Adding cycles into the neoclassical growth model☆
Introduction
The standard Solow (1956) Growth Model (SGM) represents a very simple and intuitive framework to analyze countries' long-run economic growth. For this reason, it is still widely employed as a basic setting to conduct both theoretical and empirical analyses (see, for instance, Young et al., 2013; Esfahani et al., 2014; Fernald and Jones, 2014).
The SGM is generally used to study long-run macroeconomic dynamics. Stochastic elements have been added to the SGM either in the aggregate production function (see Brock and Mirman, 1972; Novales et al., 2014) or in the productivity process (henceforth TFP) (see Mirman, 1972, 1973; Lee et al., 1997; Binder and Pesaran, 1999) or both in productivity and labour process (see Lee et al., 1997; Binder and Pesaran, 1999). However, the existing stochastic versions of the SGM exhibit several drawbacks. First, economic fluctuations are exclusively generated by exogenous shocks to aggregate output, technology and population growth. In this respect, Summers (1986) argues that all stochastic SGMs do not allow to capture the sources of these shocks. Second, Solow (1988) argues that it is difficult to “imagine shocks to taste and technology large enough on a quarterly or annual time scale to be responsible for the ups and downs of the business cycle”. More generally, Solow (2007) is worried “about the tendency of modern (American) macroeconomists to forget about the pathology of the business cycle”. Ramey and Ramey (1995) were among the first to empirically examine the link between growth and short-run fluctuations. They show that the above-mentioned relation is strongly supported by data. Therefore, ignoring this link may produce misleading results.
By relying on the long-run features of the U.S. output growth, this paper attempts to address the aforementioned issues. To do so, it introduces a novel framework where cyclical fluctuations are added to a standard stochastic SGM.1 To our knowledge no study bridges the theoretical and empirical literature and explicitly examines the theoretical and empirical properties of a SGM featuring cycles. To fill this gap we improve the stochastic SGMs discussed in Lee et al. (1997) and Binder and Pesaran (1999) by adding a cyclical component to the TFP process. Two features of our study are noteworthy. First, its empirical representation can be easily estimated via unobserved component approach without involving any capital stock measures. This is an important advantage since it is well-known that capital stock (i) suffers from measurement errors leading thus to biased estimates and (ii) is not available over long time span. Second, the dynamic properties of the newly developed model do not differ from those implied by a standard stochastic SGM. In our model, for instance, a permanent decrease in the saving rate does not alter the adjustment process toward the steady-state observed in the classical SGM.
The paper is organized as follows. In Section 2 we present a literature review. Section 3 depicts some important stylized facts about U.S. growth helping to identify the modelization of the TFP process. The novel theoretical framework is presented in Section 4. Section 5 shows some empirical results on the US economy. Section 6 discusses the dynamic properties of the model. Section 7 concludes.
Section snippets
Related literature
We collocate our paper into the strand of literature aimed at finding, both empirically and theoretically, a common ground between the discrete-time version of the SGM, (which usually studies the long-run dynamics of macroeconomic variables), and works that focus on short-run fluctuations attributable to (economic) cycles. Actually, to the best of our knowledge, no many attempts in this direction can be found in the theoretical and empirical literature.
From a theoretical point of view, many
The empirical facts
This section presents some empirical evidence that will be used to model the logarithm of the U.S. real GDP per capita (henceforth GDP) over the period 1870–2016.4 Appendix A provides evidences on the fact that the US GDP can be decomposed into a: (i) deterministic trend; (ii) two (trigonometric) cycles and (iii) an irregular component.5
Production
As in the standard SGM, final output, Yt, is produced using a simple two-factors Cobb-Douglas technology:In Eq. (1), Kt and Lt denote physical capital and labour, respectively, and At represents technology. Physical capital evolves as follows,where is the usual depreciation rate of capital and s the saving rate. In per effective labour unit, , we have:
TFP
As discussed in the
Empirical results
Table 1 reports estimation results of key parameters of the state-space model defined in Eq. (7). Entries in Table 1 are in line with existing estimates on the magnitude of the rate of convergence 1 − λ (Lee et al., 1997) and capital share α (Aiyar and Dalgaard, 2005). Note also that the value of g (close to 2%) is in line with the stylized facts depicted in Section 3.7
Dynamic properties
What about equilibrium dynamics in the presence of a cycle? Differently from the standard stochastic SGM, an additional term shows up in the dynamic equation of output, i.e., (1 − α)Δψt. Apparently, this term does not alter the dynamic properties of the model. We show this by means of a simple simulation exercise.
For the sake of simplicity, let us assume a deterministic trigonometric cycle (e.g., ψt = φ1 cos(ς ⋅ t) + φ2 sin(ς ⋅ t)).8
Conclusions
We propose a novel neoclassical growth model. Precisely, in a stochastic version of the SGM, a cyclical component is added to the TFP process. This represents a first attempt to account for business cycle features within a Solow growth framework The newly introduced growth setting is supported by U.S. secular empirical evidence. More importantly, the proposed model exhibits features that may facilitate its empirical application. In practice, the model is represented by a system of equations
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We are grateful for constructive comments from two referees, Roberto Casarin, Lorenzo Frattarolo, Renatas Kizys, Saten Kumar, and participants at several seminars.