Random walk to innovation: why productivity follows a power law

In this paper we propose a mechanism generating innovations with productivity distributed according to a power law. We assume that knowledge creation occurs as new ideas are produced from combinations of existing ideas. The productivity of an innovation is determined by an unobservable intrinsic component as well as by the productivity of the parent ideas and their parents, thus generating a network of spillovers. The second important feature is that the innovator has no global information on the network of parenthood links across ideas but has acces to local knowledge, as for example the list of cited references in a patent. The optimal behaviour of the innovator is to "walk randomly" through the network of "citations" as this algorithm leads to selecting highly connected parent nodes. We show that the distribution of productivity resulting from this optimal behaviour follows a power law. The intuition behind the result is that the innovator focuses his efforts on strengthening local spillovers because he has no command on the other sources of productivity. When this process of innovation is imbedded in a model a la Kortum (1997) balanced growth of output is generated.

Wealth inequality and dynamic stability

In this paper we explore the link between wealth inequality and stability in a two-sector neoclassical growth model with heterogeneous agents. The stability of the steady state depends on the various parameters of the model and in particular on individual preferences. We show that when consumers have identical preferences and the inverse of absolute risk aversion (or risk tolerance) is a strictly convex function, inequality is a factor that favors instability. In the opposite case, inequality favors stability. Our characterization also shows that whenever absolute risk tolerance is linear, as when preferences exhibit hyperbolic absolute risk aversion (HARA), wealth heterogeneity is neutral. As there is not yet evidence on the concavity of absolute risk tolerance, our results unfortunately do not lead to a unique conclusion on the sign of the effect of wealth inequality on stability.Economic growth; Heterogeneity; Wealth and Income Inequality; Instability

Expectations in an OG Economy

Dynamic economic models usually describe the path of economic variables as prices, consumption or capital at equilibrium. The most popular models assume that agents have perfect foresight. Implicitly this assumption requires that agents can compute the complete infinite path, an exercise that requires to solve a system of equations involving an infinite num- ber of equations and unknowns. Equivalently, one could assume that there is a well behaved and fast mechanism driving the economy to the temporary equilibrium. A major difficulty is that the behavior of the consumers in any given period depends on the present and all the fu- ture prices. In the paper, we consider an overlapping generation model in which the consumers form expectations using truncated versions of the model. The mechanism of price adjustment may then be analyzed. Both the expectational dynamics, as treated in Balasko (1994), and the Wal- ras’s tatonnement, as in Hens (1997), are considered. Sufficient conditions for stability of the perfect foresight equilibrium within these price forma- tion mechanisms are derived. We also discuss the issue of the robustness of the results to parameters used in the truncation.expectations, learning, overlapping generations, computation of equilibria.

Are Patent Citations Driven by Quality?

The present paper builds a simple model of patent citations not based on the rich-get-richer aspect of preferential attachment. In our model the dynamics of citations are driven by known heterogeneities in the applicability of existing patents and aging. The model matches closely the hazard rates of citations for the vast majority of patents in a random sample of patents granted by the USPTO between 1975 and 1999. Furthermore, we show that the long run distribution of patent citations is well fitted when the distribution of applicability across patents follows a Gamma-distribution.We also discuss the possibility that popularity of patents might influence citation decisions if innovators are not perfectly informed about patents' applicability. We find that popularity matters but the size of the effect is very small. Finally, the possibility to distinguish between citations to patents within the same class and to different classes allows us to show that the magnitude of the influence of popularity is increasing in technological distance.

Keeping up with the neighbours: social interaction in a market economy

We consider a world in which individuals have private endowments and trade in markets, while their utility is sensitive to the consumption of their neighbors. Our interest is in understanding how social structure of comparisons, taken together with the familiar fundamentals of the economy � endowments, technology and preferences � shapes equilibrium prices, allocations and welfare. We find that equilibrium prices and allocations depend on average individual centrality in the social network. As we add links to a social network, the centralities rise and this pushes up prices of the socially sensitive good. Newly linked agents demand more of the socially sensitive good, while the reverse happens with regard to the standard good. We derive a formula to compute the critical link, i.e., the new link which maximizes price increase. We then turn to a model with heterogenous endowments, and find that inequality in network centrality and in wealth inequality reinforce each other. Thus a transfer of resources from less to more central agents raises prices of the socially sensitive good and alters allocations and utilities of all agents. We show by example that poor individuals lose utility while rich individuals gain utility as society moves from segregation to integration.

When Veblen meets Krugman

We introduce relative concerns in the form of conspicuous consumption in a standard economic geography model a la Krugman. The primary intuition is that conspicuous consumption imposes a negative externality on some agents and generates a centrifugal force. We show that this is not always the case as the relative concern also rises the demand for the sophisticated good, strengthening the standard centripetal market size effect. We show that the resulting force is very sensitive to the topology of the network of "conspicuous" links in each region and on the level of economic integration. For instance, with relatively large shares of income devoted to the consumption of the standard good, we show that when trade is moderately costly and classes of workers are segregated, relative concerns tends to stabilize the symmetric equilibrium; on the other hand, if workers of different classes interact via their relative concerns, conspicuous consumption is a centripetal force generating stable fully or partially agglomerated equilibria. Finally, when the level of integration is high, the intuition holds and even small relative concerns destabilize the full agglomeration equilibrium, which is stable in the Krugman model

The Economic Effects of Restrictions on Government Budget Deficits: Imperfect Privte Credit Markets

We consider a pure-exchange overlapping-generations model We consider a pure-exchange overlapping-generations model with many consumers per generation and many goods per period. As in Ghiglino and Shell (2000), there is a government that collects taxes, distributes transfers and faces budget deficit restrictions. We introduce, for realism and symmetry with the government, imperfection in the private credit markets. We find that with constraints on individual credit and anonymous (i.e., non-personalized) lump-sum taxes, strong (or 'global') irrelevance of the government budget deficit is not possible, and weak irrelevance can hold only in very special situations. With credit constraints and anonymous consumption taxes, weak irrelevance holds provided the number of tax instruments is sufficiently large and at least one consumer's credit constraint is not binding.

The role of the wealth distribution on output volatility

We explore the link between wealth inequality and business cycle fluctuations in a two-sector neoclassical growth model with endogenous labor and heterogeneous agents. Assuming that wealth inequality is described by the distribution of shares of capital, we show that in the most plausible situations wealth equality is a stabilizing factor. In particular, when wealth is Pareto distributed and preferences generate non-linear absolute risk tolerance indices, a rise in the Gini index may only be associated to a rise in volatility. When individual preferences are such that the individual absolute risk tolerance indices are linear, as with HARA utility, even a low level of taste heterogeneity ensures that a rise in inequality may not reduce volatility, and this independently of the wealth distribution. Finally, we note that such a clear result is at odd with the existing related literature.

The role of the wealth distribution on output volatility

We explore the link between wealth inequality and business cycle fluctuations in a two-sector neoclassical growth model with endogenous labor and heterogeneous agents. Assuming that wealth inequality is described by the distribution of shares of capital, we show that in the most plausible situations wealth equality is a stabilizing factor. In particular, when wealth is Pareto distributed and preferences generate non linear absolute risk tolerance indices, a rise in the Gini index may only be associated to a rise in volatility.When individual preferences are such that the individual absolute risk tolerance indices are linear, as with HARA utility, even a low level of taste heterogeneity ensures that a rise in inequality may not reduce volatility, and this independently of the wealth distribution.Finally, we note that such a clear result is at odd with the existing related literature.Wealth Inequality, Pareto distribution, Gini index, Elastic Labor Supply, Macroeconomic Volatility, Endogenous Equilibrium Business Cycles.

The impact of heterogeneity on indeterminacy

The aim of the paper is to explore the link between agent's heterogeneity and indeterminacy in a general equilibrium economy. The framework is provided by the two-sector growth model with technological externalities of Boldrin and Rustichini (1994) in which heterogeneous agents are introduced. We first show that the occurrence of indeterminacy depends on the distribution in labor endowments and in shares on initial capital among the agents as well as on preferences and technology. We find that the sign of the effect of heterogeneity on indeterminacy is not pinned down by the standard properties of preferences, a fact that might be surprising in view of some recent results (as in Herrendorf et al. (2000)). However, when risk aversion is a concave or a slightly convex function, the heterogeneity is a factor that opposes the external effects in generating indeterminacy.Endogenous growth; Heterogeneity; Indeterminacy; Inequalities