Accessible Unlicensed Requires Authentication Published by De Gruyter Oldenbourg August 7, 2018

Output Gap Uncertainty and the Optimal Fiscal Policy in the EU

Tero Kuusi
From the journal Review of Economics

Abstract

Using a novel dataset, I quantify the magnitude of the EU-27 countries’ output gap revisions in 2002–2014, and study the implications of this uncertainty for the optimal fiscal policy with a DSGE model. I find that taking into account the output gap uncertainty (i.e. the difficulty to distinguish between cyclical and trend shocks in real time) has large implications for both the net lending and fiscal policy. In the median EU country, the primary net lending turns mildly countercyclical; a feature that is consistent with the data, but contrasts with the procyclical net lending under the full output gap information. The optimal fiscal policy, as measured by the changes in the cyclically-adjusted budget balance (CAB), is cautious and turns from strongly to weakly countercyclical because of the uncertainty. During fiscal crises, the CAB is allowed to deteriorate less and the adjustment of the CAB is gradual, while underestimation of the uncertainty may lead to more volatile policy. The uncertainty generates a substantial amount of cross-country heterogeneity in the dynamics of the total net lending, but not so much in the CAB-based fiscal policy.

JEL Classification: D84; E32; E62

Funding statement: This study has been funded by theHorizon 2020 Framework Programme of the European union under the grant agreement number 649261 (the Firstrun project), and the Academy of Finland (DEBTWELL).

Acknowledgements

I would like to thank Niku Määttänen, Tarmo Valkonen, Vesa Vihriälä, Jukka Lassila, as well as the participants in the seminars organized by ETLA and DEBTWELL for their useful comments.

Appendix

Standard error of the signal noise parameter

Formally, the estimator reduces to finding the parameter value σˆe2 that maximizes the likelihood of the filter conditional on the two predetermined parameters [ρϵ,ρg] whose probability distribution are estimated separately using the ex-post data (given the ρ coefficients, the other income process parameters can be solved from the data). To provide the standard errors of the estimator at the point estimate σˆe2, it is noticeable that its score function can be written as a linear approximation

(24)ddσˆe2logL(σe2,X)=ddσˆe2logL(σˆe2,X)+d2(dσˆe2)2logL(σˆe2,X)(σe2σˆe2)+ddσˆe2ddρϵˆlogL(σˆe2,X)(ρϵρϵˆ)+ddσˆe2ddρgˆlogL(σˆe2,X)(ρgρgˆ)

The maximization implies that ddσˆe2logL(σˆe2,X)=0. Rearranging the equation and multiplying it by the square root of the number of observations n, implies that

(25)n(σe2σˆe2)=nddσˆe2logL(σe2,X)d2(dσˆe2)2logL(σˆe2,X)ddσˆe2ddρϵˆlogL(σˆe2,X)d2(dσˆe2)2logL(σˆe2,X)n(ρϵρϵˆ)
(26)ddσˆe2ddρgˆlogL(σˆe2,X)d2(dσˆe2)2logL(σˆe2,X)n(ρgρgˆ),

and furthermore that

(27)n(σe2σˆe2)=1/nddσˆe2logL(σe2,X)1/nd2(dσˆe2)2logL(σˆe2,X)ddσˆe2ddρϵˆlogL(σˆe2,X)1/nd2(dσˆe2)2logL(σˆe2,X)1/n(ρϵρϵˆ)
(28)ddσˆe2ddρgˆlogL(σˆe2,X)1/nd2(dσˆe2)2logL(σˆe2,X)1/n(ρgρgˆ),

By the law of large numbers and the central limit theorem

(29)1/nd2(dσˆe2)2logL(σˆe2,X)nd2(dσˆe2)2logL(σˆe2)V1
(30)1/nddσˆe2logL(σe2,X)nN(0,V1)
(31)ddσˆe2ddρϵˆlogL(σˆe2,X)1/nd2(dσˆe2)2logL(σˆe2,X)nddσˆe2ddρϵˆlogL(σˆe2)d2(dσˆe2)2logL(σˆe2)V2
(32)ddσˆe2ddρgˆlogL(σˆe2,X)1/nd2(dσˆe2)2logL(σˆe2,X)nddσˆe2ddρgˆlogL(σˆe2)d2(dσˆe2)2logL(σˆe2)V3

Then,

(33)VAR(σˆe2)n1V1+V22VAR(ρϵˆ)+V32VAR(ρgˆ)
Figure 8: Country-specific real-time and ex-post output gaps. Note: The estimation exactly matches the models real-time output gaps with the actual real-time output gaps.

Figure 8:

Country-specific real-time and ex-post output gaps. Note: The estimation exactly matches the models real-time output gaps with the actual real-time output gaps.

Table 5:

Country-specific parameter estimates and their standard errors (in parenthesis)

ρϵρggbarσe2,filter
AT0.3810.9580.0202.50E-05
(0.248)(0.028)(0.009)(6.24E-06)
BE0.4510.9530.0162.40E-05
(0.201)(0.030)(0.005)(5.85E-06)
BG0.4670.8700.0202.14E-04
(0.292)(0.086)(0.012)(8.04E-05)
CY0.8830.9530.0121.66E-04
(0.128)(0.031)(0.021)(4.11E-05)
CZ0.6880.8510.0181.24E-04
(0.244)(0.116)(0.006)(4.45E-05)
DE0.4010.9380.0194.87E-05
(0.229)(0.096)(0.010)(2.64E-05)
DK0.7610.9390.0135.55E-05
(0.117)(0.040)(0.005)(1.42E-05)
EE0.6730.8270.0315.42E-04
(0.196)(0.079)(0.010)(1.99E-04)
EL0.9580.9690.0012.04E-04
(0.040)(0.025)(0.019)(4.56E-05)
ES0.9490.9460.0171.29E-04
(0.043)(0.045)(0.013)(2.86E-05)
FI0.5840.9460.0101.80E-04
(0.204)(0.032)(0.006)(6.78E-05)
FR0.7510.9630.0173.55E-05
(0.105)(0.027)(0.006)(8.99E-06)
HU0.6620.9320.0227.85E-05
(0.180)(0.041)(0.011)(2.12E-05)
IE0.7400.9410.0352.53E-04
(0.161)(0.035)(0.013)(5.57E-05)
IT0.6800.9130.0095.55E-05
(0.155)(0.082)(0.009)(1.77E-05)
LH0.5190.8380.0414.62E-04
(0.228)(0.093)(0.013)(1.42E-04)
LU0.6410.9240.0412.22E-04
(0.106)(0.080)(0.013)(8.91E-05)
LV0.6260.8500.0355.86E-04
(0.181)(0.086)(0.018)(1.49E-04)
MT0.2250.5540.0283.56E-05
(0.267)(0.164)(0.003)(9.98E-06)
NL0.7040.9790.0183.76E-05
(0.160)(0.014)(0.012)(9.71E-06)
PL0.7440.8520.0387.99E-05
(0.104)(0.087)(0.004)(2.74E-05)
PT0.8560.9820.0136.72E-05
(0.126)(0.011)(0.021)(2.16E-05)
RO0.6980.7760.0241.75E-04
(0.193)(0.204)(0.008)(9.07E-05)
SE0.5740.8980.0186.71E-05
(0.132)(0.075)(0.006)(2.43E-05)
SI0.6510.9430.0213.28E-04
(0.343)(0.056)(0.017)(2.81E-04)
SK0.6020.7920.0381.84E-04
(0.301)(0.169)(0.006)(1.16E-04)
UK0.7250.9430.0174.04E-05
(0.091)(0.032)(0.004)(8.29E-06)
Table 6:

Estimated elasticities of private net lending and the output gap semi-elasticity of the government budget balance.

The OG elasticityThe OG Semi-elasticity of the private net lendingof the government balance (OECD method)
AT0.650.58
BE1.260.61
BG0.31
CY0.52
CZ0.980.43
DE0.60.55
DK1.880.62
EE1.780.44
EL0.710.48
ES3.390.54
FI0.630.57
FR0.650.6
HU1.270.49
IE3.350.53
IT0.520.54
LH0.41
LU1.540.44
LV0.38
MT0.46
NL1.080.65
PL2.260.52
PT3.220.51
RO0.34
SE0.460.59
SI2.160.48
SK1.20.39
UK1.170.59
Median1.170.52

  1. Note: The elasticity of the private lending is estimated by first calculating the net lending of the private sector from the OECD national accounts (code NFB9P), including non-financial corporations, financial corporations, and households and non-profit institutions serving households. The data is typically available after the mid-1990s and the most recent year is 2012. The elasticity is then calculated by regressing the variable on the real-time OG.

Table 7:

Sensitivity analysis.

CorrelationCorrelationAverageCorrelationCorrelationAverage CABAverage Δ CAB
(PB, rtime OG)(PB, true OG)net debt(CAB, rtime OG)(CAB, true OG)if CAB < 0.5if CAB < 0.5
(a)(b)(c)(d)(e)(f)(g)
Benchmark (σeobs and σefilter from the data)0.050.0639.850.650.173.251.42
Expected noise (σeobs=σefilter)0.190.1439.370.470.241.860.64
No noise0.270.2638.960.790.792.741.01
Estimation using
endogenous moment weights0.050.00340.210.630.382.571.10
Data 90-0.580.3632.30.460.493.40.2 (0.53)*
Change as a response to parameter
adjustment, when compared to the benchmark:
10% AR(output gap) ρϵ0.0340.0040.590.010.0190.0460.122
10% AR(potential growth) ρg0.0180.0151.360.1250.1090.5750.475
10% potential growth gˉ0.0010.0022.230.0050.010.0480.02
10% noise perceived σefilter0.0030.0090.330.0160.0160.1860.121
10% IR shock σr20.0010.0080.060.0180.0240.0610.014
10% riskfree IR rf0.0110.0083.540.0080.0040.0870.006
10% OG shock σ20.0070.0120.200.0090.0460.028
10% pot. shock σ20.0250.0240.620.0180.0020.0650.085
10% risk aversion θ0.0020.0081.930.0130.0090.0620.068
10% time preference β0.2650.12333.160.0250.0080.3540.305
10% Debt-IR elasticity κ0.00504.570.0080.0030.1530.102
10% Actual signal noise σeobs0.0060.0020.010.0250.0190.0770.041

  1. Note: The results are based on 200 iterations with each having 200 periods of simulated shocks for each specification. The first 100 periods of each iteration are omitted as a burn-in phase.

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Published Online: 2018-08-07
Published in Print: 2018-08-28

© 2018 Oldenbourg Wissenschaftsverlag GmbH, Published by De Gruyter Oldenbourg, Berlin/Boston