# Growth and Debt: An Endogenous Smooth Coefficient Approach

## Abstract

**:**

## 1. Introduction

## 2. Empirical Methodology

#### 2.1. The Augmented Solow Growth Model

#### 2.2. An Endogenous Smooth Coefficient Model

## 3. Data

## 4. Estimation Results

#### 4.1. Homogeneous Models and Mean Parameter Estimates

#### 4.2. Parameter Heterogeneity

#### 4.2.1. Including the Period 2010–2014

#### 4.2.2. Policy Implications

#### 4.2.3. Parameter Heterogeneity in the Relationship between Growth and Other Regressors

## 5. Robustness Checks

#### 5.1. Influential Countries

#### 5.2. Alternative Measure for Democracy

#### 5.3. Additional Control Variables

## 6. Conclusions

## Acknowledgments

## Conflicts of Interest

## Appendix A

Mean | Std. Dev. | Min | Max | |
---|---|---|---|---|

Panel A. Penn World Table 7.0 (1980–2009) | ||||

Growth | 0.014 | 0.023 | −0.099 | 0.083 |

Initial income | 8.42 | 1.27 | 5.87 | 10.71 |

Lag of initial income | 8.34 | 1.23 | 5.78 | 10.55 |

Investment rate | 3.05 | 0.35 | 1.87 | 3.89 |

Lag of investment rate | 3.05 | 0.39 | 1.74 | 4.31 |

Population growth rate | −2.71 | 0.16 | −3.23 | −2.38 |

Lag of population growth rate | −2.69 | 0.16 | −3.08 | −2.28 |

Government consumption | 2.19 | 0.44 | 1.06 | 3.56 |

Lag of government consumption | 2.19 | 0.48 | 1.01 | 3.69 |

Trade openness | 66.51 | 36.49 | 9.77 | 199.86 |

Lag of trade openness | 61.01 | 35.80 | 9.70 | 180.09 |

Panel B. Penn World Table 9.0 (1980–2014) | ||||

Growth | 0.025 | 0.029 | −0.061 | 0.114 |

Initial income | 8.77 | 1.17 | 6.42 | 11.20 |

Investment rate | 2.96 | 0.45 | 0.65 | 3.92 |

Population growth rate | −2.71 | 0.15 | −3.07 | −2.38 |

Schooling | 0.77 | 0.32 | 0.036 | 1.31 |

Panel C. World Bank | ||||

Inflation rate | 2.30 | 1.17 | −1.95 | 7.57 |

Lag of inflation rate | 2.34 | 1.19 | −1.46 | 8.26 |

Life expectancy | 4.17 | 0.17 | 3.63 | 4.41 |

Lag of life expectancy | 4.14 | 0.18 | 3.63 | 4.38 |

Fertility | 3.62 | 1.73 | 1.21 | 7.78 |

Lag of fertility | 4.06 | 1.89 | 1.17 | 7.82 |

Panel D. IMF | ||||

Public debt | 4.08 | 0.61 | 2.17 | 6.33 |

Lag of public debt | 3.92 | 0.73 | 1.12 | 6.46 |

Panel E. Barro and Lee (2000) | ||||

Schooling | 0.60 | 0.77 | −2.18 | 1.97 |

Lag of schooling | 0.32 | 0.90 | −2.66 | 1.90 |

Panel F. Polity IV | ||||

Democracy | 5.74 | 3.83 | 0.00 | 10.00 |

Lag of democracy | 5.02 | 4.17 | 0.00 | 10.00 |

Executive constraints | 4.96 | 2.05 | 1.00 | 7.00 |

Lag of executive constraints | 4.51 | 2.33 | 1.00 | 7.00 |

Panel G. Freedom House | ||||

Political rights | 4.82 | 1.93 | 1.00 | 7.00 |

Lag of political rights | 4.53 | 2.08 | 1.00 | 7.00 |

Civil liberties | 4.67 | 1.68 | 1.00 | 7.00 |

Lag of civil liberties | 4.45 | 1.77 | 1.00 | 7.00 |

Variable | Source | Definition |
---|---|---|

Growth | PWT 7.0 & 9.0 | Growth rate of real per capita GDP in chain series for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). |

Initial income | PWT 7.0 & 9.0 | Logarithm of real per capita GDP in chain series at 1980, 1990, 2000, and 2010 (for extended data). Lagged values correspond to 1975, 1985, 1995, and 2005 (for extended data). |

Investment rate | PWT 7.0 & 9.0 | Logarithm of average ratios over each period of investment to real GDP per capita for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Population growth rate | PWT 7.0 & 9.0 | Logarithm of average population growth rates plus 0.05 for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Schooling | Barro and Lee (2000) | Logarithm of average years of male secondary and tertiary school attainment for ages above 25 in 1980, 1990, 1999, and 2010 (for extended data). Lagged values correspond to 1975, 1985, 1995, and 2005 (for extended data). |

Public debt | IMF, Debt Database Fall 2011 Vintage | Logarithm of average percentages over each period of public debt to GDP for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

Fertility | World Bank | Logarithm of average total fertility rate in 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Life expectancy | World Bank | Logarithm of average average life expectancy at birth for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

Trade openness | PWT 7.0 & 9.0 | Average ratios for each period of exports plus imports to real GDP per capita for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Government consumption | PWT 7.0 & 9.0 | Logarithm of average ratios for each period of government consumption to real GDP per capita for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Inflation rate | World Bank | Logarithm of average inflation plus 1 for the periods 1980–1989, 1990–1999, 2000–2009, and (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

Democracy | Polity IV | An index ranges from 0 to 10 where higher values equals a greater extent of institutionalized democracy. Average for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

Executive constraints | Polity IV | An index ranges from 1 to 7 where higher values equals a greater extent of institutionalized constraints on the power of chief executives. Average for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, 2005–2009 (for extended data). |

Political rights | Freedom House | An index ranges from 1 to 7 where higher values equals a greater extent of institutionalized constraints on the power of chief executives. Average for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

Civil liberties | Freedom House | An index ranges from 1 to 7 where higher values equals a greater extent of institutionalized constraints on the power of chief executives. Average for the periods 1980–1989, 1990–1999, 2000–2009, and 2010–2014 (for extended data). Lagged values correspond to 1975–1979, 1985–1989, 1995–1999, and 2005–2009 (for extended data). |

**Table A3.**List of countries grouped into coefficient estimates from SPSCM-IVand democracy score from the Polity IV dataset.

Negative and Significant | Insignificant | ||
---|---|---|---|

≤1 | ≥7.6 & ≤9 | ≥9 | |

Algeria (1980, 1990) | Argentina (2000) | Australia (1980, 1990, 2000) | Argentina (1980, 1990) |

Bangladesh (1980) | Bolivia (1990, 2000) | Austria (1980, 1990, 2000) | Benin (1990, 2000) |

Benin (1980) | Botswana (2000) | Belgium (1980, 1990, 2000) | Bangladesh (1990, 2000) |

Burundi (1980, 1990) | Brazil (1990, 2000) | Canada (1980, 1990, 2000) | Bolivia (1980) |

Cameroon (1980, 1990, 2000) | Chile (1990, 2000) | Costa Rica (1980, 1990, 2000) | Botswana (1980, 1990) |

Central African Republic (1980) | Colombia (1980, 1990) | Cyprus (1980, 1990, 2000) | Brazil (1980) |

Chile (1980) | Dominican Republic (2000) | Denmark (1980, 1990, 2000) | Burundi (2000) |

Cote’d Ivoire (1980, 1990) | Ecuador (1980, 1990) | Finland (1980, 1990, 2000) | Central African Republic (1990, 2000) |

Egypt (1980, 1990, 2000) | France (1980) | France (1990, 2000) | Congo Republic (1990) |

Gabon (1980, 1990, 2000) | Greece (1980) | Greece (1990, 2000) | Cote’d Ivoire (2000) |

Gambia (2000) | Guatemala (2000) | Ireland (1980, 1990, 2000) | Colombia (2000) |

Ghana (1980) | India (1980, 1990, 2000) | Italy (1980, 1990, 2000) | Dominican Republic (2000) |

Guyana (1980) | Republic of Korea (2000) | Israel (1980, 1990, 2000) | Ecuador (2000) |

Indonesia (1980, 1990) | Lesotho (2000) | Jamaica (1980, 1990, 2000) | Gambia (1980, 1990) |

Iran (1980) | Mexico (2000) | Japan (1980, 1990, 2000) | Ghana (1980, 1990) |

Kenya (1980, 1900) | Panama (1990, 2000) | Netherlands (1980, 1990, 2000) | Guatemala (1990) |

Lesotho (1980) | Paraguay (2000) | New Zealand (1980, 1990, 2000) | Guyana (1990, 2000) |

Malawi (1980) | Peru (2000) | Norway (1980, 1990, 2000) | Honduras (1980, 1990, 2000) |

Mali (1980) | Philippines (2000) | Portugal (1980, 1990, 2000) | Kenya (2000) |

Mauritania (1980, 2000) | Senegal (2000) | Spain (1980, 1990, 2000) | Lesotho (1990) |

Morocco (1980, 1990, 2000) | South Africa (1990, 2000) | Sweden (1980, 1990, 2000) | Malaysia (1980, 2000) |

Nicaragua (1980, 1990) | Thailand (1990) | United Kingdom (1980, 1990, 2000) | Malawi (1990, 2000) |

Niger (1980) | Trinidad & Tobago (1990, 2000) | United States (1980, 1990, 2000) | Mali (1990, 2000) |

Panama (1980) | Turkey (1990, 2000) | Uruguay (1990, 2000) | Mexico (1980, 1990) |

Paraguay (1980) | Venezuela (1980, 1990) | Nepal (1980, 1990, 2000) | |

Sierra Leone (1980) | Nicaragua (1990) | ||

Swaziland (1980, 1990, 2000) | Niger (1990, 2000) | ||

Syria (1980, 1990, 2000) | Pakistan (1980, 1990, 2000) | ||

Togo (1980, 1990, 2000) | Papua New Guinea (1980, 1990, 2000) | ||

Tunisia (1980, 1990, 2000) | Paraguay (1990) | ||

Zambia (1980) | Republic of Korea (1980, 1990) | ||

Zimbabwe (1990) | Peru (1980, 1990) | ||

Sierra Leone (1980, 2000) | |||

South Africa (1980) | |||

Sri Lanka (1980, 1990, 2000) | |||

Thailand (2000) | |||

Turkey (1980) | |||

Venezuela (2000) | |||

Zambia (1990, 2000) | |||

Zimbabwe (1980, 2000) |

Paper | Sample | Empirical Methodology | Debt Measure | Instrumental Variable | Findings |
---|---|---|---|---|---|

Caner et al. (2010) | 101 developing and developed countries (1980–2008) | Cross-section; Threshold Least Squares | General government gross debt (% GDP) from IMF | No instruments | Significant negative effect; debt threshold is 77% for all countries; 64% for the sample of developing countries only |

Cecchetti et al. (2011) | 18 OECD countries (1980–2010) | Panel data; FE; panel threshold; LSDV | General government debt from IMF | No instruments | Significant negative effect; threshold level is 85% |

Checherita-Westphal and Rother (2012) | 12 Euro area countries (1970–2008) | Panel data; FE; 2SLS; GMM | Gross government debt (% GDP) from AMECO | Lagged debt-to-GDP ratio up to the 5th lag; average of the debt levels of the other countries in the sample | Significant negative effect; debt turning point is in between 90% and 100% |

Minea and Parent (2012) | 20 advanced countries as in Reinhart and Rogoff (2010) (1945–2009) | Panel data; panel smooth threshold regression | Public debt from IMF | No instruments | Negative effect below the threshold level of 115%; positive effect beyond this level of debt |

Baum et al. (2013) | 12 Euro area countries (EMU) (1990–2007/2010) | Panel data (yearly); non-/dynamic panel threshold model; OLS; GMM | Public debt from AMECO | No instrument for debt variable | Significant positive effect below the threshold level of 67% for the period 1990–2007; insignificant effect beyond that threshold; significant negative effect beyond the threshold level of 95% for the period 1990–2010 |

Kourtellos et al. (2013) | 82 countries (1980–2009) | Panel data (10-year averages); structural threshold regression; 2SLS; GMM | Public debt (% of GDP) from IMF | Lag of public debt | Threshold variable is democracy; significant negative effect for low-democracy regime countries; insignificant effect for countries in high-democracy regime |

Paper | Sample | Empirical Methodology | Debt Measure | Instrumental Variable | Findings |
---|---|---|---|---|---|

Wright and Grenade (2014) | 13 Caribbean countries (1990–2012) | Panel data; PDOLS | Debt/GDP from IMF | No instruments | 61% is the threshold level |

Eberhardt and Presbitero (2015) | 118 countries (1961–2012) | Unbalanced panel data; panel time series approach; ECM | Gross general government debt from WDI and IMF | No instruments | No common threshold level of public debt for all countries; evidence for differences in debt-growth relationship across countries |

Égert (2015) | 20 advanced and 21 emerging economies (1946–2009) | Panel data; threshold regression | Central government debt from the same source in Reinhart and Rogoff (2011) | No instruments | Little evidence on 90% threshold level; some evidence for lower threshold level |

Woo and Kumar (2015) | 38 advanced and emerging economies (1970–2008) | Panel data; BE; pooled OLS; FE; SGMM | Gross government debt (% of GDP) from IMF | 5${}^{\mathrm{t}}$ lag of debt variable | Significant negative effect; threshold level of 90%, beyond which debt has a negative effect |

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1. | In another paper Newey and Powell (2003), the conditional mean of disturbances given instruments was assumed to be zero without imposing an additive structure for the endogenous variables. |

2. | The authors used B-spline smoothing in the first two steps assuming the domain of the basis functions over the closed interval. |

3. | Excluded countries are Guyana, Nicaragua, Papua New Guinea, and Syria. Guyana and Papua New Guinea are excluded since they were not reported in PWT 9.0. Data for Syria were not available in the IMF public debt database beyond 2010. |

4. | Acemoglu et al. (2001) evaluated the difference between OLS and 2SLS estimates of the democracy variable using executive constraints as an instrument. They expected that using this variable as an instrument would not solve the endogeneity problem, but that it would correctly address the measurement error if it was properly measured. The estimated effect of the institutions variable from the 2SLS method was 0.87 and highly significant. They concluded that measurement error in the institutions variable could be the primary difference between the OLS and 2SLS estimates. |

5. | Henderson et al. (2012) suggest to plot gradient estimates in a 45o plot to expose parameter heterogeneity that exists in the estimates. Their suggestion is useful especially when covariate vector is more than one dimension. Since in our model estimation the coefficients vary with respect to only one variable, from the graphical point of view it is better to plot coefficient estimates on a Cartesian coordinate system. |

6. | These countries are the Central African Republic and Malawi for the year 1990. |

7. | The figures and detailed results obtained in this section are available upon request from the author. |

**Figure 1.**Estimated coefficient curve for the public debt variable from the model in Column 9 of Table 1. The figure corresponds to the functional coefficient ${\theta}_{d}(\xb7)$, graphing the semiparametric smooth coefficient instrumental variable estimate (solid line with small circles) with 95% bootstrap percentile confidence intervals (solid lines).

**Figure 2.**Functional coefficient estimates for the public debt variable for the period 1980–2014. The figure corresponds to the functional coefficient ${\theta}_{d}(\xb7)$, graphing the semiparametric smooth coefficient instrumental variable estimate (solid line with small circles) with 95% bootstrap percentile confidence intervals (solid lines).

**Figure 3.**Functional coefficient estimates for other regressors. Plot (

**a**) corresponds to the functional coefficient of initial income. Plot (

**b**) corresponds to the functional coefficient of investment rate. Plot (

**c**) corresponds to the functional coefficient of population growth rate. Plot (

**d**) corresponds to the functional coefficient of schooling. Each plot graphs the semiparametric smooth coefficient instrumental variable estimate (solid line with small circles) with 95% bootstrap percentile confidence intervals (solid lines).

Variable | OLS | 2SLS | SPSCM-IV | |||||||
---|---|---|---|---|---|---|---|---|---|---|

(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10) | |

Intercept | 0.0355 ${}^{b}$ | 0.0258 ${}^{c}$ | −0.0203 | −0.0126 | 0.0236 ${}^{c}$ | −0.0068 | −0.0068 | 0.0409 | 0.0196 | −0.0171 |

0.0143 | 0.0143 | 0.0437 | 0.0450 | 0.0144 | 0.0444 | 0.0457 | 0.005 | 0.0391 | 0.0346 | |

Public Debt | −0.0080 ${}^{b}$ | −0.0067 ${}^{b}$ | −0.0060 ${}^{c}$ | −0.0058 ${}^{c}$ | −0.0064 ${}^{c}$ | −0.0058 ${}^{c}$ | −0.0055 ${}^{c}$ | −0.0071 ${}^{a}$ | −0.0073 ${}^{a}$ | −0.0053 ${}^{b}$ |

0.0034 | 0.0033 | 0.0033 | 0.0033 | 0.0033 | 0.0033 | 0.0033 | 0.0011 | 0.0025 | 0.0023 | |

Democracy | 0.0012 ${}^{a}$ | 0.0014 ${}^{b}$ | 0.0014 ${}^{b}$ | 0.0015 ${}^{b}$ | 0.0022 ${}^{a}$ | 0.0021 ${}^{a}$ | —– | —– | —– | |

0.0004 | 0.0006 | 0.0006 | 0.0004 | 0.0007 | 0.0007 | |||||

Initial Income | −0.0049 | −0.0051 | −0.0060 ${}^{a}$ | −0.0061 ${}^{c}$ | −0.0097 ${}^{a}$ | −0.0081 ${}^{a}$ | ||||

0.0035 | 0.0035 | 0.0021 | 0.0034 | 0.0024 | 0.0024 | |||||

Investment Rate | 0.0178 ${}^{a}$ | 0.0176 ${}^{a}$ | 0.0183 ${}^{a}$ | 0.0181 ${}^{a}$ | 0.0077 ${}^{c}$ | 0.0077 ${}^{b}$ | ||||

0.0053 | 0.0053 | 0.0053 | 0.0053 | 0.004 | 0.0039 | |||||

Population Growth Rate | −0.0111 | −0.0102 | −0.0073 | −0.0069 | −0.0283 ${}^{b}$ | −0.028 ${}^{b}$ | ||||

0.0248 | 0.0248 | 0.0247 | 0.0248 | 0.0142 | 0.014 | |||||

Schooling | 0.0050 | 0.0051 | 0.0047 | 0.0048 | 0.0090 ${}^{a}$ | 0.0090 ${}^{a}$ | ||||

0.0039 | 0.0040 | 0.0039 | 0.0040 | 0.0029 | 0.003 | |||||

Inflation Rate | −0.0015 | −0.0017 | −0.0028 ${}^{b}$ | |||||||

0.0012 | 0.0012 | 0.0011 | ||||||||

Trend | 0.0054 ${}^{a}$ | 0.0041 ${}^{b}$ | 0.0023 | 0.0017 | 0.0038 ${}^{c}$ | 0.0019 | 0.0013 | |||

0.0018 | 0.0019 | 0.0023 | 0.0018 | 0.0020 | 0.0017 | 0.0018 | ||||

In-Sample ${R}^{2}$ | 0.0832 | 0.1211 | 0.2093 | 0.2154 | 0.1191 | 0.2025 | 0.2094 | 0.1744 | 0.3799 | 0.4257 |

Out-of-Sample ${R}^{2}$ | 0.0982 | 0.1399 | 0.2684 | 0.2767 | 0.1379 | 0.2600 | 0.2698 | 0.1187 | 0.3099 | 0.3411 |

ASPE | 0.00048 | 0.00046 | 0.00044 | 0.00044 | 0.00047 | 0.00073 | 0.00074 | 0.00049 | 0.00041 | 0.00040 |

© 2019 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Koroglu, M.
Growth and Debt: An Endogenous Smooth Coefficient Approach. *J. Risk Financial Manag.* **2019**, *12*, 23.
https://doi.org/10.3390/jrfm12010023

**AMA Style**

Koroglu M.
Growth and Debt: An Endogenous Smooth Coefficient Approach. *Journal of Risk and Financial Management*. 2019; 12(1):23.
https://doi.org/10.3390/jrfm12010023

**Chicago/Turabian Style**

Koroglu, Mustafa.
2019. "Growth and Debt: An Endogenous Smooth Coefficient Approach" *Journal of Risk and Financial Management* 12, no. 1: 23.
https://doi.org/10.3390/jrfm12010023