# Population Growth and Economic Growth: Long-Run Evidence from Latin America.

Unit root tests, the Johansen maximal likelihood methodology, and Granger causality tests in the context of a one-step error correction model are used to examine the long-run relation between population and per capita GDP in seven Latin American countries over most of the 20th century. The results suggest that no long-run relation has existed and, hence, population growth neither causes per capita GDP growth nor is caused by it.1. Introduction

Population growth may affect economic performance if it affects the supply and demand for savings and the efficiency of capital (McNicoll 1984; Hammer 1986, 1987; Kelley 1988). The supply of household savings (usually the largest component of domestic savings) may be reduced by a high dependency ratio if, for a given level of output per worker, it causes consumption to rise and per capita savings to fall. The demand for savings may increase as population grows, since faster population growth absorbs investible resources, reducing capital per person. Thus, in countries with a growing labor force, the stock of capital must increase to maintain capital per worker and current productivity, otherwise productivity (and thus incomes) will stagnate or fall. Finally, the efficiency of capital may be hindered by rapid population growth if social and political pressure to employ young people leads to a large government sector, or to regulations designed to stop private-sector employers from reducing their workforce. On the other hand, several factors suggest that there may be no link between population growth and savings and investment. For example, in the early stages of development monetized savings may be produced by relatively few wealthy families with few children, so their savings may not be affected by the burden of their dependents. Also, poor families are unlikely to have financial savings that show up in the national accounts, but may save by accumulating other assets such as land or gold.

Much of the empirical evidence on the relation between population growth and per capita income is from cross-section studies. For example, Easterlin (1967), Kuznets (1967), Simon (1992), and Thirlwall (1972) find a weak or insignificant relation; in contrast, Kelly and Schmidt (1994) find a negative and significant relation, at least for less developed countries. A recent time-series study by Dawson and Triffin (1998) finds no long-run relation between the variables in the case of India. In this note, I test for the existence of a long-run relation in Argentina, Brazil, Chile, Colombia, Mexico, Peru, and Venezuela over the period 1900-1994 using cointegration and causality analyses. The results suggest that there is no long-run relation between the variables in any of the seven countries.

2. Data and Methodology

Historical data for the levels of U.S. dollar real GDP per capita and population are from Maddison (1995). Data for Argentina, Brazil, Chile, and Venezuela are for the period 1900--1994; data for Colombia are 1925-1994; data for Mexico are 1921-1994; and data for Peru are 1913-1994. Natural logarithms of series for Argentina and Chile are illustrated in Figure 1 and are representative of those of the other countries. Population has trended upward at a relatively constant rate, whereas real GDP per capita also has trended upward but more erratically.

The testing procedure is in three steps. In step 1, I determine the order of integration of the series using the augmented Dickey-Fuller (ADF) test. This is done sequentially by first testing for nonstationarity of the levels of the series around a nonzero mean, then repeating the test of the levels of the series including a time trend in addition to the nonzero mean and, finally, testing the first difference of the series for evidence of nonstationarity around a nonzero mean. [1] Sufficient lagged dependent variables are added until the Lagrange multiplier statistic rejects conclusively serial correlation up to fourth order. However, the usefulness of unit root tests is contentious (e.g., Sims 1988) and Holden and Perlman (1994) argue that using the Johansen (1988) maximal likelihood methodology obviates the need for unit root tests since the existence of a cointegrating relation between the two variables implies the presence of unit roots. Accordingly, in step two I test for cointegration of the series usin g the Johansen procedure. Recent studies suggest that results from the Johansen cointegration technique are sensitive to lag specification. Hall (1991), for example, finds that whereas the results of coefficient estimates are not very sensitive to lag specification, the likelihood ratio test statistics used to carry out tests on the parameters of the cointegrating vectors can be sensitive to the choice of the vector autoregression (VAR) lag. In this note, the lag-length in the VAR was determined using the Schwarz Bayesian criterion (SBC). In each case, the VAR contained a constant, a trend term, and current and lagged values of the relevant series.

Finally, in step three I carry out Granger-type causality tests (Granger 1988). Again, given the contentiousness of unit root tests, I do this in the context of a one-step error correction model, which captures the long-run relations explicitly by including the (one period lagged) levels of population and real GDP per capita into the equations (Stock 1987; Kremers, Ericsson, and Dolado 1992). This is formulated as:

[delta][(Y/POP).sub.t] = [[alpha].sub.0] + [[[sigma].sup.n].sub.i-1] [[beta].sub.i][delta][(Y/POP).sub.t-i] + [[[sigma].sup.n].sub.i-1] [[phi].sub.i][delta][POP.sub.t-i] + [delta][(Y/POP).sub.t-1] + [xi][(POP).sub.t-1] + [[epsilon].sub.t] (1)

[delta][POP.sub.t] = [[theta].sub.0] + [[[sigma].sup.n].sub.i-1] [[sigma].sub.i][POP.sub.t-i] + [[[sigma].sup.n].sub.i-1] [[psi].sub.i][delta][(Y/POP).sub.t-i] + [delta][(Y/POP).sub.t-1] + [xi][(POP).sub.t-1] + [[micro].sub.t] (2)

where [delta] is the difference operator, (Y/POP) is gross domestic product per capita, POP is total population, and [epsilon] and [micro] are zero-mean, serially uncorrelated random error terms. In Equation 1 [delta]POP Granger-causes' [delta](Y/POP) if some [[phi].sub.i] is not zero; similarly, in Equation 2, [delta](Y/POP) Granger-causes [delta]POP if some [[psi].sub.i] is not zero. To implement the causality test, F-statistics are calculated under the null hypothesis that all the coefficients of [[phi].sub.i], [[psi].sub.i], [[delta].sub.i], [[xi].sub.i], respectively, equal zero. Since the results from Granger causality tests are also sensitive to the selection of lag length, I also use the SBC to determine lag lengths.

3. Results and Conclusions

Table 1 presents the results of the ADF tests performed for the nulls of one and two unit roots. For each country, a significant trend is present in the ADF equations for both (Y/POP) and POP. It is clear that POP is (trend) stationary, that is, integrated of order zero I(0), whereas (Y/POP) has a unit root, that is, I(1), and is stationary in differences, suggesting that there is not a long-run relation between population and per capita income. Table 2 gives the maximum eigenvalues and trace results from the Johansen procedure. Only in one case (Peru) is there an indication of a cointegrating vector, confirming the results on the unit root tests. Finally, Table 3 gives the Granger causality test results from the one-step procedure. The test results indicate unidirectional causality from population to real GDP per capita in the cases of Colombia and Venezuela; however, the results from the unit root tests and the Johansen procedure suggest that the causality results may be spurious. A long-run relation betwee n population and real per capita GDP does not appear to exist; hence, population growth neither causes growth of per capita GDP nor is caused by it.

(*.) International Monetary Fund, Room 10-118, 700 19th Street N.W., Washington, DC 20431, USA; E-mail jthornton@imf.org.

The views expressed in this paper are those of the author and should not be attributed to the institution with which he is affiliated.

(1.) This procedure for testing Unit roots is suggested by Dickey, Jansen, and Thornton (1991).

References

Dawson, Philip S., and Richard Triffin. 1998. Is there a long-run relationship between population growth and living standards? The case of India. The Journal of Development Studies 34:149-56.

Dickey, David A., Dennis W. Jansen, and Daniel L. Thornton. 1991. A primer on cointegration with an application to the demand for money and income. Federal Reserve Bank of St. Louis Review 73:58-78.

Easterlin, Richard A. 1967. Effects of population growth in the economic development of developing countries. The Annals of the American Academy of Political and Social Science 369:98-108.

Granger, Clive W. J. 1988. Some recent developments in the concept of causality. Journal of Econometrics 39:199-211.

Hall, Stephen G. 1991. The effects of varying lag length VAR models on the maximum likelihood estimate of cointegrating parameters. Scottish Journal of Political Economy 38:317-23.

Hammer, Jeffrey S. 1986. Population growth and savings in LDCs: A survey article. World Development 1:579-91.

Hammer, Jeffrey S. 1987. Demographic transition and aggregate savings in less developed countries. Journal of Economic Development 12:21-37.

Holden, Darryl, and Roger Perlman. 1994. Unit roots and cointegration for the economist. In Cointegration for the applied economist, edited by B. Bhaskassa Rao. New York: St. Martin's Press, pp. 47-112.

Johansen, Soren. 1988. Statistical analysis of cointegration vectors. Journal of Economic Dynamics and Control 12: 1685-728.

Kelley, Allen C. 1988. Economic consequences of population change in the Third World. Journal of Economic Literature 26:1685-728.

Kelley, Allen C., and Robert M. Schmidt. 1994. Population and income change: Recent evidence. World Bank Discussion Paper No. 249.

Kremers, Jan M., Neil R. Ericsson, and Juan J. Dolado. 1992. The power of cointegration tests. Oxford Bulletin of Economic and Statistics 54:325-48.

Kuznets, Simon. 1967. Population and economic growth. American Philosophical Society Proceedings 3:170-93.

Maddison, Angus. 1995. Monitoring the world economy 1820-1992. Paris: OECD Development Centre Studies.

McNicoll, Geoffrey. 1984. Consequences of rapid population growth: An overview. World Bank Staff Working Paper No. 691.

Simon, Julian L. 1992. Population and development in poor countries. Princeton, NJ: Princeton University Press.

Sims, Christopher A. 1988. Bayesian skepticism on unit roots. Journal of Economic Dynamics and Control 12:463-74.

Stock, James H. 1987. Asymptotic properties of least squares estimators of cointegrating vectors. Econometrica 55:1035-56.

Thiriwall, Anthony P. 1972. A cross section study of population growth and the growth of output and per capita income in a production function framework. The Manchester School 40:339-56.

[Graph omitted]

Table 1. Augmented Dickey-Fuller Unit Root Results [a] Without trend First Second Level k Difference k Difference k Argentina Y/POP -0.8647 2 -6.8485 [*] 1 -- -- POP -0.3396 2 -2.3375 1 -5.4056 [*] 1 Brazil Y/POP -0.0493 1 -5.2805 [*] 1 -- -- POP -0.6059 2 -1.0892 1 -7.6877 [*] 1 Chile Y/POP -0.2986 1 -8.0681 [*] 1 -- -- POP -1.2634 2 -1.3742 1 -6.0601 [*] 1 Columbia Y/POP 0.3337 2 -5.8343 [*] 1 -- 1 POP -0.5880 1 -1.7710 1 -6.4240 [*] 1 Mexico Y/POP -1.4034 1 -4.5846 [*] 1 -- -- POP -1.4034 1 -1.8316 1 -11.2770 [*] 1 Peru Y/POP -1.9970 2 -5.3696 [*] 1 -- -- POP 0.1632 1 -2.9735 [*] 1 -6.4709 [*] 1 Venezuela Y/POP -3.0628 2 -4.9314 [*] 1 -- -- POP 0.1632 1 -1.1301 1 -9.2904 [*] 1 With trend First Second Level k Difference k Difference k Argentina Y/POP -2.7761 1 -6.8222 [*] 1 -- 1 POP -2.8969 2 -3.6248 [*] 1 -5.3966 [*] 1 Brazil Y/POP -2.2059 1 -5.2688 [*] 1 -- -- POP -2.6758 2 -0.4670 1 -7.8888 [*] 1 Chile Y/POP -3.6014 1 -8.0490 [*] 1 -- -- POP -3.1476 2 -0.7283 1 -6.2306 [*] 1 Colombia Y/POP -2.2426 1 -5.7953 [*] 1 -- -- POP -2.6821 1 -1.7624 1 -6.4474 [*] 1 Mexico Y/POP -2.8725 1 -4.5728 [*] 1 -- -- POP -2.8735 4 -1.1891 1 -11.2193 [*] 1 Peru Y/POP -0.3566 2 -5.7877 [*] 1 -- 1 POP -3.0317 1 -2.5929 1 -6.7568 [*] 1 Venezuela Y/POP -1.5720 1 -5.1610 [*] 1 -- -- POP -3.0319 1 -0.8712 1 -9.2392 [*] 1 (*)The augmented Dickey-Fuller test is based on the following regression: [delta][x.sub.t] = [[alpha].sub.0] + [[alpha].sub.t]T + [[alpha].sub.2] [x.sub.t-1] + [[[sigma].sup.n].sub.i-1] [[micro].sub.i] [delta][x.sub.t-i] + [[epislon].sub.i], where [delta] is the difference operator, T is a linear time trend (included in the 'with trend' results), and [epislon] is a stationary random error term. (*)denotes significance at the 5% level. Table 2. Johansen Test Results [a] k [[lambda].sub.max] TRACE Argentina 12 14.2359 20.1080 [*] Brazil 12 11.5676 11.6718 Chile 11 8.9404 8.9512 Colombia 4 18.5669 18.5876 Mexico 4 5.7873 5.7900 Peru 5 15.2969 [*] 17.6154 Venezula 6 8.8148 10.8517 (a)k is the number of lags in the VAR determined by Schwarz Bayesian criterion. The critical values at the 5% level are 14.88 for [[lambda].sub.max]] and 17.86 for TRACE. Table 3. Engle-Granger Causality F-Test Results [a] Y/POP Causes POP POP Causes Y/POP Y/POP ECM POP ECM Argentina 7.83 1.38 2.29 2.25 Brazil 0.20 0.66 1.26 3.29 Chile 0.91 7.80 0.75 0.68 Colombia 0.75 0.27 7.52 [**] 6.07 [**] Mexico 1.96 0.67 0.25 2.11 Peru 0.10 1.43 13.35 [**] 8.49 Venezuela 0.00 1.01 2.39 4.34 [*] (a)F-statistics are calculated under the null hypothesis that all the coefficients of the [[phi].sub.i], [[psi].sub.i], and [[delta].sub.i], and [[xi].sub.i], in equations 1 and 2, respectively, equal zero. (**) and (*) indicate significance at the 1 and 5% levels, respectively.

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Author: | Thornton, John |
---|---|

Publication: | Southern Economic Journal |

Article Type: | Statistical Data Included |

Geographic Code: | 0LATI |

Date: | Oct 1, 2001 |

Words: | 2326 |

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