How to design a stimulus package

如何设计刺激计划

2019/05/15 16:28
对照中文英文原文
自大衰退以来,学者和政策制定者都在讨论如何构建最佳刺激方案。本专栏重新讨论了与乘数大小和公共支出有用性相关的论点,并为未来的刺激计划提供了蓝图。

Academics and policymakers alike have debated how to structure an optimal stimulus package since the Great Recession. This column revisits the arguments related to the size of the multiplier and the usefulness of public spending, and offers a blueprint for future stimulus packages. It finds that the relationship between the multiplier and stimulus spending is hump-shaped, and that a well-designed stimulus package should depend on the usefulness of public expenditure. The output multiplier is not a robust statistic to use, and instead the ‘unemployment multiplier’ should be used.

自大衰退以来,学者和政策制定者都在讨论如何构建最佳刺激方案。本专栏重新讨论了与乘数大小和公共支出有用性相关的论点,并为未来的刺激计划提供了蓝图。乘数和刺激支出之间的关系是驼峰形的,精心设计的刺激方案应该取决于公共支出的有用性。产出乘数不是一个可靠的统计数据,而应使用“失业乘数”。

The Great Recession reached the US in December 2007. In 2008, unemployment rose rapidly, and in response the Fed swiftly cut interest rates. In December 2008, however, monetary policy ran out of fuel. The nominal interest rate had reached the zero lower bound, prompting the US government to look for alternative stabilisation policies. One policy that had been used before and was considered again, was to increase public expenditure through a stimulus package – the American Recovery and Reinvestment Act, described by Romer and Bernstein (2009).

美国大萧条于2007年12月开始。2008年,失业率迅速上升,而美联储迅速降息。然而,在2008年12月,货币政策耗尽了弹药。名义利率已达到零下限,促使美国政府寻求替代稳定政策。之前曾经使用过并被再次考虑的一项政策是通过一揽子刺激计划增加公共支出,即美国复苏与再投资法案。

As policymakers and academic researchers started to discuss what the appropriate amount of stimulus spending should be, the lack of consensus became evident. A number of arguments were advanced in favour of and against the stimulus package. These arguments often involved the ‘output multiplier’, which is the increase in GDP achieved by a one-dollar increase in public expenditure. A positive multiplier means that an increase in public expenditure raises GDP. A multiplier larger than one means that an increase in public expenditure raises GDP more than one-for-one, implying that the increase in public expenditure raises other components of GDP – such as household consumption.

随着决策者和学术研究人员开始讨论适当数量的刺激支出应该是什么,缺乏共识变得明显,存在着一些支持和反对刺激计划的论点。这些论点通常涉及“产出乘数”,即公共支出增加一美元所带来的GDP增长。正乘数意味着公共支出的增加会提高GDP。大于1的乘数意味着公共支出的增加使GDP增加超过一比一,这意味着公共支出的增加会增加GDP的其他组成部分 - 例如家庭消费。

One part of the debate was about the size of the multiplier, and especially whether it was bigger or smaller than one. Some argued that the stimulus package was justified because the multiplier was bigger than one. Others retorted that the multiplier was smaller than one and hence the stimulus package was a bad idea. More generally, a lot of the debate was guided by the ‘bang for the buck’ approach – the larger the multiplier, the more effective the policy, and therefore the more it should be used.

争论的一部分是关于乘数的大小,特别是它是大于还是小于1。一些人认为刺激计划是合理的,因为乘数大于1。其他人反驳说,乘数小于1,因此刺激计划是一个坏主意。更一般地说,很多辩论都是以“花最少钱得到最大的效果”的方式为指导 - 乘数越大,政策越有效,因此应该使用的越多。

Another part of the debate revolved around the usefulness of public expenditure. A concern of stimulus sceptics was that additional public expenditure may not be very useful. In the worst case, we would build bridges to nowhere, but even in a less dire view, public spending would not be as socially valuable as private spending.

争论的另一部分围绕公共支出的有用性。刺激怀疑论者担心的是,额外的公共支出可能不是很有用。在最糟糕的情况下,我们将建立无处可通的桥梁,但即使不那么可怕,公共支出也不会像私人支出那样具有社会价值。

In recent work (Michaillat and Saez 2019), we study the design of stimulus packages at the onset of recessions. We aim to revisit these arguments and offer a blueprint for when the next stimulus package will be needed. As most modern research on business-cycle stabilisation has focused on monetary policy, not much is known about the properties of an adequate stimulus package. Indeed, because the Federal Reserve has been in charge of stabilisation for several decades, the design of optimal monetary policy has attracted an enormous amount of research, while the design of optimal stimulus packages has been relatively neglected.

在最近的工作中(Michaillat和Saez 2019),我们研究了经济衰退开始时刺激计划的设计。我们的目标是重新审视这些论点,并为何时需要下一个刺激计划提供蓝图。由于大多数关于商业周期稳定的现代研究都集中在货币政策上,因此对适当刺激方案的特性知之甚少。实际上,由于美联储几十年来一直负责稳定,最优货币政策的设计吸引了大量的研究,而最佳刺激方案的设计却相对被忽视了。

Before we discuss the properties of a well-designed stimulus package, let us say a few words about the model we use for the analysis. We built a model that captures all the elements that played a prevalent role in the policy debate. Although experts may disagree on the exact values that each of the relevant statistics take, what we think might be helpful at the very least is a coherent framework in which all these different values can be plugged in.

在我们讨论精心设计的刺激方案的属性之前,让我们谈谈我们用于分析的模型。我们建立了一个模型以捕捉在政策辩论中发挥重要作用的所有元素。虽然专家可能不同意每个相关统计数据所采用的确切值,但我们认为可能至少有助于形成一个连贯的框架,在这个框架中可以插入所有这些不同的值。

Our model features unemployment, which may be at the right level or inefficiently high, as in recessions. We allow public expenditure to be anything from useless to as useful as private expenditure. The value of public expenditure is described by an ‘elasticity of substitution between public and private consumption’. This elasticity describes the utility derived from additional public goods – with zero elasticity, extra public goods are useless. A higher elasticity means that extra public goods are more valuable, and with infinite elasticity, public and private goods are interchangeable. We also allow public spending to be anything from totally ineffective to very effective at stimulating GDP and reducing unemployment. The effectiveness of public spending is measured by the output multiplier, which in our model is allowed to be negative, zero, below one, or above one.

我们的模型以失业率为特征,失业率可能处于正确水平或低效率(衰退期间)。我们允许公共支出从无用到和私人支出一样有用。公共支出的价值由“公共和私人消费之间的替代弹性”来描述。这种弹性描述了从额外的公共产品中获得的效用:零弹性时额外的公共产品是无用的,更高的弹性意味着额外的公共产品更有价值,无限弹性时,公共和私人商品是可以互换的。我们还允许公共支出从完全无效到非常有效地刺激GDP和减少失业。公共支出的有效性通过产出乘数来衡量,在我们的模型中,乘数可以是负数,零,低于1或高于1。

Several properties of a well-designed stimulus package stand out – because they challenge existing preconceptions. The first is that the size of the stimulus does not follow the bang-for-the-buck logic often invoked in policy discussions. Instead, the relationship between multiplier and stimulus spending is hump-shaped – stimulus spending should be zero for a zero multiplier, increasing in the multiplier for small multipliers, largest for a moderate multiplier, and decreasing in the multiplier beyond that. Then, a large multiplier is not a justification for a large stimulus – stimulus spending should be similarly small when multipliers are small and large. The stimulus should only be large for medium multipliers. Relatedly, the threshold value of one for the multiplier plays no role at all – any positive multiplier warrants a positive stimulus package.

精心设计的刺激计划的几个特性脱颖而出。首先,刺激的规模并不遵循政策讨论中经常引用的“花最少钱得到最大的效果”的逻辑。相反,乘数和刺激支出之间的关系是驼峰形的 - 零乘数的刺激支出应该为零,小乘数的乘数增加,中等乘数的增幅最大,超过此乘数的刺激支出下降。那么,大乘数并不是大规模刺激的理由 - 当乘数很小和很大时,刺激支出应该同样小。对于中等乘数,刺激应该很大。相关地,乘数的一个阈值根本不起作用 - 任何正乘数都需要一个积极的刺激方案。

Second, we find that a well-designed stimulus package should also depend on the usefulness of public expenditure – more precisely, on the elasticity of substitution between public and private consumption. When the elasticity of substitution is zero, so that public goods are useless, there should not be any stimulus spending.  But this is an extreme case. In reality, the elasticity of substitution is positive, so some stimulus spending always remains. Moreover, when the elasticity of substitution is higher, extra public goods are more valuable, so stimulus spending is more desirable.

其次,我们发现精心设计的刺激计划还应该依赖于公共支出的有用性 - 更准确地说,取决于公共和私人消费之间的替代弹性。当替代弹性为零时,公共商品就没用了,就不应该有任何刺激支出。但这是一个极端的例子。实际上,替代弹性是正的,所以一些刺激支出总是存在。此外,当替代弹性较高时,额外的公共商品更有价值,因此刺激支出更为可取。

Third, we find that the output multiplier is not a robust statistic to use in stimulus discussion. Instead, we should use the ‘unemployment multiplier’, which is the percentage-point decrease in unemployment when public spending increases by 1% of GDP. When the taxes used to finance public spending do not affect labour supply, unemployment and output multipliers are equal, so they can be used interchangeably. But if taxes affect behaviour, the unemployment and output multipliers are no longer the same, and the output multiplier cannot be used to design stimulus spending. This point is important because the output multiplier plays a prominent role in the stimulus debate. The unemployment multiplier can be used regardless of whether taxation affects behaviour or not because it always exactly measures the forces that are relevant to the design of an ‘optimal’ stimulus package – a package that fulfills the government’s objective. The output multiplier, on the other hand, sometimes measures forces that are irrelevant to the design of an optimal stimulus package.

第三,我们发现产出乘数不是用于刺激讨论的稳健统计量。相反,我们应该使用“失业乘数”,即当公共支出增加1%的GDP时,失业率下降的百分点。当用于资助公共支出的税收不影响劳动力供给时,失业率和产出乘数是相等的,因此它们可以互换使用。但如果税收影响行为,失业和产出乘数就不再相同,产出乘数也不能用来设计刺激支出。这一点很重要,因为产出乘数在刺激辩论中起着重要作用。无论税收是否影响行为,都可以使用失业乘数,因为它总是精确地衡量与“最优”刺激计划的设计相关的力量 - 一个满足政府目标的一揽子计划。另一方面,产出乘数有时会测量与最佳刺激方案的设计无关的力量。

When the US government decided to implement the American Recovery and Reinvestment Act stimulus package in 2009, unemployment was projected to increase from 6% to 9% absent policy intervention. Given the properties of a well-designed stimulus package and the available empirical evidence, what should this stimulus package have looked like? The stimulus package resulting from our analysis is shown in Figure 1 for a realistic range of unemployment multipliers and elasticities of substitution between private and public consumption (The evidence on multipliers comes from Ramey 2013, and the evidence on the elasticity of substitution comes from Armano and Wirjanto 1998). As a complement, Figure 2 displays how much unemployment would have been reduced with the stimulus of Figure 1.

当美国政府决定在2009年实施“美国复苏与再投资法案”刺激计划时,如果没有政策干预,预计失业率将从6%增加到9%。鉴于精心设计的刺激计划的特性和可用的经验证据,这个刺激计划应该是什么样的?我们分析得出的一揽子经济刺激计划如图1所示,显示了一系列现实的失业乘数和私人消费与公共消费之间的替代弹性。作为补充,图2显示了图1的刺激将减少多少失业率。

Figure 1 Optimal stimulus spending at the onset of the Great Recession in the US, given that unemployment was projected to increase from 6% to 9%

图1:美国大萧条开始时的最佳刺激支出,预计失业率将从6%增加到9%

Notes: Stimulus spending is measured as a share of GDP. Each line represents the stimulus package for a range of possible values of the unemployment multiplier (percentage-point decrease in unemployment when public spending increases by 1% of GDP). The three lines differ by the value used for the elasticity of substitution between public and private consumption (ε).

注:刺激支出按GDP的比例计算。每条线代表一系列失业乘数可能值的刺激方案(当公共支出增加1%时,失业率下降百分点)。这三条线的差异在于公共和私人消费(ε)之间的替代弹性所使用的值。

Figure 2 Unemployment rate that would be reached with the stimulus package of Figure 1

图2:图1刺激计划所能达到的失业率

Notes: We assume that the target efficient unemployment rate is 6% and that the economy has a 9% unemployment rate absent stimulus spending. Each line represents the unemployment rate that would be reached for a range of possible values of the unemployment multiplier (percentage-point decrease in unemployment when public spending increases by 1% of GDP). The three lines differ by the value used for the elasticity of substitution between public and private consumption (ε).

注:我们假设目标有效失业率为6%,而没有刺激支出的经济体的失业率为9%。每条线代表失业乘数的一系列可能值所能达到的失业率(公共支出增加1%时失业率下降的百分点)。这三条线的差异在于公共和私人消费(ε)之间的替代弹性所使用的值。

The stimulus package in Figure 1 illustrates the points that we have just discussed. First, even with a small multiplier (say 0.2), optimal stimulus spending is significant (above 1.5 percentage points of GDP). Second, the multiplier warranting the largest stimulus is fairly modest (between 0.3 and 0.6). Third, optimal stimulus spending is the same for small and large multipliers, and the resulting unemployment rates are of course very different. Fourth, for small multipliers, unemployment barely falls below 9%, although optimal stimulus spending is quite large. This is because public expenditure has little effect on unemployment when the multiplier is small. On the other hand, with a multiplier above one, stimulus spending almost brings back unemployment to its initial level of 6% (for instance, with a multiplier of one, the unemployment rate falls below 6.8%). Fifth, the higher the elasticity of substitution between public and private consumption, the higher the stimulus package. Yet, while the elasticity plays a significant role for small to medium multipliers, its role is much more limited for large multipliers. This is because for large multipliers, the optimal policy is essentially to fill the unemployment gap, so it is not influenced by the elasticity of substitution. Sixth, the stimulus package is plotted as a function of the unemployment multiplier, not the output multiplier, so all these results apply regardless of whether the taxes used to finance stimulus spending are distortionary or not.

图1中的刺激方案说明了我们刚才讨论的要点。首先,即使乘数较小(比如说0.2),最优刺激支出也是显着的(超过GDP的1.5个百分点)。其次,保证最大刺激的乘数相当适中(介于0.3和0.6之间)。第三,对于小型和大型乘数而言,最佳刺激支出是相同的,由此产生的失业率却是非常不同的。第四,对于小型乘数,失业率几乎不会低于9%,尽管最佳刺激支出非常大。这是因为当乘数很小时,公共支出对失业的影响很小。另一方面,乘数高于1时,刺激支出几乎将失业率恢复到6%的初始水平(例如,乘数1,失业率降至6.8%以下)。第五,公共和私人消费之间的替代弹性越高,刺激方案就越高。然而,虽然弹性对于中小型乘数起着重要作用,但它对大型乘数的作用更为有限。这是因为对于大乘数,最优政策主要是填补失业缺口,因此它不受替代弹性的影响。第六,刺激方案是作为失业乘数而不是产出乘数的函数绘制的,因此所有这些结果都适用,无论用于资助刺激支出的税收是否是扭曲的。

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