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In [[macroeconomics]], '''multiplier uncertainty''' is lack of perfect knowledge of the [[Multiplier (economics)|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.
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There are several policy implications of multiplier uncertainty: (1) If the multiplier uncertainty is [[correlation|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 function|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,<ref>{{cite journal |last=Brainard |first=William |year=1967 |title=Uncertainty and the effectiveness of policy |journal=[[American Economic Review]] |volume=57 |issue=2 |pages=411–425 |jstor=1821642 }}</ref> 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 <math>\sigma^2_a</math> and <math>\sigma^2_u</math>. Then
 
:<math>y = aP + u.</math>
 
Suppose the policy maker cares about the expected squared deviation of GDP from a preferred value <math>y_d</math>; then its [[loss function]] ''L'' is [[quadratic loss function|quadratic]] so that the objective function, expected loss, is given by:
 
:<math>\text{E}L = \text{E}(y-y_d)^2 = \text{E}(aP + u - y_d)^2 = [\text{E}(aP + u - y_d)]^2 + \text{var} (aP + u - y_d) = [(\text{E}a)P + \text{E}u - y_d]^2 + P^2 \sigma^2_a + \sigma^2_u.</math>
 
Optimizing with respect to the policy variable ''P'' gives the optimal value ''P''<sup>''opt''</sup>:
 
:<math>P^{opt} = \frac{(\text{E}a)(y_d - \text{E}u)}{(\text{E}a)^2 + \sigma^2_a}.</math>
 
Here the last term in the numerator is the gap between the preferred value ''y''<sub>''d''</sub> 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, <math>\sigma^2_a</math> 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''<sub>''d''</sub>.  However, the optimal policy equation shows that, to the extent that there is multiplier uncertainty (the extent to which <math>\sigma^2_a > 0</math>), 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.
 
==Multiple targets or policy instruments==
 
The above analysis of one target variable and one policy tool can readily be extended to multiple targets and tools.<ref name=Mitchell>{{cite journal |last=Mitchell |first=Douglas W. |year=1990 |title=The efficient policy frontier under parameter uncertainty and multiple tools |journal=Journal of Macroeconomics |volume=12 |issue=1 |pages=137–145 |doi=10.1016/0164-0704(90)90061-E }}</ref>  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 tools are available the lower expected loss can be driven.
 
==Analogy to portfolio theory==
 
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, [[Modern portfolio theory|portfolio optimization]] involving multiple investment choices having rate-of-return uncertainty.<ref name=Mitchell/>
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, [[mutual fund theorem]]s 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.
 
==Dynamic policy optimization==
 
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 the effects of policy actions exist. In this dynamic [[stochastic control]] context with multiplier uncertainty,<ref>{{cite book |last=Chow |first=Gregory P. |year=1976 |title=Analysis and Control of Dynamic Economic Systems |location=New York |publisher=Wiley |isbn=0-471-15616-7 }}</ref><ref>{{cite journal |last=Turnovsky |first=Stephen |year=1976 |title=Optimal stabilization policies for stochastic linear systems: The case of correlated multiplicative and additive disturbances |journal=[[Review of Economic Studies]] |volume=43 |issue=1 |pages=191–194 |jstor=2296741 }}</ref><ref>{{cite journal |last=Turnovsky |first=Stephen |year=1974 |title=The stability properties of optimal economic policies |journal=American Economic Review |volume=64 |issue=1 |pages=136–148 |jstor=1814888 }}</ref> 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 uncertainty were ignored, this no longer holds in the presence of multiplier uncertainty.
 
==References==
{{reflist}}
 
[[Category:Economics]]
[[Category:Macroeconomics]]

Latest revision as of 04:00, 8 January 2015

Case, have extended the John Deere range of knives with addition of yet another 13 products, taking the number up to 28 in this series. Once we known as in all the knives, though, we identified that 1 truly had micro serrations (the J.A. Henckels eight-Piece Stainless-Steel Steak Knife Set ). Interestingly, this was our least preferred in testing mainly because of how substantially sawing was necessary. You can use a knife steel to straighten out bends in the edges of the knives. I purchased a set of the advisable knives a few months ago, and I located them to be impossibly light.

Welcome to the globe of à la carte knife purchasing. The one particular that you acquire need to be the one particular that fits both your price range and your knife set - and as each a single is a top rated sharpener, you will not go far incorrect selecting from the choice located right here. The AccuSharp is a wonderful instance of the most effective compact knife sharpeners. You just location your knife upside down and run the AccuSharp up and down the blade. CRKT is 1 of the popular knife corporation.

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Japanese knives are sharper, but if you are made use of to a large western knife and do a lot of lobster killing, the Wusthof Classic is your best bet. They claim that this procedure in fact tends to make their knives stronger, but a local knife shop says otherwise. All the services offered great sharpening but The Knife Guy set himself apart by supplying the most hassle-free ordering and shipping method.

By utilizing the appropriate knife for the process you are guaranteeing each your safety and the extension of your blade's life. For instance, do not use a paring knife as a boning knife. Boning knives are specially made to be flexible to receive around the bone and utilizing a paring knife for this goal can outcome in a dull blade and the possibility of slipping triggering cuts to your hands and fingers.

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