Abstract
In this paper, our objective is to analyze sustainable debt policy rules and economic growth using a model of endogenous economic growth theory. For the government, it is possible to run into debt, but the primary surplus is a positive linear function of the debt-to-GDP ratio which guarantees that public debt is sustainable. We analyze different sustainable debt policies in this small open economy model of endogenous growth with public capital accumulation, as well we take transitions into account. We investigate the characteristics and stability of the steady state, and we analyze the effects on welfare for the different debt policies.
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Notes
From now on, we omit the time argument t if no ambiguity arises.
If \(\psi\) takes a large (small) value, the government adjusts \(b=\frac{B}{Y}\) at a fast (slow) pace.
The world interest rate exceeds the growth rate of GDP on average.
Foreign assets (FA) is wealth held abroad that generates interest income, if positive. If FA is negative, this leads to interest payments to foreign countries.
The income tax rate is fixed.
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Acknowledgements
I would like to thank two anonymous referees for their valuable comments which helped to improve the paper. I am indebted to Alfred Greiner and Christiane Clemens for the inspiring ideas and the support received in various meetings. Further, I would like to thank António Afonso, Matthias Schön, Paolo Pasimeni and other participants for very competent and detailed comments during the INFER Workshop on New Challenges for Fiscal Policy.
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Appendix
Appendix
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for the stated parameter setting with \(\sigma =2\) and \(\phi =0.04\)
\(\sigma =2\quad \phi =0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | 1.333 | − 10.135 | 0.237 | 0.01 | Real Eigenvalues (+, +, −) |
\(\psi =0.02\) | 2. | − 8.357 | 0.281 | 0.01 | Real Eigenvalues (+, −, +) |
\(\psi =0.03\) | 4. | − 3.024 | 0.414 | 0.01 | Real Eigenvalues (+, −, +) |
\(\psi =0.035\) | 8. | 7.643 | 0.681 | 0.01 | Real Eigenvalues (+, −, +) |
\(\psi =0.04\) | Complex | \(2.951 * 10^{16}\) | Complex | 0.01 | Not solvable |
\(\psi =0.041\) | − 40. | − 120,357 | − 2519 | 0.01 | Real Eigenvalues (+, −, +) |
\(\psi =0.0415\) | − 26.667 | − 84.802 | − 1.630 | 0.01 | Real Eigenvalues (+, −, +) |
\(\psi =0.1\) | − 0.667 | − 15.468 | 0.103 | 0.01 | Real Eigenvalues (+,-,-) |
\(\psi =0.2\) | − 0.25 | − 14.357 | 0.131 | 0.01 | Real Eigenvalues (+,-,-) |
\(\psi =11\) | − 0.004 | − 13.700 | 0.148 | 0.01 | Real Eigenvalues (−, +, −) |
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for the stated parameter setting with \(\sigma =0.7\) and \(\phi =-0.04\)
\(\sigma =0.7\quad \phi =-0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.005\) | − 2.435 | − 16.595 | 0.383 | 0.03 | Real Eigenvalues (+, −, +) |
\(\psi =0.01\) | − 3.5 | − 18.116 | 0.374 | 0.03 | Real Eigenvalues (+, −, +) |
\(\psi =0.02\) | − 28 | − 53.116 | 0.149 | 0.03 | Real Eigenvalues (+, −, +) |
\(\psi =0.021\) | − 93.333 | − 146.45 | − 0.451 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.025\) | 11.2 | 2.884 | 0.509 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.027\) | 7.18 | − 2.86 | 0.472 | 0.03 | Eigenvalues |
(0.536 + 0i, − 0.012 ± 0.002i) | |||||
\(\psi =0.03\) | 4.667 | − 6.45 | 0.448 | 0.03 | Eigenvalues |
(0.535 + 0i, − 0.014 ± 0.007i) | |||||
\(\psi =0.04\) | 2.154 | − 10.04 | 0.425 | 0.03 | Eigenvalues |
(0.534 + 0i, − 0.018 ± 0.012i) | |||||
\(\psi =0.05\) | 1.4 | − 11.116 | 0.419 | 0.03 | Eigenvalues |
(0.533 + 0i, − 0.022 ± 0.015i) | |||||
\(\psi =0.1\) | 0.509 | − 12.389 | 0.410 | 0.03 | Eigenvalues |
(0.526 + 0i, − 0.044 ± 0.005i) | |||||
\(\psi =0.2\) | 0.224 | − 12.796 | 0.408 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.3\) | 0.144 | − 12.911 | 0.407 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.5\) | 0.084 | − 12.997 | 0.406 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.9\) | 0.046 | − 13.051 | 0.406 | 0.03 | Real Eigenvalues (−, +, −) |
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for the stated parameter setting with \(\sigma =0.7\) and \(\phi =0.04\)
\(\sigma =0.7\) \(\phi =0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | 3.5 | − 8.116 | 0.438 | 0.03 | Real Eigenvalues (+, −, +) |
\(\psi =0.02\) | 28 | 26.884 | 0.663 | 0.03 | Real Eigenvalues (+, −, +) |
\(\psi =0.03\) | − 4.667 | − 19.783 | 0.363 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.05\) | − 1.4 | − 15.116 | 0.392 | 0.03 | Real Eigenvalues (+, −, −) |
\(\psi =0.1\) | − 0.5091 | − 13.844 | 0.401 | 0.03 | Real Eigenvalues (+, −, −) |
Different parameter setting: \(r=0.035\), \(\tau =0.2\), \(\rho = 0.02\), \(\alpha =0.3\)
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for a different parameter setting with \(\sigma =0.9\) and \(\phi =-0.04\)
\(\sigma =0.9\) \(\phi =-0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | − 2.483 | − 28.755 | 0.010 | 0.009 | Real Eigenvalues (+, +, −) |
\(\psi =0.02\) | − 6.545 | − 43.91 | − 0.279 | 0.009 | Eigenvalues |
(0.461+0i, 0.004 ± 0.007i) | |||||
\(\psi =0.03\) | 10.286 | 18.873 | 0.921 | 0.009 | Eigenvalues |
(0.459+0i, − 0.0003 ± 0.012i) | |||||
\(\psi =0.04\) | 2.88 | − 8.751 | 0.393 | 0.009 | Eigenvalues |
(0.457+0i, − 0.004 ± 0.014i) | |||||
\(\psi =0.1\) | 0.541 | − 17.475 | 0.226 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =0.2\) | 0.23 | − 18.636 | 0.204 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =1\) | 0.041 | − 19.341 | 0.190 | 0.009 | Real Eigenvalues (−, +, −) |
\(\psi =11\) | 0.004 | − 19.481 | 0.188 | 0.009 | Real Eigenvalues (−, +, −) |
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for a different parameter setting with \(\sigma =0.9\) and \(\phi =0.04\)
\(\sigma =0.9\) \(\phi =0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | 2.483 | − 10.233 | 0.364 | 0.009 | Real Eigenvalues (+, −, +) |
\(\psi =0.03\) | − 10.286 | − 57.862 | − 0.546 | 0.009 | Real Eigenvalues (+, −, +) |
\(\psi =0.05\) | − 1.674 | − 25.740 | 0.068 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =0.07\) | − 0.911 | − 22.894 | 0.122 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =0.1\) | − 0.541 | − 21.514 | 0.149 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =0.2\) | − 0.23 | − 20.352 | 0.171 | 0.009 | Real Eigenvalues (+,-,-) |
\(\psi =0.5\) | − 0.084 | − 19.809 | 0.181 | 0.009 | Real Eigenvalues (−, +, −) |
\(\psi =0.7\) | − 0.059 | − 19.716 | 0.183 | 0.009 | Real Eigenvalues (−, +, −) |
\(\psi =1\) | − 0.041 | − 19.648 | 0.185 | 0.009 | Real Eigenvalues (−, +, −) |
\(\psi =11\) | − 0.004 | − 19.508 | 0.187 | 0.009 | Real Eigenvalues (−, +, −) |
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for a different parameter setting with \(\sigma =1.5\) and \(\phi =-0.04\)
\(\sigma =1.5\) \(\phi =-0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | − 2.034 | − 28.317 | − 0.082 | 0.005 | Real Eigenvalues (+, +, +) |
\(\psi =0.02\) | − 4.138 | − 37.234 | − 0.284 | 0.005 | Eigenvalues |
(0.465 + 0i, 0.007 ± 0.007i) | |||||
\(\psi =0.03\) | 120 | 488.875 | 11.641 | 0.005 | Eigenvalues |
(0.463 + 0i, 0.003 ± 0.012i) | |||||
\(\psi =0.04\) | 3.871 | − 3.291 | 0.485 | 0.005 | Eigenvalues |
(0.461+ 0i, − 0.001 ± 0.014i) | |||||
\(\psi =0.05\) | 1.967 | − 11.359 | 0.303 | 0.005 | Eigenvalues |
(0.459 + 0i, − 0.005 ± 0.015i) | |||||
\(\psi =0.1\) | 0.569 | − 17.286 | 0.168 | 0.005 | Real Eigenvalues (+, −, −) |
\(\psi =0.3\) | 0.148 | − 19.07 | 0.128 | 0.005 | Real Eigenvalues (+, −, −) |
\(\psi =0.5\) | 0.085 | − 19.336 | 0.122 | 0.005 | Real Eigenvalues (+, −, −) |
\(\psi =1\) | 0.041 | − 19.522 | 0.118 | 0.005 | Real Eigenvalues (−, +, −) |
\(\psi =11\) | 0.004 | − 19.681 | 0.114 | 0.005 | Real Eigenvalues (−, +, −) |
Reaction coefficient \(\psi\) and its \(b^\star\), \(a^\star\) and \(c^\star\) on the SBGP for a different parameter setting with \(\sigma =1.5\) and \(\phi =0.04\)
\(\sigma =1.5\) \(\phi =0.04\) | |||||
|---|---|---|---|---|---|
\(\psi\) | \(b^\star\) | \(a^\star\) | \(c^\star\) | \(\gamma ^\star\) | Stability |
\(\psi =0.01\) | 2.034 | − 11.077 | 0.309 | 0.005 | Real Eigenvalues (+, +, −) |
\(\psi =0.02\) | 4.138 | − 2.16 | 0.511 | 0.005 | Real Eigenvalues (+, −, +) |
\(\psi =0.04\) | − 3.871 | − 36.102 | − 0.258 | 0.005 | Real Eigenvalues (+, −, +) |
\(\psi =0.1\) | − 0.569 | − 22.107 | 0.059 | 0.005 | Real Eigenvalues (+,-,-) |
\(\psi =0.3\) | − 0.148 | − 20.324 | 0.099 | 0.005 | Real Eigenvalues (+,-,-) |
\(\psi =0.5\) | − 0.085 | − 20.057 | 0.105 | 0.005 | Real Eigenvalues (−, +, −) |
\(\psi =1\) | − 0.041 | − 19.871 | 0.11 | 0.005 | Real Eigenvalues (−, +, −) |
\(\psi =11\) | − 0.004 | − 19.712 | 0.113 | 0.005 | Real Eigenvalues (−, +, −) |
Welfare in PPD-scenario and welfare resulting from a transition to BGB-scenario for \(\sigma =0.9\)
PPD-scenario | From PPD-scenario to BGB-scenario | |
|---|---|---|
F | − 10.637 | − 39.765 |
Welfare in BGB-scenario and welfare resulting from a transition to PPD-scenario for \(\sigma =0.9\)
BGB-scenario | From BGB-scenario to PPD-scenario | |
|---|---|---|
F | − 14.724 | 107.682 |
Welfare in PPD-scenario and welfare resulting from a transition to BGB-scenario for \(\sigma =1.5\)
PPD-scenario | From PPD-scenario to BGB-scenario | |
|---|---|---|
F | − 50.928 | − 97.975 |
Welfare in BGB-scenario and welfare resulting from a transition to PPD-scenario for \(\sigma =1.5\)
BGB-scenario | From BGB-scenario to PPD-scenario | |
|---|---|---|
F | − 65.242 | 57.337 |
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Dascher, F.L. Sustainable Debt Policy Rules and Growth in a Small Open Economy Model: Is a Balanced Government Budget Worthwhile?. Comp Econ Stud 62, 373–397 (2020). https://doi.org/10.1057/s41294-020-00130-3
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DOI: https://doi.org/10.1057/s41294-020-00130-3