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A “Local” Model of the Firm: Sticky prices and the Phillips Curve

Daley, Clayton (2007): A “Local” Model of the Firm: Sticky prices and the Phillips Curve.

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Assume a firm concerns itself exclusively with local shocks (copious citations including Lucas 1972 and Bomhoff 1983 validate that this type of assumption may be reasonable). Changes in a firm's production policy should occur when the actual demand in a period Dt suggests that the underlying demand function has shifted from expected demand E(Dt). Since firms face uncertainty, this is non-trivial and they must find a way to determining (given information from a single, current period) whether or not the underlying demand has changed or whether the firm has simply obtained a draw from its expected demand distribution.

In a simplified model, a firm can use a concept similar to a Statistical Hypothesis Test on E(Dt) = Dt to come to this conclusion. Rather than select an arbitrary confidence threshold (alpha), a firm can reverse the process and use the "marginal" alpha (where the hypothesis is just rejected or accepted) as its confidence that the mean has changed, allowing it to update its expectations to E(Dt+1) = (1-a) * E(Dt) + a * (Dt) and price accordingly. By weighting new demand information using this "confidence factor," the model introduces significant and persistent rigidity around NAIRU/equilibrium.

This model is also powerful because it explains the qualified success of threshold like behaivor in classical "menu cost" theories (as the threshold reflects the classic hypothesis test strategy), behavior similar to a learning model (via the weighted introduction of new data) and seeming information lags (via the low confidence in new information immediately after shifts), among others.

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