## 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.

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## Notes

In addition, international capital mobility has increased during our sample due to financial liberalization. In accordance with the description of the effects of fiscal policy under a fixed exchange rate in the Mundell-Fleming model above, this also suggests an increase in the fiscal multiplier over time.

The reason why the fiscal multiplier can be larger than 1 even though private consumption drops is that we find a rise in private investment on impact, after which it becomes insignificant

This literature focuses on anticipation effects by assuming that agents react to fiscal policy shocks when they are announced, rather than when they are implemented.

Importantly, the same critique does not apply to the automatic elasticity of government spending with respect to output.

Indeed, Blanchard and Perotti (2002) also present evidence from a specification in which private consumption is included along with government spending, taxes, and output.

Moreover, beginning in early 1983, an automatic indexation of wages and transfers to the rate of inflation was suspended. This is likely to have played an important role in bringing down the inflation rate.

Recall that \(e_{t}^{f}=f_{t}\).

Of course, when we set \(b_{3}=0\) so that \(g_{t}^{\prime }=g_{t}\), the use of \(g_{t}^{\prime }\) as an instrument in practice becomes redundant. On the other hand, when we set \(b_{3}\neq 0\), or in the specification with taxes instead of government spending, this step becomes relevant.

It should be noted that the multiplier reported by Ilzetzki et al. (2013) is a cumulative multiplier, measuring the accumulated increase in output over a number of quarters. The impact multiplier is substantially smaller in their study.

In particular, it may seem puzzling that the government spending multiplier is above 1 despite the drop in consumption. In results not reported, we find that this is explained by an increase in private investment on impact. The increase in investment is large on impact, after which it quickly reverts back around zero. In effect, the impulse response of investment mirrors that of private consumption.

In results not reported, we observe that consumption rises on impact when

*b*_{3}is sufficiently low. In fact, we find that this explains the divergence between the negative consumption response in the present study and the positive response obtained by Bergman and Hutchison (2010), who set*b*_{3}= −0.2.Note that the shock to tax revenues has been normalized to 1, so as to facilitate comparison with the shock to government spending. The response of tax revenues, however, is smaller than 1 already on impact, as the rise in taxes implies a drop in output, and hence in the tax base.

The figure also suggests that fiscal policy was not tightened sufficiently in the years leading up to the recent crisis. As seen from Fig. 6 in the Appendix A that Denmark’s trading partners exerted a strong, positive impact on the Danish economy in 2006–07. Moreover, a recent study by Ravn (2012) suggests that, as a consequence of Denmark’s fixed exchange rate towards the euro, the Danish interest rate was substantially lower than what would have been prescribed by a Taylor rule for Denmark in the years 2005–2007. These factors would have called for an even tighter stance of fiscal policy during these years than what can be observed from Fig. 3.

Our SVAR-model is of course much more rudimentary, and in particular does not feature shocks to the labor supply. In our setup, however, such shocks are likely to show up as fundamental shocks to

*Y*_{ t }; or perhaps to*C*_{ t }through the consumption/labor decision of households.

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## Additional information

The views expressed in this paper are those of the authors, and do not necessarily correspond to those of Danmarks Nationalbank. The authors would like to thank Michael Bergman, Ester Faia, Francesco Furlanetto, Jesper Lind´e, Ivan Petrella, two anonymous referees, and colleagues at Danmarks Nationalbank for useful comments and suggestions. Any remaining errors are our own.

## Appendices

### Appendix A: Additional Tables and Figures

### 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:^{Footnote 16}

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,

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:

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

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.

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Ravn, S.H., Spange, M. The Effects of Fiscal Policy in a Small Open Economy with a Fixed Exchange Rate.
*Open Econ Rev* **25**, 451–476 (2014). https://doi.org/10.1007/s11079-013-9288-2

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DOI: https://doi.org/10.1007/s11079-013-9288-2