WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE? ERIC GIAMBATTISTA AND STEVEN PENNINGS Abstract. Transfers to individuals were a larger part of the 2009 US stimulus package than government purchases. Using a two-agent New Keynesian model, we show analytically that the multiplier on transfers to financially constrained households is larger than the purchase multiplier if the zero lower bound (ZLB) binds. Targeted transfers provide the same boost to demand as purchases, but lower aggregate supply relative to purchases, as those receiving transfers want to work less. When the aggregate demand curve inverts — such as when the ZLB binds — the extra inflation from lower supply boosts the multiplier. We show this result also holds quantitatively in a medium-scale version of the model.
1. Introduction In the years preceding the Global Financial Crisis, the role of macroeconomic management had largely fallen to central banks, with fiscal policy playing a secondary role. But with the magnitude of the global recession, and the Zero Lower Bound (ZLB) on nominal interest rates binding in the United States and other countries, fiscal policy has now taken a more prominent role in policymakers’ attempts to stimulate the economy. This has lead to a renewed interest in the response of output to an increase in government purchases: the government purchase multiplier.
Date: 6 March 2017. JEL: E63 E62; Keywords: Fiscal Transfers, Fiscal policy, Fiscal stimulus, Government spending, Multipliers, New-Keynesian models, Zero Lower Bound, Monetary policy; URL: https://sites.google.com/site/stevenpennings/ Giambattista: Gen Life, 540 Bryant St Palo Alto, CA 94301 (email:
[email protected]) Pennings (corresponding author): Development Research Group, World Bank, 1818 H St NW, Washington DC 20433 USA (email:
[email protected] or
[email protected]). The views expressed here are the authors’, and do not necessarily reflect those of the World Bank, its Executive Directors, or the countries they represent. Helpful comments have been received from Eric Leeper (the editor), two anonymous referees, Mariano Kulish, Jonathan Kearns, Tommaso Monacelli, Mark Gertler, Taisuke Nakata, Alex Heath, Tim Cogley, Virgiliu Midrigan, Jess Benhahib, John Leahy, Leon Berkelmans, Gianluca Violante, Andrew Erskine and seminar participants at the 2012 Midwest Macro Meetings, New York University and the Reserve Bank of Australia. 1
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
2
Despite the focus on the government purchase multiplier in the literature (Woodford (2011), Christiano et al (2011), Cogan et al (2010), Werning (2012), Eggertsson (2010b)), the majority of the increase in government spending during the Global Financial Crisis was government transfers to households, not government purchases. According to Oh and Reis (2012), 75 per cent of the increase in US government spending between 2007 and 2009 was transfers, with similar proportions for other OECD countries. Transfers were around 35-80% 2009 American Recovery and Reinvestment Act (ARRA) (depending on the classification of intergovernmental payments), and consistent the bulk of earlier stimulus packages in 2001 and in 2008.1 In representative agent models, government transfers have no effect. This has led Cogan and Taylor (2010) to conclude: “Basic economic theory implies that temporary increases in transfer payments have a much smaller impact than government purchases” (p22). This paper examines the determinants of the government transfer multiplier in a closedeconomy two-agent model with nominal rigidities where around a third of the population is financially constrained. In the model, the fiscal package consists of a targeted transfer to financially constrained households, funded by lump-sum taxes on the unconstrained households. The targeted transfer doesn’t represent a specific stimulus measure, but rather provides an analytic benchmark which (i) isolates effects of transfers on supply (which have been overlooked in the literature) and (ii) can be easily adjusted for the level of targeting of a particular policy (by scaling the multiplier by the degree of targeting).2 We call the transfer multiplier “large” if it is (i) greater than the purchases multiplier (for analytical results), and/or (ii) greater than one (for quantitative results).3 Our main result is that the transfer multiplier is extremely sensitive to the monetary policy rule of the central bank — much more so than the purchases multiplier. When the central 1
See Online Appendix 9 for a discussion. According to NIPA definitions, 86% of ARRA current expenditures were classified as transfer payments. Drautzburg and Uhlig (2015) argue 59% of the ARRA is transfers. 2 An alternative assumption is that transfers are completely untargeted, which would usually underestimate the transfer multiplier, and requires a less straightforward adjustment for imperfect targeting. In Section 4 (analytical results) and Section 5 (numerical results) we report both targeted and untargeted multipliers. 3 The government purchases multiplier literature focuses on a multiplier greater than one —the cutoff we follow here — because it means that the government purchase must crowd in private sector activity, and consumption or nvestment. One could argue that an analogous approach would suggest that the transfer multiplier is large if it is above zero , though we prefer the more conservative threshold of unity.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
3
bank responds aggressively to inflation, the transfer multiplier is small — often close to zero for very aggressive monetary policy rules — and is smaller than the purchases multiplier. However, when the Zero Lower Bound (ZLB) on nominal interest rates binds, the targeted transfer multiplier is almost always larger than the purchases multiplier, and is usually larger than one. The transfer multiplier is extremely sensitive to the central bank’s monetary policy rule because targeted transfers generate more inflation than government purchases. While both targeted transfers and purchases boost aggregate demand, only purchases increase aggregate supply (as wealth effects on labour supply cancel across households for transfers). In normal times (when the central bank follows a Taylor rule), this extra inflation reduces the transfer multiplier relative to the purchase multiplier: the central bank raises real interest rates, reducing consumption demand from unconstrained households. However, the when the ZLB binds, the extra inflation increases the transfer multiplier relative to the purchases multiplier, as it reduces real interest rates (increasing demand from unconstrained households). We show analytically in Section 4 that the transfer multiplier is larger than the purchases multiplier whenever the economy’s aggregate demand curve inverts — that is, an increase in inflation is associated with higher aggregate demand.4 Our secondary finding is that sticky wages reduce the difference between the targeted transfer multiplier and the purchases multiplier (we show this numerically in Section 3). As wages become increasingly sticky, wealth effects on labour supply become weak, and hence the aggregate supply response to transfers is similar to that of purchases. Targeted transfer and purchase multipliers are also identical when preferences are such that wealth effects on labour supply are zero (such as Greenwood–Hercowitz–Huffman (GHH) preferences). Given the importance of this mechanism, we review the evidence on labour supply elasticities in 4
We call tendency for higher inflation to reduce demand from unconstrained households the Taylor Principle Effect. As the model also includes financially constrained households, inflation has a secondary effect: higher inflation reduces markups, increasing wages, incomes and hence demand of constrained households. We call this increase in demand from constrained households the Disposable Income Effect. When the Disposable Income Effect outweighs the Taylor Principle Effect, the aggregate demand curve inverts. While the ZLB binding is a sufficient condition for the inversion of the aggregate demand curve, inversion can also occur under a Taylor rule when fiscal policy is not very persistent, the share of constrained households is high, or prices are very sticky.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
4
Section 3, and find that the literature does find evidence in favour wealth effects on labour supply, albeit ones that are modest in size. In the absence of wealth effects, the efficacy of transfer-based stimulus comes down to targeting transfers at constrained households — halving the fraction of transfers going to constrained households also halves the transfer multiplier.5 What does this mean for the quantitative size of transfer multipliers? In Section 5, we calculate the size of output multipliers using a medium-scale DSGE model calibrated to match the response of consumption to a transfers shock from the 2001 Bush tax rebates as estimated by Johnson et al (2006).6 We find that a once-off 1 per cent of GDP targeted transfer or government purchase raises the present value of output by about 0.9 per cent.7 Policies with a persistence similar to that of the transfer component of the 2009 US stimulus package (auto-correlation of 0.9), have a long-run present value multiplier of around 0.25 for targeted transfers or 0.4 for purchases in normal times. If monetary policy is constrained by the ZLB for five years, the targeted transfer multiplier is around 1.3 for once-off stimulus, and 1.7 for persistent stimulus (with purchase multipliers being around 1.3 in either case). If transfers are completely untargeted, the transfer multiplier is around 0.5 (with 5 years of ZLB), though can be above one if the ZLB binds for an extended period with a slightly higher share of constrained households (for example, during a recession with tightened borrowing constraints). In Section 6 we evaluate the effects of the policy similar to the transfers component of the ARRA on output and unemployment during the height of the Great Recession. We follow Galí (2011) and model involuntary unemployment as stemming from market power and wage stickiness that prevents wages from falling to clear the labour market. We follow 5
Without wealth effects, imperfect targeting would mean that in practice the transfer multiplier is less than the purchase multiplier. However, timely implementation of a transitory increase in government spending is also very difficult, where as once-off transfer-based stimulus is common. 6 Johnson et al (2006) find that around 20-40 per cent of once-off Bush transfers were spent in the months that they arrived, and the consumption response was around one-for-one for those with low levels of liquid assets and close to zero for those with high levels of liquid assets. This is inconsistent with a standard frictionless model, where only the present value of the payments — and not their timing — affect consumption, but consistent with our model where around a third of households are financially constrained. 7 That is, the multiplier for a policy similar to the 2001 Bush tax cuts would be around 0.3 (0.9×1/3) if it was untargeted.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
5
Christiano et al (2011) in generating a crisis where the ZLB binds caused by a combination of a discount factor shock (which increases desired savings) and an increase in spreads faced by investors in capital. The model captures the path of output almost exactly, and also leads to a large increase in unemployment (slightly too large). In this context, a policy like the transfers component of the ARRA — assuming it is completely untargeted, and abstract from other components of the ARRA — would at its peak reduce unemployment by around 1.2ppt and reduce the output gap by a around 0.75ppts. Having said that, these are peak estimates (which fall over time), the ARRA contained many other components, we adopt a very conservative definition of transfers, and our model abstracts from many important real-world features of the Great Recession. As such these figures should be interpreted with caution. For US policymakers seeking to stimulate the economy during a recession, our results suggest that the transfer multiplier tends to be large when (i) transfers are targeted at the financially constrained (who are more likely to spend the transfer); and, (ii) the ZLB binds during the time of the fiscal stimulus (when wealth effects on labour supply increase inflation).8 Literature Although there are many recent papers examining the effect of government purchases in DSGE models (for example, Christiano et al (2011), Cogan et al (2010), Woodford (2011) and Uhlig (2010), Eggertsson (2010b)), there are only a few papers that consider transfers in a setting similar to ours. The closest published paper is contemporaneous work by Bilbiie, Monacelli and Perotti (2013) who use a saver-borrower New Keynesian model and find a positive transfer multiplier with sticky prices, and a small or zero transfer multiplier with flexible prices. We also find these results, but we extend the literature to (i) study the transfer multiplier at the ZLB, and (ii) compare the size of purchase and transfer multipliers (neither of which are discussed by Bilbiie et al 2013). 8
The findings of this paper apply most closely to once-off small cash stimulus payments like the 2001 and 2008 Bush tax rebates or the 2009 Social Security payments where eligibility was predetermined (usually based on information from previous tax years). Transfers based on unemployment status may have further incentive effects, which is beyond the scope of this paper. As our model is linear, the effect of the transfer does not depend on either the size of the payment or how far output is below steady state. Relaxing these assumptions is an interesting area for future research.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
6
Our paper is also related to Mehrotra (2014), who studies the effect of untargeted transfers in a two-agent New Keynesian model with a debt-elastic interest spread. Mehrotra (2014) also finds a small (or sometimes negative) transfer multiplier with flexible prices, a modest transfer multiplier with sticky prices and a Taylor Rule, and a (potentially) large transfer multiplier at the ZLB (though always smaller than the purchase multiplier). Mehrota’s transfer multipliers are generally smaller than ours because (i) his “borrower” households face a debt-elastic interest spread rather than being fully financially constrained, (ii) for most of the analysis he considers deficit-financed untargeted transfers, rather than [partly] targeted transfers as we do. Mehrotra (2014) does not characterise the transfer multiplier analytically in the general case with either a Taylor Rule or at the ZLB, though he does consider analytical expressions in a number of special cases (such as with a flexible prices, rigid wages or no wealth effects on labour supply). Neither Mehrotra (2014) nor Bilbiie et al (2013) include a medium-scale model with features like capital and sticky wages in order to quantify the effects of a transfer shock. Several papers find an inverted aggregate demand curve or the Keynesian “paradox of toil” (Bilbiie 2008, Eggertsson and Krugman 2012, Eggertsson 2012, 2010a, 2010b), but none of these papers consider transfers.9 Coenen et al (2012) (among others) consider the effects of fiscal stimulus in large scale DGSE models used at policy institutions. While their quantitative transfer multipliers are broadly similar to ours, the use of large models makes it difficult describe mechanisms (which is a focus of our paper). Coenen et. al. (2012) also don’t mention our key finding: that transfers multipliers are much more sensitive to the degree of monetary accommodation (relative to purchase multipliers). More broadly, our paper is related to Oh and Reis (2012) and Athreya et al (2014), who study transfers in a heterogeneous agent model and find small (positive or negative) 9
Kaplan and Violante (2014) show that wealthy households can behave in a hand-to-mouth fashion if they hold low levels of liquid assets, but they do not discuss the effects of transfers on output. Monacelli and Perotti (2011), use a model similar to Bilbiie, et al (2013) and find that the government purchase multiplier is larger when taxes are levied on the savers (rather than the borrowers). They briefly discuss the effects of fiscal transfers, and find a positive impact multiplier. Drautzburg and Uhlig (2015) investigate the effects of the ARRA in a model similar to the Smets-Wouters with distortionary taxes. While they do consider transfers (as it was part of the ARRA), it is not a focus of their paper.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
7
multipliers. While these papers provide a much more detailed characterization of income distribution, transfer policies and savings behaviour, they also simplify the monetary policy response — usually to a strict form of price-level targeting. We take the opposite path of simplifying the income distribution, but analysing a range of monetary policy responses. Interestingly, we also find small transfer multipliers with a strict form of price-level targeting, even when transfers are targeted at households with a high MPC. This reinforces our main finding that the degree of monetary accommodation is a key determinant of the transfer multiplier — without allowing for some monetary accommodation of inflation, the transfer multiplier is likely to be small. A number of papers, including Davig and Leeper (2011) and Leeper, Traum, and Walker (2015), find that a combination of an active fiscal policy and passive monetary policy can generate large fiscal multipliers. In contrast, in our paper fiscal policy is always passive. Although we assume a balanced budget in every period, we also assume taxes are lump sum and only levied on the unconstrained households who are Ricardian. Hence the timing of tax payments and the size of the government deficit do not affect the economy. 2. Model We examine the effect of government transfers and purchases in a New Keynesian DSGE model with two types of agents that differ in their access to financial markets. The unconstrained Ricardian household (agent 1) has full access to financial markets and the constrained Hand-to-Mouth household (agent 2, HtM) consumes his entire income each period in a handto-mouth fashion as in Galí et al (2007). Although simple, the two agent setup captures a number of empirical regularities such as a positive propensity to consume out of temporary transfers (Johnson et al 2006), a positive response of consumption to government purchase shocks (Galí et al 2007) and imperfect consumption smoothing (Campbell and Mankiw 1989). In our setup, the government levies lump-sum taxes on the Ricardian household to pay for government purchases and transfers to the HtM household. The Ricardian household owns capital (which they rent to intermediate goods firms). Retailers then transform intermediate goods into final goods. Retailers’ prices are sticky in the Calvo sense and so aggregate demand
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
8
and monetary policy will matter for real outcomes. Wages are sticky as in Erceg, Henderson, and Levin (2000) and Galí (2008). We log-linearise the model, and solve it quantitatively in Section 5. In Section 4 we present a simplified version of the model which can be solved analytically. A full list of non-linear and linearised equations are listed in Online Appendix 6.
2.1. Ricardian household’s problem. The Ricardian household consists of a unit mass of individuals, indexed by i ∈ [0, 1]. Different individuals within the household provide differentiated labour inputs to intermediate-goods producers (see Online Appendix 6 for more detail on the HH’s problem). The only heterogeneity across individual members of the household is whether they are able to change their nominal wage each period (as wages are sticky in a Calvo sense). There are complete markets within the household, so consumption and all other variables are equalised across individuals and so we drop the i index for these variables.10 Actual hours are determined by the demand of the firm at the given (sticky) wage (discussed further in Section 2.4 below). Each individual chooses real consumption (c1,t ), desired labour hours (L1,t (i)), real debt (−bt ) and investment (It ) to maximise his utility, taking real interest rates (Rt−1 /πt ), lump-sum taxes (T axt ), real wages (w1,t (i) = W1,t (i)/Pt ), the real gross rate of return on capital (M P Kt ) and profits from retailers (Πt ) as given.11 Therefore the Ricardian household member’s problem is:
(2.1)
max{c1,t ,bt ,It ,L1,t (i)} E0
∞ X
(ξtb β1 )t U (c1,t L1,t (i))
t=0
10We
omit these Arrow securities from the household’s budget constraint. See Colciago (2011) for a discussion of sticky wages and HtM HH with alternative labour market assumptions. 11In the full model, we assume that the HtM HH receives a transfer of 1 − α share of steady state capital income (net of depreciation) and retailer’s profits, and pays a share 1 − α of government spending (though new government spending is paid for by the Ricardian HH). This means that the HtM HH receives a share of 1 − α of total consumption, which equalizes steady state labour supply across households, which simplifies the steady state when ϑ 6= 1. In the simple model, assume a wage subsidy equal to s = X − 1 (where X is the gross markup), funded by a lump sum tax of (X − 1)Y on Ricardian HHs, who own retailers. In addition to ensuring HtM HHs receive 1 − α of total consumption, the subsidy also ensures their wage income is 1 − α of GDP. This assumption is quantitatively unimportant, but allows us to deliver cleaner analytical expressions for multipliers.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
where U (c1, L1,t (i)) = ln(c1,t ) −
9
Lϕ+1 1,t (i) and subject to budget, capital accumulation conϕ+1
straints, labour demand:
(2.2)
c1,t + It + bt = (Rt−1 /πt )bt−1 + M P Kt Kt−1 + w1,t (i)L1,t (i) + Πt − T axt
(2.3)
Kt = (1 − δ)Kt−1 + [1 + S(It /It−1 )]It
(2.4)
? L1,t (i) = (W1,t (i)/W1,t )−εw L1,t
Here ϕ−1 is the Frisch elasticity of labour supply. For most of the paper ξtb is fixed at unity (and so does not affect the model), though in Section 6 we consider a financial crisis which is in part driven by an increase in ξtb that increases desired savings.12 For decisions other than wage setting, β1 = β. The capital adjustment cost takes form of an cost S(.) to produce an extra unit of capital when It 6= It−1 in Equation 2.3. Following Christiano et al (2005), Altig et al (2011) and Smets and Wouters (2007), S(1) = S 0 (1) = 0 and S 00 (1) > 0 in steady state. Relative to an adjustment cost in terms of changes in the capital stock (Kt − Kt−1 )2 , this formulation is better able to replicate the hump-shaped response of investment to a monetary policy shock in Christiano et al (2005), and helps us match the dynamics of the Great Recession in Section 6. In log-linear terms, investment(ˆit ), depends on its own lagged and (expected) future value, as well as shadow price of capital qˆt (Equation 2.5).
(2.5)
12In
ˆit =
1 ˆ β 1 it−1 + Etˆit+1 + qˆt 1+β 1+β (1 + β)S 00
non-linearised terms Euler equation becomes cˆ1,t = Et cˆ1,t+1 − Rˆt − Et π ˆt+1 + ξˆtb
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
10
The shadow price of capital qˆt is determined by its expected future price, the expected return to capital, and the opportunity cost of investing in a risk-free bond. We introduce a reduced-form financial friction as a spread ξts between the interest rate relevant for investment, and the risk free rate.13 A shock to this spread generates a financial crisis in Section 6.
(2.6)
ˆ t − Et π qˆt = β(1 − δ)Et qt+1 + [1 − β(1 − δ)]Et M PˆKt+1 − (R ˆt+1 + ξˆtb + ξˆts )
The Ricardian household’s problem in the simple model is similar, except that there is no capital or investment, and labour markets are competitive with flexible wages. Hence in the simple model L1,t (i) = L1,t and w1,t (i) = w1,t ∀i.
2.2. Hand-to-Mouth (HtM) household’s problem. The HtM household member’s problem is much simpler than that of the Ricardian household: each individual household member i ∈ [0, 1] only has to choose desired labour hours (L2,t (i)) as he/she can not smooth consumption over time. Real consumption (c2,t ) is equal to labour income plus lump-sum transfers ( T rt ) from the government, and will be equal across household members due to our assumption of perfect within-household insurance of Calvo wage shocks. In the simple model, L2,t (i) = L2,t and w2,t (i) = w2,t ∀i as labour markets are competitive.
(2.7)
max{c2,t ,L2,t (i)} E0
∞ X
β2 t U (c2,t L2,t (i))
t=0
where U (c2,t L2,t (i)) = ln(c2,t ) − (2.8)
13In
Lϕ+1 2,t (i) such that: ϕ+1
w2,t (i)L2,t (i) + T rt = c2,t
Bernanke et al (1999), the price of capital evolves in the same way (a combination of their Equations 2.17 and 4.18), but where the spread ξts is proportional to leverage (q + k − n) of entrepreneurs. A financial crisis shock will reduce the net worth of entrepreneurs (n), increasing leverage and the spread ξts . The discount factor shock ξˆtb also affects the opportunity cost of investment via Ricardian HH’s stochastic discount factor.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
11
? L2,t (i) = (W2,t (i)/W2,t )−εw L2,t
(2.9)
Here ϕ−1 gives the Frisch elasticity of labour supply. For decisions other than wage setting, β2 = β. 2.3. Sticky prices, Retailers, Intermediate and Final Output. Intermediate output is Cobb-Douglas in capital and labour, and is produced by a unit continuum of competitive intermediate goods producers. Aggregate labour is Cobb-Douglas in the labour inputs of the two households (see below and Online Appendix 2 for alternative assumption). There is no capital (µ = 0) in the simple model.
(2.10)
Yt = K µt L1−µ t
(1−α)
where Lt = Lα1,t L2,t
As in Bernanke et al (1999) and Iacoviello (2005), final output is produced by a unit continuum of retailers, indexed by l, who buy intermediate output Yt at price Ptint in a competitive market, costlessly differentiate it, and sell a variety of final output Yl,t at price σ ´ σ−1 σ−1 1 Pl,t . Aggregate final output is given by the index Ytf = 0 Yl,t σ dl and aggregate prices ´ 1 1−σ 1/(1−σ) are given by Pt = ( 0 Pl,t dl) . Each retailer faces a downward sloping demand curve for his variety, and he must choose the optimal nominal price taking into consideration the Calvo probability θ that he may not be able to change his price. The pricing problem of retailers leads to a standard New Keynesian Phillips curve (Equation 2.11), which is shown in log deviation from steady state, where π ˆt = lnPt − lnPt−1 is the inflation rate (steady state ˆ t = lnXt − lnX is the deviation in the retailer’s average markup from inflation is zero), X steady state (where X =
σ σ−1
and κ = (1 − θp )(1 − βθp )/θp ). The parameter κ is the slope of
the Phillips curve — the higher κ, the more responsive inflation (and less responsive output) is to a given shift in demand. With flexible prices κ → ∞, so shifts in demand affect prices and not output. With more sticky prices (higher θp ) a larger share of firms are unable to change their prices to move markups towards their desired level, resulting in a muted response
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
12
of inflation and a boost in output to increases in demand (such as government purchases or transfers).
ˆt π ˆt = βEt π ˆt+1 − κX
(2.11)
The price of intermediate output in terms of final output is the inverse of the retailer’s P int 1 average markup t = . As such, the marginal product of labour or capital in terms of Pt Xt intermediate goods must be divided by the markup to generate the real marginal product. As in Galí (2008), deviations of Ytf from Yt are second-order in the neighbourhood of the steady state, and so for our first-order approximation Yˆt = Yˆtf . Aggregate real wages are given by: (2.12)
w1,t = α
1 Y 1 Yt , w2,t = (1 − α) Xt L1,t Xt L2,t
2.4. Sticky wages. The government transfer multiplier depends crucially on the labour supply response of different types of households. Christiano et al (2005) argue that sticky wages are important for fitting the response of a monetary policy shock to the data. Because wage stickiness necessitates adding extra state variables (lagged real wages), we assume flexible wages in the simplified model (but include sticky wages in the full model in Section 5). We model wage stickiness as in Erceg, Henderson, and Levin (2000) and Galí (2008). The labour supply of household type {Ricardian, HtM }, L1,t and L2,t respectively, are now CES ´1 composites of differentiated labour inputs (indexed by i): L1,t = [ 0 L1,t (i)di] and L2,t = ´1 [ 0 L2,t (i)di] where the demand for each variety i is given by Equation 2.4 and 2.9.14 Since households posses market power in their labour supply decisions, they are able to set their wage at a steady state markup above their marginal rate of substitution µw = εw /(εw − 1).
14The
nominal wage indices (upper case) are defined as: W 1,t = [ ´1 1 [ 0 W 2,t (i)1−w di] 1−w
´1 0
1
W 1,t (i)1−w di] 1−w and W 2,t =
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
13
Each member i of the Ricardian and HtM households is allowed to reset its nominal wage with constant probability 1 − θw in each period. As such, the wage decision of the Ricardian ? HH in time t = 0 is to choose W1,0 (i), to maximize Equation 2.1 subject to Equation 2.4
and other constraints, where the discount rate β1 = βθw is lower to reflect the fact that ? the further into the future, the less chance the fixed nominal wage W1,0 (i) will apply. The
HtM HH’s problem is analogous. The optimal nominal wage of HHs of type i (who gets to reset at time t = 0) can be expressed as a weighted average of expected future wage level for other households and the log deviation of the wage mark-up from its steady state ˆ k,t − cˆk,t . If µ level µ ˆw ˆk,t − ϕL ˆw k,t = w k,t > 0 means that the households are willing to supply more labour than is demanded by firms at given wage, which we interpret in Section 6 as unemployment above its natural rate.15 Aggregating over types that cannot reset wages, we get the New Keynesian wage Philips curve (Equation 2.13), where nominal wage inflation for each household π ˆw k,t = lnWk,t − lnWk,t−1 , k = 1, 2 will be a function of expected wage inflation tomorrow and the deviations of each household’s marginal rate of substitution from its steady state level µ ˆw k,t (variables with hats generally denote deviations from steady-state).
π ˆw ˆw µw k,t = βEt π k,t+1 − λˆ i,t
(2.13) where λ =
(1−θw )(1−θw β) , θw (1+ϕ)
and wˆk,t = wˆk,t−1 + π ˆw ˆ t , k = 1, 2 is the real wage. k,t − π
Relation to Gali et al (2007)’s imperfectly competitive labour markets In a related model, Galí et al (2007) argue that imperfectly competitive labour markets are needed to fit the response of consumption to a government purchases shock with a reasonable share of HtM HHs. It turns out that their formulation with perfect substitutes across HH types generates exactly the same aggregate allocations and multipliers as the Cobb-Douglas specification used here in Equation 2.10 (including a generalization to sticky wages). In 15That
is, the supply side of the labour mark adjusts to meet excess demand or supply caused by sticky wages. In the former case, workers are still willing to supply labour for a smallˆ µw k,t < 0 due to the steady state wage mark-up.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
14
Online Appendix 2.1 we show the equivalence analytically between our simple model with a Cobb-Douglas specification, and a similar model with perfect substitutes and a union as in Galí et al (2007). We also verify the equivalence numerically for the full model with sticky wages.
2.5. Monetary and Fiscal Policy. During normal times, the central bank follows a Taylor ˆ t = lnRt − lnRSS is the log Rule (in linearised form) with interest rate smoothing, where R deviation of the gross nominal interest rate from its steady state level. We allow for the possibility that the central bank is constrained by the ZLB and keeps the nominal rate fixed for a certain number of periods before resuming the Taylor rule (Equation 2.14). The degree of interest rate smoothing is governed by the parameter φR .
ˆ t = φR R ˆ t−1 + (1 − φR )(φπ π R ˆt + φY Yˆt )
(2.14)
Government expenditures consist of unproductive government purchases Gt , and targeted transfers to the HtM households T rt . Government expenditure is financed by a lump sum ˆ t are tax on the Ricardian households T axt . Note here that throughout the paper, Tˆrt and G the deviation of transfers and government purchases from steady state as a share of GDP, i.e. Tˆrt ≡
T rt −T rSS , YSS
T ˆaxt ≡
T axt −T axSS YSS
ˆt ≡ and G
Gt −GSS . YSS
This simplifies the expressions for
multipliers and allows for the possibility that purchases are zero in steady state. The notation only applies to transfers and purchases: other variables with “hats” are log deviations from their respective steady-states. The government runs a balanced budget each period (Equation 2.15). Whether the government runs a balanced budget does not matter for the path of the economy as taxes are only levied on the unconstrained households, who are Ricardian — it is only the timing of the transfers and purchases that affect allocations.16
16This
is not the case if taxes are levied only on the HtM HHs or if taxes are distortionary. Equation 2.15 excludes steady state transfers across households to ensure consumption shares equal labour shares.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
(2.15)
15
T axt = T rt + Gt
ˆ t are exogenous and are assumed to follow an AR(1) process. The path of Tˆrt and G
(2.16)
Tˆrt+1 = ρTˆrt + eT r,t+1
(2.17)
ˆ t+1 = ρG ˆ t + eG,t+1 G
where {eT r,t+1 , eG,t+1 } are zero-mean i.i.d shocks. The model is closed by the standard aggregate resource constraint:
(2.18)
Yt = c1,t + c2,t + It + Gt
3. Mechanisms on Labour Supply, Empirical Evidence and Calibration The effect of targeted transfers on aggregate demand is identical to that of purchases — they are both spent — and the only difference depends on supply. Absent general equilibrium effects through wages, transfers and purchases generate the same increase in taxes for the Ricardian household in our model: they both make the Ricardian HH worse off, which makes it want to work more (the neoclassical wealth/income effect). When the HtM HH receives a transfer, they spend some of the transfer on higher leisure (as leisure is a normal good) which lowers labour supply. The key difference between targeted transfers and purchases is that for transfers, the increased labour supply for the Ricardian HH offsets the reduced labour supply of the HtM HH, leaving total labour supply mostly unchanged. In contrast, as only Ricardian HHs pay taxes, government purchases have no direct effect on the labour supply of HtM HHs, and so government purchases increase aggregate labour supply via the increased
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
16
labour supply of the Ricardian HH. The rest of this paper traces out the implications of increase in labour supply of purchases (relative to transfers) in general equilibrium. As such, most of our results hinge on the wealth/income effect on labour supply. Without the wealth effect – for example, with Greenwood–Hercowitz–Huffman (GHH) preferences – transfers have the same effect on aggregate supply as purchases, and hence the targeted transfer multiplier is the same as the purchases multiplier. In practice, the absence of a wealth effect means that transfer-based stimulus will always deliver a smaller boost to output than a similarly sized purchase-based stimulus because transfers cannot be perfectly targeted at the HtM, verifying the traditional intuition than purchase-based stimulus is more effective. The wealth effect enters the model through the household’s labour-leisure first order condition. With standard (separable) preferences as in Section 2, a transfer to the HtM HH increases consumption (as c2 = w2 L2 + T r2 ), which increases the denominator of the LHS of Equation (3.1), and therefore reduces labour supply L2 . In contrast, with GHH preferences, consumption and transfers do not appear in the labour-leisure FOC (RHS of Equation 3.1), and so there is no effect of the transfers on supply.
(3.1) Standard pref. :
L2 = [w2 /c2 ]1/ϕ = [w2 /(w2 L2 + T r2 )]1/ϕ
GHH pref :
1/ϕ
L2 = w2
Given the importance of wealth/income effect on labour supply to the mechanism in this paper, in Section 3.1 we present empirical evidence on its strength and the size of the related Frisch elasticity, and discuss its interaction with labour market features like as sticky wages (3.2).
3.1. Empirical evidence on the size of the income effect. The income effect is defined in the labour economics literature as the change in labour earnings due to an increase in non-labour income (Keane 2011), which is also called the “marginal propensity to earn”. With our notation, this becomes:
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
17
(3.2) IncomeEf f ect(Std pref, w) ¯ ≡ w2
∂L2 1 ≈− <0 ∂T r2 ϕ+1
(zero f or
GHH
pref )
where we are assuming that transfers are small relative to labour income to simplify this expression (ϕ−1 is the Frisch elasticity).17 As expected, with standard preferences (as we use in this paper) the income effect is negative — an increase in transfers reduces labour supply and hence labour earnings (at constant wages). With GHH preferences, an increase in non-transfer income has no effect on labour supply, and hence has no effect on labour income. As such, it is relatively easy to compare these preferences by testing the whether the marginal propensity to earn is negative. The empirical labour literature generally find negative and significant estimates of the income effect, albeit ones that vary across studies and are often modest in size. Estimates are summarized as follow (see Online Appendix 10 for a more detailed discussion). First, studies using lotteries (Imbens et al (2001), Cesarini et al (2015)) find a significant MPE of around -0.12. Second, some estimates are more negative (and also significant), such as -0.3 in a South African natural experiment (Bengtsson 2012) or -0.37 for a survey of near-retirees in the US (Kimball and Shapiro 2008) (near-retirees often have a higher MPE). Third, literature surveys find a variety of estimates, which range from -0.3 to 0 (mean of -0.1) for negative income tax experiments in the US, -0.7 to 0.08 (mean -0.13) for other US studies on men, and -0.5 to -0.04 (mean -0.36) for British studies (Pencavel 1986). Finally, income/wealth effects are needed to match the relative long-run stability of hours combined with rising real wages (Kimball and Shapiro 1998). Our default calibration of ϕ−1 = 1 implies income effects of around -0.5, which are at the lower end of this range. In Online Appendix 1 we show our results are reasonably robust to
∂L2 σS2 w2 L2 =− where S2 = . We assume ∂T r2 ϕ + σS2 w2 L2 + T r2 σ → 1 (log utility) and S2 ≈ 1 (transfers are small relative to labour income) in deriving Equation 3.2. (see Keane (2011) Eqn 10) 17The
full expression with CRRA preferences is w2
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
18
assuming ϕ−1 = 0.2, which implies income effects of around -0.17 — close to the mean of the studies above. Relation to the Frisch Elasticity From Equation 3.2, one can see that the strength of the income effect depends on the Frisch elasticity, such that as ϕ−1 → 0, the income effect goes to zero. One might think this implies that for low Frisch elasticities, the transfer multiplier is equal to the purchase multiplier. Actually, conditional of there being wealth effects on labour supply, the Frisch elasticity is relatively unimportant for the relative size of transfer and purchases multipliers because as ϕ−1 → 0, a larger increase in wages are needed to increase labour supply to meet demand, which has other effects in general equilibrium. In the simple model (Section 4), the size of the Frisch does not matter at all for the relative size of the purchase and transfer multipliers. A higher Frisch decreases both multipliers proportionately when the transfer multiplier is larger than the purchases multiplier (such as at the ZLB), but increases both multipliers proportionately otherwise. In the full model (Section 5), transfer and purchase multipliers also move together as the Frisch changes, though not exactly proportionately (assuming the slope of the wage Philips curve doesn’t change much).18 A higher Frisch elasticity means that wages (and hence inflation) don’t have to increase as much in order to meet a given increase in demand. This generally increases multipliers in normal times (as higher inflation raises real interest rates), but decreases multipliers at the ZLB when higher inflation reduces real interest rates. Frisch elasticities in macroeconomics are usually much larger than in microeconomic studies, and there is a vast literature documenting this fact and proposing ways of reconciling the differences. Macro Frisch elasticities are generally identified based on variation in aggregate hours worked over the business cycle, whereas micro estimates are based on the response of individual hours worked to tax and other policy changes. Chetty et al (2011a) summarize 18Changes
in the Frisch elasticity can also affect the slope of the wage Philips curve (recall λw = (1 − θw )(1 − θw β)/[θw (1 + ϕεw )]), such that a lower Frisch has the same effect as an increase in wage stickiness (see next subsection) which causes the transfer multiplier to move towards the purchase multiplier (which is relatively unaffected). However, when we lower the Frisch in robustness tests we also reduce the cross-variety substitution elasticity εw , which largely offsets the change in the Frisch.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
19
the macro estimates at around 2.8 and micro estimates at around 0.8. Peterman (2015) summarizes micro Frisch estimates around 0-0.5 whereas macroeconomists find 2-4. On the micro side, and the Congressional Budget Office (Reichling and Whalen 2012) find Frisch elasticities of 0.27-0.53. On the macro side, Smets and Wouters (2007) estimate a Frisch of around 2. There are a number of possible explanations of the differences (see Online Appendix 10 for details): (i) differences in samples, for example prime-aged married men (the focus of the literature) generally have lower Frisch elasticities than women (Peterman 2015, Keene 2011); (ii) individual’s labour supply may under-respond to policies because of a lack of information (Chetty et al 2013) and (iii) frictions and indivisibilities which stop individuals from changing hours even if they wanted to, biasing microeconomic estimates towards zero. Chetty et al (2011b) partly adjust for this and conclude: “Even accounting for indivisible labour, micro studies do not support representative-agent macro models that generate Frisch elasticities above one” (p4). Based on this evidence, we choose a default Frisch elasticity of ϕ−1 = 1, which has also been used in the macro literature (Christiano et al (2005) and Nakamura and Steinsson (2014)). Our alternative calibration ϕ−1 = 0.2 (see Online Appendix 1) is towards the middle of the estimates of the micro literature as surveyed by Peterman (2015).
3.2. Sticky Wages. Sticky wages weaken wealth effects on labour supply, which drive the differences between targeted transfers and purchases. When wages are flexible, µ ˆw 2,t = 0 in Equation 2.13, such that an increase in consumption by the HtM HHs in response to a transfer must be offset by lower labour supply (or higher wages, which drive inflation). When wages are sticky, part of the downward pressure on labour supply is absorbed by variation in the labour markup µ ˆw 2,t , which will fall in response to a transfer shock. This means that at a constant wage, HtM labour supply will fall by less in response to a transfer shock in the short run, or alternatively, wages don’t need to rise as much in order to get the HtM HH to offset the wealth effect. This latter effect reduces the excess inflation generated by transfers, which
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
5
4
20
ρ=.9, Transfer Mult. ρ=.9, Purchases Mult. ρ=0, Transfer Mult. ρ=0, Purchases Mult.
PV Multiplier
3
2
1
0
−1 0
0.2
0.4
0.6
0.8
1
Nominal wage stickiness (θw)
Figure 3.1. Wage stickiness and the PV multiplier (full model). The vertical line indicates default parametrisation made the transfer multiplier more sensitive to the strength of the monetary policy response in the simple model. Sticky wages drive most of the differences between the full and simple models.19 In general, the more sticky the wage, the closer the multiplier on purchases and targeted transfers. Figure 3.1 shows the effect of varying the Calvo probability of unchanged nominal wages (θw ) on the multipliers in the full model. With θw = 0, nominal wages are flexible and multipliers are similar to those in the simple model (and the purchase multiplier is very different from the transfer multiplier). When θw = 1, nominal wages are perfectly sticky and the purchases and transfer multipliers are identical.20 3.3. Parameters and related empirical evidence. Parameters (listed in Table 1) are taken from the literature, but are also chosen to be consistent with empirical evidence on the response of consumption for different groups to a transfer shock. Figure 3.2 shows the MPC estimated by Johnson et al (2006) in response to the 2001 Bush Tax rebates and compares 19When
wages are sticky, last period’s real wage is a state variable and hence output will no longer be a constant multiple of the exogenous fiscal shock, ruling out an analytical solution for the multiplier. 20The extent to which nominal wages or the wage markup change will depend on the persistence of the shock. Households are much less willing to change their nominal wage in response to a once-off shock (in case they cannot change it next period), and so choose to withstand a larger change in the wage markup. The opposite is true for more persistent shocks: households prefer to adjust nominal wages rather than markups. Hence sticky wages have a much larger effect for temporary versus permanent shocks.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
21
Table 1. Full Model Parametrisation and Steady State Parameter
Value
Parameter
Value
Discount Rate (β)
0.995*
Investment adj. cost (S 00 )
1.5
Frisch Labour Elasticity (ϕ−1 )
1* or 0.2
Capital depreciation rate (δk )
0.03
Labour share HtM HH (1 − α)
0.3*
Calvo Prob. constant wage (θw )
0.75
Calvo Prob. constant P (θp )
0.75*
Sticky Wage elasticity (ε)
20.5 or 4.5
Taylor Rule Inflation (φπ )
1.27*
Capital share (µ)
0.25
SS markup (X = σ/(σ − 1))
1.05*
Taylor Rule Smoothing (φR )
0.73
SS Govt Purchases Share (GSS )
0.2
Taylor Rule Output (φY )
0.13
* Indicates parameter is also in simple model (others are zero in the simple model).
them to an analogous group from the full model.21 In both the model and data, the lowest third of consumers by liquid assets tend to spend all their income, whereas the top two thirds of consumers defined by their holdings of liquid assets do not. The model’s estimates are well within one standard error of the data (not reported). The MPC profile is most sensitive to the share of HtM in the model, 1 − α = 0.3. Kaplan et al (2014) present a range of micro evidence that that a third of households are hand-to-mouth in the US, UK and Germany.22 A calibration of 0.3 is in the middle of the range of macroeconomic estimates of the share of constrained HHs, such 0.36 in Iacoviello (2005), 0.5 from Campbell and Mankiw (1989) and Galí et al (2007) and 0.26 from Cogan et al (2010). Other parameters are fairly common in the literature. Evidence on the Frisch elasticity is surveyed above, and we take values of unity (baseline) and 0.2 (Section 6) from Galí (2011) which are consistent with that evidence (as well as wage markups). We assume that wages change on average once a year, in line with evidence from Barattieri et al (2014). Investment adjustment costs are estimated by Altig et al (2014), and the capital share (µ) chosen to match a steady state I/Y of around 20%, the average 2001-15 (WDI: NE.GDI.FTOT.ZS). 21In
the full model, this is the response to an untargeted once-off transfer. Specifically, HtM HH are compared to those with less than US$1000 in liquid assets, and Ricardian households are compared to those with more than US$8000 in liquid assets, and those with US$1000-US$7000 in liquid assets. The data are from the bottom of Table 5 in Johnson et al (2006), and refer to MPC for non-durables. 22Though the majority of these are “wealthy HtM” (rich in illiquid assets but poor in liquid assets).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
22
Taylor rule coefficients, price stickiness and depreciation rate are estimated by Iacoviello (2005). In the full model, steady state government purchases are set at 20 per cent of GDP (GSS = 0.2) (as is common in the literature), funded by a lump sum tax on each household in proportion to labour income. Government transfers for fiscal stimulus, T rt , are zero in steady state, though the HtM HH does receive steady state transfers equal to a share (1 − α) of total firm profits and capital income (after depreciation), such that the two households receive a fraction αand 1 − α of total consumption. We solve the full model numerically using Dynare. Marginal Propensity to Consume: by assets 2001 Bush tax rebate: model vs data (Johnson et al 2006)
1.5 1.25 1
Data
Model
0.75 0.5 0.25 0 -0.25 Highest Assets 1/3 Middle Assets 1/3 Lowest Assets 1/3 Consumers Consumers Consumers Notes: Data: point estimates from Table 5 of Johnson et al (2006). Model: MPC to a imperfectly targeted once-off transfer (full model). One third is approximate for both model and data.
Figure 3.2. Marginal Propensity to Consume: Data and Model
4. When is the transfer multiplier larger than the purchase multiplier? Analytical results from a simplified model In this section we derive analytical expressions for the targeted transfer and purchases multipliers in “normal” times when the central bank follows a Taylor rule (Section 4.1) or when nominal interest rates are at the Zero Lower Bound (ZLB, Section 4.2). Given the analytical approach, we focus on the relative size of the transfer and purchases multipliers which we can characterize exactly, rather than the numerical size of the transfer multiplier which requires a richer model (Section 5).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
23
The effects of targeted transfers and purchases on output and inflation are best understood in a modified aggregate supply-aggregate demand setup (which we derive analytically). Transfers and purchases provide the same boost to aggregate demand, but only purchases increase aggregate supply via the neoclassical wealth effect. When the aggregate demand curve is downward sloping, the purchases multiplier is larger than the transfers multiplier.23 But when the aggregate demand curve inverts, the transfer multiplier will be larger than the purchases multiplier because the extra inflation from lower supply boosts the multiplier. We show that the transfer multiplier is occasionally larger (depending on parameters) than the purchases multiplier when monetary policy follows a Taylor rule (Section 4.1), but is always larger than the purchases multiplier when the ZLB binds (Section 4.2). As such, the transfer multiplier is more sensitive to the monetary policy response to inflation than the purchases multiplier, which we show analytically in Proposition 4. Section 4.3 presents some tractable generalizations, such as when transfers are imperfectly targeted at the HtM HH or when fiscal policy is financed by persistent debt. We have to make some simplifying assumptions to derive the analytical results in this section, and they fall into two categories. The first group of assumptions make sure the ˆ t or Tˆrt — multiplier is constant over time — that is, output is a constant multiple of G by removing endogenous state variables such as capital, lagged wages or the lagged interest rate. Specifically, we assume (i) wages are flexible (λ → ∞), (ii) the production function is Cobb-Douglas in labour only (µ → 0), and (iii) the central bank does not smooth interest rates (φR = 0). The second group of assumptions simplify the expressions by assuming (i) the central bank does not respond to output (φY = 0) and (ii) ensuring that the steady state consumption share of each household is equal to their share of wage income (we relax this last assumption in Section 4.3.3).24 23As
discussed above, if preferences are GHH the targeted transfer and purchases multipliers and are −1 1 αϕκ [φπ − ρ] − (1 − α) .With either perfect inflation targeting (φπ → ∞) or flexible prices ϕ ϕ + 1 (1 − ρ)(1 − ρβ) (κ → ∞), the GHH multiplier will go to zero. 24That is, we set steady state government purchases to zero (G = 0), and assume a wage subsidy equal to ss sss = Xss − 1 (where Xss is the steady state gross markup), funded by a lump sum tax of (Xss − 1)YSS on Ricardian HHs such that consumption and wage income of each HH is a share α or 1 − α of total GDP. A
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
24
4.1. The transfer multiplier when Monetary Policy follows a Taylor rule. The list of log-linearised equations (A1-A9) is shown in the box where a hat (^) denotes percentage deviation from steady state (except for transfers and purchases, where it represents the change in fiscal policy as a share of GDP). Box 1: Equations in the Analytical Model (A1-A9) ˆ 1t + (1 − α)L ˆ 2t [A1 Production Function] Yˆt = αL ˆt [A2 Resource Constraint] Yˆt = αˆ c1,t + (1 − α)ˆ c2,t + G ˆ 2,t ) [A3 HtM Budget Constraint] (1 − α)ˆ c2,t = Tˆrt + (1 − α)(wˆ2,t + L ˆ t − Et π [A4 Ricardian Euler Equation] cˆ1,t = − R ˆt+1 + Et cˆ1,t+1 [A5 Taylor Rule] Rˆt = φπ π ˆt ˆt [A6 Phillips Curve] π ˆt = βEt π ˆt+1 − κX ˆ t+1 = ρG ˆ t + eˆG,t+1 [A7 Fiscal policy (exogenous)] Tˆrt+1 = ρTˆrt + eˆT r,t+1 or G ˆ kt , ∀k = 1, 2 [A8 Labour-Leisure FOC] wˆkt = cˆkt + ϕL ˆ k,t − X ˆ t , ∀k = 1, 2 [A9 MPL=wage] wˆk,t = Yˆt − L Proposition 1. Flexible price multiplier. In the limit of the simple model when prices are flexible (κ → ∞), the transfer multiplier is zero and the government purchase multiplier is 1/(ϕ + 1) (where ϕ−1 is the Frisch elasticity of substitution). Proof. Combine Equations A8, A9, A1, A2 to form Equation 4.1. When prices are flexible ˆt = 0 (κ → ∞), retailers keep their markups constant at the profit-maximising optimum, so X and hence Yˆt =
(4.1)
1 ˆ G. ϕ+1 t
Yˆt =
1 ˆ 1 ˆ Gt − Xt ϕ+1 ϕ+1
The flexible price multiplier is driven entirely by wealth effects on labour supply. Both targeted transfers and purchases are funded by a lump-sum tax on the Ricardian household which cause it to increase labour supply (a negative wealth effect) when its consumption falls similar approach used by Bilbiie (2008) is to assume a fixed cost of operating each firm that exactly offsets profits in steady state.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
25
to pay the tax. For purchases this is the end of the story: higher labour supply boosts output leading to a positive multiplier of (1 + ϕ)−1 (the neoclassical wealth effect - the negative of Equation 3.2). For transfers, this negative wealth effect for the Ricardian household is exactly offset by the positive wealth effect on the HtM HH who receives the transfer, leaving output unchanged. An implication of Equation 4.1 is that transfers affect output through variation ˆt. in markups X Note that Proposition 1 is a special case when the consumption share of each household is equal to its labour share, which means that wealth effects exactly cancel. In Section 4.3.3 and Online Appendix 4 we show that the flex-price transfer multiplier can be positive (negative) if the HtM HH’s consumption labour share is larger (smaller) than his labour share. Solving the analytical model with sticky prices We solve the analytical model — and show how it works — in five steps. In the first step we rearrange the Equations A1-A9 into a modified New Keynesian IS Curve (Equation 4.2) and a standard New Keynesian Phillips curve (Equation 4.3, which does not depend on the HtM share). In the case that there are no HtM HHs (α = 1) (transfers are not defined in this case), the modified NK IS curve collapses to its standard version: Yˆt = ˆ t − Et G ˆ t+1 ). The Philips curve is the same as it would be in a Et Yˆt+1 − (φπ π ˆt − Et π ˆt+1 ) + (G standard NK model without HtM HHs. In the second step, restrict the parameter space to where Assumption A1 holds (φπ > 1 and 1 − α < (2 + ϕ)−1 ), which we show in Lemma 1 is a sufficient condition for determinacy (see Section 4.1.1 and the Online Appendix 5 for a further discussion).25 All our results with a Taylor rule — even when the transfer multiplier is larger than the purchase multiplier — are in this region of the parameter space. Assumption A1: The Taylor Principle holds (φπ > 1) and the HtM share is not too high (1 − α < (2 + ϕ)−1 ).
25In
a related model, Gali et al (2004) find that only the Taylor principle is required so long as the HtM share is below a certain cut-off (around 0.57 with default parameters, their Figure 2), which is consistent with the finding here. Bilbiie (2008) also finds that when the HtM share is reasonably low the Taylor Principle is sufficient for determinacy (his Proposition 7).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
26
Lemma 1. The conditions in Assumption A1 are a sufficient condition for determinant equilibrium of the simple model (Equation 4.2-4.3). Proof. Rearrange Equation 4.2-4.3) in state-space form, and use Woodford (2003) Proposition
C1 (p670).
Box 2: Dynamic two-equation system in the simple model Modified New Keynesian IS Curve (with a fraction 1 − α of HtM HHs):
(4.2)
Yˆt = Et Yˆt+1 −
h i h i ˆ t+1 − G ˆ t + α−1 Et Tˆrt+1 − Tˆrt (φπ π ˆt − Et π ˆt+1 ) + Et G 1 − α−1 (1 − α)(ϕ + 1)
Standard New Keynesian Phillips Curve
(4.3)
h i ˆ t − (ϕ + 1)Yˆt π ˆt = βEt π ˆt+1 − κ G
In the third step, we use Lemma 2 to solve for expectations of future variables in terms of current variables, which removes all dynamics from the model.26 Because all variables follow an AR(1) process with the same persistence ρ, the static solution of the model at t+1 is just a shrunk-down version of the static solution of model at t. Lemma 2. Following an unanticipated transfers or purchases shock with persistence ρ, all model variables follow an AR(1) process with persistence ρ along the adjustment path. That is, for any variable Zˆt then Et Zˆt+1 = ρZˆt Proof. Follows from the linearity of the model and lack of endogenous state variables. Can be shown by guess and verify.
Aggregate supply and demand 26When
prices are flexible, the model is essentially static because real interest rate adjusts to make the Euler equation hold.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
27
The fourth step is to show the equilibrium can be characterized by an aggregate supply and aggregate demand relationship linking current output Yˆt and current inflation π ˆt . This is similar to the “Old Keynesian” aggregate demand and aggregate supply relationships in undergraduate textbooks, but with rational expectations micro-foundations.27 The supply curve (Definition 1) is virtually unchanged from the standard NK model, so we don’t dwell on it, other than to note that labour supply decisions of households (which affect firms’ marginal costs) affect the supply curve but not the demand curve (note the inverse of Frisch elasticity substitution ϕ in Equation 4.4). The slope of the aggregate demand curve (Definition 2) is key in determining the relative size of transfers and purchases multipliers, so we provide a further decomposition of the opposing forces driving its slope: the Taylor Principle (TP) effect (Definition 3) and the Disposable Income (DI) Effect (Definition 4). The two factors correspond (respectively) to the determinants of the two endogenous components of aggregate demand (Equation A2): consumption by the Ricardian household as a share of GDP αˆ c1,t and consumption by the HtM HH as a share of GDP (1 − α)ˆ c2,t . In the final step, we identify the multiplier by intersecting the aggregate demand and supply curves (substituting out for inflation). Transfers and purchases both increase demand by the same amount (Remark 2), but only government purchases expand supply (Remark 1). This means that the targeted transfer multiplier will be larger than the purchases multiplier iff the aggregate demand equation inverts (slopes upwards). Proposition 2 presents the transfer and purchase multipliers and Proposition 3 lists some implications. Proposition 4 shows that the transfer multiplier is more sensitive to the monetary policy response to inflation than the purchases multiplier. Definition 1. Aggregate Supply Curve. The aggregate supply curve is given by Equation 4.4, and reflects the desired output of firms YˆtAS at a given level of inflation π ˆtAS . The curve is the generalization of the Phillips curve (Equation A6), solving out for expectations (using 27For
a given price level last period, solving for the inflation rate (as we do here) or the price level (as in the Old Keynesian Model) are isomorphic.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
28
ˆ t (using Equation 4.1). Lemma 2) and markups X π ˆtAS =
(4.4)
κ(ϕ + 1) ˆ AS −κ ˆ Yt + Gt (1 − ρβ) (1 − ρβ)
Remark 1. Purchases increase aggregate supply, but transfers do not (i.e. only purchases appear in Equation 4.4).
Definition 2. Aggregate Demand Curve.
The aggregate demand curve is given by
Equation 4.5, and represents the level of output YˆtAD demanded for private and government consumption for a given level of inflation π ˆtAD . The curve is derived by combining the aggregate resource constraint (Equation A2) and Equations 4.6 and 4.7. The aggregate demand curve is the generalisation of the standard New Keynesian IS curve in terms of current inflation, solving out for expectations using Lemma 2, and solving for consumption demand of the HtM household.
AD
π ˆtAD
(4.5)
αYˆt =− Γ
+
ˆt Tˆrt + G Γ
where Γ = [α(φπ − ρ)/(1 − ρ)] − [(1 − α)(1 − ρβ)/κ] | {z } | {z } T P Ef f ect
DI Ef f ect
Remark 2. Purchases and targeted transfers have the same effect on aggregate demand.
Definition 3. Taylor Principle (TP) Effect. The fall in aggregate demand from the Ricardian household from an increase in inflation is given by α(φπ −ρ)/(1−ρ). Consumption of the Ricardian household is driven by the Euler equation (Equation A4), and so the Taylor Principle effect comes from substituting the Taylor rule (Equation A5) into the Euler Equation, and using Lemma 2 to solve for the expectations of future consumption and inflation (Equation 4.6). As its name suggests, α(φπ − ρ)/(1 − ρ) > 0 whenever the Taylor principle holds (i.e. φπ > 1), which ensures an increase in inflation raises real interest rates and lowers the consumption of the Ricardian household. When the ZLB binds, the Taylor Principle
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
29
Effect reverses its sign because a rise in inflation lowers real interest rates (Section 4.2 — effectively φπ = 0).
αˆ c1,t = − [α(φπ − ρ)/(1 − ρ)] π ˆ | {z } t
(4.6)
T P Ef f ect
Definition 4. Disposable Income (DI) Effect. The boost to aggregate demand by the HtM household from an increase in inflation, is given by (1 − α)(1 − βρ)/κ, other things (transfers and aggregate output) equal. Consumption of the HtM household is driven by its disposable income each period, and along the adjustment path inflation increases wages (by reducing markups), thereby boosting labour income. The disposable income effect is derived by substituting the firm’s FOC (Equation A9) into the HtM HH’s budget constraint (Equation A3), and using the Phillips curve (Equation A6) plus Lemma 2 to substitute out ˆ t to yield Equation 4.7. variation in markups X
(1 − α)ˆ c2,t = Tˆrt + (1 − α)Yˆt + [(1 − α)(1 − ρβ)/κ] π ˆ | {z } t
(4.7)
DI Ef f ect
Proposition 2. Sticky price multiplier. In the simple model when prices are sticky and monetary policy follows a Taylor rule and assumption A1 holds, the targeted transfer and purchases multipliers are given by Equation 4.8.
−1 κ(ϕ + 1) κ ˆ ˆ ˆ ˆ Yt = α + Γ T rt + Gt + ΓGt (1 − ρβ) (1 − ρβ)
(4.8) where:
−1 κ(ϕ + 1) • MT r = α + Γ > 0 is the transfer multiplier, (1 − ρβ) −1 κ(ϕ + 1) κ • MG = α + Γ 1+ Γ > 0 is the purchases multiplier, (1 − ρβ) 1 − βρ
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
30
• Γ = [α(φπ − ρ)/(1 − ρ)] − [(1 − α)(1 − ρβ)/κ] | {z } | {z } T P Ef f ect
DI Ef f ect
Proof. Use the aggregate demand (Equation 4.5) and aggregate supply (Equation 4.4) relations to eliminate π ˆt , and solve for Yˆt .
Proposition 3. Transfer and Purchase Multipliers and Inverted Aggregate Demand Curve. In the simple model when assumption A1 holds, the targeted transfer multiplier is larger than the purchase multiplier whenever: a) the Disposable Income effect dominates the Taylor Principle effect (i.e. Γ = [α(φπ − ρ)/(1 − ρ)] − [(1 − α)(1 − ρβ)/κ] < 0 | {z } | {z } T P Ef f ect
DI Ef f ect
or equivalently: b) the demand curve is inverted (slopes upward in (ˆ π , Yˆ )-space). Proof. Follows from Proposition 2 and Definition 2.
Discussion Proposition 2 describes the targeted transfer multiplier and the purchases multiplier when prices are sticky, and Proposition 3(a) shows that the transfer multiplier will be larger whenever the Disposable Income effect dominates the Taylor Principle effect.28 There are four key drivers of the relative size of the transfer and purchases multipliers: α, ρ, κ, and φπ . First, a higher share of HtM HH (↓ α) increases the share of aggregate consumption that is sensitive to labour income, and hence strengthens the Disposable Income effect, and weakens the Taylor Principle effect, increasing the relative size of the transfer multiplier. Second, along ˆ t /ˆ the adjustment path, the ratio of markup adjustment to inflation is −X πt = (1 − ρβ)/κ, which is decreasing in ρ. Hence, for more transitory shocks (↓ ρ) retailers prefer to lower their markups rather than increase prices (in case they cannot change prices back in the future) the central bank responds to output in# the Taylor rule, Equation 4.8 becomes Yˆt = −1 " ˆ αφY κ(1 + ϕ) ˆ t + Tˆrt + Γ κGt , which does not affect the relative size of the transα+ +Γ G (1 − ρ) 1 − ρβ 1 − ρβ fer and purchase multipliers (though reduces their absolute size). 28If
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
31
which strengthens the DI effect relative to the TP effect. Figure 4.1 Panel B shows that the transfer multiplier is larger than the purchases multiplier (white region) when fiscal policy is short-lived and the share of HtM HH is not too low (other standard parameters are listed in Table 1).
Figure 4.1. Panel A (left side): Regions of (φπ , α) parameter space that are determinant (white) or indeterminant (black). Panel B (right side): Regions of (ρ, α) parameter space where the transfer multiplier is larger (white), where the purchase multiplier is larger (grey/blue), or where the simple model is indeterminate (black). Notes: ρ is the persistence of the fiscal shock (transfers or purchases), and 1 − α is the share of constrained (HtM) HHs, and φπ is the Taylor rule coefficient on inflation. The other two important parameters are price stickiness and the coefficient on inflation in the central bank’s policy rule. As prices become perfectly sticky (κ → 0), the Disposable Income effect is always larger than the Taylor Principle effect, because a small increase in inflation leads to a large decrease in markups, and hence a large increase in wage income for the HtM household. Conversely, as κ → ∞, the disposable income effect goes to zero as inflation will have no effect on disposable income because markups are fixed (we also see this in Proposition 1). Finally, as the name suggests, a larger φπ increases the strength of the Taylor Principle effect, and decreases the transfer multiplier relative to the purchases multiplier. In Section 4.2, we show that having the ZLB bind is equivalent to φπ = 0, which will mean the transfer multiplier is always larger than the purchases multiplier.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
32
The effect of a transfer or purchases shock can be seen in shifts in the aggregate demand and aggregate supply curves in Figure 4.2.29 Because all transfers are targeted at the HtM HH who will consume them (we relax this assumption below in Section 4.3.1), transfers and purchases shift the demand curve out by the same amount (Equation 4.5)30 but only government purchases shift the aggregate supply curve (via the neoclassical wealth effect).31 As seen in Proposition 1, government purchases increase the desired labour supply of the Ricardian household (because they are worse off due to higher taxes), but transfers have no effect on aggregate supply because the extra labour supply of Ricardian households (who are worse off) exactly offsets the reduced labour supply of the HtM HH (who are better off). When the aggregate demand curve is downward sloping (for example with a high persistence shock, ρ = 0.9 in the left-hand panel of Figure 4.2), the increase in aggregate supply from a government purchases shock increases the purchases multiplier above the transfer multiplier. However, when the Disposable Income effect dominates the Taylor Principle effect, the aggregate demand curve inverts.32 As foreshadowed in Proposition 3b, this means that the transfer multiplier will be larger than the purchase multiplier. From the RHS of Figure 4.2 one can see that when the demand curve inverts, higher inflation boosts aggregate demand (by increasing the disposable income of the HtM HH more than it reduces the consumption
ˆ π ) with the original (solid) Aggregate Figure 4.2 Ox , (x = 1, 2) represents the steady state equilibrium (Y,ˆ Supply (AS) and Aggregate Demand (AD) curves. Ax represents the new equilibrium with a 0.2% GDP transfer shock contemporaneously, which shifts the AD curve to the right, but doesn’t affect AS. Bx reflects the new equilibrium with a 0.2% of GDP government purchases shock in the first period, which shifts both AD and AS curves to the right. At any period t in the future the figure looks identical except all points are scaled by ρt . 30 In Online Appendix 2.1, we show that the simple model A1-A9 in Box 1 is equivalent to assuming perfect substitutes with a union as in Galí et al (2007). In Online Appendix 2.2 we by assume that the labour of the two households are imperfect substitutes (with elasticity of substitution ϑ), without a union. This reduces the transfer multiplier, and substantially complicates the analysis, though doesn’t change the results much so long as the elasticity of substitution between labour inputs is not too high. Imperfect substitutes means that the aggregate demand curve shifts by less for a transfer than for a government purchase, because some of the income from the transfer is spent on leisure instead of consumption (this doesn’t happen in the Cobb-Douglas model because lower labour supply for a household is offset by higher wages, keeping the labour income constant). As a result, the AD curve has to be even more inverted for the transfer multiplier to be greater than the purchase multiplier. 31 ˆ t shifts the demand curve right by 1/α, which is the “old Keynesian” multiplier A one unit increase in Tˆrt + G of 1/(1-MPC). 32The slope of the supply curve is always positive. It increases with (1 + ϕ) and decreases with κ — this means that the supply curve is flatter (more Keynesian) with a higher Frisch elasticity or more sticky prices. 29In
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE? Agg supply & Demand; High Persistence (Baseline; Supply=red, Demand=blue )
Agg supply & Demand; Low Persistence (Baseline; Supply=red, Demand=blue )
0.2
0.2
0.15
Tr 0.1
A1
B2
G
0.05
G
0.05 B1
Inflation
Inflation
A2
0.15 Tr
0.1
O1
0
−0.05
−0.1
−0.1
−0.15
−0.15
−0.5
0 % Change Output
0.5
1
O2
0
−0.05
−0.2 −1
33
−0.2 −1
−0.5
0 % Change Output
0.5
1
Figure 4.2. Aggregate demand and supply when the purchases multiplier is larger (LHS: high persistence of fiscal policy (ρ = 0.9) and when the transfer multiplier is larger (RHS: low persistence of fiscal policy (ρ = 0.5)). See footnote 29 for details. of the Ricardian HH via higher real interest rates). This means that the increase in supply from a government purchases shock actually reduces the multiplier relative to a comparable targeted transfer. 4.1.1. Determinacy and comparison with the literature. Before proceeding, it is important to discuss the determinacy conditions of our original two-equation system: the NK IS curve (Equation 4.2) and the NK Philips curve (Equation 4.3). Lemma 1 stated that as long as the conditions in Assumption A1 held (which they always do for our simulations), the equilibrium is determinant. We also verify this numerically by calculating the eigenvalues of the relevant matrices in (Equation 4.2-4.3), checking that both eigenvalues of the relevant matrices are greater than unity in modulus (as there are two forward looking variables (e.g. Uhlig 1999).33 The top RHS area of Panel A of Figure 4.1 contains the region where Assumption A1 holds φπ > 1 and (1 − α) < (2 + ϕ)−1 (the HtM share is less than 1/3 with ϕ = 1), and contains our default calibration of φπ = 1.27 and 1 − α = 0.3. We restrict ourselves to this region throughout this section (Assumption A1). The inversion of the aggregate demand curve in Proposition 3 is different from other similar-sounding conditions in the literature. “Inverted aggregate demand logic” (IADL, Bilbiie 2008) arises in NK models with a large share of HtM HH, which we rule out in 33
We solve for the eigenvalues numerically for different combinations of φπ , α (assuming β = 0.995, ϕ = 1 θp = 0.75 from Table 1).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
34
Assumption A1. In this case, an increase in real interest rates increases aggregate demand via the NK IS curve — i.e. the denominator of Equation 4.2 is negative ((1 − α) > (2 + ϕ)−1 ). Determinacy with IADL requires very passive monetary policy (φπ 1), which is the bottom LHS region of Panel A of 4.1. Bilbiie’s (2008) IADL region is entirely distinct from the parametrization in Assumption A1, which are in the upper RHS of Panel A of Figure 4.1 with (1 − α) < (2 + ϕ)−1 . In Bilbiie’s (2008) IADL region, the transfer multiplier is not large — in fact it is negative. When the transfer multiplier is negative, Γ < 0 actually means the transfer multiplier is smaller (more negative) than the purchase multiplier. Assumption A1 restricts our attention to a different region for our main results.34 The regions where the AD curve is inverted and the transfer multiplier is greater than the purchase multiplier (Γ < 0 in Proposition 3) are different from the indeterminant regions of the parameter space. For example, shock persistence (ρ) is important for whether the transfer or purchase multiplier is larger, but has no influence on determinacy. One can see this in the right pane of Figure 4.1. With our default calibration (φπ = 1.27 and 1 − α = 0.3) — which is determinant — the transfer multiplier is larger than the purchase multiplier when ρ = 0, but smaller when ρ = 0.9. The black indeterminate region at the bottom of the Figure is approximately where (1 − α) > (2 + ϕ)−1 (which does not change with ρ) and is entirely distinct from the condition of Γ < 0 in Proposition 3 (white region of Figure 4.1 panel B).35 In AD-AS space, a well-behaved equilibria (i.e. weakly positive transfer multiplier) depends on the AD curve being steeper than the AS curve, rather than whether the AD curve is backward bending or not. So long as the AD curve is steeper than the AS curve, then rightward shift in demand will always lead to an equilibrium with higher output and higher inflation (regardless of whether it is backward bending or not). In contrast, if the AD curve is backward bending and less steep than the AS curve, then an increase in demand leads to a fall in output and inflation, which seems unlikely in practice. More specifically, the condition for the AD curve to be “steeper” than the AS curve (when Γ < 0) is −α/Γ > κ(ϕ + 1)/(1 − ρβ), 34More
specifically the transfer multiplier is positive if 1−(1−α)(ϕ+2) > −α(φπ −ρ)κ(ϕ+1)/[(1−ρ)(1−ρβ)]. Assumption A1 is a sufficient to ensure the LHS is positive and the RHS is negative, and so the condition holds. 35Bilbiie’s (2008) IADL does not appear anywhere on Panel B of Figure 4.1 because φ > 1. π
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
35
which is equivalent to the transfer multiplier being positive in Equation 4.8. Note that because government purchases also shift the supply curve, it is possible to have a positive purchase multiplier even when the AD curve is not steeper than the AS curve. Our result of an inverted AD curve also echoes that of Eggertsson and Krugman (2012), Eggertsson (2010a) and Eggertson (2012), who argue that the “paradox of toil” means that increase in aggregate supply can reduce output. However, the conditions under which the aggregate demand curve inverts are different. In these papers, the AD curve only inverts at the Zero Lower Bound, whereas Proposition 3 applies when the central bank follows a Taylor Rule.36 The differences are important: an increase in price flexibility (↑ κ) increases the stimulatory effect of restrictive labour market practices in Eggertsson (2012), but here it reduces the transfer multiplier and makes it less likely the AD curve will invert. 4.1.2. The sensitivity of the transfer multiplier to the central bank’s response to inflation. Proposition 4. Assume A1. A more aggressive monetary policy response to inflation leads to a larger proportional fall in the transfer multiplier than the purchasers multiplier, i.e. ∂lnMT r /∂φπ < ∂lnMG /∂φπ where ∂lnMT r /∂φπ < 0 and ∂lnMG /∂φπ < 0. Proof. Differentiating the expressions for the multipliers in Proposition 2 with respect to φπ yields: ∂lnMT r κ(ϕ + 1) α = −MT r <0 ∂φπ (1 − ρβ) 1 − ρ and ∂lnMG ∂lnMT r 1 ∂lnMT r = − ∂φπ ∂φπ MG (ϕ + 1) ∂φπ where MT r and MG are the transfer and purchase multipliers respectively. As ∂lnMT r /∂φπ < 0 and − [MG (ϕ + 1)]−1 < 0, then ∂lnMT r /∂φπ < ∂lnMG /∂φπ .
Proposition 4 shows analytically one of the key results of this paper: the transfer multiplier is more sensitive to the monetary policy response to inflation than the purchases multiplier. To some extent this should be obvious given φπ appears in the numerator and denominator 36In
Eggertsson (2010a) and Eggertson (2012) there are no HtM HHs, and hence no Disposable Income effect. In our model, as 1 − α → 0, the only way for the AD curve to invert is for the ZLB to bind (see Section 4.2).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
36
of the expression for the purchases multiplier, but only in the denominator of the expression for the transfer multiplier. As discussed above, transfers tend to produce more inflation than purchases, and so an increase in φπ will lead to a larger increase in real rates for transfers than purchases (as φπ > 1), leading to a greater fall in the multiplier. 4.1.3. Two alternative monetary policy rules during normal times. This subsection investigates the size of multipliers with two alternative monetary policy rules which are the most/least accommodating of inflation in normal times (see the next section for results when the ZLB binds, which is even more accommodating of inflation). In the framework above, the effect of monetary policy on demand is governed by the strength of the Taylor Principle effect (the fall in consumption demand from unconstrained HHs when inflation rises). In normal times, the Taylor Principle effect is at its strongest when any rise in inflation cuts off all consumption demand from unconstrained HHs. It is at its weakest when inflation has no effect on consumption of the Ricardian household (i.e consumption of the Ricardian HH is constant). These rules are captured by perfect inflation targeting, and a constant real interest rate policy, respectively. Perfect inflation targeting (a strict form of price-level targeting) A number of papers have examined the effect of transfers in heterogeneous agent models, but have assumed a strict form of price-level targeting to keep the model tractable. For example, Oh and Reis (2012) assume monetary policy is such that the price level is constant, and Athreya et al (2014) assume the price level returns to its original pre-shock level after one period.37 Introducing a strict form of price-level targeting into our analytical model is straightforward. If the monetary authority enforces a constant price level, then inflation is zero in all periods π ˆt = 0 ∀t. From the Phillips curve (Equation A6), this implies that markups will ˆt = 0), and so one gets the flex-price multipliers from Proposition 1. An be constant (X 37Oh
and Reis (2012) note that replacing the price-level targeting rule with nominal-income targeting and a Wicksellian interest-rate rule does not change the results, though they do not discuss the details of the alternative rules considered. In Oh and Reis (2012), the government purchase multiplier is also very small (0.06), well below estimates elsewhere.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
37
alternative way to see this is to assume that the central bank implements a constant price level by following the Taylor rule (Equation A5), but responds infinitely strongly to inflation deviations. That is, φπ → ∞, implying Γ → ∞ for the multipliers in Proposition 2. As Γ is only in the denominator of MT r , MT r → 0 as φπ → ∞, whereas MG → (ϕ + 1)−1 as φπ → ∞. Given these results, it is not surprising that papers which assume a strict form of price-level targeting also find a transfer multiplier close to zero (though this does not guarantee larger multipliers with alternative rules). Constant real interest rate targeting At the more accommodative end of the monetary policy spectrum (in normal times) is a constant real interest rate rule (Woodford 2011). If real interest rates are constant, then so is consumption of unconstrained HHs — the Taylor Principle Effect will be zero. This is similar to setting φπ → 1+ , though to implement constant real interest rates we also need make the Taylor rule forward looking: replace Equation A5 with Rˆt = φFπ L Et π ˆt+1 and take φFπ L → 1+ .38 Solving using the same method as above, the transfer multiplier approaches [α − (1 + ϕ)(1 − α)]−1 and the purchase multiplier approaches α [α − (1 + ϕ)(1 − α)]−1 . As such, the transfer multiplier is always larger than the purchase multiplier with a constant real interest rate rule so long as the share of HtM HHs is positive (α < 1).39
4.2. The transfer multiplier when the ZLB binds. It is well documented that government purchases are much more potent when monetary policy is at the ZLB (Eggertsson 2010b, Christiano et al 2011, Woodford 2011). We show analytically that the targeted transfer multiplier is even larger than the purchases multiplier at the ZLB (Proposition 5). In Section 5, we get similar numerical results in medium-scale DSGE model. 38In
L our model, if φF π = 1, the model is indeterminate, though we can get arbitrarily close from above. Some L forward-looking interest rate rules can generate indeterminacy (for a small share of HtH HHs) when φF is π very large (eg in Gali et al 2004 Figure 5, Bilbiie 2008 Proposition 1), though are determinant for values of L φF π just above 1 which is what we assume here (also verified numerically). With a standard contemporaneous Taylor rule and a low share of HtM HHs, any value of φπ > 1 is determinate (Lemma 1), including the large values required for price level targeting above. 39If α = 1, transfers and purchases are identical policies, and have identical multipliers of unity. Woodford (2011) also found a purchase multiplier of unity with a constant real interest rate rule in a model without HtM HHs.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
38
We show the transfer multiplier is larger than the purchases multiplier at the ZLB using a tractable two-state setup similar to that in Eggertsson (2010b) and Woodford (2011), where the ZLB and contemporaneous fiscal expansion persist with probability ξ each period. In this set-up, the reason the ZLB is binding does not matter (Christiano et al 2011): the multiplier is determined by the fact that nominal interest rates don’t respond to fiscal policy. For simplicity, we abstract from the reason the ZLB binds, and model “the ZLB binding” as a constant nominal interest rate policy of the central bank while this regime lasts.40 The key reason that targeted transfers are more stimulatory than purchases at the ZLB is that they generate more inflation: transfers and purchases provide the same boost to demand, but transfers do not boost supply. In normal times, the extra increase in inflation will increase wages, and hence the disposable income of the HtM HH, which will boost demand (the DI effect). But it will also raise real interest rates, which will reduce demand of the Ricardian HH (the TP Effect). At the ZLB there is no tension between the TP effect and the DI effect: higher inflation lowers the real interest rate, and hence increases consumption by the Ricardian household. Hence, the aggregate demand curve is always inverted at the ZLB, and the transfers multiplier is always larger than the purchases multiplier. Assumption A2: (i) The ZLB regime is not too persistent (Markov probability ξ < 0.38 with our default parameters), (ii) non-ZLB regime is an absorbing state and (iii) Taylor principle (φπ > 1) holds in the non-ZLB regime. ˆ t and a constant nominal interest rate Lemma 3. Consider a fiscal shock of size Tˆrt or G at time t (the “Zero Lower Bound regime”). With probability ξ, the fiscal shock and constant ˆ t+1 = 0 and the nominal rate policy continues at t + 1. With probability 1 − ξ, Tˆrt+1 = G central bank resumes a Taylor rule (the non-ZLB regime). Assume assumption A2 holds. Then while the ZLB binds, the equilibrium is characterized by the same equations as before ( 4.1-4.8), but with φπ = 0 and ρ = ξ. 40A
caveat is that the fiscal expansion does not affect the number of periods that the ZLB is binding, which will be the case in the two-state example and a large enough negative shock (e.g. a discount factor shock). Mathematically, the size of the shock that causes the ZLB to bind in our two state example would appear as a constant in Equation 4.9, and so does not affect the multiplier.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
Proof. Can be shown by guess and verify.
39
Proposition 5. When the ZLB binds (as described in Lemma 3), a) transfer multiplier will be greater than the purchases multiplier b) the economy’s aggregate demand curve will be inverted c) the transfer and purchases multipliers are given by Equation 4.9.
(4.9)
−1 κ(ϕ + 1) κ ˆ ˆ ˆ ˆ Yt = α + ΓZLB T rt + Gt + ΓZLB Gt (1 − ξβ) (1 − ξβ)
where: −1 κ(ϕ + 1) • α + ΓZLB is the transfer multiplier (1 − ξβ) −1 κ(ϕ + 1) κ • α + ΓZLB 1+ ΓZLB is the purchases multiplier. (1 − ξβ) 1 − βξ • ΓZLB = [α(−ξ)/(1 − ξ)] − [(1 − α)(1 − ξβ)/κ] | {z } | {z } T P Ef f ect
DI Ef f ect
Proof. Follows from Lemma 3.
Determinacy The determinacy of the ZLB equilibrium depends on the persistence of the ZLB and non-ZLB regimes and other model parameters. In the Online Appendix 5, we follow Davig and Leeper (2007) and model the ZLB as a two-regime markov process, which allows for transition between ZLB and non-ZLB regimes in both directions. We show numerically that with other default parameters (Table 1), so long as the non-ZLB state is absorbing and the expected persistence of ZLB regime is expected to be relatively short, then the Taylor principle (φπ > 1) in the non-ZLB regime is a sufficient condition for determinacy, which is summarized in Assumption A2.
41
4.3. Some extensions to the simple model. 41Analytically,
we can also assume [1 − (1 − α)(2 + ϕ)] (1 − ξ)(1 − βξ) − αξκ(1 + ϕ) > 0, which ensures a positive multiplier, which has the same form (with α = 1) as in Eggertsson (2012).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
40
4.3.1. Imperfect targeting of transfers. Adjusting for imperfect targeting of transfers is straightforward: if only a fraction 1 − χ of transfers are targeted at the HtM HH, then the multiplier will be scaled down by a factor of 1 − χ.42 To see this, note that the rest of the transfer (a fraction χ) flows from the Ricardian household to itself and hence have no effect on the economy. This can be incorporated in the model by replacing Equation A3 with ˆ 2,t ) (scaling down the transfer by a factor (1 − χ)). (1 − α)ˆ c2,t = (1 − χ)Tˆrt + (1 − α)(wˆ2,t + L That is, Equation 4.8 becomes Equation 4.10 (where Γ is defined as in Equation 4.8), and a stronger DI effect/weaker TP effect Γ < −χ(1 − βρ)/κ is required for the transfer multiplier to be greater than the purchases multiplier.43
(4.10)
−1 n o κ(ϕ + 1) κ 1 − βρ ˆ ˆ ˆ ˆ Yt = α + Γ (1 − χ) T rt + Gt + Γ+χ Gt (1 − ρβ) 1 − βρ κ
An interesting special case is when transfers are entirely untargeted, i.e. 1 − χ = 1 − α. In this case the transfer multiplier will be larger than the purchases multiplier when α (φπ − ρ) /(1 − ρ) < (1 − 2α)(1 − βρ)/κ, which will rarely hold with reasonable parameters if the central bank follows a Taylor rule or when the ZLB binds for a short period (when it binds for longer, the model becomes indeterminate).
4.3.2. When fiscal policy is financed by persistent government debt. In our baseline analysis, we assume that the government runs a balanced budget (Equation 2.15). Our analytical results are completely unchanged if instead purchases and targeted transfers are debt-funded by issuing perpetuities (i.e. the government raises lump sum taxes to pay the interest each period, but the principal is never repaid), regardless of the allocation of the perpetual lumpsum taxes across the two households. 42This
result also holds in the full model (Section 5), but relies on the assumption that transfers are funded by lump-sum taxes on the Ricardian household. 43The government spending multiplier where a fraction 1 − χ of taxes fall on the HtM HH can be represented by a combination of the standard purchase multiplier and a negative imperfectly targeted transfer (details in Online Appendix 3). When purchases are entirely funded by the HtM (χ = 0), the HtM-funded purchases multiplier will be positive if the TP effect is larger than the DI effect (i.e. if the purchases multiplier is larger than the targeted transfers multiplier).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
41
To see this, note that a policy where a fraction 1 − ν of the perpetual tax falls on the HtM households is isomorphic to the combination of the standard fiscal policy in the rest of the paper plus a negative permanent targeted transfer (i.e from the HtM HH to the Ricardian HH).44 As the model is linear, the multiplier on the debt-funded transfer/purchase is just the standard expression from Proposition 2, plus the multiplier on the negative permanent targeted transfer. By Proposition 2, the transfer multiplier goes to zero as ρ → 1, and so the financing of the transfer/purchase (by perpetuity) will not affect the multiplier.
4.3.3. When consumption and labour shares differ. If we assumed that the share of labour income of each household was not same as their share of aggregate consumption, then the wealth effects of the two households would not exactly cancel in response to a targeted transfer. This means that the aggregate supply curve would shift in response to a targeted transfer and the flex price transfer multiplier will be non-zero.45 Nonetheless, because targeted transfers always shift the supply curve by less than purchases, Proposition 3 still holds: the transfer multiplier will still be larger than the purchases multiplier when the AD curve inverts which is when the (slightly modified) DI effect dominates the TP effect. See Online Appendix 4 for further details.
5. The Transfer Multiplier in a Medium-scale DSGE Model By including realistic features such as sticky wages, capital, and a more flexible parametrisation, the full model allows us to show (i) that the transfer multiplier is often large in a quantitative sense (i.e. greater than one) — especially when the ZLB binds — and (ii) that the analytical results of Section 4 hold qualitatively in a richer model. See Table 1 for parameters, and Section 2 for a statement of the full model. ˆ −1 − 1)(1 − ν)/(1 − βρ). Note (Tˆr + G)/(1 ˆ size of the negative transfer each period is (Tˆr + G)(β − βρ) −1 is the present value of the original transfer or purchases, (β − 1) is the net steady state interest rate and (1 − ν) is the HtM HH’s share. ρ is the persistence of the purchase or transfer the government is borrowing to fund. When all of the lump sum taxes fall on the Ricardian HH, the timing of these taxes clearly do not affect allocations. 45Specifically, the flex price targeted transfer multiplier will be positive (negative) if the labour share of the HtM HH is less (greater) than its consumption share. 44The
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
42
In this section we analyse once-off fiscal shocks (persistence ρ = 0), and persistent fiscal shocks (ρ = 0.9). The once-off shock is designed to capture once-off transfers, like the 2001 and 2008 Bush stimulus payments. The more persistent shock closely aligns with the transfer component of the 2009 ARRA (see Online Appendix 9). In the full model, output will not be a constant multiple of the fiscal stimulus (as there are additional state variables), and so we report the present value multiplier (Uhlig 2010). This is the discounted sum of increases to output relative to the discounted sum of fiscal expenditure, where the discounting is at the HH’s discount rate β :
P∞
(5.1)
P V M ultipler ≡
β i Yˆt+i P∞i=0 i ˆ i=0 β T rt+i
P∞
i=0 or P∞ i=0
β i Yˆt+i ˆ t+i β iG
Determinacy The full model is much less susceptible to indeterminacy than the simple model, likely because sticky wages limit the extent that demand shocks increase inflation. If the central bank follows a Taylor rule (with the Taylor principle in effect φπ > 1), there are no values of the HtM share (away from corners) where there model is indeterminate.46 When the ZLB binds for a fixed non-stochastic number of periods (we have checked up to 7 years), we get similar results. 5.1. Quantitative Results when the central bank follows a Taylor rule. In this section we calculate the targeted transfer and purchase multipliers in “normal” times when the central bank follows a Taylor rule. The transfer multiplier in the full model (when policy follows a Taylor rule) is larger than one when fiscal policy is not very persistent or the share of HtM HH is not too small (as in Section 4 above) — as seen the lower left hand region in Figure 5.1 Panel B. The transfer multiplier is rarely larger than the purchase multiplier — except for once-off stimulus with very high shares of HtM HHs. In part this reflects the fact that the purchase multiplier itself is large for temporary stimulus and moderate shares of HtM HHs (Figure 5.1 Panel A). 46In
the full model we check determinacy numerically by making sure that the Blanchard-Kahn and rank conditions are satisfied in Dynare.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
43
Figure 5.1. Regions of parameter space where the transfer multiplier is large (white) when monetary policy follows a Taylor rule (Panel A (LHS): transfer multiplier > purchases multiplier, Panel B (RHS): transfer multiplier> 1). The first row of Table 2 (Columns A and B) presents the targeted transfer and purchase multipliers (respectively) when the central bank follows a Taylor Rule. When fiscal policy is a once-off — like the Bush 2001 tax rebates — both transfer and purchase multipliers are slightly below 1. With persistence ρ = 0.9 (similar to the ARRA) the transfer multiplier is around 0.25 and the purchase multiplier is larger at around 0.4.47 Impulse response functions with a Taylor rule or 2 years ZLB are presented in Section 5.3.
5.2. Zero Lower Bound (ZLB) in the full model. The Federal Reserve maintained nominal interest rates from 0-0.25 per cent from December 2008 to December 2015, a period of around 7 years. It is well documented in the literature that government purchases are much more potent when monetary policy is at the ZLB; for example, Christiano et al (2011) find a purchase multiplier well above two in the case that the ZLB binds. Given that the conditions under which the ZLB binds have been modelled elsewhere, we follow Christiano et al (2011) and Cogan et al (2010) and assume the central bank commits to keeping the 47Apart
from sticky wages, other additions to the full model include capital and steady-state government spending. The addition of capital does not change the multiplier substantially (Christiano et al 2011 find a similar result for purchases). Steady state government spending doesn’t have much effect on the multipliers, conditional on taxes being shared across both households so that the income distribution is unaffected.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
44
Table 2. Full Model — Present Value Multipliers A. Targeted Transfers Default Frisch ϕ
−1
B. Purchases
=1
Untargeted Transfers C. Default Calib. D. 50% HtM Share
Fiscal persistence:
ρ=0
ρ = 0.9
ρ=0
ρ = 0.9
ρ=0
ρ = 0.9
ρ=0
ρ = 0.9
Taylor Rule
0.89
0.25
0.91
0.38
0.27
0.07
0.58
0.15
6 quarters ZLB
1.34
0.81
1.33
0.77
0.40
0.24
0.89
0.54
2 years ZLB
1.32
1.04
1.30
0.91
0.40
0.31
0.87
0.71
5 years ZLB
1.33
1.67
1.32
1.32
0.40
0.50
0.90
1.07
7 years ZLB
1.34
1.77
1.32
1.42
0.40
0.53
0.90
1.12
nominal interest rate constant for a certain number of periods (and then returns to a Taylor rule).48 As shown in Proposition 5, the targeted transfer multiplier tends to be larger than the purchase multiplier at the ZLB. Figure 5.2 (Panel A) shows (in white) the regions of the (ρ, α)-space where the transfer multiplier is greater than the purchase multiplier as the ZLB binds for two years. One can see that ZLB dramatically increases the area where the targeted transfer multiplier is larger than the purchase multiplier — which is now almost the whole parameter space. Moreover, the transfer multiplier is greater than one almost everywhere (except for very persist transfers with a small share of HtM HHs) — see figure in Online Appendix 1.49 Table 2 shows that with constant nominal interest rates for two years (as considered by Cogan et al 2010), all transfer multipliers are greater than one, and purchase multipliers are usually close to or above one.50 With five years of constant rates, the multipliers are now quite large for ρ = 0.9, specifically 1.7 for targeted transfers and 1.3 for purchases. Multipliers are similar with 7 years at the ZLB. Particularly striking are the increases for 48We
implement this using the same methodology as Cogan et al (2010) — and we thank them for making their Dynare code publicly available. The number of periods of constant interest rates is known by households and the central bank is believed to be credible. In a linear model with perfect foresight, it is the path of nominal rates that determines the multiplier, rather than the reason nominal rates take that path (Christiano et al 2011). 49As shown by Woodford (2011), the multiplier is very sensitive to fiscal policy that occurs after the ZLB stops binding. Hence, longer horizons of the ZLB binding have a larger effect on the multipliers for very persistent fiscal policy. 50While short term rates have been constant for much longer than two years ex-post, it is not clear that markets fully anticipated this at the time (Swanson and Williams 2012).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
45
persistent transfer-based stimulus: the targeted transfer multiplier for ρ = 0.9 increases by 1.4 going from a Taylor rule to five years of the ZLB, whereas the purchase multiplier only increases by 0.9 (for less persistent fiscal policy the ZLB only increases the multiplier by 0.4) — verifying Proposition 4 in the full model (Transfer multipliers more sensitive to monetary policy than purchase multipliers).51 Full model (2yr ZLB): dY/dTr>dY/dG (White region)
Full Model (2Yrs ZLB): Untargeted dY/dTr>1 (White Region)
1
1
0.9
0.9
0.8
0.8
α 0.7
0.7
0.6
0.6
α 0.5
0.5
0.4
0.4
0.3
0.3
0.2
0.2
0.1
0.1
0 0
0.2
0.4
0.6
ρ
0.8
1
0 0
0.2
0.4
0.6
0.8
1
ρ
Figure 5.2. Regions where the transfer multiplier is larger with 2yrs ZLB. Panel A (LHS): targeted transfer multiplier > purchases multiplier. Panel B (RHS): untargeted transfer multiplier >1.
5.3. Impulse Responses and the effect of transfers on investment. Figure 5.3 plots the impulse responses of the key variables for the economy as a whole (top 6 graphs) and for each type of household (bottom 3 graphs) for a 1 percent of GDP targeted transfer shock with persistence ρ = 0.9. As expected, the variables move further from steady state when the ZLB binds for 2 years (dashed lines) compared with when the central bank follows a Taylor rule (solid line). A comparable figure for purchases is shown in Online Appendix 1. Looking across households in the bottom three panels, the HtM HH increases its consumption substantially, and the Ricardian household cuts back on consumption largely in order to pay its tax bill (though Ricardian consumption increases at the ZLB). Both households work harder (at least initially), though the increase is larger for the Ricardian household as 51A
reduction in the Frisch elasticity to ϕ−1 = 0.2 (Online Appendix 1) reduces transfer and purchase multipliers in normal times, but increases them at the ZLB. This is because a lower Frisch elasticity means a large increase in wages (and hence inflation) is required to meet a given increase in demand, which raises real interest rates under a Taylor Rule, but reduces them at the ZLB. A change in the Frisch can also change wage stickiness, though we change sticky wage CES elasticity (ε) at the same time, which largely offsets that effect.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
Path of Trasfers (% of GDP)
Output (% from SS)
3
Markup (% from SS)
3 Baseline 2yrs ZLB
2
46
0
2 −0.5
1 0
1
2
4
6
8
10
0
Investment (% GDP from SS)
2
4
6
8
10
−1
Inflation (ppt from SS, annualized) 1
1
0
0.5
0.5
2
4
6
8
10
0
2
4
6
8
10
0
2
Labor (% from SS)
6
8
10
4
6
8
10
Real wage (% from SS)
3
Consumption (% GDP from SS)
4
Nom. interest rate (ppt, ann.)
0.5
−0.5
2
0.5
2
2
1
1
0
0 0 2
4
6
8
Ricardian (C, W or L)
10
−1
0
5 Ricardian +ZLB
10
−0.5
0
HtM HH
5
10
HtM HH + ZLB
Figure 5.3. Impulse response functions (quarterly): Full model, 1 per cent of GDP transfers shock with ρ = 0.9 it becomes poorer. Note the relatively muted and sluggish movement in real wages — due to wage stickiness — which limits wealth effects. Investment Transfers have a very different effect on investment at the ZLB vs in normal times, which amplifies the effects of the real interest rate through the consumption Euler equation discussed in Section 4. In normal times, an increase in inflation raises real interest rates, which causes investment to fall by around 1/3ppt of GDP after a year (Figure 5.3). In contrast, at the ZLB an increase in inflation reduces real interest rates which raises investment (combined with an increase in labour supply) by about 1/4ppt of GDP after a year. As such, higher investment is responsible for around half of the 1ppt increase in output between ZLB and Taylor rule after a year. Investment also increases in response to a purchases shock at the the ZLB (and falls under a Taylor rule, see Online Appendix 1), but as there is a larger change in real interest rates with a transfer (Proposition 4) and hence larger increase in investment at the ZLB. 5.4. Targeting of transfers (revisited). In the real world, it is unlikely that a government could perfectly target transfers to HtM households, and so the targeted transfer multipliers
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
47
reported here are likely to be an upper bound. An alternative assumption — which could be considered a lower bound — is that transfers are completely untargeted. As we showed in Section 4.3.1, the multiplier on untargeted transfers is just a scaled down version of the targeted transfer multiplier. Table 2 Column C presents the untargeted transfer multiplier with our default calibration, which is around 0.25 for once-off transfers, 0.1 for persistent transfers if monetary policy follows a Taylor rule, and usually around 0.5 for persistent transfers when the ZLB binds for an extended period. The size of the untargeted transfer multiplier is much more sensitive to the fraction of HtM HHs than the targeted transfer multiplier (as it increases both the size of the targeted transfer multiplier and the scaling factor). We also might expect that share of HtM HHs would be higher during a recession when fiscal stimulus actually takes place. Table 2 Column D shows that with a 50% HtM share (Campbell and Mankiw 1989, Mankiw 2000, Galí et al (2007)) the untargeted transfer multiplier is above one with persistent fiscal policy and 5 years of ZLB, and fairly close to one for less persistent fiscal policy. Figure 5.2 (Panel B) shows that when the ZLB binds for 2 years, the untargeted transfer multiplier is greater than one so long as the HtM share is around 0.5 and fiscal policy is not too persistent.
5.5. Extension: Distortionary Taxation. As Leeper, Plante and Traum (2010), Drautzburg and Uhlig (2015) and others have emphasized, multipliers can be substantially lower if fiscal stimulus is funded by distortionary taxation (as in the real world), rather than lump-sum taxes on Ricardian households (as we assume the rest of this paper). On the other hand, Eggertsson (2010b) argues that at the ZLB, higher capital and labour taxes may actually increase output, as reduced labour supply and associated higher inflation lowers real interest rates when the ZLB binds, stimulating consumption. In Online Appendix 8 we extend our model to allow for distortionary taxes and deficit financing of fiscal stimulus. It should be noted that the effect of distortionary taxes on multipliers is sensitive to the type of taxes that adjust (eg consumption taxes are much less distortionary), how fast the taxes adjust, steady state debt/tax rates and other factors (see see Drautzburg and Uhlig 2015 for a discussion),
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
48
so any one set of estimates should be treated with caution. Distortionary taxation generally has a fairly similar effect on targeted transfer and purchase multipliers, and so usually does not alter whether the transfer multiplier is larger than the purchase multiplier. It also generally has much more effect on present value multipliers than short-run multipliers. With a Taylor rule and distortionary taxes we find both purchases and targeted transfers fall enough to become negative with persistent stimulus (though temporary transfer multipliers can still be positive in some circumstances). But the effects of distortionary taxes are much more benign at the ZLB: with 5 years ZLB and persistent fiscal policy the fall in the multiplier is much smaller, which still leaves targeted transfer multipliers well above one. In a recent paper, Drautzburg and Uhlig (2015) calculate the multiplier on the ARRA in a model similar to Smets and Wouters (2007), extended to include distortionary taxation, the ZLB and HtM HH. They find a median ARRA PV multiplier of -0.36 with distortionary taxation with 2 years ZLB, but 0.61 with lump-sum taxes (their table 3). Targeting transfers at the HtM boosts their multiplier by around 0.5, which brings their PV targeted multiplier to around unity, similar to our results in Table 2.
6. The Great Recession, Unemployment and Transfers The fiscal packages containing transfers — such as the ARRA, as well as the Bush tax rebates of 2001 and 2008 — were meant to stimulate the economy during a time of recession and reduce unemployment. In the sections above, we reported analytical and present-value multipliers. While these are a good general benchmark, they provide little guidance of the effect of stimulus packages in a real-world recession, or even whether our full model is sufficiently rich to be be able to capture such a recession. So in this section we hit a version of the full model with “financial crisis” shock to generate a version of the Great Recession, and examine the response of the economy to the transfers component of ARRA. We also introduce unemployment into the model, based on Galí (2011), as reducing unemployment was a key motivation of stimulus packages.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
49
6.1. Adding unemployment into the model. While New Keynesian style models of the type used in this paper are able to capture many aspects of real-world business cycles, a common criticism is that they lack any metric of unemployment (Galí and Gertler 2007). In response, Galí (2011) introduces involuntary unemployment based on sticky wages which do not fall until they generate full employment. In steady state, there is “natural” unemployment based on market power on the part of wage earners (perhaps represented by labour unions, or other forms of restriction on competition). In recessions, unemployment increases with the wage mark-up because sticky nominal wages prevent wages from falling in the event of weak labour demand. There is wealth of evidence that wages are rigid — especially downwardly rigid — even at times of high unemployment. Combined with a downward sloping demand curve for labour, this implies above-equilibrium wages as a plausible cause of involuntary unemployment. For example, Schmitt-Grohe and Uribe (2015) argue that following the financial crisis, nominal wages in the European periphery did not fall, even as the unemployment rate doubled.52 In the US, Daly et al (2012) note the relative strength of real wage growth in the recent recession, despite the increase in unemployment and Christiano et al (2005) argue nominal wage rigidity is more important for explaining the response of output to a monetary shock. Galí (2011) reformulates the household’s problem as one where for each type of labour service i within a household, there there are a continuum of family members indexed by j whose disutility of work is j ϕ . Each member (i, j) either works or doesn’t (with the household structure providing consumption insurance for family members who don’t work), depending on whether it is worthwhile for them to do so at the offered wage. The period utility function in Equations 2.1 and 2.7 is replaced by Equation 6.1, where there second equality comes from integrating across all workers who work.
52They
also provide evidence from Argentina in the early 2000s, where despite a high unemployment (and underemployment) rate, nominal wages did not fall. Following the 2002 devaluation of the peso, and subsequent increase in inflation and fall in real wages, unemployment (and underemployment) started to fall.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
ˆ
1
ˆ
Lk (i)
1 j djdi = lnck,t − 1+ϕ
ˆ
ϕ
(6.1) U (ck,t Lk,t (i)) = lnck,t − 0
0
50
1
Lk (i)ϕ+1 di k = 1, 2 0
Denote labour supply (LS ) as all workers who are willing to work at the offered wage. For ϕ the marginal worker this condition is Wk,t (i)/Pt = Ck,t ×LSk.t (i). Defining the unemployment
rate at the log difference between labour supply and the number of workers who worked, Galí (2011) shows that the unemployment rate is proportional to the log wage markup µk,w .
(6.2)
uk,t ≡ log(LSk,t ) − log(Lk,t ) = ϕ−1 µk,w
where µj,w ≡ log(wi,t ) − ϕlog(Li,t ) − log(ci,t ) = µ ˆj,w + log(εw /(εw − 1)) is the log wage markup (not the deviation from SS). Because labour supply now only varies at the extensive margin, one needs to recalibrate the model slightly. Galí (2011) estimates an equation related to the wage Philips curve on US data, and estimates of the Frisch elasticity of ϕ−1 = 0.2.53 This is close to Chetty et al’s (2011) central value of the extensive margin Frisch from the micro literature of 0.28.54 6.2. A crisis experiment. We view the great recession being driven by (i) a break down of financial intermediation as reflected by an increase in spreads between the interest rates on risky and risk-free securities; and (ii) an increased desire to save on the part of households (perhaps driven by greater uncertainty). Like most New Keynesian models used to study multipliers, our model is not sufficiently rich enough to micro-found the financial frictions and higher desired savings, so instead we introduce them in a reduced-form way as exogenous shocks.55 First, following Christiano et al (2011) we increase in the spread over the risk free rate that firms can use to evaluate their investment decisions (ξˆts in Equation 2.6) from zero to 53Using
a Bayesian approach, Galí et al (2011) estimate ϕ−1 = 0.25. Following Galí (2011), we also adjust the elasticity of substitution across labour varieties to εw = 4.52 to ensure a 5% natural rate of unemployment. 54 To form the aggregate unemployment rate, we weight u1,t and u2,t by their labour shares α and 1 − α respectively. 55 Models with a financial frictions, such as Bernanke et al (1999) can generate increases in spreads between interest risky and risk-free securities due to a worsening in financial frictions resulting from a decease in net worth of borrowers. But this is not a focus of our paper.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
51
3.6% (at annualized rate) starting in 2008Q4 and lasting for 3 years.56 Second, we introduce a discount factor shock (an increase in ξtb in Equation 2.1) that increases desired savings. This shock reduces the “shadow” interest rate to fall below zero, causing the Zero Lower Bound to bind. Christiano et al (2011) calibrate the discount factor to increase by 2% (annualized) for 6 quarters, though because our model includes a fraction of HtM HHs who are insensitive to the interest rate, we increase it to around 2.5%. Combined, the discount factor shock and increase in the financial spread cause the Fed’s desired interest rate to fall below zero for 6 quarters, starting in 2009Q1. Of course, the ZLB lasted much longer than this (until December 2015), but the time commentators and markets were expecting zero interest rates for somewhat less than 2 years (Swanson and Williamson 2012) suggesting a calibration of 6 quarters is appropriate.57 In addition to this benchmark, we add two measures of the transfer component of the ARRA: (i) the narrowest measure, which is well approximated by an 1% GDP AR(1) shock with ρ = 0.9, starting in 2009Q2 or (ii) the actual path of the narrowest measure plus transfers to states for Medicaid (see Online Appendix 9 for further details). The results of the crisis experiment are displayed in Figure 6.1, and shows that the model captures the height of the crisis extremely well. On the left hand side in red is the path of the US output gap relative to 2008q1, which fell by about 5.5 percentage points from late 2008 to mid 2009, before starting a slow recovery in late 2009. In blue, the model generates about a 6% fall in output (without any transfers), which is slightly too large, though the model accurately replicates the dynamics of the fall in output.58 Adding in untargeted transfers
56Christiano
et al (2011) start their crisis experiment in 2008Q3, but Lehman brothers only went bankrupt mid-quarter, meaning that most of the effects only started to be felt in the real economy in 2008Q4. From 2008Q4, the future path of the spread and discount rate shocks are known and we solve for the perfect foresight path of the economy using Dynare. 57Swanson and Williamson (2012) measure the market’s expectation of the length that the ZLB binds by whether treasury bills of that maturity respond to economic news. They found that T-bills less than 6m do not respond to news, bills with maturities greater than 2 years do respond, with bills of one to two years being an intermediate case. Six quarters is in the middle of this intermediate range, and so is an appropriate default value. Cogan et al (2010), writing in late December 2009 state that “We begin by assuming that [the Fed] keeps the interest rate equal to zero and constant through 2009 and 2010...Keeping interest rates constant for 2 years still does not seem very realistic and would likely result in an increase in inflation, but it is certainly more realistic than pegging the interest rates at zero forever, or even for 4 years.” 58The path of output depends on using the investment adjustment costs in Christiano et al (2005) and Smets and Wouters (2007), rather than the capital adjustment costs we used in an earlier draft.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
52
(green and purple lines), the model is able to match the path of the output gap from 2008q4 almost exactly. Figure 6.1 (RHS) shows the crisis shock in the model is able to generate a large and reasonably persistent increase in unemployment, but one that is larger than the standard measure in the data (known as U3). Specifically, U3 unemployment increased from about 5% in 2008Q1 to a peak of 10% in 2009Q4 in the data (a 5 ppt increase). In contrast, the crisis shock in the model without transfers generates an increase in unemployment peaking at 13% in mid 2009 (an 8 ppt increase). With untargeted transfers, the unemployment rate increases to 12%, which is close to the data but is still above the peak official employment rate (a 7 ppt increase). However, a number of commentators have suggested that during the Great Recession there was a large increase in underemployment and the number of discouraged workers, neither of which are captured by the official U3 measure. A broader U6 measure of unemployment which includes both discouraged workers and the underemployed (though is likely too broad), increased by 8ppt from 9.1% in 2008q1 to 17.1% in 2009q4, which an even larger increase than in the model with transfers.59 Model simulations suggest that the transfers component of the ARRA would have boosted output by around 2/3-1%, and reduced unemployment by around 1-1.5ppts at the peak impacts in 2009q2 when the transfers were largest. We view these peak estimates as likely on low side, as they use a fairly conservative definition of transfers (comprising 35-50% of the ARRA total), assume that transfers were completely untargeted (likely they were partially targeted), that the HtM share did not increase during the recession and the economy was at the ZLB for only 6 quarters. These peak effects on output are reasonably similar to the untargeted transfer impact multiplier when ZLB binds for 6 quarters of 0.6 multiplied by size of the stimulus in that quarter (1-1.3% of GDP). Note that the present value multiplier in Online Appendix Table 1 (with Frisch ϕ−1 = 0.2) is much smaller than the impact multiplier because output returns to baseline much faster than the transfer itself. 59The
U6 measure is too broad because it counts all “part-time workers for economic reasons” as unemployed, rather than only a fraction of them. The U5 rate which includes “marginally attached” unemployed, but not the underemployed, increased by around 5.5ppts during 2008 and 2009.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE? hŶĞŵƉůŽLJŵĞŶƚZĂƚĞ
KƵƚƉƵƚ ĞǀŝĂƚŝŽŶĨƌŽŵďĂƐĞůŝŶĞ;ƉĞƌĐĞŶƚͿ
ϭ
53
WĞƌĐĞŶƚ
ϭϰ
ϭϴ hϲ
DŽĚĞů;ŶŽƚƌĂŶƐĨĞƌƐͿ
Ϭ
ϭϮ
ϭϲ
DŽĚĞůǁŝƚŚƵŶƚĂƌŐĞƚĞĚƚƌĂŶƐĨĞƌƐ ;ŶĂƌƌŽǁĚĞĨŝŶŝƚŝŽŶͿ
ϭϬ
ϭϰ
DŽĚĞůǁŝƚŚƵŶƚĂƌŐĞƚĞĚƚƌĂŶƐĨĞƌƐ ;ŶĂƌƌŽǁнDĞĚŝĐĂŝĚͿ
ϴ
ϭϮ
ϲ
ϭϬ
ĂƚĂ;KƵƚƉƵƚ'ĂƉƌĞů͘ϮϬϬϴƋϭͿ
Ͳϭ ͲϮ Ͳϯ Ͳϰ
ϰ
Ͳϱ
Ϯ
Ͳϲ
DŽĚĞů;ŶŽƚƌĂŶƐĨĞƌƐͿͲ>,^ h^ƵŶĞŵƉůŽLJŵĞŶƚƌĂƚĞ;hϯͿͲ>,^ DŽĚĞůǁŝƚŚƵŶƚĂƌŐĞƚĞĚƚƌĂŶƐĨĞƌƐ;ŶĂƌƌŽǁĚĞĨŝŶŝƚŝŽŶͿͲ>,^ DŽĚĞůǁŝƚŚƵŶƚĂƌŐĞƚĞĚƚƌĂŶƐĨĞƌƐ;ŶĂƌƌŽǁнDĞĚŝĐĂŝĚͿͲ>,^ hŶĞŵƉůŽLJĞĚнƵŶĚĞƌĞŵƉůŽLJĞĚͬŚŝĚĚĞŶƵŶĞŵƉ͘;hϲͿͲZ,^
Ϭ
Ͳϳ ϮϬϬϴƋϭ
ϮϬϬϴƋϯ
ϮϬϬϵƋϭ
ϮϬϬϵƋϯ
ϮϬϭϬƋϭ
ϴ ϲ ϰ
ϮϬϬϴƋϭ
ϮϬϬϴƋϯ
ϮϬϬϵƋϭ
ϮϬϬϵƋϯ
ϮϬϭϬƋϭ
Figure 6.1. The Great Recession in the model vs the data In Online Appendix 1, we also consider the effect of the transfer policy on investment and consumption. Relative to 2008q1, consumption fell by around 2-2.5% during 2009, which our model without transfers matches reasonably well (though the fall in consumption is a bit too small). However, transfers boost consumption by around 1ppt in 2009q2, whereas in the data consumption starts recovering in 2009q3, leading to a 1ppt gap between model (with transfers) and the data. Relative to 2008Q1, investment fell around 25-32% during 2009. The model matches the general path of investment reasonably well, as well as values in late 2008 and late 2009, though has a fall in investment that is a bit too small (a trough of 25% rather than 32%).60 The size of the fall in investment is relatively insensitive to transfer-based stimulus. 7. Conclusion Government transfers to individuals were a larger share of the 2009 US stimulus package than government purchases. At the same time, with depressed growth prospects in the United States and other economies, there has been a debate about the efficacy of fiscal policy. We have demonstrated that, in a New Keynesian model modified to have two types of agents that 60The
exact size of the fall in investment is sensitive to the size of the adjustment cost S 00 , of which there are a range of estimate in the literature.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
54
differ in their access to financial markets, the transfer multiplier is more sensitive than the purchase multiplier to the degree of accommodation of inflation of the central bank. When the ZLB is binding, the targeted transfer multiplier is larger the purchases multiplier, and usually larger than one. Using a simplified model that we can solve analytically, we show that while purchases and transfers both increase aggregate demand, only purchases increase aggregate supply (as wealth effects cancel across households for transfers). This means that transfer-based stimulus is more inflationary than purchase-based stimulus. In normal times, when the central bank follows a Taylor rule, the aggregate demand curve is usually downward sloping, so that higher rates of inflation lead to an increase in real interest rates and a lower multiplier. However, when the ZLB is binding, the economy’s aggregate demand curve inverts, so that higher levels of inflation lower real interest rates and increase the multiplier. These results are quantitatively robust in a medium-scale DSGE model with capital and sticky wages. The potential for a large targeted transfer multiplier (under certain circumstances) raises the policy question: should transfers be a larger part of future stimulus packages? A complete answer involves a full welfare calculation, which is sensitive to how individuals value government spending and is beyond the scope of this paper. An argument in favour of targeted transfers (versus purchases) in this context is that the people receiving the transfers choose what to spend them on, which might yield higher marginal utility than government purchases. Moreover, if constrained households are also poorer, they may have higher marginal utility, leading to an increase in social welfare from a utilitarian perspective. Practicalities are also important. Expedient implementation of a temporary stimulus package — which has the highest multipliers under a Taylor rule — is much easier for a transfer than a purchase (or public investment – see Leeper et at (2010)). On the other hand, transfers cannot be perfect targeted at constrained households and so the multipliers on real-world transfer packages are lower that the perfect-targeting benchmark. An online appendix is available at: https://sites.google.com/site/stevenpennings/GP2017appendix.pdf
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
55
References [1] Altig, D., L. Christiano, M Eichenbaum, and J Lindé (2011) “Firm-specific capital, nominal rigidities and the business cycle” Review of Economic Dynamics 14(2), pp225-247 [2] Athreya K., A. Owens, and F. Schwartzman (2014), “Does Redistribution Increase Output? The Centrality of Labor Supply”, Federal Reserve Bank of Richmond Working Paper 14-04R [3] Barattieri, A., S., Basu and P., Gottschalk (2014) "Some Evidence on the Importance of Sticky Wages." American Economic Journal: Macroeconomics, 6(1): 70-101. [4] Bernanke B, Gertler M and S Gilchrist (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework,” Handbook of Macroeconomics 1, pp 1341-1393. [5] Bengtsson N. (2012) “The Marginal Propensity to Earn and Consume out of Unearned Income: Evidence Using an Unusually Large Cash Grant Reform”, Scandinavian. Journal of Economics 114(4), 1393–1413 [6] Bilbiie F (2008), “Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate Demand Logic,” Journal of Economic Theory, 140(1), pp 162-196. [7] Bilbiie F, Monacelli, T and R Perotti (2013), “Public Debt and Redistribution with Borrowing Constraints,” The Economic Journal, 123 (February), pp F64-F98. [8] Broda C And J Parker (2012), “The Economic Stimulus Payments of 2008 and the Aggregate Demand for Consumption” mimeo [9] Campbell J and G Mankiw (1989), “Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence,” NBER Macroeconomics Annual 4, pp 185-246. [10] Cesarini, D., E. Lindqvist, M.Notowidigdo and R. Östling (2015) “The Effect of Wealth on Individual and Household Labor Supply: Evidence from Swedish Lotteries”, NBER Working Paper 21762 [11] Chetty, R, A. Guren, D Manoli and A Weber (2011a), “Are Micro and Macro Labor Supply Elasticities Consistent? A Review of Evidence on the Intensive and Extensive Margins”, American Economic Review PP 101(3), pp 471-75 [12] Chetty, R, A. Guren, D Manoli and A Weber (2011b), “Does Indivisible Labor Explain the Difference Between Micro and Macro Elasticities? A Meta-Analysis of Extensive Margin Elasticities”, NBER Working Paper No. 16729, (January 2011) [13] Chetty, R., J. Friedman and E. Saez. (2013) "Using Differences in Knowledge across Neighborhoods to Uncover the Impacts of the EITC on Earnings." American Economic Review, 103(7): 2683-2721. [14] Colciago A (2011), “Rule-of-Thumb Consumers Meet Sticky Wages,” Journal of Money, Credit, and Banking 43(2-3), pp 325-353. [15] Coenen, G., C. Erceg, C. Freedman, D. Furceri, M. Kumhof, R. Lalonde, D. Laxton, J. Lindé, A. Mourougane, D. Muir, S. Mursula, C. Resende, J. Roberts, W. Roeger, S. Snudden, M. Trabandt, and J. in’t Veld. (2012) “Effects of Fiscal Stimulus in Structural Models.” American Economic Journal: Macroeconomics, 4(1) pp 22-68. [16] Cogan J and J Taylor (2010), “What the Government Purchases Multiplier Actually Multiplied in the 2009 Stimulus Package,” NBER Working Paper 16505. [17] Cogan J, Cwik T, Taylor J and V Wieland (2009), “New Keynesian versus Old Keynesian Government Spending Multipliers,” Journal of Economic Dynamics and Control, 34(3), pp 281-295. [18] Christiano L, Eichenbaum M and C Evans (2005), “Nominal Rigidities and the Dynamic Effects of a Shock to Monetary Policy” Journal of Political Economy, 113(1), pp 1-45. [19] Christiano L Eichenbaum M, and S Rebelo (2011), “When Is the Government Spending Multiplier Large,” Journal of Political Economy, 119(1), pp 78-121. [20] Daly, M. B. Hobijn and B. Lucking (2012), “Why Has Wage Growth Stayed Strong?”, FRBSF Economic Letter 2012-10 [21] Davig T and E Leeper (2007), “Generalizing the Taylor Principle”, American Economic Review, 97(3), pp 607-635. [22] Davig T and E Leeper (2011), “Monetary-Fiscal Policy Interactions and Fiscal Stimulus”, European Economic Review, 55(2), pp 211-227.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
56
[23] Drautzburg T and H Uhlig (2015), “Fiscal Stimulus and Distortionary Taxation”, Review of Economic Dynamics 18, 894–920 [24] Eggertsson G (2010a), “The Paradox of Toil” Federal Reserve Bank of New York Working Paper. [25] Eggertsson G (2010b), “What Fiscal Policy is Effective at Zero Interest Rates?” NBER Macroeconomics Annual 25, pp 59-112. [26] Eggertsson, G (2012) "Was the New Deal Contractionary?" American Economic Review, 102(1), pp 524-55. [27] Eggertsson G and P Krugman (2012), “Debt, Deleveraging, and the Liquidity Trap: A FischerMinsky-Koo Approach”, The Quarterly Journal of Economics, 127(3): 1469-1513 [28] Erceg C, Henderson D and A Levin (2000), “Optimal Monetary Policy with Staggered Wage and Price Contracts,” Journal of Monetary Economics, 46(2), pp 281-313. [29] Galí J (2008), Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework, Princeton University Press, Princeton, USA [30] Galí J (2011), “The Return of the Wage Phillips Curve”, Journal of the European Economic Association, 9(3):436–46 [31] Galí, J., and M. Gertler (2007) “Macroeconomic Modeling for Monetary Policy Evaluation.” Journal of Economic Perspectives 21 (4): 25–45. [32] Galí J, Lopez-Salido D and J Valles (2007), “Understanding the Effects of Government Spending on Consumption,” Journal of the European Economic Association, 5(1), pp 227-270. [33] Galí J., F Smets and R Wouters (2012) “Unemployment in an Estimated New Keynesian Model”, NBER Macroeconomics Annuall, vol. 26(1), 329 - 360. [34] Imbens, G., D. Rubin and B. Sacerdote (2001) "Estimating the Effect of Unearned Income on Labor Earnings, Savings, and Consumption: Evidence from a Survey of Lottery Players." American Economic Review, 91(4): 778-794. [35] Hausman J (2012), “Fiscal Policy and Economic Recovery: The Case of the 1936 Veterans’ Bonus”, mimeo, UC Berkeley [36] Iacoviello M (2005), “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle,” American Economic Review, 95(3), pp 739-764. [37] Johnson D, Parker J and N Souleles (2006), “Household Expenditure and the Income Tax Rebates of 2001,” American Economic Review, 96(5), pp 1589-1610. [38] Kaplan G., G. Violante and J. Weidner (2014) “The Wealthy Hand-to-Mouth”, Brookings Papers on Economic Activity, (Spring 2014), pp 77-138 [39] Keane, M (2011) "Labor Supply and Taxes: A Survey." Journal of Economic Literature, 49(4): 961-1075. [40] Kimball, M. and M Shapiro (2008) “Labor Supply: Are the Income and Substitution Effects Both Large or Both Small?”, NBER Working Paper No. 14208 (July 2008) [41] Leeper E., T. Walker, and S. Yang (2010), “Government investment and fiscal stimulus” Journal of Monetary Economics 57, 1000–1012 [42] Leeper, E, Plante M and N Traum (2010), “Dynamics of Fiscal Financing in the United States” Journal of Econometrics, 156, 304-321. [43] Leeper E, Traum N and T Walker (2015), “Clearing up the Fiscal Multiplier Morass”, mimeo, Indiana University. [44] Mankiw, N (2000), “The Savers-Spenders Theory of Fiscal Policy” American Economics Review PP, 90(2), pp 120-125 [45] Mehrotra N (2014), “Fiscal Policy Stabilization: Purchases or Transfers?”, Brown University mimeo. [46] Monacelli T and R Perotti (2011), “Redistribution and the Multiplier,” IMF Economic Review, 59(4), pp 630-651, November. [47] Nakamura, E and J Steinsson (2014) "Fiscal Stimulus in a Monetary Union: Evidence from US Regions." American Economic Review, 104(3): 753-92. [48] Oh H, and R Reis (2012), “Targeted Transfers and the Fiscal Response to the Great Recession,” Journal of Monetary Economics, 59(S). [49] Pencavel, J. (1986) “Labor Supply of Men: A survey” Handbook of Labor Economics (Vol 1) [50] Peterman W. (2016), “Reconciling Micro and Macro Estimates of the Frisch Labor Supply Elasticity ”Economic Inquiry Vol. 54, No. 1, 100–120
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
57
[51] Reichling F. and C.Whalen (2012), “Review of Estimates of the Frisch Elasticity of Labor Supply”, Congressional Budget Office Working Paper 2012-13 [52] Smets F and R Wouters (2007), “Shocks and Frictions in US Business Cycles: A Bayesian DSGE Approach,” American Economic Review, 97(3), pp 586-606. [53] Schmitt-Grohe S. and M. Uribe (2016) “Downward Nominal Wage Rigidity, Currency Pegs, and Involuntary Unemployment”, Journal of Political Economy, 124(5) [54] Swanson E and J Williams (2012), “Measuring the Effect of the Zero Lower Bound on Mediumand Longer-Term Interest Rates”, Federal Reserve Bank of San Francisco Working Paper 2012-02 [55] Uhlig H (1999), “A Toolkit for Analyzing Dynamic Stochastic Models Easily,” In Computational Methods for the Study of Dynamic Economies, R. Marimon and A. Scott, eds. Oxford University Press. [56] Uhlig H (2010), “Some Fiscal Calculus,” American Economic Review, 100(2), pp 30-34. [57] Werning I (2012), “Managing a Liquidity Trap: Monetary and Fiscal Policy”, MIT mimeo. [58] Woodford M. (2003), Interest and Prices, Princeton University Press [59] Woodford M (2011), "Simple Analytics of the Government Expenditure Multiplier," American Economic Journal: Macroeconomics, 3(1), pp 1–35.
