Cyclical features of the Uzawa–Lucas endogenous growth model

Abstract

This paper analyzes the cyclical properties of a generalized version of Uzawa-Lucas endogenous growth model. We study the dynamic features of different cyclical components of this model characterized by a variety of decomposition methods. The decomposition methods considered can be classified in two groups. On the one hand, we consider three statistical filters: the Hodrick-Prescott filter, the Baxter-King filter and GonzaloGranger decomposition. On the other hand, we use four model-based decomposition methods. The latter decomposition procedures share the property that the cyclical components obtained by these methods preserve the log-linear approximation of the Euler-equation restrictions imposed by the agent's intertemporal optimization problem. The paper shows that both model dynamics and model performance substantially vary across decomposition methods. A parallel exercise is carried out with a standard real business cycle model. The results should help researchers to better understand the performance of Uzawa-Lucas model in relation to standard business cycle models under alternative definitions of the business cycle.

Tuning in RBC Growth Spectra

“…From this it follows that by using equation (108) and (113) to obtain time series for consumption, investment, and output, will generate series with a unit root with a drift. This as pointed out by Restrepo-Ochoa & Vazquez (2004) is in line with evidence in the literature over the presence of a unit root in aggregate time series also highlighted by Nelson & Plosser (1982). Given the non-stationary time series obtained from the model for the log-levels of output, consumption, and investment, now the band pass …lter can be applied at di¤erent frequencies as de…ned earlier following Basu et al (2012), and Comin & Gertler (2006).…”

“…In order to characterize the cyclical and long-run components of the simulated data an asymmetric Christiano & Fitzgerald (2003) type band-pass …lter is applied at di¤erent frequencies de…ned in Section 4. Since Model 1 and 2 are solved for human capital normalized variables we use the method described by Restrepo-Ochoa & Vazquez (2004) to construct log-level simulated series by using the model solution given by equations (102) and (103).Using the method of Restrepo-Ochoa & Vazquez (2004) non-stationary log-level series are constructed for output, consumption, and physical investment, while. Then these series are used to calculate simulated RBC correlations; volatilities; and growth persistence as it can be seen in Section 4.…”

Decentralized Allocation of Human Capital and Nonlinear Growth

“…Other work on the UzawaLucas model stresses particular features like the role of fiscal policy in guaranteeing an optimal decentralized equilibrium [García-Castrillo and Sanso (2000), Gómez (2003Gómez ( , 2005] and the efficiency of the competitive equilibrium under sector specific externalities associated to human capital in the goods sector [Gómez (2004[Gómez ( , 2006]. An additional note goes to the work of Restrepo-Ochoa and Vázquez (2004), who adopt a stochastic version of the two-sector model in order to compare results on fluctuations with the benchmark Real Business Cycles setup.…”

Polluting Productions and Sustainable Economic Growth: A Local Stability Analysis

“…Moving a step forward from AH, we also deeply concentrate on the study of the transitional dynamics of the model, and provide the whole necessary and sufficient conditions for the existence of a feasible steady-state equilibrium path associated with a positive long-run growth. Moreover, we conclude that a determinate saddle path sustainable equilibrium can be reached even in presence of a long run positive level of polluting emissions, thanks to a growing level of new home-made inventories, without whom some indeterminacy problems are likely to emerge [11,12].…”

“…12 A specific utility function is assumed here to have the following CES structure This functional form guarantees that both C and E grow at the same rate, so that the E C / ratio is constant in equilibrium [16]. 13 We show in the next 9 One interpretation would be forests, which contribute to welfare both as sources of timber and also as stocks which provide many ecosystem services to society (for example, carbon's sequestration, preservation of bio-diversity) 10 For simplicity, time subscripts will be omitted in the rest of the paper 11 Constraints to the optimization problem could, for example, be introduced by defining critical minimum levels for natural capital (Barbier and Markandya, 1990) or by excluding decreasing utility paths (Pezzey, 1992). But as these restrictions usually involve inequality constraints, they may complicate the optimization problem considerably 12 While AH deal (to simplify the analysis) with a logarithmic, thus separable, utility function, we prefer to introduce a non-separable function instead (as in Musu, 1995), that allows to compare consumption and environmental quality as two substitutes, according to agents' tastes towards them.…”