Two revised papers

I have thoroughly revised two papers, and I believe they have substantially improved. So I uploaded them to my file repository to make them accessible.

The first one is “The scope for ideological bias in structural macroeconomic models”. It can be downloaded here. This is the abstract:

ABSTRACT:  This paper studies the trade-offs that an expert with ideological biases faces in designing his model. I assume the perceived model must be autocoherent, in that its use by all agents delivers a self-confirming equilibrium. The exercise is carried in the context of a simplified AS-AD model, where in principle the expert can influence policy by manipulation a number key parameters, including in particular the Keynesian multiplier, the Phillips curve parameters, and the variances of supply and demand shocks. The analysis suggests that ideological bias may arise in the construction of macroeconomic models, in a way that resembles well-known historical controversies. Typically, for example, a larger reported Keynesian multiplier is favored by more left-wing economists, as is a flatter inflation output trade-off.
Another important aspect of the analysis is that autocoherence conditions imply constraints and trade-offs between parameters. For example a larger reported Keynesian multiplier must be associated with a lower interest elasticity of aggregate demand for the economists’s model to match the data. Also, some parameters or some combinations of parameters must be truthfully revealed for the expert to remain autocoherent. These are the parameters that are “identified” from the empirical moments of the distribution of observables. This illustrates the tight link between parameter identification and the scope for bias that is generated by the autocoherence conditions.

The second revised paper is “A quantized approach to rational inattention”. It is downloadable here.

Here is an excerpt from the Introduction:

In this paper, I study optimal behavior under rational inattention when one imposes the constraint that agents must follow deterministic rules. The idea is that the choice variable may be a deterministic function of an exogenous shock with continuous support and still make use of a finite amount of information if the choice variable is discrete rather than continuous; that is, the mapping from the realization of the exogenous variables to the endogenous ones is piece-wise constant, reflecting the fact that the agent can only elect a finite number of values for the choice variable, because of the informational constraint.
Thus, limited information is now a source of lumpiness in behavior, rather than a source of noise. The state space faced by the agent is partitioned into clusters and all points in the same cluster yield the same action. Of course, limited information is not the only source of lumpy behavior; it is well known that there are other sources, such as fixed or linear adjustment costs. But the approach proposed here yields many potentially testable predictions: In general, we expect that the greater the information processing ability of an economic entity, the less lumpy its behavior.
Section 2 provides some preliminary results. Under a deterministic assignment, the mutual information between the exogenous and endogenous variables is simply equal to the entropy of the endogenous variable. This property, which is evident in the discrete case, is extended to the case of a continuous exogenous variable and a discrete endogenous variable. It is then shown that, for preferences satisfying a generalized single-crossing condition, optimal clusters are typically convex. In the one dimensional case, they will be intervals. Consequently, agents will pursue behaviorial rules that has been studied in the information theory literature under the name of entropy-coded quantization (ECG). That is, they partition the set of realizations of the exogenous variable into intervals, assign a constant value of the endogenous variable to each interval, and determine the optimal partitioning and assignment by maximizing their utility subject to a constraint on the entropy of the endogenous variable. Next, some discussion is provided about the allocation of attention across clusters, based on optimality conditions that were derived in Farvardin and Modestino (1984).
Finally, some results are provided regarding the quadratic case, that will be used in the application to price-setting. First, I show that the size of clusters goes to zero when information capacity becomes infinite, which is not obvious if the support of the exogenous variable is unbounded. Second, I discuss and numerically tabulate optimal clustering in the standardized normal case, from which optimal clustering for any normal distribution can be straightforwardly derived. A interesting aspect is that it is optimal to devote considerable attention to the tails of the distribution.
Section 3 applies this to a static New Keynesian model of optimal price setting when there are aggregate money shocks as well as idiosyncratic productivity shocks. The effect of aggregate money shocks on output and prices is studied. The main result of the paper, Theorem 3, shows that as the variance of idiosyncratic shocks become large, the aggregate log price level converges to a linear function of the aggregate money shock, with a coefficient which is strictly between 0 and 1. Consequently, unanticipated aggregate money shocks have real effects on output, in contrast to the sticky price model of Caplin and Spulber (1986). But these effects are smaller than in standard rational inattention models or in the Lucas (1972) misperception model.

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