher [omega]p, the more sluggish is the adjustment of nominal prices. In the particular case of [omega]p = 0, prices are flexible. The problem of each domestic monopolistic firm is the one of choosing the sequence [{[K.sub.t](i), [N.sub.t](i), [P.sub.H,t](i)}.sup.[infinity].sub.t=0] in order to maximize expected discounted real profits:

(18) [E.sub.0] {[[infinity].summation over t=0] [[beta].sup.t] [U.sub.c,t] [[GAMMA].sub.t]/[P.sub.H,t]}

subject to the constraint:

(19) [Y.sub.t] (i) = [A.sub.t]F([N.sub.t](i), [K.sub.t](i)) [greater than or equal to][([P.sub.H,t](i)/[P.sub.H,t]).sup.-[??]] [X.sup.W.sub.t]

where [[GAMMA].sub.t] [equivalent to] [P.sub.H,t](i)[Y.sub.t](i)- ([W.sub.t][N.sub.t](i) + [Z.sub.t][K.sub.t](i))-[P.sub.H,t](i)[??](i) and where [X.sup.W.sub.t] [equivalent to] [X.sub.H,t] + [X.sup.*].sub.X,t] world demand for the domestic intermediate variety i, and [Z.sub.t] is the rental rate of capital. Since adjustment costs are symmetric across firms and since ultimately all firms will charge the same price, we can impose symmetry on the optimality conditions. Let us denote by [{[mc.sub.t]}.sup.[infinity].sub.t] = 0 the lagrange multiplier on the demand constraint, (10) by [[??].sub.H,t] = [P.sub.H,t](i)/[P.sub.H,t] the relative price of variety i, and by [[pi].sub.H,t] [equivalent to] [P.sub.H,t](i)/[P.sub.H,t-1] the gross inflation rate. The first-order conditions of the above problem read as follows:

(20) [W.sub.t]/[P.sub.H,t] = [mc.sub.t] [A.sub.t] [F.sub.n,t]

(21) [Z.sub.t]/[P.sub.H,t] = [mc.sub.t] [A.sub.t] [F.sub.k,t]

(22) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

D. The Entrepreneurs in the Home and Foreign Country

Entrepreneurs consume, invest in capital markets, and run production in the competitive unit. In each period, they rent to firms in the competitive unit the existing capital stock that they own and finance investment in new capital. To finance the purchase of new capital, they need to acquire a loan from a competitive intermediary that raises funds through deposits.

The return on capital is subject to an idiosyncratic shock, [[omega].sup.j]. At the beginning of each period, the entrepreneur observes the aggregate shock. Before buying capital, the entrepreneur goes to the loan markets and borrows money from the intermediary by making a contract, which is written before the idiosyncratic shock is recognized. For the relationship with the lender is subject to an agency cost problem, the entrepreneur needs to pay an external finance premium on the loan. I assume that entrepreneurs are risk neutral, and they have a survival probability [zeta]. (11)

I start by spelling out the optimization problem of the entrepreneur in the home country. The next section is devoted to the analysis of the optimal contract between the intermediary and the entrepreneur. As we shall see later in the section describing the optimal contract between the lender and the entrepreneur, the assumption of a monitoring technology exhibiting constant returns to scale implies linearity and symmetry of the relationships that characterize the contracting problem. Hence, we can spell out the consumption/investment problem of the entrepreneurs by imposing symmetry ex-ante.

Each entrepreneur chooses a sequence [{[C.sup.e.sub.t], [I.sub.t], [K.sub.t+1], [L.sub.t+1]}.sup.[infinity].sub.t=0] to maximize:

(23) [E.sub.0] [[infinity].summation over (t=0)] [([zeta][beta]).sup.t] [C.sup.e.sub.t], [zeta][beta] [less than or equal to] [beta]

subject to the following sequence of constraints:

(24) [Z.sub.t]/[P.sub.t] [K.sub.t] + [L.sub.t+1] [[THETA].sub.t] = [C.sup.e.sub.t] + [I.sub.t] + [R.sup.L.sub.t][L.sub.t+1]

[K.sub.t+1] = (1 - [delta]) [K.sub.t] + [I.sub.t] [PHI]/2 [([I.sub.t]/[K.sub.t] - [delta]).sup.2][K.sub.t]. (25)

Equation (24) is the Entrepreneurs' budget constraint in units of final goods. Wealth is derived from rental income [Z.sub.t] [K.sub.t] for production, new loans [L.sub.t+1] and a transfer of wealth, [[THETA].sub.t], from old agents. The presence of the transfer [[THETA].sub.t] assures that aggregate net wealth is different from zero in the steady state. Expenditure is allocated in final good consumption [C.sup.e.sub.t], investment [I.sub.t], and in the service of the predetermined loan debt, [R.sup.L.sub.t][L.sub.t]. The term - [PHI]/2 [([I.sub.t]/[K.sub.t] - [delta]).sup.2][K.sub.t] the constraint (Equation (25)) indicates that, when investing in capital, entrepreneurs face adjustment costs. The entrepreneurs' optimization problems deliver a consumption function and an optimal demand for capital. In order to derive the aggregate consumption function, it is worth noting that the probability of dying for the entrepreneurs corresponds, by law of large numbers, to the fraction of entrepreneurs who die in each period. The population is held steady by the birth of a new entrepreneur for each dying one. Under those assumption, entrepreneurs behave as permanent income consumers since they consume a constant fraction, g, of their end of period wealth, [NW.sub.t], net of the transfers to the new born, [[THETA].sub.t]:

(26) [C.sup.e.sub.t] = [zeta] ([NW.sub.t] - [[THETA].sub.t]

In presence of adjustment costs, the price of capital, [Q.sub.t], is given by:

(27) [Q.sub.t] = [[1 - [PHI]([I.sub.t]/[K.sub.t] - [delta]).sup.2]

while the return from holding one unit of capital between t and t + 1 reads as:

(28) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

E. The Loan Contract Between the Entrepreneurs and the Financial Intermediary

A financial intermediary collects money from deposits, pools resources, and supplies loans to the entrepreneurs facing an incentive problem due to asymmetric information. The asymmetric information in this economy arises from the fact that firms observe the idiosyncratic shock, [[??].sup.j], but banks can do so only at some cost, Ix. The financial contract follows the tradition and assumes the form of the costly state verification contract a la Gale and Hellwig (1985). (12) I introduce financial frictions in the general equilibrium following the strategy of Bemanke, Gertler, and Gilchrist (1999), Carlstrom and Fuerst (1997), and Nam and Cooley (1998).

The entrepreneur and the lender negotiate a one-period contract that induces the entrepreneur not to misrepresent his earnings and that minimizes the expected deadweight agency costs. This is achieved via a standard debt contract with costly bankruptcy, which has two basic properties. The first feature of the contract is given by the incentive compatibility property, which states that when the return to investment is above the cutoff value that determines the default states entrepreneurs repay a fixed amount, [R.sup.L.sub.t]. The second is the maximum recovery property that states that under the default states, the bank monitors the investment activity and repossess the assets of the firm.

For the time being, each individual variable carries an index j. In the current period, domestic entrepreneurs need to finance an investment value [Q.sub.t][K.sup.j.sub.t+1]. To this end, they employ existing collateral [NW.sup.j.sub.t+1] and resort to external funds via a financial intermediary. The amount of capital investment that needs to be financed is therefore, in real terms, [L.sup.j.sub.t+1]= [Q.sub.t] [K.sup.j.sub.t+1] - [NW.sup.j.sub.t+1].

Default occurs when the return from the investment activity is lower than the amount that needs to be repaid. Hence, the cutoff value is determined by the following zero profit condition--that is, participation constraint to the borrower:

(29) [[bar.[omega]].sup.j] [equivalent to] [R.sup.L.sub.t+1][L.sup.j.sub.t] / [R.sup.k.sub.t+1][Q.sub.t][K.sup.j.sub.t].

The contract maximizes the capital expected income for the entrepreneur, which is defined as follows:

(30) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

with [GAMMA]'([[bar.[omega]].sup.j]) > 0. The participation constraint for the bank states that the expected return from the lending activity must equal the return paid on the deposits to workers/lenders. Expected return form the lending activity is given by:

(31) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

with G'([[bar.[omega]].sup.j]) > 0. The return paid on deposits is given by [R.sub.t][L.sup.j.sub.t].

Hence, the contract specifies the optimal cutoff value, [[bar.[omega]].sup.j.sub.t+1], and the amount of capital, [K.sup.j.sub.t+1], which solve the following maximization problem:

(32) Max[GAMMA]([[bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t][K.sup.j.sub.t]

(33) s.to G([[bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t][K.sup.j.sub.t] = [R.sub.t]([Q.sub.t][K.sup.j.sub.t] - [NW.sup.j.sub.t]).

Let us define [[chi].sub.t] as the lagrange multiplier on Equation (33). First-order conditions to this contract read a follows:

* [K.sup.j.sub.t+1]:

(34)

[GAMMA]([[bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t] + [[chi].sub.t][G([[bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t] - [R.sub.t][Q.sub.t]] = 0

* [[bar.[omega]].sup.j.sub.t+1]

(35) [GAMMA]'([bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t] + [Q.sub.t][K.sup.j.sub.t] [[chi].sub.t][G'[bar.[omega]].sup.j])[R.sup.k.sub.t+1][Q.sub.t][K.sup.j.sub.t] = 0.

Two assumptions make aggregation feasible: (1) a constant fraction [??] entrepreneurs remains alive in every period and (2) the optimal contract linear relations. Using the first-order conditions with respect to {[[bar.[omega]].sup.j.sub.t+1], [K.sup.j.sub.t+1]} and aggregating yield, a wedge between the return on capital and the safe return paid on deposits:

Et{[R.sup.k.sub.t+1]} = [rho]([[bar.[omega]].sub.t+1])[r.sub.t]

where

(36) [rho]([[bar.[omega]].sub.t+1]) = [[(1 - [GAMMA]([[bar.[omega]].sub.t+1]))G'([[bar.[omega]].sub.t+1]]) / [GAMMA]'([[bar.[omega]].sub.t+1])].sup.-1]

with [rho]'([bar.[omega]]) > 0. (13) Let us define [[psi].sub.t] [equivalent to] [E.sub.t]{[R.sup.k.sub.t+1] / [R.sub.t]} as the premium on external finance. This ratio captures the difference between the cost of finance reflecting the existence of monitoring costs and the safe interest rate (which per se reflects the opportunity cost for the lender). By combining Equation (33) with Equation (36), one can write a relationship between capital expenditure [Q.sub.t][K.sub.t+1] and net worth [NW.sub.t+1] whose proportionality factor depends endogenously on [[psi].sub.t]:

(37) [Q.sub.t][K.sub.t+1] = (1 / 1 - [[psi].sub.t]([GAMMA]([[bar.[omega]].sub.t+1]) - [mu]M([[bar.[omega]].sub.t+1])))[NW.sub.t+1].

Equation (37) is a key relationship in this context, for it explicitly shows the link between capital expenditure and entrepreneurs' financial conditions (summarized by aggregate net worth). On the one hand, one can view Equation (37) as a demand equation in which the demand of capital depends inversely on the price and positively on the aggregate financial conditions.

On the other hand, one can write the finance premium [[psi].sub.t] as:

(38) [[psi].sub.t] = h([[bar.[omega]].sub.t+1]) (1 - [NW.sub.t+1] / [Q.sub.t][K.sub.t+1])

where h ([[bar.[omega]].sub.t+1] [equivalent to] [[[GAMMA]([[bar.[omega]].sub.t+1]) - [mu]M([[bar.[omega]].sub.t+1])].sup.-1] One can easily show that h'(*) > 0. This expression suggests that the external finance premium is an equilibrium inverse function of the aggregate financial conditions in the economy, expressed by the (inverse) leverage ratio [NW.sub.t+1] / [Q.sub.t][K.sub.t+1]. An increase in net worth or a decrease in the leverage ratio reduces the optimal cutoff value, as shown by Equation (29). By reducing the size of the default space, it also reduces the size of the monitoring cost and the external finance premium.

Aggregate net wealth accumulation of the economy, which is given by proceeds from capital investment minus the repayment on loan services, reads as follows:

(39) [NW.sub.t+1] = [zeta][[R.sup.k.sub.t][Q.sub.t-1][K.sub.t] - ([R.sub.t] + [[psi].sub.t-1]([Q.sub.t-1][K.sub.t] / [NW.sub.t])) ([Q.sub.t-1] [K.sub.t] - [NW.sub.t]) - [[THETA].sub.t]].

Note that by law of large numbers, the fraction of entrepreneurs that remains alive in every period corresponds to the probability of staying alive for the single entrepreneur.

F. The Equilibrium in Good and Asset Markets

To satisfy market clearing, I assume that the total net supply of bonds at a world level is zero. Market clearing for domestic variety i must satisfy:

(40) [Y.sub.t](i) = [X.sub.H,t](i) + [X.sup.*.sub.H,t](i) [[??].sub.t] + [U.sub.t](i)[K.sub.t](i)

for all i [member of] [0, 1] and t, where [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] and represents the output resources spent in the monitoring activity. Market clearing for foreign varieties holds symmetrically for the foreign country too. Market clearing in the final good sector in both countries implies:

(41) [X.sub.t] = [C.sub.t] - [I.sub.t] + [C.sup.e.sub.t]

(42) [X.sup.*.sub.t] [C.sup.*.sub.t] + [I.sup.*.sub.t] + [C.sup.*e.sub.t].

Asset markets have to clear as well. I assume that at a world level, bonds are in zero net supply. At country level, deposits equal loans:

[D.sub.t] / [P.sub.t] = [L.sub.t], [D.sup.*.sub.t] / [P.sup.*.sub.t] = [L.sup.*.sub.t].

G. Monetary Policy Rules

There is an active monetary policy. The monetary authority sets the short-term nominal interest rate by reacting to endogenous variables. I consider the general class of the Taylor rules of the following form:

(43) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where [R.sup.n.sub.t] = [R.sub.t] [P.sub.t+1] / [P.sub.t], [[bar.[omega]].sub.[pi]] is the weight the monetary authority puts on the deviation of inflation from the target [bar.[pi]], [[bar.[omega]].sub.e] is the weight that the monetary authority puts on the deviation of the exchange rate from the target level, and [M.sub.t] is a monetary policy shock that evolves according to [M.sub.t] = [M.sup.[rho]M.sub.t-1][[epsilon].sup.M.sub.t]. A regime of pure floating exchange rate is identified by the case [[bar.[omega]].sup.e] = 0. I then consider managed exchange rate regimes identified by a Taylor rule of the form (43) in which [[bar.[omega]].sup.e] > 0. In the pure peg case, I assume that [[bar.[omega]].sup.e] is large enough to ensure [R.sup.n.sub.t] = [R.sup.*n.sub.t]

The monetary authority of the foreign country always follows a Taylor rule of the form (43). When analyzing temporary monetary policy shocks, I assume some degree of interest rate smoothing (see Clarida, Gali, and Gertler 2000) and one-period investment delays. These assumptions help to recover the lack of persistence that typically characterizes these shocks; however, they do not affect the quantitative results concerning the ranking of exchange rate regimes.

H. The Competitive Equilibrium in this Economy

DEFINITION 1. For given nominal interest rate [{[R.sup.n.sub.t], [R.sup.n*.sub.t]}.sup.[infinity].sub.t=0] initial conditions for asset evolution [{[K.sub.0], [D.sub.0], [B.sub.0], [K.sup.*.sub.0], [D.sup.*.sub.0]}.sup.[infinity].sub.t=0], and for given set of the exogenous processes [{[A.sub.t], [M.sub.t], [At.sup.*], [M.sup.*.sub.t]}.sup.*.sub.t=0], a determinate competitive equilibrium of the two-country model is a sequence of allocation and prices [{[C.sub.t], [N.sub.t], [I.sub.t], [K.sub.t+1], [Y.sub.t], [[phi].sub.H,t], [[pi].sub.t] , [X.sub.H,t], [X.sub.F,t], [X.sub.t], [mc.sub.t , [NW.sub.t], [Q.sub.t], [R.sup.k.sub.t], [[psi].sub.t], [[bar.[omega]].sub.t], [S.sub.t], [e.sub.t][B.sup.*.sub.t], [R.sup.F.sub.t]}.sup.[infinity].sub.t=0] for the home country and a sequence of allocation and prices for the foreign country [{[C.sup.*.sub.t], [N.sup.*.sub.t], [I.sup.*.sub.t], [K.sup.*.sub.t+1], [Y.sup.*.sub.t], [[pi].sub.F,t.sup.*], [[pi].sup.*.sub.t], [X.sup.*.sub.H,t], [X.sup.*.sub.F,t], [X.sup.*.sub.t], [c.sup.*.sub.t], [NW.sup.*.sub.t], [Q.sup.*.sub.t], [R.sup.*k.sub.t], [[psi].sup.*.sub.t], [[bar.[omega]].sup.*.sub.t] which satisfies Equations (3), (4), (8), (12), (13), (15), (17), (20)-(22), (27)-(29), (38), (39), and (41), an equivalent set of equations for the foreign country and Equations (5)-(7), and (14).

The above set of equations summarizes the optimality conditions for the competitive economy allocation of the two countries. In fact, Equations (3)-(5), (8), (12), (13), and (15) are the optimality conditions of the workers' consumption optimization problem in the home country. Equations (17) and (20)-(22) are the optimality conditions of the monopolistic firms' problem in the home country. Equations (27) and (28) are the optimality conditions of the entrepreneurs' consumption/investment optimization problem in the home country. Equations (29), (38), and (39) are the optimality conditions for the loan contract. An equivalent set of equations solves the optimization problems for the agents in the foreign economy. Finally, Equations (5)-(7), (14), (41), and (42) are equilibrium conditions for the world economy.

I. Calibration

The two countries are assumed to be symmetric in preference and technology specifications. Time is taken to be measured in quarters.

Preferences. I set the discount factor [beta] = .99 so that the annual interest rate is equal to 4%. The utility function is separable and takes the following form: U(C)- V(N) = [C.sup.1-[sigma]] / 1 - [sigma] - [N.sup.1+[tau]] / 1 + [tau]. The utility parameters on consumption, [omega], and on labor, x, are set, respectively, equal to 2 and 1. I set the degree of openness at [??] = .2, which is consistent with trade share within European (EU) countries. The elasticity of substitution between domestic and foreign goods [eta] equals to 1.5 as in Backus, Kehoe, and Kydland (1992). Following Schmitt-Grohe and Uribe (2003) and consistently with Lane and Milesi-Ferretti (2003), I set the elasticity of the spread on foreign bonds to the net asset position equal to 0.000742.

Technology. The share of capital in the production functions [alpha] = .35 while the quarterly depreciation rate [delta] = .025. The latter implies an annual depreciation rate of roughly 10%. Following Basu and Fernald (1997), I set the steady-state markup value to 1.2. Loglinearizing the pricing conditions for the monopolistic sector yields a typical Phillips curve. Given the assigned value for the markup and consistently with estimates by Sbordone (1998), I set [[omega].sub.p] = 17.5. The elasticity of the price of capital with respect to investment output ratio is set to 0.5 to generate a volatility of investment higher than the volatility of consumption.

Financial frictions parameters. The financial contract is characterized by three deep parameters that are the volatility of the idiosyncratic shock, [[sigma].sup.2.sub.[omega]], the probability of the firm being alive next period, g, and the monitoring/bankruptcy cost as percentage of bank assets, Ix. Given the values for these parameters, the contract yields the external finance premium in steady state, [[rho].sub.ss], the elasticity of the external finance premium with respect to the leverage ratio, [rho](.), and the business failure rate, F([bar.[omega]]). It is assumed that the idiosyncratic shock is lognormally distributed. The calibration strategy is as follows. I set the survival probability of firms, g, so as to generate a default probability, F([bar.[omega]]), of 5.4% on an annual basis. This value is compatible with earlier studies--that is, Bernanke, Gertler, and Gilchrist (1999) and Carlstrom and Fuerst (1997)--which calibrate this parameter using data for industrialized countries. The external finance premium in steady state is set to 300 basis point, value compatible with industrialized countries, while the elasticity of the same premium to collateral takes a value of 0.05. The volatility of the idiosyncratic shock and the monitoring costs are calibrated indirectly so as to generate the assigned values for the external finance premium.

Monetary policy parameters. I fix the weight on inflation in the Taylor rule at [[bar.[omega]].sub.[pi]] = 1.5. The parameter, [[bar.[omega]].sup.e], is set equal to zero in the floating exchange rate regime and equal to 0.5 in the managed exchange rate regime. Consistently with Clarida, Gali, and Gertler (2000), the interest rate smoothing parameter is set to 0.8.

Exogenous shocks. The monetary policy shock is assumed to be i.i.d, since I assume that any persistence in the short-term interest rate is captured by the interest rate smoothing parameter. I calibrate standard deviation (for the annual interest rate) to 1.007% using data on monetary policy shocks for Germany obtained as estimated residuals of a VAR with the identification scheme employed by Mojon and Peersman (2000). (14)

The productivity shock, [A.sub.t], is an AR(1) and is symmetric in the two countries. To calibrate the latter, I refer to Backus, Kehoe, and Kydland (1992) who using data for EU countries estimate the process for the Solow residual and find an autocorrelation of .906, a standard deviation of 0.00852, and a cross-correlations of .25.

[FIGURE 1 OMITTED]

III. COMPARISON OF EXCHANGE RATE REGIMES UNDER EXTERNAL SHOCKS

As our main goal was to test the insulating property of floating exchange rate, we begin our quantitative assessment by considering foreign shocks. We start by comparing impulse responses, volatilities, and welfare under three alternative exchange rate systems: pure floating; pure fixed; and an intermediate regime, managed floating in which the central banks partly adjust the interest rate in response to exchange rate movements. To appreciate the role played by financial frictions, I will compare the results of the present model with the one without credit frictions. Using a simple welfare measure, I also establish a ranking among the three exchange regimes.

A. Monetary Tightening in the Foreign Country

Figure 1 shows the dynamics of the home country variables in response to a 1% increase in the foreign interest rate, under floating (solid line) and fixed exchange (dashed line) rate regimes. Under fixed exchange rates, almost all macroeconomic variables, with the obvious exception of the exchange rate and the trade balance, show higher persistence and volatility. The external shock generates devaluation pressures in the home economy. The monetary authority reacts by increasing the nominal interest rate. Under sticky prices, the real interest rate also increases. The increase of the real interest rate raises the cost of loans, thereby deteriorating balance sheet conditions. As a consequence, the external finance premium increases, thereby exacerbating the decrease in the demand for loans, investment, and employment. Under floating exchange rates, instead, the effects of the external shock are absorbed by the movements in the exchange rates. The nominal and real interest rates remain almost unchanged as if the economy was perfectly insulated from the foreign monetary tightening.

Table 1 shows standard deviations of several macroeconomic variables--output, investment, asset prices, return on capital, inflation, consumption, and the terms of trade--under three different exchange rate regimes. The standard deviations for all variables (except for the terms of trade) are highest under the fixed exchange rate regime, followed by the managed exchange rate regime and the floating exchange rates.

The ranking identified remains valid for both the model with financial frictions and the model without financial frictions. However, in presence of financial frictions, both the absolute stabilization cost (measured by the standard deviation of the main macroeconomic variables) and the relative stabilization cost (measured by the difference in the standard deviations across regimes) widen. Table 1 shows that all variables are more volatile in presence of financial frictions, independently of the regime considered. Second, for all macroeconomic variables, the difference in the standard deviations between the floating and the fixed exchange rate regime is higher in presence of borrowing constraints on investment. Hence, in this model, and assuming that collective welfare is inversely related to macroeconomic volatility, the relative benefits (costs) of abandoning (joining) a currency peg are higher in presence of financial distortions.

The ranking so far obtained among monetary policy arrangements is confirmed by the comparison of welfare costs. The welfare metric I use is a fraction of steady-state consumption that households would be willing to give up in order to be indifferent between a constant sequence of consumption and working hours and the stochastic sequences of the same variables under the monetary regime considered. (15) The measure is constructed by second-order Taylor approximation of workers' utility: (16)

[upsilon] = - 1/2 [(1 - [[chi].sub.c]Var([[??].sub.t]) + (1 - [[chi].sub.n])Var([[??].sub.t])]

(44)

where Var([[??].sub.t]) and Var ([[??].sub.t]) are the unconditional second moments and [[chi].sub.c] = [U.sub.cc] / [U.sub.c]C, [[chi].sub.n] = - [U.sub.nn] / [U.sub.n]N.

[FIGURE 2 OMITTED]

It is important to note that this welfare metric is intended to capture only first-order effects of volatilities but does not account for the indirect effect of volatilities on mean welfare: this choice does not alter the welfare ranking in the context of the present article as other authors have shown that in presence of financial frictions, alternative welfare matrix tends to reproduce similar ranking. (17) Table 6 shows that welfare costs increase in presence of credit frictions and under fixed exchange rate regimes. Moreover, the increase in the welfare costs observed when moving from fixed to floating is higher in presence of credit frictions.

B. Productivity Decline in the Foreign Country

Figure 2 is analogue to Figure 1 but instead of a monetary tightening assumes a negative technology shock in the foreign country. In the foreign country, a productivity decline induces an increase in marginal costs and inflation. Under both regimes, the international transmission mechanism of a foreign productivity shock is characterized by three effects. First, there is an absorption effect due to which the decrease in foreign output induces a fall in domestic exports. Second, a demand switch from foreign to domestically produced goods caused by the increase in foreign inflation. Since the latter effect is predominant, we observe an increase in domestic exports and inflation. This triggers a tightening in monetary policy for the home country and a nominal and a real appreciation. Under sticky prices, this induces an increase in the real interest rates as well. If the model is augmented with borrowing constraints, the increase in the real interest rate induces an increase in the cost of loans, which reduces investment demand, worsens balance sheet conditions, and raises the external finance premium. The domestic country in this case reacts as if it had imported the productivity slowdown in a way that the real and financial tightening of the foreign country is mirrored domestically. This happens despite the increase in domestic net exports.

As one would intuitively expect, this financial tightening at home is higher under fixed or pegged exchange rates. The impulse response functions show clearly that the recession is much more pronounced under fixed than under floating exchange rate regimes.

Another interesting feature of this case is the overshooting displayed by the impulse response of inflation. Under fixed rates and in response to a productivity shock, the domestic price level is pinned down to the initial level. The initial downward movement of inflation is compensated by the expected, and actual, future overshooting. A Taylor rule, which allows greater monetary policy flexibility, does not deliver this feature of anchoring the domestic nominal variables. In a way, we can interpret this as a credibility gain that the domestic central bank acquires by resorting to an irrevocable fixed exchange rate as a nominal anchor. This outcome rationalizes the choice of high inflation countries (Greece, Italy, and Spain) that joined the EMS with the goal of reducing inflation variability by anchoring the exchange rate to the German deutsche mark, thereby adopting a strategy of importing credibility.

As before, Table 2 shows the volatilities, also comparing the model with and without agency costs. Once again, standard deviations of all macro variables (except the terms of trade) are higher under fixed than under floating exchange rate regimes. Again, the differential increase in standard deviations between the floating and the fixed exchange rate regime is higher in presence of agency costs, except for inflation, where the differential increase remains almost the same under the two regimes. I will return to this when analyzing the "sacrifice ratio" in Section VII.

Finally, Table 6 shows that welfare costs are higher under fixed exchange rates. Moreover, the increase in the welfare costs observed when moving from fixed to floating is higher in presence of credit frictions.

IV. SYMMETRIC AND CORRELATED SHOCKS

In this section, I extend the analysis to consider domestic shocks and shocks in both countries (symmetric and correlated). Though somewhat apart from the main focus of this article, this case is nonetheless of interest because it allows to test robustness of the results. The theory for an optimal currency area generally links the superiority of the floating exchange rate regimes as a stabilization device to the presence of asymmetric shocks. The goal in this section was to explore whether in a model with agency costs the superiority of floating rates is preserved under domestic shocks and symmetric/correlated shocks.

Figure 3 shows the response of the usual set of domestic macroeconomic variables in a model with financial frictions under a negative domestic technology shock. The graphs also compare the responses under floating (solid lines) and fixed (dashed lines) exchange rates. The detrimental effect coming from a worsening of the investment opportunities is higher under floating than under fixed exchange rates. Under floating exchange rates, a negative technology shock at home generates a decrease in the marginal productivity and a consequent increase in the real interest rate and in the cost of loans. This deteriorates the firms' financial conditions, depressing investment demand, and employment. On the contrary, under fixed or managed exchange rates, the monetary authority controls the domestic interest rate in order to stabilize the exchange rate. The reaction of the monetary authority dampens the detrimental effect coming form the decrease in the marginal productivity to investment, thereby smoothing the deflationary effect. In general, all macroeconomic variables seem now more volatile under floating exchange rates.

[FIGURE 3 OMITTED]

Under symmetric and correlated productivity technology shocks (Table 4), floating exchange rates are slightly more destabilizing than managed and fixed exchange rates, the more so with financial frictions. As observed earlier, floating exchange rates tend to be less destabilizing under foreign productivity shocks but more destabilizing under domestic productivity shocks. When the domestic and the foreign productivity shocks are considered in combination, the effect of the domestic shock tends to prevail; hence, floating exchange rates become more destabilizing than fixed exchange rate.

Finally, I consider symmetric and correlated monetary policy shocks. Table 3 shows that, for the case with financial frictions, standard deviations of all macroeconomic variables (except terms of trade) are almost the same under floating exchange rates and under fixed exchange rates. The reason is once again related to the fact that floating exchange rates are more destabilizing than fixed under domestic shocks and vice versa under foreign shocks. When we consider the combination of those two shocks, the opposite effects tend to balance each other.

V. EXCHANGE RATE INDEXATION OF DEBT DOES NOT CHANGE THE RESULTS

A frequent experience of countries pegging their exchange rate systems is the proliferation of debt denominated in foreign currency. Currently, all accession countries belonging to the ERM II agreement experienced a strong wave of capital inflows from the euro zone, and residents of those countries are increasing the fraction of their asset portfolio denominated in euros. In this case, a system of floating exchange rates might be destabilizing as much as a system of fixed exchange rates but for a different reason. Under external shocks and if loans are denominated in foreign currency, allowing for exchange rate devaluations increases the domestic currency cost of servicing the debt, hence worsening the firms' balance sheet conditions. Depending on the fraction of loans denominated in foreign currency, a floating exchange rate might become more destabilizing than a fixed one.

To test this hypothesis, I repeated some of the previous experiments (negative productivity and monetary policy shocks in the foreign country) by assuming that all debt is denominated in foreign currency. The volatility of output and investment (18) in this case are slightly higher under floating exchange rates, but they remain below the one under fixed exchange rate (which did not change significantly).

The key reason for this is that a depreciation does not change significantly the overall value of balance sheets. For example, consider the effect of a foreign monetary policy shock. Under floating exchange rates, this induces a depreciation of the domestic currency. With liabilities denominated in foreign currency, this channel produces a decrease in net worth. However, there are also positive consequences from the asset side of firms' balance sheets: since the depreciation makes domestic goods cheaper, export revenue rises, creating a positive impact on net worth. If the two effects compensate each other, the overall impact of the depreciation need not be contractionary.

VI. SHOCKS TO THE UNCOVERED INTEREST RATE PARITY

At last, I consider shocks to the uncovered interest rate parity. Those shocks play an important role for two reasons. First, there is much evidence that the uncovered interest rate parity does not hold because of exogenous shocks that affect the exchange rate itself. Second, such source of volatility could in principle tilt the balance in favor of pegs, and against floating as in the latter case, the additional exchange rate volatility might destabilize consumption and consequently output. Following Kollmann (2004), this shock has been calibrated using a data sample that cover the period 1971-1998 and by regressing the deviation from the uncovered interest parity (UIP) over a four lags for the Gross Domestic Product and the interest rate for some pairs of industrialized countries. The estimation results give a standard for this type of shocks around 4.4%. There is no significant degree of persistence for this shock.

Table 5 shows volatilities of selected variables in the model with and without financial frictions and under alternative exchange rate regimes. Results show once more that fixed exchange rates are more destabilizing than floating exchange rates both in the case with financial frictions and in the case without. As usual, in presence of financial frictions, volatilities are higher under all regimes. It is worth noting that in absence of financial frictions, managed exchange rates perform better than floating exchange rates: this is so as some degree of exchange rate stabilization allows the policy maker to optimize the trade-off between improving consumption smoothing and maintaining monetary policy independence.

VII. SUMMARY OF RESULTS AND THE SACRIFICE RATIO

Table 8 summarizes the results found until now. The table reports in every box two statistics: the first is the ratio of output volatility under fix over the one under floating exchange rate and the second is the corresponding welfare ratio. The statistics are shown for both the case with financial friction and the case without. We see that for both types of foreign shocks, those ratios raise under financial frictions, while they decrease (or do not change significantly) for symmetric and correlated shocks. This shows once more that in presence of financial frictions, the superiority of floating exchange rates depends on whether we consider asymmetric or symmetric shocks.

Before concluding, it is worth analyzing a synthetic measure of monetary policy tradeoffs across different scenarios and exchange rate regimes. We focus on the sacrifice ratios. An interesting feature that emerges from the analysis is that fixed exchange rates tend to destabilize real and financial variables much more than inflation. And this is even more so when we add credit frictions. This effect is emblematic of the trade-off faced by monetary policy between output and inflation stabilization. In the standard open macroeconomic models, it is emphasized that the severity of such trade-off is amplified in presence of supply side shocks. In this section, I show that fixed exchange rates and borrowing constraints on investment are also factors that contribute to aggravate this trade-off.

Table 7 compares a measure of sacrifice ratio (the output-inflation volatility ratio) implied by the model under different regimes and in the model with and without credit frictions. The sacrifice ratio is the most commonly used measure of the trade-off between output and inflation stabilization. Higher values for this statistics imply steeper trade-off since the monetary authority needs to generate more output volatility to stabilize inflation. The table shows clearly that the sacrifice ratio becomes higher under fixed exchange rates and in presence of credit frictions. Moreover, the increase in the sacrifice ratio observed when moving from floating to fixed exchange rates is higher in presence of credit frictions. This is true for all shocks with the exception given by the symmetric and correlated productivity shocks. In the latter case, indeed, the presence of domestic shocks tends to lessen the trade-off.

VIII. CONCLUSIONS

The traditional theory of the optimal currency area argues for the superiority of floating exchange rate regimes as a stabilization device mostly in the presence of asymmetric shocks. This article shows that the presence of credit frictions strengthens the case for floating exchange rate regimes and also tends to exacerbate the typical output-inflation trade-off. The policy implication is that if currency pegs are adopted to stabilize domestic inflation then this is likely to come at the cost of significantly higher output volatility. This is even more so in presence of credit frictions.

The treatment of the fixed exchange rates case in this article only applies to a situation where the regime is fully credible. In fact, a foreign exchange peg may be characterized by less-than-full credibility. Analyzing the latter case would require a different model for expectations, something I leave to future research.

ABBREVIATIONS

CPI: Consumer Price Index

DSGE: Dynamic Stochastic General Equilibrium

ECB: European Central Bank

EMS: European Monetary System

EMU: European Monetary Union

ERM II: European Exchange Rate Mechanism II

EU: European

GDP: Gross Domestic Product

doi: 10.1111/j.1465-7295.2009.00231.x

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(1.) As of May 1, 2004, the ten national central banks of the new member countries became party to the ERM II Central Bank Agreement. EU countries that have not adopted the euro are expected to participate for at least 2 yr in the ERM II before joining the euro zone.

(2.) See among many others, Chari, Kehoe, and McGrattan (2002).

(3.) In this respect, I follow the structure proposed in the closed economy by Carlstrom and Fuerst (1997) and Bernanke, Gertler, and Gilchrist (1999), which assumes heterogeneity between borrowers and lenders and formalizes a costly state verification contract in the general equilibrium.

(4.) See Bernanke, Gertler, and Gilchrist (1999), Carlstrom and Fuerst (1997), and Kiyotaki and Moore (1997).

(5.) See Obstfeld and Rogoff (1995) and Corsetti and Pesenti (2001) as first contribution in the new open economy literature, known as NOEM. For an exposition of the main characteristics and developments of the NOEM model, see Corsetti (2007), New Palgrave Dictionary.

(6.) See Cespedes, Chang, and Velasco (2004) and Gertler, Gilchrist, and Natalucci (2007).

(7.) Faia (2007a, 2007b).

(8.) Let [s.sup.t] = {[s.sub.0],...., [s.sub.t]} denote the history of events up to date t, where [s.sub.t] denotes the event realization at date t. The date 0 probability of observing history [s.sup.t] is given by [rho]([s.sup.t]). The initial state so is given so that [rho]([s.sup.0]) = 1. Henceforth, and for the sake of simplifying the notation, let us definethe operator [E.sup.t]{.} [equivalent to] [summation][s.sub.t+1] [rho]([s.sup.t+1]|[s.sup.t]) as the mathematical expectations over all possible states of nature conditional on history [s.sup.t].

(9.) As shown in Schmitt-Grohe and Uribe (2003) and Benigno (2002), this assumption is useful in order to maintain the stationarity of consumption in the model. Note however that Schmitt-Grohe and Uribe (2003) have shown that such friction does not alter significantly the dynamic of the open economy compared to the complete market case and to alternative setting for the incomplete market case.

(10.) Note that [mc.sub.t] plays the role of the real marginal cost of production.

(11.) See also Kiyotaki and Moore (1997) and Carlstrom and Fuerst (1997).

(12.) As in Bernanke, Gertler, and Gilchrist (1999), I restrict attention to one-period contracts, which are not necessarily optimal in the dynamic setting. See Monnet and Quintin (2005).

(13.) The specific form of this relation depends on assumptions on the probability distribution of shocks. Necessary and sufficient conditions for the uniqueness of the solution for the cutoff value, [bar.[omega]], require a probability distribution featuring a decreasing hazard rate--that is, a uniform or a lognormal. Here, I assume a lognormal distribution.

(14.) Mojon and Peersman (2000) analyze the effects of monetary policy shocks in 10 countries of the euro area for the pre-European Monetary Union (EMU) period. For each country, the identification scheme imposed depends on the monetary integration with Germany and the nominal anchor to the EMS.

(15.) See also Lucas (1987).

(16.) Since entrepreneurs have a linear utility, they do not suffer from variability of the business cycle.

(17.) See Devereux, Lane, and Xu (2006) and Faia and Monacelli (2007).

(18.) Results not reported here for brevity but available upon request.

ESTER FAIA,I thank Ignazio Angeloni, William Baumol, Pierpaolo Benigno, Thomas Cooley, Carsten Detken, Gunter Coenen, Mark Gertler, Philipp Hartmann, Tommaso Monacelli, and Frank Smets for useful discussions. I thank seminar participants at the European Central Bank, New York University, Ente Einaudi, 2001 SED Conference in Stockholm, 2001 EEA Conference in Lausanne, and 2001 MMF Conference in Belfast. I gratefully acknowledge financial support from the Dynamic Stochastic General Equilibrium (DSGE) model grant of the Spanish Ministry of Education and the Unicredit research grant. This article has been previously circulated as European Central Bank (ECB) w.p. Number 56 in April 2001. All errors are mine.

Faia: Chair in Monetary and Fiscal Policy, Department of Money and Macroeconomics, House of Finance, Goethe University Frankfurt, Campus Westend, Grueneburgplatz 1, Frankfurt 60323, Germany. E-mail faia@wiwi.unifrankfurt.de; Kiel Institute for the World Economy; and CEPREMAP.
TABLE 1
Foreign Monetary Policy Shock

Exchange
Rate Regime Floating Exchange Rates

Variables [rho](.) = 0 [rho](.) = .05

Output 0.15 0.14
Investment 0.18 0.39
Asset prices 0.17 0.26
Return on capital 0.16 0.22
CPI inflation 0.15 0.14
Consumption 0.11 0.18
Terms of trade 0.67 0.81

Exchange
Rate Regime Fixed Exchange Rates

Variables [rho](.) = 0 [rho](.) = .05

Output 0.46 1.09
Investment 0.91 4.32
Asset prices 0.87 2.23
Return on capital 0.87 1.51
CPI inflation 0.32 0.40
Consumption 0.42 0.65
Terms of trade 0.00 0.02

Exchange
Rate Regime Managed Exchange Rates

Variables [rho](.) = 0 [rho](.) = .05

Output 0.20 0.60
Investment 0.68 2.50
Asset prices 0.55 1.30
Return on capital 0.49 0.84
CPI inflation 0.23 0.30
Consumption 0.27 0.42
Terms of trade 0.03 0.04

Notes: Standard deviations of selected macroeconomic variables
under different regimes with financial frictions, [rho](.) = 0.05,
and without, [rho](.) = 0. All values are in percentage.

TABLE 2
Foreign Productivity Shock

 Floating Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.20 0.12
Investment 0.59 1.04
Asset prices 0.33 0.54
Return on capital 0.25 0.34
CPI inflation 0.14 0.11
Consumption 0.49 0.50
Terms of trade 1.80 1.81

 Fixed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.33 0.56
Investment 0.84 3.10
Asset prices 0.64 1.57
Return on capital 0.59 0.98
CPI inflation 0.26 0.21
Consumption 0.58 0.69
Terms of trade 1.64 1.62

 Managed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.20 0.26
Investment 0.78 1.90
Asset prices 0.50 1.03
Return on capital 0.39 0.61
CPI inflation 0.23 0.18
Consumption 0.55 0.60
Terms of trade 1.69 1.71

Notes: Standard deviations of selected macroeconomic variables under
different regimes with financial frictions, [rho](.) = 0.05, and
without, [rho](.) = 0. All values are in percentage.

TABLE 3
Home and Foreign Monetary Policy Shock (Symmetric and Correlated)

 Floating Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.58 1.10
Investment 0.80 4.06
Asset prices 0.76 2.07
Return on capital 0.78 1.37
CPI inflation 0.42 0.46
Consumption 0.36 0.56
Terms of trade 0.79 0.96

 Fixed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.46 1.09
Investment 0.91 4.03
Asset prices 0.87 2.23
Return on capital 0.87 1.51
CPI inflation 0.32 0.40
Consumption 0.42 0.65
Terms of trade 0.00 0.02

 Managed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.39 0.89
Investment 0.79 3.50
Asset prices 0.72 1.81
Return on capital 0.71 1.22
CPI inflation 0.30 0.33
Consumption 0.35 0.54
Terms of trade 0.41 0.48

Notes: Standard deviations of selected macroeconomic variables under
different regimes with financial frictions, [rho](.) = 0.05, and
without, [rho](.) = 0. All values are in percentage.

TABLE 4
Home and Foreign Productivity Shocks (Symmetric and Correlated)

 Floating Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 2.06 2.30
Investment 2.88 4.60
Asset prices 1.36 2.00
Return on capital 0.59 0.89
CPI Inflation 0.28 0.24
Consumption 1.20 1.20
Terms of trade 2.54 2.50

 Fixed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 1.94 1.95
Investment 2.86 3.90
Asset prices 1.33 1.80
Return on capital 0.64 1.00
CPI Inflation 0.37 0.34
Consumption 1.18 1.23
Terms of trade 2.31 2.29

 Managed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 1.06 2.10
Investment 2.83 4.05
Asset prices 1.31 1.86
Return on capital 0.55 0.82
CPI Inflation 0.32 0.28
Consumption 1.18 1.21
Terms of trade 2.39 2.41

Notes: Standard deviations of selected macroeconomic variables under
different regimes with financial frictions, [rho](.) = 0.05, and
financial frictions, [rho](.) = 0. All values are in percentage.

TABLE 5
Shocks to the Uncovered Interest Rate Parity

 Floating Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 1.18 1.40
Investment 0.66 2.91
Asset prices 1.10 1.88
Return on capital 1.72 2.06
CPI inflation 0.87 0.88
Consumption 0.64 0.64
Terms of trade 2.90 3.14

 Fixed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.81 0.85
Investment 1.00 1.31
Asset prices 0.56 0.71
Return on capital 0.54 0.58
CPI inflation 0.54 0.57
Consumption 0.28 0.30
Terms of trade 1.63 1.69

 Managed Exchange Rates
Exchange Rate Regime
Variables [rho](.) = 0 [rho](.) = .05

Output 0.41 2.10
Investment 0.28 8.58
Asset prices 1.94 4.55
Return on capital 2.66 3.74
CPI inflation 0.48 0.52
Consumption 0.97 1.23
Terms of trade 2.07 2.76

Notes: Standard deviations of selected macroeconomic variables under
different regimes with financial frictions, [rho](.) = 0.05, and
financial frictions, [rho](.) = 0. All values are in percentage.

TABLE 6
Welfare Costs (Percentage Units of Steady-State Consumption) Across
Different Exchange Rate Regimes, Under Different Shocks, with and
without Financial Frictions

 Floating Exchange Rates

Type of Shock [rho](.) = 0 [rho](.) = 0.05

Foreign monetary policy shock 0.19 0.14
Symmetric and correlated monetary 0.71 0.81
 policy shocks
Foreign productivity shock 0.15 0.10
Symmetric and correlated productivity 0.22 0.14

 Fixed Exchange Rates

Type of Shock [rho](.) = 0 [rho](.) = 0.05

Foreign monetary policy shock 0.48 0.70
Symmetric and correlated monetary 0.48 0.70
 policy shocks
Foreign productivity shock 0.27 0.23
Symmetric and correlated productivity 0.67 0.65
 shocks

TABLE 7
Sacrifice Ratios (Output-Inflation Volatility Ratios) Implied by the
Model Under Different Exchange Rate Regimes in the Models with and
without Financial Frictions

 Floating Exchange Rates

Type of Shock [rho](.) = 0 [rho](.) = 0.05

Foreign monetary policy shock 1.05 1.01
Symmetric and correlated monetary 1.39 2.37
 policy shocks
Foreign productivity shock 1.47 1.11
Symmetric and correlated 7.14 9.62
 productivity shocks

 Fixed Exchange Rates

Type of Shock [rho](.) = 0 [rho](.) = 0.05

Foreign monetary policy shock 1.43 2.72
Symmetric and correlated monetary 1.43 2.72
 policy shocks
Foreign productivity shock 1.23 2.57
Symmetric and correlated 5.14 5.72
 productivity shocks

TABLE 8
Summary of Results

Type of Shock [rho](.) = 0 [rho](.) = 0.05

Foreign monetary policy shock 3.06; 2.52 7.78; 5.00
Foreign productivity shock 1.65; 2.6 4.66; 5.05
Symmetric and correlated 0.79; 0.67 0.99; 0.86
 monetary policy shocks
Symmetric and correlated 0.94; 0.68 0.84; 0.86
 productivity shocks

Notes: First entry in each box is the [[sigma].sub.y]
(fix)/[[sigma].sub.y] (flex). Second entry is welfare(fix)/
welfare(flex).
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Author:Faia, Ester
Publication:Economic Inquiry
Geographic Code:4E
Date:Oct 1, 2010
Words:11492
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