Discretely proceeding from cycle to chaos on Goodwin's path

Goodwin's [Goodwin, R.M., 1951. The nonlinear accelerator and the persistence of business cycles. Econometrica 19, 1–17; Goodwin, R.M., 1955. A model of cyclical growth. In: Lundberg, E. (Ed.), The Business Cycle in the Post-war World. Macmillan, London, pp. 203–221] nonlinear multiplier–accelerator model, worked out in continuous-time, is a recognised contribution to business cycle theory. It is rarely observed that its first version was a linear model formulated in discrete-time [Goodwin, R.M., 1946. Innovations and the irregularity of economic cycles. Review of Economics and Statistics 28, 95–104]. A few decades later, he restated the fully-fledged nonlinear version of the model in discrete-time showing that such a version may account better for the complex behaviour of empirical time series [e.g., Goodwin, R.M., 1985. An irregular, asymmetric oscillator, or The discrete charm of erraticism, Mimeo, Siena (reproduced, with the title The discrete charm of erraticism, in Goodwin, R.M., 1989. Essays in Nonlinear Economic Dynamics. Peter Lang, Frankfurt am Main, pp. 139–156); Goodwin, R.M., 1988. The multiplier/accelerator discretely revisited. In: Ricci, G., Velupillai, K. (Eds.), Growth Cycles and Multisectoral Economics: The Goodwin Tradition. Springer-Verlag, Berlin, pp. 19–29]. The article reconstructs the evolution of the multiplier–accelerator model in Goodwin's thought with special emphasis on the early and late discrete version. First, the genesis of the model is considered in some depth in order to clarify its foundations based on the constraints of a monetary economy. Second, the results of Goodwin's late contributions are amended and generalised. Finally, the path followed by Goodwin is reconstructed and appraised in the light of the dialectics between continuity and discontinuity, regularity and irregularity, stability and instability that steered its direction. The main conclusion is that Goodwin's path should be further pursued as an effective alternative to the equilibrium business cycle models.     

A generalized additive Tobit model

This paper proposes a semi-parametric approach to estimation in Tobit models. A generalized additive Tobit model of residential local long distance (intra-LATA) telephone demand is estimated on a cross-section of residential telephone consumers across twenty-eight states. While past studies of telecommunications demand have used fully parametric models, the model presented here is non-parametric in two dimensions: first no distributional assumption is made for the error distribution, and second, the demand equation is non-parametric with respect to price. We find that the elasticity of demand is substantially lower (in absolute value) that found in previous studies for a 40% cut in tariffs. First version received: July 2000/Final version received: March 2001 RID="*" ID="*"  I thank the referee and Associate Editor for suggestions which improved the paper. The views expressed here are of the author and not Analysis Group | Economics.     

A generalized panel data switching regression model

This paper considers a generalized panel data model of polychotomous and/or sequential switching which can also accommodate the dependence between unobserved effects and covariates in the model. We showcase our model using an empirical illustration in which we estimate scope economies for the publicly owned electric utilities in the US during the period from 2001 to 2003.     

A generalized double-hurdle model of Swedish gambling expenditures

This article estimates the relationship between demand for Swedish gambling, income and the other socioeconomic variables using empirical models of participation and gambling expenditure. It also indirectly attempts to account for the effect of a recent recession on gambling behaviour by examining gambling behaviour when the economy was growing versus the period immediately after a major recession. The aim of the article is to analyse the factors influencing gambling decisions. This is done using the double-hurdle method adjusted for the problems of heteroscedasticity and nonnormality using an approach that can handle extreme values and address skewness. The empirical results ruled out Tobit-type models and normally distributed double-hurdle models. The pattern on income elasticities across income classes implies that implicit Swedish gaming taxes are regressive. Income elasticities become smaller after the recession and the decision to participate changed with respect to the several of the demographic variables.     

Towards a disequilibrium theory of structural dynamics: Goodwin's contribution

In this paper, we reconstruct the complex itinerary towards the solution of a conceptual and mathematical problem, how to obtain growth and fluctuations in a framework where structural change is an endogenous, though intermittent, phenomenon and irregularity a natural dynamic property. This has been Goodwin's life-long research program, driven by the effort of marrying Poincaré's qualitative approach to dynamical systems with the earliest (and some of the later) attempts to formalise economic structure as a set of interacting economic units, i.e. the cells of the modern cellular dynamics. This eventually led him to computational dynamics. Our interpretation integrates the more conventional one that emphasises conceptual connections with the thoughts of Marx, Schumpeter and Keynes. Focussing upon modelling issues of an apparently pure technical nature permits a comparison of Goodwin's evolving views with those that have emerged more recently in dynamics, e.g. in the real business cycle and endogenous theories of growth. In a brief assessment towards the end of the paper, it is argued that while there is still much to be done along the path he chose, Goodwin left enough indications for us to know in which direction to go.     

A competitive idea-based growth model

ABSTRACT

In this paper, we present a model in which endogenous growth arises in competitive markets. Knowledge is described as a factor used directly in the final goods' production. Firms demand both basic nonrival knowledge contents, which are supplied jointly and inelastically with raw labor, and further contents supplied by patent holders. This fact, together with Lindahl prices for knowledge, allows competition to work, while it also implies that workers' income share declines overtime. In a first version of the model with constant cost of knowledge production, the first best is attained. In a further version of the model, in which the cost of knowledge production is allowed to change over time and thus intertemporal externalities arise, in a decentralized economy a second best equilibrium occurs in the transitional period, while in the long run there is convergence to efficiency.     

A new generalized volatility proxy via the stochastic volatility model

This article proposes power transformation of absolute returns as a new proxy of latent volatility in the stochastic model. We generalize absolute returns as a proxy for volatility in that we place no restriction on the power of absolute returns. An empirical investigation on the bias, mean square error and relative bias is carried out for the proposed proxy. Simulation results show that the new estimator exhibiting negligible bias appears to be more efficient than the unbiased estimator with high variance.     

A Metzlerian business cycle model with nonlinear heterogeneous expectations

Metzler's model is an important contribution to our understanding of the dynamics of business cycles. In his model, the production of consumption goods depends on expected future sales. However, Metzler assumes that producers are homogeneous and follow a simple expectation formation rule. Taking into account that in reality producers might not only follow several expectation formation rules, but might also even switch between them, we reformulate Metzler's original model. As it turns out endogenous business cycles may emerge within our model, i.e. changes in production and inventory are (quasi-)periodic for certain parameter combinations.     

A discrete model of optimal economic growth

Contrary to most of the literature on optimal economic growth a discrete rather than a continuous model is investigated. It is shown that in such a discrete model it is easy to account for relatively freely changing functions and parameters. Thus, the production function, labor, the investment ratio, and the parameters for time preference, marginal utility, and depreciation are all allowed to depend on time. Using discrete dynamic programming methods, optimal investment policies are determined explicitly. These generalize important results from previous literature on optimal economic growth.     

A model of technology adoption and growth

Summary We construct a model of economic growth in which firms adopt more advanced technologies. In order to advance its technology, a firm must make an investment. The size of this investment depends on the size of the technology adoption barriers in the firm's country Assuming a Markov chain for these barriers, we examine the amount of variation and persistence in the chain for which the model matches the observed output disparity across countries and the mobility of nations. Our calibration suggests a range for the size of these barriers of a factor five, and the presence of a barrier trap.The author is grateful to V. V. Chari, Larry Christiano, Javier Díaz-Giménez, David Johnson, Edward C. Prescott, Richard Rogerson, James Schmitz, and Javier Vallés for their comments. An earlier version of this paper circulated under the title of Economic Institutions and External Factors: Implications for the Replacement of Inferior Technologies and Growth.     

The effect of population growth on wealth and saving in the Modigliani-Brumberg life cycle model

The effect of a change in the rate of population growth on the aggregate savings-income ratio and on the aggregate wealth-income ratio is evaluated in a life cycle model of capital accumulation and growth. It is shown that the former will increase and the latter will decrease when the rate of population growth increases.     

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.     

A structural VAR business cycle model for a volatile small open economy

New Zealand is a small economy exposed to a volatile climate, relatively volatile international trade prices, and its exposure to international financial markets has increased markedly since economic reforms in the 1980s. This paper applies identification techniques suggested by Cushman and Zha [Cushman, D.O. and Zha T.A., 1997. Identifying monetary policy in a small open economy under flexible exchange rates, Journal of Monetary Economics, 39, pp. 433–448.], Zha [Zha, T.A., (1999). Block recursion and structural vector autoregression, Journal of Econometrics, 90, pp. 291–316.] and Dungey and Pagan [Dungey, M. and Pagan, A., 2000. A structural VAR model of the Australian economy, The Economic Record, 76, pp. 321–342.] to develop a large four block structural VAR model of the New Zealand business cycle to capture these features. The model reveals that climate and international trade price shocks have been more important sources of business cycles fluctuations than international or domestic financial shocks. Furthermore, the model does not encounter the price and exchange rate puzzles that have bedevilled attempts to identify monetary policy shocks in small open economy SVAR models.