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Book: Introduction to Dynamic Stochastic General Equilibrium Models (Draft)

Working Papers

Malthusian Stagnation is Efficient (with Xiying Liu)                                                                                

Malthusian economies are generally deemed inefficient: stagnated, highly unequal, and densely populated by a labourering class prone to high fertility. This article defines and characterizes efficient allocations in Malthusian environments of fixed resources and endogenous fertility. We show, that under general conditions, efficient allocations exhibit stagnation in standards of living, inequality, differential fertility, and a high population density of poorer individuals. File

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The Elasticity of Intergenerational Substitution, Parental Altruism, and Fertility Choice (with Marla Ripoll)                                                        

Dynastic models common in macroeconomics use a single parameter to control the willingness of individuals to substitute consumption both intertemporally, or across periods, and intergenerationally, or across parents and their children. This paper defines the concept of Elasticity of Intergenerational Substitution (EGS), and extends a standard dynastic model in order to disentangle the EGS from the EIS, or Elasticity of Intertemporal Substitution. A calibrated version of the model lends strong support to the notion that the EGS is significantly large than 1, and probably around 2.5. In contrast, estimates of the EIS suggests that it is lower than 1. What disciplines the identification is the need to match empirically plausible fertility rates for the U.S. File

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Altruism, Fertility and Risk (with Xiying Liu)                                                                                

This paper studies fertility choices and fertility policies when children's earning abilities are random and parents are altruistic. We characterize equilibrium allocations arising in endowment economies with either complete or incomplete markets. Both models can replicate a number of empirical regularities, such as inequality, social mobility and fertility decreasing with ability, but the incomplete markets model provides a number of more plausible predictions. We find that fertility policies are generally welfare detrimental in our models even when fertility is inefficiently high. File

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Beyond GDP: Is there a law of one shadow price? (with F. Murtin, R. Boarini and M. Ripoll)                                                       

This paper builds a welfare measure encompassing household disposable income, unemployment and longevity, while using two different sets of shadow prices for non-income variables. The valuations of vital and unemployment risks estimated from life satisfaction data (subjective shadow prices) and those derived from model-based approaches and calibrated utility functions (model-based shadow prices) are shown to be broadly consistent once a number of conditions are fulfilled. Subjective shadow prices appear to be inflated by the downward bias on the income variable in life satisfaction regressions conducted at the individual level, while the latter bias is largely removed when running regressions at the country level. On the other hand, model-based shadow prices are typically underestimated as: i) the valuation of the unemployment risk is assumed to take place under the veil of ignorance (i.e. for a representative agent that has no information on her current or future unemployment situation); ii) the standard model relies on a Constant Relative Risk Aversion (CRRA) utility function, which has no specific relative risk aversion parameter for unemployment and vital risks; iii) the Value of Statistical Life that is used in standard calibration pertains to the adult lifespan while life expectancy at birth covers the entire lifetime. File

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Beyond Expected Utility in the Economics of Health and Longevity (with Marla Ripoll)                                                       

We document various limitations of the expected utility model for the study of health and longevity. The model assumes individuals are indifferent between early and late resolution of uncertainty. This assumption gives rise to predictions regarding the economic value of life that are inconsistent with relevant evidence. For example, poor individuals would price life below the present value of foregone income or even negatively. We show that a non-expected utility model disentangling intertemporal substitution from risk aversion can overcome these limitations. We illustrate the quantitative implications of our model for the economic value of life across countries and time. File

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Life, Death and World Inequality (with Marla Ripoll)                                                                                    

Life expectancy around the world has increased substantially since 1970. In contrast, consump-tion per capita has fallen in some countries, remained stagnant, or sharply increased in others.What are the welfare gains of the systematic increase in life expectancy around the world? How does a "full measure" of per capita income, one that adjusts for life expectancy, compare to standard measures of world inequality that only consider income? This paper documents how standard models used to answer these questions give rise to a number of predictions that are inconsistent with well-documented evidence, particularly on the value of statistical life. It then proposes a generalized model with non-separable preferences that exhibits a low elasticity of intertemporal substitution and a low degree of mortality aversion. The non-separable model reverts the counterfactual predictions of the standard model, and it also provides plausible measures of changes in welfare and inequality around the world. File

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Barro-Becker with Credit Frictions (with Marla Ripoll)                                                                                    

The Barro-Becker model of fertility has three controversial predictions: (i) fertility and schooling are independent of family income; (ii) children are a net financial burden to society; and (iii) individual consumption is negatively associated to individual income. We show that introducing credit frictions into the model helps overturn these predictions. In particular, a negative relationship between fertility and individual wage income can be obtained when the intertemporal elasticity of substitution is larger than one. The credit constrained model can also explain the quantity-quality trade-off: individuals with higher wage income choose more schooling and fewer children. (A substantially modified version of this paper is being published under the title "Intergenerational Transfers and the Fertility-Income Relationship" in the Economic Journal). File

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A Contribution to the Economic Theory of Fertility (with Marla Ripoll)                                                        

Altruistic individuals regard fertility as a form of longevity. As a result, standard time-separable altruistic models of the type commonly used in macroeconomics cannot account for the evidence of increasing longevity but decreasing fertility as income rises, a puzzle. We show that a non- separable formulation of preferences that allows for a low elasticity of intertemporal substitution (EIS) but a high elasticity of intergenerational substitution (EGS) can explain the longevity- fertility puzzle. The model with a single elasticity cannot account for both. Our results suggests a major role for a new parameter in macro, the EGS. While the EIS mostly influences short-term economic decisions, the EGS influences mostly long-term economic choices. File

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Malthus to Romer: On the Colonial Origins of the Industrial Revolution                                                       

We propose a unified theory to explain the diverse paths of economic and institutional development of colonized and colonizers following the great discoveries at the end of the XV century. In our theory, the institutional and economic divergence between Spain and England observed during the age of colonization obeys to the same forces put forward by Engerman and Sokoloff (1997) to explain the divergence between Latin America and North America: factor endowments at the moment of the conquest. File

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The Role of Education in Development (with Marla Ripoll)                                                                                    

Most education around the globe is public. Moreover, invest rates in education as well as schooling attainment differ substantially across countries. We contruct a general equilibrium life-cycle model that is consistent with these facts. We provide simple analytical solutions for the optimal educational choices, which may entail pure public provision of education, and their general equilibrium effects. We calibrate the model to fit cross-country differences in demographic and educational variables. The model is able to replicate a number of key regularities in the data beyond the matching targets. We use the model to identify and quantify sources of world income differences, and find that demographic factors, in particular mortality rates, explain most of the differences. We also use the model to study the role of public education, and the effects of the HIV/AIDS pandemic in development. A version of this paper was published in the Journal of Monetary Economics under the title "What Explains Schooling Differences Across Countries?"Citations (Google Scholar) File

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Agriculture, Aggregation, Wage Gaps, and Cross-Country Income Differences (with Marla Ripoll)                                                        

In spite of its low productivity, agriculture employs most of the labor force in countries in the lower part of the world income distribution. Moreover, agriculture differs from other activities in its intensive use of land. We show that ignoring agriculture, as most one-sector aggregate models do, gives rise to substantially biased results regarding the sources of cross-country income differences. We first show that standard Solow Residuals underestimate underlying productivity differences across countries. Specifically, Solow residuals are less disperse than both agricultural and nonagricultural TFPs. More importantly, we show that the large labor productivity gap between agriculture and non-agriculture is not accounted for by migration costs or schooling differences. Instead, the gap seems to be explained by the particularly low quality of human capital in rural areas. This finding implies that most of the income dispersion across countries is not due to TFP differences but to differences in factor endowments, particularly human capital in rural areas. Part of this research was published in Economic Letters as "Agriculture and Aggregation." Citations (Google Scholar) File

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Lucas vs. Lucas: On Inequality and Growth (with Genevieve Verdier)                                                       

MF Working Paper, July 2007. This paper was published in the JEDC as "Inequality and Growth: Some Welfare Calculations." Citations (Google Scholar) File

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