Analysts associated with the Cowles Commission attached great importance to the distinction between structural and reduced-form models: in their view structural models, but not reduced-form models, allow the analysis of causal relations. They did not present clear justification for this view....

Analysts associated with the Cowles Commission attached great importance to the distinction between structural and reduced-form models: in their view structural models, but not reduced-form models, allow the analysis of causal relations. They did not present clear justification for this view....

In continuous-time stochastic calculus a limit in probability is used to extend the definition of the stochastic integral to the case where the integrand is not square-integrable at the endpoint of the time interval under consideration. When the extension is applied to portfolio strategies,...

markets, as well as predictions for optimal default by borrowers.

Recent years have seen a protracted debate on the "fiscal theory of the price level". This doctrine is based on the intertemporal government budget constraint, which says that the real value of the government debt equals the discounted value of future government surpluses. It is observed that...

The single most important proposition in economic theory, first stated by Adam Smith, is that competitive markets do a good job allocating resources. Vilfredo Pareto’s later formulation was more precise than Smith’s, and also highlighted the dependence of Smith’s proposition on assumptions...

Bubbles, such as money, cannot be valued in efficient equilibria in overlapping generations models (a borderline case aside). Analysts frequently attribute this result to the fact that if bubbles were valued, the bubble must eventually exceed the endowment of the young. This implies negative...

Mortgage lenders impose a default premium on the loans they originate to compensate for the possibility that borrowers won’t make payments. The housing boom of the 2000s was characterized by increasing riskiness of the borrowers approved for mortgages and the structures of the loans...