The Effects of Fiscal Policy in a Small Open Economy with a Fixed Exchange Rate

Abstract

We study the empirical effects of fiscal policy in Denmark since the adoption of a fixed exchange rate policy in 1982. Denmark’s fixed exchange rate implies that the nominal interest rate remains fixed after a fiscal expansion, facilitating a substantial impact of the fiscal stimulus on the real economy. On the other hand, the large degree of openness of the Danish economy means that a sizeable share of the fiscal stimulus will be directed towards imported goods. Our results suggest that the ‘monetary accomodation channel’ dominates the ‘leakage effect’ in the short run. We demonstrate that fiscal stimulus has a rather large impact on economic activity in the very short run, with a government spending multiplier of 1.1 on impact in our preferred specification. We also find that the effects of fiscal stimulus are rather short-lived in Denmark, with the effect on output becoming insignificant after around two years. The fiscal multiplier is above 1 only in the first quarter, and drops to 0.6 one year after the shock. We also find that in the short run, the government spending multiplier is larger than the tax multiplier. Finally, we demonstrate that exogenous shocks to government spending account for less than 10 % of the movements in output over the business cycle in Denmark.

Appendices

Appendix A: Additional Tables and Figures

Table 3 Unit root and stationarity tests

Table 4 Specificationtests for the VAR

Fig. 4

The effects of a shock to government spending, specification with stochastic trend

Fig. 5

The sensitivity of the estimated impact multiplier of government spending to the elasticity of government spending to output. The red dot indicates our baseline estimate of b ₃ = 0

Fig. 6

Historical decomposition. The blue line shows deviations in output growth relative to its trend growth. The red line shows the share explained by deviations in the growth rate of F _t relative to its trend

Fig. 7

Historical decomposition. The blue line shows deviations in output growth relative to its trend growth. The red line shows the share explained by deviations from trend in other domestic variables than government spending

Appendix B: Computing the Output Elasticity of Taxes

This appendix provides a detailed account of how we obtain an estimate of the elasticity of taxes to changes in output, as employed in Section 4.

We decompose the total tax revenue into four categories: Income taxes, corporate taxes, indirect taxes, and social contributions. We then obtain the elasticity of each of these types of taxes from a study by the OECD (Girouard and André 2005). Moreover, recall that we use a measure of taxes net of transfers. We therefore also need an estimate of the elasticity of transfers to changes in output. Finally, we weigh the elasticities together according to their average share of total net revenues during our sample period.

The tax elasticities estimated by Girouard and André (2005) for Denmark are the following: Income taxes; 1.0. Indirect taxes; 1.0. Corporate taxes; 1.6. Social contributions; 0.7. We refer the reader to that study for further details.

As for transfers, we follow Girouard and André and assume that unemployment benefits is the only type of transfers that contains a significant cyclical component. We therefore compute the sample average share of unemployment-related transfers to total transfers, and multiply this share by the elasticity of unemployment with respect to the output gap, which Girouard and André estimate to −7.9 for Denmark.

As noted in the main text, we arrive at an output elasticity of net tax revenues of 2.09.

Appendix C: Computing Variance Decompositions

To perform the variance decompositions, we rely on results from spectral analysis. Recall that any covariance-stationary time series can be represented equally well in the frequency domain as in the time domain (Hamilton 1994). In the frequency domain, the spectral density of the process is a measure of the share of the overall variance of the process accounted for at various frequencies. If the spectral density is high at low frequencies, much of the variation of the process can be interpreted as long-term movements in the data, perhaps reflecting an underlying trend.

For our VAR-model outlined in Section 2, the spectral density of X _t at any frequency ω is given by:¹⁶

$$ S_{X}\left( \omega \right) =\left[ I-A\left( e^{-i\omega }\right) \right]^{-1}CC^{\prime }\left[ I-A\left( e^{-i\omega }\right)^{\prime }\right]^{-1} $$

(11)

Here, A is the coefficient matrix from the VAR regression, and I is the identity matrix. C is the matrix linking the reduced-form residuals of the VAR-regression to the structural shocks of the model, with the property CC′ = V, as described in Subsection 2.2. i denotes complex i, so that i ² = −1. Thus, the function assigns to any frequency ω a square matrix of complex numbers. However, as pointed out in Hamilton (1994), the complex part of the diagonal elements in this matrix will in fact be zero. The spectral density at frequency ω for each of the variables in Y _t is given exactly by these (real and non-negative) diagonal elements of the matrix.

We want to compute the variance of each of the variables in X _t that is accounted for by each of the shocks in ε _t . Recall that in the expression for the spectral density, CC′ = V denotes the variance-covariance matrix when all the shocks are ‘turned on’. Following Altig et al. (2005), in order to compute the spectral density of X _t when only the j’th shock (j = 1,..,4) is turned on, we can replace CC′ by $CI_{j}C^{\prime }$, where I _j is a square matrix of zeros, except for a unit entry in the j’th diagonal element. In other words,

$$ S_{X}^{j}\left( \omega \right) =\left[ I-A\left( e^{-i\omega }\right) \right]^{-1}CI_{j}C^{\prime }\left[ I-A\left( e^{-i\omega }\right)^{\prime }\right]^{-1} $$

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denotes the spectral density of X _t when only shock j is active.

As the spectral density for variable k is given by the k’th diagonal element of $S_{X}\left ( \omega \right )$, we can then compute the fraction of the variance of the k’th variable accounted for by the j’th shock at frequency ω as:

$$ var_{k,j}\left( \omega \right) =\frac{\left[ S_{X}^{j}\left( \omega \right) \right]_{kk}}{\left[ S_{X}\left( \omega \right) \right]_{kk}} $$

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-where $\left [ M\right ]_{kk}$ denotes element (k,k) of matrix M. Observe that by construction:

$$ \sum\limits_{j=1}^{4}var_{k,j}\left( \omega \right) =1 $$

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Having decomposed the variance of any variable at any frequency, we can then sum the variance ratios over various frequency bands, for example the business cycle frequencies, and see how important each shock is for each variable within these frequency bands.