Annex. Urbanization, growth and use of materials. Results of the econometric tests
Texte intégral
1The purpose of this Annex is to display some of the main results of the tests carried out with econometric models, which were not included in the main body of this text in order to simplify its reading and not to lose track of the central arguments in it. Although these tests play a relatively secondary role with respect to the set of arguments put forward in the book, they may be interesting to study subsequent research, or to refine certain hypotheses, the way of presenting them, or of finding empirical evidence no matter how limited the data and the econometric method with simplified models might be. Not all of the tests are presented here either, for in many cases it was considered unnecessary.
2Two groups of correlations are displayed: cross-sectional ones to correlate product growth alongside urban population growth with out-of-phase panel data and synchronic tests for the period 1950-2010 in order to contribute to the question of urbanization and growth; and also time series correlating the production of certain basic commodities with world GDP in order to show differential behaviors along several stages of the urbanization process according to the periods described in the text. In this last case, the non-random behavior of the residuals seems useful and revealing, which is why the data and figures are presented1.
3In order to simplify the reading of the data displayed as results of the E-Views model, some of the most frequently mentioned tags are explained below:
Actual: the original data of the series.
Fitted: the results of the adjusted R-squared according to the specific equation in the E-Views model.
Residual: the series with values of the residuals, that is, the difference between the original data and the results of the regression.
1. 1. Models to correlate product growth by urban population growth with out-of-phase panel data and synchronic tests (1950 to 2010). Results and tests
Table 1. Results of the correlation between GDP growth in the period 1990-2008 and population increase in large cities in the period 1975-1990
| Dependent Variable: GDP_90_08 | ||||
| Method: Least Squares | ||||
| Date: 22/08/16 Time: 15:37 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probabiity |
| INC_CIT_1975_1990_thousands | 102.2849 | 6.586404 | 15.52971 | 0.0000 |
| D-ed C. | 235494.2 | 112551.8 | 2.092319 | 0.0391 |
| C | -99929.41 | 52218.93 | -1.913663 | 0.0587 |
| R-squared | 0.724688 | Mean of the dependent variable | 231589.9 | |
| Adjusted R-squared | 0.718767 | Standard deviation of the dependent variable | 811587.3 | |
| Standard deviation of the equation | 430396.2 | Akaike info criterion | 28.81355 | |
| Sum of the square of residuals | 1.72E+13 | Schwarz criterion | 28.89369 | |
| Log probability | -1380.050 | Hannan-Quinn criterion | 28.84594 | |
| F-statistic | 122.3990 | Durbin-Watson statistic | 2.016899 | |
| Prob(F-statistic) | 0.000000 | |||
Note: since, given their nature, these data show heteroskedasticity (cf. Table 2), the White method is used.
The variables mean:
INC_CIT_1975_1990_THOUSANDS = population increase in large cities between 1975 and 1990.
GDP_90_08 = GDP increase between 1990 and 2008.
Table 2. White Test
Heteroskedasticity: White Test | ||||
F-statistic | 155.4224 | Prob. F(4,91) | 0.0000 | |
Observations*R-squared | 83.74221 | Prob. Chi-Square(4) | 0.0000 | |
Normalized sum of squares | 673.5129 | Prob. Chi-Square(4) | 0.0000 | |
Test Equation: | ||||
Dependent Variable: RESID^2 | ||||
Method: Least Squares | ||||
Date: 08/22/16 Time: 16:09 | ||||
Sample: 1 96 | ||||
Included observations: 96 | ||||
Collinearity test of the regressors | ||||
Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
C | -9.39E+09 | 3.77E+10 | -0.249380 | 0.8036 |
INC_CIT_1975_1990_thousands^2 | 2074.851 | 363.4443 | 5.708856 | 0.0000 |
INC_CIT_1975_1990_thousands*D-edC | 82339190 | 16746862 | 4.916694 | 0.0000 |
INC_CIT_1975_1990_thousands | 19965489 | 14269629 | 1.399160 | 0.1652 |
D-epC^2 | -8.91E+10 | 8.23E+10 | -1.081850 | 0.2822 |
R-squared | 0.872315 | Mean of the dependent variable | 1.79E+11 | |
Adjusted R-squared | 0.866702 | Standard deviation of dep. variable | 7.47E+11 | |
Standard Deviation of the equation | 2.73E+11 | Akaike info criterion | 55.55161 | |
Sum of the squared residuals | 6.77E+24 | Schwarz criterion | 55.68517 | |
Log probability | -2661.477 | Hannan-Quinn criterion | 55.60560 | |
F-statistic | 155.4224 | Durbin-Watson statistic | 1.829269 | |
Prob(F-statistic) | 0.000000 | |||
Table 3. White Method
| Dependent Variable: GDP_90_08 | ||||
| Method: Least Squares | ||||
| Date: 22/08/16 Time: 16:54 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| White heteroskedasticity - consistent standard errors and covariance | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| INC_CIT_1975_1990_thousands | 101.1888 | 28.30434 | 3.575026 | 0.0005 |
| C | -47474.21 | 44016.10 | -1.078565 | 0.2832 |
| R-squared | 0.703917 | Mean of the dependent variable | 211820.6 | |
| Adjusted R-squared | 0.701124 | Standard Deviation of dependent variable | 768336.2 | |
| Standard Deviation of the equation | 420046.3 | Akaike info criterion | 28.75246 | |
| Sum of the squared residuals | 1.87E+13 | Schwarz criterion | 28.80213 | |
| Log probability | -1550.633 | Hannan-Quinn criterion | 28.77260 | |
| F-statistic | 252.0074 | Durbin-Watson statistic | 1.911589 | |
| Prob(F-statistic) | 0.000000 | Wald F-statistic | 12.78081 | |
| Prob(Wald F-statistic) | 0.000529 | |||
Table 4. Data used for the correlations between GDP increase in the period 1990-2008 and population increase in large cities in the period 1975-1990
| Country | Inc. cit. 1975-1990 Thousands | GDP 90-08 | Log INC-CIT 1975-1990 | Log INC GDP 1990-2008 | DevelopedCountry (D-edC) |
| Angola | 903 | 13904 | 2.96 | 4.14 | 0 |
| Argentina | 2786 | 232599 | 3.44 | 5.37 | 0 |
| Armenia | 263 | 14043 | 2.42 | 4.15 | 0 |
| Australia | 2183 | 240323 | 3.34 | 5.38 | 1 |
| Azerbaijan | 304 | 32824 | 2.48 | 4.52 | 0 |
| Bangladesh | 6290 | 106134 | 3.80 | 5.03 | 0 |
| Belarus | 498 | 48723 | 2.70 | 4.69 | 0 |
| Belgium | 95 | 74661 | 1.98 | 4.87 | 1 |
| Benin | 263 | 6546 | 2.42 | 3.82 | 0 |
| Bolivia | 742 | 13963 | 2.87 | 4.14 | 0 |
| Brazil | 21629 | 518514 | 4.34 | 5.71 | 0 |
| Bulgaria | 214 | 14760 | 2.33 | 4.17 | 0 |
| Burkina Faso | 381 | 9486 | 2.58 | 3.98 | 0 |
| Cambodia | 515 | 27109 | 2.71 | 4.43 | 0 |
| Cameroon | 993 | 7985 | 3.00 | 3.90 | 0 |
| Canada | 2726 | 314724 | 3.44 | 5.50 | 1 |
| Chad | 245 | 4599 | 2.39 | 3.66 | 0 |
| Chile | 1790 | 132910 | 3.25 | 5.12 | 0 |
| China | 43976 | 6785042 | 4.64 | 6.83 | 0 |
| Colombia | 3916 | 125879 | 3.59 | 5.10 | 0 |
| Congo | 583 | 3037 | 2.77 | 3.48 | 0 |
| Costa Rica | 298 | 19334 | 2.47 | 4.29 | 0 |
| Czech Republic | 86 | 39816 | 1.94 | 4.60 | 0 |
| Dominican Rep. | 611 | 24937 | 2.79 | 4.40 | 0 |
| Ecuador | 1141 | 16964 | 3.06 | 4.23 | 0 |
| Egypt | 3434 | 161383 | 3.54 | 5.21 | 0 |
| El Salvador | 373 | 9972 | 2.57 | 4.00 | 0 |
| Finland | 289 | 43573 | 2.46 | 4.64 | 1 |
| France | 1324 | 397071 | 3.12 | 5.60 | 1 |
| Germany | 174 | 448967 | 2.24 | 5.65 | 1 |
| Ghana | 758 | 22218 | 2.88 | 4.35 | 0 |
| Greece | 461 | 73993 | 2.66 | 4.87 | 0 |
| Guatemala | 87 | 28947 | 1.94 | 4.46 | 0 |
| Guinea | 328 | 2851 | 2.52 | 3.45 | 0 |
| Honduras | 286 | 8849 | 2.46 | 3.95 | 0 |
| Hong Kong | 1859 | 122746 | 3.27 | 5.09 | 0 |
| Hungary | 0 | 27354 | -0.40 | 4.44 | 0 |
| India | 38674 | 2317083 | 4.59 | 6.36 | 0 |
| Indonesia | 8563 | 556849 | 3.93 | 5.75 | 0 |
| Iran | 6398 | 257636 | 3.81 | 5.41 | 0 |
| Ireland | 83 | 74490 | 1.92 | 4.87 | 1 |
| Israel | 1302 | 69061 | 3.11 | 4.84 | 1 |
| Italy | 252 | 231982 | 2.40 | 5.37 | 1 |
| Japan | 9768 | 582988 | 3.99 | 5.77 | 1 |
| Jordan | 352 | 22975 | 2.55 | 4.36 | 0 |
| Kazakhstan | 220 | 50216 | 2.34 | 4.70 | 0 |
| Kenya | 881 | 15596 | 2.95 | 4.19 | 0 |
| Kuwait | 704 | 20373 | 2.85 | 4.31 | 0 |
| Laos | 104 | 7234 | 2.02 | 3.86 | 0 |
| Liberia | 816 | 428 | 2.91 | 2.63 | 0 |
| Madagascar | 494 | 5419 | 2.69 | 3.73 | 0 |
| Malawi | 195 | 5217 | 2.29 | 3.72 | 0 |
| Malaysia | 907 | 170303 | 2.96 | 5.23 | 0 |
| Mali | 383 | 8077 | 2.58 | 3.91 | 0 |
| Mauritania | 316 | 2144 | 2.50 | 3.33 | 0 |
| Mexico | 13472 | 360620 | 4.13 | 5.56 | 0 |
| Mongolia | 216 | 46 | 2.33 | 1.66 | 0 |
| Morocco | 2387 | 54915 | 3.38 | 4.74 | 0 |
| Mozambique | 478 | 31865 | 2.68 | 4.50 | 0 |
| Nepal | 218 | 16363 | 2.34 | 4.21 | 0 |
| New Zealand | 141 | 31111 | 2.15 | 4.49 | 1 |
| Niger | 234 | 3300 | 2.37 | 3.52 | 0 |
| Nigeria | 7933 | 115499 | 3.90 | 5.06 | 0 |
| Norway | 40 | 54032 | 1.60 | 4.73 | 1 |
| Pakistan | 7700 | 204892 | 3.89 | 5.31 | 0 |
| Panama | 319 | 11406 | 2.50 | 4.06 | 0 |
| Paraguay | 436 | 8583 | 2.64 | 3.93 | 0 |
| Peru | 2357 | 92245 | 3.37 | 4.96 | 0 |
| Philippines | 3772 | 138095 | 3.58 | 5.14 | 0 |
| Poland | 275 | 196252 | 2.44 | 5.29 | 0 |
| Portugal | 590 | 46705 | 2.77 | 4.67 | 1 |
| Romania | 338 | 28625 | 2.53 | 4.46 | 0 |
| Russia | 4295 | 130919 | 3.63 | 5.12 | 0 |
| Rwanda | 130 | 4265 | 2.11 | 3.63 | 0 |
| Senegal | 623 | 163 | 2.79 | 2.21 | 0 |
| Sierra Leone | 245 | 86191 | 2.39 | 4.94 | 0 |
| Singapore | 754 | 30248 | 2.88 | 4.48 | 0 |
| South Africa | 3361 | 86320 | 3.53 | 4.94 | 0 |
| Spain | 1026 | 323561 | 3.01 | 5.51 | 1 |
| Sudan | 1474 | 41504 | 3.17 | 4.62 | 0 |
| Sweden | 24 | 68593 | 1.38 | 4.84 | 1 |
| Switzerland | 293 | 43428 | 2.47 | 4.64 | 1 |
| Syria | 1592 | 94199 | 3.20 | 4.97 | 0 |
| Thailand | 2137 | 317341 | 3.33 | 5.50 | 0 |
| Togo | 305 | 743 | 2.48 | 2.87 | 0 |
| Tunisia | 93 | 35981 | 1.97 | 4.56 | 0 |
| Turkey | 6209 | 305987 | 3.79 | 5.49 | 0 |
| Uganda | 357 | 21411 | 2.55 | 4.33 | 0 |
| United States | 17124 | 3681936 | 4.23 | 6.57 | 1 |
| Uruguay | 143 | 14303 | 2.16 | 4.16 | 0 |
| Uzbekistan | 488 | 57025 | 2.69 | 4.76 | 0 |
| Venezuela | 2394 | 119249 | 3.38 | 5.08 | 0 |
| Vietnam | 1445 | 186827 | 3.16 | 5.27 | 0 |
| Yemen | 593 | 33894 | 2.77 | 4.53 | 0 |
| Zambia | 373 | 3423 | 2.57 | 3.53 | 0 |
| South Korea | 10110 | 575756 | 4.00 | 5.76 | 1 |
Source: United Nations (2012) and World Economics.
Figure 1. Residuals of the correlation between GDP increase in the period 1990-2008 and population increase in large cities in the period 1975-1990
Source: E-Views program for United Nations data (2012) and World Economics.Note: since, given their nature, these data show heteroskedasticity, the White method is used (cf. Table 6).
The variables mean:
INC_CIT_1980_2000_thousands = population increase in large cities between 1980 and 2000.
GDP_90_08 = GDP increase between 1990 and 2008.
Table 5. Results of the correlation between GDP increase in the period 1990-2008 and population increase in large cities in the period 1980-2000
| Dependent Variable: GDP_90_08 | ||||
| Method: Least Squares | ||||
| Date: 16/10/14 Time: 18:17 | ||||
| Sample: 1 108 | ||||
| Included observations: 108 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| INC_CIT_1980_2000_thousands | 49.72460 | 1.599010 | 31.09712 | 0.0000 |
| D-ed C | 275961.9 | 58830.35 | 4.690810 | 0.0000 |
| C | -51579.65 | 26924.51 | -1.915714 | 0.0581 |
| R-squared | 0.902929 | Mean of the dependent variable | 211820.6 | |
| Adjusted R-squared | 0.901081 | Standard Deviation of dependent variable | 768336.2 | |
| Standard Deviation of the equation | 241653.0 | Akaike info criterion | 27.65578 | |
| Sum of the squared residuals | 6.13E+12 | Schwarz criterion | 27.73028 | |
| Log probability | -1490.412 | Hannan-Quinn criterion | 27.68599 | |
| F-statistic | 488.3438 | Durbin-Watson statistic | 1.840618 | |
| Prob(F-statistic) | 0.000000 | |||
Note: since, given their nature, these data show heteroskedasticity, the White method is used (cf. Table 6).
The variables mean:
INC_CIT_1980_2000_thousands = population increase in large cities between 1980 and 2000.
GDP_90_08 = GDP increase between 1990 and 2008.
Table 6. White Test
| Heteroskedasticity: White Test | ||||
| F-statistic | 24.54942 | Prob. F(2,105) | 0.0000 | |
| Observations*R-squared | 34.41087 | Prob. Chi-Square(2) | 0.0000 | |
| Sum of the squares (scaled) | 631.1007 | Prob. Chi-Square(2) | 0.0000 | |
| Test Equation: | ||||
| Dependent Variable: resid^2 | ||||
| Method: Least Squares | ||||
| Date: 16/10/14 Time: 18:21 | ||||
| Sample: 1 108 | ||||
| Included observations: 108 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | -5.23E+10 | 3.83E+10 | -1.365420 | 0.1750 |
| INC_CIT_1980_2000_thousands^2 | -358.7756 | 57.24864 | -6.266972 | 0.0000 |
| INC_CIT_1980_2000_thousands | 48236666 | 6932885. | 6.957661 | 0.0000 |
| R-squared | 0.318619 | Mean of the dependent variable | 6.87E+10 | |
| Adjusted R-squared | 0.305640 | Standard Deviation of dependent variable | 4.26E+11 | |
| Standard Deviation of the equation | 3.55E+11 | Akaike info criterion | 56.05463 | |
| Sum of the squared residuals | 1.32E+25 | Schwarz criterion | 56.12913 | |
| Log probability | -3023.950 | Hannan-Quinn criterion | 56.08483 | |
| F-statistic | 24.54942 | Durbin-Watson statistic | 1.806053 | |
| Prob(F-statistic) | 0.000000 | |||
Table 7. White Method
| Dependent Variable: GDP_90_08 | ||||
| Method: Least Squares | ||||
| Date: 17/10/14 Time: 11:57 | ||||
| Sample: 1 108 | ||||
| Included observations: 108 | ||||
| Heteroskedasticity (White) - consistent standard errors and covariance | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| INC_CIT_1980_2000_thousands | 49.34173 | 3.284620 | 15.02205 | 0.0000 |
| C | 3694.590 | 15969.21 | 0.231357 | 0.8175 |
| R-squared | 0.882587 | Mean of the dependent variable | 211820.6 | |
| Adjusted R-squared | 0.881480 | Standard Deviation of dependent variable | 768336.2 | |
| Standard Deviation of the equation | 264513.3 | Akaike info criterion | 27.82752 | |
| Sum of the squared residuals | 7.42E+12 | Schwarz criterion | 27.87718 | |
| Log probability | -1500.686 | Hannan-Quinn criterion | 27.84765 | |
| F-statistic | 796.7997 | Durbin-Watson statistic | 1.790820 | |
| Prob(F-statistic) | 0.000000 | F-statistic (Wald) | 225.6620 | |
| Prob(Wald F-statistic) | 0.000000 | |||
Table 8. Data used for the correlation test between GDP increase in the period 1990-2008 and population increase in large cities in the period 1980-2000
| Country | GDP_90_08 | INC_CIT_1980_2000_thousands | D-epC |
| Angola | 13904 | 1629,716 | 0 |
| Argentina | 232599 | 3534,072 | 0 |
| Armenia | 14043 | 69,714 | 0 |
| Australia | 240323 | 2689,868 | 0 |
| Austria | 67528 | 10,447 | 0 |
| Azerbaijan | 32824 | 231,69 | 0 |
| Bangladesh | 106134 | 10085,837 | 0 |
| Belarus | 48723 | 380,665 | 0 |
| Belgium | 74661 | 172,945 | 1 |
| Benin | 6546 | 305,307 | 0 |
| Bolivia | 13963 | 1309,945 | 0 |
| Brazil | 518514 | 26899,2 | 0 |
| Bulgaria | 14760 | 53,852 | 0 |
| Burkina Faso | 9486 | 655,608 | 0 |
| Cambodia | 27109 | 910,436 | 0 |
| Cameroon | 7985 | 1855,453 | 0 |
| Canada | 314724 | 4110,467 | 1 |
| Chad | 4599 | 379,751 | 0 |
| Chile | 132910,002 | 1923,104 | 0 |
| China | 6785042 | 134438,196 | 0 |
| Colombia | 125879 | 6158,746 | 0 |
| Congo | 3037 | 897,325 | 0 |
| Costa Rica | 19334 | 506,296 | 0 |
| Czech Republic | 39816 | -6,504 | 0 |
| Denmark | 40174 | -19,002 | 1 |
| Dominican Republic | 24937 | 603,205 | 0 |
| Ecuador | 16964 | 1534,527 | 0 |
| Egypt | 161383 | 3894,607 | 0 |
| El Salvador | 9972 | 546,892 | 0 |
| Finland | 43573 | 345,356 | 1 |
| France | 397071 | 1897,083 | 1 |
| Georgia | -13614 | 9,599 | 0 |
| Germany | 448967 | 282,712 | 1 |
| Ghana | 22218 | 1545,896 | 0 |
| Greece | 73993 | 295,281 | 1 |
| Guatemala | 28947 | 158,329 | 0 |
| Guinea | 2851 | 562,977 | 0 |
| Honduras | 8849 | 421,778 | 0 |
| Hong Kong | 122746 | 2160,409 | 0 |
| Hungary | 27354 | -269,957 | 0 |
| India | 2317083 | 60161,884 | 0 |
| Indonesia | 556849 | 8184,545 | 0 |
| Iran | 257636 | 6888,995 | 0 |
| Iraq | -14981 | 4146,29 | 0 |
| Ireland | 74490 | 85,048 | 1 |
| Israel | 69061 | 2005,087 | 1 |
| Italy | 231982 | -185,958 | 1 |
| Japan | 582988 | 9582,023 | 1 |
| Jordan | 22975 | 381,526 | 0 |
| Kazakhstan | 50216 | 186,992 | 0 |
| Kenya | 15596 | 1685,515 | 0 |
| Kuwait | 20373 | 441,759 | 0 |
| Kyrgyzstan | -602 | 227,702 | 0 |
| Laos | 7234 | 233,998 | 0 |
| Lebanon | 11587 | -136,364 | 0 |
| Liberia | 428 | 510,747 | 0 |
| Madagascar | 5419 | 781,449 | 0 |
| Malawi | 5217 | 353,091 | 0 |
| Malaysia | 170303 | 1206,662 | 0 |
| Mali | 8077 | 652,682 | 0 |
| Mauritania | 2144 | 361,434 | 0 |
| Mexico | 360620 | 16988,318 | 0 |
| Mongolia | 46 | 342,471 | 0 |
| Morocco | 54915 | 2950,769 | 0 |
| Mozambique | 31865 | 764,725 | 0 |
| Nepal | 16363 | 328,935 | 0 |
| Netherlands | 152961 | 142,914 | 1 |
| New Zealand | 31111 | 289,126 | 1 |
| Niger | 3300 | 406,374 | 0 |
| Nigeria | 115499 | 11464,428 | 0 |
| Norway | 54032 | 130,775 | 1 |
| Pakistan | 204892 | 12323,046 | 0 |
| Panama | 11406 | 459,428 | 0 |
| Paraguay | 8583 | 736,988 | 0 |
| Peru | 92245 | 3105,595 | 0 |
| Philippines | 138095 | 5030,922 | 0 |
| Poland | 196252 | 157,686 | 1 |
| Portugal | 46705 | 373,742 | 0 |
| Romania | 28625 | 316,405 | 0 |
| Russia | 130919 | 2766,795 | 1 |
| Rwanda | 4265 | 369,202 | 0 |
| Saudi Arabia | -15473 | 5791,019 | 0 |
| Senegal | 163 | 1071,138 | 0 |
| Serbia | -14 | 49,236 | 0 |
| Sierra Leone | 86191 | 326,94 | 0 |
| Singapore | 30248 | 1504,737 | 0 |
| South Africa | 86320 | 5766,353 | 0 |
| Spain | 323561 | 1705,317 | 1 |
| Sudan | 41504 | 2341,222 | 0 |
| Sweden | 68593 | 214,037 | 1 |
| Switzerland | 43428 | 371,369 | 1 |
| Syria | 94199 | 2541,931 | 0 |
| Thailand | 317341 | 1976,795 | 0 |
| Togo | 743 | 559,974 | 0 |
| Tunisia | 35981 | 134,489 | 0 |
| Turkey | 305987 | 9166,187 | 0 |
| Uganda | 21411 | 628,101 | 0 |
| Ukraine | -81001 | 20,94 | 0 |
| United Kingdom | 502349 | 231,513 | 1 |
| United States | 3681936 | 32228,288 | 1 |
| Uruguay | 14303 | 150,916 | 0 |
| Uzbekistan | 57025 | 316,686 | 0 |
| Venezuela | 119249 | 2882,268 | 0 |
| Vietnam | 186827 | 2987,074 | 0 |
| Yemen | 33894 | 1340,53 | 0 |
| Zambia | 3423 | 540,421 | 0 |
| Zimbabwe | -4925 | 762,939 | 0 |
| South Korea | 575756 | 9563,643 | 0 |
Figure 2. Residuals of the correlation between GDP increase in the period 1990-2008 and population increase in large cities in the period 1980-2000
Source: E-Views program for United Nations data (2012) and World Economics.Note: Since, given their nature, the data displayed in Table 2 contain samples of very different sizes, values expressed in natural logarithms are used for the estimations, as a way of dealing with heteroskedasticity. The correlation decreases, but its statistical relevance increases.
The variables mean:
LogINC_CIT_1975_1990_THOUSANDS = natural logarithm of population increase in large cities between 1975 and 1990.
LOG_INC_GDP_1990_2008 = natural logarithm of GDP_90_08 or GDP increase between 1990 and 2008.
Table 9. 1975-1990 Model with binary variables
| Dependent Variable: INC_GDP_1990_2008 | ||||
| Method: Least Squares | ||||
| Date: 17/10/14 Time: 16:17 | ||||
| Sample: 1 108 | ||||
| Included observations: 107 | ||||
| Heteroskedasticity (White) - consistent standard errors and covariance | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| INC_POP__CIT_1975_1990 | 55.20691 | 9.663841 | 5.712730 | 0.0000 |
| large_D-ingC | -289633.0 | 206474.8 | -1.402753 | 0.1638 |
| USA | 2739162. | 153958.2 | 17.79160 | 0.0000 |
| China | 4359865. | 413224.5 | 10.55084 | 0.0000 |
| D-edC | 153893.4 | 41238.02 | 3.731833 | 0.0003 |
| C | -2597.454 | 15855.74 | -0.163818 | 0.8702 |
| R-squared | 0.977295 | Mean of the dependent variable | 213725.6 | |
| Adjusted R-squared | 0.976171 | Standard Deviation of dependent variable | 771695.6 | |
| Standard Deviation of the equation | 119125.0 | Akaike info criterion | 26.26818 | |
| Sum of the squared residuals | 1.43E+12 | Schwarz criterion | 26.41805 | |
| Log probability | -1399.347 | Hannan-Quinn criterion | 26.32893 | |
| F-statistic | 869.4562 | Durbin-Watson statistic | 1.562894 | |
| Prob(F-statistic) | 0.000000 | |||
Table 10. 1980-2000 Model with binary variables
| Normalized Coefficients | ||||||
| Date: 17/10/14 Time: 16:18 | ||||||
| Sample: 1 108 | ||||||
| Included observations: 107 | ||||||
| Variable | Coefficient | Standardized Coefficient | Elasticity at the mean | |||
| INC_POP__CIT_1975_1990 | 55.20691 | 0.457764 | 0.665698 | |||
| large_D-ingC | -289633.0 | -0.062249 | -0.037995 | |||
| USA | 2739162 | 0.343147 | 0.119778 | |||
| CHINA | 4359865 | 0.546179 | 0.190648 | |||
| D-edC | 153893.4 | 0.060850 | 0.074024 | |||
| C | -2597.454 | -6.12E-27 | -0.012153 | |||
| Dependent Variable: INC_GDP_1990_2008 | ||||||
| Method: Least Squares | ||||||
| Date: 17/10/14 Time: 16:22 | ||||||
| Sample: 1 108 | ||||||
| Included observations: 107 | ||||||
| Heteroskedasticity (White) - consistent standard errors and covariance | ||||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability | ||
| INC_POP__CIT_1980_2000__ | 38.45909 | 5.344313 | 7.196264 | 0.0000 | ||
| China | 1610774. | 712818.3 | 2.259726 | 0.0260 | ||
| USA | 2438568. | 166836.0 | 14.61656 | 0.0000 | ||
| large_D-ingC | -272373.8 | 173253.8 | -1.572108 | 0.1191 | ||
| D-edC | 160972.3 | 40351.72 | 3.989230 | 0.0001 | ||
| C | 3897.716 | 12076.38 | 0.322755 | 0.7475 | ||
| R-squared | 0.979394 | Mean of the dependent variable | 213725.6 | |||
| Adjusted R-squared | 0.978374 | Standard Deviation of dependent variable | 771695.6 | |||
| Standard Deviation of the equation | 113483.6 | Akaike info criterion | 26.17114 | |||
| Sum of the squared residuals | 1.30E+12 | Schwarz criterion | 26.32102 | |||
| Log probability | -1394.156 | Hannan-Quinn criterion | 26.23190 | |||
| F-statistic | 960.1070 | Durbin-Watson statistic | 1.567188 | |||
| Prob(F-statistic) | 0.000000 | |||||
Table 11. Synchronic Model in logarithms of urban population percentage with respect to product per capita. Year 1950. Results and Tests
| Normalized Coefficients | |||||
| Date: 17/10/14 Time: 16:24 | |||||
| Sample: 1 108 | |||||
| Included observations: 107 | |||||
| Variable | Coefficient | Standardized Coefficient | Elasticity at the mean | ||
| INC_POP__CIT_1980_2000__ | 38.45909 | 0.732410 | 0.762995 | ||
| China | 1610774. | 0.201789 | 0.070436 | ||
| USA | 2438568. | 0.305490 | 0.106634 | ||
| large_D-ingC | -272373.8 | -0.058540 | -0.035731 | ||
| D-edC | 160972.3 | 0.063649 | 0.077429 | ||
| C | 3897.716 | 9.18E-27 | 0.018237 | ||
| Dependent Variable: LGDPC_1950 | |||||
| Method: Least Squares | |||||
| Date: 27/10/14 Time: 11:51 | |||||
| Sample: 1 147 | |||||
| Included observations: 128 | |||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability | |
| URB_POP_1950 | 0.728235 | 0.052379 | 13.90328 | 0.0000 | |
| C | 3.682204 | 0.043014 | 85.60396 | 0.0000 | |
| R-squared | 0.605388 | Mean of the dependent variable | 3.176487 | ||
| Adjusted R-squared | 0.602256 | Standard Deviation of dependent variable | 0.411890 | ||
| Standard Deviation of the equation | 0.259766 | Akaike info criterion | 0.157431 | ||
| Sum of the squared residuals | 8.502280 | Schwarz criterion | 0.201994 | ||
| Log probability | -8.075591 | Hannan-Quinn criterion | 0.175537 | ||
| F-statistic | 193.3011 | Durbin-Watson statistic | 1.578072 | ||
| Prob(F-statistic) | 0.000000 | ||||
Table 12. White Test results for Table 11
| Heteroskedasticity: White Test | ||||
| F-statistic | 4.145481 | Prob. F(2,125) | 0.0181 | |
| Observations*R-squared | 7.961854 | Prob. Chi-Square(2) | 0.0187 | |
| Normalized Sum of the squares | 13.60424 | Prob. Chi-Square(2) | 0.0011 | |
| Test Equation: | ||||
| Dependent Variable: resid^2 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 11:52 | ||||
| Sample: 1 147 | ||||
| Included observations: 128 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.153224 | 0.032033 | 4.783328 | 0.0000 |
| URB_POP_1950^2 | 0.120618 | 0.049985 | 2.413085 | 0.0173 |
| UBR_POP_1950 | 0.242130 | 0.087823 | 2.757005 | 0.0067 |
| R-squared | 0.062202 | Mean of the dependent variable | 0.066424 | |
| Adjusted R-squared | 0.047197 | Standard Deviation of dependent variable | 0.125231 | |
| Standard Deviation of the equation | 0.122240 | Akaike info criterion | -1.342497 | |
| Sum of the squared residuals | 1.867837 | Schwarz criterion | -1.275652 | |
| Log probability | 88.91980 | Hannan-Quinn criterion | -1.315338 | |
| F-statistic | 4.145481 | Durbin-Watson statistic | 1.992782 | |
| Prob(F-statistic) | 0.018065 | |||
Table 13. Synchronic model in logarithms of urban population percentage with respect to product per capita. Year 1970. Results and tests
| Dependent Variable: LGDPC_1970 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 11:59 | ||||
| Sample: 1 147 | ||||
| Included observations: 128 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LURB_POP_1970 | 1.014909 | 0.069230 | 14.66004 | 0.0000 |
| C | 3.914643 | 0.041980 | 93.24935 | 0.0000 |
| R-squared | 0.630408 | Mean of the dependent variable | 3.409782 | |
| Adjusted R-squared | 0.627475 | Standard Deviation of dependent variable | 0.445023 | |
| Standard Deviation of the equation | 0.271619 | Akaike info criterion | 0.246669 | |
| Sum of the squared residuals | 9.295892 | Schwarz criterion | 0.291232 | |
| Log probability | -13.78684 | Hannan-Quinn criterion | 0.264776 | |
| F-statistic | 214.9167 | Durbin-Watson statistic | 1.402789 | |
| Prob(F-statistic) | 0.000000 | |||
Table 14. White Test results for Table 13
| Heteroskedasticity: White test | ||||
| F-statistic | 3.043914 | Prob. F(2,125) | 0.0512 | |
| Observations*R-squared | 5.944427 | Prob. Chi-Square(2) | 0.0512 | |
| Normalized sum of the squares | 6.953205 | Prob. Chi-Square(2) | 0.0309 | |
| Test Equation: | ||||
| Dependent Variable: resid^2 | ||||
| Method: Least Squares | ||||
| Date: 10/27/14 Time: 11:54 | ||||
| Sample: 1 147 | ||||
| Included observations: 128 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.112220 | 0.025345 | 4.427703 | 0.0000 |
| LURB_POP_1970^2 | 0.162429 | 0.066713 | 2.434755 | 0.0163 |
| LURB_POP_1970 | 0.199666 | 0.091213 | 2.188999 | 0.0305 |
| R-squared | 0.046441 | Mean of the dependent variable | 0.072624 | |
| Adjusted R-squared | 0.031184 | Standard Deviation of dependent variable | 0.113286 | |
| Standard Deviation of the equation | 0.111506 | Akaike info criterion | -1.526325 | |
| Sum of the squared residuals | 1.554189 | Schwarz criterion | -1.459480 | |
| Log probability | 100.6848 | Hannan-Quinn criterion | -1.499165 | |
| F-statistic | 3.043914 | Durbin-Watson statistic | 1.775466 | |
| Prob(F-statistic) | 0.051195 | |||
Table 15. Synchronic model in logarithms of urban population percentage with respect to product per capita. Year 1980. Results and tests
| Dependent Variable: LGDPC_1980 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 12:19 | ||||
| Sample: 1 147 | ||||
| Included observations: 128 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LURB_POP_1980 | 1.223489 | 0.083025 | 14.73643 | 0.0000 |
| C | 4.006542 | 0.043117 | 92.92181 | 0.0000 |
| R-squared | 0.632827 | Mean of the dependent variable | 3.490373 | |
| Adjusted R-squared | 0.629913 | Standard Deviation of dependent variable | 0.467619 | |
| Standard Deviation of the equation | 0.284475 | Akaike info criterion | 0.339158 | |
| Sum of the squared residuals | 10.19667 | Schwarz criterion | 0.383721 | |
| Log probability | -19.70610 | Hannan-Quinn criterion | 0.357264 | |
| F-statistic | 217.1624 | Durbin-Watson statistic | 1.302503 | |
| Prob(F-statistic) | 0.000000 | |||
| Heteroskedasticity: White Test | ||||
| F-statistic | 2.552506 | Prob. F(2,125) | 0.0819 | |
| Observations*R-squared | 5.022416 | Prob. Chi-Square(2) | 0.0812 | |
| Normalized sum of the squares | 9.748678 | Prob. Chi-Square(2) | 0.0076 | |
| Test Equation: | ||||
| Dependent Variable: RESID^2 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 12:22 | ||||
| Sample: 1 147 | ||||
| Included observations: 128 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.082647 | 0.034806 | 2.374520 | 0.0191 |
| LURB_POP_1980^2 | 0.183483 | 0.126254 | 1.453281 | 0.1487 |
| LURB_POP_1980 | 0.124376 | 0.147916 | 0.840856 | 0.4020 |
| R-squared | 0.039238 | Mean of the dependent variable | 0.079661 | |
| Adjusted R-squared | 0.023865 | Standard Deviation of dependent variable | 0.160075 | |
| Standard Deviation of the equation | 0.158153 | Akaike info criterion | -0.827350 | |
| Sum of the squared residuals | 3.126543 | Schwarz criterion | -0.760506 | |
| Log probability | 55.95041 | Hannan-Quinn criterion | -0.800191 | |
| F-statistic | 2.552506 | Durbin-Watson statistic | 1.457594 | |
| Prob(F-statistic) | 0.081941 | |||
Table 16. Synchronic model in logarithms of urban population percentage with respect to product per capita. Year 1990. Results and tests
| Dependent Variable: LGDPC_1990 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 12:42 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LURB_POP_1990 | 1.295361 | 0.099973 | 12.95713 | 0.0000 |
| C | 3.984857 | 0.043092 | 92.47352 | 0.0000 |
| R-squared | 0.536574 | Mean of the dependent variable | 3.538078 | |
| Adjusted R-squared | 0.533378 | Standard Deviation of dependent variable | 0.458721 | |
| Standard Deviation of the equation | 0.313351 | Akaike info criterion | 0.530525 | |
| Sum of the squared residuals | 14.23736 | Schwarz criterion | 0.571211 | |
| Log probability | -36.99356 | Hannan-Quinn criterion | 0.547056 | |
| F-statistic | 167.8873 | Durbin-Watson statistic | 1.082544 | |
| Prob(F-statistic) | 0.000000 | |||
| Heteroskedasticity: White Test | ||||
| F-statistic | 7.785266 | Prob. F(2,144) | 0.0006 | |
| Observations*R-squared | 14.34393 | Prob. Chi-Square(2) | 0.0008 | |
| Normalized sum of the squares | 21.76386 | Prob. Chi-Square(2) | 0.0000 | |
| Test Equation: | ||||
| Dependent Variable: RESID^2 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 12:44 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.130304 | 0.033314 | 3.911405 | 0.0001 |
| LURB_POP_1990^2 | 0.479805 | 0.153106 | 3.133805 | 0.0021 |
| LURB_POP_1990 | 0.355446 | 0.162190 | 2.191533 | 0.0300 |
| R-squared | 0.097578 | Mean of the dependent variable | 0.096853 | |
| Adjusted R-squared | 0.085044 | Standard Deviation of dependent variable | 0.171630 | |
| Standard Deviation of the equation | 0.164170 | Akaike info criterion | -0.755637 | |
| Sum of the squared residuals | 3.881036 | Schwarz criterion | -0.694608 | |
| Log probability | 58.53932 | Hannan-Quinn criterion | -0.730840 | |
| F-statistic | 7.785266 | Durbin-Watson statistic | 2.025444 | |
| Prob(F-statistic) | 0.000616 | |||
Table 17. Synchronic model in logarithms of urban population percentage with respect to product per capita. Year 2000. Results and tests
| Dependent Variable: LGDPC_2000 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 12:49 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LURB_POP_2000 | 1.479104 | 0.128907 | 11.47422 | 0.0000 |
| C | 4.024872 | 0.049542 | 81.24147 | 0.0000 |
| R-squared | 0.475887 | Mean of the dependent variable | 3.568485 | |
| Adjusted R-squared | 0.472272 | Standard Deviation of dependent variable | 0.492950 | |
| Standard Deviation of the equation | 0.358103 | Akaike info criterion | 0.797519 | |
| Sum of the squared residuals | 18.59447 | Schwarz criterion | 0.838206 | |
| Log probability | -56.61768 | Hannan-Quinn criterion | 0.814051 | |
| F-statistic | 131.6577 | Durbin-Watson statistic | 1.237058 | |
| Prob(F-statistic) | 0.000000 | |||
| Heteroskedasticity: White Test | ||||
| F-statistic | 4.112877 | Prob. F(2,144) | 0.0183 | |
| Observations*R-squared | 7.943372 | Prob. Chi-Square(2) | 0.0188 | |
| Normalized sum of the squares | 11.36283 | Prob. Chi-Square(2) | 0.0034 | |
| Test Equation: | ||||
| Dependent Variable: RESID^2 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 13:04 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.147481 | 0.043620 | 3.381028 | 0.0009 |
| LURB_POP_2000^2 | 0.570867 | 0.272439 | 2.095395 | 0.0379 |
| LURB_POP_2000 | 0.341295 | 0.246817 | 1.382786 | 0.1689 |
| R-squared | 0.054037 | Mean of the dependent variable | 0.126493 | |
| Adjusted R-squared | 0.040898 | Standard Deviation of dependent variable | 0.217648 | |
| Standard Deviation of the equation | 0.213150 | Akaike info criterion | -0.233441 | |
| Sum of the squared residuals | 6.542364 | Schwarz criterion | -0.172411 | |
| Log probability | 20.15789 | Hannan-Quinn criterion | -0.208644 | |
| F-statistic | 4.112877 | Durbin-Watson statistic | 1.983319 | |
| Prob(F-statistic) | 0.018321 | |||
Table 18. Synchronic model in logarithms of urban population percentage with respect to product per capita. Year 2008-2010. Results and tests
| Dependent Variable: LGDPC_2008 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 13:09 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LURB_POP_2010 | 1.529951 | 0.153868 | 9.943258 | 0.0000 |
| C | 4.102470 | 0.053390 | 76.83968 | 0.0000 |
| R-squared | 0.405417 | Mean of the dependent variable | 3.680414 | |
| Adjusted R-squared | 0.401316 | Standard Deviation of dependent variable | 0.507463 | |
| Standard Deviation of the equation | 0.392648 | Akaike info criterion | 0.981705 | |
| Sum of the squared residuals | 22.35500 | Schwarz criterion | 1.022391 | |
| Log probability | -70.15533 | Hannan-Quinn criterion | 0.998236 | |
| F-statistic | 98.86839 | Durbin-Watson statistic | 1.199927 | |
| Prob(F-statistic) | 0.000000 | |||
| Heteroskedasticity: White Test | ||||
| F-statistic | 3.351982 | Prob. F(2,144) | 0.0378 | |
| Observations*R-squared | 6.539195 | Prob. Chi-Square(2) | 0.0380 | |
| Normalized sum of the squares | 8.902426 | Prob. Chi-Square(2) | 0.0117 | |
| Test Equation: | ||||
| Dependent Variable: RESID^2 | ||||
| Method: Least Squares | ||||
| Date: 27/10/14 Time: 13:11 | ||||
| Sample: 1 147 | ||||
| Included observations: 147 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | 0.125724 | 0.049978 | 2.515559 | 0.0130 |
| LURB_POP_2010^2 | 0.399108 | 0.382886 | 1.042366 | 0.2990 |
| LURB_POP_2010 | 0.078666 | 0.315120 | 0.249638 | 0.8032 |
| R-squared | 0.044484 | Mean of the dependent variable | 0.152075 | |
| Adjusted R-squared | 0.031213 | Standard Deviation of dependent variable | 0.255268 | |
| Standard Deviation of the equation | 0.251252 | Akaike info criterion | 0.095478 | |
| Sum of the squared residuals | 9.090388 | Schwarz criterion | 0.156508 | |
| Log probability | -4.017659 | Hannan-Quinn criterion | 0.120275 | |
| F-statistic | 3.351982 | Durbin-Watson statistic | 1.878025 | |
| Prob(F-statistic) | 0.037768 | |||
Table 19. Correlation between the values of natural logarithms of GDP increase and prior population growth in cities, by developed and developing countries
| Dependent Variable: LOG_INC_GDP_1990_2008 | ||||
| Method: Least Squares | ||||
| Date: 15/08/16 Time: 09:51 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LOG_INC_CIT_1975_1990 | 0.645991 | 0.089435 | 7.223007 | 0.0000 |
| D-epC | 0.812033 | 0.168565 | 4.817322 | 0.0000 |
| C | 2.612455 | 0.266939 | 9.786701 | 0.0000 |
| R-squared | 0.434280 | Mean of the dependent variable | 4.605665 | |
| Adjusted R-squared | 0.422114 | Standard Deviation of dependent variable | 0.846414 | |
| Standard Deviation of the equation | 0.643434 | Akaike info criterion | 1.986756 | |
| Sum of the squared residuals | 38.50264 | Schwarz criterion | 2.066892 | |
| Log probability | -92.36428 | Hannan-Quinn criterion | 2.019148 | |
| F-statistic | 35.69618 | Durbin-Watson statistic | 1.956877 | |
| Prob(F-statistic) | 0.000000 | |||
Note: Since, given their nature, the data displayed in Table 2 contain samples of very different sizes, values expressed in natural logarithms are used for the estimations, as a way of dealing with heteroskedasticity. The correlation decreases, but its statistical relevance increases.
The variables mean:
LogINC_CIT_1975_1990_THOUSANDS = natural logarithm of population increase in large cities between 1975 and 1990.
LOG_INC_GDP_1990_2008 = natural logarithm of GDP_90_08 or GDP increase between 1990 and 2008.
Figure 3. Residuals of the correlation between GDP increase in the period 1990-2008 and population increase in large cities in the period 1980-2000 (logarithmic model)
Source: E-Views program for United Nations data (2012) and World Economics.Note: If population increase is explained by expected future wealth equaling the recorded one, the result of the regression is lower, which, though not solving the question of causality, at least points out that prior population growth in cities with respect to wealth creation should be logically expected.
The variables mean:
LogINC_CIT_1975_1990_THOUSANDS = natural logarithm of population increase in large cities between 1975 and 1990.
LOG_INC_CIT_1990_2008 = natural logarithm of GDP_90_08 or GDP increase between 1990 and 2008.
Table 20. Correlation between the values of natural logarithms of population increase in large cities explained for future wealth, by developed and developing countries
| Dependent Variable: INC_CIT_1975_1990_THOUSANDS | ||||
| Method: Least Squares | ||||
| Date: 15/08/16 Time: 11:58 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LOG_INC_GDP_1990_2008 | 5126.491 | 693.8039 | 7.388962 | 0.0000 |
| D-edC | -3988.523 | 1496.695 | -2.664886 | 0.0091 |
| C | -20053.60 | 3158.739 | -6.348610 | 0.0000 |
| R-squared | 0.369997 | Mean of the dependent variable | 2809.448 | |
| Adjusted R-squared | 0.356449 | Standard Deviation of dependent variable | 6704.868 | |
| Standard Deviation of the equation | 5378.755 | Akaike info criterion | 20.04905 | |
| Sum of the squared residuals | 2.69E+09 | Schwarz criterion | 20.12919 | |
| Log probability | -959.3545 | Hannan-Quinn criterion | 20.08144 | |
| F-statistic | 27.30922 | Durbin-Watson statistic | 2.116880 | |
| Prob(F-statistic) | 0.000000 | |||
Note: If population increase is explained by expected future wealth equaling the recorded one, the result of the regression is lower, which, though not solving the question of causality, at least points out that prior population growth in cities with respect to wealth creation should be logically expected.
The variables mean:
LogINC_CIT_1975_1990_THOUSANDS = natural logarithm of population increase in large cities between 1975 and 1990.
LOG_INC_CIT_1990_2008 = natural logarithm of GDP_90_08 or GDP increase between 1990 and 2008.
Table 21. Results of the correlation between GDP increase 1990-2008 explained by population increase in large cities in the period 1975-1990 (absolute values divided by the square root of the explanatory variable as a way of preventing the wide dispersion of the variables)
| Dependent Variable: INC_GDP_1990_2008_CORREC | ||||
| Method: Least Squares | ||||
| Date: 08/20/16 Time: 08:26 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| INC_CIT_1975_90_CORRECTED | 95.36594 | 13.38548 | 7.124584 | 0.0000 |
| D-edC_CORRECTED | 71151.65 | 14660.89 | 4.853160 | 0.0000 |
| Z | 28617.77 | 3078.133 | 9.297120 | 0.0000 |
| C | -2073.540 | 786.3344 | -2.636970 | 0.0098 |
| R-squared | 0.591435 | Mean of the dependent variable | 4139.614 | |
| Adjusted R-squared | 0.578112 | Standard Deviation of dependent variable | 7183.072 | |
| Standard Deviation of the equation | 4665.613 | Akaike info criterion | 19.77460 | |
| Sum of the squared residuals | 2.00E+09 | Schwarz criterion | 19.88145 | |
| Log probability | -945.1808 | Hannan-Quinn criterion | 19.81779 | |
| F-statistic | 44.39278 | Durbin-Watson statistic | 1.876070 | |
| Prob(F-statistic) | 0.000000 | |||
Note: This test means to correct heteroskedasticity by dividing the absolute values of the variables by the square root of the independent variable.
The variables mean:
INC_GPD_1990_2008_CORRECTED = Absolute values of GDP increase between 1990 and 2008 divided by the square root of the absolute value of population increase in cities between 1975 and 1990.
INC_CIT_1975_90_CORRECTED = Absolute value of population increase in cities between 1975 and 1990 divided by its square root.
D-edC CORRECTED = Binary variable with value 1 if it is a developed country and 0 if it is not, divided by the square root of the absolute value of population increase in cities between 1975 and 1990.
Z = 1 divided by the square root of the absolute value of population increase in cities between 1975 and 1990.
Table 22. Results of the White Test for the regression model between GDP growth between 1990 and 2008 explained by population increase in large cities between 1975 and 1990 (absolute values divided by the square root of the explanatory variable)
| Heteroskedasticity: White Test | ||||
| F-statistic | 2.880812 | Prob. F(7,88) | 0.0093 | |
| Observations*R-squared | 17.89759 | Prob. Chi-Square(7) | 0.0124 | |
| Normalized sum of the squares | 132.8685 | Prob. Chi-Square(7) | 0.0000 | |
| Test Equation: | ||||
| Dependent Variable: RESID^2 | ||||
| Method: Least Squares | ||||
| Date: 20/08/16 Time: 09:48 | ||||
| Sample: 1 96 | ||||
| Included observations: 96 | ||||
| Collinear test of the regressors | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| C | -13408581 | 63775152 | -0.210248 | 0.8340 |
| INC_CIT_1975_90_CORRECTED^2 | 3927.841 | 5406.472 | 0.726507 | 0.4695 |
| INC_CIT_1975_90_CORRECTED*D-edC _CORRECTED | 8797421 | 46711182 | 0.188337 | 0.8510 |
| INC_CIT_1975_90_CORRECTED | -14254.55 | 1242143. | -0.011476 | 0.9909 |
| D-edC_CORRECTED^2 | -1.13E+10 | 6.62E+09 | -1.708202 | 0.0911 |
| D-edC_CORRECTED | 2.05E+09 | 1.27E+09 | 1.618427 | 0.1091 |
| Z^2 | -1.70E+08 | 4.76E+08 | -0.356496 | 0.7223 |
| Z | 2.77E+08 | 7.88E+08 | 0.350931 | 0.7265 |
| R-squared | 0.186433 | Mean of the dependent variable | 20860948 | |
| Adjusted R-squared | 0.121718 | Standard Deviation of dependent variable | 84317939 | |
| Standard Deviation of the equation | 79020003 | Akaike info criterion | 39.28796 | |
| Sum of the squared residuals | 5.49E+17 | Schwarz criterion | 39.50165 | |
| Log probability | -1877.822 | Hannan-Quinn criterion | 39.37433 | |
| F-statistic | 2.880812 | Durbin-Watson statistic | 2.014254 | |
| Prob(F-statistic) | 0.009324 | |||
Figure 4. Residuals of the correlation between GDP growth in the period 1990-2008 and population increase in large cities in the period 1975-1990 (model with corrected absolute values)
Source: E-Views program for United Nations data (2012) and World Economics.
1. 2. Urbanization stages and consumption of raw materials: autocorrelation in variables associated to GDP (cases: energy, cement, steel, copper and food). Results and residuals of the regressions
Table 23. Logarithm of world energy use with respect to the logarithm of GDP. Maddison Series
| Dependent Variable: LOG_energy | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 06:30 | ||||
| Sample: 1965 2012 | ||||
| Included observations: 48 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| LOG_GDP_Maddison | 0.665885 | 0.012333 | 53.99212 | 0.0000 |
| C | -1.056994 | 0.091386 | -11.56629 | 0.0000 |
| R-squared | 0.984465 | Mean of the dependent variable | 3.875307 | |
| Adjusted R-squared | 0.984128 | Standard Deviation of dependent variable | 0.136039 | |
| Standard Deviation of the equation | 0.017139 | Akaike info criterion | -5.254161 | |
| Sum of the squared residuals | 0.013512 | Schwarz criterion | -5.176195 | |
| Log probability | 128.0999 | Hannan-Quinn criterion | -5.224698 | |
| F-statistic | 2915.149 | Durbin-Watson statistic | 0.108943 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 5. Residuals of the correlation between the logarithm of world energy use and world GDP
Source: Maddison data series and BP.
Note: Hypothesis: stages associated to urban growth and low prices until 1975-1978; fall until new rise as a consequence of the China effect 2003-2010.
Table 24. World use of cement with respect to GDP. Maddison Series (values in tons and dollars of 1990)
| Dependent Variable: CEMENT | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 06:44 | ||||
| Sample: 1950 2012 | ||||
| Included observations: 63 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_Maddison | 61.55886 | 1.753255 | 35.11118 | 0.0000 |
| C | -3.17E+08 | 47987483 | -6.598180 | 0.0000 |
| R-squared | 0.952852 | Mean of the dependent variable | 1.12E+09 | |
| Adjusted R-squared | 0.952079 | Standard Deviation of dependent variable | 9.06E+08 | |
| Standard Deviation of the equation | 1.98E+08 | Akaike info criterion | 41.07911 | |
| Sum of the squared residuals | 2.40E+18 | Schwarz criterion | 41.14715 | |
| Log probability | -1291.992 | Hannan-Quinn criterion | 41.10587 | |
| F-statistic | 1232.795 | Durbin-Watson statistic | 0.106401 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 6. Residuals of the correlation between world cement use and world GDP
Source: Maddison data series and United States Geological Survey (USGS).
Note: Hypothesis: growth as of 2000 as a consequence of the impact of China and India’s urbanization.
Table 25. World use of steel with respect to GDP. Maddison Series (values in tons and dollars of 1990)
| Dependent Variable: STEEL | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 06:55 | ||||
| Sample: 1950 2012 | ||||
| Included observations: 63 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_MADDISON | 21.91864 | 0.829576 | 26.42148 | 0.0000 |
| C | 1.82E+08 | 22705925 | 8.007482 | 0.0000 |
| R-squared | 0.919641 | Mean of the dependent variable | 6.94E+08 | |
| Adjusted R-squared | 0.918324 | Standard Deviation of dependent variable | 3.28E+08 | |
| Standard Deviation of the equation | 93801077 | Akaike info criterion | 39.58248 | |
| Sum of the squared residuals | 5.37E+17 | Schwarz criterion | 39.65052 | |
| Log probability | -1244.848 | Hannan-Quinn criterion | 39.60924 | |
| F-statistic | 698.0947 | Durbin-Watson statistic | 0.150849 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 7. Residuals of the correlation between world steel use and world GDP
Source: Maddison data series and United States Geological Survey (USGS).
Note: Hypothesis: growth until 1975, first urbanization stage; fall as a consequence of urbanization decline and substitution of materials between 1976 and 2000, and new rise as of 2000 as a result of the impact of China and India’s urbanization, with the impact of the 2009 crisis.
Table 26. World use of copper with respect to GDP. Maddison Series (values in tons and dollars of 1990)
| Dependent Variable: COPPER | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 06:57 | ||||
| Sample: 1950 2012 | ||||
| Included observations: 63 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_Maddison | 0.295951 | 0.004463 | 66.30660 | 0.0000 |
| C | 1372980. | 122164.9 | 11.23874 | 0.0000 |
| R-squared | 0.986315 | Mean of the dependent variable | 8289683. | |
| Adjusted R-squared | 0.986091 | Standard Deviation of dependent variable | 4279255. | |
| Standard Deviation of the equation | 504678.9 | Akaike info criterion | 29.13246 | |
| Sum of the squared residuals | 1.55E+13 | Schwarz criterion | 29.20050 | |
| Log probability | -915.6726 | Hannan-Quinn criterion | 29.15922 | |
| F-statistic | 4396.565 | Durbin-Watson statistic | 0.282864 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 8. Residuals of the correlation between world copper use and world GDP
Source: Maddison data series and United States Geological Survey (USGS)
Note: Hypothesis: growth until 1975, first urbanization stage; fall as a consequence of urbanization decline and substitution of materials between 1976 and 1995. New rise as of 1995 as a result of the impact of China and India’s urbanization. Factor: spread of electricity grids and use of electric appliances and engines.
Table 27. World use of aluminum with respect to GDP. Maddison Series (values in tons and dollars of 1990)
| Dependent Variable: ALUMINUM | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 07:14 | ||||
| Sample: 1950 2012 | ||||
| Included observations: 63 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_Maddison | 0.788258 | 0.013881 | 56.78610 | 0.0000 |
| C | -2173384 | 379934.8 | -5.720413 | 0.0000 |
| R-squared | 0.981434 | Mean of the dependent variable | 16249048 | |
| Adjusted R-squared | 0.981130 | Standard Deviation of dependent variable | 11425974 | |
| Standard Deviation of the equation | 1569559. | Akaike info criterion | 31.40172 | |
| Sum of the squared residuals | 1.50E+14 | Schwarz criterion | 31.46976 | |
| Log probability | -987.1542 | Hannan-Quinn criterion | 31.42848 | |
| F-statistic | 3224.661 | Durbin-Watson statistic | 0.238445 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 9. Residuals of the correlation between world aluminum use and world GDP
Source: Maddison data series and United States Geological Survey (USGS).
Note: Hypothesis: growth until 1975, first urbanization stage; fall as a consequence of urbanization decline until 2000. New rise as of 2000 as a result of the impact of China and India’s urbanization, with impact of 2009 crisis.
Table 28. World consumption of food with respect to GDP. Maddison Series (case: agriculture total) (values in tons and dollars of 1990)
| Dependent Variable: AGRICULTURE (total) | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 07:21 | ||||
| Sample: 1961 2010 | ||||
| Included observations: 50 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_MADDISON | 0.790107 | 0.008958 | 88.19707 | 0.0000 |
| C | 23.00074 | 0.567925 | 40.49962 | 0.0000 |
| R-squared | 0.993867 | Mean of the dependent variable | 68.19060 | |
| Adjusted R-squared | 0.993739 | Standard Deviation of dependent variable | 21.89249 | |
| Standard Deviation of the equation | 1.732220 | Akaike info criterion | 3.975863 | |
| Sum of the squared residuals | 144.0282 | Schwarz criterion | 4.052344 | |
| Log probability | -97.39657 | Hannan-Quinn criterion | 4.004987 | |
| F-statistic | 7778.724 | Durbin-Watson statistic | 0.297553 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 10. Residuals of the correlation between world food consumption and world GDP
Note: Hypothesis: rise in the share in the product in stages of urban growth stabilization or cities with low expansion with respect to the large urbanization waves.
Table 29. World consumption of food with respect to GDP. Maddison Series (case: cereals) (values in tons and dollars of 1990)
| Dependent Variable: CEREALS | ||||
| Method: Least Squares | ||||
| Date: 22/06/16 Time: 07:27 | ||||
| Sample: 1961 2010 | ||||
| Included observations: 50 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| GDP_Maddison | 0.726119 | 0.028540 | 25.44179 | 0.0000 |
| C | 32.94293 | 1.809335 | 18.20720 | 0.0000 |
| R-squared | 0.930964 | Mean of the dependent variable | 74.47300 | |
| Adjusted R-squared | 0.929525 | Standard Deviation of dependent variable | 20.78809 | |
| Standard Deviation of the equation | 5.518631 | Akaike info criterion | 6.293315 | |
| Sum of the squared residuals | 1461.854 | Schwarz criterion | 6.369796 | |
| Log probability | -155.3329 | Hannan-Quinn criterion | 6.322439 | |
| F-statistic | 647.2845 | Durbin-Watson statistic | 0.237552 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 11. Residuals of the correlation between world food consumption and world GDP
Note: Hypothesis: rise in the share in the product in stages of urban growth stabilization or cities with low expansion with respect to the large urbanization waves.
Table 30. World consumption of cement and value added of the construction sector on a world scale in the period 1970-2012 (values in current dollars and in tons)
| Dependent Variable: CEMENT | ||||
| Method: Least Squares | ||||
| Date: 12/01/16 Time: 07:28 | ||||
| Sample: 1970 2012 | ||||
| Included observations: 43 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| VA_CORR_CONSTRUCTON_$_C | 822.1510 | 23.67424 | 34.72766 | 0.0000 |
| C | 2.45E+08 | 43447434 | 5.632454 | 0.0000 |
| R-squared | 0.967121 | Mean of the dependent variable | 1.50E+09 | |
| Adjusted R-squared | 0.966319 | Standard Deviation of dependent variable | 8.66E+08 | |
| Standard Deviation of the equation | 1.59E+08 | Akaike info criterion | 40.65033 | |
| Sum of the squared residuals | 1.03E+18 | Schwarz criterion | 40.73225 | |
| Log probability | -871.9822 | Hannan-Quinn criterion | 40.68054 | |
| F-statistic | 1206.010 | Durbin-Watson statistic | 0.307921 | |
| Prob(F-statistic) | 0.000000 | |||
Figure 12. Residuals of the correlation between cement use and value added of the construction sector on a world scale in the period 1970-2012
Note: After 1985 and until the beginning of China’s urbanization process, the residuals series declines. Then it rises, though it is interrupted at the time of the 2009 crisis. The rising trend of the value added series of the construction sector and of the series of cement use are very pronounced as of the beginning of the twentieth century, but they tend to decelerate after the 2009 crisis, in line with the arguments regarding the drive of both variables produced by the dynamics of urbanization processes.
Table 31. World use of steel and value added of the construction sector on a world scale in the period 1970-2012 (values in current dollars and in tons)
| Dependent Variable: STEEL | ||||
| Method: Least Squares | ||||
| Date: 12/01/16 Time: 07:53 | ||||
| Sample: 1970 2012 | ||||
| Included observations: 43 | ||||
| Variable | Coefficient | Standard Deviation | t-Statistic | Probability |
| VA_CORR_CONSTRUCTON_$_C | 239.3467 | 12.32558 | 19.41869 | 0.0000 |
| C | 4.92E+08 | 22620153 | 21.73492 | 0.0000 |
| R-squared | 0.901934 | Mean of the dependent variable | 8.56E+08 | |
| Adjusted R-squared | 0.899542 | Standard Deviation of dependent variable | 2.61E+08 | |
| Standard Deviation of the equation | 82707443 | Akaike info criterion | 39.34491 | |
| Sum of the squared residuals | 2.80E+17 | Schwarz criterion | 39.42683 | |
| Log probability | -843.9156 | Hannan-Quinn criterion | 39.37512 | |
| F-statistic | 377.0855 | Durbin-Watson statistic | 0.255062 | |
| Prob(F-statistic) | 0.000000 | |||
Source: series of value added of the construction sector by UNCTADSTAT. Steel use series. United States Geological Survey (USGS)
Figure 13. Residuals of the correlation between steel use and value added of the construction sector on a world scale in the period 1970-2012
Note: As of 1975, but even more so after 1985 and until the beginning of China’s urbanization process, the residuals series declines. Then it rises, though it is interrupted at the time of the 2009 crisis. The rising trend of the value added series of the construction sector and of the series of steel use are very pronounced as of the beginning of the twentieth century, but they tend to decelerate after the 2009 crisis, in line with the arguments regarding the drive of both variables produced by the dynamics of urbanization processes. As was to be expected, residuals series in the last two figures are noticeably similar.
Notes de bas de page
1 Three texts may help interpret the data displayed in this section:
de Arce, R. & Mahía, R (2001). Conceptos básicos sobre la heterocedasticidad en el modelo básico de regresión lineal tratamiento con E-Views.
Gujarati, D. & Porter, D. (2009). Basic Econometrics. Mac Graw Hill Education
Carrascal, U. , Rodríguez, B., & González, Y. (2001). Análisis econométrico con Eviews. Mexico: Alfaomega RA-MA.
Le texte seul est utilisable sous licence Creative Commons - Attribution - Pas d'Utilisation Commerciale - Pas de Modification 4.0 International - CC BY-NC-ND 4.0. Les autres éléments (illustrations, fichiers annexes importés) sont « Tous droits réservés », sauf mention contraire.
Memorias en lucha
Recuerdos y silencios en el contexto de subordinación y alteridad
Ana Ramos, Carolina Crespo et María Alma Tozzini (dir.)
2016
Contribuciones a la Didáctica de la Lengua y la Literatura
La investigación desde el interaccionismo sociodiscursivo
Dora Riestra (dir.)
2016
Lotes sin dueño
Derecho de propiedad y abandono como problema urbano
Jorge Paolinelli, Tomás Guevara, Guillermo Oglietti et al.
2017
Migraciones en la Patagonia
Subjetividades, diversidad y territorialización
Ana Inés Barelli et Patricia Dreidemie (dir.)
2015
Araucanía-Norpatagonia
Discursos y representaciones de la materialidad
María Andrea Nicoletti, Paula Núñez et Andrés Núñez (dir.)
2016
Impuesto a los bienes urbanos ociosos
Una herramienta tributaria contra la especulación inmobiliaria y al servicio de la planificación
Jorge Paolinelli, Tomás Guevara et Guillermo Oglietti
2014
Cómo lograr el Estado de bienestar en el siglo XXI
Pensamiento económico, desarrollo sustentable y economía mundial (1950-2014)
Roberto Kozulj
2017
Memorias en lucha
Recuerdos y silencios en el contexto de subordinación y alteridad
Ana Ramos, Carolina Crespo et María Alma Tozzini (dir.)
2016
Contribuciones a la Didáctica de la Lengua y la Literatura
La investigación desde el interaccionismo sociodiscursivo
Dora Riestra (dir.)
2016
Lotes sin dueño
Derecho de propiedad y abandono como problema urbano
Jorge Paolinelli, Tomás Guevara, Guillermo Oglietti et al.
2017
Migraciones en la Patagonia
Subjetividades, diversidad y territorialización
Ana Inés Barelli et Patricia Dreidemie (dir.)
2015
Araucanía-Norpatagonia
Discursos y representaciones de la materialidad
María Andrea Nicoletti, Paula Núñez et Andrés Núñez (dir.)
2016
Impuesto a los bienes urbanos ociosos
Una herramienta tributaria contra la especulación inmobiliaria y al servicio de la planificación
Jorge Paolinelli, Tomás Guevara et Guillermo Oglietti
2014
Cómo lograr el Estado de bienestar en el siglo XXI
Pensamiento económico, desarrollo sustentable y economía mundial (1950-2014)
Roberto Kozulj
2017
