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 government transfers to financially constrained households is larger than the purchase multiplier if the zero lower bound binds, or if the persistence of fiscal policy is sufficiently low and the share of constrained households is sufficiently high. Targeted transfers provide the same boost to demand as purchases, but lower aggregate supply as those receiving transfers want to work less. When the aggregate demand curve inverts, the extra inflation from lower supply boosts the multiplier.
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. Date: 28 April 2014. 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/ Email:
[email protected] and
[email protected] Address: Department of Economics, New York University (NYU) 19 W. 4th St, 6th Floor, New York, NY, 10009, USA. 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, 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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Despite the focus on the government purchase multiplier in the literature (Woodford (2011), Christiano et al (2011), Cogan et al (2010), Werning (2012)), 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, slightly above the OECD median of 64 per cent. Using a more conservative classification of transfers (see Online Appendix), we find that during the ten quarters from 2009:Q1, transfers accounted for around US$250 billion, or more than 50 per cent of the spending component of the the American Recovery and Reinvestment Act (ARRA). 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 closed-economy two-agent model with nominal rigidities where around a third of the population are 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. We find that the government transfer multiplier can be large, in the sense that it is either (i) larger than the purchases multiplier, or (ii) larger than one. When monetary policy follows a Taylor Rule, the transfer multiplier is likely to be large (by either definition) when fiscal policy is short-lived or the share of financially constrained households is not too low. 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 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 in Section 3). Both transfers and purchases boost aggregate demand, but only purchases increase aggregate supply via the
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neoclassical wealth effect. When the aggregate demand curve is downward sloping, the purchases multiplier is larger than the transfers multiplier. But if the ZLB binds or there is a high-enough share of hand-to-mouth households or low levels of fiscal persistence (when monetary policy follows a Taylor rule), the aggregate demand curve inverts and the targeted transfers multiplier is larger than the purchases multiplier. Sticky wages reduce the strength of wealth effects on labour supply, making the transfer multiplier and purchases multiplier a similar size. The slope of the aggregate demand curve — and hence the comparative size of the targeted transfers and purchase multipliers — depends on the relative strength of the Disposable Income effect and the Taylor Principle effect. The Disposable Income effect is the tendency for higher inflation to boost the consumption demand of the Hand-to-Mouth household. Inflation reduces markups, increases wages, and boosts disposable income — which is spent on consumption by hand-to-mouth households. The Taylor Principle effect is the tendency for higher inflation to reduce the consumption demand of the Ricardian HH as the central bank raises nominal (and real) interest rates. In normal times, the Disposable Income effect and Taylor Principle effect work in opposing directions, with the targeted transfer multiplier larger than purchase multiplier when the the Disposable Income effect dominates. When the ZLB binds, the Taylor Principle effect changes signs (as inflation now lowers real interest rates, and raises consumption of the Ricardian HH), which is why the demand curve is always inverted at the ZLB. In Section 4, we calculate the targeted transfer multiplier in a calibrated medium-scale DSGE model with capital and sticky wages. 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 ARRA (auto-correlation of 0.9), have a present value multiplier of around 0.4 for targeted transfers or 0.6 for purchases. If monetary policy is constrained by the ZLB for five years, the targeted transfer multiplier is around 1.5 for a once-off stimulus, and 2.0 for a persistent stimulus (with purchase multipliers being around 1.4 in either case).
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For US policymakers, our results suggest that transfers can be used to stimulate the economy, but are most effective when (i) they are targeted at those that are financially constrained (who are more likely to spend them), (ii) the ZLB binds during the time of the fiscal stimulus or they are once-off (if monetary policy is not constrained by the ZLB).1 In terms of policy design, targeting transfers at the financially constrained is the most challenging. If transfers are completely untargeted — which can be considered a lower bound — the transfer multiplier is often around 0.5, though can reach unity if the ZLB binds (with a slightly higher share of constrained HH). Our approach approximately matches the marginal propensities to consume (MPC) for different groups from 2001 Bush tax rebates estimated by Johnson et al (2006). The timing of these lump-sum rebates was randomised by social security number and so rigorous identification of their impact is possible. Despite the program being pre-announced, Johnson et al (2006) find that in total around 20-40 per cent of the rebates were spent in the months that they arrived, and the response was around 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.2 Literature Although there are many recent papers examining government purchases in DSGE models (for example, Christiano et al (2011), Cogan et al (2010), Woodford (2011) and Uhlig (2010)), there are only a few papers that consider transfers in a setting similar to ours. Closest to our paper is contemporaneous work by Bilbiie, Monacelli and Perotti (2013) and Mehrota 1
Three caveats (and areas for future research) are that in the model, taxation is lump-sum (rather than distortionary), the economy is closed, and that we rely on linearisation and thus ignore the fact that the effectiveness of stimulus may depend on how far the economy is from steady state. During the most recent recession many policymakers justified stimulus by noting that the economy was far below potential, with a large output gap and high unemployment — our linearised environment necessarily ignores differential effects of policy when the economy is far away from steady state. 2 Based on the life-cycle and differences in returns, Kaplan and Violante (2014) show that wealthy households can behave in a hand-to-mouth fashion if they hold low levels of liquid assets. Hausman (2012) shows that a large fraction of the 1936 veteran’s bonus was spent, which is consistent with a model where agents are financially constrained.
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(2013). Both papers use a saver-borrower New Keynesian model and find a positive transfer multiplier with sticky prices, and a small or zero transfer multiplier under flexible prices. Nonetheless, our key analytical finding — that the targeted transfers multiplier is larger than the purchases multiplier at the ZLB or (sometimes) when monetary policy follows a Taylor rule — is new, as is our characterization of results in terms of aggregate demand, aggregate supply and Taylor Principle/Disposable Income effects. Neither paper includes a medium-scale model with features like capital and sticky wages in order to quantify the effects of a transfer shock.3 More broadly, our paper is related to Oh and Reis (2012) who document the size of transfers in the ARRA, and find the transfer multiplier to be small using a heterogeneous agent model where a continuum of agents suffer health and employment shocks. Their model is different from ours in that they do not model monetary policy, which is a focus of our paper. Several papers find an inverted aggregate demand curve or the Keynesian “paradox of toil”, but in Eggertsson and Krugman (2012), Eggertsson (2012) and Eggertsson (2010a) this only occurs at the ZLB and Bilbiie (2008) does not consider fiscal policy. The conditions under which this occurs is different from ours, and none of these papers consider transfers. 2. Model We examine the effect of government transfers and purchases in a New Keynesian DSGE model with two agents that differ in their access to financial markets. The Ricardian household (household 1) has full access to financial markets and the Hand-to-Mouth Household (household 2, HtM) consumes his entire income each period in a hand-to-mouth fashion as in Galí et al 3
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 (2011) investigate the effects of the ARRA in a model similar to the Smets-Wouters model with distortionary taxes. While they do consider transfers (as it was part of the ARRA) it is not a focus on their paper. Bilbiie, Monacelli and Perotti (2013) do not consider government purchases or the ZLB, and Mehrota (2013) does not provide an analytical solution for the multiplier when monetary policy follows a Taylor rule. Both papers do include quantitative estimates of the multiplier, but just in simpler models without capital or Calvo sticky wages.
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(2007). Although simple, the two household 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 consumer to pay for government purchases, as well as transfers to the HtM household. The Ricardian household owns capital (which they rent to intermediate goods firms) and retailers which 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 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 the Online Appendix. 2.1. Ricardian household’s problem. The Ricardian household consists of a unit mass of individuals indexed by j ∈ [0, 1], where 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 (RRt ), lump-sum taxes (T axt ), real wages (w1t (j) = W1t (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). As there are complete markets within the household, consumption and all other variables are equalised across members and so we drop the j index for these variables.4 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 4We
follow the simplified notation in Galí (2008) and omit these Arrow securities from the household’s budget constraint. A similar assumption that prevents consumption heterogeneity across households is that of Schmitt-Grohe and Uribe (2005), in which each household supplies a continuum of differentiated labour inputs. This assumption gives rise to a similar Phillips curve, albeit one with a larger coefficient on the wage markup. See Colciago (2011) for an implementation of this alternative labour market assumption with HtM HH.
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ACKt (j) = ψ (It /Kt−1 − δ)2 Kt−1 /(2δ). Therefore the Ricardian household’s problem is:
(2.1)
max{c1,t ,b1t ,It ,L1,t (j)} E0
∞ X t=0
Lϕ+1 1,t (j) β [ln(c1t ) − ] ϕ+1 t
(where ϕ−1 gives the Frisch elasticity of labour supply), subject to budget and capital accumulation constraints:
(2.2) c1t + It + ACKt + bt = RRt bt−1 + M P Kt Kt−1 + w1t (j)L1t (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 L1t (j) = L1t and w1t (j) = w1t ∀j. 2.2. Hand-to-Mouth (HtM) household’s problem. The HtM HH’s problem is much simpler than that of the Ricardian household: each household member j ∈ [0, 1] only has to choose desired labour hours (L2,t (j)) as he can not smooth consumption over time. Real consumption (c2t ) is equal to labour income plus lump-sum transfers ( T rt ) from the government, and will be equal across household members due our assumption of perfect insurance of Calvo wage shocks. In the simple model, L2t (j) = L2t and w2t (j) = w2t ∀j as labour markets are competitive.5
(2.4)
max{c2,t ,L2,t (j)} E0
∞ X t=0
5In
β2 t [ln(c2,t ) −
Lϕ+1 2,t (j) ] ϕ+1
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 zeroprofits in steady state. This tax is rebated to the HtM HH in the form of a wage subsidy. This assumption is quantitatively unimportant, but allows us to deliver cleaner analytical expressions for the multiplier.
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such that: (2.5)
w2,t (j)L2t (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 wages are important in 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 additional 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 and L2 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 wage indices 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 2t (j)1−w dj] 1−w . As with Calvo pricing, each member of the Ricardian and HtM HH 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 = logWi,t − logWi,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 (variables with hats generally denote deviations from steady-state). 6 6Note
that in the simple model labour markets are perfectly competitive, while in the model with sticky wages they are monopolistic competitive. The difference in market power is unimportant because if wages are flexible adding labour market monopoly power to the simple model would imply a constant markup of wages over each household’s MRS. Thus,
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
(2.6)
ˆw ˆw π ˆw i,t i,t+1 − λi µ i,t = βEt π
(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)
9
and wˆi,t = wˆi,t−1 + π ˆw ˆ t i = 1, 2 is the real wage. i,t − π
2.4. Sticky prices, Retailers, Intermediate and Final Output. Intermediate output is Cobb-Douglas in capital and the labour from each of the households. 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 households in the simple model (when wages are flexible) (µ = 0 in the simple model).7
(2.8)
(1−µ)α
Yt = Ktµ L1t
(1−µ)(1−α)
L2t
As in Bernanke et al (1999) and Iacoviello (2005), final output is produced by a unit continuum of retailers, indexed by i, who buy intermediate output in competitive market, costlessly differentiate it, and sell a variety of final output σ σ−1 ´ σ−1 1 f σ di . Yi,t . Aggregate final output is given by the index Yt = Y 0 i,t 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 ˆ t = lnXt − lnX is the is the inflation rate (steady state inflation is zero), X σ deviation in the retailer’s average markup from steady state (where X = 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 wages and each household’s MRS would move proportionately, and the model dynamics would be unaffected. 7In the Appendix we consider an alternative where the labour of the two households is (1−µ) perfect substitutes, i.e. Equation 2.8 is replaced by Yt = Ktµ Lt where Lt = L1,t + L2,t In this case, there is measure α of Ricardian households and 1 − α of HtM HH.
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κ → ∞, and so shifts in demand affect prices and not output. With more sticky prices (higher θp ) most 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). 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 P int 1 retailer’s average markup t = . As such, the marginal product of labour Pt Xt or capital in terms of 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, and so for our first-order approximation Yˆt = Yˆtf . (2.10)
w1,t = α
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 Rule (in linearised form) with interest rate smoothing, where ˆ t = lnRt −lnR is the log deviation of the nominal interest rate from its steady R 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 .
(2.11)
ˆ t = φR R ˆ t−1 + (1 − φR )(φπ π R ˆt + φY Yˆt )
2.5.1. Fiscal policy. 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 tax on the Ricardian households ˆ t are transfers and T axt . Note here that throughout the paper, Tˆrt and G rt t , T ˆaxt ≡ TYax and government purchases as a share of GDP, i.e. Tˆrt ≡ YTSS SS Gt ˆ Gt ≡ YSS . This simplifies the expressions for multipliers and allows for the
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possibility that purchases are zero in steady state. This 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 2.12). 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.8
(2.12)
T axt = T rt + Gt
ˆ t are exogenous and we assume here that they take The path of Tˆrt and G an AR(1) process.
(2.13)
Tˆrt+1 = ρTˆrt + eT r,t+1
(2.14)
ˆ t+1 = ρG ˆ t + eG,t+1 G
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 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
8This
is not the case if taxes are levied on the constrained households, or if taxes are distortionary.
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size of the transfer and purchases multipliers which we can characterize exactly, rather than 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). Both transfers and purchases boost 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. But if there is a high shares of HtM HH or low levels of fiscal persistence (even when when monetary policy follows a Taylor rule), the aggregate demand curve inverts and the transfers multiplier is larger than the purchases multiplier. In Section 3.2 we show that the multiplier has a similar form when the Zero Lower Bound (ZLB) on interest rates binds, but in this case the transfer multiplier is always larger than the purchases multipliers. Section 3.3 presents some tractable generalizations, such as when transfers are imperfectly targeted at the HtM HH. 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 multiplier is constant over time — that is output ˆ t or Tˆrt — by removing state endogenous state is a constant multiple of G 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 simplify the algebra 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 3.3.2.).9 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 9That
is, we set steady state government purchases to zero (Gss = 0), and assume a small profits tax that is rebated as a wage subsidy to the HtM household such that c1,ss /Yss = α and c2,ss /Yss = 1 − α A similar approach used by Bilbiie (2008) is to assume fixed costs of operating that exactly offset profits in steady state.
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hat (^) denotes percentage deviation from steady state (except for government transfers and purchases, where it represents the change in fiscal policy as a share of GDP). For a version of the model where the labour of the households is perfectly substitutable (rather than Cobb-Douglas), see the Appendix. Equations in the Analytical Model (A1-A9) ˆ 1t + (1 − α)L ˆ 2t [A1 Production Function] Yˆt = αL [A2 Resource constraint] Yˆt = αˆ c1,t + (1 − α)ˆ c2,t + gˆt ˆ [A3 HtM Budget Constraint] (1 − α)ˆ c2,t= Tˆt + (1 − α)( wˆ2,t + L2,t ) 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 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 price are flexible (κ → ∞), retailers keep their markups constant at the profitˆ. ˆ t = 0 and hence Yˆt = 1 G maximising optimum, so X 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
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unchanged. Note that this 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 3.3.2 we show that the flex-price multiplier can be positive (negative) if the HtM HH’s labour share is smaller (larger) than his consumption 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. We solve the analytical model — and show how it works — in three steps. First we use Lemma 1 to solve for expectations of future future variables in terms of current variables, which removes all dynamics from the model.10 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 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 this similar to the “Old Keynesian” aggregate demand and aggregate supply relationships in undergraduate textbooks, but with rational expectations micro-foundations.11 The supply curve 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 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 10When
prices are flexible, the model is essentially static because real interest rate adjusts to make the Euler equation hold. 11For 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.
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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. Transfers and purchases both increase demand by the same amount (Remark 2), but only government purchases expands supply (Remark 1). This means that the transfer multiplier will be larger than the purchases multiplier if the aggregate demand equation inverts (slopes upwards). 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 . The curve is the generalization of the Phillips curve (Equation A6), solving out for expectations using Lemma 1 and markups (using Equation 3.1). (3.2)
π ˆtAS =
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 3.2) and Equations (3.3) and (3.4). The aggregate demand curve is the generalization 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.12 12Our
models nests a standard three equation NK model when the share of HtM households is zero (1 − α = 0) (transfers are not defined in this case). The New Keynesian IS curve ˆ t − Et π ˆ t − Et G ˆ t+1 ), which can be rearranged to give becomes Yˆt = Et Yˆt+1 − R ˆt+1 + (G ˆt −Yˆt + G . As long as the Taylor principle is satisfied φπ > 1 , the aggregate (φπ − ρ)/(1 − ρ) demand curve is always downward sloping in the baseline NK model without HtM HH. The supply curve is the same as it would be be in the baseline NK model. π ˆt =
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
16
AD ˆt Tˆrt + G αYˆt + (3.3) =− ∆ ∆ where ∆ = [α(φπ − ρ)/(1 − ρ)] − [(1 − α)(1 − ρβ)/κ] | {z } | {z }
π ˆtAD
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 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 Zero Lower Bound binds, the Taylor Principle Effect reverses its sign because a rise in inflation lowers real interest rates (Section 3.2).
(3.4)
αˆ c1,t = − [α(φπ − ρ)/(1 − ρ)] π ˆ {z } t | T P Ef f ect
Definition 4. Disposable Income (DI) Effect. The boost to aggregate demand from the HtM household from an increase in inflation, other things (transfers and aggregate output) equal, is given by (1 − α)(1 − βρ)/κ. 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) ˆ t to yield Equation plus Lemma 1 to substitute out for variation in markups X 3.5.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
17
ˆ (1 − α)ˆ c2,t = Tˆrt + (1 − α)Yˆt + [(1 − α)(1 − ρβ)/κ] π {z } t |
(3.5)
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 transfer and purchases multipliers are given by Equation (3.6).
n o ˆt + γ Yˆt = γ Tˆt + G
(3.6)
κ ˆt ∆G 1 − βρ
where: • γ = 1 − (1 − α)(2 + ϕ) + (1 + ϕ)
α(φπ − ρ)κ (1 − βρ)(1 − ρ)
−1 is the transfer mul-
tiplier • γ 1+
κ ∆ is the purchases multiplier. 1 − βµ • ∆ = [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 . Proposition 3. Transfer and Purchase Multipliers and Inverted Aggregate Demand Curve. The transfer multiplier is larger than the purchase multiplier whenever: a) the Disposable Income effect dominates the Taylor Principle effect (i.e. ∆ = [α(φπ − ρ)/(1 − ρ)] − [(1 − α)(1 − ρβ)/κ] < 0, or equivalently {z } | {z } | T P Ef f ect
DI Ef f ect
b) the demand curve is inverted (slopes upward in (ˆ π , Yˆ )-space). Proof. Follows from Proposition 2 and Definition 2.
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. 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
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
18
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 the adjustment path, the ratio of markup adjustment ˆ t /ˆ 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 listed in Table 1). 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 a 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 the next section, 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. Because all transfers are targeted at the HtM HH with a MPC of one (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) but only government purchases shift the aggregate supply curve (via the neoclassical wealth effect).13 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 ˆ t shifts the demand curve right by 1/α, which is the “old one unit increase in Tˆt + G Keynesian” multiplier of 1/(1-MPC).
13A
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
19
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 credit constrained households. 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 better off).14 When the aggregate demand curve is downward sloping (for example with a high persistence shock, ρ = 0.9 in the left-hand panels 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.15 As foreshadowed in Proposition 3b, this means that the transfer multiplier will be larger than the purchase multiplier. In the RHS of Figure 3.2 one can see that when the demand curve inverts, higher inflation boosts aggregate demand (by increasing the disposable 14
This is a special case due to Cobb-Douglas preferences. As we see in the Appendix, with perfect substitutes transfers increase demand by less than purchases because the wealth effect on labour supply reduces the HtM HH’s income, and hence expenditure. 15The 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?
20
income of the HtM HH more than it reduces the consumption 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 transfer. The inversion of the aggregate demand curve in Proposition 3 is distinct from other similar-sounding 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 ∆ < 0 in Proposition 3 (white region of Figure 3.1).16 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.17 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. 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 (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 4). In Section 4, we get similar numerical results in medium-scale DSGE model. We show the transfers multiplier is larger than the purchases multiplier at the ZLB using a tractable two-state setup similar to that in Woodford (2011), where the ZLB and contemporaneous fiscal expansion persist with probability NK IS curve can be derived by combing Equation A1-A4 and A8-A9 Yˆt = Et Yˆt+1 + h i ˆ ˆ ˆ ˆ −αrr ˆ t + Tt + αGt − Et (Tt+1 + αGt+1 ) / [1 − (1 − α)(2 + ϕ)] 17 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).
16The
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
0.1
A1
B2
G B
1
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 Inflation
Inflation
A2
0.15
0.05
−0.2 −1
21
−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: low persistence of fiscal policy) and when the transfer multiplier is larger (RHS: high persistence of fiscal policy). Ox , (x = 1, 2) represents the steady state equilibˆ π ) with the original (solid) Aggregate Supply (AS) and rium (Y,ˆ Aggregate Demand (AD) curves. Ax represents the new equilibrium with a 0.2% GDP transfer shock, 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, which shifts both AD and AS curves to the right. ξ each period. As the model is linear, 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.18 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 the wages, and hence 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 18A
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 binds in our two state example appears as a constant in Equation 3.7, and so does not affect the multiplier.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
22
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 Lemma 2. Consider a fiscal shock of size Tˆrt or G interest rate at time t (the “Zero Lower Bound binds”). With probability ξ, the fiscal shock and constant nominal rate policy continues at t + 1, and with ˆ t+1 = 0 and the central bank resumes a Taylor rule. probability 1−ξ, Tˆrt+1 = G 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 4. 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.
o n ˆ ˆ ˆ Yt = γZLB T rt + Gt + γ
(3.7)
κ ˆt ∆ZLB G 1 − βξ
where: • γZLB
= 1 − (1 − α)(2 + ϕ) +
−1 α(0 − ξ)κ (1 + ϕ) is the trans(1 − βξ)(1 − ξ)
fer multiplier κ ∆ZLB is the purchases multiplier. • γZLB 1 + 1 − βξ • ∆ZLB = [α(φπ − ξ)/(1 − ξ)] − [(1 − α)(1 − ξβ)/κ] | {z } | {z } T P Ef f ect
DI Ef f ect
Proof. Follows from Lemma 2.
3.3. Two Extensions to the simple model. 3.3.1. Imperfect targeting of transfers (plus the financing of govt purchases). The model can be easily generalised to situations where transfers are imperfectly targeted at credit constrained households. Suppose that only a fraction
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
23
1 − χ of transfers are targeted at the HtM HH, and the rest (a faction 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 ˆ 2,t ). Because the model is linear, with (1 − α)ˆ c2,t = (1 − χ)Tˆrt + (1 − α)(wˆ2,t + L imperfect targeting just scales down the transfer multiplier by a factor of 1−χ. That is, Equation 3.6 becomes Equation 3.8 (where γ and ∆ are defined as in Equation 3.6), and a stronger DI effect/weaker TP effect ∆ < −χ(1 − βρ)/κ is required for the transfer multiplier to be greater than the purchases multiplier.
(3.8)
n o ˆt + γ Yˆt = (1 − χ)γ Tˆrt + G
κ 1 − βρ
1 − βρ ∆+χ κ
ˆt G
An interesting special case is when transfers are entirely untargeted, i.e. χ = α. In this case the transfer multiplier will 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. But with our standard parameters (Table 1) it will hold at the ZLB if the expected duration of the ZLB is longer than about 3 quarters. The financing of government purchases In most of the paper, we assume that government purchases are financed by taxes on the Ricardian HH. Instead, suppose only a fraction χ of the lumpsum taxes to fund government purchases fall on the Ricardian household (a fraction 1−χ falls on the HtM HH), and let the multiplier on these government purchases be denoted dY /dG (χ).19 This policy is isomorphic to financing purchases with taxes on the Ricardian household (as before), combined with a negative contemporaneous untargeted transfer with fraction 1 − χ of transfers targeted at the HtM HH. As the model is linear, shocks are additive and the multiplier on these transfers is given by Equation 3.9 (where γ and ∆ are defined in Equation 3.6).20 When purchases are entirely funded by the HtM, χ = 0 (and hence χ(1 − βρ)/κ = 0) and the HtM-funded purchases 19Previously,
the timing of taxes did not matter because those taxes fell on the Ricardian Households, but here it is important to assume the taxes are contemporaneous. 20Readers will note that this the second term in Equation 3.8, where Tˆ = −ˆ gt removes t the first term. The multiplier purchases funded by the Ricardian HH (as in the rest of the paper) is dY /dG (1), which is the purchases multiplier from Proposition 2.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
24
multiplier will be positive if the TP effect is larger than the DI effect (i.e. if the purchases multiplier is larger than the targteted transfers multiplier). The RHS of Equation 3.9 is increasing in χ which corroborates the findings of Monacelli and Perotti (2011) that the purchase multiplier is larger when funded by taxes on savers.
(3.9)
κ dY /dG (χ) = γ 1 − βρ
1 − βρ ∆+χ κ
3.3.2. When consumption and labour shares differ. In the baseline analysis, we assumed that the share of labour income of each household was the same as their share of aggregate consumption. While this substantially simplifies the analysis, in general it will not hold exactly due to the production technology or the presence of steady state transfers. Let α be the consumption share of GDP of the Ricardian HH and let ω be the share of the the Ricardian Household’s labour in the Cobb-Douglas production function (previously these were both ˆ 1 + (1 − ω)L ˆ 2 will replace Equation A1, (1 − α)ˆ α). Then Yˆt = ω L c2,t = ˆ t ) will replace Equation A3 (Equation A2 is unchanged). Tˆrt + (1 − ω)(Yˆt − X When α = ω, the transfer multiplier was zero when prices were flexible because the wealth effects of the two agents exactly cancelled (Prop. 1). When α 6= ω, the flexible price multiplier is given by Equation 3.10. Specifically, the flex-price transfer multiplier will be positive (negative) whenever the consumption share of the HtM Households is greater (less) than their labour share ((1 − α) > (1 − ω)). Intuitively, as the labour share of the HtM HH falls relative to their consumption share, the size of positive wealth effect falls and so the wealth effect of the Ricardian household dominates, leading to a positive flex price transfers multiplier.21 ˆ t + α(1 − ω)G ˆt [(1 − α) − (1 − ω)] Tˆrt + G ˆ (3.10) Yt = (1 − α)α(ϕ + 1) + (ω − α)2 When prices are sticky and α 6= ω, the aggregate demand side of the model is mostly unchanged: ω replaces α in the Disposable Income effect (it becomes 21In
the limit as (1 − ω) → 0, the transfer multiplier approaches the purchase multiplier.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
25
(1 − ω) (1 − ρβ) /κ), and the TP effect and the form of the aggregate demand function are unchanged. However the aggregate supply curve is quite different: the wealth effects on labour supply of two households do not cancel, and so any policy that redistributes consumption — such as a targeted transfer — will shift the supply curve. Equation 3.13 states that the supply curve will shift out whenever consumption is tilted towards the household with the lower relative labour weight. For example if ω>α, the HtM household has a lower relative labour share than the Ricardian Household, so shifting consumption towards the HtM household by way of a targeted transfer will increase aggregate supply.
(3.11)
π ˆtAS =
κ ˆ t − (ω − α) (ˆ η YˆtAS − G c2,t − cˆ1,t ) (1 − ρβ)
The sticky price multiplier when ω 6= α is given by Equation 3.12. Despite a more complicated form, the transfer multiplier is still greater than the purchases multiplier only when the demand curve is inverted (∆ < 0). Although transfers now can shift the supply curve, they will increase it by less than a comparable government purchase, and so the aggregate demand curve still needs to be inverted for the transfers multiplier to be greater than the purchases multiplier. (3.12) (ω − α) ˆ A+∆ T rt ˆt (A + ∆) G 1−α ˆ + Yt = 1−ω 1−ω ∆(1 + ϕ) + Aω − ∆ (ω − α) ∆(1 + ϕ) + Aω − ∆ (ω − α) 1−α 1−α 1 − ρβ φπ − ρ 1 − ω 1 − ρβ where A = +(ω − α) + and ∆ is as in Equaκ 1−ρ 1−α κ tion 3.6.
4. The Transfer Multiplier in a Medium-scale DSGE Model By including realistic features such as sticky wages, capital and a richer 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) and (ii) that
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
26
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.22 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. 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 : P40
(4.1)
P V M ultipler =
iˆ i=0 β Yt+i P40 i ˆ i=0 β T rt+i
P40
i=0 or P40 i=0
β i Yˆt+i ˆ t+i β iG
4.1. Parameters and empirical evidence. Parameters 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 (Table 1). 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.23 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, which is taken to be 0.36 from Iacoviello (2005). This is consistent with a range of evidence. Kaplan and Violante (2014) present evidence from Survey of Consumer Finances that around 1/3 of the population is HtM, though the majority of these are “wealthy HtM” (rich in illiquid assets but poor in liquid assets). Moreover, 36% of people in the Survey of Consumer Finances report regular spending greater than their income (Kaplan and Violante 2014), 1/3 of households would not be able to come up with $2000 in the next month in 22In
earlier versions of the paper, we assumed that HtM HH was able to borrow against consumer durables or housing. With standard parameters for adjustment costs this did not substantially affect the results. 23In 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?
27
the event of a financial emergency (Lusardi et al 2011) and 40% of households do not have at least two months income in liquid savings (Broda and Parker 2012). Our value is in the middle of the range of macroeconomic estimates such as 0.5 from Campbell and Mankiw (1989) and 0.26 from Cogan et al (2010). Other parameters are taken from Iacoviello (2005) or elsewhere in the literature and are fairly standard. 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.24 Government transfers, T rt , are zero in steady state, though results are fairly robust to positive steady state transfers. As argued by Kaplan and Violante (2014), many HtM HH are not poor, so it is unclear the size of the transfers they might receive in steady state. The Frisch elasticity of substitution ϕ−1 = 2 is taken from the estimated value in Smets and Wouters (2007). We choose this value because it is in 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). A lower Frisch elasticity increases the transfer multiplier in the simple model and if the Frisch elasticity is too low the transfer multiplier goes to ∞ and the model becomes indeterminate.25 We solve the full model numerically using Dynare. Where the ZLB binds for a predetermined number of periods, we solve the model using the deterministic response to an initial fiscal policy shock using the same method as Cogan et al (2010).
24We
assume that these are funded by lump sum taxes, which are proportional to the labour and capital income of each household, net of depreciation.Thus, the Ricardian household’s share of GDP in steady-state is given by (α(1 − µ) + µ − ISS ) / (1 − ISS ). This reflects that all income earners pay payroll taxes etc. that fund government purchases in steady state. 25Specifically the condition for determinacy in the simple model is ϕ−1 > (1/(1 − α) − 2)−1 . With ϕ−1 = 1 for example, the model is indeterminate for any share of HtM HH greater than 1/3, which includes our baseline calibration. ϕ−1 = 2 is close to the average of the values used in Bernanke et al (1999) and Christiano et al (2005). In the full model (which has sticky wages, which reduce the effect of ϕ−1 ), the multiplier with ϕ−1 = 1 is almost identical to that with ϕ−1 = 2, except with 5yrs of ZLB, where the transfer multiplier for ρ = 0.9 is about 0.3 lower. In general, a steady state transfers of 0.1 of GDP to the HtM HH, either has no effect on the transfer multiplier or increases it except with 5yrs ZLB for ρ = 0.9 where the transfer multiplier is 0.3 lower. In either case, the transfer multiplier is still larger than the purchases multiplier (and larger than one) with 5yrs of ZLB.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
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Table 1. Parametrisation and Steady State Parameter
Symbol
Simple Model
Full Model
Panel A: Parameters in Analytical Model and Full Model Discount Rate
β
0.99
0.99
Inverse Frisch Elasticity
ϕ
0.5
0.5
Labour share Ricardian household
α
0.64
0.64
Calvo Prob. constant price
θp
0.75
0.75
Inflation Coefficient (Taylor rule)
φπ
1.27
1.27
σ ) σ−1
X
1.05
1.05
Steady State Markup (X =
Panel B: Parameters only in Full model Capital share
µ
0
0.3
Capital adjustment cost
ψ
-
2
Capital depreciation rate
δk
-
0.03
Calvo Prob. constant wage
θw
-
0.75
Sticky Wage CES elasticity
ε
-
21
Output coefficient (Taylor rule)
φY
0
0.13
Interest rate smoothing (Taylor rule)
φR
0
0.73
Steady State Government Purchases
GSS
0
0.2
Sources: Most of the model’s parameters come from Iacoviello (2005). Exception are ϕ (leisure utility parameter) which leads to a Frisch Elasticity of labour supply of 2 which is taken from Smets and Wouters (2007). Wage stickiness parameters (Calvo probability and CES elasticity) are taken from Christiano et al (2005). The steady state government share is the same as Christiano et al (2011). Notes: Steady state GSS funded by SS labour and capital income share in the full model. Ricardian consumer share=(α(1 − µ) + µ − ISS )/(1 − ISS ) = 0.68.
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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 4.2. Sticky Wages. Sticky wages drive most of the differences between the full and simple models.26 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 26When
wages are sticky, last period’s real wage is a state variable and hence output will not longer be a constant multiple of exogenous fiscal policy
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5 4
Multiplier
3
Rho=.9, Transfer Mult. Rho=.9, Purchases Mult. Rho=0, Transfer Mult. Rho=0, Purchases Mult.
2 1 0 −1 0
0.2
0.4
0.6
θw
0.8
1
Figure 4.2. Wage stickiness and the multiplier (full model). The vertical line indicates default parametrisation for its labour, which 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.27 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 27The
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).
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Table 2. Full Model — Present Value Multipliers A. Targeted Transfers
B. Purchases
C. Untargeted Transfers
Fiscal persistence:
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
2 years ZLB
1.5
1.1
1.4
1.0
0.5
0.4
5 years ZLB
1.5
2.0
1.4
1.4
0.5
0.7
small (as in Section 3 above). This is most easily seen as the lower left hand region in Figure 4.3 (Panel B), where “large” is defined quantitatively as a multiplier greater than one. This region shrinks when comparing to the purchases multiplier, but is qualitatively similar.28 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 a persistence ρ = 0.9 (similar to the ARRA) the transfer multiplier is around 0.4 and the purchase multiplier is larger at around 0.6.29
28
With the full model there are no regions (away from corners) of the α, ρ space that are indeterminate. 29The addition of capital and 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, but is conditional on steady state purchases not affecting the income distribution, as both households pay steady state taxes in proportion to their income share.The results are very similar if we assume that different household labour are perfect substitutes instead of being Cobb-Douglas in the production function (Equation 2.8). If we follow Cogan et al (2010) and Drautzburg and Uhlig (2011) and assume a labour union, sticky wages and that the production function has perfect substitutes in labour, the multipliers deviate on average by only 0.05 from Table 2 if the union weights the two households utility in proportion to their consumption shares. If the union gives full weight to the Ricardian household’s utility (as assumed by Cogan et al (2010) and Drautzburg and Uhlig (2011)), the transfer and purchase multipliers are identical because wealth effect of the constrained household does not affect the model.
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Figure 4.3. Regions of parameter space where the transfer multiplier is large (white) by various definitions (Panel A: greater than the purchases multiplier, Panel B: greater than 1). 4.4. Zero Lower Bound (ZLB). Since December 2008, the Federal Reserve has maintained nominal interest rates at 0-0.25 per cent, and recent announcements suggest that the policy rate will be maintained at zero for some while longer. 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. Despite the focus on the ZLB itself, in a linear model it is the path of nominal rates that determines the multiplier, rather than the reason nominal rates take that path (Christiano et al 2011). Given that the conditions under which the ZLB binds have been modelled in other papers, we simply 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).30 As shown in Proposition 4, 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 30We
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.
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purchase multiplier as the ZLB binds for two years. One can see that ZLB dramatically increases the area where the transfer multiplier is larger than purchase multiplier. If the ZLB binds for three years, the targeted transfer multiplier is always larger (not reported). Table 2 shows that with constant interest rates for two years (as considered by Cogan et al 2010), all multipliers are greater than or equal to one.31 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 a more persistent transfer-based stimulus: the transfer multiplier for ρ = 0.9 increases by 1.6 in going from a Taylor rule to five years of the ZLB, whereas the purchase multiplier only increases by 0.8, and less persistent fiscal policy increases the multiplier by 0.3-0.4 for both purchases and transfers.32 4.5. Targeting of transfers (revisited). In the real world, it is unlikely that a government could perfectly target transfers to HtM households (as we assume in most of this paper), 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. We see the transfer components of the ARRA or the 2001 and 2008 stimulus packages as being partially targeted — so the multiplier would fall somewhere in the middle of this range. As we showed 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 shows that the untargeted transfer multiplier, which is around 0.5 for once-off transfers, is very low for persistent transfers if monetary 31While
short term rates have been constant for much longer than two years ex-post, it is not clear whether this was anticipated by markets at the time. Swanson and Williams (2012) find that yields on Treasury bonds with 6 months or less to maturity were much less responsive than usual to high-frequency macroeconomic announcements over the period 2009 to mid-2011, while yields on bonds with more than 2 years to maturity were just as responsive as normal. This is consistent with markets anticipating a ZLB will bind for two years or less, though it is also possible that it is due to anticipation of Fed purchases of long term bonds. 32As 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.
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Full Model (2Yrs ZLB): Untargeted dY/Tr>1 (White Region)
Full model (2yr ZLB): White Region is where the transfer multiplier is larger
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. Effect of the Zero Lower Bound (2yrs) on the region where the transfer multiplier is larger than the purchases multiplier (White): targeted transfers (LHS) or untargeted transfer (RHS)
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 scaling factor). 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. Although slightly higher than our baseline calibration, a HtM share of 0.5 is within the range estimated in the literature, especially considering the HtM share is likely to be higher during a recession when fiscal stimulus takes place (Kaplan and Violante 2014).
5. Conclusion Government transfers to individuals were a larger share of the 2009 ARRA 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 stimulus. We have demonstrated that, in a New
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Keynesian model modified to have two types of agents that differ in their access to financial markets, the targeted transfer multiplier is often larger than one, and larger than the government purchase multiplier. Using a simplified model that we can solve analytically, we show that the targeted transfer multiplier will be larger than the purchase multiplier when the Disposable Income effect dominates the standard Taylor Principle effect, leading the economy’s aggregate demand curve to become inverted. Purchases increase aggregate supply, but transfers do not (as wealth effects cancel across households). When the aggregate demand curve is inverted, a lower level of supply boosts the multiplier. In normal times (when the central bank follows a Taylor rule), fiscal policy must not be too persistent and the share of constrained households must not be too small for the targeted transfer multiplier to be large. When the ZLB binds, the transfer multiplier is usually larger than the purchase multiplier because constant nominal interest rates weaken the Taylor Principle effect. 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 is the that the people receiving the transfers choose what to spend them on, which might yield higher marginal utility than government purchases. Moreover, if credit constrained households are also poorer, they may have higher marginal utility, leading to an increase in social welfare from a utilitarian perspective. To maximise effectiveness, transfers should be targeted at the credit-constrained, and should be short-lived or implemented when the ZLB is binding. An online appendix is available at: https://sites.google.com/site/stevenpennings/GP2014appendix.pdf
References [1] Bernanke B, Gertler M and S Gilchrist (1999), “The Financial Accelerator in a Quantitative Business Cycle Framework,” Handbook of Macroeconomics 1, pp 13411393.
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
36
[2] Bilbiie F (2008), “Limited Asset Markets Participation, Monetary Policy and (Inverted) Aggregate Demand Logic,” Journal of Economic Theory, 140(1), pp 162-196. [3] Bilbiie F, Monacelli, T and R Perotti (2013), “Public Debt and Redistribution with Borrowing Constraints,” The Economic Journal, 123 (February), pp F64-F98. [4] Broda C. And J. Parker (2012), “The Economic Stimulus Payments of 2008 and the Aggregate Demand for Consumption” mimeo [5] Campbell J and G Mankiw (1989), “Consumption, Income and Interest Rates: Reinterpreting the Time Series Evidence,” NBER Macroeconomics Annual 4, pp 185246. [6] Chetty R (2008), “Moral Hazard versus Liquidity and Optimal Unemployment Insurance,” Journal of Political Economy 116(2), pp. 173-234 [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] Cogan J and J Taylor (2010), “What the Government Purchases Multiplier Actually Multiplied in the 2009 Stimulus Package,” NBER Working Paper 16505. [10] 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. [11] 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. [12] Christiano L Eichenbaum M, and S Rebelo (2011), “When Is the Government Spending Multiplier Large,” Journal of Political Economy, 119(1), pp 78-121. [13] Curdia, V and M Woodford (2010), “Credit Spreads and Monetary Policy”, Journal of Money, Credit and Banking, 42(1), pp 3-35. [14] Drautzburg T and H Uhlig (2011), “Fiscal Stimulus and Distortionary Taxation”, NBER Working Paper 17111. [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. [17] Eggertsson, G. (2012) "Was the New Deal Contractionary?" American Economic Review, 102(1), pp 524-55. [18] Eggertsson G and P Krugman (2012), “Debt, Deleveraging, and the Liquidity Trap: A Fischer-Minsky-Koo Approach”, The Quarterly Journal of Economics, 127(3): 1469-1513
WHEN IS THE GOVERNMENT TRANSFER MULTIPLIER LARGE?
37
[19] Erceg C, Henderson D and A Levin (2000), “Optimal Monetary Policy with Staggered Wage and Price Contracts,” Journal of Monetary Economics, 46(2), pp 281313. [20] Galí J (2008), Monetary Policy, Inflation, and the Business Cycle: An Introduction to the New Keynesian Framework, Princeton University Press, Princeton, USA [21] 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. [22] Hall R (2011), “The Long Slump,” American Economic Review, 101(2), pp 431-469. [23] Hausman J (2012), “Fiscal Policy and Economic Recovery: The Case of the 1936 Veterans’ Bonus”, mimeo, UC Berkeley [24] Iacoviello M (2005), “House Prices, Borrowing Constraints, and Monetary Policy in the Business Cycle,” American Economic Review, 95(3), pp 739-764. [25] 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. [26] Kaplan G, and G Violante (2014), “A Model of the Consumption Response to Fiscal Stimulus Payments,” Econometrica (forthcoming). [27] Lusardi, A, D Schneider and P Tufano (2011), “Financially Fragile Households: Evidence and Implications” Brookings Papers on Economic Activity, 42(1), 83-150 [28] Mehrota N (2013), “Fiscal Policy Stabilization: Purchases or Transfers?”, Columbia University mimeo. [29] Monacelli T and R Perotti (2011), “Redistribution and the Multiplier,” IMF Economic Review, 59(4), pp 630-651, November. [30] Oh H, and R Reis (2011), “Targeted Transfers and the Fiscal Response to the Great Recession,” Journal of Monetary Economics, 59(S). [31] Schmitt-Grohe S and M Uribe (2005), “Optimal Fiscal and Monetary Policy in a Medium-Scale Macroeconomic Model,” NBER Macroeconomics Annual 20, pp 383-425. [32] 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. [33] Swanson E and J Williams (2012), “Measuring the Effect of the Zero Lower Bound on Medium- and Longer-Term Interest Rates”, Federal Reserve Bank of San Francisco Working Paper 2012-02 [34] Uhlig H (2010), “Some Fiscal Calculus,” American Economic Review, 100(2), pp 30-34. [35] Werning I (2012), “Managing a Liquidity Trap: Monetary and Fiscal Policy”, MIT mimeo. [36] Woodford M (2011), "Simple Analytics of the Government Expenditure Multiplier," American Economic Journal: Macroeconomics, 3(1), pp 1–35.
