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Population growth and economic growth: A reconsideration
economic= letters Economics Letters 52 (1996) 319-324
ELSEVIER
Population growth and economic growth: A reconsideration Chong K. Yipa'*, Junxi Zhangb "Department of Economics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong "University of Dundee, Dundee, UK Received 27 November 1995; final revision received 20 May 1996; accepted 25 June 1996
Abstract
In an endogenous growth model with endogenous fertility, a neo-Maithusian relation emerges only when all exogenous variables are controlled for. This suggests that conflicting findings in the literature may originate from heterogeneity in unobserved variables in cross-country panel data sets.
Keywords: Population growth; Economic growth; Neo-Malthusian relation JEL classification: J13; O41
1. Introduction The relationship between population growth and economic growth has been a controversial topic in the literature of economic development. Early work by Coale and Hoover (1958), and recently by Blanchet (1991), suggested that high fertility suppresses per capita income growth, which has been the dominant view in the existing literature. Recent work by Kelley (1988) and Srinivasan (1988), however, expressed ambivalence about this neo-Malthusian relation between population growth and economic growth. Simon (1989) argued further that "[t]he empirical studies of the relationship between the rate of economic development and population growth may reasonably be interpreted.., as consistently strong evidence of the absence of a negative causal effect of the latter upon the former." This paper provides a reconciliation between the above conflicting opinions. We emphasize the fact that the rates of both population growth and income growth are endogenous variables within a general equilibrium framework. Borrowing from the recent endogenous growth literature (e.g. Romer, 1986, and Lucas, 1988), we develop an endogenous growth model with * Corresponding author. Tel.: (852) 26097057; fax: (852) 26035805; e-mail: [email protected]. 0165-1765/96/$12.00 © 1996 Elsevier Science S.A. All rights reserved PII S0165-1765(96)00876-2
320
C.K. Yip, J. Zhang / Economics Letters 52 (1996) 319-324
endogenous fertility. It is found that when all exogenous variables are controlled for, there exists an inverse relation between population growth and economic growth. However, when some exogenous factors change, such as an improvement in technological progress, this relation becomes ambiguous. This suggests that the conflicting findings in the literature may be because of the presence of substantial heterogeneity in unobserved variables across countries and over time in cross-country panel data sets.
2. The model
Our model economy consists of a continuum of identical infinitely-lived households who are endowed with one unit of productive time in each period t > 0J The unit time endowment is allocated to two activities- production (l) and child-rearing (O(n)), i.e. I + ~ ( n ) = 1, where n is the fertility or population growth rate. 2 We assume the child-rearing cost function ~ ( n ) ~ C 2 and is strictly increasing in n. However, its second-order derivative, 0", can be of either sign, implying that the marginal time cost of taking care of children can be either increasing, constant, or decreasing (see Palivos, 1995). The household's preferences are represented by an additively time-separable utility function: e -pt log(c)+
U=
1 - e- 1 dt,
(1)
0
where p > 0 is the constant rate of time preference and e > 0 gives the elasticity of the marginal utility of fertility. Notice that we adopt the logarithmic utility function since it is the only formulation of preferences that is consistent with stationary labor supply in a growing economy (see Benhabib and Farmer, 1994). Thus, the optimization problem for the representative household is to choose (c, n, k) such that utility in (1) is maximized subject to the resource constraint and the initial condition: I~ ffi A k " ( 1
-
d~(n))~-~K
k(O)--ko>O,
~-~ -
nk - c ,
(2) (3)
where A is a scale parameter and a E (0, 1). The externality in capital accumulation, £, which equals k in equilibrium, is used to generate perpetual growth as in Romer (1986). Let A be the co-state variable, then the first-order necessary conditions of the maximization problem are C-l-A,
(4)
it is a common practice to adopt infinite-horizon models to analyze fertility dynamics; for example, see Palivos and Yip (1993) and Razin and Yuen (1955). If we insist on the reality demonstrated in finite-horizon models, then the infinite-horizon model used here can be regarded as an aggregate version of the overlappit~g-generations models with stochastic death of Cass and Yaari (1967) and Blanchard (1985). Superfluous time subscripts are dropped hereafter for simplicity.
C.K. Yip, J. Zhang / Economicr Letters 52 (1996) 319-324
321
n -~ = A[(1 - a ) A k ' - ~ k ~ ( 1 - 4~)-~4~ ' + k ] ,
(5)
,,( = pA - A[aA/~'-"k~'-'(1 - ~ ) ' - ~ - n],
(6)
as well as the law of motion for k, (2) and the standard transversality condition: (7)
lim e-P'Ak = O . t.---~ 00
With the population growth rate, n, as a control variable, non-linearities and non-convexities are introduced into the budget constraint. Thus, the sufficiency of the above first-order conditions is not guaranteed. To assure it, some restrictions have to be imposed on the child-rearing cost function, which are provided in the following proposition. Proposition 1. I f [t~(4~')2/(1 - 4 ~ ) + q~"] ~>0 (Condition S), then the above necessary conditions are also sufficient. Proof. A direct application of the Mangasarian sufficiency theorem yields the results.
El
If there is a constant or increasing marginal cost in child-rearing (i.e. ~"(n)~>0), then condition S is automatically fulfilled. However, if there are economies of scale in childrearing, then condition S imposes an upper limit on the increasing returns.
3.
Equilibrium
analysis
We first define the balanced-growth-path equilibrium concept as follows. Definition. A balanced-growth-path (BGP) equilibrium is a collection of functions of time {c, k} such that they grow at constant (maybe different) rates, and n is constant.
Next, differentiating (4) with respect to time yields c
(8)
A"
Combining (6) and (8), we obtain
cc"- -
aA(1
- 4,(n))'-"
Then, defining x - c / k
(9)
-p-n.
and making use of (4) and (5), we can write x as a function of n:
x = nell + A ( 1 - a ) ( 1 - 4 ~ ( n ) ) - " 4 ~ ' ( n ) ] •
(lO)
Rewriting (10) as n = ~(x) together with (2) and (9) give us the law of motion for x: - = x - A(1 x
- a)[1
- 4,(g"(x))]'-"
-p=h(x).
(11,)
C.K. Yip, J. Zhang / Economics Letters 52 (i996) 319-324
322
Notice that (11) is a one-dimensional differential equation that completely characterizes the global dynamics of the model. To close this section, we analyze the BGP equilibrium and its associated transitional dynamics, and summarize our result in the following proposition.
Proposition 2. Under Condition S, there exists a unique but unstable BGP equilibrium. Proof. Under Condition S, straightforward differentiation of (10) implies that q t , > 0. Taking the derivative of h(x), we have h'(x) = 1 + A ( I - a)2(1 - $ ) - " $ ' ~ ' > 0. This implies that the BGP equilibrium is unique and determinate.
(12) D
4. Fertility and growth Along a balanced growth path, it can be shc;vn that c and k both grow at the same constant rate, 3'* (hereafter an asterisk denotes the BGP equilibrium value of a variable). Then (9) implies that 3'* - aA(1 - ~b(n*)) ~-'~ - p - n * .
(13)
From the resource constraint (2), we obtain 3,* ffi A(1 - ~(n*)) ~°" - n* - qt-~(n*).
(14)
We are now ready to examine the relation between population growth and economic growth, which is documented as follows.
Proposition 3. There exists an inverse relation between population growth and economic growth when all exogenous factors are controlled for. Proof. Straightforward differentiation of (13) yields dT* tin* - - [ 1
+ a A ( 1 - a ) ( 1 - ~)-*~b'] < 0 ,
and the results follow.3 D N~tice that (13) and (14) yield a 2 x 2 system for 3'* and n*. For instance, consider a ~To further elaborate Proposition 3, we use (13) and (14) together and consider a change in the parameter e that affects only (14) via the inverse function of qt. It is straightforward to derive that dn*/de>0 and dT*/de<0. There is a negative relationship between the fertility rate and the economic growth rate in the steady state. We thank the referee for pointing this out to us.
C.K. Yip, J. Zhang I Economics Letters 52 (1996) 319-324
323
technological improvement where A rises. Then we have the following comparative statics from (13) and (14):
dn*
( 1 - a)(1- tk)'-"
dA - A(1
- o02(1 - ~)-a~,
+
1/W' > 0 ,
° dA -
A(1 - a)2(1 - ¢ ) - ~ '
(15)
1)] + I/W'
--~
.
(16)
Since d~/*/dA is ambiguous in sign, the relation between n* and 3'* is generally indeterminate. Thus, given other exogenous variables that are not controlled for, the neo-Malthusian (inverse) relation between fertility and growth may not emerge. To gain further insights into dy*/dA, we consider a simple linear child-rearing cost function, which implies that 0 ' > 0 and 0 "= 0. Such a specification can be found in a number of theoretical models with endogenous fertility (see, for example, Eckstein and Wolpin, 1985). For simplicity, we also set e = 1. Under these simplifications, it is then straightforward to show from (10) that llW'>x*ln*, where variables are evaluated at the BGP equilibrium.4 To perform the calibration, we use the US data. First, notice that x * = (c/k)*= (c/y)*/(k/y)*. The US (cly)* is about 0.73 (see, for example, Christiano, 1988, and Lucas, 1990), and (k/y)* is in the range of 2.4 (Lucas, 1990) to 10.59 (Christiano, 1988), depending on the exact measures of capital stock. These numbers imply that (c/k)* or x* is in the range of 0.07 to 0.3. Secondly, the US population growth rate, n*, which is the same as the fertility rate here, is about 0.013 (Lucas, 1988). Finally, we take the minimum value of x* = 0.07, since any larger number would only reinforce our result. We obtain that 1/q t' must be at least as large as 5.38. For a =0.25, this suggests that [ 1 - a(1 + 1/gt')] < 0 , and so d3'*/dA > 0 according to (16). Thus, fertility and growth can be positively correlated. This further supports our conclusion that the inverse relation between population growth and economic growth is obtained only when all exogenous factors are'controlled for.
References Benhabib, J. and R.E. Farmer, 1994, Indeterminacy and increasing returns, Journal of Economic Theory 63, 19-41. Blanchard, O.J., 1985, Debt, deficits, and finite horizons, Journal of Political Economy 93, 223-247. Blanchet, D., 1991, Estimating the relationship between population growth and aggregate economic growth in developing countries: Methodological problems, Discussion paper, Institut National d'Etudes D~mographiques, Paris. Cass, D. and M.E. Yaari, 1967, Individual savings, aggregate capital accumulation, and efficient growth, in: K. Shell, ed., Essays on the theory of optimal economic growth (MIT Press, Cambridge, MA). aFrom (10), we have dx*/dn*= l/q t' =[1 + A ( 1 - a ) ( 1 - 0 ) - ~ $ ' ] + A a ( 1 - a ) ( 1 - 0 ) - ~ - t ( $ ' ) 2 > 1 + A ( I or)(1- $ ) - ~ ' = x* In*, since the term, A a ( 1 - a ) ( l - ~)-~-t($,)2, is always positive. This, in turn, implies that the :onsumption-capital ratio, x, is elastic with respect to fertility, n, in this model.
324
C.K. Yip, J. Zhang / Economics Letters 52 (1996) 319-324
Christiano, L.J., 1988, Why does inventory investment fluctuate so much? Journal of Monetary Economics 21, 247-280. Coale, A. and E. Hoover, 1958, Population growth and economic development in low income countries: A case study of India's prospects (Princeton University Press, Princeton). Eckstein, Z. and K. Wolpin, 1985, Endogenous fertility and optimal population growth, Journal of Public Economics 27, 93-106. Kelley, A.C., 1988, Economic consequences of population change in the third world, Journal of Economic Literature 26, 1685-1728. Lucas, R.E., Jr., 1988, On the mechanics of economic development, Journal of Monetary Economics 22, 3-42. Lucas, R.E., Jr., 1990, Supply-side economics: An analytical review, Oxford Economic Papers 42, 293-316. Palivos, T., 1995, Endogenous fertility, multiple growth paths, and economic convergence, Journal ,~f Economic Dynamics and Control 19, 1489-1510. Palivos, T. and C.K. Yip, 1993, Optimal population size and endogenous growth, Economics Letters 41,107-110. Razin, A. and C. Yuen, 1995, Utilitarian tradeoff between population growth and income growth, Journal of Population Economics 8, 81-87. Romer, P.M., 1986, Increasing returns and long run growth, Journal of Political Economy 94, 1002-1038. Simon, J., 1989, On aggregate empirical studies relating population variable to economic development, Population Development Review 15, 323-332. Srinivasan, T.N., 1988, Population growth and economic development, Journal of Policy Modelling 10, 7-28.
ELSEVIER
Population growth and economic growth: A reconsideration Chong K. Yipa'*, Junxi Zhangb "Department of Economics, The Chinese University of Hong Kong, Shatin, N.T., Hong Kong "University of Dundee, Dundee, UK Received 27 November 1995; final revision received 20 May 1996; accepted 25 June 1996
Abstract
In an endogenous growth model with endogenous fertility, a neo-Maithusian relation emerges only when all exogenous variables are controlled for. This suggests that conflicting findings in the literature may originate from heterogeneity in unobserved variables in cross-country panel data sets.
Keywords: Population growth; Economic growth; Neo-Malthusian relation JEL classification: J13; O41
1. Introduction The relationship between population growth and economic growth has been a controversial topic in the literature of economic development. Early work by Coale and Hoover (1958), and recently by Blanchet (1991), suggested that high fertility suppresses per capita income growth, which has been the dominant view in the existing literature. Recent work by Kelley (1988) and Srinivasan (1988), however, expressed ambivalence about this neo-Malthusian relation between population growth and economic growth. Simon (1989) argued further that "[t]he empirical studies of the relationship between the rate of economic development and population growth may reasonably be interpreted.., as consistently strong evidence of the absence of a negative causal effect of the latter upon the former." This paper provides a reconciliation between the above conflicting opinions. We emphasize the fact that the rates of both population growth and income growth are endogenous variables within a general equilibrium framework. Borrowing from the recent endogenous growth literature (e.g. Romer, 1986, and Lucas, 1988), we develop an endogenous growth model with * Corresponding author. Tel.: (852) 26097057; fax: (852) 26035805; e-mail: [email protected]. 0165-1765/96/$12.00 © 1996 Elsevier Science S.A. All rights reserved PII S0165-1765(96)00876-2
320
C.K. Yip, J. Zhang / Economics Letters 52 (1996) 319-324
endogenous fertility. It is found that when all exogenous variables are controlled for, there exists an inverse relation between population growth and economic growth. However, when some exogenous factors change, such as an improvement in technological progress, this relation becomes ambiguous. This suggests that the conflicting findings in the literature may be because of the presence of substantial heterogeneity in unobserved variables across countries and over time in cross-country panel data sets.
2. The model
Our model economy consists of a continuum of identical infinitely-lived households who are endowed with one unit of productive time in each period t > 0J The unit time endowment is allocated to two activities- production (l) and child-rearing (O(n)), i.e. I + ~ ( n ) = 1, where n is the fertility or population growth rate. 2 We assume the child-rearing cost function ~ ( n ) ~ C 2 and is strictly increasing in n. However, its second-order derivative, 0", can be of either sign, implying that the marginal time cost of taking care of children can be either increasing, constant, or decreasing (see Palivos, 1995). The household's preferences are represented by an additively time-separable utility function: e -pt log(c)+
U=
1 - e- 1 dt,
(1)
0
where p > 0 is the constant rate of time preference and e > 0 gives the elasticity of the marginal utility of fertility. Notice that we adopt the logarithmic utility function since it is the only formulation of preferences that is consistent with stationary labor supply in a growing economy (see Benhabib and Farmer, 1994). Thus, the optimization problem for the representative household is to choose (c, n, k) such that utility in (1) is maximized subject to the resource constraint and the initial condition: I~ ffi A k " ( 1
-
d~(n))~-~K
k(O)--ko>O,
~-~ -
nk - c ,
(2) (3)
where A is a scale parameter and a E (0, 1). The externality in capital accumulation, £, which equals k in equilibrium, is used to generate perpetual growth as in Romer (1986). Let A be the co-state variable, then the first-order necessary conditions of the maximization problem are C-l-A,
(4)
it is a common practice to adopt infinite-horizon models to analyze fertility dynamics; for example, see Palivos and Yip (1993) and Razin and Yuen (1955). If we insist on the reality demonstrated in finite-horizon models, then the infinite-horizon model used here can be regarded as an aggregate version of the overlappit~g-generations models with stochastic death of Cass and Yaari (1967) and Blanchard (1985). Superfluous time subscripts are dropped hereafter for simplicity.
C.K. Yip, J. Zhang / Economicr Letters 52 (1996) 319-324
321
n -~ = A[(1 - a ) A k ' - ~ k ~ ( 1 - 4~)-~4~ ' + k ] ,
(5)
,,( = pA - A[aA/~'-"k~'-'(1 - ~ ) ' - ~ - n],
(6)
as well as the law of motion for k, (2) and the standard transversality condition: (7)
lim e-P'Ak = O . t.---~ 00
With the population growth rate, n, as a control variable, non-linearities and non-convexities are introduced into the budget constraint. Thus, the sufficiency of the above first-order conditions is not guaranteed. To assure it, some restrictions have to be imposed on the child-rearing cost function, which are provided in the following proposition. Proposition 1. I f [t~(4~')2/(1 - 4 ~ ) + q~"] ~>0 (Condition S), then the above necessary conditions are also sufficient. Proof. A direct application of the Mangasarian sufficiency theorem yields the results.
El
If there is a constant or increasing marginal cost in child-rearing (i.e. ~"(n)~>0), then condition S is automatically fulfilled. However, if there are economies of scale in childrearing, then condition S imposes an upper limit on the increasing returns.
3.
Equilibrium
analysis
We first define the balanced-growth-path equilibrium concept as follows. Definition. A balanced-growth-path (BGP) equilibrium is a collection of functions of time {c, k} such that they grow at constant (maybe different) rates, and n is constant.
Next, differentiating (4) with respect to time yields c
(8)
A"
Combining (6) and (8), we obtain
cc"- -
aA(1
- 4,(n))'-"
Then, defining x - c / k
(9)
-p-n.
and making use of (4) and (5), we can write x as a function of n:
x = nell + A ( 1 - a ) ( 1 - 4 ~ ( n ) ) - " 4 ~ ' ( n ) ] •
(lO)
Rewriting (10) as n = ~(x) together with (2) and (9) give us the law of motion for x: - = x - A(1 x
- a)[1
- 4,(g"(x))]'-"
-p=h(x).
(11,)
C.K. Yip, J. Zhang / Economics Letters 52 (i996) 319-324
322
Notice that (11) is a one-dimensional differential equation that completely characterizes the global dynamics of the model. To close this section, we analyze the BGP equilibrium and its associated transitional dynamics, and summarize our result in the following proposition.
Proposition 2. Under Condition S, there exists a unique but unstable BGP equilibrium. Proof. Under Condition S, straightforward differentiation of (10) implies that q t , > 0. Taking the derivative of h(x), we have h'(x) = 1 + A ( I - a)2(1 - $ ) - " $ ' ~ ' > 0. This implies that the BGP equilibrium is unique and determinate.
(12) D
4. Fertility and growth Along a balanced growth path, it can be shc;vn that c and k both grow at the same constant rate, 3'* (hereafter an asterisk denotes the BGP equilibrium value of a variable). Then (9) implies that 3'* - aA(1 - ~b(n*)) ~-'~ - p - n * .
(13)
From the resource constraint (2), we obtain 3,* ffi A(1 - ~(n*)) ~°" - n* - qt-~(n*).
(14)
We are now ready to examine the relation between population growth and economic growth, which is documented as follows.
Proposition 3. There exists an inverse relation between population growth and economic growth when all exogenous factors are controlled for. Proof. Straightforward differentiation of (13) yields dT* tin* - - [ 1
+ a A ( 1 - a ) ( 1 - ~)-*~b'] < 0 ,
and the results follow.3 D N~tice that (13) and (14) yield a 2 x 2 system for 3'* and n*. For instance, consider a ~To further elaborate Proposition 3, we use (13) and (14) together and consider a change in the parameter e that affects only (14) via the inverse function of qt. It is straightforward to derive that dn*/de>0 and dT*/de<0. There is a negative relationship between the fertility rate and the economic growth rate in the steady state. We thank the referee for pointing this out to us.
C.K. Yip, J. Zhang I Economics Letters 52 (1996) 319-324
323
technological improvement where A rises. Then we have the following comparative statics from (13) and (14):
dn*
( 1 - a)(1- tk)'-"
dA - A(1
- o02(1 - ~)-a~,
+
1/W' > 0 ,
° dA -
A(1 - a)2(1 - ¢ ) - ~ '
(15)
1)] + I/W'
--~
.
(16)
Since d~/*/dA is ambiguous in sign, the relation between n* and 3'* is generally indeterminate. Thus, given other exogenous variables that are not controlled for, the neo-Malthusian (inverse) relation between fertility and growth may not emerge. To gain further insights into dy*/dA, we consider a simple linear child-rearing cost function, which implies that 0 ' > 0 and 0 "= 0. Such a specification can be found in a number of theoretical models with endogenous fertility (see, for example, Eckstein and Wolpin, 1985). For simplicity, we also set e = 1. Under these simplifications, it is then straightforward to show from (10) that llW'>x*ln*, where variables are evaluated at the BGP equilibrium.4 To perform the calibration, we use the US data. First, notice that x * = (c/k)*= (c/y)*/(k/y)*. The US (cly)* is about 0.73 (see, for example, Christiano, 1988, and Lucas, 1990), and (k/y)* is in the range of 2.4 (Lucas, 1990) to 10.59 (Christiano, 1988), depending on the exact measures of capital stock. These numbers imply that (c/k)* or x* is in the range of 0.07 to 0.3. Secondly, the US population growth rate, n*, which is the same as the fertility rate here, is about 0.013 (Lucas, 1988). Finally, we take the minimum value of x* = 0.07, since any larger number would only reinforce our result. We obtain that 1/q t' must be at least as large as 5.38. For a =0.25, this suggests that [ 1 - a(1 + 1/gt')] < 0 , and so d3'*/dA > 0 according to (16). Thus, fertility and growth can be positively correlated. This further supports our conclusion that the inverse relation between population growth and economic growth is obtained only when all exogenous factors are'controlled for.
References Benhabib, J. and R.E. Farmer, 1994, Indeterminacy and increasing returns, Journal of Economic Theory 63, 19-41. Blanchard, O.J., 1985, Debt, deficits, and finite horizons, Journal of Political Economy 93, 223-247. Blanchet, D., 1991, Estimating the relationship between population growth and aggregate economic growth in developing countries: Methodological problems, Discussion paper, Institut National d'Etudes D~mographiques, Paris. Cass, D. and M.E. Yaari, 1967, Individual savings, aggregate capital accumulation, and efficient growth, in: K. Shell, ed., Essays on the theory of optimal economic growth (MIT Press, Cambridge, MA). aFrom (10), we have dx*/dn*= l/q t' =[1 + A ( 1 - a ) ( 1 - 0 ) - ~ $ ' ] + A a ( 1 - a ) ( 1 - 0 ) - ~ - t ( $ ' ) 2 > 1 + A ( I or)(1- $ ) - ~ ' = x* In*, since the term, A a ( 1 - a ) ( l - ~)-~-t($,)2, is always positive. This, in turn, implies that the :onsumption-capital ratio, x, is elastic with respect to fertility, n, in this model.
324
C.K. Yip, J. Zhang / Economics Letters 52 (1996) 319-324
Christiano, L.J., 1988, Why does inventory investment fluctuate so much? Journal of Monetary Economics 21, 247-280. Coale, A. and E. Hoover, 1958, Population growth and economic development in low income countries: A case study of India's prospects (Princeton University Press, Princeton). Eckstein, Z. and K. Wolpin, 1985, Endogenous fertility and optimal population growth, Journal of Public Economics 27, 93-106. Kelley, A.C., 1988, Economic consequences of population change in the third world, Journal of Economic Literature 26, 1685-1728. Lucas, R.E., Jr., 1988, On the mechanics of economic development, Journal of Monetary Economics 22, 3-42. Lucas, R.E., Jr., 1990, Supply-side economics: An analytical review, Oxford Economic Papers 42, 293-316. Palivos, T., 1995, Endogenous fertility, multiple growth paths, and economic convergence, Journal ,~f Economic Dynamics and Control 19, 1489-1510. Palivos, T. and C.K. Yip, 1993, Optimal population size and endogenous growth, Economics Letters 41,107-110. Razin, A. and C. Yuen, 1995, Utilitarian tradeoff between population growth and income growth, Journal of Population Economics 8, 81-87. Romer, P.M., 1986, Increasing returns and long run growth, Journal of Political Economy 94, 1002-1038. Simon, J., 1989, On aggregate empirical studies relating population variable to economic development, Population Development Review 15, 323-332. Srinivasan, T.N., 1988, Population growth and economic development, Journal of Policy Modelling 10, 7-28.