Reference: Olivier Blanchard, Jonathan D. Ostry, Atish R. Ghosh, and Marcos Chamon (2015): Expansionary or contractionary effects of capital inflows: It depends what kind: "Some scholars view capital inflows as contractionary, but many policymakers view them as expansionary. Evidence supports the policymakers.... For a given policy rate, bond inflows lead to currency appreciation and are contractionary, while non-bond inflows lead to an appreciation but also to a decrease in the cost of borrowing, and thus may be expansionary..."
A bond inflow is: a $ {\Delta}{\epsilon}_o < 0 $
A non-bond inflow is:
So holding i constant:
$ {\Delta}Y = {\mu}(x_{\epsilon}{\Delta}{\epsilon}_o - (I_r + x_{\epsilon}{\epsilon}_r){\Delta}{\rho}) $
Basic Model:
$ Y = C + I + G + NX $
$ C = c_o + c_y(1-t)Y $
$ I = I_o - I_rr $
$ G $
$ NX = GX - IM $
$ IM = im_y $
$ GX = x_fY^f + x_{\epsilon}{\epsilon} $
$ {\epsilon} = {\epsilon}_o + {\epsilon}_r(r^f - r) $
$ r = i + {\rho} - {\pi} $
$ MPE = c_y(1-t) - im_y $
$ \mu = \frac{1}{1 - MPE} $
$ A_o = [c_o + I_o + G] + [x_fY^f + x_{\epsilon}{\epsilon}_o + x_{\epsilon}{\epsilon}_rr^f] $
$ Y = \mu(A_o - (I_r + x_{\epsilon}{\epsilon}_r)r) $