872:
The above discussion assumed a static world in which policy actions and outcomes for only one moment in time were considered. However, the analysis generalizes to a context of multiple time periods in which both policy actions take place and target variable outcomes matter, and in which time lags in
845:
The above analysis of one target variable and one policy tool can readily be extended to multiple targets and tools. In this case a key result is that, unlike in the absence of multiplier uncertainty, it is not superfluous to have more policy tools than targets: with multiplier uncertainty, the more
877:
context with multiplier uncertainty, a key result is that the "certainty equivalence principle" does not apply: while in the absence of multiplier uncertainty (that is, with only additive uncertainty) the optimal policy with a quadratic loss function coincides with what would be decided if the
576:
863:
apply: under certain conditions, the optimal portfolios of all investors regardless of their preferences, or the optimal policy mixes of all policy makers regardless of their preferences, can be expressed as linear combinations of any two optimal portfolios or optimal policy mixes.
67:
with additive uncertainty, its presence causes greater cautiousness to be optimal (the policy tools should be used to a lesser extent). (2) In the presence of multiplier uncertainty, it is no longer redundant to have more policy tools than there are targeted economic variables. (3)
858:
involving multiple investment choices having rate-of-return uncertainty. The usages of the policy variables correspond to the holdings of the risky assets, and the uncertain policy multipliers correspond to the uncertain rates of return on the assets. In both models,
725:
276:
832:
44:
to the size of the government spending change—but is not likely to know the exact value of this ratio. Similar uncertainty may surround the magnitude of effect of a change in the
854:
There is a mathematical and conceptual analogy between, on the one hand, policy optimization with multiple policy tools having multiplier uncertainty, and on the other hand,
773:
186:
154:
603:
227:
257:
979:
Turnovsky, Stephen (1976). "Optimal stabilization policies for stochastic linear systems: The case of correlated multiplicative and additive disturbances".
837:
Thus the basic effect of multiplier uncertainty is to make policy actions more cautious, although this effect can be modified in more complicated models.
571:{\displaystyle {\text{E}}L={\text{E}}(y-y_{d})^{2}={\text{E}}(aP+u-y_{d})^{2}=^{2}+{\text{var}}(aP+u-y_{d})=^{2}+P^{2}\sigma _{a}^{2}+\sigma _{u}^{2}.}
77:
28:
effect of a particular policy action, such as a monetary or fiscal policy change, upon the intended target of the policy. For example, a
963:
69:
796:. However, the optimal policy equation shows that, to the extent that there is multiplier uncertainty (the extent to which
1041:
1046:
981:
104:
be an additive term capturing both the linear intercept and all unpredictable components of the determination of
897:
927:
Mitchell, Douglas W. (1990). "The efficient policy frontier under parameter uncertainty and multiple tools".
855:
267:
799:
25:
720:{\displaystyle P^{opt}={\frac {({\text{E}}a)(y_{d}-{\text{E}}u)}{({\text{E}}a)^{2}+\sigma _{a}^{2}}}.}
63:
There are several policy implications of multiplier uncertainty: (1) If the multiplier uncertainty is
746:
159:
127:
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37:
232:
Suppose the policy maker cares about the expected squared deviation of GDP from a preferred value
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would be zero, and policy would be chosen so that the contribution of policy (the policy action
743:
in the absence of any policy action. If there were no uncertainty about the policy multiplier,
959:
116:
are random variables (assumed here for simplicity to be uncorrelated), with respective means E
33:
194:
936:
235:
878:
uncertainty were ignored, this no longer holds in the presence of multiplier uncertainty.
57:
17:
1035:
940:
260:
73:
53:
45:
29:
1008:
Turnovsky, Stephen (1974). "The stability properties of optimal economic policies".
49:
92:
be the size of a policy action (a government spending change, for example), let
64:
730:
Here the last term in the numerator is the gap between the preferred value
895:
Brainard, William (1967). "Uncertainty and the effectiveness of policy".
1021:
994:
910:
783:) would be to exactly close this gap, so that with the policy action E
84:
Effect of multiplier uncertainty on the optimal magnitude of policy
48:
or its growth rate upon some target variable, which could be the
581:
where the last equality assumes there is no covariance between
41:
834:), the magnitude of the optimal policy action is diminished.
270:
so that the objective function, expected loss, is given by:
846:
tools are available the lower expected loss can be driven.
96:
be the value of the target variable (GDP for example), let
873:
the effects of policy actions exist. In this dynamic
802:
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32:maker may have a prediction as to the value of the
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76:: optimal policy is not equivalent to a policy of
589:. Optimizing with respect to the policy variable
956:Analysis and Control of Dynamic Economic Systems
739:of the target variable and its expected value E
8:
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841:Multiple targets or policy instruments
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827:{\displaystyle \sigma _{a}^{2}>0}
88:For the simplest possible case, let
24:is lack of perfect knowledge of the
100:be the policy multiplier, and let
72:no longer applies under quadratic
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768:{\displaystyle \sigma _{a}^{2}}
181:{\displaystyle \sigma _{u}^{2}}
149:{\displaystyle \sigma _{a}^{2}}
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36:—the ratio of the effect of a
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941:10.1016/0164-0704(90)90061-E
868:Dynamic policy optimization
850:Analogy to portfolio theory
779:times its known multiplier
1063:
982:Review of Economic Studies
954:Chow, Gregory P. (1976).
929:Journal of Macroeconomics
124:and respective variances
1010:American Economic Review
898:American Economic Review
593:gives the optimal value
222:{\displaystyle y=aP+u.}
856:portfolio optimization
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22:multiplier uncertainty
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252:{\displaystyle y_{d}}
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70:Certainty equivalence
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861:mutual fund theorems
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78:ignoring uncertainty
958:. New York: Wiley.
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38:government spending
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34:fiscal multiplier
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1016:(1): 136–148.
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989:(1): 191–194.
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935:(1): 137–145.
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905:(2): 411–425.
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58:inflation rate
18:macroeconomics
13:
10:
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54:exchange rate
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46:monetary base
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31:
30:fiscal policy
27:
23:
19:
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787:would equal
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65:uncorrelated
62:
50:money supply
21:
15:
259:; then its
1036:Categories
882:References
60:, or GDP.
40:change on
26:multiplier
805:σ
752:σ
698:σ
657:−
552:σ
534:σ
497:−
447:−
398:−
349:−
303:−
268:quadratic
165:σ
133:σ
108:. Both
1022:1814888
995:2296741
911:1821642
188:. Then
1020:
993:
962:
909:
56:, the
52:, the
1018:JSTOR
991:JSTOR
907:JSTOR
120:and E
960:ISBN
819:>
585:and
156:and
112:and
74:loss
937:doi
428:var
266:is
42:GDP
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