RDP 2010-01: Reconciling Microeconomic and Macroeconomic Estimates of Price Stickiness Equation

\begin{array}{l} l_{t} = \sum_{j = 1}^{N} l_{j, t}^{d} \\ {\tilde{y}}_{t} = {\tilde{c}}_{t} + {\tilde{m}}_{t}^{d} \\ {\tilde{m}}_{t}^{d} = \sum_{j = 1}^{N} {\tilde{m}}_{j, t}^{d} \\ 1 = \sum_{j = 1}^{N} γ_{j} r_{j, t}^{1 - ε} . \end{array}