Human capital and the time-profile of human fertility

This is a 1st attempt at an explicitly intertemporal, microeconomic theory of the distribution of births over a woman's fertile period. The main results are that: 1) the optimal time-profile will satisfy the Hotelling rule for the depletion of a natural resource (in the present case of the women's stock of human capital at marriage); and 2) under certain simplifying assumptions, women with "high" initial endowments of human capital will have all their children in the 1st part of married life and then return to full-time employment, while women with "low" initial endowments will spread childbearing more evenly over the fertile period. It must also be pointed out that the characteristics of the optimal fertility profile might be different if utility depended directly on the profile itself--e.g., if the quality of children increased with the interval between the pregnancies, as assumed in the literature on birth spacing.     

The Effect of Transfer Policies on Economic Growth

In a world in which people have different incomes owing to differences in initial factor endowments, a government may use transfer policies if it cares about equity as well as efficiency. It will be shown that, in a simple endogenous growth model in which the engine of growth is a linear capital accumulation technology, if a Ramsey policy is not available, then the government should transfer output but leave the differences in factor endowments unchanged in order to achieve economic growth and income equity at the same time.
JEL Classification Number: 023     

Testing the Assumptions and Predictions of the Hotelling Model

In this paper, we empirically examine whether the assumptions and predictions of the Hotelling model are consistent with patterns observed in data. We consider nonlinear functional forms for the extraction cost and resource demand to develop an empirical Hotelling model with technological progress and stock dependent extraction costs. Using panel data on fourteen nonrenewable natural resources to estimate this empirical Hotelling model, we get qualitatively different results as compared to the related literature. We find evidence of stock-dependent extraction costs for most resources. There is no evidence against the linearity of the optimal extraction rate in the resource stock for almost all resources studied. Furthermore, the Hotelling model may sustain a zero long-run growth rate in resource prices. These results depend on whether firms use different extractive technologies or whether the structural break observed on resource prices is taken into account.     

Growth and inequality in an endogenous fiscal policy model with taxes on labor and capital

I study an economy where individuals have different initial endowments and fiscal policy is decided by majority voting. Public investment is financed by two flat rate taxes, one on labor income and the other one on capital income. The model shows a positive (negative) correlation between growth and the tax rate on labor (capital) income and a negative (positive) correlation between the tax rate on labor (capital) income and inequality. The results reconcile the theory with empirical evidence.     

Spatial dynamics and convergence: The spatial AK model

We study the optimal dynamics of an AK economy where population is uniformly distributed along the unit circle. Locations only differ in initial capital endowments. Spatio-temporal capital dynamics are described by a parabolic partial differential equation. The application of the maximum principle leads to necessary but non-sufficient first-order conditions. Thanks to the linearity of the production technology and the special spatial setting considered, the value function of the problem is found explicitly, and the (unique) optimal control is identified in feedback form. Despite constant returns to capital, we prove that the spatio-temporal dynamics, induced by the willingness of the planner to give the same (detrended) consumption over space and time, lead to convergence in the level of capital across locations in the long-run.     

OPTIMAL TRANSITION DYNAMICS IN THE LEONTIEF TWO‐SECTOR GROWTH MODEL WITH DURABLE CAPITAL: THE CASE OF CAPITAL INTENSIVE CONSUMPTION GOODS*

We present results on undiscounted optimal policies in the Leontief two‐sector growth model with durable capital. Unlike the results with a labour intensive consumption goods sector, we show that a monotonic optimal programme is only one special case out of many richer possibilities of transition dynamics. Depending on the initial capital stock, and a key parameter ζ that could be interpreted as a marginal rate of transformation of capital between today and tomorrow, an optimal programme may converge to a period‐two cycle; and even when it converges to the golden rule stock, it can do so (damped) cyclically or with a “jump”.     

Does the presence of high-skilled employees increase total and high-skilled employment in the long run? Evidence from Austria

Studies conducted for the US have found a positive effect of human capital endowments on employment growth, with human capital endowments diverging at the same time. In contrast, studies for European countries have found convergence of human capital endowments. This paper tests these relationships for the 99 Austrian districts for the observation period 1971–2011 by estimating how the presence of high-skilled employment affects total, low-skilled and high-skilled employment growth. To this end, OLS, fixed-effects and first-difference regressions are estimated. The results indicate continuous convergence of high-skilled employment which, however, slowed down significantly since the 1990s. In contrast to previous studies, evidence for positive effects of high-skilled on total and low-skilled employment is only weak and varies over time. Furthermore, the results show that total and high-skilled employment in suburban areas grew faster than in other regions, while districts which bordered the Eastern Bloc were disadvantaged. Nevertheless, spatial neighbourhood effects within Austria are only weak.     

Optimal capital accumulation and durable goods production

Summary We have examined the optimal production of a consumer durable with the aid of a capital stock subject to deterioration. We assumed the durable was owned by the producer and its services rented; this is equivalent to assuming sale with perfect foresight and used good markets. If the firm has no more than modest initial endowments of productive capital and durable good, the deterioration of capital induces a hump-like profile of the stock of the durable product, with the top of the hump above the eventual steady state level. The rental price of the consumer durable, therefore, falls from its initial level to a low from which it ascends to its steady state value. This implication might be amenable to empirical testing.Among the possible extensions of this work might be an analysis of the relationship between market structure and the choice of durability along the lines of [7] with allowance for deterioration of the capital stock. Recent generalizations of the traditional model of capital accumulation to take into account obsolescence and maintenance, as in [19], [11] and [13], might also be applied to this model. Lastly, policy questions regarding the consequences of an investment credit tax addressed in [4] and [16] might also be investigated in the context of the model presented in this paper.     

Optimal fertility along the life cycle

We explore the optimal fertility timing in a four-period OLG economy with physical capital, whose specificity is to include not one, but two reproduction periods. It is shown that, for a given total fertility rate, the economy exhibits quite different dynamics, depending on the timing of births. If all births take place in the late reproduction period, there exists no stable stationary equilibrium and the economy exhibits cyclical dynamics due to labor growth fluctuations. We characterize the long-run social optimum and show that optimal consumptions and capital depend on the optimal cohort growth factor, so that there is no one-to-one substitutability between early and late fertility. We also extend Samuelson’s Serendipity Theorem to our economy and study the robustness of our results to: (1) endogenizing fertility timing, (2) assuming rational anticipations about factor prices, (3) adding a third reproduction period.     

A nearly complete test of a capital accumulating,vertically integrated,nonrenewable resource extracting theory of a competitive firm

A new approach to testing a generalized Hotelling theory of a nonrenewable resource extracting firm is developed. In contrast to approaches extant, it (i) permits empirical testing of all the refutable implications of the theory, (ii) does not require estimates of, or data on, the shadow value of the resource stock, (iii) does not require estimation of the feedback control functions or the necessary conditions associated with the underlying optimal control problem, and (iv) treats the capital stock in a theoretically sound manner in the econometric model. Because of certain limitations in the data, most, but not all, of the refutable implications of the theory are tested using a Bayesian approach. Other limitations in the data mean that the paper is better viewed as an illustration of how one would go about rigorously testing the extended Hotelling theory, rather than as one which presents convincing empirical evidence that supports or refutes it.     

Rapacious Resource Depletion,Excessive Investment and Insecure Property Rights: A Puzzle

For a country fractionalized in competing factions, each owning part of the stock of natural exhaustible resources, or with insecure property rights, we analyze how resources are transformed into productive capital to sustain consumption. We allow property rights to improve as the country transforms natural resources into capital. The ensuing power struggle about the control of resources is solved as a non-cooperative differential game. Prices of resources and depletion increase faster than suggested by the Hotelling rule, especially with many competing factions and less secure property rights. As a result, the country substitutes away from resources to capital too rapidly and invests more than predicted by the Hartwick rule. The theory suggests that power struggle boosts output but depresses aggregate consumption and welfare, especially in highly fractionalized countries with less secure property rights. Also, adjusted net saving estimates calculated by the World Bank using market prices over-estimate welfare-based measures of genuine saving. Since our theory suggests that genuine saving is zero while empirically they are negative in resource-rich, fractionalized countries, we suggest ways of resolving this puzzle.     

Endowments,Specialization, and Policy

The paper explores the relationship between industry shares in production and their determinants including factor endowments, technology, and government policies, in a GDP–function framework. We use a new international panel dataset on production and trade compiled by the World Bank. As an intermediate step we calculate Hicks‐neutral productivity indices that vary across industries, time, and countries. We find that own‐TFP is robustly associated with industry shares across time and countries and that, after correcting for these productivity differences, output shares are related to factor endowments (Rybczynski effects) in a plausible way. Once Rybczynski effects are controlled for, we find little evidence of demand‐side policies (import tariffs) affecting the allocation of resources; we find, however, more role for supply‐side policies as the relative size of capital‐intensive industries is positively associated with infrastructure–capital endowments.     

A nonsmooth, nonconvex model of optimal growth

This paper analyzes the nature of economic dynamics in a one-sector optimal growth model in which the technology is generally nonconvex, nondifferentiable, and discontinuous. The model also allows for irreversible investment and unbounded growth. We develop various tools to overcome the technical difficulties posed by the generality of the model. We provide sufficient conditions for optimal paths to be bounded, to converge to zero, to be bounded away from zero, and to grow unboundedly. We also show that under certain conditions, if the discount factor is close to 1, any optimal path from a given initial capital stock converges to a small neighborhood of the golden rule capital stock, at which sustainable consumption is maximized. If it is maximized at infinity, then as the discount factor approaches 1, any optimal path either grows unboundedly or converges to an arbitrarily large capital stock.     

Subsistence consumption and natural resource depletion: Can resource-rich low-income countries realize sustainable consumption paths?

This contribution is concerned with efficient use of a resource if households are characterized by Stone–Geary preferences with a minimum subsistence level of consumption. Subsistence consumption implies particular minimum requirements for initial endowments with reproducible man-made capital and resources. If these are not met, the economy is not able to cover subsistence consumption such as nutrition. Focusing on the steady state, we find that the equilibrium can be governed by zero or positive growth. The latter occurs if the rate of exogenous technical change exceeds the rate of time preference. In the former case, we can show that Hartwick’s investment rule applies in a steady state. Finally, we calibrate the model for developing but resource-rich countries and trace the full dynamic development of the economy. Furthermore, we evaluate this full adjustment process regarding several sustainability indicators.     

Undiscounted optimal growth with consumable capital and labor-intensive consumption goods

This paper presents a complete characterization of the optimal policy in a two sector undiscounted growth model. The model is an extension of the Leontief two sector model, which analyzes the optimal allocation of capital and labor to a consumption good sector and an investment good sector. The paper extends this framework to include consumable capital. Thus, the planner has preferences over the consumption good and the consumable capital. Future welfare levels are treated equally as current ones. Geometric techniques are applied to characterize the optimal policy if the consumption good is labor-intensive. The results suggest that if the initial capital stock is above a threshold level, that depends upon the consumption of capital, every optimal program is monotonic, converges to the golden rule stock in a finite number of periods, and undergoes either unemployment or excess capacity of capital.     

Endogenous Time Preference, Inflation, and Capital Accumulation

In an infinitely lived, representative agent model with the Becker-Mulligan (1997) endogenous time preference, this paper reexamines the effects of monetary growth. An increase in the inflation rate reduces the resources spent on imagining the future, which increases the rate of time preference and decreases the steady-state value of capital stock. This model relates inflation and consumer patience, and shows that inflation will make people less patient. Finally, Friedman's optimal monetary growth rule is also investigated and found not to hold.     

The timing of childbearing: The role of human capital and personal preferences

As significant as the shift from quantity to quality in fertility decisions, a rise in the median age at first birth has been commonly observed in the more developed world. This paper attempts to understand the latter demographic trend from the empirical perspective. We first construct a conditional hazard model that incorporates determinants of birth spacing, with a primary emphasis on human capital and personal preference factors. We then examine the importance of these factors, using a rich data set comprised of a selected sample of women from various cohorts reported in the 1980 Taiwan Census. Our results show that, in addition to the age at marriage, human capital factors such as the woman’s education, job security and occupation are all significant in influencing the first spacing. The roles played by these human capital factors become even more important for the second spacing. In the third spacing, the relative importance of education and occupation still persists, while gender preferences become much stronger. Overall, while job security shortens the timing of childbearing, better education and occupation as well as more girls from previous births all lead to delays in births. As for preference factors, we find that elementary school teachers have a shorter birth-spacing compared to junior high school teachers, indicating possible personal preferences for children that are consistent with women’s job selection.     

Redistribution as a selection device

This paper studies the role of the wealth distribution for the market selection of entrepreneurs when agents differ in talent. It argues that the redistribution of initial endowments can increase an economy's surplus because more talented individuals get credit for their risky investment projects. Moreover, the redistribution of initial endowments may lead to a Pareto-improvement although all agents are non-satiable. An agent's entrepreneurial ability is his private information and there is moral hazard in production. I find conditions such that unproductive rich entrepreneurs crowd out productive poor ones on the capital market. Then redistribution of initial endowments may lead to a new equilibrium where market participants are better informed about the entrepreneurs’ ability. The new equilibrium is characterized by (i) the selection of better entrepreneurs, (ii) a higher riskless rate of return on capital, (iii) lower repayments of successful entrepreneurs to their creditors and (iv) the fact that all agents are better off.     

VORACIOUS TRANSFORMATION OF A COMMON NATURAL RESOURCE INTO PRODUCTIVE CAPITAL*

I analyze a power struggle where competing factions have private financial assets and deplete a common stock of natural resources with no private property rights. I obtain a feedback Nash equilibrium to the dynamic common‐pool problem and obtain political variants of the Hotelling depletion rule and the Hartwick saving rule. Resource prices and depletion occur too fast, so substitution away from resources to capital occurs too fast and the saving rate is too high. The power struggle boosts output, but depresses sustainable consumption. Genuine saving is nevertheless zero in a fractionalized society. World Bank estimates may be too optimistic.     

Endogenous growth with a limited fossil fuel extraction capacity

Campbell (1980) and following authors have discussed a limited resource extraction capacity as an augmentation of the well‐known Hotelling model. We integrate a limited extraction capacity and related investments in the endogenous growth model of Tsur and Zemel (2005) to study its effect on economic development. The capacity constraint gives rise to three effects. On the one hand, higher energy costs and the reallocation of production towards capacity investments decrease production available for consumption, research and/or capital investments (energy costs and reallocation effect). On the other hand, research investments may increase, which boosts available production (research effect). Depending on the capital endowment and the strength of the effects, long‐run consumption may be boosted or depressed. In particular, the capacity constraint may render everlasting consumption growth non‐optimal in a resource‐rich economy. Furthermore, we find that capacity investments may be postponed to later points in time if the capital endowment is high.