Abstract A general equilibrium model that characterizes the gap between optimal and equilibrium f... more Abstract A general equilibrium model that characterizes the gap between optimal and equilibrium fertility and investment in human capital is developed. The aggregate production function exhibits increasing returns to population arising from specialization, but households face a quantity–quality trade-off when choosing their fertility and how much education these children receive. We show that equilibrium fertility is too low and investment per child is too high, in contrast to a current planner who internalizes the externality of current fertility on the next generation's productivity. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment lowers next generation mortality. This model endogenously generates a demographic transition but, since households do not internalize the negative effects of human capital on mortality, the equilibrium demographic transition takes place many years later than the efficient solution. We show that ${\rm {\cal A}}$-efficient fertility and human capital investment pair can switch; in high-mortality regimes, ${\rm {\cal A}}$-efficient fertility is lower than equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is higher than equilibrium investment. In the zero mortality regime, however, ${\rm {\cal A}}$-efficient fertility exceeds equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is lower than the equilibrium choice.
This paper documents the existence of a negative cross-sectional correlation between the price of... more This paper documents the existence of a negative cross-sectional correlation between the price of living space and fertility using U.S. Census data over the period 1940-2000. This correlation is not spurious, nor does it reflect the tendency of larger families to locate within lessexpensive areas of a given metropolitan area. We examine the extent to which the results reflect the sorting of married couples across metropolitan areas on desired fertility. The relationship between the unit price of living space and fertility in fact tends to be more negative for households that have moved recently. However, the probability of migration between metropolitan areas is smaller for larger families, even those originating in more expensive cities. Moreover, Durbin-Wu-Hausman tests reveal only limited evidence of endogeneity. The weaker effects of the price of living space for less mobile couples seems to be at least in part a result of their choosing to live in less-expensive portions within a given metropolitan area. "Increased splendor, with higher prices for the necessaries of life, keep men from marrying in the cities." Johann Suessmilch, 1760 (in Adna F. Weber, 1899, p. 330). 1. Introduction A good deal of research has examined the emergence of low fertility rates in Europe. Kohler et. al. (2002) investigates the emergence of what they call "lowest-low fertility" in Europe. Among other factors, they noted that the availability of housing was of particular concern, especially in Italy and Spain. Recent research by Giannelli and Monfardini (2003) found that the price of housing had an effect on household membership among Italian youths. The importance of housing in the family economic decisions is not limited to Europe. Recently, Egan (2005) wrote in the New York Times that "Portland is one of the nation's top draws for the kind of educated, self-starting urbanites that midsize cities are competing to attract. But … [o]fficials say that the very things that attract people who revitalize a city-dense vertical housing, fashionable restaurants and shops and mass transit that makes a car unnecessary-are driving out children by making the neighborhoods too expensive for young families." To take another example, San Francisco is legendary for the small fraction of children in its population, due at least in part to its high cost of housing, with a median price of about $700 thousand (Gonazales 2005). This paper examines the relationship between fertility and the price of living space across metropolitan areas. A growing literature, much of it focused on developing countries, has found just such a relationship. Although researchers have used U.S. data to examine the relationship between the price of living space and living arrangements (Hughes 2003; Borsch-Supan 1986; Haurin et. al. 1993), there is, to our knowledge no work on fertility per se. This paper examines the relationship between fertility and the scarcity of living space across U.S. metropolitan areas over the period 1940-2000 using data from the Integrated Public Use Microdata Samples (IPUMS) and the 1985-96 American Housing Surveys (AHS). To
We propose a new macroeconomic mechanism for generating patterns in age-earnings profiles based o... more We propose a new macroeconomic mechanism for generating patterns in age-earnings profiles based on directed technical change. The mechanism does not depend on changes in the human capital of the individual; rather differences in the fraction of total human capital supplied by different age groups affect the profitability of developing age-specific technologies, biasing innovation toward improving the productivity of workers whose cohorts provide large fractions of the labor force's human capital. The theory should be taken as supplemental to (rather than replacing) human-capital-based theories of age-earnings profiles. Using recently developed data and human capital estimates, we simulate reductions in wages due to age-biased directed technical change over workers' lives for most of the world's nations over two centuries. Our simulations indicate that age-specific directed technical change contributes to wage concavity for the average country×cohort group. Because younger workers provide up a larger fraction of human capital in most years and countries, most cohorts in most countries experienced wage gains early in life and losses later in life from age-specific directed technology, making life-cycle earnings profiles flatter. The late-life losses are larger than the early-life gains, increasing concavity in life-cycle earnings profiles. We also calculate the present value of lifetime wage gains from age-specific endogenous technology, and find particularly large and economically-significant gains for baby boomers and losses for cohorts born during low population growth periods.
An endogenous growth model arising from task specialization is used to examine the effects of dif... more An endogenous growth model arising from task specialization is used to examine the effects of differing initial human capital distributions. Two macroeconomic phenomena are produced: income convergence and leapfrogging of living standards. Income convergence occurs for all countries in the same market, arising from diminishing returns to individual human capital. Leapfrogging occurs by comparing countries in two separate markets. Income leapfrogging can occur because the stationary growth rate increases with market size, and human capital heterogeneity reduces growth. The introduction of coordination costs of task assignment can produce gains in welfare and growth from human capital heterogeneity.
This paper examines the role of individual instruction and teacher quality in determining economi... more This paper examines the role of individual instruction and teacher quality in determining economic growth and convergence across school districts. The model shows that if teacher quality is more important for human capital accumulation than individual instruction, human capital convergence will occur between two school districts. This convergence arises because a poor school district hires relatively better teachers but uses them in larger classes in comparison with a rich school district. The model is estimated on panel data of the states of the United States from 1882 to 1990. The estimates indicate that teacher quality is relatively more important for human capital accumulation than individual instruction. The model accounts for all the mean growth in state per capita incomes and between 80 and 100 percent of convergence in state per capita incomes.
Journal of Economic Dynamics and Control, Jun 1, 1996
ABSTRACT Altruistic parents rationally choose fertility and human capital investments in their ch... more ABSTRACT Altruistic parents rationally choose fertility and human capital investments in their children. A rising rate of return to human capital investment and a conditional external effect in human capital investment produce: 1.(1) two development regimes, a Malthusian regime of high fertility and no human capital investment and a perpetual growth regime of low fertility and rising human capital2.(2) conditional human capital convergence within regimes.3.(3) a demographic transition to economic growth4.(4) accelerating growth. As richer countries grow, the conditional external effect continually raises the rate of return on human capital and causes a demographic transition to economic growth by Malthusian countries.
We examine whether dynastic human capital (DHC) can explain the black-white wage gap. We fit a qu... more We examine whether dynastic human capital (DHC) can explain the black-white wage gap. We fit a quantity-quality model to state-level data on fertility, mortality, and schooling but, notably, not earnings. Racial discrimination raised the cost of black schooling, thus depressing DHC not only of the current generation but of future generations via its role in producing human capital. Birth-state DHC helps explain the wage gap among stayers, while current-state DHC helps explain the gap among movers. These findings highlight the role of intergenerational transmission in the persistence of the wage gap and the role of migration in reducing it.
This paper introduces new data on state-level physical capital by sector and land in the farm sec... more This paper introduces new data on state-level physical capital by sector and land in the farm sector for the states of the United States from 1840 to 2000. These data are incorporated into aggregate accounting exercises, with the aim of comparing cross-state results to those found in crosscountry samples. Our aggregate results agree closely with the crosscountry literature: input accumulation accounts for most of output growth, but variation in the level and growth of TFP accounts for most of the variation in the level and growth of output per worker.
An overlapping generations model with parental altruism is examined. The existence of the optimal... more An overlapping generations model with parental altruism is examined. The existence of the optimal value function in a model with an endogenous discount rate is proven. Two development regimes are produced: a high fertility, low income and no growth steady state, and a perpetual growth equilibrium with low fertility and rising income.
Journal of Economic Dynamics and Control, May 1, 1996
The effects of regional differences in population and per capita human capital on income levels a... more The effects of regional differences in population and per capita human capital on income levels and economic growth rates are examined. Sufficient human capital heterogeneity can reduce specialization and inhibit the formation of large markets. The model contains static and dynamic agglomeration economies of market participation. Thus human capital heterogeneity can lower per capita income, and economic growth rates. Over
This paper develops a general equilibrium model of fertility and human capital investment under u... more This paper develops a general equilibrium model of fertility and human capital investment under uncertainty. Uncertainty exists in the form of a probability that a young adult does not survive to old age. Parents maximize expected utility arising from own consumption, their fertility, and the discounted utility of future generations. There exists a precautionary demand for children. Young adult mortality is negatively related to the average human capital of young adults. Therefore, rising human capital leads to falling mortality, which eventually induces a demographic transition and an acceleration in human capital investment. The model can fit data on world and country populations, per capita incomes, age at entry into the labor force, total fertility rates, life expectancy, conditional life expectancy, and infant mortality.
Abstract A general equilibrium model that characterizes the gap between optimal and equilibrium f... more Abstract A general equilibrium model that characterizes the gap between optimal and equilibrium fertility and investment in human capital is developed. The aggregate production function exhibits increasing returns to population arising from specialization, but households face a quantity–quality trade-off when choosing their fertility and how much education these children receive. We show that equilibrium fertility is too low and investment per child is too high, in contrast to a current planner who internalizes the externality of current fertility on the next generation's productivity. We next introduce mortality of young adults in the model and assume that households have a precautionary demand for children. Human capital investment lowers next generation mortality. This model endogenously generates a demographic transition but, since households do not internalize the negative effects of human capital on mortality, the equilibrium demographic transition takes place many years later than the efficient solution. We show that ${\rm {\cal A}}$-efficient fertility and human capital investment pair can switch; in high-mortality regimes, ${\rm {\cal A}}$-efficient fertility is lower than equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is higher than equilibrium investment. In the zero mortality regime, however, ${\rm {\cal A}}$-efficient fertility exceeds equilibrium fertility, and ${\rm {\cal A}}$-efficient human capital investment is lower than the equilibrium choice.
This paper documents the existence of a negative cross-sectional correlation between the price of... more This paper documents the existence of a negative cross-sectional correlation between the price of living space and fertility using U.S. Census data over the period 1940-2000. This correlation is not spurious, nor does it reflect the tendency of larger families to locate within lessexpensive areas of a given metropolitan area. We examine the extent to which the results reflect the sorting of married couples across metropolitan areas on desired fertility. The relationship between the unit price of living space and fertility in fact tends to be more negative for households that have moved recently. However, the probability of migration between metropolitan areas is smaller for larger families, even those originating in more expensive cities. Moreover, Durbin-Wu-Hausman tests reveal only limited evidence of endogeneity. The weaker effects of the price of living space for less mobile couples seems to be at least in part a result of their choosing to live in less-expensive portions within a given metropolitan area. "Increased splendor, with higher prices for the necessaries of life, keep men from marrying in the cities." Johann Suessmilch, 1760 (in Adna F. Weber, 1899, p. 330). 1. Introduction A good deal of research has examined the emergence of low fertility rates in Europe. Kohler et. al. (2002) investigates the emergence of what they call "lowest-low fertility" in Europe. Among other factors, they noted that the availability of housing was of particular concern, especially in Italy and Spain. Recent research by Giannelli and Monfardini (2003) found that the price of housing had an effect on household membership among Italian youths. The importance of housing in the family economic decisions is not limited to Europe. Recently, Egan (2005) wrote in the New York Times that "Portland is one of the nation's top draws for the kind of educated, self-starting urbanites that midsize cities are competing to attract. But … [o]fficials say that the very things that attract people who revitalize a city-dense vertical housing, fashionable restaurants and shops and mass transit that makes a car unnecessary-are driving out children by making the neighborhoods too expensive for young families." To take another example, San Francisco is legendary for the small fraction of children in its population, due at least in part to its high cost of housing, with a median price of about $700 thousand (Gonazales 2005). This paper examines the relationship between fertility and the price of living space across metropolitan areas. A growing literature, much of it focused on developing countries, has found just such a relationship. Although researchers have used U.S. data to examine the relationship between the price of living space and living arrangements (Hughes 2003; Borsch-Supan 1986; Haurin et. al. 1993), there is, to our knowledge no work on fertility per se. This paper examines the relationship between fertility and the scarcity of living space across U.S. metropolitan areas over the period 1940-2000 using data from the Integrated Public Use Microdata Samples (IPUMS) and the 1985-96 American Housing Surveys (AHS). To
We propose a new macroeconomic mechanism for generating patterns in age-earnings profiles based o... more We propose a new macroeconomic mechanism for generating patterns in age-earnings profiles based on directed technical change. The mechanism does not depend on changes in the human capital of the individual; rather differences in the fraction of total human capital supplied by different age groups affect the profitability of developing age-specific technologies, biasing innovation toward improving the productivity of workers whose cohorts provide large fractions of the labor force's human capital. The theory should be taken as supplemental to (rather than replacing) human-capital-based theories of age-earnings profiles. Using recently developed data and human capital estimates, we simulate reductions in wages due to age-biased directed technical change over workers' lives for most of the world's nations over two centuries. Our simulations indicate that age-specific directed technical change contributes to wage concavity for the average country×cohort group. Because younger workers provide up a larger fraction of human capital in most years and countries, most cohorts in most countries experienced wage gains early in life and losses later in life from age-specific directed technology, making life-cycle earnings profiles flatter. The late-life losses are larger than the early-life gains, increasing concavity in life-cycle earnings profiles. We also calculate the present value of lifetime wage gains from age-specific endogenous technology, and find particularly large and economically-significant gains for baby boomers and losses for cohorts born during low population growth periods.
An endogenous growth model arising from task specialization is used to examine the effects of dif... more An endogenous growth model arising from task specialization is used to examine the effects of differing initial human capital distributions. Two macroeconomic phenomena are produced: income convergence and leapfrogging of living standards. Income convergence occurs for all countries in the same market, arising from diminishing returns to individual human capital. Leapfrogging occurs by comparing countries in two separate markets. Income leapfrogging can occur because the stationary growth rate increases with market size, and human capital heterogeneity reduces growth. The introduction of coordination costs of task assignment can produce gains in welfare and growth from human capital heterogeneity.
This paper examines the role of individual instruction and teacher quality in determining economi... more This paper examines the role of individual instruction and teacher quality in determining economic growth and convergence across school districts. The model shows that if teacher quality is more important for human capital accumulation than individual instruction, human capital convergence will occur between two school districts. This convergence arises because a poor school district hires relatively better teachers but uses them in larger classes in comparison with a rich school district. The model is estimated on panel data of the states of the United States from 1882 to 1990. The estimates indicate that teacher quality is relatively more important for human capital accumulation than individual instruction. The model accounts for all the mean growth in state per capita incomes and between 80 and 100 percent of convergence in state per capita incomes.
Journal of Economic Dynamics and Control, Jun 1, 1996
ABSTRACT Altruistic parents rationally choose fertility and human capital investments in their ch... more ABSTRACT Altruistic parents rationally choose fertility and human capital investments in their children. A rising rate of return to human capital investment and a conditional external effect in human capital investment produce: 1.(1) two development regimes, a Malthusian regime of high fertility and no human capital investment and a perpetual growth regime of low fertility and rising human capital2.(2) conditional human capital convergence within regimes.3.(3) a demographic transition to economic growth4.(4) accelerating growth. As richer countries grow, the conditional external effect continually raises the rate of return on human capital and causes a demographic transition to economic growth by Malthusian countries.
We examine whether dynastic human capital (DHC) can explain the black-white wage gap. We fit a qu... more We examine whether dynastic human capital (DHC) can explain the black-white wage gap. We fit a quantity-quality model to state-level data on fertility, mortality, and schooling but, notably, not earnings. Racial discrimination raised the cost of black schooling, thus depressing DHC not only of the current generation but of future generations via its role in producing human capital. Birth-state DHC helps explain the wage gap among stayers, while current-state DHC helps explain the gap among movers. These findings highlight the role of intergenerational transmission in the persistence of the wage gap and the role of migration in reducing it.
This paper introduces new data on state-level physical capital by sector and land in the farm sec... more This paper introduces new data on state-level physical capital by sector and land in the farm sector for the states of the United States from 1840 to 2000. These data are incorporated into aggregate accounting exercises, with the aim of comparing cross-state results to those found in crosscountry samples. Our aggregate results agree closely with the crosscountry literature: input accumulation accounts for most of output growth, but variation in the level and growth of TFP accounts for most of the variation in the level and growth of output per worker.
An overlapping generations model with parental altruism is examined. The existence of the optimal... more An overlapping generations model with parental altruism is examined. The existence of the optimal value function in a model with an endogenous discount rate is proven. Two development regimes are produced: a high fertility, low income and no growth steady state, and a perpetual growth equilibrium with low fertility and rising income.
Journal of Economic Dynamics and Control, May 1, 1996
The effects of regional differences in population and per capita human capital on income levels a... more The effects of regional differences in population and per capita human capital on income levels and economic growth rates are examined. Sufficient human capital heterogeneity can reduce specialization and inhibit the formation of large markets. The model contains static and dynamic agglomeration economies of market participation. Thus human capital heterogeneity can lower per capita income, and economic growth rates. Over
This paper develops a general equilibrium model of fertility and human capital investment under u... more This paper develops a general equilibrium model of fertility and human capital investment under uncertainty. Uncertainty exists in the form of a probability that a young adult does not survive to old age. Parents maximize expected utility arising from own consumption, their fertility, and the discounted utility of future generations. There exists a precautionary demand for children. Young adult mortality is negatively related to the average human capital of young adults. Therefore, rising human capital leads to falling mortality, which eventually induces a demographic transition and an acceleration in human capital investment. The model can fit data on world and country populations, per capita incomes, age at entry into the labor force, total fertility rates, life expectancy, conditional life expectancy, and infant mortality.
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Papers by Robert Tamura