The policy rules

In this section we present the Taylor rules employed by the union central bank and the government spending rules of the scal authorities. We consider both contemporaneous and forward looking Taylor rules that react to union in ation and the union output gap. While the monetary authorities seek to offset union wide shocks, scal policy reacts to relative shocks by either adjusting expenditure to uctuations in the terms of trade, relative in ation or the domestic output gap.

Monetary policy rules

We consider two standard Taylor rules where the central bank adjusts interest rates to uctuations in the output gap and in ation. The contemporaneous Taylor rule is given by:

rt =' Wt +'Yy

W

t (4.11)

In this chapter we only consider Taylor rules that react to union variables, since as explained inchapter 1, in the absence of asymmetric price rigidities monetary policy has no impact on relative variables. Furthermore,article 105of theTreaty on European Union

states that maintaining price stability is the Eurosystem of Central Banks' main objective. The target in ation of the ECB is theHarmonized Index of Consumer Pricesin which each country is given a weight equal to its proportion of union consumption, which is equivalent to W

t in our model. Furthermore, the ECB has some scope to support economic activity of

the Euro Area as long as this is not done at the expense of price stability. Hence the above policy rule includes the union output gap in addition to union in ation.

In addition to (4:11), as in previous chapters we consider an interest rate rule that is

forecast based:

rt =' Et W_t+1 +'YEt y W

t+1 (4.12)

The relative importance the central bank attaches to in ation and output is determined by the relative magnitudes of' and'_Y.

In what follows, we will denote the cases where(4:11)is employed by the superscript

C for contemporaneous, while the superscript F will be used when monetary policy is forward looking according to(4:12).

Fiscal policy rules

While restrictions on EMU members' scal policy have been put in place to ensure stability of the euro-zone economy, scal policy can still be used, to some extent, to offset country-speci c or relative shocks. The greater the asymmetry of shocks in a monetary union, the more important is the role of scal policy as an instrument for stabilization.

Below we consider some simple government spending rules for the two countries of our monetary union model. These policy rules differ from the tax rule considered by Evans et al. (2008), in that scal policy is fully nanced in our case.11

We consider three scal policy rules in turn, each to be combined with each of the two Taylor rules outlined above, giving six different policy combinations.

Consider rst the case in which government expenditure reacts to the terms of trade. A deterioration of the terms of trade makes goods produced in home country less competi- tive in relation to those produced in the foreign country. Fomestic government expenditure is therefore increased following such shocks. The policy rule is given by:

G H t = g H T Tt and G F t =g F TTt (4.13)

We stress that(4:13)does not stabilize the terms of trade, but rather hinders stabiliza-

tion. This is in contrast to the interest rate rule considered in chapter 3, which stabilized the terms of trade.

As an alternative to the terms of trade scal policy rule, we consider a rule in which the scal authorities react to relative in ation. As with the terms of trade, rather than off- setting relative in ation, governments use expenditure to support economic activity altered by a shock to relative in ation. The scal policy rule takes the form:

G

H

t = gHR R_t and G

F

t =gFR R_t (4.14)

Finally, we consider the case in which the scal authorities use government expen- diture to close the domestic output gap. This is perhaps the more realistic case as govern- ments have been known to use expansionary budgets in downturns while improving public

nances during booms.

G H t = g H Y y H t and G F t = g F Yy F t (4.15)

Because the state variables of our partitioned system(4:7) (4:10)arenyW_t ; W

t ;

R

t ; Tt

o

, we must manipulate(4:15)to obtain it in terms of these variables. Using the de nition of

union and relative variables to rewrite the conditions in(4:15)yields:

G W t = ngHY + (1 n)gYF y W t n(1 n) g F Y gYH y R t = g_YWyW_t n(1 n)g_YRyR_t and

G R t = gYF gYH y W t ng H Y + (1 n)gYF y R t = g_YRyW_t g_YWyR_t

Furthermore, combining the market clearing conditions(4:1)and rearranging gives:

yR_t = _cTt+ (1 c)G R t

We substitute this expression back into the scal policy rules and rearrange before solving the resulting two expressions simultaneously to obtain union and relative scal policy as a function of the union output gap and the terms of trade. The resulting policy rules are: G W t = W Y y W t + W T Tt and G R t = R Yy W t + R TTt (4:15a)

where we have de ned:

W Y gWY n(1 n)(1 c)(gRY) 2 1+gW Y (1 c) , W T n(1 n)(1 c)(gRY) 1+gW Y (1 c) , R Y h _gR Y 1+gW Y (1 c) i and R T h _gW Y c 1+gW Y (1 c) i

To obtain analytical results we consider a special case of(4:15a)in whichgH Y =gFY

and consequently W T =

R Y = 0.

In sum, the scal policy rules dictate that government spending is either adjusted to the terms of trade(4:13), relative in ation(4:14)or uctuations in the domestic output gap (4:15). We will denote these cases by the superscriptsTT,RIandDY, respectively.

4.2.3 Calibration

To illustrate our results graphically, we assign values to the structural parameters of our model using the calibration suggested by Beetsma & Jensen (2005). For robustness we have also examined our results using two alternative calibrations by Benigno (2004) and Rotemberg & Woodford (1998). We found that our qualitative ndings were not altered, so in what follows we will present only the parameter values of Beetsma & Jensen (2005). We set the intertemporal rate of substitution to 0:99and the coef cient of relative risk

aversion is set to a value of2:5.12 Given that0:6and0:2are reasonable approximations

of the consumption and government expenditure shares of output respectively, we set the steady state consumption to be three times larger than the steady state government expendi- ture, that is _c = 0:75. In choosing the labour supply elasticity and the mark-up , there

is a trade off between getting reasonable values for these and getting a realistic response of in ation to changes in the real variables. By setting = = 3, we get a Phillips curve

coef cient ofk = 0:0086, implying that the elasticity of in ation with respect to the con-

sumption gap is around0:04.13 Price contracts are assumed to last for a year on average (4

quarters) and hence we set = 0:75.14 Finally, we assume, where not otherwise speci ed,

that both countries are of equal size, i.e.n = 0:5.

We now proceed to present our results. We consider each scal policy rule in turn by rst combining it with the contemporaneous and then with the forward looking interest rate rule. In each case, we rst examine determinacy and then E-stability.

12 _{See Beetsma and Schotman (2001).} 13 _{See Beetsma & Jensen (2005, p. 334).}