2,115 research outputs found
Reconciling econometrics with continuous maximum-entropy models
In the study of economic networks, econometric approaches interpret the
traditional Gravity Model specification as the expected link weight coming from
a probability distribution whose functional form can be chosen arbitrarily,
while statistical-physics approaches construct maximum-entropy distributions of
weighted graphs, constrained to satisfy a given set of measurable network
properties. In a recent, companion paper, we integrated the two approaches and
applied them to the World Trade Web, i.e. the network of international trade
among world countries. While the companion paper dealt only with
discrete-valued link weights, the present paper extends the theoretical
framework to continuous-valued link weights. In particular, we construct two
broad classes of maximum-entropy models, namely the integrated and the
conditional ones, defined by different criteria to derive and combine the
probabilistic rules for placing links and loading them with weights. In the
integrated models, both rules follow from a single, constrained optimization of
the continuous Kullback-Leibler divergence; in the conditional models, the two
rules are disentangled and the functional form of the weight distribution
follows from a conditional, optimization procedure. After deriving the general
functional form of the two classes, we turn each of them into a proper family
of econometric models via a suitable identification of the econometric function
relating the corresponding, expected link weights to macroeconomic factors.
After testing the two classes of models on World Trade Web data, we discuss
their strengths and weaknesses.Comment: 18 pages, 3 figures, 2 table
Counterfactual Sensitivity and Robustness
Researchers frequently make parametric assumptions about the distribution of
unobservables when formulating structural models. Such assumptions are
typically motived by computational convenience rather than economic theory and
are often untestable. Counterfactuals can be particularly sensitive to such
assumptions, threatening the credibility of structural modeling exercises. To
address this issue, we leverage insights from the literature on ambiguity and
model uncertainty to propose a tractable econometric framework for
characterizing the sensitivity of counterfactuals with respect to a
researcher's assumptions about the distribution of unobservables in a class of
structural models. In particular, we show how to construct the smallest and
largest values of the counterfactual as the distribution of unobservables spans
nonparametric neighborhoods of the researcher's assumed specification while
other `structural' features of the model, e.g. equilibrium conditions, are
maintained. Our methods are computationally simple to implement, with the
nuisance distribution effectively profiled out via a low-dimensional convex
program. Our procedure delivers sharp bounds for the identified set of
counterfactuals (i.e. without parametric assumptions about the distribution of
unobservables) as the neighborhoods become large. Over small neighborhoods, we
relate our procedure to a measure of local sensitivity which is further
characterized using an influence function representation. We provide a suitable
sampling theory for plug-in estimators and apply our procedure to models of
strategic interaction and dynamic discrete choice
Hybrid Behaviour of Markov Population Models
We investigate the behaviour of population models written in Stochastic
Concurrent Constraint Programming (sCCP), a stochastic extension of Concurrent
Constraint Programming. In particular, we focus on models from which we can
define a semantics of sCCP both in terms of Continuous Time Markov Chains
(CTMC) and in terms of Stochastic Hybrid Systems, in which some populations are
approximated continuously, while others are kept discrete. We will prove the
correctness of the hybrid semantics from the point of view of the limiting
behaviour of a sequence of models for increasing population size. More
specifically, we prove that, under suitable regularity conditions, the sequence
of CTMC constructed from sCCP programs for increasing population size converges
to the hybrid system constructed by means of the hybrid semantics. We
investigate in particular what happens for sCCP models in which some
transitions are guarded by boolean predicates or in the presence of
instantaneous transitions
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