The name is absent

In light of equation (32), unconditional loss is given by

tr[pω] +   ∖tr [nⁱpnς] ,

1 — p L -I

where p (s_t) denotes the density function for s_t and Ω represents the unconditional variance
of s_t. The performances shown in Figure IA were calculated using (1 — β)L_t, while those in
Figure IB were calculated using (1 — β)L.

Rather than integrate with respect to the entire state, s_t, as equation (35) does, I propose
to integrate with respect to q_t conditional on x_t, and to evaluate timeless perspective policies
where p (q_t∖x_t) denotes the density function for q_t conditional on x_t. To evaluate this integral,
partition Ω (and subsequently M_ss and P) conformably with x_t and q_t, then the mean and
variance of q_t conditional on x_t, are given by

^qt = Ωq_xΩ_x3^^xt,                                    ⁽³7⁾

^q_t ∣χ_t = Ωqq^-ΩqχΩ^χ∙XΩχq^{,                           (3}8⁾

and equation (36) is equivalent to

Lt = xt (Pxx + PχqΩqχΩχX + Ω^χX^lΩqχPqχ) xt + tr [P_qqΩ_qt∣χ] +ɪtr [NPN∑] . (39)

Equation (39) contains three terms. The first and third terms represent the penalties
attributable to the known initial state and to the stochastic shocks, respectively. The second
term represents the penalty associated with the conditional variance of the auxiliary states
that are introduced by timeless perspective policymaking. By integrating out the auxiliary
state variables, equation (39) measures average loss for a given state, x_t. In the absence of
any auxiliary states, equation (39) is equivalent to equation (32). Further, in the limit as
P ↑ 1, equation (39) converges to equation (35).

Before leaving this section, it is worth noting that policy performance, as assessed by equa-
tion (39), is invariant to how the timeless perspective equilibrium is represented, unaffected
by the particular choice of d_t or by the fact that G^χl may not be unique. To understand
why, note that the substantive difference between the optimal commitment equilibrium and

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