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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Multiplier uncertainty ： ウィキペディア英語版 Multiplier uncertainty In macroeconomics, multiplier uncertainty is lack of perfect knowledge of the multiplier effect of a particular policy action, such as a monetary or fiscal policy change, upon the intended target of the policy. For example, a fiscal policy maker may have a prediction as to the value of the fiscal multiplier—the ratio of the effect of a government spending change on GDP 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 monetary base or its growth rate upon some target variable, which could be the money supply, the exchange rate, the inflation rate, or GDP. There are several policy implications of multiplier uncertainty: (1) If the multiplier uncertainty is uncorrelated 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) Certainty equivalence no longer applies under quadratic loss: optimal policy is not equivalent to a policy of ignoring uncertainty. ==Effect of multiplier uncertainty on the optimal magnitude of policy== For the simplest possible case, let ''P'' be the size of a policy action (a government spending change, for example), let ''y'' be the value of the target variable (GDP for example), let ''a'' be the policy multiplier, and let ''u'' be an additive term capturing both the linear intercept and all unpredictable components of the determination of ''y''. Both ''a'' and ''u'' are random variables (assumed here for simplicity to be uncorrelated), with respective means E''a'' and E''u'' and respective variances $\backslash sigma^2\_a$ and $\backslash sigma^2\_u$. Then :$y\; =\; aP\; +\; u.$ Suppose the policy maker cares about the expected squared deviation of GDP from a preferred value $y\_d$; then its loss function ''L'' is quadratic so that the objective function, expected loss, is given by: :$\backslash textL\; =\; \backslash text(y-y\_d)^2\; =\; \backslash text(aP\; +\; u\; -\; y\_d)^2\; =\; (+\; u\; -\; y\_d))^2\; +\; \backslash text\; (aP\; +\; u\; -\; y\_d)\; =\; (+\; \backslash textu\; -\; y\_d)^2\; +\; P^2\; \backslash sigma^2\_a\; +\; \backslash sigma^2\_u.$ where the last equality assumes there is no covariance between ''a'' and ''u''. Optimizing with respect to the policy variable ''P'' gives the optimal value ''P''''opt'': :$P^\; =\; \backslash fracu)\}.$ Here the last term in the numerator is the gap between the preferred value ''y''''d'' of the target variable and its expected value E''u'' in the absence of any policy action. If there were no uncertainty about the policy multiplier, $\backslash sigma^2\_a$ would be zero, and policy would be chosen so that the contribution of policy (the policy action ''P'' times its known multiplier ''a'') would be to exactly close this gap, so that with the policy action E''y'' would equal ''y''''d''. However, the optimal policy equation shows that, to the extent that there is multiplier uncertainty (the extent to which $\backslash sigma^2\_a\; >\; 0$), the magnitude of the optimal policy action is diminished. Thus the basic effect of multiplier uncertainty is to make policy actions more cautious, although this effect can be modified in more complicated models. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Multiplier uncertainty」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.