σ: The long and short of it

Research on the elasticity of substitution between capital and labor – σ – has been proceeding for 75 years. While there is clearly a strong case for the importance of σ in the analysis of growth and other economic issues, much less agreement exists on the value of σ. This paper offers some perspectives on prior estimates of σ, emphasizing the fundamental tension between the short-run data that are available and the long-run parameter that is required. Estimates of σ based on various short-run and long-run models are discussed and, while the estimates range widely, the weight of the evidence suggests a value of σ in the range of 0.40–0.60. There is little evidence to sustain the assumption of a Cobb–Douglas production function.     

The biological determinants of long-wave behavior in socioeconomic growth and development

In this paper, it is claimed that the effective causality of long-term macroeconomic rhythms, most commonly referred to as long waves or Kondratieff waves, is founded in our biological realm. The observed patterns of regularity in human affairs, manifest as socioeconomic rhythms and recurrent phenomena, are constrained and codetermined by our natural human biological clocks, themselves the result of instructions impressed in the human genome and human cognitive capacity by the physical regularity of fixed cosmic cycles. Considering that a long wave can be conceived as an evolving learning dissipative structure consisting of two successive logistic structural cycles, an innovation cycle and a consolidation cycle, and applying considerations from population dynamics, chaos theory and logistic growth dynamics, a Generational-Learning Model is proposed that permits comprehension of the unfolding and time duration of the phenomenon. The proposed model is based on two kinds of biological constraints that impose the rhythm of collective human behavior — generational and cognitive. The generational consist of biologically based rhythms, namely, the Aggregate Virtual Working Life Tenure and the Aggregate Female Fecundity Interval, both subsets of the normative human life span or human life cycle. The cognitive consist of a limiting learning growth rate, manifest in the alternating sequence of two succeeding learning phases, a new knowledge phase and a consolidation phase. It is proposed that the syncopated beats of succeeding effective generational waves and the dynamics of the learning processes determine the long-wave behavior of socioeconomic growth and development. From the relationship between the differential and the discrete logistic equations, it is demonstrated that the unfolding of each structural cycle of a long wave is controlled by two parameters: the diffusion-learning rate δ and the aggregate effective generation t_G, whose product maintained in the interval 3<δt_G<4 (deterministic chaos) grants the evolution and performance of social systems. Moreover, it is speculated that the triggering mechanism of this long-term swinging behavior may result from the cohesion loss of a given technoeconomic system in consequence of reaching a threshold value of informational entropy production.     

Comment on “σ: The long and short of it”

I comment on some of the issues discussed by Robert Chirinko (Chirinko, R.S., 2008. σ: The long and short of it. Journal of Macroeconomics 30 (2), 671-686). I also offer some additional evidence and discuss the theoretical implications of the empirical findings regarding σ.     

Exports and growth: Granger causality analysis on OECD countries with a panel data approach

This paper investigates the possibility of Granger causality between the logarithms of real exports and real GDP in twenty-four OECD countries from 1960 to 1997. A new panel data approach is applied which is based on SUR systems and Wald tests with country specific bootstrap critical values. Two different models are used. A bivariate (GDP–exports) model and a trivariate (GDP–exports–openness) model, both without and with a linear time trend. In each case the analysis focusses on direct, one-period-ahead causality between exports and GDP. The results indicate one-way causality from exports to GDP in Belgium, Denmark, Iceland, Ireland, Italy, New Zealand, Spain and Sweden, one-way causality from GDP to exports in Austria, France, Greece, Japan, Mexico, Norway and Portugal, two-way causality between exports and growth in Canada, Finland and the Netherlands, while in the case of Australia, Korea, Luxembourg, Switzerland, the UK and the USA there is no evidence of causality in either direction.     

An explicit solution to an optimal tax problem

Under specific but perhaps not over-restrictive assumptions on social welfare and consumer preferences, an explicit closed-form solution for an optimal linear income tax is derived. Specifically, given linear income supply functions and a rank-order social welfare function, the optimal tax rate and benefit level are characterized by four parameters: I, a measure of pre-tax inequality in the ability (wage) distribution; r, the fraction of potential total income required for (non-redistributed) government revenue; σ, the fraction of potential total income required for consumer subsistence expenditures; and a disincentive parameter, δ, the marginal propensity to spend on leisure or the amount by which earned income is reduced in response to a unit increase in unearned benefit. Defining , the ratio I/(1 - σ - r), the optimal tax rate τ is given by: The formula is used to fully characterize τ in terms of the parameters. Results include the following: τ = 0 if I = 0; τ = 1 if δ = 0; τ is increasing in I, σ and r; τ may be increasing or decreasing in δ depending on the value of ; when disincentive effects are large, τ becomes close to so that, in such economies, if σ and r are small, the optimal tax rate is equal to the measure of pre-tax inequality. Formulae for the deadweight loss associated with the tax are derived and some observations are offered on the empirical issues associated with the model.     

Unfolding Social Hierarchies

Consider a large population of finitely-lived agents organized into n different hierarchical levels. Every period, all those placed at each level are randomly matched to play a given symmetric game. Based on the resulting outcome, a ρ-fraction of agents who (within their own level) attain the highest payoffs are promoted upwards. On the other hand, newcomers replacing those who die every period enter at the lowest level and choose irreversibly the strategy to be played for the rest of their life. This choice is made, with some noise, by imitating one of the strategies adopted at the highest level.  In this setup, the unique long-run behavior of the system is fully characterized for the whole class of 2×2 coordination games and two alternative variations of the model. The results crucially depend on the key “institutional” parameters ρ and n. In particular, it is shown that inefficient behavior prevails in the long run (even when risk-dominated) if promotion is only mildly selective—high ρ—and the social system is quite hierarchical—large n. In a stylized manner, these parameter conditions may be viewed as reflecting a sort of institutional deficiency that impairs economic performance. Journal of Economic Literature Classification Numbers: C70, C72, C73, D72.     

Concatenate coordination and mutual coordination

We tell of the evolving meaning of the term coordination as used by economists. The paper is based on systematic electronic searches (on “coord,” etc.) of major works and leading journals. The term coordination first emerged in professional economics around 1880, to describe the directed productive concatenation of factors or activities within a firm. Also, transportation economists used the term to describe the concatenation of routes and trips of a transportation system. These usages represent what we term concatenate coordination. The next major development came in the 1930s from several LSE economists (Hayek, Plant, Hutt, and Coase), who extended that concept beyond the eye of any actual coordinator. That is, they wrote of the concatenate coordination of a system of polycentric or spontaneous activities. These various applications of concatenate coordination prevailed until the next major development, namely, Thomas Schelling and game models. Here coordination referred to a mutual meshing of actions. Game theorists developed crisp ideas of coordination games (like “battle of the sexes”), coordination equilibria, convention, and path dependence. This “coordination” was not a refashioning, but rather a distinct concept, one we distinguish as mutual coordination. As game models became more familiar to economists, it was mutual coordination that economists increasingly had in mind when they spoke of “coordination.” Economists switched, so to speak, to a new semantic equilibrium. Now, mutual coordination overshadows the older notion of concatenate coordination. The two senses of coordination are conceptually distinct and correspond neatly to the two dictionary definitions of the verb to coordinate. Both are crucial to economics. We suggest that distinguishing between the two senses can help to clarify “coordination” talk. Also, compared to talk of “efficiency” and “optimality,” concatenate coordination allows for a richer, more humanistic, and more openly aesthetic discussion of social affairs. The narrative is backed up by Excel worksheets that report on systematic content searches of the writings of economics using the worldwide web and, using JSTOR, of Quarterly Journal of Economics, Economic Journal, Journal of Political Economy, American Economic Review, and Economica.     

Scaling the volatility of GDP growth rates

The distribution of shocks to GDP growth rates is found to be exponential rather than normal. Their standard deviation scales with GDP^β where β=−0.15±0.03. These macroeconomic results place restrictions on the microeconomic structure of interactions between agents.     

Probability Logic for Type Spaces

Using a formal propositional language with operators “individual i assigns probability at least α” for countably many α, we devise an axiom system which is sound and complete with respect to the class of type spaces in the sense of Harsanyi (1967–1968, Management Science, 14 159–182). A crucial inference rule requires that degrees of belief be compatible for any two sets of assertions which are equivalent in a suitably defined natural sense. The completeness proof relies on a theorem of the alternative from convex analysis, and uses the method of filtration by finite sub-languages. Journal of Economic Literature Classification Numbers: D80, D82.     

Testing the balanced growth hypothesis: evidence from China

We investigate whether China’s experience during 1952–2004 supports the balanced growth entailment of the neoclassical growth model. Estimation of long-run relations among output, consumption and investment for the full period reject the balanced growth hypothesis for both the national and regional economies. When the economic reforms of the late 1970s are modelled as a structural break by the methods of Johansen et al. (Economet J 3(2):216–249, 2000) and Perron (Econometrica 57(6):1361–1401, 1989), we find some evidence of balanced growth in the pre-break period but in the post-break period the ‘great ratios’ are trend-stationary, precluding fully balanced growth, though permitting a common (stochastic) productivity trend.      

Optimal balanced growth in a general multi-sector endogenous growth model with constant returns

I will study a multi-sector endogenous growth model with general constant returns to scale technologies and demonstrate the existence, uniqueness and the saddle-path stability of the balanced growth equilibrium. I will first demonstrate the existence of a balanced growth equilibrium, by showing that the balanced growth rate associated with the balanced growth equilibrium is solely determined by solving a Frobenius root problem of the price equations derived from the Euler equations and the property of the nonsubstitution theorem. Then I will show the saddle-path stability of the balanced growth equilibrium without any capital intensity conditions, which is a generalized property proved in the two-sector endogenous growth models by de Guevara et al. (J Econ Dyn Control 21, 115–143, 1997), Bond et al. (J Econ Theory 68, 149–173 1996) and Mino (Int Eco Rev 37, 227–251 1996). The theorem clearly implies that the balanced growth equilibrium has a transition path in the neighborhood of the balanced growth equilibrium. The paper was presented at the conferences “Irregular Growth: Beyond Balanced Growth” held on June 19–21, 2003 in Paris and “Economic Growth and Distribution: On the Nature and Causes of the Wealth of Nations” held on June 16–18, 2004 in Lucca, Italy. From the discussion with Alain Venditti at CNRS-GREQAM, Gerhard Sorger at University of Vienna and the conference participants, I have been benefited much by writing this paper. Especially Alain Venditte had given me a chance to take a look at his unpublished paper titled ” Indeterminacy and the Role of Factor Substitutability” jointly written with Kazuo Nishimura at Kyoto University and published in Macroeconomic Dynamics, Vol. 8. The author also would like to thank an anonymous referee for useful suggestions.     

Contracts and externalities: How things fall apart

A single principal interacts with several agents, offering them contracts. The crucial assumption of this paper is that the outside-option payoffs of the agents depend positively on how many uncontracted or “free” agents there are. We study how such a principal, unwelcome though he may be, approaches the problem of contract provision to agents when coordination failure among the latter group is explicitly ruled out. Two variants are considered. When the principal cannot re-approach agents, there is a unique equilibrium, in which contract provision is split up into two phases. In phase 1, simultaneous offers at good (though varying) terms are made to a number of agents. In phase 2, offers must be made sequentially, and their values are “discontinuously” lower: they are close to the very lowest of all the outside options. When the principal can repeatedly approach the same agent, there is a multiplicity of equilibria. In some of these, the agents have the power to force delay. They can hold off the principal's overtures temporarily, but they must succumb in finite time. In both models, despite being able to coordinate their actions, agents cannot resist an “invasion” by the principal and hold to their best payoff. It is in this sense that “things [eventually] fall apart”.     

The ghost of financing gap: testing the growth model used in the international financial institutions

The Harrod–Domar growth model supposedly died long ago. Still today, economists in the international financial institutions (IFIs) apply the Harrod–Domar model to calculate short-run investment requirements for a target growth rate. They then calculate a “financing gap” between the required investment and available resources and often fill the “financing gap” with foreign aid. The financing gap model has two simple predictions: (1) aid will go into investment one for one, and (2) there will be a fixed linear relationship between growth and investment in the short run. The data soundly reject these two predictions of the financing gap model.     

A note on work–leisure choice, human capital accumulation, and endogenous growth

The growth model of Lucas [Lucas Jr., R.E., 1988. On the mechanics of economic development. Journal of Monetary Economics 22 (1), 3–42] is enriched with people having the opportunity to optimally allocate a fraction of their time to non-productive activities (‘leisure’). It is found that the chosen amount of leisure reduces the steady-state rate of growth of per capita output. This implies that the association between income and welfare may not be as strong as it is usually assumed to be. The optimal allocation of time among activities depends on some of the parameters and the marginal product of physical capital per capita.     

Are stocks desirable in tax-deferred accounts?

Existing literature suggests that, in order to maximize the tax benefit of retirement accounts, investors should follow a “pecking order” location rule of placing highly taxed assets (e.g., bonds) in a tax-deferred account and lightly taxed assets (e.g., stocks) in a taxable account. Empirical evidence, however, documents that a large number of investors violate this rule. In this paper, we show that such violations can be optimal for risk-averse investors who face portfolio constraints. In particular, while the strategy of placing bonds in the tax-deferred account maximizes the expected level of tax benefit, it may lead to volatile benefits under different realizations of stock returns. By holding a similar portfolio in both accounts, investors can achieve a more balanced growth in the two accounts, minimize the likelihood of violating the constraints in the future and hence “smooth” the volatility of the tax benefit. For some risk-averse investors, this smoothing motive can lead to the observed violation of the pecking order location rule. Our model predicts that such violations are more likely when future tax benefits are more volatile, which can occur, for example, when: (i) the tax rate differential across assets increases over time due either to tax law changes or to tax bracket changes for investors; (ii) asset returns are more volatile; and (iii) investors anticipate large future liquidity needs.     

Truthful mechanism design for multidimensional scheduling via cycle monotonicity

We consider the makespan-minimization problem on unrelated machines in the context of algorithmic mechanism design. No truthful mechanisms with non-trivial approximation guarantees are known for this multidimensional domain. We study a well-motivated special case (also a multidimensional domain), where the processing time of a job on each machine is either “low” or “high.” We give a general technique to convert any c-approximation algorithm (in a black-box fashion) to a 3c-approximation truthful-in-expectation mechanism. Our construction uses fractional truthful mechanisms as a building block, and builds upon a technique of Lavi and Swamy [Lavi, R., Swamy, C., 2005. Truthful and near-optimal mechanism design via linear programming. In: Proc. 46th FOCS, pp. 595–604]. When all jobs have identical low and high values, we devise a deterministic 2-approximation truthful mechanism. The chief novelty of our results is that we do not utilize explicit price definitions to prove truthfulness. Instead we design algorithms that satisfy cycle monotonicity [Rochet, J., 1987. A necessary and sufficient condition for rationalizability in a quasilinear context. J. Math. Econ. 16, 191–200], a necessary and sufficient condition for truthfulness in multidimensional settings; this is the first work that leverages this characterization.     

Beyond the Linearity Critique: The Knife-edge Assumption of Steady-state Growth

The “linearity critique” of endogenous growth models is presented in a general context of an arbitrary growth model and reassessed. It is argued that presence of linearities is not a valid criterion for rejecting growth models. Existence of exponential/geometrical steady-state growth (i.e. of a balanced growth path with strictly positive growth rates) necessarily requires some knife-edge condition which is not satisfied by typical parameter values. Hence, balanced growth paths are fragile and sensitive to smallest disturbances in parameter values. Adding higher order differential/difference equations to a model does not change the knife-edge character of steady-state growth.     

Imitation processes with small mutations

This note characterizes the impact of adding rare stochastic mutations to an “imitation dynamic,” meaning a process with the properties that absent strategies remain absent, and non-homogeneous states are transient. The resulting system will spend almost all of its time at the absorbing states of the no-mutation process. The work of Freidlin and Wentzell [Random Perturbations of Dynamical Systems, Springer, New York, 1984] and its extensions provide a general algorithm for calculating the limit distribution, but this algorithm can be complicated to apply. This note provides a simpler and more intuitive algorithm. Loosely speaking, in a process with K strategies, it is sufficient to find the invariant distribution of a K×K Markov matrix on the K homogeneous states, where the probability of a transit from “all play i” to “all play j” is the probability of a transition from the state “all agents but 1 play i, 1 plays j” to the state “all play j”.     

Creative capital,information and communication technologies,and economic growth in smart cities

ABSTRACT

We study aspects of economic growth in a stylized smart city with two distinct features. First, the modeled inhabitants of this city are smart because they possess skills. Using the language of Richard Florida, these inhabitants comprise the city’s creative class and hence they possess creative capital. Second, the city is smart because it uses information and communication technologies (ICTs) and we model one specific kind of ICT use. In this setting, we first derive expressions for three growth related metrics. Second, we use these metrics to show that the economy of smart city A converges to a balanced growth path (BGP). Third, we compute the growth rate of output per effective creative capital unit on this BGP. Fourth, we study how heterogeneity in initial conditions affects outcomes on the BGP by introducing a second smart city B into the analysis. At time t?=?0 two key savings rates in city A are twice as large as in city B. We compute the ratio of the BGP value of income per effective creative capital unit in city A to its value in city B. Finally, we compute the ratio of the BGP value of skills per effective creative capital unit in city A to its value in city B.     

Intergenerational natural-capital equality in an overlapping-generations model with logistic regeneration

Following Mourmouras [Scandinavian Journal of Economics 93 (1991): 585–591], in a Diamond [American Economic Review 55 (1965): 1126–1150] type overlapping-generations model with renewable natural resources a competitive path of manmade capital accumulation exists which meets the sustainability criterion of intergenerational natural-capital equ(al)ity (= sustainable growth). The alleged compatibility of decentralized optimization with natural-capital sustainability is appealing, but the rel-evance of this compatibility result is questionable: the growth factor of the renewable natural resource is assumed to be independent of the resource stock. Employing instead a nonlinear (logistic) regeneration function, this paper reconsiders Mourmouras' compatibility statement in another natural environment. It is shown that only under a certain complex relationship between the parameters of the utility, production, and natural-growth function does a nontrivial stationary state exist which is saddle-point stable. It exhibits by definition intergenerational natural-capital equality, but the non-linear setting precludes in general, natural-capital equality across generations on the growth path towards the stationary state.