1 Introduction
2 Benchmark model
2.1 Preferences
2.2 Technology, output and prices
2.2.1 Worldwide economy
2.2.2 Country economy
2.2.3 Country tasks
2.2.4 Country wages and threshold task
2.3 Intermediate-goods: technology, output and prices
2.4 Relative prices, output, and wages between sectors
2.5 R&D activity: technology, patent value, and expenditures
3 General equilibrium
3.1 R&D equilibrium and law of motion of technological knowledge
3.2 Transitional dynamics and steady-state results
Corruption parameters | ||
---|---|---|
\(z_{2}\) | \(h_{2}\) | |
(a) Considering the presence of scale effects, \(0<\xi <1\) | ||
\({{\frac{\partial g^{*}}{\partial (.)}}}\) | − | − |
\({{\frac{\partial Q^{*}}{\partial (.)}}}\) | − | − if \(\alpha \left( \epsilon -1\right) <\frac{\xi }{1-\xi }\) |
\(+\) if \(\alpha \left( \epsilon -1\right) >\frac{\xi }{1-\xi }\) | ||
\({{\frac{\partial \left( \frac{Y_{2}}{Y_{1}}\right) ^{*}}{\partial (.)}}}\) | − | − |
\({{\frac{\partial \left( \frac{P_{2}}{P_{1}}\right) ^{*}}{\partial (.)}}}\) | \(+\) | − |
\({{\frac{\partial \left( \frac{w_{L_{2}}}{w_{L_{1}}}\right) ^{*}}{\partial (.)}}}\) | − if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon >\alpha (\epsilon -1)+1\) | − if \(\epsilon \alpha <\frac{1}{2\left( 1-\xi \right) }+\alpha\) |
\(+\) if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon <\alpha (\epsilon -1)+1\) | \(+\) if \(\epsilon \alpha >\frac{1}{2\left( 1-\xi \right) }+\alpha\) | |
\({{\frac{\partial \left( \frac{w_{H_{2}}}{w_{H_{1}}}\right) ^{*}}{\partial (.)}}}\) | − if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon >\alpha (\epsilon -1)+1\) | − if \(\epsilon \alpha <\frac{1}{2\left( 1-\xi \right) }+\alpha\) |
\(+\) if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon <\alpha (\epsilon -1)+1\) | \(+\) if \(\epsilon \alpha >\frac{1}{2\left( 1-\xi \right) }+\alpha\) | |
(b) Considering the absence of scale effects, \(\xi =1\) | ||
\({{\frac{\partial g^{*}}{\partial (.)}}}\) | − | 0 |
\({{\frac{\partial Q^{*}}{\partial (.)}}}\) | − | 0 |
\({{\frac{\partial \left( \frac{Y_{2}}{Y_{1}}\right) ^{*}}{\partial (.)}}}\) | − | 0 |
\({{\frac{\partial \left( \frac{P_{2}}{P_{1}}\right) ^{*}}{\partial (.)}}}\) | \(+\) | 0 |
\({{\frac{\partial \left( \frac{w_{L_{2}}}{w_{L_{1}}}\right) ^{*}}{\partial (.)}}}\) | − if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon >\alpha (\epsilon -1)+1\) | 0 |
\(+\) if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon <\alpha (\epsilon -1)+1\) | 0 | |
\({{\frac{\partial \left( \frac{w_{H_{2}}}{w_{H_{1}}}\right) ^{*}}{\partial (.)}}}\) | − if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon >\alpha (\epsilon -1)+1\) | 0 |
\(+\) if \((\epsilon \alpha )^{2}-\epsilon \alpha ^{2}+\epsilon <\alpha (\epsilon -1)+1\) | 0 |
4 Quantitative results
4.1 Calibration and data
Parameters | Description | Source |
---|---|---|
\(\alpha =0.64\) | Share in income | Jones et al. (1993) |
\(\beta =2\) | Learning-by-past domestic R&D | Afonso (2012) |
\(\zeta =1.13\) | Cost of complexity | Hummels and Klenow (2005) |
\(q=2.78\) | Constant quality upgrade | \(q=\frac{1}{1-\alpha }\) |
\(\epsilon =1.05\) | Elasticity of substitution between countries | Willman (2002) |
\(\rho =0.01\) | Rate time of preference | Arrow (1999) |
\(\theta =0.5\) | Inverse of the inter-temporal elasticity of substitution | De la Croix and Delavallade (2009) |
\(\xi =0\), \(\xi =0.5\) and \(\xi =1\) | Scale benefits on profits | Assumed |
Non-corrupt countries | Corrupt countries | ||||||||||
---|---|---|---|---|---|---|---|---|---|---|---|
Sweden | Canada | Australia | Germany | The US | Spain | Portugal | Greece | Brazil | India | Mexico | |
\(z_{s}\) | |||||||||||
Value | 0.10 | 0.15 | 0.17 | 0.21 | 0.26 | 0.36 | 0.37 | 0.57 | 0.62 | 0.66 | 0.67 |
Description | Corruption degree of each country | ||||||||||
Source | Transparency International Organization | ||||||||||
\(h_{s}\) | |||||||||||
Value | 1.40 | 1.31 | 1.32 | 1.36 | 1.33 | 1.06 | 0.90 | 0.73 | 0.52 | 0.39 | 0.49 |
Description | Absolute productivity advantage of skilled labor | ||||||||||
Source | Penn World Table (version 9.1) | ||||||||||
\(L_{s}\) | |||||||||||
Value | 0.32 | 0.19 | 0.29 | 0.34 | 0.27 | 0.26 | 0.37 | 0.27 | 0.30 | 0.15 | 0.28 |
Description | Number of unskilled employees engaged in the labor market normalized by population in each country | ||||||||||
Source | International Labor Organization database | ||||||||||
\(H_{s}\) | |||||||||||
Value | 0.17 | 0.30 | 0.22 | 0.13 | 0.20 | 0.15 | 0.08 | 0.10 | 0.05 | 0.03 | 0.06 |
Description | Number of unskilled employees engaged in the labor market normalized by population in each country | ||||||||||
Source | International Labor Organization database |
\(\chi _{1}\) | Non-corrupt countries | ||||
---|---|---|---|---|---|
Sweden | Canada | Australia | Germany | The US | |
Corrupt countries | |||||
Spain | 0.72 | 0.67 | 0.69 | 0.64 | 0.68 |
Portugal | 0.78 | 0.74 | 0.75 | 0.71 | 0.74 |
Greece | 0.82 | 0.79 | 0.80 | 0.77 | 0.80 |
Brazil | 0.94 | 0.92 | 0.93 | 0.91 | 0.92 |
India | 0.99 | 0.99 | 0.99 | 0.99 | 0.99 |
Mexico | 0.94 | 0.92 | 0.93 | 0.91 | 0.92 |
Description | Relative importance of each non-corrupt country, \(\chi _{1}\) | ||||
Source | World Bank Database |
\(\chi _{2}\) | Non-corrupt countries | ||||
---|---|---|---|---|---|
Sweden | Canada | Australia | Germany | The US | |
Corrupt countries | |||||
Spain | 0.28 | 0.33 | 0.31 | 0.36 | 0.32 |
Portugal | 0.22 | 0.26 | 0.25 | 0.29 | 0.26 |
Greece | 0.18 | 0.21 | 0.20 | 0.23 | 0.20 |
Brazil | 0.06 | 0.08 | 0.07 | 0.09 | 0.08 |
India | 0.01 | 0.01 | 0.01 | 0.01 | 0.01 |
Mexico | 0.06 | 0.08 | 0.07 | 0.09 | 0.08 |
Description | Relative importance of each corrupt country, \(\chi _{2}\) | ||||
Source | World Bank Database |
4.2 Corruption and economic growth
Corrupt country versus non-corrupt country | Values for \(\frac{z_{2}}{z_{1}}\) | Values for \(\frac{h_{2}}{h_{1}}\) | ||||||||
---|---|---|---|---|---|---|---|---|---|---|
India versus Sweden | 10.92 | 8.43 | 6.55 | 5.10 | 3.93 | 0.16 | 0.22 | 0.28 | 0.34 | 0.40 |
Mexico versus Sweden | 11.12 | 8.58 | 6.67 | 5.19 | 4.00 | 0.23 | 0.29 | 0.35 | 0.41 | 0.48 |
Brazil versus Sweden | 10.27 | 7.92 | 6.16 | 4.79 | 3.70 | 0.25 | 0.31 | 0.37 | 0.43 | 0.49 |
Greece versus Sweden | 9.43 | 7.28 | 5.66 | 4.40 | 3.40 | 0.41 | 0.46 | 0.52 | 0.57 | 0.63 |
Portugal versus Sweden | 6.17 | 4.76 | 3.70 | 2.88 | 2.22 | 0.57 | 0.61 | 0.65 | 0.68 | 0.72 |
Spain versus Sweden | 5.97 | 4.61 | 3.58 | 2.79 | 2.15 | 0.68 | 0.72 | 0.76 | 0.80 | 0.84 |
India versus Canada | 7.14 | 5.51 | 4.28 | 3.30 | 2.57 | 0.17 | 0.23 | 0.30 | 0.36 | 0.41 |
Mexico versus Canada | 7.27 | 5.60 | 4.36 | 3.39 | 2.62 | 0.24 | 0.30 | 0.37 | 0.44 | 0.52 |
Brazil versus Canada | 6.71 | 5.17 | 4.02 | 3.13 | 2.41 | 0.27 | 0.33 | 0.39 | 0.46 | 0.53 |
Greece versus Canada | 6.16 | 4.75 | 3.70 | 2.88 | 2.22 | 0.43 | 0.49 | 0.55 | 0.62 | 0.68 |
Portugal versus Canada | 4.03 | 3.11 | 2.42 | 1.88 | 1.45 | 0.60 | 0.64 | 0.69 | 0.73 | 0.78 |
Spain versus Canada | 3.90 | 3.01 | 2.34 | 1.82 | 1.40 | 0.72 | 0.77 | 0.81 | 0.86 | 0.91 |
India versus Australia | 6.62 | 5.11 | 3.97 | 3.09 | 2.48 | 0.16 | 0.23 | 0.29 | 0.36 | 0.43 |
Mexico versus Australia | 6.74 | 5.20 | 4.05 | 3.15 | 2.43 | 0.24 | 0.30 | 0.37 | 0.44 | 0.51 |
Brazil versus Australia | 6.23 | 4.80 | 3.74 | 2.91 | 2.24 | 0.27 | 0.33 | 0.39 | 0.46 | 0.53 |
Greece versus Australia | 5.72 | 4.41 | 3.43 | 2.67 | 2.06 | 0.43 | 0.49 | 0.55 | 0.61 | 0.68 |
Portugal versus Australia | 3.74 | 2.89 | 2.24 | 1.75 | 1.35 | 0.60 | 0.66 | 0.69 | 0.73 | 0.78 |
Spain versus Australia | 3.62 | 2.79 | 2.17 | 1.69 | 1.30 | 0.72 | 0.76 | 0.81 | 0.86 | 0.90 |
India versus Germany | 5.23 | 4.03 | 3.14 | 2.44 | 1.88 | 0.16 | 0.22 | 0.28 | 0.35 | 0.42 |
Mexico versus Germany | 5.32 | 4.10 | 3.19 | 2.48 | 1.92 | 0.23 | 0.29 | 0.36 | 0.43 | 0.50 |
Brazil versus Germany | 4.91 | 3.79 | 2.95 | 2.29 | 1.77 | 0.26 | 0.32 | 0.38 | 0.44 | 0.51 |
Greece versus Germany | 4.51 | 3.48 | 2.71 | 2.11 | 1.62 | 0.41 | 0.47 | 0.53 | 0.60 | 0.66 |
Portugal versus Germany | 2.95 | 2.28 | 1.77 | 1.38 | 1.06 | 0.57 | 0.62 | 0.66 | 0.71 | 0.76 |
Spain versus Germany | 2.86 | 2.20 | 1.71 | 1.33 | 1.03 | 0.69 | 0.73 | 0.78 | 0.83 | 0.88 |
India versus The US | 4.15 | 3.20 | 2.49 | 1.93 | 1.49 | 0.16 | 0.22 | 0.29 | 0.36 | 0.44 |
Mexico versus The US | 4.22 | 3.26 | 2.53 | 1.97 | 1.52 | 0.23 | 0.30 | 0.37 | 0.44 | 0.47 |
Brazil versus The US | 3.90 | 3.01 | 2.34 | 1.82 | 1.40 | 0.26 | 0.32 | 0.39 | 0.46 | 0.53 |
Greece versus The US | 3.58 | 2.76 | 2.15 | 1.67 | 1.29 | 0.42 | 0.48 | 0.55 | 0.61 | 0.69 |
Portugal versus The US | 2.34 | 1.81 | 1.40 | 1.09 | 0.84 | 0.58 | 0.63 | 0.68 | 0.73 | 0.79 |
Spain versus The US | 2.27 | 1.75 | 1.36 | 1.06 | 0.82 | 0.70 | 0.75 | 0.80 | 0.86 | 0.91 |
Sweden | Canada | Australia | Germany | The US | |
---|---|---|---|---|---|
India | \(-0.007\) | \(-0.008\) | \(-0.008\) | \(-0.008\) | \(-0.008\) |
Mexico | \(-0.011\) | \(-0.012\) | \(-0.012\) | \(-0.011\) | \(-0.012\) |
Brazil | \(-0.009\) | \(-0.010\) | \(-0.010\) | \(-0.009\) | \(-0.012\) |
Greece | \(-0.007\) | \(-0.007\) | \(-0.007\) | \(-0.006\) | \(-0.007\) |
Portugal | \(-0.003\) | \(-0.003\) | \(-0.003\) | \(-0.003\) | \(-0.004\) |
Spain | \(-0.002\) | \(-0.002\) | \(-0.002\) | \(-0.002\) | \(-0.003\) |
4.3 Corruption and inter-country unskilled and skilled premiums
Sweden | Canada | Australia | Germany | The US | |
---|---|---|---|---|---|
India | |||||
Unskilled | 2.26 | 2.34 | 2.29 | 3.43 | 3.27 |
Skilled | 3.86 | 7.06 | 4.65 | 4.99 | 6.69 |
Mexico | |||||
Unskilled | 9.67 | 9.74 | 9.83 | 14.62 | 11.89 |
Skilled | 14.96 | 26.63 | 18.10 | 19.26 | 22.02 |
Brazil | |||||
Unskilled | 7.73 | 7.84 | 9.24 | 11.87 | 9.73 |
Skilled | 14.29 | 25.60 | 20.33 | 18.69 | 21.54 |
Greece | |||||
Unskilled | 19.10 | 19.52 | 23.06 | 29.89 | 24.73 |
Skilled | 22.09 | 39.88 | 31.76 | 29.44 | 34.24 |
Portugal | |||||
Unskilled | 9.60 | 10.28 | 12.98 | 16.83 | 14.59 |
Skilled | 14.59 | 27.60 | 23.47 | 21.77 | 26.52 |
Spain | |||||
Unskilled | 15.30 | 16.37 | 19.65 | 26.70 | 23.17 |
Skilled | 14.53 | 27.46 | 22.22 | 21.59 | 26.35 |
Sweden | Canada | Australia | Germany | The US | |
---|---|---|---|---|---|
India | |||||
Unskilled | 193.31 | 207.01 | 174.91 | 216.19 | 268.96 |
Skilled | |||||
Mexico | |||||
Unskilled | 217.34 | 226.61 | 197.42 | 242.08 | 256.76 |
Skilled | |||||
Brazil | |||||
Unskilled | 146.08 | 153.27 | 156.01 | 165.26 | 176.65 |
Skilled | |||||
Greece | |||||
Unskilled | 103.75 | 109.70 | 111.97 | 119.64 | 129.07 |
Skilled | |||||
Portugal | |||||
Unskilled | 37.12 | 41.13 | 44.83 | 47.98 | 54.16 |
Skilled | |||||
Spain | |||||
Unskilled | 37.53 | 41.55 | 43.08 | 48.26 | 54.62 |
Skilled |