Abstract
We develop a novel model of fertility choice predicting an increase and subsequent decrease in fertility levels without introducing a quality–quantity tradeoff, mortality changes, or urbanization. The model highlights the roles of a subsistence constraint and non-wage income deriving from the ownership of land. We show that the sign of the effect of the wage rate on fertility depends on whether non-wage income is greater or less than a minimum consumption level. Suggestive evidence supporting the model, on changes in fertility from 1851 to 1891 across French départements, is provided. Finally, we embed our static model in a model of endogenous growth, and provide a numerical illustration of the working of the model.
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Notes
Some of the more important contributions building on Becker (1960) are: Becker and Lewis (1973), Razin and Ben-Zion (1975), Becker and Barro (1988), Barro and Becker (1989), Becker et al. (1990), Ehrlich and Lui (1991), Galor and Weil (2000), Galor and Moav (2002), and Moav (2005). For excellent surveys of the theory and the evidence on the demographic transition, see Guinnane (2011) and Galor (2012).
For an interesting growth model (not specifically related to the fertility transition) introducing a minimum consumption requirement, see Chatterjee and Ravikumar (1999).
An important recent exception is Galor et al. (2009), which analyzes the effect of land inequality on public education and thus on growth.
Tamura (1994) analyzes an endogenous growth model in which, for low human capital countries, the effect of income is different from the effect of the wage, where the latter is the return to skilled human capital.
See Tamura (2006) for a complementary general equilibrium model featuring endogenous timing of demographic transitions.
Note that non-wage income resulting from land ownership is relevant only when the farmer either cultivates his own land or when he rents his land out, but not when he is a sharecropper. Where the farmer cultivates his own land, his “non-wage” income is the imputed return to the land which he owns, since he has the option of renting out his land and working at the market wage rate.
We are indebted to Oded Galor for pointing this out.
This, of course, is a simplifying assumption. The results would be qualitatively the same as long as children are a relatively time-intensive commodity.
It should be noted that altruistic parents (not a feature of our model) will tend to prefer partible inheritance to the extent that land is sufficiently productive to make \(v>c_{\min }\) , thus ensuring an adequate (non-wage) income to their heirs. This suggests that partible inheritance may be endogenous to the value of land. In our empirical work (Sect. 5) we account for this possibility in the regression displayed in Table 2, by using a dummy variable for partible inheritance related to inheritance customs a century earlier than the time period analyzed by the regression.
Thus our model may provide an alternative explanation of the fact, noted by Galor et al. (2009), that countries where land ownership initially was relatively equally divided have experienced relatively rapid growth. Galor et al. point to the differing growth paths of the US and Canada, where land ownership was relatively equally distributed, and Latin America, where land ownership was highly concentrated. See also Deininger and Squire (1998) who document a negative cross-sectional correlation between initial land inequality and long-term growth.
See Acemoglu (2003) for micro-foundations supporting the proposition that technological change will be labor augmenting in long-run growth. See also O’Rourke et al. (1996) and O’Rourke and Williamson (2005) for evidence that this was the case in nineteenth century Europe. O’Rourke et al. (1996, Table 4, Panel D) estimate that 52.2 % of the rise in the wage-rental ratio in France from 1875 to 1914 was due to land-saving technological change.
If we were to make the simpler assumption that the elasticity of substitution is unity, the production function would be Cobb-Douglas, and the only way to model labor-augmenting technological change would be to increase the production elasticity of labor and simultaneously to decrease the production elasticity of land (to keep their sum constant at unity). This would impose a limit on technological change (production elasticity of labor = 1), which is clearly unattractive and unrealistic.
The condition that the w rises relative to v is intended to minimize the confounding, positive income effect of increasing v, on fertility.
Weir (1983) ran a regression of primarily pre-Revolutionary changes in fertility on (among other variables) 1866 inheritance custom data for a sample of 40 French villages. Due to the small sample size and the time gap between the 1866 inheritance data and pre-Revolutionary fertility changes, it is somewhat difficult to draw conclusions from this part of his important study.
The data on the relative change in real wages are from Sicsic (1991, Chapter 1). We used Sicsic’s nominal agricultural wage data for 1852, and deflated his nominal wage data for 1892 by his index of ratio of 1893 non-rental (essentially food) agricultural prices to 1852 non-rental agricutural prices, weighted by the share of non-rental prices in the overall basket. For the rental part of the basket, we relied on his claim that rural housing rental prices did not change over the period. Thus the price deflator for 1892 is
$$\begin{aligned} s\left( \frac{\pi _{non-rental,1893}}{\pi _{non-rental,1852}}\right) +(1-s). \end{aligned}$$where s is the share of non-rental goods in the overall basket and \(\pi _{t}\) denotes the price level.
The data on fertility and mortality are from Bonneuil (1997). The fertility rates are overall fertility rates (the Coale \(I_{f}\) index).
For simplicity and because of data limitations, we treat mortality as exogenous, despite the fact that, in reality, mortality is partly endogenous (parents can choose the level of care they take to prevent their infants from dying).
Sicsic’s (1991) estimates of the cost of a basket of food items and of urban rents indicate that real rents increased from 1852 to 1890.
The interaction term with work-own i is insignificant in both regressions, presumably reflecting small landholdings for agricultural workers (though we have no direct evidence on this point).
The index assigns a value of 1 for the following (modern) French regions: Basse-Normandie, Bretagne, Champagne-Ardenne, Haute-Normandie, Ile-de-France, Pays del la Loire, and Poitou-Charentes. It assigns a value of 0.5 to the following two regions: Centre and Nord-Pas-de-Calais, which appear to have been “mixed” with respect to the prevalence of partible inheritance. The index for the remaining regions takes a value of zero.
Differentiating (11) with respect to \(a_{t}\equiv A_{t}/N_{t},\)
$$\begin{aligned} \frac{\partial v_{t}}{\partial a_{t}}=\left( \ell _{t}^{\rho }+a_{t}^{\rho }\right) ^{\frac{1}{\rho }}a_{t}^{\rho -1}\left[ \frac{\rho \ell _{t}^{\rho }+a_{t}^{\rho }}{\left( \ell _{t}^{\rho }+a_{t}^{\rho }\right) ^{2}}\right] . \end{aligned}$$Since \(\rho\) is assumed to be −1, the numerator in the square brackets is
$$\begin{aligned} \frac{1}{a_{t}}-\frac{1}{\ell _{t}}=\frac{\ell _{t}-a_{t}}{a_{t}\ell _{t}}. \end{aligned}$$Thus the sign of \(\partial v_{t}/\partial a_{t}\) is the same as the sign of \(\ell _{t}-a_{t}.\)
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We thank Raphael Franck, Jonathan Liebowitz, Tommy E. Murphy, and Pierre Sicsic for generously providing the data used in this study. We are also indebted to James Ang, Oded Galor, George Grantham, Eric Jones, Deirdre McCloskey, Jakob Madsen, David Mitch, Omer Moav, Sam Peltzman, David Weil, the Editor-in-Chief, and two anonymous referees, as well as participants in seminars at Bar-Ilan University, Monash University, and the University of Hong Kong, for helpful comments and discussions.
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Guttman, J.M., Tillman, A. Land ownership, the subsistence constraint, and the demographic transition. Rev Econ Household 15, 1017–1036 (2017). https://doi.org/10.1007/s11150-015-9286-9
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DOI: https://doi.org/10.1007/s11150-015-9286-9