A closed-form solution to the transitional dynamics of the Lucas–Uzawa model

This paper studies how the intertemporal allocation determines the transitional dynamics to a given steady state and the long-term growth of an economy. Our main contribution consists in determining the solutions path for all the variables of the model, under fairly general conditions on σ and β.     

On a closed-form solution to the stochastic Lucas–Uzawa model

Bucci et al. (J Econ 103:83–99, 2011) argue that under two parametric restrictions, there exists a closed-form solution path to the two-sector endogenous growth model of Lucas–Uzawa. However, they assume that the value function is a function of both the current and the initial values of the state variables. As Wälde (J Econ Dyn Control 35:616–622, 2011a) argues, the value function should depend only on the current state variables when the technology follows a geometric Brownian motion. I follow Wälde (J Econ Dyn Control 35:616–622, 2011a) and obtain, under some inequality constraints, a different value function.     

Stochastic accumulation of human capital and welfare in the Uzawa–Lucas model: an analytical characterization

Stochastic growth models are often solved numerically, because they are not tractable in general. However, recent several studies find the closed-form solution to the stochastic Uzawa–Lucas model in which technological progress or population dynamics follow a Brownian motion process with one or two parameter restriction(s). However, they assume that the return on the accumulation of human capital is deterministic, which is inconsistent with empirical evidence. Therefore, I develop the Uzawa–Lucas model in which the accumulation of human capital follows a mixture of a Brownian motion process and many Poisson jump processes, and obtain the closed-form solution. Moreover, I use it to examine the nexus between human capital uncertainty, technological progress, expected growth rate of human capital, and welfare.     

Population dynamics and utilitarian criteria in the Lucas–Uzawa Model

This paper introduces population growth in the Uzawa–Lucas model, analyzing the implications of the choice of the welfare criterion on the model's outcome. Traditional growth theory assumes population growth to be exponential, but this is not a realistic assumption (see Brida and Accinelli, 2007). We model exogenous population change by a generic function of population size. We show that a unique non-trivial equilibrium exists and the economy converges towards it along a saddle path, independently of population dynamics. What is affected by the type of population dynamics is the dimension of the stable manifold, which can be one or two, and when the equilibrium is reached, which can happen in finite time or asymptotically. Moreover, we show that the choice of the utilitarian criterion will be irrelevant on the equilibrium of the model, if the steady state growth rate of population is null, as in the case of logistic population growth. Then, we show that a closed-form solution for the transitional dynamics of the economy (both in the case population dynamics is deterministic and stochastic) can be found for a certain parameter restriction.     

On the existence and uniqueness of solution to the Lucas–Uzawa model

In this paper we define the concept of admissible solution and then provide closed-form solutions for all variables of the model along the transitional dynamics path. We present numerical simulations and compare our results with those obtained through the methods developed by Boucekkine and Ruiz-Tamarit and, Barro and Sala-I-Martin.     

The Uzawa–Lucas model without scale effects: theory and empirical evidence

Numerous cross-sectional tests have been performed to evaluate the predictions of recent growth theories such as the Uzawa–Lucas growth model. In a series of papers and in his book, Jones [Q. J. Econ. 110 (1995a) 495; J. Political Econ. 103 (1995b) 759; The upcoming slowdown in US economic growth, Stanford University, Stanford] has shifted the attention toward the time series predictions of endogenous growth models. By contrasting endogenous growth models with facts, one is frequently confronted with the prediction that levels of economic variables, such as human capital, imply lasting effects on the per capita growth rate of an economy. As stylized facts show, measures of education or human capital in most advanced countries have dramatically increased, mostly more than the gross domestic production (GDP). Yet, the growth rates have roughly remained constant or even declined. In this paper we modify the growth effects of education and human capital in our variant of the Uzawa–Lucas growth models and test the model using time series data for the US and Germany from 1962.1 to 1996.4. We consider two versions. In the first, we treat the time spent for education as exogenously given and we neglect the external effect of human capital. In the second version, the time spent for education is an endogenous variable and the external effect of human capital is taken into account. Our results demonstrate that the model is compatible with the time series for aggregate data in those countries. The parameters fall into reasonable ranges.     

Multiple steady states and indeterminacy in the Uzawa–Lucas model with educational externalities

This paper examines a foreign technology holder’s licensing choices between royalty and fixed-fee scheme. We emphasize that foreign licensor chooses the quality of licensed technology when the licensee country does not implement perfect intellectual property protection for licensor’s technology. We study quality choice as the foreign licensor’s selection for a particular grade of technical skills. We show that fixed fee emerges as the equilibrium licensing scheme when both the transfer of his technology is relatively efficient and the licensee is sufficiently cost competitive in the domestic market, and that royalty licensing prevails otherwise. We further show it need not hold the general belief that welfare in the licensor country unambiguously rise with a stronger patenting system in the licensee country when, in particular, such patenting system in place is sufficiently lax.     

Testing the Uzawa–Lucas model with OECD data

The paper tests the Uzawa–Lucas model of endogenous growth using a modified Granger-causality test and panel data for 20 OECD countries. The results favour the human capital augmented endogenous growth model against both the exogenous growth model à la Solow and endogenous growth models of the AK type.     

Optimal taxation in the Uzawa–Lucas model with externality in human capital

In this paper we study the optimal policy in the Uzawa–Lucas model with externality in human capital when agents value both consumption and leisure. We find that the government pursuing the first best can achieve its goal by a subsidy which depends on foregone earnings while studying and which is financed through a lump sum tax. Anyway, the optimal policy, that should be designed to provide incentives for agents to devote more time to schooling and cut both on leisure and working, is not unique. There exists an infinite number of combinations of consumption, capital income, labor income and lump sum taxes that can decentralize the first best.     

Black and official exchange rates in Morocco: an analysis of their long-run behaviour and short-run dynamics (1974–1992)

Using Vector Error-Correction (VEC) model estimation on monthly data from Morocco for the period January 1974 to December 1992, this article tests the hypothesis that there is a long-run stable relationship between the official and the black-market exchange rates for US dollars. We also examine the short-run dynamics in the relationship between the two markets. The econometric results indicate that the two exchange rates are cointegrated. Furthermore, we reject weak exogeneity in the case of the official exchange rate, but fail to reject it in the case of the black-market rate. Granger causality tests show that the black-market rate causes the official exchange rate. The results seem to support the efficiency hypothesis, suggesting that participants in the black-market are able to anticipate changes in the official exchange rate. The findings also suggest that Morocco's decision (in January 1993) to introduce only current account convertibility and keep controls on capital accounts was wise.     

Investment–productivity dynamics and distribution dynamics in a multisector economy: some theory and an application to Italian regions

In this paper, we study the investment–productivity dynamics in the Framework Space, presented by Böhm and Punzo [Cycles, Growth and Structural Change, Routledge, London (2001) 47], as the distribution dynamics of the production sectors of an economy. We apply such theoretical framework to data from Italian regions to identify differences in sectoral behaviors both within and across regions. Our main findings are: sectors within a region generally follow different regime dynamics; Southern Italian regions are generally characterized by higher degrees of heterogeneity in sectoral growth behaviors and of regime instability. Also, we find support to the hypothesis of a positive relation between this type of instability and unemployment, as argued by the Neo-Austrian theory of structural dynamics.     

Learning,experience and the dynamics of north–south Trade and technology transfer

This paper examines the dynamics of learning and experience that underlie technology transfer using a North-South trade model with a continuum of goods. Since North is historically more experienced than South, it initially produces the most advanced goods and pays higher wages. Whenever there is a market-driven transfer of technology and production over time, there will be some wage convergence as South gradually gains experience. Nevertheless, wage inequality must persist in the steady state. Product innovation typically increases steady-state wage inequality because new goods are produced in North, and North ultimately learns than South. [F12, O19]     

Firm adaptiveness and performance heterogeneity: the case of sales–advertising dynamics in an evolving product market

We combine evolutionary theory concepts and multivariate persistence methodology to develop and test expectations about the adaptiveness of firm decisions and its implications for performance heterogeneity. We focus on the relatively reversible advertising decisions in an evolving product market, domains typically ignored by evolutionary research. We find that an adaptive decision routine helps an incumbent firm maintain its advantages and overcome the challenge posed by a major competitive entry.

A story of large landowners and math skills: Inequality and human capital formation in long-run development, 1820–2000

We create a new dataset to test the influence of land inequality on long-run human capital formation in a global cross-country study and assess the importance of land inequality relative to income inequality. Our results show that early land inequality has a detrimental influence on math and science skills even a century later. We find that this influence is causal, using an instrumental variable (IV) approach with geological, climatic and other variables that are intrinsically exogenous. A second major contribution of our study is our assessment of the persistence of numerical cognitive skills, which are an important component of modern human capital measures. Early numeracy around 1820 is estimated using the age-heaping strategy. We argue that countries with early investments in numerical education entered a path-dependency of human capital-intensive industries, including skill-intensive agriculture and services. The combined long-run effects of land inequality and human capital path-dependence are assessed for the first time in this article.     

The impact of the ACFTA on ASEAN–PRC trade: estimates based on an extended gravity model for component trade

This article uses an extended gravity model to examine the impact of the free trade agreement between the Association of Southeast Asian Nations (ASEAN) and the People’s Republic of China (PRC) on their trade flows and patterns. New determinants are utilized to capture the growing importance of global production sharing and intraregional trade in parts and components in East Asia. We show that the free trade agreement leads to substantially higher and more pronounced bilateral trade flows between ASEAN and the PRC than what a conventional gravity model predicts and the increase is concentrated in ASEAN countries that have stronger industrial linkages with the PRC.     

Relating inertia and experience in technology markets: an analysis of households’ personal computer choices

This article empirically analyses how households’ PC purchasing behaviours change with market experience. We find that: households generally exhibit inertia in their PC purchases, the level of inertia is increasing as a function of experience on the PC market, and, for households switching brands, the likelihood of buying a lesser-known brand increases with experience, regardless of the brand of the previous purchase. These findings are consistent with the predictions of a simple learning model, and extend our understanding of how market experience affects purchasing behaviour to an important technology product, with implications that may apply to other similar products.     

Lange's 1938 model: dynamics and the “optimum propensity to consume”

Abstract

Oskar Lange's 1938 article “The Rate of Interest and the Optimum Propensity to Consume” is usually associated with the original IS-LM approach of the late 1930s. However, Lange's article was not only an attempt to illuminate Keynes's main innovations but the first part of a wide project that included the development of a theory of economic evolution. This paper aims at showing that Lange's article can help in illuminating critical aspects of this project: in particular, Lange's idea that a synthesis between Kaldor's and Kalecki's theories and that of Schumpeter, might have been possible and that it represented (in intentions) a “modern” and consistent reconstruction of the Marxist theory of the business cycle. Section 2 clarifies Lange's early reflection on dynamics. Section 3 centres on Lange's 1938 static model and indicates the effects of a change of saving on investment. Section 4 suggests a dynamic reconstruction from which are addressed important arguments raised by Lange in a series of papers written between 1934 and 1942.     

Predator–prey dynamics in general equilibrium and the role of trade

We examine the implications of trade in an economy with two interrelated natural resources, focusing on the case of a simple predator–prey relationship. We derive a three-sector general equilibrium model where production functions are linked via the ecological dynamics of the natural system. Under autarky, this economy exhibits a steady-state equilibrium that overexploits the prey stock, reducing the linked predator population and overall welfare in the absence of harvesting controls. When two economies engage in trade, differences in the dynamics of the two resource systems can become the basis for comparative advantage. In this case, the predator–prey relationship leads to a source of comparative advantage in harvesting prey for a country with a lower autarky steady-state proportion of predators to prey. This feature has not been noticed in the literature and leads to a counterintuitive implication: free trade can help conserve predator and prey stocks in the country with the higher autarkic steady-state proportion of predators to prey. To illustrate the relevance of our analytic findings, we present the stylized empirical example of the effect of Chinook salmon imports on killer whale populations.     

Regional distribution and dynamics of human capital in China 1985–2014

This study investigates the regional distribution and dynamics of human capital in China. We develop a new comprehensive human capital measure based on the Jorgenson-Fraumeni (J-F) lifetime income framework, in addition to using the traditional education-based human capital measures. We find that the new J-F human capital measure reflects more closely the regional economic disparity than the education-based measures. We also conduct a Divisia decomposition analysis to investigate the contributions of different factors to the quantity and quality growth of human capital and to regional disparity. Our results show that the regional human capital gaps in China are enlarging in general. Education and urbanization contribute most to human capital growth, while population aging shows a strong negative effect. Our estimates create a new provincial level human capital panel dataset from 1985 to 2014, which is useful for empirical work and policy analysis.