But, for people in the industry, it also denotes real expertise.
( {H}_t ) is the household's total financial assets, ( {c}_t ) denotes real cash balances, ( {d}_t ) deposits, and ( {m}_t ) real mobile money balances ( {d}_t=0 ) for households without bank accounts.
The real (CPI-deflated) per capita value of end-of-period government debt, (b_{t}equiv B_{t}/P_{t}), evolves according to a standard debt accumulation equation, begin{aligned} b_{t}=frac{R_{t-1}}{pi _{t}}b_{t-1}+PD_{t}, end{aligned}where (PD_{t}) denotes real (CPI-deflated) per capita primary deficit.
Boldface lower-case letters denote vectors, ∗ stands for complex conjugate, T represents transpose, H represents conjugate transpose, E. is used for expectation, ∥·∥ denotes the Euclidean vector norm, CN 0,N0) denotes the set of Gaussian distributed complex numbers with the standard variance of N0 (i.e., 0.5 N0 per dimension), and Re denotes real part.
where (mathbf {phi } = [phi _{1}, phi _{2}, ldots, phi _{N}]^{T} in mathbb {R}^{N}), (mathbb {R}^{N} ) denotes real N-space and Re and Im represent the real and imaginary part of a complex number, respectively (see the derivation in Appendix B).
The dynamic IS curve summarizes the aggregate goods demand in the economy: begin{aligned} y_t^{mathrm{d}}=psi Ey_{t+1}^{mathrm{d}} + (1-psi ) y_{t-1}^{mathrm{d}} - alpha (i_t-E pi _{t+1}-overline{r}) - eta d_t^{{{mathrm{P}}}} + v_t^{mathrm{d}} end{aligned} (1)in which y denotes (real) output, i the short-term nominal interest rate, (pi) the rate of inflation in the general price level.
Suppose that,, where and each denote real coefficient symmetric filters,,,, and.
and both subscripts R and I denote real and imaginary parts, respectively.
Let (Y_{t}^{tot}) and (Y_{t}^{tot,*}) denote real (PPI-deflated) per capita GDP in the home and foreign country, respectively.
We use the symbols Ξ, K, and H to denote real separable Hilbert spaces, with scalar products ((cdot,cdot)_{Xi}), ((cdot,cdot)_{K}), and ((cdot,cdot)_{H}), respectively.
However, the efficacy of psychological interventions has been shown in randomised controlled trails, therefore suggesting that these changes could denote real treatment effects.
