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 purchases multiplier. 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 Date: 24 November 2015. 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: Department of Economics, New York University (NYU) 19 W. 4th St, 6th Floor, New York, NY, 10009, USA (email:
[email protected]) Pennings: Development Research Group, World Bank, 1818 H St NW, Washington DC 20433 USA (email:
[email protected] or
[email protected]). Helpful comments have been received from 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
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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, slightly above the OECD median of 64 per cent. Transfers were a key component the 2009 American Recovery and Reinvestment Act (ARRA), as well as 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. Because the unconstrained households are Ricardian, the timing of tax payments and the size of the government deficit do not affect the economy. 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). 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 bank responds aggressively to inflation, the transfer multiplier is small — often close to zero 1
Of the $499bn expenditure component of the American Recovery and Reinvestment Act (ARRA), $429bn (86%) are classified as “transfer payments” according to the National Income and Product Accounts (http://bea.gov/recovery/pdf/arra_table_02.pdf, accessed 15 July 2014). In a related calculation, we find that transfers accounted for somewhere between 35-80 per cent of the total $787bn ARRA package, depending on the classification of transfers to state and local governments and various tax measures (see Online Appendix 0.9). 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 3 (analytical results) and Section 4 (numerical results) we report both targeted and untargeted multipliers.
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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 3 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.3 Our secondary finding is that sticky wages reduce the difference between the targeted transfer multiplier and the purchases multiplier (we show this numerically). 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. In the limit as wages become perfectly sticky, the purchases and transfer multipliers are identical. The transfer multiplier also depends on the degree of targeting — halving the fraction of transfers going to constrained households halves the transfer multiplier — as well as other factors such as the level of price stickiness. 3
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.
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What does this mean for the quantitative size of transfer multipliers? In Section 4, 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).4 We find that a once-off 1 per cent of GDP targeted transfer or government purchase raises the present value of output by about 1.1 per cent. 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 0.4 for targeted transfers or 0.6 for purchases in normal times. If monetary policy is constrained by the ZLB for five years, the targeted transfer multiplier is around 1.5 for once-off stimulus, and 2.0 for persistent stimulus (with purchase multipliers being around 1.4 in either case). If transfers are completely untargeted, the transfer multiplier is often around 0.5, 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). 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.5 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 4
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. 5 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.
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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). Our paper is also related to Mehrota (2014), who studies the effect of untargeted transfers in a two-agent New Keynesian model with a debt-elastic interest spread. Mehrota (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. Mehrota (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 Mehrota (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.6 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 6
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, Monacelli and Perotti (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 (2013) 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.
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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) 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 . 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 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
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in Section 4. In Section 3 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 0.6.
2.1. Ricardian household’s problem. The Ricardian household consists of a unit mass of families, each of which is comprised of a unit mass of individuals, indexed by j ∈ [0, 1]. Different individuals within the family provide differentiated labour inputs to intermediategoods producers. Since families are identical, we focus on the problem of individual j (see Online Appendix 0.6 for a more formal explication). Each individual chooses real consumption (c1,t (j)), desired labour hours (L1,t (j)), real debt (−bt (j)) and investment (It (j)) to maximise his utility, taking real interest rates (Rt−1 /πt ), lump-sum taxes (T axt ), real wages (w1,t (j) = W1,t (j)/Pt ), the real gross rate of return on capital (M P Kt ) and profits from retailers (Πt ) as given. 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 family, so consumption and all other variables are equalised across individuals and so we drop the j index for these variables.7 Actual hours are determined by the demand of the firm at the given (sticky) wage (discussed further in Section 2.3 below). Changing the level of capital is subject to adjustment costs of ACKt (j) = ψ (It /Kt−1 − δ)2 Kt−1 /(2δ). Therefore the Ricardian household member’s problem is:
(2.1)
max{c1,t ,bt ,It ,L1,t (j)} E0
∞ X t=0
Lϕ+1 1,t (j) β [ln(c1,t ) − ] ϕ+1 t
(where ϕ−1 gives the Frisch elasticity of labour supply), subject to budget and capital accumulation constraints:
7We
follow the simplified notation in Galí (2008) and 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.
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(2.2)
8
c1,t + It + ACK,t + bt = (Rt−1 /πt )bt−1 + M P Kt Kt−1 + w1,t (j)L1,t (j) + Πt − T axt
(2.3)
Kt = (1 − δ)Kt−1 + It
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 (j) = L1,t and w1,t (j) = w1,t ∀j. 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 family member j ∈ [0, 1] only has to choose desired labour hours (L2,t (j)) 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 family members due to our assumption of perfect within-family insurance of Calvo wage shocks. In the simple model, L2,t (j) = L2,t and w2,t (j) = w2,t ∀j as labour markets are competitive.8
(2.4)
max{c2,t ,L2,t (j)} E0
∞ X t=0
Lϕ+1 2,t (j) β [ln(c2,t ) − ] ϕ+1 t
such that: (2.5)
w2,t (j)L2,t (j) + T rt = c2,t
2.3. 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 8In
the simple model, in order to keep the HtM HH’s wage share equal to his consumption share, we also assume that a lump sum profits tax is levied on firms that delivers zero profits in steady state T axπ,ss = (Xss − 1)YSS (where Xss is the steady state gross markup). The tax is used to fund a steady state wage subsidy sss = Xss − 1 This assumption is quantitatively unimportant, but allows us to deliver cleaner analytical expressions for the multiplier.
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wages are important for fitting the response of a monetary policy shock to the data, and Galí et al (2007) argue that some form of wage rigidity (a union in their case) is needed to fit the response of consumption to a government purchases shock. 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 4). We model wage stickiness as in Erceg, Henderson, and Levin (2000) and Galí (2008). The production function is Cobb-Douglas (Equation 2.8), and L1,t and L2,t are now CES composites of differentiated labour inputs (indexed by j): ´1 ´1 w w 1 1 L1,t = [ 0 L1,t (j)1− w dj] w −1 and L2,t = [ 0 L2,t (j)1− w dj] w −1 The nominal wage indices (upper case) are defined as follows : ´1 ´1 1 1 W 1,t = [ 0 W 1,t (j)1−w dj] 1−w and W 2,t = [ 0 W 2,t (j)1−w dj] 1−w . As with Calvo pricing, each member of the Ricardian and HtM households is allowed to reset its nominal wage with constant probability 1−θw in each period. Since households posses market power in their labour supply decisions, they are able to set their wage at a markup above their marginal rate of substitution. Given the wage-setting decisions by households that do re-optimise, and the fact that households that do not re-optimise must keep their nominal wages at last period’s value, there is an analogue of a Phillips curve for each type of household. In particular, nominal wage inflation for each household π ˆw i,t = lnWi,t − lnWi,t−1 , i = 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 i,t (variables with hats generally denote deviations from steady-state).
(2.6)
π ˆw ˆw ˆw i,t = βEt π i,t+1 − λi µ i,t
(2.7)
ˆ i,t − cˆi,t µ ˆw ˆi,t − ϕL i,t = w
where λi =
(1−θw )(1−θw β) , θw (1+ϕ)
and wˆi,t = wˆi,t−1 + π ˆw ˆ t , i = 1, 2 is the real wage. i,t − π
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2.4. Sticky prices, Retailers, Intermediate and Final Output. Intermediate output is Cobb-Douglas in capital and the labour from each of the households, and is produced by a unit continuum of competitive intermediate goods producers. L1,t and L2,t are either the composite labour indices in the full model (if wages are sticky) or the labour supply of each household in the simple model (when wages are flexible) (µ = 0 in the simple model):9
(2.8)
(1−µ)α
Yt = K µt L1,t
(1−µ)(1−α)
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 f σ Pl,t . Aggregate final output is given by the index Yt = 0 Yl,t 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 2.9), which is shown in log deviation from steady state, where π ˆt = lnPt − lnPt−1 is the inflation rate (steady ˆ t = lnXt − lnX is the deviation in the retailer’s average markup state inflation is zero), X from steady state (where X =
σ σ−1
and κ = (1 − θp )(1 − βθp )/θp ). The variable κ can be
thought of as 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 of inflation and a boost in output to increases in demand (such as government purchases or transfers).
9In
Online Appendix 0.1 we consider an alternative where the labour of the two households is perfect substi(1−µ) tutes, i.e. Equation 2.8 is replaced by Yt = Ktµ Lt where Lt = αL1,t + (1 − α)L2,t . In this case, there is measure α of Ricardian households and 1 − α of HtM HH and L1,t and L2,t are labour supply per capita.
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ˆt π ˆt = βEt π ˆt+1 − κX
(2.9)
The price of intermediate output in terms of final output is the inverse of the retailer’s 1 P int . As such, the marginal product of labour or capital in terms of average markup t = 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 . w1,t = α
(2.10)
1 Yt 1 Yt , w2,t = (1 − α) Xt L1,t Xt L2,t
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 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 2.11). 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 )
(2.11)
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.
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The government runs a balanced budget each period (Equation 2.12). 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.10
(2.12)
T axt = T rt + Gt
ˆ t are exogenous and are assumed to follow an AR(1) process. The path of Tˆrt and G
(2.13)
Tˆrt+1 = ρTˆrt + eT r,t+1
(2.14)
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:
(2.15)
Yt = c1,t + c2,t + It + Gt
3. 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 3.1) or when nominal interest rates are at the Zero Lower Bound (ZLB, Section 3.2). Given the analytical approach, we focus on the relative size of the transfer and purchases multipliers
10This
is not the case if taxes are levied only on the HtM HHs or if taxes are distortionary.
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which we can characterize exactly, rather than the numerical size of the transfer multiplier which requires a richer model (Section 4). 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.11 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 3.1), but is always larger than the purchases multiplier when the ZLB binds (Section 3.2). As such, the transfer multiplier is more sensitive to the monetary policy response to inflation than the purchases multiplier, which we we show analytically in Proposition 4. Section 3.3 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 — by multiplier is constant over time — that is output is a constant multiple of G removing endogenous state variables such as capital, lagged wages or the lagged interest rate. Specifically, we assume (i) wages are flexible (λj → ∞, j = 1, 2), (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 11If
preferences are GHH, targeted transfer and purchases multipliers are identical. This is because the labour supply depends only on the real wage (and not on consumption), and so there will be no supply-side effects −1 1 αϕκ [φπ − ρ] of transfers (or purchases). The multiplier is − (1 − α) .With either perfect ϕ ϕ + 1 (1 − ρ)(1 − ρβ) inflation targeting (φπ → ∞) or flexible prices (κ → ∞), the multiplier will go to zero.
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assumption in Section 3.3.3.).12 In Online Appendix 0.1 we present a version of the model where we assume the labour of the households is perfectly substitutable (rather than CobbDouglas). The Cobb-Douglas assumption substantially simplifies the analytical expressions, but also increases the size of the targeted transfer multiplier.13 In the full model (Section 4), whether labour is Cobb-Douglas or perfect substitutes is not quantitatively important due to the presence of sticky wages.
3.1. 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). 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 jt , ∀j = 1, 2 [A8 Labour-Leisure FOC] wˆjt = cˆjt + ϕL ˆ t = wˆj,t + L ˆ j,t , ∀j = 1, 2 [A9 MPL=wage] Yˆt − X
12That
is, we set steady state government purchases to zero (Gss = 0), and assume a small profits tax that is rebated as a wage subsidy such that c1,ss /Yss = α and c2,ss /Yss = 1 − α. A similar approach used by Bilbiie (2008) is to assume a fixed cost of operating each firm that exactly offset profits in steady state. 13 Specifically, when labour of the households is perfect substitutes, the wealth effect on labour supply will limit the increase in the disposable income of HtM HH when it receives a transfer (with constant inflation/markups). As disposable income determines consumption demand of the HtM HH, this leisure effect (as we call it) means that a targeted transfer will increase aggregate demand less than a government purchase of a similar size. Hence, with perfect substitutes the targeted transfer multiplier will generally be smaller than the government purchase multiplier under a Taylor rule or when the ZLB binds for a short period (when it binds for a longer, the model becomes indeterminate). The leisure effect does not exist with a Cobb-Douglas production function because the relative wages of the two households adjust to maintain their shares of aggregate income. See Online Appendix 0.1 for further details.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
15
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 3.1. When prices are flexible ˆt = 0 (κ → ∞), retailers keep their markups constant at the profit-maximising optimum, so X and hence Yˆt =
1 ˆ G. ϕ+1 t
(3.1)
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 to pay the tax. For purchases this is the end of the story: higher labour supply boosts output leading a positive multiplier of (1 + ϕ)−1 (the neoclassical wealth effect). For transfers, this negative wealth effect for Ricardian household is exactly offset by the positive wealth effect on the HtM HH who receives the transfer, leaving output unchanged. An implication of ˆt. Equation 3.1 is that transfers affect output through variation 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 3.3.3 and Online Appendix 0.3 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. Lemma 1. 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.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
16
We solve the analytical model — and show how it works — in three steps. First we use Lemma 1 to solve for expectations of future variables in terms of current variables, which removes all dynamics from the model.14 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. Second, we 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.15 The supply curve (Definition 1) is virtually unchanged from the simplest 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 3.2). The slope of 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 third 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 14When
prices are flexible, the model is essentially static because real interest rate adjusts to make the Euler equation hold. 15For 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?
17
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 3.2, 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 ˆ t (using Equation 3.1). Lemma 1) and markups X π ˆtAS =
(3.2)
κ(ϕ + 1) ˆ AS −κ ˆ Yt + Gt (1 − ρβ) (1 − ρβ)
Remark 1. Purchases increase aggregate supply, but transfers do not. Definition 2. Aggregate Demand Curve.
The aggregate demand curve is given by
Equation 3.3, 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 3.4 and 3.5. 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 1, and solving for consumption demand of the HtM household.16
AD
π ˆtAD
(3.3)
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. 16Our
model nests a standard three equation NK model when the share of HtM households is zero (1−α =0) ˆ t − Et π ˆt+1 + (transfers are not defined in this case). The New Keynesian IS curve becomes Yˆt = Et Yˆt+1 − R ˆt −Yˆt + G . As long as the Taylor principle is (φπ − ρ)/(1 − ρ) satisfied φπ > 1 , the aggregate demand curve is always downward sloping in the baseline NK model without HtM HH. The supply curve is the same as it would be in the baseline NK model. ˆ t − Et G ˆ t+1 ), which can be rearranged to give π (G ˆt =
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
18
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 1 to solve for the expectations of future consumption and inflation (Equation 3.4). As its the 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 Effect reverses its sign because a rise in inflation lowers real interest rates (Section 3.2 — effectively φπ = 0).
αˆ c1,t = − [α(φπ − ρ)/(1 − ρ)] π ˆ | {z } t
(3.4)
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 1 to substitute out ˆ t to yield Equation 3.5. variation in markups X
(3.5)
(1 − α)ˆ c2,t = Tˆrt + (1 − α)Yˆt + [(1 − α)(1 − ρβ)/κ] π ˆ | {z } t DI Ef f ect
Proposition 2. Sticky price multiplier. In the simple model when prices are sticky and monetary policy follows a Taylor rule, the targeted transfer and purchases multipliers are given by Equation 3.6.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
19
−1 κ(ϕ + 1) κ ˆ ˆ ˆ ˆ Yt = α + Γ ΓGt T rt + Gt + (1 − ρβ) (1 − ρβ)
(3.6) 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 • 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 3.2) and aggregate supply (Equation 3.3) relations to eliminate π ˆt , and solve for Yˆt .17
Proposition 3. Transfer and Purchase Multipliers and Inverted Aggregate Demand Curve. 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.18 There are 17We
also assume that (1 − α) < (2 + ϕ)−1 (the HtM share is not too large). This means that we avoid the indeterminate region in Figure 3.1, an increase in real interest rates reduces aggregate demand (the opposite of Bilbiie’s (2008) Inverted aggregate demand logic) and MT r and MG are positive (combined with the standard parameter restrictions φπ > 1 > ρ and β < 1). 18If the central bank responds to output in the Taylor rule, Equation 3.6 becomes Y ˆt = # −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).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
20
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) which strengthens the DI effect relative to the TP effect. Figure 3.1 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 3.1. Regions of 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). ρ is the persistence of the fiscal shock (transfers or purchases), and 1 − α is the share of constrained (HtM) HHs. 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 increase 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
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
21
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 3.2, 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. The effect of a transfer or purchases shock can be seen in shifts in the aggregate demand and aggregate supply curves in Figure 3.2.19 Because all transfers are targeted at the HtM HH who will consume them (we relax this assumption below in Section 3.3.1), transfers and purchases shift the demand curve out by the same amount (Equation 3.3)20 but only government purchases shift the aggregate supply curve (via the neoclassical wealth effect).21 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 3.2), 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.22 As foreshadowed in Proposition 3b, this means that the transfer multiplier will be larger than the purchase multiplier. From the RHS of Figure 3.2 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 19In Figure 3.2 O , (x = 1, 2) represents the steady state equilibrium (Y,ˆ ˆ π ) with the original (solid) Aggregate x 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 . 20 In Online Appendix 0.1, with perfect substitutes targeted transfers increase demand by less than purchases because the wealth effect on labour supply reduces the HtM HH’s income, and hence consumption expenditure. 21 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). 22The 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.
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 TR
0.15
0.1
A1
0.05
B2
G B
0
O1
−0.05
−0.1
−0.1
−0.15
−0.15
0 % Change Output
0.5
1
O2
0
−0.05
−0.5
TR
0.05
1
Inflation
Inflation
A2
0.15
0.1
−0.2 −1
22
−0.2 −1
−0.5
0 % Change Output
G
0.5
1
Figure 3.2. 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 19 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. The inversion of the aggregate demand curve in Proposition 3 is distinct from other similarsounding conditions in the literature. “Inverted aggregate demand logic” (Bilbiie 2008) arises in NK models with a large share of HtM HH. In this case, an increase in real interest rates increases aggregate demand via the IS curve. In our model, this occurs when (1 − α) > 1/(2 + ϕ), which is the black indeterminate region in Figure 3.1 and is entirely distinct from the condition of Γ < 0 in Proposition 3 (white region of Figure 3.1).23 Our result 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 distinct. 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.24 The differences are important: an increase in price flexibility (↑ κ) increases the stimulatory effect of restrictive labour market
23 Equation A1-A4 and A8-A9 Yˆt = Et Yˆt+1 + h The NK IS curve can be derived by combing i ˆ ˆ ˆ ˆ ˆ −α(Rt − π ˆt+1 ) + Tt + αGt − Et (Tt+1 + αGt+1 ) / [1 − (1 − α)(2 + ϕ)] 24 In 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 3.2).
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
23
practices in Eggertsson (2012), but here it reduces the transfer multiplier and makes it less likely the AD curve will invert. 3.1.1. The sensitivity of the transfer multiplier to the central bank’s response to inflation. Proposition 4. 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 < 0 and ∂lnMT r /∂φπ < ∂lnMG /∂φπ . 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.25 To some extent this should be obvious given φπ appears in the numerator and denominator 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 (given the absence of neoclassical wealth effects for transfers), 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 larger fall in the multiplier. 3.1.2. 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 framework above, the effect of 25Proposition
4 also holds with a perfect substitutes production function.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
24
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 unconstrained household (i.e consumption of the unconstrained 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.26 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 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 26Oh
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 in other papers.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
25
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+ .27 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).28 3.2. 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 4, we get similar numerical results in medium-scale DSGE model. 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.29 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, 27In
L our model, if φF π = 1, the model is indeterminate, though we can get arbitrarily close from above. 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. 29A 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 3.7, and so does not affect the multiplier. We also assume that [1 − (1 − α)(2 + ϕ)] (1 − ξ)(1 − βξ) − αξκ(1 + ϕ) > 0 for determinacy, which has the same form (with α = 1) as in Eggertsson (2012).
28If
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
26
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. ˆ t and a constant nominal interest rate Lemma 2. Consider a fiscal shock of size Tˆrt or G at time t (the “Zero Lower Bound binds”). With probability ξ, the fiscal shock and constant ˆ t+1 = 0 and the nominal rate policy continues at t + 1, and with probability 1 − ξ, Tˆrt+1 = G central bank resumes a Taylor rule. While the ZLB binds, the equilibrium is characterized by the same equations as before (3.1-3.6), but with φπ = 0 and ρ = ξ.
Proof. Can be shown by guess and verify. Proposition 5. When the ZLB binds (as described in Lemma 2), 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 3.7.
(3.7)
κ(ϕ + 1) Yˆt = α + ΓZLB (1 − ξβ)
−1
κ ˆt + ˆt Tˆrt + G ΓZLB G (1 − ξβ)
where: −1 κ(ϕ + 1) • α + ΓZLB is the transfer multiplier (1 − ξβ) −1 κ κ(ϕ + 1) • α + ΓZLB 1+ ΓZLB is the purchases multiplier. (1 − ξβ) 1 − βξ • ΓZLB = [α(φπ − ξ)/(1 − ξ)] − [(1 − α)(1 − ξβ)/κ] | {z } | {z } T P Ef f ect
Proof. Follows from Lemma 2.
DI Ef f ect
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
27
3.3. Some extensions to the simple model.
3.3.1. 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.30 To see this, note that the rest of the transfer (a fraction χ) flow 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 3.6 becomes Equation 3.8 (where Γ is defined as in Equation 3.6), 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.31
(3.8)
−1 n o κ(ϕ + 1) κ 1 − βρ ˆ ˆ ˆ ˆ Yt = α + Γ Gt (1 − χ) T rt + Gt + Γ+χ (1 − ρβ) 1 − βρ κ
An interesting special case is when transfers are entirely untargeted, i.e. χ = 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).
3.3.2. When fiscal policy is financed by persistent government debt. In our baseline analysis, we assume that the government runs a balanced budget (Equation 2.12). 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 30This
result also holds in the full model (Section 4), but relies on the assumption that transfers are funded by lump-sum taxes on the Ricardian household. 31The 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 0.2). 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).
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period, but the principal is never repaid), regardless of the allocation of the perpetual lumpsum taxes across the two households. 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).32 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.
3.3.3. 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.33 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 0.3 for further details.
4. The Transfer Multiplier in a Medium-scale DSGE Model By including realistic features such as sticky wages, capital, and a more flexible parametrization, 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) 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. 33Specifically, 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.
32The
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Table 1. Full Model Parametrisation and Steady State Parameter
Value
Parameter
Value
Discount Rate (β)
0.99*
Capital adjustment cost (ψ)
2
Inverse Frisch (ϕ)
0.5*
Capital depreciation rate (δk )
0.03
Labour share Ric. HH (α)
0.64*
Calvo Prob. constant wage (θw )
0.75
Calvo Prob. constant P (θp )
0.75*
Sticky Wage CES elasticity (ε)
21
Taylor Rule Inflation (φπ )
1.27*
Capital share (µ)
0.3
Taylor Rule Output (φY )
0.13
SS markup (X = σ/(σ − 1))
1.05
Taylor Rule Smoothing (φY )
0.73
SS Govt Purchases Share (GSS )
0.2
* Indicates parameter is also in simple model (others are zero in the simple model). Parameter sources: Iacoviello (2005) except inverse Frisch (ϕ) (Smets and Wouters 2007) and wage stickiness parameters ε and θw (Christiano et al 2005).
that the analytical results of Section 3 hold qualitatively in a richer model. See Table 1 for parameters, and Section 2 for a statement of the full model. 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∞ i ˆ iˆ Y β t+i i=0 β Yt+i or P∞ P V M ultipler ≡ P∞i=0 i ˆ ˆ t+i β T rt+i β iG P∞
(4.1)
i=0
i=0
4.1. Parameters and 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 4.1 shows the MPC estimated by Johnson et al (2006) in response to the 2001 Bush Tax rebates and compares them to an analogous group from the full model.34 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 34In
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.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
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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). Marginal Propensity to Consume: by assets 2001 Bush tax rebate: model and data (Johnson et al 2006)
1.6 1.4 1.2 1 0.8
Data
Model
0.6 0.4 0.2 0 -0.2 -0.4 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 4.1. Marginal Propensity to Consume: Data and Model 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. Multipliers calculated using an AR(1) process with ρ = 0.9 are fairly similar to multipliers using the ARRA profile of Cogan et al (2010) (see Online Appendix 0.9). Parameters are mostly taken from Iacoviello (2005), which is one of the few medium-scale estimated models with constrained and non-constrained households. The MPC profile is most sensitive to the share of HtM in the model, 1 − α = 0.36, though our value is consistent with a range of empirical evidence reported in Kaplan and Violante (2014) and elsewhere (see the Online Appendix 0.5 for a discussion). As Iacoviello’s (2005) Frisch elasticity is well above others in the literature, we take ϕ−1 = 2 from Smets and Wouters (2007) which is in the middle of the range of a number of macro studies (2.8) and micro studies (0.8) surveyed by Chetty et al (2011). Iacoviello (2005) does not have sticky wages, so we use the estimated
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parameters in Christiano et al (2005). We solve the full model numerically using Dynare. See Online Appendix 0.5 for further details about the steady state and parametrization. 5
PV Multiplier
4 3
ρ=.9, Transfer Mult. ρ=.9, Purchases Mult. ρ=0, Transfer Mult. ρ=0, Purchases Mult.
2 1 0 −1 0
0.2
0.4
0.6
0.8
1
Nominal wage stickiness (θw)
Figure 4.2. Wage stickiness and the PV multiplier (full model). The vertical line indicates default parametrisation
4.2. Sticky Wages. Sticky wages drive most of the differences between the full and simple models.35 In general, the more sticky the wage, the closer the multiplier on purchases and targeted transfers. Figure 4.2 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. Sticky wages weaken wealth effects on labour supply, which we showed in Section 3 drive the differences between targeted transfers and purchases. When wages are flexible, µ ˆw 2,t = 0 in Equation 2.7, such that an increase in consumption by the HtM HH 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 wages don’t need to rise as much in order to get the HtM HH to meet demand for its labour, which 35When
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.
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32
reduces the excess inflation which drove the differences between the transfer and purchase multiplier in Section 3. The 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 than permanent shocks, which explains why the purchases and targeted transfer multipliers are closer in Figure 4.2 for less persistent shocks.
4.3. 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.36 The transfer multiplier in the full model (when policy follows a Taylor rule) is large when fiscal policy is not very persistent or the share of HtM HH is not too small (as in Section 3 above). This is most easily seen as the lower left hand region in Figure 4.3 (RHS), where “large” is defined quantitatively as a multiplier greater than one. This region shrinks when the transfer multiplier is compared to the purchases multiplier, but is qualitatively similar (Figure 4.3 LHS).37 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 around 1.1. With persistence ρ = 0.9 (similar to the ARRA) the transfer multiplier is around
36The
smoothing of interest rates φR (which was zero in the simple model) has the effect of reducing the present value multiplier on transfers and purchases by about 0.08 (if ρ = 0.9) to 0.17 (if ρ = 0). 37 Numerically, in the full model there are no regions (away from corners) of the α, ρ space that are indeterminate.
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0.4 and the purchase multiplier is larger at around 0.6.38 Impulse response functions with a Taylor rule or 2 years ZLB are presented in Online Appendix 0.4.
Table 2. Full Model — Present Value Multipliers A. Targeted Transfers
B. Purchases
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
1.1
0.4
1.1
0.6
0.4
0.1
0.7
0.2
2 years ZLB
1.5
1.1
1.4
1.0
0.5
0.4
0.9
0.7
5 years ZLB
1.5
2.0
1.4
1.4
0.5
0.7
0.9
1.2
4.4. Zero Lower Bound (ZLB). The Federal Reserve has maintained nominal interest rates at 0-0.25 per cent since December 2008, a period of more than 6 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) assume the central bank commits to keeping the nominal interest rate constant for a certain number of periods (and then returns to a Taylor rule).39
As shown in Proposition 5, the targeted transfer multiplier tends to be larger than the purchase multiplier at the ZLB. Figure 4.4 (LHS) shows (in white) the regions of the (ρ, α)space where the transfer multiplier is greater than the purchase multiplier as the ZLB binds 38Apart
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. If we assume the labour of the households in perfect substitutes in production (rather than Cobb-Douglas) the multipliers deviate (on average) by only 0.05 from Table 2. See Online Appendix 0.1 for a further discussion. 39We 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).
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Figure 4.3. Regions of parameter space where the transfer multiplier is large (white) when monetary policy follows a Taylor rule (LHS: > purchases multiplier, RHS: > 1). for two years. One can see that ZLB dramatically increases the area where the targeted transfer multiplier is larger than the purchase multiplier. If the ZLB binds for three years or longer, the targeted transfer multiplier is always larger (not reported). Table 2 shows that with constant nominal interest rates for two years (as considered by Cogan et al 2010), all multipliers are greater than or equal to one.40 With five years of constant rates, the multipliers are now large for ρ = 0.9, specifically 2.0 for targeted transfers and 1.4 for purchases. Particularly striking are the increases for persistent transfer-based stimulus: the targeted transfer multiplier for ρ = 0.9 increases by 1.6 going from a Taylor rule to five years of the ZLB, whereas the purchase multiplier only increases by 0.8 (for less persistent fiscal policy the ZLB only increases the multiplier by 0.3-0.4).41 4.5. 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 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.42 As we showed 40While
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). 41As 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. 42For programs such as unemployment benefits, a concern is that transfers will create incentive problems, reducing the multiplier below the untargeted benchmark. However, for the stimulus policies that are the
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in Section 3.3.1, 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 0.5 for once-off transfers, 0.1 for persistent transfers if monetary policy follows a Taylor rule, and usually above 0.5 for persistent transfers when the ZLB binds. 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 (Kaplan and Violante 2014). Table 2 Column D shows that with a 50% HtM share (Campbell and Mankiw 1989, Mankiw 2000) 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 4.4 (RHS) shows that when the ZLB binds for 2 years, the untargeted transfer multiplier is greater than one so long as the HtM share is above about 0.5 and fiscal policy is not too persistent. Full model (2yr ZLB): dY/dTr>dY/dG (White region)
Full Model (2Yrs ZLB): Untargeted dY/dTr>1 (White Region)
1
1
0.8
0.8
α
0.6
0.6
α 0.4
0.4
0.2
0.2
0 0
0.2
0.4
ρ
0.6
0.8
1
0 0
0.2
0.4
ρ
0.6
0.8
1
Figure 4.4. Regions where the transfer multiplier is larger with 2yrs ZLB. LHS: targeted transfer multiplier > purchases multiplier. RHS: untargeted transfer multiplier >1.
5. 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 focus of this paper such as the Bush tax rebates, transfer payments were once-off and based on information from previous tax years, making eligibility largely pre-determined.
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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 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 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. The main argument in favour of targeted transfers (versus purchases) 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. However, there are two important caveats. First, transfers cannot be perfectly targeted at constrained households and so the multipliers on real-world transfer packages are lower that the perfect-targeting benchmark. However, we show that in deep recessions characterized by a long period at the ZLB and a higher share of constrained HHs, the multiplier on untargeted transfers can still be greater than one. Second, real world fiscal stimulus tends to be funded
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by distortionary taxation. Leeper et al (2010) argues that this reduces multipliers in normal times, though Eggertsson (2010b) argues that by raising inflation, distortionary taxation can be stimulatory at the ZLB. In further simulations (discussed in Online Appendix 0.7), we find that so long as the ZLB is binding for an extended period, the targeted transfer multiplier can still be above one (though distortionary taxes cause a large fall in the multiplier in normal times). An online appendix is available at: https://sites.google.com/site/stevenpennings/GP2015appendix.pdf References [1] 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 [2] Bernanke B, Gertler M and S Gilchrist (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework,” Handbook of Macroeconomics 1, pp 1341-1393. [3] Bilbiie F (2008), “Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate Demand Logic,” Journal of Economic Theory, 140(1), pp 162-196. [4] Bilbiie F, Monacelli, T and R Perotti (2013), “Public Debt and Redistribution with Borrowing Constraints,” The Economic Journal, 123 (February), pp F64-F98. [5] Broda C And J Parker (2012), “The Economic Stimulus Payments of 2008 and the Aggregate Demand for Consumption” mimeo [6] Campbell J and G Mankiw (1989), “Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence,” NBER Macroeconomics Annual 4, pp 185-246. [7] Chetty, R, A. Guren, D Manoli and A Weber (2011), “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 [8] Colciago A (2011), “Rule-of-Thumb Consumers Meet Sticky Wages,” Journal of Money, Credit, and Banking 43(2-3), pp 325-353. [9] 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. [10] Cogan J and J Taylor (2010), “What the Government Purchases Multiplier Actually Multiplied in the 2009 Stimulus Package,” NBER Working Paper 16505. [11] 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. [12] 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. [13] Christiano L Eichenbaum M, and S Rebelo (2011), “When Is the Government Spending Multiplier Large,” Journal of Political Economy, 119(1), pp 78-121. [14] Drautzburg T and H Uhlig (2013), “Fiscal Stimulus and Distortionary Taxation”, Federal Reserve Bank of Philadelphia WP 13-46 [15] Eggertsson G (2010a), “The Paradox of Toil” Federal Reserve Bank of New York Working Paper. [16] Eggertsson G (2010b), “What Fiscal Policy is Effective at Zero Interest Rates?” NBER Macroeconomics Annual 25, pp 59-112.
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