Financial market segmentation and choice of exchange rate regimes

Financial market segmentation and choice of exchange rate regimes

Accepted Manuscript Financial market segmentation and choice of exchange rate regimes Vipul Mathur, Chetan Subramaniany PII: DOI: Reference: S0165-17...

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Accepted Manuscript Financial market segmentation and choice of exchange rate regimes Vipul Mathur, Chetan Subramaniany PII: DOI: Reference:

S0165-1765(16)30064-7 http://dx.doi.org/10.1016/j.econlet.2016.02.035 ECOLET 7099

To appear in:

Economics Letters

Received date: 11 October 2015 Revised date: 5 February 2016 Accepted date: 29 February 2016 Please cite this article as: Mathur, V., Subramaniany, C., Financial market segmentation and choice of exchange rate regimes. Economics Letters (2016), http://dx.doi.org/10.1016/j.econlet.2016.02.035 This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Highlights (for review)

Highlights for “Financial market segmentation and choice of exchange rate regimes” a. We study a small open economy model with segmented asset markets and financial sector shocks. b. We show analytically that the state- contingent optimal monetary policy facilitates risk sharing between participants and non-participants and is countercyclical. c. We compare welfare analytically across fixed and flexible exchange rate regimes. d. Flexible exchange regime mimics dynamics under optimal policy and welfare dominates the fixed regime.

Title Page

Financial market segmentation and choice of exchange rate regimes Vipul Mathur

Chetan Subramaniany

Abstract We study the choice of exchange rate regime in a small open economy with segmented asset markets subjected to …nancial sector shocks. We show that the state-contingent optimal policy facilitates risk sharing between asset market participants and non-participants, and is countercyclical. Our results establish that contrary to existing literature, ‡exible exchange rates mimic optimal policy and welfare dominate …xed exchange rates. .

.

Keywords: Exchange Rates, Financial Shocks, Segmented Asset Markets, Optimal Monetary Policy JEL Classification: E52, F41, G12, G15

Fellow, Department of Economics & Social Sciences, Indian Institute of Management Bangalore, India 560076. E-mail: [email protected], Phone: (91)-888-453-3598. y Corresponding author: Associate Professor, Department of Economics & Social Sciences, Indian Institute of Management Bangalore, India 560076. E-mail: [email protected], Phone: (91)-80-26993345.

1

*Manuscript Click here to view linked References

1

Introduction

There is a growing interest in how monetary policy should respond to shocks originating in the …nancial sector as distinct from shocks originating in other sectors (productivity and monetary). These shocks have been modeled largely as exogenous ‡uctuations in the supply and demand for capital in the …nancial sector. Jermann and Quadrini (2012), Christiano et.al. (2008), show that …nancial shocks contributed signi…cantly to the observed dynamics of real and …nancial variables in the US. In this paper, we extend Zervou’s (2013) closed economy segmented markets1 framework to a small open economy and compute welfare analytically across exchange rate regimes under …nancial sector shocks. Our work compliments Lahiri-Singh-Vegh (LSV) (2007) who in a seminal paper, show that the Mundell-Fleming results are overturned when the source of the friction is in the asset markets as opposed to the product markets. Speci…cally, they demonstrate that when real shocks a¤ect both …nancial market participants and nonparticipants symmetrically, then optimal policy is procyclical and …xed exchange rates outperform ‡exible exchange rates. By contrast, we show that if such shocks are speci…c to the …nancial sector then optimal policy is counter-cyclical and ‡exible exchange rates are preferable.

2

Environment

There is a small open economy with agents who consume a single consumption good c, which can be perfectly traded in world markets at a …xed world price of unity. Under purchasing power parity, the home price of consumption good is equal to the nominal exchange rate, S. Further, St St 1 t = ( St 1 ), the devaluation rate at time t is also the rate of in‡ation in the economy. The households’intertemporal utility function is Wt = E0

1 X

t s

u(cs )

(1)

s=t

Markets are segmented such that only a fraction 2 (0; 1] of the population, called traders, have access to the stock and bond market and the rest, (1 ), called non-traders, can only hold domestic money. Following Zervou (2013), while both groups receive a …xed endowment y~ every period, the traders additionally receive a share of the stochastic real dividend t . The dividend shock t follows an iid process with mean . The total output in the economy is therefore given by yt

t

The mean output can therefore be written as y

+ y~

(2)

+ y~.

1

Typically, in such a set-up only a fraction of agents have access to asset markets (see Alvarez et al. (2009), Alvarez et al. (2001)).

1

2.1 2.1.1

Households Trader Households

The traders begin any period with assets in the form of money balances, bond and stock holdings carried over from the previous period. Asset markets open …rst where the trader rebalances the household’s asset position, which, for any period t, can be represented as ^ T = M T + Tt + (1 + it M t t + St (1 + r)ft

1)

Bt

St ft+1 + qt zt

Bt+1

(3)

qt zt+1

^ tT and MtT respectively denote the money balances with which the trader leaves and entered where M the asset market. B denotes aggregate one-period nominal government bonds which pay a nominal interest rate, i; f are foreign bonds which pay an exogenous and constant world real interest rate r; T are aggregate lump-sum transfers from the government, q is the price of a stock and z is the ^ tT , the trader household then proceeds to the number of stocks. Armed with this nominal cash M goods market to purchase consumption for the period t. The cash-in-advance constraint is ^T M t

St cTt

(4)

The trader household also sells its endowment y~ and encashes the dividend t , both of which become the cash which it carries over in the next period t + 1 T Mt+1 = St y~ + St zt

(5)

t

Combining (3) and (4) (assuming that the cash-in-advance constraint binds, see Alvarez et al. (2001)) we get the budget constraint as St cTt = MtT +

Tt

+ (1 + it

1)

Bt

+ St (1 + r)ft 2.1.2

Bt+1 St ft+1 + qt zt

(6) qt zt+1

Non-Trader Households

The non-trader household uses cash, M N , carried over from the previous period to procure current period consumption. The cash-in-advance constraint is St cN t

MtN

(7)

The non-trader also sells its endowment for cash which is carried over to the next period N Mt+1 = St y~

(8)

Combining (7) and (8), we get the budget constraint as N Mt+1 = MtN + St y~

2

St cN t

(9)

2.1.3

Government

The government’s budget constraint is given by Mt+1

Mt = St ht+1

St (1 + r)ht + (1 + it

1 )Bt

Bt+1 + Tt

(10)

where ht is the foreign bonds that the government enters with in period t. Importantly, monetary policy impacts only traders directly as they are the only ones in the economy with access to asset markets.

2.2

Equilibrium

In the money market, the equilibrium condition is given by Mt = MtT + (1

)MtN

(11)

Combining (5), (8) and (11) we get St =

Mt Mt = yt y+ t

(12)

In the stock market, the total stocks of the …rm which are distributed among the traders should sum upto unity, i.e. zt+1 = 1 (13) Using (2), (11), (13) one obtains the goods market equilibrium cTt + (1

)cN t = yt + (1 + r)kt

kt+1

(14)

where k h + f denote the total foreign bonds in the economy. The consumption of non-traders is obtained using (7) and (8) is given by cN t =

1 1+

y~

(15)

t

It follows from (15), that an increase in the in‡ation tax , redistributes resources away from the non-trader and thereby lowering their consumption. For traders’consumption, we use equations, (6) (10) and (12) to get cTt = y~ + The component 1 in the economy.

(~ y

y~ 1+

t

t

+ (1 + r)

kt

kt+1

+

1

(~ y

y~ 1+

)

(16)

t

) captures the redistribution caused due to changes in monetary policy

3

3 3.1

Monetary Policy Optimal Monetary Policy

The central bank chooses the devaluation rate to maximize the objective function given below max E0 t

1 X 0

t

f u(cTt ) + (1

)u(cN t )g

(17)

0 T subject to the economy wide constraint (14). The …rst order conditions imply u0 (cN t ) = u (ct ) implying cTt = cN t .

Proposition 1 Under …nancial shocks, optimal monetary policy is countercyclical. Proof: Using (15) and (16) the optimal devaluation rate is given by t

=

(1 ) t+ rkt + y + (1

+ rkt )( t )

(18)

Further

(1 )(~ y) @ j t = ;kt =0 = <0 (19) 2 @ t y Optimal policy by being countercyclical facilitates increased risk sharing by redistributing consumption in favor of the non-trader. Interestingly, our results are in contrast to LSV who show that in the optimal reaction to real shocks is procyclical. Crucially, in their model and unlike in ours, output shocks impact both traders and non-traders so procyclical optimal policy improves welfare by insulating the non-trader from output ‡uctuations.

3.2

Fixed Exchange Rates

Under …xed exchange rates, the monetary authority sets a constant path of the exchange rate equal to S. In particular, we assume that the nominal exchange rate is …xed at S=

M0 Mt = y0 yt

(20)

where M0 is the total money supply and y0 is the total output at t = 0. Further, equation (15), shows that the consumption of non-traders under this regime is …xed ix cN;f = y~ t

(21)

Thus the non-trader is completely insulated from …nancial shocks. This implies that the trader bears the full impact of the dividend shocks. Combining equations (2), (16) and (20) the consumption of the trader households becomes (1 ) 1 r ix cT;f yt ( )(~ y) (22) = kt + y + t The increase in real output due to a positive current period dividend shock causes prices to fall and the exchange rate to appreciate. In order to stabilize the currency the central bank intervenes by buying up foreign bonds and increasing the money supply in the economy. Since only traders have access to these money injections it raises their current consumption. 4

3.3

Flexible Exchange Rates

Under ‡exible exchange rates, the monetary authority …xes the total money supply Mt = M0

(23)

From the quantity equation (12), the depreciation rate is given by t

=

t 1

t

(24)

yt

Combining (15) and (24), the consumption of non-traders under ‡exible exchange rates is cN y) t = (~

yt yt

(25) 1

Unlike …xed exchange rates, the consumption of the non-traders is not insulated from the shocks to the dividend. Speci…cally, a positive shock to dividend in period (t 1), decreases prices in that period and from (8) reduces the amount of cash balances non-traders carry into period t. Consequently, consumption falls in period t. On the other hand, an increase in dividend in the current period, increases consumption of the non-trader by reducing the burden of the in‡ation tax they face. This implies that analogous to optimal policy, ‡exible exchange rates leads to greater risk sharing in the event of …nancial sector shocks. To arrive at the consumption of traders we iterate equation (16) yielding lex cT;f =r t

kt

(1

+

(1

)

) (1

yt +

(1

y

)(~ y) y yt

(1

)(~ y )(1 )

2 (~ y)

)

1 1+

(26) t

(1 + )

where = y2 =y 2 . The consumption of traders under ‡exible exchange rate varies directly with an increase in endowment and the in‡ation tax.

4

Welfare

We compute welfare by comparing the unconditional expectation of lifetime welfare at time t = 0. To keep the welfare analytically tractable, we assume a quadratic utility speci…cation. Our discussion in this section follows LSV (2007) closely where the welfare function is W

i;j

= Ef

1 X t=0

t

h ci;j

ci;j

2

i

g i = T,N

j = ‡ex, …x

(27)

where W j = W T;j + (1

) W N;j

(28)

Under quadratic utility the expected welfare can be written as Efc

c2 g = E(c)

[E(c)]2 5

V ar[c]

(29)

where where V ar(c) denotes the variance of consumption and in welfare across the two regimes is W f lex

f ix

=

1 X t=0

t

lex [ f(E0 (cT;f ) t

lex 2 ((E0 (cT;f )) t lex (V ar(cT;f ) t

lex 2 ((E0 (cN;f )) t lex (V ar(cN;f ) t

W f lex

Lemma 1 The above equation,

f ix

ix E0 (cT;f )) t

(30)

ix 2 (E0 (cT;f )) ) t ix V ar(cT;f ))g t

lex )f(E0 (cN;f ) t

+ (1

> 0 is a parameter. The di¤erence

ix E0 (cN;f )) t

ix 2 (E0 (cN;f )) ) t ix V ar(cN;f ))g] t

= 0; has two roots

= 1 and

=

=

(1+(1 2(1

)2 ) . ) y

Proof: (See Appendix (A.3)). Proposition 2 In a small open economy, with shocks to the …nancial sector (dividend), the ‡exible exchange rate regime welfare dominates the …xed exchange rate regime for all : Proof: We provide the proof in Appendix (A.1), (A.2), and (A.3). It follows from Proposition 2, that as long as the actual participation is less than the threshold participation, , the ‡exible regime will dominate over the …xed regime. To get a sense of the value of , note that from Lemma 1 the value of depends upon y and . For our benchmark calculations (see Table 1, Appendix (A.4)) we use the parameter values from Zervou (2013) which correspond to a quarterly model of US and …nd = 75:6%. Further, in Figure 1 (Appendix (A.4)) continues to be we carry out sensitivity analysis for alternate values of y and establish that greater than 50%. These values are higher than the reported value of market participation in US which is in the range of 21.75% (Vissing-Jørgensen (2002)) and 27.3% (Zervou (2013)). In emerging economies, the participation rates are likely to be even lower. Further, to understand the intuition for the welfare result in Proposition 2, note that under the …xed regime the following holds ix E0 (cN;f ) = y~ t

V

(31)

ix ar(cN;f ) t

=0 1 ix E0 (cT;f )= y t

1 (1 ) (1 ) 2 2 ix V ar(cT;f ) = (t + 1)( ) y t

6

Similarly under the ‡exible regime, we have lex E0 (cN;f ) = (~ y )(1 + ) t lex V ar(cN;f ) = (~ y )2 (1 + )(2 ) t 1 1 lex E0 (cT;f )= y (1 + ) t (1 ) (1 )2 lex g y 2 f1 V ar(cT;f ) ' (t + 1)f t 2

(32)

2

g

where , ; 2 > 0 are de…ned in the Appendix (A.2). By comparing equations (31) and (32) one …nds that while the mean and variance of the consumption of the trader is higher under the …xed regime, the corresponding values for the non-trader are higher under the ‡exible regime. The lower expected income of the non-trader coupled with higher volatility in consumption of the trader under …xed regime leads to a lower degree of overall welfare when compared to the ‡exible regime. Our results are contrary to those obtained by LSV who show that when an economy is subject to real shocks …xed regime outperform ‡exible regime. The crucial di¤erence between the two papers arises because in the LSV paper, shocks are symmetric across both the trader and the non-trader household whereas in our case it hits only the trader household. Thus while the ‡exible regime facilitates risk sharing thereby improving welfare in our framework it increases volatility of the non-trader household and reduces welfare in their paper.

5

Conclusion

This paper extends the segmented asset markets framework to study how …nancial sector shocks a¤ect exchange rate policy in a small open economy. We …nd that ‡exible regime, by enabling greater risk sharing welfare dominate the …xed regime. Our analysis suggest that in the case where real shocks originate in the …nancial sector, the standard Mundell-Fleming prescription continues to hold under asset market segmentation.

References [1] Alvarez, Fernando, Robert E. Lucas, and Warren E. Weber., "Interest rates and in‡ation," American Economic Review 91, no. 2 (2001): 219-225.

[2] Alvarez, F., Atkeson, A., & Kehoe, P. J. (2009). "Time-varying risk, interest rates, and exchange rates in general equilibrium,". The Review of Economic Studies, 76(3), 851-878.

[3] Christiano, Lawrence, Roberto Motto, and Massimo Rostagno.(2008). "Financial Factors in Business Cycle". Unpublished manuscript, Northwestern University and European Central Bank.

[4] Fleming, J. M. (1962), "Domestic Financial Policies under Fixed and under Floating Exchange Rates," Sta¤ Papers-International Monetary Fund, 369-380.

[5] Jermann, U., & Quadrini, V. (2012). Macroeconomic E¤ects of Financial Shocks. American Economic Review, 102(1), 238-71.

[6] Lahiri, A., Singh, R., & Vegh, C. (2007), "Segmented asset markets and optimal exchange rate regimes". Journal of International Economics, 72(1), 1-21.

7

[7] Mundell, R. A. (1963), "Capital mobility and stabilization policy under …xed and ‡exible exchange rates," Canadian Journal of Economics and Political Science 29(04), 475-485.

[8] Vissing-Jørgensen, A. (2002). Limited Asset Market Participation and the Elasticity of Intertemporal Substitution. Journal of Political Economy, 110(4).

[9] Zervou, A. S. (2013)., "Financial market segmentation, stock market volatility and the role of monetary policy,"European Economic Review, 63, 256-272.

A A.1

Appendix Fixed Exchange Rate

The expected consumption and variance of the non-trader follows trivially from (21). For the trader, using (22) we get ix E(cT;f ) = rE( t

kt

)+

ix V ar(cT;f ) = r2 V ar( t

kt

1

y

(

)+(

1

)(~ y)

(1

)

)2

(A.1)

2 y

Combining (16) and (22) we get kt+1 Assuming

k0

=

kt

+

yt

y:

(A.2)

= 0, implies E( kt+1 ) = E( kt ). Solving (A.2) recursively yields V ar(

kt

) = (t)( )2

2 y

ix ix ) in (31). Substituting E( kt ) and V ar( kt ) in (A.1) we get E(cT;f ) and V ar(cT;f t t

A.2

Flexible Exchange Rates

lex lex Assuming the distribution of yt is IID over time and also symmetric, we get E0 (cN;f ), V ar(cN;f ) t t in (32) by taking a second order approximation of (25). The expected consumption and variance of the trader is obtained using (26) lex E0 (cT;f ) = rE0 ( t

lex V ar(cT;f ) = r2 V ar( t

+(

kt

kt

)+

)2 V ar(

2(1

)

2(1

)

)+

1

)2

(1 2

y ) yt

(1

y

2 y

)(~ y)

+

2r Cov(

kt

yt )+2 yt 1 y Cov(yt ; ) yt

Cov(yt ;

8

2

;

(1 + )

V ar( yt

yt 2

yt yt

) 1

) 1

Cov(

yt y ; ) yt 1 yt

where

(1

)(~ y )(1

)

=

kt+1

> 0. Combining (16) and (26) we get

=

kt

yt

+

yt (1

) yt

2

y yt

+ 1

y+

(1

)

(1 + ):

Immediately it follows that E0 ( kt+1 ) = E0 ( kt ). Without the loss of generality we can assign lex ) in (32) It follows that E0 ( kt ) = 0 and we obtain E0 (cT;f t V ar(

kt

) = ( )2 2

2

2

2 yt

(1

)2 (1 + )(2 )(t 1) + ( )2 + ( )2 (1 )t (1 ) (1 ) t 1 t 1 2 X X ys y y ) 2 Cov(ys ; +2 Cov(ys ; ) ) ys 1 (1 ) y ys

)

)

kt

s=0

Cov(

ys y ; ) ys 1 ys

2

t 2 X

Cov(

ys+1 y ; ) ys ys

2

s=0

On simpli…cation we get V ar(

s=1 t 1 X s=1

2

(1

) ' ( )2 y 2 t + ( 2

= 0:

+(

2

(1

k0

(1

)

(1

)

y

2

(1

(1

)2 (2 )(t

2

(

)

t 2 X

Cov(ys ;

)

)

s=0

1) + (

(y )(t) + 2

(1

)2 + (

) 2

(1

)

ys+1 ) ys

(A.3)

)2 t

( ) + O(~ 2 )

Further, yt

y kt yt ) = (1 ); Cov( ; )= (1 yt 1 yt yt 1 y yt y yt ) = y (1 + ); Cov(yt ; ) = y ; Cov( ; )= (1 + ): Cov(yt ; yt 1 yt yt 1 yt V ar(

) = (1 + )(2 ); V ar(

);

Substituting in V ar(cT;f lex ) lex V ar(cT;f ) ' r2 V ar( t

2(1

kt )

)+

)2

(1 2

y (1 + ) +

2 y

2

+

2(1

(1 + )(2 ) + ( )

y

lex Upon rearranging, we get V ar(cT;f ) in (32), where t value of 0 for = 1.

A.3

2

2

2

=

2 y

=

)2 (1

)

(1 + ) + O( 2(1

)(~ y )(1 y

)

2r 2

)

(A.4)

0 and takes a

Welfare Comparison: Fixed vs Flexible

Upon substituting for the respective consumption moments in (30) we …nd that W f lex

f ix

'

1 (1 1

[

1 )

]

1

(~ y )2 ( + 2) +

[

2 ( y

1 2 2

9

y2

2 1 (1 1

1 )

)] +

(1 1

[(~ y )2 (1 + )(2 )]

)

(~ y)

Rewriting the above as W f lex

f ix

' + (1

(1

)(~ y )(1 )(1

This equation has two roots,

A.4

)

) (~ y) = 1 and

(1

+2

)(~ y )(1

)4(~ y )2 (1

(1 =

(1+(1 2(1

)

y

)+

2(1

)(~ y )(1 y

)

y 2 (1

)2

)2 ) . ) y

Numerical Analysis

Following Zervou (2013), we set the following values for our benchmark calculations Parameter

y y

Value 0:99 3:67 10:83 0:338

Table 1: Benchmark Parameter Values

We conduct a sensitivity analysis for alternate values of y . Figure 1 shows that is monotonically increasing with y and is su¢ ciently greater than the reported values for US economy.

Figure 1: Variation of

10

with =y