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CAPITAL CONTROLS, MONETARY POLICY, AND BALANCE SHEETS IN A SMALL OPEN ECONOMY.

I. INTRODUCTION

Although capital controls are not a new policy instrument, it is not until the recent global financial crisis that the potential effects of capital control policies have been rigorously examined from the theoretical perspective as one of the most important topics in international finance. (1) Given the recent financial crisis, volatile international capital movements in emerging market economies have been the subject of rigorous discussion among concerned policymakers and economists. Volatile capital flows amplify boom-bust cycles and destabilize emerging market economies. The recent global financial crisis led to a reconsideration of the merits of capital account restrictions. An increasing number of policymakers believe that capital controls can effectively stabilize economies against volatile capital flows. In fact, some emerging market countries have recently responded to instability by imposing capital controls. (2) As well known, even the International Monetary Fund (IMF), a former critic of capital controls, has been forced to reconsider such measures as an important policy response to volatile capital flows under certain circumstances. (3)

Against this background, there has emerged a rapidly growing body of literature related to capital controls. (4) Jeanne and Korinek (2010) and Bianchi (2011) showed that there are pecuniary externalities associated with financial crises and provide a rationale for prudential capital controls. Using a two-country model, Brunnermeier and Sannikov (2014) showed that pecuniary externalities can lead to constrained inefficient outcomes and capital controls can be welfare improving. (5)

In recent years, an increasing number of studies examine the effects of capital controls as a regular instrument of economic policy from a broader perspective (e.g., De Paoli and Lipinska 2013; Farhi and Werning 2012; Kitano and Takaku 2017c; Schmitt-Grohe and Uribe 2016). (6,7) For example, Kitano and Takaku (2017a) show that as the degree of financial frictions between banks and foreign creditors increases, more aggressive capital controls are appropriate.

Another strand of the literature focuses the relationship between capital controls and various types of monetary policies (Agenor and Jia 2015; Chang, Liu, and Spiegel 2015; Davis and Presno 2014; Liu and Spiegel 2015). For example, Kitano and Takaku (2017b) show that capital controls can play an alternative role to the direct credit policy in mitigating the contraction after a crisis.

Our paper is most closely related to De Paoli and Lipinska (2013), Davis and Presno (2014), and Liu and Spiegel (2015) in that we too apply a Ramsey-type analysis for capital controls. However, we examine optimal capital controls in models that highlight balance sheet effects in the presence of liability dollarization. (8) Therefore, our paper is also rather closely related to Cespedes, Chang, and Velasco (2004), Devereux, Lane, and Xu (2006), and Elekdag and Tchakarov (2007). Building upon the framework developed by Bernanke, Gertler, and Gilchrist (1999), Cespedes, Chang, and Velasco (2004), Devereux, Lane, and Xu (2006), and Elekdag and Tchakarov (2007) incorporated a financial accelerator coupled with liability dollarization, in which foreign debt is denominated in foreign currency (not domestic currency). In these models, the financial accelerator works through an endogenous risk premium that is linked to the balance sheets of entrepreneurs. These balance sheets are also vulnerable to exchange rate fluctuations owing to the problem of liability dollarization.

Cespedes, Chang, and Velasco (2004) and Devereux, Lane, and Xu (2006) found that the conventional wisdom, that the flexible exchange rate is preferable to the fixed exchange rate, holds in spite of the financial accelerator effects. Elekdag and Tchakarov (2007) also confirmed that the flexible exchange rate regime has better welfare properties than the fixed exchange rate regime when the country has perfect access to international capital markets. However, when their model incorporates a financial accelerator and the leverage ratio exceeds a threshold, they find that the fixed exchange rate regime could become welfare superior.

We develop a small open economy, New Keynesian model with and without a financial accelerator mechanism, the model structure of which is basically similar to Cespedes, Chang, and Velasco (2004), Devereux, Lane, and Xu (2006), and Elekdag and Tchakarov (2007). We then apply a Ramsey-type analysis and examine the welfare implications of capital control policies.

In the case without the financial accelerator, we compare three cases: optimal monetary policy under flexible exchange rates, optimal capital control policy (on households) under fixed exchange rates, and fixed exchange rates (without capital controls). Our Ramsey-type analysis results indicate that although the optimal capital control policy significantly improves welfare under fixed exchange rates, the optimal monetary policy is the most welfare-maximizing in an economy without the financial accelerator.

In the case with the financial accelerator, we compare the following five cases: an optimal monetary policy under flexible exchange rates, fixed exchange rates (without capital controls), an optimal capital control policy on entrepreneurs, an optimal capital control policy on households, and an optimal capital control policy on both entrepreneurs and households under fixed exchange rates. Our analysis results indicate that the optimal monetary policy still outperforms the optimal capital control policy on households. However, the optimal capital control policy on entrepreneurs outperforms the optimal monetary policy. The most welfare-maximizing is the optimal capital control policy on both entrepreneurs and households.

The intuition underlying our analysis results is straightforward. Entrepreneurs finance investment partly with foreign borrowing, which is subject to financial frictions in the presence of balance sheet vulnerabilities. In an economy with a financial accelerator, the key variable is the foreign interest rate augmented by an external finance premium. Monetary policy works only through domestic interest rates. However, capital controls on entrepreneurs have a direct control on the key variable of interest rates at which entrepreneurs borrow abroad. Therefore, capital controls can be welfare improving in an economy with financial frictions.

The remainder of the paper is organized as follows. In Section II, we present a sticky price, small open economy model with and without a financial accelerator in combination with liability dollarization. In Section III, we perform a comparative analysis of welfare for alternative policy regimes in this economy. For the economy without the financial accelerator, we compare (1) the flexible exchange rate regime accompanied by an optimal monetary policy, (2) the fixed exchange rate regime accompanied by optimal capital controls on households, and (3) the fixed exchange rate regime (without capital controls). For the economy with the financial accelerator, we compare (1) the fixed exchange rate regime accompanied by optimal capital controls on households and entrepreneurs, (2) the fixed exchange rate regime accompanied by optimal capital controls on entrepreneurs, (3) the flexible exchange rate regime accompanied by an optimal monetary policy, (4) the fixed exchange rate regime accompanied by optimal capital controls on households, and (5) the fixed exchange rate regime (without capital controls). In Section IV, we check the robustness of our results. In the previous section, we show the welfare rankings for three shocks together: productivity shock, export shock, and foreign interest rate shock. In this section, we show that our results are robust even when we consider these shocks individually. Conclusions are presented in Section V.

II. MODEL

We employ the small open economy structure developed by Gali and Monacelli (2005) and Faia and Monacelli (2008). We incorporate the financial accelerator a la Bernanke, Gertler, and Gilchrist (1999) into the small open economy model in combination with liability dollarization. Our model is close to those in Cespedes, Chang, and Velasco (2004), Devereux, Lane, and Xu (2006), and Elekdag and Tchakarov (2007). The small open economy consists of households, production firms, entrepreneurs, and the government.

A. Households

A representative household maximizes its expected lifetime utility:

(1) [E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t] {[C.sup.1-[sigma].sub.t]/(1 - [sigma]) - [L.sup.1+[phi].sub.t]/(1 + [phi])},

where [E.sub.t] denotes the mathematical expectations operator conditional on information available at time t, [beta] [member of] (0, 1) is the discount factor, [C.sub.t] signifies a composite consumption index, and [L.sub.t] represents labor effort. Households consume differentiated goods (produced by both domestic and foreign firms). The composite consumption index [C.sub.t] is given by

(2) [mathematical expression not reproducible].

[eta](> 0) is the elasticity of substitution between domestic and foreign goods, and [gamma] [member of] (0, 1) represents the measure of openness. [C.sub.H,t] and [C.sub.F,t] are, respectively, the indices for consumption of domestic and foreign goods, expressed by

(3) [mathematical expression not reproducible],

where [epsilon](> 1) is the parameter for the elasticity of substitution among differentiated goods. A household's optimal expenditure allocation in each goods category yields the demand functions for domestic and foreign differentiated goods:

(4) [C.sub.H,t] (j) = [([P.sub.H,t] (j)/[P.sub.H,t]).sup.-[epsilon]] [C.sub.H,t]; [C.sub.F,t] (j) = [([P.sub.F,t] (j)/[P.sub.F,t]).sup.-[epsilon]] [C.sub.F,t],

where [P.sub.H,t] (j) and [P.sub.F,t] (j) denote the domestic-currency-denominated prices of differentiated goods j produced by domestic and foreign firms, respectively. [P.sub.H,t] and [P.sub.F,t] are the domestic and import price indices, respectively:

(5) [P.sub.H,t] [equivalent to] [[[integral].sup.1.sub.0] [P.sub.H,t][(j).sup.1-[epsilon]] dj].sup.1/1-[epsilon]]; [P.sub.F,t] [equivalent to] [[[integral].sup.1.sub.0] [P.sub.F,t][(j).sup.1-[epsilon]] dj].sup.1/1-[epsilon]].

From Equation (5), we obtain

(6) [[integral].sup.1.sub.0] [P.sub.H,t] (j) [C.sub.H,t] (j) dj = [P.sub.H,t] [C.sub.H,t]; [[integral].sup.1.sub.0] [P.sub.F,t] (j) [C.sub.F,t] (j) dj = [P.sub.F,t] [C.sub.F,t].

The optimal expenditure allocation between domestic and imported goods gives

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

where [P.sub.t] represents the consumer price index (CPI):

(8) [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]].

From Equations (7) and (8), we obtain

(9) [P.sub.H,t] [C.sub.H,t] + [P.sub.F,t] [C.sub.F,t] = [P.sub.t][C.sub.t].

Households have access to domestic and international financial markets. A household's budget constraint in period t is given as

(10) [mathematical expression not reproducible].

Herein, [A.sub.t] is the domestic currency debt position, [B.sub.t] is the foreign currency debt position, [i.sub.t] is the interest rate of domestic currency assets, [i.sup.*.sub.t] is the interest rate of foreign currency assets, and [E.sub.t] is the nominal exchange rate (in terms of the domestic currency). (9) [W.sub.t] is the nominal wage, [[PI].sup.F.sub.t] is dividends from firms, [[tau].sub.h,t] is the tax on the foreign currency debt of households, and [T.sub.h,t] is the lump-sum transfer. [P.sub.t][[psi].sub.B][([B.sub.t] - B).sup.2]/2 is the portfolio adjustment costs, which induce the stationarity of the equilibrium dynamics in the small open economy. (10)

The households' optimality conditions are given by

(11) [[lambda].sup.h.sub.t] = [C.sup.-[sigma].sub.t],

(12) [[lambda].sup.h.sub.t] = [L.sup.[phi].sub.t]/([W.sub.t]/[P.sub.t]),

(13) 1 = [beta](1 + [i.sub.t])[E.sub.t]{([[lambda].sup.h.sub.t+1]/[[lambda].sup.h.sub.t])([P.sub.t]/[P.sub.t+1])}, and

(14) [mathematical expression not reproducible]

Combining (13) and (14) yields the interest parity condition:

(15) [mathematical expression not reproducible]

Since we assume that the law of one price holds for individual goods, the terms of trade are given as

(16) [S.sub.t] [equivalent to] [P.sub.F,t]/[P.sub.H,t] = [E.sub.t][P.sup.*.sub.t]/[P.sub.H,t],

where [P.sup.*.sub.t] denotes the CPI in the foreign country (in terms of foreign currency). (11) It follows from (16) that

(17) [S.sub.t]/[S.sub.t-1] - [DELTA][E.sub.t]/[[PI].sub.H,t],

where [DELTA][E.sub.t]([equivalent to][E.sub.t]/[E.sub.t-1]) and [[PI].sub.H,t] ([equivalent to][P.sub.H,t]/[P.sub.H,t-1]) denote the depreciation rate of the nominal exchange rate and the rate of domestic inflation, respectively. It follows from CPI (8) and (16) that

(18) [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]).

From (18), CPI inflation [[PI].sub.t]([equivalent to][P.sub.t]/[P.sub.t-1]) is expressed as

(19) [[PI].sub.t] = [[PI].sub.H,t] (g ([S.sub.t])/g ([S.sub.t-1])).

From (16) and (18), we obtain the real-exchange rate [q.sub.t] as the function of [S.sub.t]:

(20) [q.sub.t] [equivalent to] [E.sub.t][P.sup.*.sub.t]/[P.sub.t] = [S.sub.t]/g ([S.sub.t]) [equivalent to] q ([S.sub.t]).

B. Production Firms

Monopolistically competitive firms produce differentiated goods by using capital and labor. Each monopolistic firm j in the home economy produces a differentiated good. The firm's production function is given by

(21) [Y.sub.t] (j) = [Z.sub.t][K.sub.t] [(j).sup.[alpha]] [L.sub.t] [(j).sup.1-[alpha]],

where [Y.sub.t](j), [K.sub.t](j), [L.sub.t](j), and [Z.sub.t] denote the firm's output level, its capital and labor inputs, and a stochastic productivity shock, respectively.

From the first-order conditions associated with the firm's cost minimization problem, we obtain

(22) (1 - [alpha]) ([R.sub.t]/[P.sub.H,t]) [K.sub.t] (j) = [alpha] ([W.sub.t]/[P.sub.H,t]) [N.sub.t] (j),

where [R.sub.t] is the rental rate of capital. The firm's cost minimization implies that the firm's real marginal cost is given by

(23) [MC.sub.t] (j) = [MC.sub.t] = [([R.sub.t]/[P.sub.H,t]).sup.[alpha]] [([W.sub.t]/[P.sub.H,t]).sup.1-[alpha]]/[Z.sub.t] [[alpha].sup.[alpha]] [(1 - [alpha]).sup.1-[alpha]]

The capital accumulation process in the economy is given as

(24) [K.sub.t+1] = [([I.sub.t]/[K.sub.t]) - ([[phi].sub.I]/2) [([I.sub.t]/[K.sub.t] - [delta]).sup.2]] [K.sub.t] + (1 - [delta])[K.sub.t],

where [I.sub.t] is aggregate investment and [delta] is the depreciation rate of capital. ([[phi].sub.I]/2)[(([I.sub.t]/[K.sub.t]) - [delta]).sup.2] [K.sub.t] denotes the adjustment costs of capital, and [[phi].sub.I] is its parameter value. (12) [I.sub.t] is composed of domestic and imported goods:

(25) [mathematical expression not reproducible]

where [I.sub.H,t] and [I.sub.F,t] are represented by

(26) [mathematical expression not reproducible]

From the optimal allocation of expenditure in each goods category, we obtain the following demand functions:

(27) [I.sub.H,t] (j) = [([P.sub.H,t] (j)/[P.sub.H,t]).sup.-[epsilon]] [I.sub.H,t]; [I.sub.F,t] (j) = [([P.sub.F,t] (j) / [P.sub.F,t]).sup.-[epsilon]] [I.sub.F,t].

The optimal allocation of expenditures between domestic and imported goods yields

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

From the profit-maximization problem of capital producers, we can obtain the (nominal) price of capital [Q.sub.t]:

(29) [Q.sub.t] = [P.sub.H,t] [[1 - [[phi].sub.I] (([I.sub.t]/[K.sub.t]) - [delta])].sup.-1].

C. Price Setting

Following Calvo (1983), we assume that in each period, a fraction 1 - [zeta] of monopolistically competitive firms change their prices, whereas a fraction [zeta] do not change their prices. This implies that we can express the domestic price index as

(30) [P.sub.H,t] [equivalent to] [[[zeta][P.sup.1-[epsilon].sub.H,t-1] + (1 - [zeta]) [[bar.P].sup.1-[epsilon].sub.H,t].sup.1/1-[epsilon]],

where [[bar.P].sub.H,t] denotes the price reset in period t. From (30), we obtain

(31) 1 - [zeta][[PI].sup.-1+[epsilon].sub.H,t] + (1 - [zeta]) [[??].sup.1-[epsilon].sub.H,t],

where [[??].sub.H,t] [equivalent to] [[bar.P].sub.H,t]/[P.sub.H,t]

Each firm resets its price to maximize the present discounted value of its profit stream:

(32)

[mathematical expression not reproducible]

subject to

(33) [Y.sub.t+k|t] = [([[bar.P].sub.H,t]/[P.sub.H,t+k]).sup.-[epsilon]] [Y.sub.t+k],

where [Y.sub.t+k|t] and [MC.sup.n.sub.t+k|t] represent the output level and the nominal marginal cost, respectively, in t + k for a firm that last reset its price in period t. [[LAMBDA].sub.t,t+k] [equivalent to] [[beta].sup.k] ([[lambda].sup.h.sub.t+k]/[[lambda].sup.h.sub.t]) ([P.sub.t]/[P.sub.t+k]) is the discount factor. [Y.sub.t+k] is the aggregate output level in period t + k. From the first-order condition associated with the above problem, we obtain the optimal price:

(34) [mathematical expression not reproducible]

which can be rewritten as

(35) [[??].sub.H,t] = ([epsilon]/([epsilon] - 1)) ([X.sup.1.sub.t]/[X.sup.2.sub.t]),

where

(36) [X.sup.1.sub.t] = [Y.sub.t] [MC.sub.t] + [zeta][E.sub.t] {[[LAMBDA].sub.t,t+1] [[PI].sup.[epsilon]+1.sub.H,t+1] [X.sup.1.sub.t+1]},

and

(37) [X.sup.2.sub.t] = [Y.sub.t] + [zeta][E.sub.t] {[[LAMBDA].sub.t,t+1] [[PI].sup.[epsilon].sub.H,t+1] [X.sup.2.sub.t+1]}.

D. Entrepreneurs

Entrepreneurs have available net worth [N.sub.t] denominated in domestic currency. To finance the difference between their expenditures on capital goods and their net worth, entrepreneurs borrow from foreign lenders. That is, the entrepreneur finances investment partly with foreign currency denominated debt. The entrepreneur's balance sheet is therefore given by

(38) [P.sub.H,t] [N.sub.t] = [Q.sub.t][K.sub.t+1] - [E.sub.t][D.sub.t],

where [D.sub.t] is the entrepreneur's foreign currency debt position. Note that an unanticipated depreciation reduces net worth in the balance sheet (38), which reflects the problem of liability dollarization in emerging market economies.

Following Bernanke, Gertler, and Gilchrist (1999), we assume that foreign lenders charge an external finance premium to entrepreneurs owing to asymmetric information. Entrepreneurs choose [D.sub.t] and [K.sub.t+1] so that the expected return on capital ([R.sup.K]) equals the cost of foreign borrowing:

(39) [R.sup.K.sub.t+1] = (1 + [[tau].sub.e,t])(1 + [i.sup.*.sub.t])([E.sub.t+1]/[E.sub.t]) [F.sub.t],

where [F.sub.t] is the external finance premium and [[tau].sub.e,t] is a tax on the entrepreneur's foreign borrowing. Following Cespedes, Chang, and Velasco (2004), we assume that the external finance premium is an increasing function of the value of capital relative to net worth:

(40) [F.sub.t] = [PSI] [[Q.sub.t][K.sub.t+1]/[P.sub.H,t][N.sub.t]), [PSI] (1) = 1, [PSI]' (*) > 1,

where the functional form for [PSI] is given by [PSI](g) = [g.sup.[mu]] ([mu] > 0). (13)

At the beginning of each period, entrepreneurs collect returns from capital and repay their foreign debt. Following Cespedes, Chang, and Velasco (2004) and Elekdag and Tchakarov (2007), we assume that entrepreneurs consume a fraction 1-[omega] of the remainder on imports. The evolution of net worth is thus given as

(41) [P.sub.H,t] [N.sub.t] = [omega][[R.sup.K.sub.t] [Q.sub.t-1] [K.sub.t] - (1 + [[tau].sub.e,t-1]) (1 + [i.sup.*.sub.t-1])[F.sub.t-1][E.sub.t][D.sub.t-1] + [T.sub.e,t]],

where [T.sub.e,t] denotes a lump-sum transfer from the government.

Finally, the return on capital for entrepreneurs [R.sup.K.sub.t+1] is expressed by the sum of the rental rate of capital [R.sub.t+1] and the return from capital investment, divided by the original price of capital [Q.sub.t]:

(42) [mathematical expression not reproducible]

E. Government

We assume that the government transfers the collected tax on foreign debt to households and entrepreneurs in a lump-sum manner. The government's budget constraints are thus given by

(43) [[tau].sub.h,t-1] (1 + [i.sup.*.sub.t-1])[E.sub.t][B.sub.t-1] = [T.sub.h,t] and

(44) [[tau].sub.e,t-1] (1 + [i.sup.*.sub.t-1])[F.sub.t-1] [E.sub.t] [D.sub.t-1] = [T.sub.e,t].

F. Equilibrium and Exogenous Shocks

The market clearing for domestic goods requires

(45) [P.sub.H,t] [Y.sub.t] = [P.sub.H,t] [C.sub.H,t] + [P.sub.H,t] [I.sub.H,t] + [E.sub.t] E[X.sub.t],

where E[X.sub.t] denotes demand for exports, which is assumed to be an exogenous stochastic process. Dividing both sides of (45) by [P.sub.H,t] we obtain

(46) [Y.sub.t] = [C.sub.H,t] + [I.sub.H,t] + [S.sub.t]E[X.sub.t]

(47) = (1 - [gamma])g [([S.sub.t]).sup.[eta]] ([C.sub.t] + [I.sub.t]) + [S.sub.t] E[X.sub.t],

where we derive the second equality by considering the demand functions (7), (18), and (28).

From Equation (21) and the fact that the production function is homogeneous with degree 1, we obtain

(48) [[integral].sup.1.sub.0] [Y.sub.t](j)dj = [Z.sub.t][K.sup.[alpha].sub.t][L.sup.1-[alpha].sub.t],

where [K.sub.t] = [[integral].sup.1.sub.0] [K.sub.t] (j) dj and [L.sub.t] = [[integral].sup.1.sub.0] [L.sub.t] (j) dj. From the demand function for differentiated goods, we obtain

(49) [[integral].sup.1.sub.0] [(([P.sub.H,t] (j))/[P.sub.H,t]).sup.-[epsilon]] [Y.sub.t] dj = [Z.sub.t][K.sup.[alpha].sub.t] [L.sup.1-[alpha].sub.t].

We define [[theta].sub.t] [equivalent to] [[integral].sup.1.sub.0] [(([P.sub.H,t] (j))/[P.sub.H,t]).sup.-[epsilon]] dj, which can be expressed as (14)

(50) [[theta].sub.t] = (1 - [zeta])[[??].sup.-[epsilon].sub.H,t]] + [zeta][[PI].sup.[epsilon].sub.H,t] [[theta].sub.t-1].

Then, we can rewrite (49) as

(51) [Y.sub.t] = [[theta].sup.-1.sub.t] [Z.sub.t][K.sup.[alpha].sub.t] [L.sup.1-[alpha].sub.t],

where [[theta].sub.t] measures the resource costs induced by price dispersion in the Calvo model.

The productivity shock [Z.sub.t], export shock E[X.sub.t], and foreign (nominal) interest-rate shock [i.sup.*.sub.t] are exogenously evolving according to the following processes:

(52) log [Z.sub.t] = (1 - [[rho].sub.z]) log Z + [[rho].sub.z] log [Z.sub.t-1] + [[epsilon].sub.z,t], [[epsilon].sub.z,t] ~ i.i.d.N (0, [[sigma].sup.2.sub.z]),

(53) log E[X.sub.t] = (1 - [[rho].sub.ex]) log EX + [[rho].sub.ex] log E[X.sub.t-1] +[[epsilon].sub.ex,t], [[epsilon].sub.ex,t] i.i.d.N (0, [[sigma].sup.2.sub.ex]),

and

(54) [i.sup.*.sub.t] = (1 - [[rho].sub.i]) i* + [[rho].sub.i] [i.sup.*.sub.t-1] + [[epsilon].sub.i,t], [[epsilon].sub.i,t] ~ i.i.d.N (0, [[sigma].sup.2.sub.i]).

The equilibrium of this economy is a set of stationary stochastic processes [{[C.sub.t], [L.sub.t], [B.sub.t], [[PI].sub.t], [S.sub.t], [P.sub.t]/[P.sub.H,t], [[PI].sub.H,t], [q.sub.t], [Y.sub.t], [MC.sub.t], [K.sub.t], [I.sub.t], [Q.sub.t]/[P.sub.H,t], [P.sub.H,t], [N.sub.t], [R.sup.K.sub.t], [F.sub.t], [D.sub.t], [R.sub.t]/[P.sub.t], [W.sub.t]/[P.sub.t], [X.sup.1.sub.t], [X.sup.2.sub.t], [[theta].sub.t], [i.sub.t], [E.sub.t]}.sup.[infinity].sub.t=0] satisfying Equations (10)-(14), (17)-(20), (22)-(24), (29), (35)--(37), (38)-(42), (47), (50), and (51) (combined with the equations for other variables), given initial values for [B.sub.-1], [K.sub.0], [N.sub.-1], and [D.sub.-1], and exogenous stochastic processes [Z.sub.t], [EX.sub.t], and [i.sup.*.sub.t].

G. Optimal Ramsey Policies

We consider optimal Ramsey monetary and capital control policies. We obtain the Ramsey optimal policies by setting up a Lagrangian problem in which the social planner maximizes the conditional lifetime utility of the representative household subject to the first-order conditions of the private agents and the market-clearing conditions of the economy. We compute this numerically using the Matlab procedures developed by Levin et al. (2006). (15)

We let [x.sub.t] denote the N x 1 vector of endogenous variables. Except for the policy instrument, the remaining N - 1 endogenous variables in x, satisfy the N - 1 structural conditions, which is expressed with

(55) [E.sub.t] f ([x.sub.t], [x.sub.t+1], [[zeta].sub.t]) = 0,

where the vector [[zeta].sub.t] denotes the exogenous variables. We derive the optimal Ramsey policy from the maximization problem:

(56) [mathematical expression not reproducible]

We set up a Lagrangian problem: (57)

[L.sub.0] = [E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t] {U ([x.sub.t], [[zeta].sub.t]) + [[lambda].sub.'t] f ([x.sub.t], [x.sub.t+1], [[zeta].sub.t])},

where [[lambda].sub.t] denotes the Lagrange multipliers associated with the first-order conditions of the private agents and the market-clearing conditions of the economy in (55). Taking derivatives of [L.sub.0] with respect to the N endogenous variables, we obtain the N first-order conditions which are characterized by the following equation: (16)

(58) [U.sub.1] ([x.sub.t], [[zeta].sub.t]) + [E.sub.t] [[lambda].sub.'t] [f.sub.1] ([x.sub.t], [x.sub.t+1], [[zeta].sub.t]) + [[beta].sup.-1] [[lambda].sub.'t-1][f.sub.2] ([x.sub.t-1], [x.sub.t], [[zeta].sub.t-1]) = 0.

Taking derivatives of [L.sub.0] with respect to [[lambda].sub.t], we obtain the N-1 equilibrium conditions in the private sector in (55). The Ramsey equilibrium process is therefore characterized by the N-1 equation, (55), and the N equations (58). We have the N elements of x and the N-1 multipliers, [lambda]. In total, there are 2 N-1 variables and 2 N-1 equations.

In Section III, we will examine the optimal Ramsey monetary and capital control policies. In the peg case without capital controls (i.e., [E.sub.t] = [bar.E], and [[tau].sub.h,t], = [[tau].sub.e,t] = 0 for all t), we have N endogenous variables and N equilibrium conditions. In the peg case with the optimal capital control policies, we include [[tau].sub.h,t], and/or [[tau].sub.e,t], in the endogenous variables and obtain the Ramsey capital control policies by letting [[tau].sub.h,t] and/or [[tau].sub.e,t], be policy instruments. In this case, we have N-1 (or N-2) equilibrium conditions for N endogenous variables. Including the N-1 (or N-2) multipliers, in total, we have 2N-1 (or 2N-2) variables and 2 N-1 (or 2N-2) equations. In the flexible exchange rate case in which [E.sub.t] is included in the endogenous variables, we let [i.sub.t] be a policy instrument and obtain the Ramsey monetary policy. In this case, we have N-1 equilibrium conditions for N endogenous variables. Including the N-1 multipliers, in total, we have 2 N-1 variables and 2 N-1 equations.

H. Parameterization

We choose standard parameter values given in the relevant literature, which are summarized in Table 1. Following many previous studies, we set the quarterly discount factor [beta] to 0.99. Following Elekdag and Tchakarov (2007) and Devereux, Lane, and Xu (2006), we set the inverse of intertemporal elasticity of substitution [sigma], elasticity of labor supply [phi], and capital adjustment cost parameter [[psi].sup.K] to 2, 1, and 12, respectively. We set capital share in production [alpha] to 0.32 as in Schmitt-Grohe and Uribe (2003). Following Kollmann (2002) and Devereux, Lane, and Xu (2006), we set the quarterly depreciation rate [delta] to 0.025. Following Gali and Monacelli (2005), we set the elasticity of substitution among differentiated goods [epsilon] and fraction of firms that do not reset their prices [zeta] to 6 and 0.75, respectively. As in Ravenna and Natalucci (2008), we set the elasticity of substitution between domestic and foreign goods [eta] to 1.5. With respect to the degree of openness [gamma], we follow Cook (2004) and set it to 0.28. The parameter for bond adjustment cost [[psi].sup.B] and steady-state debt ratio to gross domestic product (GDP) B/Y are set to 0.0007 and 0.4, respectively, as in Devereux, Lane, and Xu (2006). We set the steady-state level of leverage ratio QK/[P.sub.H]N at 2.2, which is higher than in Bernanke, Gertler, and Gilchrist (1999) who use 2, but not as high as in Devereux, Lane, and Xu (2006) who use 3. Following Cespedes, Chang, and Velasco (2000) and Merola (2010), we set the elasticity of external finance premium to leverage ratio [mu] to 0.02. (17) We use the same values as in Elekdag and Tchakarov (2007) for the exogenous shocks. The persistence and the standard deviation of the productivity shock ([[rho].sub.z] and [[sigma].sub.z]) are set to 0.8 and 0.02, respectively. The persistence and the standard deviation of the export shock ([[rho].sub.ex] and [[sigma].sub.ex]) are set to 0.5 and 0.06, respectively. The persistence and the standard deviation of the foreign interest shock ([[rho].sub.i] and [[sigma].sub.i]) are set to 0.8 and 0.003, respectively.

1. Welfare Evaluation

We calculate and compare welfare levels under alternative policy regimes. Since there exist households and entrepreneurs in our model, the overall welfare measure of the economy is the weighted sum of households' and entrepreneurs' welfare. However, as argued by Bernanke, Gertler, and Gilchrist (1999), we can reasonably assume that the fraction of entepreneurs' consumption is negligible. Following Faia and Monacelli (2005) and Elekdag and Tchakarov (2007), we therefore assume that the entepreneurs' share of consumption is negligible and the overall welfare measure of the eocnomy corresponds to the households' welfare level. We let [V.sup.a.sub.0] denote the conditional welfare level associated with case (a) (a = i, ii, iii ...):

(59) [V.sup.a.sub.0] [equivalent to] [E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t]U([C.sup.a.sub.t], [L.sup.a.sub.t]), = [E.sub.0] [[infinity].summation over (t=0)] [[beta].sup.t]U (([1 - [[lambda].sup.a]) C, L).

Here, [[lambda].sup.a] is the welfare cost of adopting policy (a) on the condition of the calibrated steady state. The conditional welfare measure is obtained using the second-order perturbation methods as described in Schmitt-Grohe and Uribe (2004) and Schmitt-Grohe and Uribe (2007). (18) We let the most welfare-maximizing case be the reference case (ref). Therefore, [[lambda].sup.a] - [[lambda].sup.ref] is the welfare loss in each case, which is the fraction of consumption that compensates a household to a level that is considered as well off under policy (a) as in the reference case (ref).

III. RESULTS

In this section, we present the main results of our analysis. We evaluate the welfare implications of alternative policy and exchange rate regimes with and without the financial accelerator. In Section III.A, we consider an economy without the financial accelerator and compare the welfare consequences of an optimal monetary policy under flexible exchange rates (policy instrument [i.sub.t]), an optimal capital control policy on households under fixed exchange rates (policy instrument [[tau].sub.h], [E.sub.t] = [bar.E] for all t), and a peg regime without an optimal capital control policy ([E.sub.t] = [bar.E] for all t). In Section III.B, we analyze an economy with the financial accelerator and compare the welfare consequences of an optimal monetary policy under flexible exchange rates (policy instrument [i.sub.t]), an optimal capital control policy on households under fixed exchange rates (policy instrument [[tau].sub.h], [E.sub.t] = [bar.E] for all t), an optimal capital control policy on entrepreneurs (policy instrument [[tau].sub.e], [E.sub.t] = [bar.E] for all t), optimal capital control policies on households and entrepreneurs (policy instruments [[tau].sub.h] and [[tau].sub.e], [E.sub.t] = [bar.E] for all t), and a peg regime without optimal capital control policy ([E.sub.t] = [bar.E] for all t).

A. No Financial Accelerator

Following Devereux, Lane, and Xu (2006), we also examine the model without entrepreneurs in order to explore the importance of the balance sheet effect. In this case, households accumulate capital without the external finance premium. The Appendix explains the model without entrepreneurs in detail.

We compare welfare levels in an economy without the financial accelerator in the following cases: (i) an optimal monetary policy under flexible exchange rates (policy instrument [i.sub.t]), (ii) an optimal capital control policy under fixed exchange rates (policy instrument [[tau].sub.h], [E.sub.t] = [bar.E] for all t), and (iii) a fixed exchange rate regime (without capital controls, [E.sub.t] = [bar.E] for all t). Since the optimal monetary policy case under flexible exchange rates (i) turns out to be the most welfare-maximizing, we let (i) be the reference case (ref).

The conditional welfare costs in each case (i, ii, and iii) compared with the reference case (ref) are shown in Table 2. The welfare cost in the case of an optimal capital control policy under fixed exchange rates (ii) is 0.106%, whereas the welfare cost in the fixed exchange rate regime (iii) is 0.306%. Hence, we can say that the optimal capital control policy more than halves the welfare gap between the flexible exchange rate case (i) and the fixed exchange rate case (iii). However, it is obvious that the optimal monetary policy under flexible exchange rates (i) outperforms the optimal capital control policy under fixed exchange rates (ii) in an economy without the financial accelerator.

Tables 3 and 4 show the means and standard deviations of the main variables in the case without the financial accelerator. Since the capital control policy is adopted only in case (ii), by definition, the means and standard deviations of [[tau].sub.h] in cases (i) and (iii) are zero in Tables 3 and 4. Since the fixed exchange rate eliminates the volatility of the nominal exchange rate, by definition, the standard deviation of [DELTA]E in cases (ii) and (iii) is zero in Table 4. Furthermore, note that since the optimal monetary policy under flexible exchange rates (i) is an "inward looking" policy, it has the lowest domestic price inflation ([[PI].sub.H]) volatility among the three regimes in Table 4. In contrast, since the optimal capital control policy under fixed exchange rates (ii) and the fixed exchange rate regime (iii) are "outward looking" policies, the terms of trade (S) in (ii) and (iii) are more stabilized (i.e., the standard deviations of S in (ii) and (iii) are smaller) compared to that in case (i) in Table 4.

B. With Financial Accelerator

We next consider alternative policies in an economy with the financial accelerator. We compare the welfare levels in the following cases: (i) optimal capital controls on both households and entrepreneurs under fixed exchange rates (policy instruments [[tau].sub.h] and [[tau].sub.e], [E.sub.t] = [bar.E] for all t), (ii) optimal capital controls on entrepreneurs under fixed exchange rates (policy instrument [[tau].sub.e], [E.sub.t] = [bar.E] for all t), (iii) an optimal monetary policy under flexible exchange rates (policy instrument [i.sub.t]), (iv) optimal capital controls on households under fixed exchange rates (policy instrument [[tau].sub.h], [E.sub.t] = [bar.E] for all t), and (v) a fixed exchange rate regime (without capital controls, [E.sub.t] = [bar.E] for all t). Since optimal capital controls on both households and entrepreneurs under fixed exchange rates (i) is the most welfare-maximizing, we let (i) be the reference case (ref).

We show the welfare ranking for the alternative regimes in Table 5. It should be noted that the optimal monetary policy under flexible exchange rates (iii), which was the most welfare-maximizing in the previous subsection III.A for the economy without the financial accelerator, is now ranked third. As argued above, the most welfare-maximizing is optimal capital controls on both households and entrepreneurs under fixed exchange rates (i). Optimal capital controls on households (iv) improves the welfare level of the economy under fixed exchange rates (v). However, the welfare-improving effect of optimal capital controls on households (iv) is limited. Optimal capital controls on households (iv) is inferior to the optimal monetary policy under flexible exchange rates (iii). In contrast, optimal capital controls on entrepreneurs (ii) outperforms the optimal monetary policy (iii). Furthermore, optimal capital controls on entrepreneurs (ii) is second only to the most welfare-maximizing case (i).

Tables 6 and 7 show the means and standard deviations of the main variables in the case with the financial accelerator. Comparing column (v) in Table 7 to column (iii) in Table 4, we can see that the standard deviations of Y, C, I, L, S, [PI], and [[PI].sub.H] in column (v) are larger, which implies that the introduction of a financial accelerator mechanism into an economy increases the volatilities of the economy to the same shocks. Figure 1 represents the impulse responses of Y, C, I, L, S, [PI], and [[PI].sub.H] to a foreign interest rate shock in the peg case with and without the financial accelerator. From Figure 1, we can also confirm that the financial accelerator makes the economy more volatile. It should be noted that in Table 6, the mean of the external finance premium F is the lowest in case (ii) and second-lowest in case (i). We can say that capital controls on entrepreneurs curtail the external finance premium level more significantly than a monetary policy or capital controls on households.

The intuition underlying our analysis results is as follows. Entrepreneurs finance investment partly with foreign borrowing, which is subject to financial frictions. Entrepreneurs borrow abroad at an interest rate, which is equal to the foreign interest rate, adjusted for expected exchange rate fluctuations, and augmented by an external finance premium. Although it affects the economy through domestic interest rates, a monetary policy does not directly affect the interest rate at which entrepreneurs borrow from abroad. In contrast, capital controls on entrepreneurs have a direct control on the interest rate at which entrepreneurs borrow from foreign lenders, and may yield higher welfare in an economy with the financial accelerator.

IV. SENSITIVITY ANALYSIS

In this section, we examine the robustness of our analysis results in the previous section. In the previous section, we showed the welfare rankings in the case in which all the shocks are included. In this section, we will show that our results are robust even when we consider these shocks individually.

First, we considered the welfare rankings in an economy without the financial accelerator. Table 2 shows the welfare ranking in the case in which all the three shocks are included. The welfare rankings for the individual shocks, which are productivity shock, export shock, and foreign interest shock, are shown in Tables 8-10, respectively. In Tables 8-10, we can see that the optimal monetary policy under flexible exchange rates (i) outperforms the optimal capital control policy under fixed exchange rates (ii). The welfare rankings for individual shocks in Tables 8-10 are then identical to that for all the shocks in Table 2. Therefore, we confirm that our results are robust even when we consider the individual shocks in an economy without the financial accelerator.

However, there are some notable differences among the three cases. Comparing Tables 8-10, we can see that the welfare benefit of monetary policy (i.e., the difference between (i) and (iii)) is the largest for the productivity shock but the smallest for the foreign interest shock. Another notable difference is that although the capital control policy is not as good as the monetary policy in any case, the capital control policy is the closest to the monetary policy for the foreign interest shock (i.e., (ii) in Table 10 is smaller than that in Tables 8 and 9).

Next, we consider the welfare rankings in an economy with the financial accelerator. Table 5 shows the welfare ranking in the case in which all the three shocks are included. The welfare rankings for the individual shocks, which are productivity shock, export shock, and foreign interest shock, are shown in Tables 11-13, respectively. In Tables 11-13, we can see that the welfare rankings for individual shocks are identical to that for all the shocks in Table 5. Therefore, we confirm that our results are robust even when we consider the individual shocks in an economy with the financial accelerator.

However, there are some notable differences among the three cases. Comparing Tables 11-13, we can see that the welfare benefit of capital controls (i.e., the difference between (i) and (v)) is the largest for the foreign interest shock. Another notable difference is that the monetary policy is furthest behind capital controls for the foreign interest shock (i.e., the difference between (i) and (iii) in Table 13 is larger than that in Tables 11 and 12).

V. CONCLUSION

We have developed a small open economy, New Keynesian model that highlights the vulnerability of balance sheets to exchange rate fluctuations. We then apply a Ramsey-type analysis and examine the welfare implications of optimal monetary and capital control policies. To our knowledge, our paper is the first that examines the welfare implications of optimal capital control policies in a small open economy, New Keynesian model that incorporates a financial accelerator coupled with liability dollarization.

In the case without the financial accelerator, we have compared three cases: an optimal monetary policy under flexible exchange rates, an optimal capital control policy (on households) under fixed exchange rates, and fixed exchange rates (without capital controls). Our Ramsey-type analysis results have shown that although the optimal capital control policy significantly improves welfare under fixed exchange rates, the optimal monetary policy is the most welfare-maximizing in an economy without the financial accelerator.

In the case with the financial accelerator, we compared five cases: an optimal monetary policy under flexible exchange rates, fixed exchange rates (without capital controls), an optimal capital control policy on entrepreneurs, an optimal capital control policy on households, and an optimal capital control policy on both entrepreneurs and households under fixed exchange rates. Our results have shown that the optimal monetary policy still outperforms the optimal capital control policy on households. However, the optimal capital control policy on entrepreneurs outperforms the optimal monetary policy. The most welfare-maximizing is the optimal capital control policy on both entrepreneurs and households.

The intuition underlying our analysis results is straightforward. Entrepreneurs finance investment partly with foreign borrowing, which is subject to financial frictions. In an economy with a financial accelerator, the key variable is the foreign interest rate augmented by an external finance premium. Although monetary policy works through domestic interest rates, capital controls on entrepreneurs have a direct control on the interest rate at which entrepreneurs borrow from abroad. Hence, capital controls under fixed exchange rates can yield higher welfare in an economy with a financial accelerator coupled with liability dollarization.

As we mention in the introduction, Liu and Spiegel (2015) showed that the welfare gain of capital controls depends on the presence of sterilization, and that capital controls and sterilization are complementary policies. Although it is beyond the scope of this study, their findings suggest that if we introduce sterilization into our model, it is highly likely that the welfare gain of capital controls becomes larger. Another useful extension would be to study the role of pecuniary externalities that lead borrowers to over-borrow in a small open economy, as examined by Jeanne and Korinek (2010) and Bianchi (2011). If we incorporate the externalities associated with overborrowing into our model, it would magnify the financial-accelerator mechanism effect in an economy. It would be an interesting project to examine the role of capital controls in an economy with a larger amplification effect due to pecuniary externalities. We leave these extensions for future research.

APPENDIX

In this appendix, we explain the differences between the models with and without entrepreneurs. In the economy without entrepreneurs, households directly make investment and accumulate capital. In this case, the households' budget constraint is given by (A1)

[mathematical expression not reproducible]

Therefore, the optimal conditions associated with households' problem include the following equation:

(A2) 1 = [beta][E.sub.t] {[[lambda].sup.h.sub.t+1]/[[lambda].sup.h.sub.t] [R.sup.K.sub.t+1] [P.sub.t]/[P.sub.t+1]},

where [R.sup.K.sub.t] now denotes the return on capital for households.

Since there are no entrepreneurs in this economy, we omit the optimal conditions associated with entrepreneurs' problem (38)-(41). The equilibrium of the economy without entrepreneurs is therefore characterized by a set of stationary stochastic processes [{[C.sub.t], [L.sub.t], [B.sub.t], [[PI].sub.t], [S.sub.t], [P.sub.t]/[P.sub.H,t], [[PI].sub.H,t], [q.sub.t], [Y.sub.t], [MC.sub.t], [K.sub.t], [I.sub.t], [Q.sub.t]/[P.sub.H,t], [[??].sub.H,t], [R.sup.K.sub.t], [R.sub.t]/[P.sub.t], [W.sub.t]/[P.sub.t], [X.sup.1.sub.t], [X.sup.2.sub.t], [[theta].sub.t], [i.sub.t], [E.sub.t]}.sup.[infinity].sub.t=0] satisfying Equations (11)-(14), (17)-(20), (22)-(24), (29), (35)-(37), (42), (47), (50), (51), (A1), and (A2) (combined with the equations for other variables), given initial values for [B.sub.-1], and [K.sub.0], and exogenous stochastic processes [Z.sub.t], [EX.sub.t], and [i.sup.*.sub.t].

In the peg case without capital controls (i.e., [E.sub.t] = [bar.E], and [[tau].sub.h] = 0 for all t), we have 21 endogenous variables and the same number of conditions. In the peg case with the optimal capital control policy, we include [[tau].sup.h.sub.t] in the endogenous variables and obtain the Ramsey capital control policy by letting [[tau].sup.h.sub.t] be a policy instrument. In the flexible exchange rate case in which [E.sub.t] is included in the endogenous variables, we let [i.sub.t] be a policy instrument and obtain the Ramsey monetary policy.

ABBREVIATIONS

CPI: Consumer Price Index

DSGE: Dynamic Stochastic General Equilibrium

GDP: Gross Domestic Product

IMF: International Monetary Fund

doi: 10.1111/ecin.12544

Online Early publication December 29, 2017

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(1.) An exception is Kitano (2004). Kitano (2004) showed that capital controls not only stem the capital inflow but also reverse the associated macroeconomic effects, and are effective measures against the capital inflow problem.

(2.) For details, see, for example, Jongwanich and Kohpaiboon (2012), Ahmed and Zlate (2014), Forbes et al. (2016), and Ghosh, Ostry, and Qureshi (2017).

(3.) For details on the IMF position, see Ostry et al. (2010) and Ostry, Ghosh, and Korinek (2012).

(4.) For details, see, for example, Korinek (2011) or Jeanne, Subramanian, and Williamson (2012). For the earlier literature on capital controls, see the introduction in Kitano (2011). Kitano (2011) showed that there exists an optimal degree of capital-account restriction that achieves a higher level of welfare than that under perfect capital mobility, if the economy has costly financial intermediaries.

(5.) Benigno et al. (2013) consider both ex ante and ex post policies in a model with pecuniary externalities. They show that the design of ex ante policies depends on that of ex post policies.

(6.) Ostry et al. (2013) argue that the use of capital controls is justified under limited circumstances. Jeanne. Subramanian, and Williamson (2012) go further, arguing that "[p]roperly designed capital controls may even be effective as a regular instrument of economic policy"(p. 110).

(7.) Kitano and Takaku (2017c) incorporate a banking sector with balance sheet frictions into a model of a small open economy and compare the effectiveness of capital controls and macroprudential regulation.

(8.) Emerging economies have difficulty in borrowing abroad in their own currencies, and face a mismatch in the currency denomination of their liabilities and assets. Eichengreen and Hausmann (1999) refer to this incompleteness in financial markets as "original sin." Eichengreen and Hausmann (2005) also argue that "[w]hile the quality of institutions and policies varies enormously among developing countries, the extent of original sin does not"(p.6) and that "the difficulty emerging markets experience in attempting to borrow abroad in their own currencies has something to do with the structure of the international system"(p.6).

(9.) The position of the domestic asset [A.sub.t] turns out to be zero in equilibrium in our model. However, the inclusion of the domestic asset [A.sub.t] enables us to introduce the domestic interest rate [i.sub.t] into the model as in Equation (10). Following Devereux, Lane, and Xu (2006) and Elekdag and Tchakarov (2007), we therefore include the domestic asset [A.sub.t] so that we can analyze the effect of monetary policy of changing the domestic interest rate [i.sub.t].

(10.) The small open economy model with incomplete asset markets features equilibrium dynamics that possess a random walk component (Schmitt-Grohe and Uribe 2003). To yield stationarity of the equilibrium dynamics in a small open economy, Neumeyer and Perri (2005) used a model with convex portfolio adjustment costs. The portfolio adjustment cost is often used for "closing" a small open economy. Schmitt-Grohe and Uribe (2003) presented alternative approaches to induce stationarity.

(11.) Without loss of generality, we assume that [P.sup.*.sub.t] is exogenous and constant (= 1) for all t.

(12.) The capital (or investment) adjustment cost is widely adopted in dynamic stochastic general equilibrium (DSGE) models, mainly because it generally improves their empirical fit (e.g., Christiano, Eichenbaum, and Evans 2005). Without the adjustment cost, investment would respond to shocks too much compared to empirical evidence. The capital adjustment cost is also important to obtain the price of capital and to generate movements of asset prices. Changes in asset prices provide an amplification mechanism in models with financial frictions (Bernanke, Gertler, and Gilchrist 1999; Kiyotaki and Moore 1997).

(13.) Bernanke, Gertler, and Gilchrist (1999) showed that given the assumptions related to the agency problem including the characteristics of the distribution of an idiosyncratic return shock, parameter values associated with monitoring costs, and constant returns to scale in production and monitoring costs, the agency problem implies that the external finance premium is an increasing function of the ratio of capital to net worth as in Equation (40). Especially, the assumption of constant returns to scale in production and monitoring costs is important for the aggregation so that the value of capital relative to net worth and the external premium become equal across all entrepreneurs.

(14.) For the derivation of Equation (50), see Schmitt Grohe and Uribe (2006).

(15.) Levin et al.'s (2006) program read a Dynare model file and generates the first-order conditions of a Ramsey policymaker. See Adjemian et al. (2011) for details on Dynare.

(16.) The first-order necessary condition for optimality at t = 0 is (59) with [[lambda].sub.-1] = 0.

(17.) Using a maximum-likelihood procedure and post-1979 U.S. data, Christensen and Dib (2008) reported a higher estimated value of 0.042 for this parameter.

(18.) Kim and Kim (2003) revealed that second-order solutions are necessary because conventional linearization may generate spurious welfare reversals.

SHIGETO KITANO and KENYA TAKAKU*

* Earlier versions of the paper were presented at the 9th Annual MIFN Conference, the SWET 2015 at Otaru University, the JEA annual meeting at Niigata University, and the 11th Annual APEA Conference at National Taiwan University. We are grateful to the referee and the coeditor William Branch for their helpful comments that have improved the paper. We are especially grateful to Mark Spiegel, Tomohiro Hirano, Kosuke Aoki, Yongseung Jung, Ippei Fujiwara, and Shin-ichi Fukuda for their valuable comments. All remaining errors are ours. This work was supported by JSPS KAKENHI (15H05729, 16 K03741).

Kitano: Professor, Research Institute for Economics and Business Administration, Kobe University, Kobe, 6578501, Japan. E-mail kitano@rieb.kobe-u.ac.jp

Takaku: Associate Professor, Faculty of International Studies, Hiroshima City University, Hiroshima, 731-3194, Japan. E-mail takaku@hiroshima-cu.ac.jp

Caption: FIGURE 1 Model with (-) and without (--) the Financial Accelerator; Peg Case: Impulse Responses to a Foreign Interest Rate Shock
TABLE 1
Parameterization

Parameters         Value

[beta]              0.99    Discount factor
[sigma]              2      Inverse of intertemporal elasticity of
                              substitution
[phi]                1      Elasticity of labor supply
[[psi].sup.K]        12     Capital adjustment cost parameter
[alpha]             0.32    Share of capital in output
[sigma]            0.025    Depreciation rate of capital
[epsilon]            6      Elasticity of substitution among
                              differentiated goods
[xi]                0.75    Fraction of firms that do not reset their
                              prices
[eta]               1.5     Elasticity of substitution between domestic
                              and foreign goods
[gamma]             0.28    Degree of openness
[[psi].sup.B]      0.0007   Parameter for bond adjustment cost
B/Y                 0.4     Steady-state ratio of debt to GDP
QK/[P.sub.H]N       2.2     Steady-state ratio of capital to net worth
[mu]                0.02    Elasticity of external finance premium
[[rho].sub.Z]       0.8     Persistence: productivity shock
[[sigma].sub.Z]     0.02    Standard deviation: productivity shock
[[rho].sub.ex]      0.5     Persistence: export shock
[[sigma].sub.ex]    0.06    Standard deviation: export shock
[[rho].sub.i]       0.8     Persistence: foreign interest rate shock
[[sigma].sub.i]    0.003    Standard deviation: foreign interest rate
                              shock

TABLE 2
Conditional Welfare Costs: No Financial Accelerator

                       (i) Mon.   (ii) Cap. Con.   (iii) Peg
Welfare cost
([[lambda].sup.a] -       0           0.106          0.306
[[lambda].sup.ref])
x 100

Note: The conditional welfare costs in (ii) and (iii) are
measured with the most welfare-maximizing case (i) being
the reference case.

Cap. Con., capital controls; Mon., monetary policy.

TABLE 3 Means: No Financial Accelerator

                    (i) Mon.   (ii) Cap. Con.   (iii) Peg

Y                    1.8042        1.8042        1.7987
C                    1.4571        1.4565        1.4535
I                    0.3426        0.3422        0.3420
L                    0.6943        0.6944        0.6944
[DELTA]E             1.0000        1.0000        1.0000
S                    0.9968        0.9967        0.9945
[PI]                 1.0000        1.0000        1.0000
[[PI].sub.H]         1.0000        1.0000        1.0000
[i.sub.d]            0.0099        0.0099        0.0100
[[tau].sub.h]        0.0000       -0.0001        0.0000

Cap. Con., capital controls; Mon., monetary policy.

TABLE 4
Standard Deviations (%): No Financial
Accelerator

                   (i) Mon.   (ii) Cap. Con.   (iii) Peg

Y                    3.55          3.21          2.97
C                    1.67          2.06          1.40
1                    7.60         10.13          6.17
L                    0.86          1.93          3.62
[DELTA]E             2.75          0.00          0.00
S                    4.06          2.14          2.63
[PI]                 0.79          0.19          0.59
[[PI].sub.H]         0.05          0.27          0.81
[i.sub.d]            1.00          0.96          0.50
[[tau].sub.h]        0.00          1.05          0.00

Cap. Con., capital controls; Mon., monetary policy.

TABLE 5
Conditional Welfare Costs: With Financial Accelerator

                      (i) Cap. Con.   (ii) Cap.
                      ent. & hous.    Con. ent.

Welfare cost                0           0.215
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

                      (iii) Mon.   (iv) Cap.    (v) Peg
                                   Con. hous.

Welfare cost            1.624        1.900       2.385
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

Note: The conditional welfare costs in (ii) to (v) are measured
with the most welfare-maximizing case (i) being the reference case.

Cap. Con., capital controls; ent., entrepreneurs;
hous., households; Mon., monetary policy.

TABLE 6
Means: With Financial Accelerator

                   (i) Cap. Con.    (ii) Cap. Con.    (iii) Mon.
                    ent. & hous.         ent.

Y                      1.7327           1.7295          1.7136
C                      1.2672           1.2647          1.2533
I                      0.2348           0.2341          0.2238
L                      0.7819           0.7825          0.7865
[DELTA]E               1.0000           1.0000          1.0001
S                      0.9966           0.9957          0.9958
[PI]                   1.0000           1.0000          1.0001
[[PI].sub.H]           1.0000           1.0000          1.0001
[i.sub.d]              0.0098           0.0100          0.0099
F                      1.0109           1.0107          1.0153
[[tau].sub.h]         -0.0002           0.0000          0.0000
[[tau].sub.e]          0.0031           0.0034          0.0000

                   (iv) Cap. Con.   (v) Peg
                       hous.

Y                      1.7065       1.6948
C                      1.2495       1.2409
I                      0.2204       0.2163
L                      0.7874       0.7894
[DELTA]E               1.0000       1.0000
S                      0.9935       0.9915
[PI]                   1.0000       1.0000
[[PI].sub.H]           1.0000       1.0000
[i.sub.d]              0.0096       0.0100
F                      1.0164       1.0173
[[tau].sub.h]         -0.0002       0.0000
[[tau].sub.e]          0.0000       0.0000

Cap. Con., capital controls; ent., entrepreneurs; hous.,
households; Mon., monetary policy.

TABLE 7
Standard Deviations (%): With Financial Accelerator

                    (i) Cap.    (ii) Cap.   (iii)   (iv) Cap.     (v)
                    Con. ent.   Con. ent.   Mon.    Con. hous.    Peg
                     & hous.

Y                     2.83        3.13      3.77       2.88      3.52
C                     2.69        1.69      2.04       3.17      2.04
I                     7.12        10.23     9.17       8.73      11.02
L                     3.35        3.48      2.43       3.90      4.50
[DELTA]E              0.00        0.00      4.61       0.00      0.00
S                     1.75        2.81      5.13       1.91      2.85
[PI]                  0.21        0.57      1.46       0.19      0.65
[[PI].sub.H]          0.30        0.79      0.29       0.26      0.91
[i.sub.d]             1.31        0.50      2.05       1.68      0.50
F                     0.10        0.17      0.20       0.15      0.34
[[tau].sub.h]         1.40        0.00      0.00       1.85      0.00
[[tau].sub.e]         0.83        1.31      0.00       0.00      0.00

Cap. Con., capital controls; ent., entrepreneurs;
hous., households; Mon., monetary policy.

TABLE 8
Conditional Welfare Costs: No Financial
Accelerator--Productivity Shock

                       (i) Mon.   (ii) Cap. Con.   (iii) Peg
Welfare cost
([[lambda].sup.a] -       0           0.056          0.182
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; Mon., monetary policy.

TABLE 9
Conditional Welfare Costs: No Financial
Accelerator--Export Shock

                      (i) Mon.   (ii) Cap. Con.   (iii) Peg
Welfare cost
([[lambda].sup.a] -      0           0.044          0.075
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; Mon., monetary policy.

TABLE 10

Conditional Welfare Costs: No Financial
Accelerator--Foreign Interest Shock

                       (i) Mon.   (ii) Cap. Con.   (iii) Peg
Welfare cost
([[lambda].sup.a] -       0           0.007          0.049
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; Mon., monetary policy.

TABLE 11
Conditional Welfare Costs: With Financial
Accelerator--Productivity Shock

                       (i) Cap. Con.   (ii) Cap.   (iii) Mon.
                       ent. & hous.    Con. ent.

Welfare cost                 0           0.123       1.663
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

                       (iv) Cap.    (v) Peg
                       Con. hous.

Welfare cost             1.741       1.922
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; ent., entrepreneurs;
hous., households., Mon., monetary policy.

TABLE 12

Conditional Welfare Costs: With Financial
Accelerator--Export Shock

                        (i) Cap. Con.   (ii) Cap.   (iii) Mon.
                        ent. & hous.    Con. ent.

Welfare cost                  0           0.049       1.630
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

                        (iv) Cap.    (v) Peg
                        Con. hous.

Welfare cost              1.757       1.871
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; ent., entrepreneurs;
hous., households., Mon., monetary policy.

TABLE 13

Conditional Welfare Costs: With Financial
Accelerator--Foreign Interest Shock

                       (i) Cap. Con.   (ii) Cap.   (iii) Mon.
                       ent. & hous.    Con. ent.

Welfare cost                 0           0.043       1.800
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

                       (iv) Cap.    (v) Peg
                       Con. hous.

Welfare cost             1.870       2.064
([[lambda].sup.a] -
[[lambda].sup.ref])
x 100

Cap. Con., capital controls; ent., entrepreneurs;
hous., households; Mon., monetary policy.
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Author:Kitano, Shigeto; Takaku, Kenya
Publication:Economic Inquiry
Date:Apr 1, 2018
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