Stochastic continuous time growth models that allow for closed form solutions

We find a closed form solution that maximises the expected utility of an agent’s inter-temporal consumption subject to a stochastic technology, which is a linear combination of AK and Cobb–Douglas technologies. Additionally, we consider two cases of agent preferences: (i) Constant Relative Risk Aversion (CRRA) preferences, which treat optimal consumption as a linear function of capital, and (ii) Hyperbolic Absolute Risk Aversion (HARA) preferences, which treat optimal consumption as an affine function of capital. By establishing a minimum (subsistence) level of consumption in the HARA model, we are able to create a framework that more accurately represents real-world circumstances than previous studies have done. Furthermore, for both the CRRA and HARA cases we show the suitable, consistent stochastic differential equation which describes the capital dynamics. Finally, we perform a numerical simulation based on the CRRA case and calibrate US data for the HARA case.     

Human capital accumulation in R&D-based growth models

This paper develops a model that reproduces the essential aspects of the recent ICT-based economy using the framework of endogenous growth theory in which a central role is played by human capital accumulation. In particular, it considers a multi-sectoral growth model in discrete time with infinite horizon, endogenous growth, embodied technological progress, horizontal differentiation and “lab-equipment” specification of R&D, and with human capital accumulation (represented by the fact that households devote a fraction of their time to schooling), in order to take into account the crucial role of the latter when new technologies are present. In this model it is possible to obtain some important results, both analytically and through simulations, either in the case of constant productivity of schooling and in the case in which this productivity is a function of technological progress. The first conclusion is that the productivity of schooling affects the long run growth of the economy, contrary to the productivities of the other sectors, hence in this model human capital accumulation is the true engine of growth. It is then possible to study the reaction of the economy to different types of shocks, and to compare the results with the empirical evidence. The conclusion is that the model is able to reproduce such evidence, suggesting that the interaction between ICT and human capital is one of the drivers of the recent economic performance.     

Solving optimal growth models with vintage capital: The dynamic programming approach

This paper deals with an endogenous growth model with vintage capital and, more precisely, with the AK model proposed in [R. Boucekkine, O. Licandro, L.A. Puch, F. del Rio, Vintage capital and the dynamics of the AK model, J. Econ. Theory 120 (1) (2005) 39-72]. In endogenous growth models the introduction of vintage capital allows to explain some growth facts but strongly increases the mathematical difficulties. So far, in this approach, the model is studied by the Maximum Principle; here we develop the Dynamic Programming approach to the same problem by obtaining sharper results and we provide more insight about the economic implications of the model. We explicitly find the value function, the closed loop formula that relates capital and investment, the optimal consumption paths and the long run equilibrium. The short run fluctuations of capital and investment and the relations with the standard AK model are analyzed. Finally the applicability to other models is also discussed.     

Finance capital in dynamic factor-demand models

Researchers often use the discrepancy between self-reported and biochemically assessed active smoking status to argue that self-reported smoking status is not reliable, ignoring the limitations of biochemically assessed measures and treating it as the gold standard in their comparisons. Here, we employ econometric techniques to compare the accuracy of self-reported and biochemically assessed current tobacco use, taking into account measurement errors with both methods. Our approach allows estimating and comparing the sensitivity and specificity of each measure without directly observing true smoking status. The results, robust to several alternative specifications, suggest that there is no clear reason to think that one measure dominates the other in accuracy.     

Imperfect capital markets in empirical life-cycle models

In the context of Frisch demand functions that have prices and the marginal utility of income as independent variables, we show how to incorporate imperfect capital markets into empirical models. The analysis is for rational agents in an uncertain world.     

Stochastic growth: asymptotic distributions

Summary. This note studies conditions under which sequences of state variables generated by discrete-time stochastic optimal accumulation models have law of large numbers and central limit properties. Productivity shocks with unbounded support are considered. Instead of restrictions on the support of the shock, an “average contraction” property is required on technology. Received: August 27, 2001; revised version: January 9, 2002 RID="*" ID="*"The author thanks John Creedy and Rabee Tourky for helpful comments, and the Economic Theory Center, University of Melbourne for financial support.     

Discrimination among alternative models of international capital markets

Most empirical capital flow studies have estimated individual models, many by assuming exogenous interest rates. None of these studies has examined interest rate interdependence from the perspective of the models. In this study, a simultaneous equation model of capital flows containing previous models as special cases is estimated using the cross spectral technique of model discrimination. Based on examination of both the flow-differential link and interest rate interdependence resulting from capital flows, the evidence 1) supports a simultaneous equation stock adjustment model, and 2) suggests that interest rate endogeneity may not imply serious simultaneous equation bias for those previous studies which assume exogenous interest rates.     

Efficiency‐adjusted public capital,capital grants,and growth

A debate on whether capital grants, and especially European Union (EU) funds, actually contribute to growth has gained prominence lately. This article empirically assesses the relationship between the quality of public investment, capital grants, and growth in a sample of 43 emerging and peripheral economies over 1991–2015. To this end, the contribution of public capital to growth is estimated using efficiency‐adjusted public capital stock series, which reflects the quality of public investment management institutions. In addition, the determinants of effective public investment are analyzed. The results suggest that capital grants contribute positively to effective public investment, and the latter is significant in explaining variations in economic growth. Finally, the article illustrates the impact of raising EU funds absorption on potential growth in emerging and peripheral EU countries.     

Stochastic growth with correlated production shocks

This paper extends the stochastic growth model of Brock and Mirman [J. Econ. Theory4 (1972), 497–513] to allow the production shocks to be correlated over time. The resultant optimal savings and consumption policies depend not only upon the current level of output but also upon the most recent realization of the random shock. The properties of these policy functions are studied and it is shown that the Markov process on output, capital stock and consumption resulting from the application of these policies converges to a stationary distribution.     

Stochastic growth: a duality approach

We re-examine the representative agent's optimal consumption and savings under uncertainty in the presence of investment constraints using martingale representation and convex analysis techniques. This framework allows us to explicitly quantify precautionary savings which induces a higher average growth rate than in a certainty setup. We provide a closed form solution for a Cobb-Douglas economy. The effect of uncertainty on portfolio selection is analyzed. Consumption growth rate and risk free interest rate exhibit a U-shaped relationship. Uncertainty negatively affects expected consumption growth rate; such a result seems to be supported by empirical evidence.     

Human capital and economic growth: A macroeconomic model for Pakistan

The paper presents a small macro model for Pakistan economy focusing the impact of investment in human capital on the key macroeconomic variables. The demand side is modeled along the Keynesian lines while the supply side is modeled as per neoclassical theory of production. This framework allows analyzing the effects of investment in human capital on supply side variables (like labor, physical and human capital) and demand side variables (like consumption and investment) at the same time.The model has small forecasting horizon in which three alternative scenarios regarding government spending on education are evaluated from 2012 to 2016. The model shows that the link between human capital and labor market is weak however a change in education spending affects output through enhancing productivity and through multiplier-accelerator principle. Though the model is small in size and forecasting horizon, it can help in evaluating the future paths of key macroeconomic variables associated with education spending.     

Panel data analysis of multi-factor capital asset pricing models

In this article, we propose MFCAPM panel models with fixed effects and test theories associated with risk exposures and anomalies postulated by Fama and French, and we assess their out-of-sample predictive performances. Based on the portfolios formed by French, we construct 10 panel models, each consisting of 10 portfolios grouped by size deciles, and another 10 panels by value deciles. In the presence of cross-section dependence, the MFCAPM panel model is estimated by the feasible generalized least squares (FGLS) method for the sample period 1963(1)-2018(9). The results show that the market, firm-size and value risk exposures are significant and robust across three-, five- and six-factor panel models. Significant time-fixed effects indicate that there are several portfolios resilient to dot.com bubble peak in 2000, while some others resilient to GFC in 2007. We estimate the models for the in-sample period 1963(1)–1999(12) and generate the out-of-sample portfolio returns for the period 2000(1)–2018(9). We find that portfolio returns forecasts generated by the six-factor panel model are superior to other MFCAPM panel models, mostly due to the momentum factor (investor behaviour) explaining large return variations and volatility exposures. The findings have implications for investors, security traders and portfolio risk managers.     

Real fixed capital costs under steady growth

From the standpoint of national economic planning real capital cost represents the investment necessary to maintain output capacity intact within the unit period of time. This definition avoids Cambridge objections to capital cost measurement. So defined capital cost is a rapidly decreasing function of the rate of growth even with unchanged technology. Different life profiles of capital goods imply different capital cost functions, but numerical results for the relevant ranges of parameters do not vary much. Three time profiles are examined, each with the finite and infinite life spans: constant output capacity, linear decay and proportional decay of fixed assets.     

Human capital distribution, growth and convergence

This paper studies the dynamic relationship between distribution and endogenous growth in an overlapping generations model with accumulation of human and physical capital. It is shown how human capital can determine a relationship between per capita growth rates and inequality in the distribution of income. Family background effects and spillovers in the transmission of human capital generate dynamics in which aggregate variables depend not only on the stock, but also on the distribution of human capital. The evolution of this distribution over time is then characterized under different assumptions on private returns and the form of the externality in the technology for human capital. Conditions for existence, uniqueness and stability of a constant growth equilibrium with a stationary distribution are derived. Increasing returns, idiosyncratic abilities and the possibility of poverty traps are explicitely characterized in a closed form solution of the equilibrium dynamics, showing the role played by technology and preferences parameters.     

Vintage capital accumulation: Endogenous growth conditions

Optimal vintage capital accumulation is examined here under asymptotic endogenous growth conditions without input parametrization. It is shown that technological embodiment implies endogeneity of innovations. Vintange capital accumulation and time preference are shown to determine the endogenous rate of vintage capital depletion and the rate at which endogenous innovations occur. A vintage-truncation in capital utilization is shown to induce a time-truncation in the infinite-horizon vintage capital accumulation problem. Factor-augmenting technological change is not assumed a priori, but is shown to be a property of optimal vintage selection under balanced growth conditions.     

Dynamic optimal capital growth with risk constraints

In this paper, risk metrics in capital growth and drawdown as a financial risk measure were considered. Moreover, we developed a dynamic portfolio management model with constraints on the maximal drawdown. Exact optimization algorithms run into difficulties in this framework and this motivates the investigation of simulated annealing optimized algorithm to solve the problem of maximizing long term growth of simultaneous risky investment. Empirical research indicates that the approach is inspiring for this class of portfolio optimization problems.     

International capital movements: A synthesis of alternative models

The several alternative approches to international capital movements have not been compared theoretically. By showing that each represents a special case from a general simultaneous equation model, this note clarifies the theoretical relationships among the approaches, thus providing a convenient framework for their evaluation.     

The taxation of capital returns in overlapping generations models

This paper shows that in the Diamond (1965) overlapping generations economy with production and capital savings, there is a period-by-period balanced fiscal policy supporting a steady state allocation that Pareto-improves upon the laissez-faire competitive equilibrium steady state (whether dynamically inefficient or efficient) without resorting to intergenerational transfers. The policy consists of taxing linearly (or subsidizing, in the dynamically efficient case) the returns to capital, while balancing the budget period by period through a lump-sum transfer (or tax, respectively) in second period. This intervention grants every generation the highest steady state utility attainable through markets (i.e. remunerating factors by their marginal productivities and without transfers) which under laissez-faire is not a competitive equilibrium outcome. A transition from the competitive equilibrium steady state to this other steady state is also Pareto-improving when the former is dynamically inefficient. The result disentangles from redistributive considerations the impact of the taxation of capital returns on steady state welfare, and thus provides a rationale for the taxation of capital returns that is based on efficiency considerations and not on redistributive goals.