Monetary Policy and Exchange Rate Volatility in a Small Open Economy

Directory

1. Introduction

2. Gali and Monacelli's small open economy
2.1 The supply side
2.2 The demand side
2.2.1 Several aggregating indices
2.2.2 Household optimization
2.2.3 Exchange rates and terms of trade
2.2.4 Risk sharing and uncovered interest rate parity
2.3 The equilibrium

3. Monetary policy and welfare
3.1 A benchmark regime
3.2 Taylor rules and pegging
3.3 A welfare evaluation

4. Extensions of G+M’s economy

5. Conclusion

Bibliography

Appendix

1. Introduction

Does inflation reduce welfare? What is worse, a volatile exchange rate or a high inflation rate? And is the central bank able to drive these variables?

These questions are the topic of a paper by Jordi Gali and Tommaso Monacelli, published in 2005 and titled “Monetary Policy and Exchange Rate Volatility in a Small Open Economy”.

As apparent by the title Gali and Monacelli (G+M) analyze the influence of monetary policy on the volatility of the exchange rate, more precisely the nominal exchange rate and the terms of trade. For this purpose they create a small open economy with sticky prices of Calvo-type. Due to its minor size this economy does not influence the world economy. However, depending on the degree of openness this economy is affected by the rest of the world.¹

Having specified this framework, G+M introduce three different monetary regimes and evaluate the resulting exchange rate volatilities . Using a central bank loss function G+M rank these three rules according to the implied welfare which shows a positive correlation between welfare and exchange rate volatility.² Thence G+M prefer Taylor rules over an exchange rate pegging.

To get a general idea of Gali and Monacelli's argumentation this expose will start in chapter 2 with an abbreviated overlook over G+M’s model of a small open economy. In the following chapter there will be the introduction of the three central bank rules, necessary to close the model, as well as an analysis of the underlying welfare levels. Since the welfare evaluation is based on some special assumptions, chapter 4 will give an overview of recent literature which discusses possible extensions as well as their implications for G+M’s ranking of implied wel­fare. Concluding chapter 5 will summarize G+M’s most important results as well as evaluate if the possible extensions render G+M’s analysis, respectively their results, worthless.

2. Gali and Monacelli's small open economy

The following description of Gali and Monacelli's small open economy depicts only a portion of the original equations and only the final results, no derivations. It thus is an abbreviated descrip­tion. If reasonable log linear first order approximations will be used instead of the original equa­tions - as G+M themselves did.

As in G+M variables without an index denote the small open economy under observation (the “home economy”) while an i subscript denotes a trading partner, country i. A star superscript is used in variables of the world economy, which the home economy is too small to influence.

After this remarks the expose will describe the supply side, then the demand side and subse­quently the resulting equilibrium of the small open economy.

2.1 The supply side

The home economy’s aggregate output is described by equation (1): [Abbildung in dieser Leseprobe nicht enthalten] (1)

where yt is (log) aggregate domestic output. Since the production does not need any capital

output is determined solely by (log) employment (nt ) and a productivity factor (at ). This TFP follows an AR(1) process,³ and is the source of the exogenous shocks affecting the home econ­ omy in the volatility discussion below.

Using this output function it follows that marginal costs mct are given by (2): [Abbildung in dieser Leseprobe nicht enthalten] (2)

with [Abbildung in dieser Leseprobe nicht enthalten] and τ an employment subsidy necessary to smooth the effects of monopo­listic distortions in order to get an optimal allocation. (Log) nominal wage is the variable wt while ^H t describes the log of the domestic price level.

The price setting follows Calvo (1983)⁴ Thus only a fraction 1-Θ of firms are randomly se­lected to optimize their prices in period t while the rest has to keep the price set in the previous price setting cycle. If β is the common one period discount factor and μ = log βγ the mark up of the firms on marginal costs due to monopolistic markets then the newly chosen domestic

price pH,t will be:⁵

Abbildung in dieser Leseprobe nicht enthalten

(3)

The price thus depends on forward looking variables. More precisely, it is determined by expec­tations of future marginal costs and the current price level since the firm knows that it may be unable to re-optimize its price in the following period(s). This is just like in the standard closed economy models with Calvo price setting.⁶

2.2 The demand side

As the supply side is described by aggregating the optimization problems of the various firms the demand side is in turn determined by the optimization of a representative household who gains utility from consumption (Ct ) and disutility from delivering work (Nt ).

Since there is no “unique consumption good” in the home economy it is necessary to use indices which aggregate the various goods which are available in the economy.

2.2.1 Several aggregating indices

The whole consumption of the home economy (Ct ) consists of consuming home and foreign produced goods (CH ,t and CF,t ). As to be seen by equation (4) the exact composition is depend­ant on the substitutability between domestic and foreign goods (η) as well as by the degree of openness of the economy (a) .⁷

good j produced at home, ε represents the elasticity of substitution between goods produced

o

within a given country. C, t is an index for all goods imported from country i, so that γ, a

measurement for the substitutability between goods produced in different foreign countries, de­termines the exact composition of CF t, the index of imported goods.

Price indices are denoted, and aggregated, likewise so that PH,t is (as stated above) the domestic price level, Pi t a price index of goods imported from country⁸ i while Pp t is the price index of all goods which are imported by the home economy.⁹

Therefore the consumer price index Pt, a weighted average of the price levels of home produced and imported goods, is characterized by equation (5).¹⁰ [Abbildung in dieser Leseprobe nicht enthalten](5)

2.2.2 Household optimization

The households gain utility from consumption and leisure.¹¹ Since they face a budget constraint, they have the following optimization problem:

Abbildung in dieser Leseprobe nicht enthalten

(6)

with Tt a lump sum tax/transfer, [Abbildung in dieser Leseprobe nicht enthalten] a discount factor and Dt+1 the pay off from a one period bond bought in period t.

[...]

¹ Cp. Gali/Monacelli (2005, pp.709-719)

² Cp. Gali/Monacelli (2005, pp.719-727)

³ ^ = Paat-1 + £

⁴ Cp. Calvo (1983, pp.383-398)

⁵ Cp. Gali/Monacelli (2005, p.715)

⁶ Cp. Lane (2001, p.241)

⁷ (1 - a) depicts the degree of home bias in consumption

⁸ This ε influences the mark up of the production sector, see equation (3).

⁹ Cp. Gali/Monacelli (2005, pp.709-711)

¹⁰ Abbreviated CPI and log linearized pt = (1 - a)t + apF t

¹¹ Or equivalently disutility from working