RDP 9511: Superannuation and Saving Equation (10)

\begin{array}{l} \begin{array}{l} Δ {\frac{⌈ S^{n} ⌉}{⌊ y ⌋}}_{t} = ϕ + Σ_{b = 0}^{k} β_{b} Δ {\frac{⌈ S^{s} ⌉}{⌊ y ⌋}}_{t - b} + Σ_{c = 1}^{k} β_{c} Δ {\frac{⌈ S^{n} ⌉}{⌊ y ⌋}}_{t - c} + Σ_{d = 0}^{k} β_{d} Δ {\frac{⌈ {\hat{y}}_{L} ⌉}{⌊ y ⌋}}_{t - d} + Σ_{e = 0}^{k} β_{e} Δ {\frac{⌈ A ⌉}{⌊ y ⌋}}_{t - e} \\ + Σ_{f = 1}^{k} β_{f} r_{t - f} + Σ_{g = 1}^{k} β_{g} Δ D_{t - g} + Σ_{h = 1}^{k} β_{h} Δ {\tilde{Y}}_{t - h} + Σ_{i = 1}^{k} β_{i} Δ Π_{t - i} + Σ_{j = 1}^{k} β_{j} Δ U_{t - j} \end{array}} s h o r t r u n \\ \begin{array}{l} + α_{1} {\frac{⌈ A ⌉}{⌊ y ⌋}}_{t - 1} + α_{2} {\frac{⌈ {\hat{y}}_{L} ⌉}{⌊ y ⌋}}_{t - 1} + α_{4} D_{t - 1} + α_{6} Π_{t - 1} + α_{7} U_{t - 1} \\ + (α_{8} - 1) {\frac{⌈ S^{s} ⌉}{⌊ y ⌋}}_{t - 1} + γ {\frac{⌈ S^{n} ⌉}{⌊ y ⌋}}_{t - 1} + ε_{t} \end{array}} L o n g r u n \end{array}