Productivity levels and growth are extremely heterogeneous among firms. A vast literature has developed to explain the origins of productivity shocks, their dispersion, evolution and their relationship to the business cycle. We examine in detail the distribution of labor productivity levels and growth, and observe that they exhibit heavy tails. We propose to model these distributions using the four parameter Lévy stable distribution, a natural candidate deriving from the generalised Central Limit Theorem. We show that it is a better fit than several standard alternatives, and is remarkably consistent over time, countries and sectors. In all samples considered, the tail parameter is such that the theoretical variance of the distribution is infinite, so that the sample standard deviation increases with sample size. We find a consistent positive skewness, a markedly different behaviour between the left and right tails, and a positive relationship between productivity and size. The distributional approach allows us to test different measures of dispersion and find that productivity dispersion has slightly decreased over the past decade.

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Economics has seen a recent rise in interest in information theory as an alternative framework to the conventional notion of equilibrium as a fixed state, such as Walrasian marketclearing general equilibrium. The information theoretic approach is predicated on the notion of statistical equilibrium (SE) that takes a distribution over all possible states as an equilibrium, and therefore predicts the endogenous fluctuations of the system along with its central tendency simultaneously. For this reason, SE approaches can explain the observed data without relying on arbitrary assumptions about random noise and provide useful insights for many interesting economic problems that conventional methods have not been able to satisfactorily deal with. In this paper, we review the key elements of information theory focusing on the notions and applications of entropy and SE in economics, particularly paying attention to how entropy concepts open up a new frontline of economic research.

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This paper studies the pattern of technical change at the firm level by applying and extending the Quantal Response Statistical Equilibrium model (QRSE). The model assumes that a large number of cost minimizing firms decide whether to adopt a new technology based on the potential rate of cost reduction. The firm in the model is assumed to have a limited capacity to process market signals so there is a positive degree of uncertainty in adopting a new technology. The adoption decision by the firm, in turn, makes an impact on the whole market through changes in the factor-price ratio. The equilibrium distribution of the model is a unimodal probability distribution with four parameters, which is qualitatively different from the Walrasian notion of equilibrium in so far as the state of equilibrium is not a single state but a probability distribution of multiple states. This paper applies Bayesian inference to estimate the unknown parameters of the model using the firm-level data of seven advanced OECD countries over eight years and shows that the mentioned equilibrium distribution from the model can satisfactorily recover the observed pattern of technical change.