The Role of Energy in a Real Business Cycle Model with an Endogenous Capital Utilization Rate in a Government Sector: Lessons from Bulgaria (1999–2016) Cover

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The Role of Energy in a Real Business Cycle Model with an Endogenous Capital Utilization Rate in a Government Sector: Lessons from Bulgaria (1999–2016)

Central European Economic Journal

Volume 5 (2018): Issue 52 (January 2018)

By: Aleksandar Vasilev

Open Access

|Jul 2019

Figures & Tables

Impulse responses to a 1% surprise innovation in technology.

Impulse responses to a 1% surprise innovation in energy price.

Business Cycle Moments

σ_y	Data	Model
σ_c/σ_y	0.55	0.14
σ_i/σ_y	1.77	1.97
σ_g/σ_y	1.21	1.00
σ_h/σ_y	0.63	0.63
σ_w/σ_y	0.83	0.39
σ_y/h/σ_y	0.86	0.39
σ_u/σ_y	3.22	0.63
σ_w/σ_h	1.32	1.61

corr(c, y)	0.85	0.47
corr(i, y)	0.61	0.75
corr(g, y)	0.31	1.00
corr(h, y)	0.49	0.96
corr(w, y)	-0.01	0.97
corr(u, y)	-0.47	-0.96
corr(h, y/h)	-0.14	0.92

Autocorrelations for Bulgarian data and the model economy

		k

Method	Statistic	0	1	2	3
Data	corr(u_t, u_{t − k})	1.000	0.765	0.552	0.553
Model	corr(u_t, u_{t − k})	1.000	0.955	0.901	0.837
	(s.e.)	(0.000)	(0.027)	(0.051)	(0.073)
Data	corr(n_t, n_t − _k)	1.000	0.484	0.009	0.352
Model	corr(n_t, n_{t − k})	1.000	0.955	0.901	0.837
	(s.e.)	(0.000)	(0.027)	(0.051)	(0.074)
Data	corr(y_t, y_{t − k})	1.000	0.810	0.663	0.479
Model	corr(y_t, y_{t − k})	1.000	0.955	0.901	0.836
	(s.e.)	(0.000)	(0.027)	(0.050)	(0.073)
Data	corr(a_t, a_{t − k})	1.000	0.702	0.449	0.277
Model	corr(a_t, a_{t − k})	1.000	0.955	0.900	0.836
	(s.e.)	(0.000)	(0.026)	(0.050)	(0.072)
Data	corr(c_t, c_{t − k})	1.000	0.971	0.952	0.913
Model	corr(c_t, c_{t − k})	1.000	0.955	0.903	0.845
	(s.e.)	(0.000)	(0.026)	(0.050)	(0.073)
Data	corr(i_t, i_{t − k})	1.000	0.810	0.722	0.594
Model	corr(i_t, i_{t − k})	1.000	0.954	0.901	0.841
	(s.e.)	(0.000)	(0.026)	(0.050)	(0.073)
Data	corr(w_t, w_{t − k})	1.000	0.760	0.783	0.554
Model	corr(w_t, w_{t − k})	1.000	0.920	0.900	0.836
	(s.e.)	(0.000)	(0.026)	(0.050)	(0.073)

Dynamic correlations for Bulgarian data and the model economy

		k

Method	Statistic	-3	-2	-1	0	1	2	3
Data	corr(n_t, (y/n)_{t − k})	-0.342	-0.363	-0.187	-0.144	0.475	0.470	0.346
Model	corr(n_t, (y/n)_{t − k})	0.123	0.195	0.292	0.918	0.288	0.221	0.171
	(s.e.)	(0.320)	(0.286)	(0.250)	(0.146)	(0.243)	(0.281)	(0.317)
Data	corr(n_t, w_{t − k})	0.355	0.452	0.447	0.328	-0.040	-0.390	-0.57
Model	corr(n_t, w_{t − k})	0.123	0.195	0.292	0.918	0.288	0.221	0.171
	(s.e.)	(0.320)	(0.286)	(0.250)	(0.146)	(0.243)	(0.281)	(0.317)

Data Averages and Long-run Solution

Variable	Description	Data	Model
y	Steady-state output	N/A	1.000
c/y	(non-energy) Consumption-to-output ratio	0.624	0.624
i/y	Investment-to-output ratio	0.201	0.175
pe/y	Energy consumption-to-output ratio	0.151	0.151
gt/y	Government transfers-to-output ratio	0.220	0.149
wh/y	Labor income-to-output ratio	0.571	0.571
ruk/y	Capital income-to-output ratio	0.429	0.429
h	Share of time spent working	0.333	0.333
r¯	After-tax net return on capital	0.014	0.016

Model Parameters

Parameter	Value	Description	Method
β	0.982	Discount factor	Calibrated
α	0.429	Capital share	Data average
1 − α	0.571	Labor share	Calibrated
ψ	0.873	Relative weight attached to consumption	Calibrated
σ	2.000	Curvature parameter, utility function	Set
δ	0.013	Depreciation rate on physical capital	Data average
ω₀	0.013	Scale parameter, depreciation function	Calibrated
ω₁	1.250	Curvature parameter, depreciation function	Set
ν₀	0.0143	Scale parameter, energy utilization function	Data average
ν₁	1.610	Curvature parameter, energy utilization function	Set
τ^y	0.100	Average tax rate on income	Data average
τ^c	0.200	VAT/consumption tax rate	Data average
A	0.604	Steady-state value of TFP process	Calibarated
p	1.000	Steady-state energy price level	Calibrated
ρ_a	0.701	AR(1) persistence coefficient, TFP process	Estimated
ρ_p	0.980	AR(1) persistence coefficient, energy price process	Estimated
σ_a	0.044	st. error, TFP process	Estimated
σ_p	0.013	st. error, energy process	Estimated

DOI: https://doi.org/10.1515/ceej-2018-0011 | Journal eISSN: 2543-6821 | Journal ISSN: 2544-9001

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Language: English

Page range: 130 - 141

Published on: Jul 12, 2019

Published by: Faculty of Economic Sciences, University of Warsaw

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

Keywords:

business fluctuations,

capital utilization rate,

endogenous depreciation rate,

Related subjects:

Business and economics,

Political economics,

Economic theory, systems and structures,

Microeconomics,

Macroeconomics,

Economic policy

© 2019 Aleksandar Vasilev, published by Faculty of Economic Sciences, University of Warsaw
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

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