1. IT WAS a great achievement of Gibrat2 to show that the distribution of the logarithms of some economic variates (for instance, the distribution of factories according to the number of workers) is approximately normal. The explanation of this phenomenon by Gibrat may be presented in a rigorous form as follows: Let us denote the variate X (for instance the number of workers in a factory) at a certain date by XO. Let us further assume that subsequently it undergoes a series of random independent proportionate changes mi, M2, *, mn, (Gibrat's loi de l'effet proportionnel).3 Thus at the end of the period in which these changes have taken place the value of the variate will have become XO(1+ml)(1M+m2) * (1 ++m,) and its natural logarithm=log Xo+log (1+ml)+log (1+m2)+ + +log (1 +mn). If we denote the deviation from the mean of log XO by Yo and the deviation from the mean of log (l+mk) by yk, the deviation from the mean of this expression becomes YO+yl+Y2+ +Yn. The absolute value of mk may be assumed small as compared with 1. It follows that the absolute value of log (1 +mk) and consequently that of yk is also small as compared with 1. As the second moment of yl+y2+ * +y. is equal to the sum of the second moments of Y1, Y2, * .., yn, it may be assumed that if n is sufficiently large the standard deviation of Yl+y2+ * +yn is equal to or greater than 1 (provided the standard deviation of yn does not fall below a certain level as n increases.) Thus yk is small as compared with the standard deviation of Yl+Y2+ +Yn. With this condition fulfilled the distribution of Yl+Y2+ +y,, is approximately normal (according to the Laplace-Liapounoff theorem4). Further if n is so large that the standard deviation of yl+y2+ + yn is large as compared with the standard deviation of Yo also, the distribution of Yo+yl+y2+ * * * +yn will not differ much from normality. Whatever the distribution of Y at the initial date, with the lapse of time it approaches normality more and more. 2. This argument is formally correct but it may be shown that its

CERTAIN questions have arisen' concerning my macrodynamic theory of business cycles2 which I consider of sufficient importance to warrant a detailed answer. I also wish to complete some parts of my original study which I think were presented too briefly. 1. Tinbergen makes the statement concerning my original article that, remarkably enough, prices do not appear at all in the theory.3 It can be easily shown that in reality my basic equation implies the dependence of investment activity on the ratio of prices to wages. My basic equation was4

Many time series exhibit “long memory”: Their autocorrelation function decays slowly with lag. This behavior has traditionally been modeled via unit roots or fractional Brownian motion and explained via aggregation of heterogeneous processes, nonlinearity, learning dynamics, regime switching, or structural breaks. This paper identifies a different and complementary mechanism for long‐memory generation by showing that it can naturally arise when a large number of simple linear homogeneous economic subsystems with short memory are interconnected to form a network such that the outputs of the subsystems are fed into the inputs of others. This networking picture yields a type of aggregation that is not merely additive, resulting in a collective behavior that is richer than that of individual subsystems. Interestingly, the long‐memory behavior is found to be almost entirely determined by the geometry of the network, while being relatively insensitive to the specific behavior of individual agents.

This paper investigates relational incentive contracts with a continuum of privatelyobserved agent types that are persistent over time.For a sufficiently productive relationship, a full pooling contract exists in which all agent types continuing the relationship choose the same action.When some separation is feasible, the parties can do better than with full pooling.When future actions are optimal, however, full separation of all types is not possible.There is, though, an equilibrium with separation into pools each containing a non-degenerate interval of types and fully separating individual types is not generally optimal.Separation results in an increase in output.

This paper introduces a general method to convert a model defined by moment conditions involving both observed and unobserved variables into equivalent moment conditions involving only observable variables. This task can be accomplished without introducing infinite-dimensional nuisance parameters using a least-favourable entropy-maximising distribution. We demonstrate, through examples and simulations, that this approach covers a wide class of latent variables models, including some game-theoretic models and models with limited dependent variables, interval-valued data, errors-in-variables, or combinations thereof. Both point- and set-identified models are transparently covered. In the latter case, the method also complements the recent literature on generic set-inference methods by providing the moment conditions needed to construct a GMM-type objective function for a wide class of models. Extensions of the method that cover conditional moments, independence restrictions and some state-space models are also given.