Money-Financed Fiscal Stimulus: The E ects of Implementation Lag

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1 Money-Financed Fiscal Stimulus: The E ects of Implementation Lag Takayuki Tsuruga y and Shota Wake z First draft: March 26 This version: April 28 Abstract The previous studies based on the New Keynesian framework nd that the scal stimulus nanced by money creation has a strong positive e ect on output under a reasonable degree of nominal price rigidities. This paper focuses on implementation lag in the money- nanced government purchase. We show that, if a money- nanced government purchase has a time lag between the decision and the implementation, () it may cause a recession rather than a boom in normal times; (2) it may deepen the recession when the economy is in the liquidity trap; (3) the longer the implementation lag, the deeper the recession; (4) whether or not the money- nanced scal stimulus with implementation lag causes a recession depends on the interest semi-elasticity of money demand. Our results imply that policymakers who conduct the money- nance scal stimulus should shorten implementation lag and have detailed knowledge on the money demand function to improve its e cacy. JEL Classi cation: E32; E52; E62 Keywords: Anticipation e ect, Fiscal multiplier, Government spending, Seigniorage We would like to thank Bill Dupor, Ryo Horii, Kenneth Kuttner, Taisuke Nakata, and Masahiko Shibamoto and seminar and conference participants at Kobe University, the University of Tokyo, and Asian Meeting of Econometric Society for helpful discussions and comments. This paper is previously circulated as Money- nanced scal stimulus: the e ect of anticipated shock. Takayuki Tsuruga acknowledges the nancial support for the Grants-in-Aid of Scienti c Research (5H5729 and 5H5728), the Murata Science Foundation, and Zengin Foundation for Studies on Economics and Finance. Views expressed in this paper are those of the authors and do not necessarily re ect the o cial views of Government of Japan. y Osaka University; Cabinet O ce, the Government of Japan; Centre for Applied Macroeconomic Analysis z Ministry of Internal A airs and Communications, the Government of Japan

2 Introduction Government spending to stimulate the economy is typically nanced through government debt and eventually taxes. The global nancial crisis in the last decade led to high levels of the government-debt-to-gdp ratio in many countries and these countries policy interest rates hit the zero lower bound (ZLB). Against this backdrop, Galí (27) discusses the scal stimulus nanced by money creation, as a policy option to boost the aggregate demand. This policy option does not rely on lowering the nominal interest rate and further issuance of the government debt, because the government purchase or tax cut are nanced by seigniorage. Using the standard New Keynesian model with a reasonable degree of nominal rigidities, Galí (27) shows that an unexpected shock to money- nanced government purchase and tax cut can generate a large positive impact on output along with crowing-in e ect on consumption. English, Erceg and López-Salido (27) also argue that the money- nanced scal stimulus is a powerful tool for boosting the aggregate demand if such scal policy is credible. Overall, these previous studies nd that the money- nanced scal stimulus can increase output and in ation as well as reducing the debt-to-gdp ratio substantially. This paper focuses on the role of implementation lag in the e ect of money- nanced government purchase. The introduction of implementation lag of scal policy into the standard New Keynesian model is a straightforward extension of the model. However, it captures an important aspect of scal policy and thus has widely been discussed in the literature. Ramey (2) provides empirical evidence that government purchase tends to involve long lags between the decision to spend and an actual increase in spending. Cwik and Wieland (2) assess the e ect of the debt- nanced scal policy with implementation lag, using a variety of empirical New Keynesian models. Yang (25), Leeper, Richter and Walker (2), Mertens and Ravn (2), and Fujiwara and Waki (26), among others, analyze a distortionary tax and nd that model responses to an announced tax change di er substantially from those to an unanticipated tax change as well as their policy implications. We nd that implementation lag plays an important role in evaluating the money- nanced scal stimulus. We rst study the e ect of the money- nanced scal stimulus when the economy is in the normal times with a strictly positive nominal interest rate. If a money- nanced scal stimulus is implemented immediately, as analyzed in the literature, it strongly boosts aggregate demand and thus causes a boom, through expansionary scal policy and concurring monetary expansion. For more practical discussions on the e cacy of money- nanced scal stimulus, see also Turner (25). 2

3 However, we show that, if the money- nanced scal stimulus involves implementation lag, the scal stimulus may cause a recession rather than a boom. We then consider the economy in the liquidity trap. If the money- nanced scal stimulus is implemented without lag, the economy caught by the liquidity trap experiences a fast recovery from the recession. However, in the presence of implementation lag, the scal stimulus may cause a slower recovery from the recession than the case of no policy change. We also show that, the recession becomes deeper as the implementation lag lengthens. The mechanism behind this result can be understood from an in uential work by Ball (994), who nds that a credible disin ationary announcement in the presence of nominal rigidities causes a boom rather than a recession. In his analysis, if a decline in the money growth rate is anticipated, forward-looking rms reduce prices prior to the actual decline in the money growth rate. Ball (994) assumes that households consumption is constrained by their real money balances (i.e., the cash-in-advance (CIA) constraint). In this case, the lower aggregate prices result in higher real money balances and relax the CIA constraint. The resulting higher aggregate demand leads to an expansion prior to the decline in the money growth rate. The argument of Ball (994) is applicable to our context, but in an opposite direction. In our analysis, if the money- nanced scal stimulus is anticipated due to implementation lag, forwardlooking rms increase prices prior to the actual increase in money supply that nances new government purchase. The higher aggregate prices result in the lower real money balances and tighten the CIA constraint. The resulting lower aggregate demand leads to a recession prior to the increase in the money growth rate for the government to nance their spending. If the implementation lags lengthen, the rms have more chances to increase prices before the implementation of scal policy. As a result, the higher aggregate prices deepen the recession. Our analysis also suggests the importance of the interest semi-elasticity of money demand for the e cacy of the money- nanced scal stimulus. Suppose that the announcement of the money- nanced scal stimulus raises the nominal interest rate due to the high expected in ation. If the money demand is elastic to the nominal interest rate, the households want to reduce their money holdings, other things being constant. Given the money supply and sticky prices, real money balance in the economy cannot quickly decrease so that they must hold money for transaction of goods. The money holdings for transaction give rise to the strong aggregate demand even prior to the actual increase in the government purchase. This is in a sharp contrast to the case of the CIA constraint. 3

4 We thus conclude that the e cacy of money- nanced scal stimulus depends on the length of implementation lag and the interest semi-elasticity of money demand. An implication for scal policy is that policymakers should be keen on the interest semi-elasticity of money demand in evaluating the money- nanced scal stimulus. If policymakers are faced with a low interest semielasticity of money demand, they should shorten the implementation lag of the scal stimulus. In this sense, designing of better automatic scal stabilizer may be important to improve the e cacy of the scal stimulus. 2 If the implementation lag is di cult to shorten, the money- nanced scal stimulus would be a useful policy option only under a high interest semi-elasticity of money demand. 2 The model The model we consider is a stylized New Keynesian model with the occasionally binding ZLB constraint on the nominal interest rate. We also allow for the cash-in-advance (CIA) constraint in modeling the money demand. The previous studies such as English, Erceg, and López-Salido (27) and Galí (27) study the money- nanced scal stimulus that is implemented without lag and compare the allocation with the debt- nanced scal stimulus. By contrast, we focus on implementation lag in the money- nanced scal stimulus and investigate the impact of implementation lag on the e ect of the scal stimulus. Following Galí (27), we solve the deterministic model that imposes the occasionally binding ZLB and CIA constraints. 2. Households and rms The representative household maximizes her lifetime utility given by P t= t U (C t ; N t ) ;where h i U (C t ; N t ) = Ct = ( ) N +' t = ( + ') Z t. Here, C t, N t, and Z t represent consumption, labor supply, and an exogenous preference shifter, respectively. The parameters >, ' >, and < < denote the degree of relative risk aversion, the inverse of the Frisch elasticity of labor supply, and the discount factor, respectively. Throughout the model, the unit of time t is a quarter. The household faces the budget constraint and the CIA constraint: M t + B t = ( + I t )B t + (M t P t C t ) + W t N t + P t D t P t T t ; () M t P t C t (2) 2 In the related studies, Blanchard, Dell Ariccia, and Mauro (2) also argue for the importance of better automatic scal stabilizer. 4

5 where M t is the nominal money holdings, B t denotes households nominal holdings of one-period government bond that pays the nominal interest rate I t, P t represents the aggregate prices, and W t is nominal wages. Also, D t denotes rms real pro ts and T t is lump-sum taxes in real terms. The left-hand side of () is the nominal value of total wealth that the household brings into period t. The right-hand side indicates that the household receives the nominal income W t N t + P t D t and pays taxes P t T t. She also carries the nominal bond and cash holdings remaining after consumption into period t. As usual, a no Ponzi game condition holds. Equation (2) is the CIA constraint. The rst-order conditions are standard: U C;t = ( + I t ) U C;t+ ; P t P t+ (3) U N;t = W t ; U C;t P t (4) M t P t C t ; (5) where U C;t = C t Z t and U N;t = N ' t Z t. When I t >, (5) holds with equality. This is because nominal money holdings beyond the level of P t C t incur the opportunity cost of nominal interest. When I t =, M t is a perfect substitute for B t in transferring the wealth into the next period and the CIA constraint is not necessarily binding. The representative rm produces the nal good in a perfectly competitive market. It combines R =( ), a continuum of intermediate goods, using the technology Y t = Y t(j) dj ( )= where Y t (j) denotes output produced by the intermediate good producers j 2 [; ] and (> ) is the elasticity of substitution among di erentiated intermediate goods. The aggregate price index P t R =( ). is associated with intermediate good prices P t (j) by P t = P t(j) dj The production function for intermediate good producers is Y t (j) = N t (j), where 2 (; ]. Each intermediate rm is allowed to reset its price with probability. Let P t be the optimal nominal price set by an intermediate good producer. The intermediate good producer seeks to solve max P t X k= k Q t; t+k (=P t+k ) Pt Y t+kjt W t+k Y t+kjt ; subject to the demand function Y t+kjt = (P t =P t+k ) Y t+k where Y t+kjt denotes output in period t+k of an intermediate good producer that last reset its price in period t and Q t; t+k U C;t+k =U C;t denotes the discount factor of the rm. The rst-order condition for P t is 5

6 X k Q t; t+k (=P t+k )Y t+kjt P t MW t+kjt Y k= t+kjt = ; (6) where M =( ). Along with the price index, log-linearizing this equation around the zero steady-state in ation leads to the standard New Keynesian Phillips curve. 2.2 Government Our experiment examines the impact of the money- nanced government purchase with implementation lag of h periods. Let g t be government purchase exceeding its steady-state level expressed as a fraction of steady-state output (i.e., g t (G t G)=Y where G t is the government purchase and G and Y are the steady-state value of government purchase and output, respectively). At t =, the government announces the following plan of the scal stimulus: 8 < for t < h g t = : t h for t h ; (7) where h. Here 2 [; ) measures the persistence of exogenous increase in the government purchase since g t+ = g t for t h. When h =, the scal stimulus is implemented without lag. Our experiment allows for h >. Economic agents can take some actions between t < h before G t actually increases. For any h, the magnitude of the initial increase in the government purchase is normalized to one percent of the steady-state output, since g t is de ned as g t = (G t G) =Y. To analyze the money- nanced scal stimulus, we follow English, Erceg, and López-Salido (27) and Galí (27) and consider the government as a single consolidated entity consisting of the scal authority and the central bank. Let M s t be the money supply. The government s consolidated budget constraint is P t G t + ( + I t ) B t = P t T t + B t + M s t ; (8) where Mt s = Mt s Mt s. The left-hand side of (8) means that the government purchases the nal good of G t and repays one-period government bonds with interest rate, ( + I t ) B t. On the right-hand side of (8), the government collects the lump-sum taxes and issues new government bond and the non-interest-bearing money to nance the government expenditure. Let us divide 6

7 both sides of (8) by P t to obtain the consolidated budget constraint in real term: G t + R t B t = T t + B t + M s t =P t ; (9) where R t = ( + I t ) P t =P t+, and B t = B t =P t. In the equation, Mt s =P t is real seigniorage revenue. We assume that seigniorage is zero in the steady state (Mt s = ) and G t and T t have the steady state value. This assumption implies that G + RB = T + B in the steady state, where a variable without a subscript indicates the steady-state value. Let t and b t be the lump-sum taxes and the issuance of real government bond exceeding its own steady-state level expressed as a fraction of steady-state output, respectively. (i.e., t = (T t T ) =Y, and b t = (B t B) =Y.) We take the di erence between G + RB = T + B and (9) and express the resulting equation as a fraction of steady-state output. As a result, the linearly approximated consolidated budget constraint is b t = Rb t + Rb (i t t ) + g t t V m s t; () where b = B=Y, i t = ln [( + I t ) =R], t = ln (P t =P t ), m s t = ln Mt s =Mt s, and V is the steadystate income velocity of money. The rst and second terms of the right-hand side of () result from (R t B t RB) =Y ' R (B t B) =Y + (B=Y ) (R t R) ' Rb t + Rb (i t t ). The last term is the linear approximation of the real seigniorage revenue around Mt s = and t = in the steady state. More speci cally, the real seigniorage expressed as the steady-state output is Mt s = (P t Y ) and can be approximated as M s t P t Y = M t s P t Mt s Mt s P t P t Y ' V m s t: We now de ne the money- nanced scal stimulus as the monetization of government purchase satisfying G t G = M s t P t : That is, the government purchase exceeding its steady-state level is fully nanced by the seigniorage. 3 By dividing both sides by the steady-state output, we have g t = m s t=v. Therefore, the 3 Gali (27) considers the policy experiment that keeps the issuance of government bond unchanged. We do not take this policy experiment because this policy experiment does not satisfy the Blanchard-Kahn condition under our assumption of the CIA constraint. 7

8 money supply in the money- nanced scal stimulus is determined by m s t = V g t : () The lump-sum tax in () is speci ed by the following reaction function: t = b b t ; (2) Substituting () and (2) into (), we have b t = (R b ) b t + br (i t t ) ; (3) where we assume that R b < to ensure the stationarity of b t. The dynamics of the debt-to- GDP ratio here are residually determined from the system of equations under () and (2). In this model, b t is driven by the interest payment on the government debt and its persistence depends on how we specify b in (2). 2.3 Market clearing Equilibrium in the nal goods market requires Y t = C t + G t. We also assume that labor market clears at all t, i.e., N t = R N t (j) dj. In the model, whether or not the ZLB constraint on the nominal interest rate is binding is translated into whether or not the CIA constraint is binding. In particular, As long as I t > (i.e., the ZLB constraint is not binding), the CIA constraint is binding so that the household s desired level of money equals the money supply: M s t = M t = P t C t. However, if I t = (i.e., the ZLB constraint is binding), the CIA constraint is not binding so that all the money may not be used for purchasing goods: M t > P t C t. Nevertheless, even if I t =, the money can still be used for transferring the household s wealth into the next period. Therefore, we assume that the money supply fully determines the household s nominal holdings of money and M s t = M t holds for all t. Likewise, the government bond market also clears if I t. If I t =, the nominal bond holdings by the household is determined by the supply in the economy. 8

9 3 Results To assess the impact of implementation lag of the money- nanced scal stimulus on equilibrium dynamics, we use the (log) linearized version of the above deterministic model around the zero in ation steady state. 4 We begin by discussing the e ect of the money- nanced scal stimulus when the economy is initially in the steady state with I t >. Although some argue that the money- nanced scal stimulus is a policy that should be implemented in the economy in the liquidity trap, this analysis helps better understanding of the policy impact on the economy in the liquidity trap. We then move to the assessment of the money- nanced scal stimulus when the economy is in the liquidity trap. 3. Calibration For simulations, we select = :995, =, ' = 5, = =4, = 9, = 3=4 and b = :2. These parameters are all standard in the literature and taken from Galí (27). Because of zero steady-state in ation, = :995 implies that the annualized real interest rate is two percent in the steady state (i.e., R = :5). The steady state share of government purchase to output is 2 percent (i.e., = G=Y = :2), consistent with the US data. By de nition, the income velocity V t = (P t Y t ) =M t = [(P t C t ) =M t ] (Y t =C t ). Assuming that the CIA constraint in the steady state holds with equality, the steady-state income velocity is given by V = Y=C = = ( ) = :25. In terms of implementation lag h, there seems no strong consensus about how long it takes for the government to implement their policy in general or how far in advance agents become aware of possible changes to the money- nanced scal stimulus. Therefore, we consider a relatively wide range of h for simulations. Using a narrative-approach tax shock series of Romer and Romer (2), Mertens and Ravn (2) nd that the median implementation lag is six quarters for a tax shock. Ramey (2) argues that defense spending shocks identi ed by vector autoregressions using postwar U.S. data are forecastable four quarters in advance. She also argues that even nondefense spending would be known at least months in advance. Taking these previous studies into account, we set h = 6 as a benchmark and, later, we look into h = ; 4; and 8 for robustness. 4 The linearized equations are described in the Appendix of this paper. 9

10 3.2 The e ect of the money- nanced scal stimulus on output We conduct two experiments of the money- nanced scal stimulus with implementation lag, based on the initial state of the economy Experiment I: The economy in the normal times The rst experiment considers the money- nanced scal stimulus in the normal times. More speci cally, we assume that the economy for t < is initially in the steady-state with I t >. Given this state of the economy, the money- nanced scal stimulus is announced at t = and implemented at t = h >. Figure plots the output response to the money- nanced scal stimulus with and without implementation lag (denoted by h = 6 and h = in the gure). The blue line points to the output response when the money- nanced scal stimulus is implemented without lag. In this case, the money- nanced scal stimulus can also be understood as an unanticipated scal stimulus implemented at t =. In response to this unanticipated scal stimulus, output exhibits a large expansion, with the government spending multiplier larger than unity. In fact, when g t increases by one percent of the steady-state output, output at the same period increases by.4 percent. By contrast, if the scal stimulus has implementation lag, the output responses dramatically di er from the previous case. Output gradually decreases and the decline is substantial: about :77 percent immediately before the implementation. That is, the money- nanced scal stimulus causes a recession rather than a boom. Once the scal stimulus is implemented at t = 6, we observe the positive e ect of the scal stimulus on output for t h. However, output increases only by.87 percent, implying that the government spending multiplier is less than unity. The reason for the recession is straightforward. Aggregate demand is depressed by the increases in prices before the implementation of the scal stimulus. To better understand this, let us express the money and good market equilibrium conditions as the log-linearized form. The money market equilibrium condition is c t = m s t p t and the good market equilibrium condition is y t = ( ) c t + g t, where m s t and p t represent the log-deviation from their initial values of m s and p, respectively. Also, c t and y t are the log-deviation from the steady state. Combining these two equations yields y t = ( )(m s t p t ) + g t : (4) Without loss of generality, we assume that the initial values of m s and p is normalized to

11 zero. Therefore, m s t and g t are zero before the money- nanced scal stimulus is implemented (i.e., m s t = g t = for t < h). However, p t can change during periods between the announcement and implementation (i.e., t < h). When the money- nanced scal stimulus are announced, a higher aggregate demand in the future increases prices p t. Therefore, we have y t = ( )p t < ; (5) for t < h. This implies that the money- nanced scal stimulus for h > causes a recession rather than a boom. The mechanism behind the output reduction is the same as what Ball (994) discovered in the context of the credible announcement of disin ationary policy. Ball (994) shows that the credible announcement of disin ationary policy (i.e., an announcement of a decline in the money growth rate) causes a boom rather than a recession in a sticky price model. In our model with government purchase, the announcement of the money- nanced scal stimulus is essentially equivalent to an announcement of in ationary policy, causing a recession rather than a boom. Let us turn to the responses of other macroeconomic variables. Figure 2 displays the responses to the announcement of the same scal stimulus with implementation lag. As shown in the upperright panel, in ation immediately responds to the announcement of scal stimulus due to the forward-looking property of in ation. In the second row, consumption exhibits dynamic patterns similar to output, although the increase in consumption at the time of implementation is smaller than that in output. This is because the increase in the government purchase (shown in the same row) is included in output for t h. The nominal and real interest rates are volatile, peaking in period 5. This is because an extremely high growth in consumption at the time of the scal stimulus requires high real interest rate. Indeed, the consumption Euler equation at the period of the implementation is ( + I 5 ) P 5 =P 6 = (C 6 =C 5 ). 5 Given the relatively low in ation due to sticky prices, the nominal interest rate also shows a spike before the scal stimulus. We also note that the nominal interest rate is completely insensitive before it exhibits the spike in period 5. As we will see in the next experiment with the liquidity trap, this insensitive response of nominal interest rate during the rst few periods is preserved and thus the duration of ZLB spells is unlikely to be shortened by this type of scal stimulus. 5 When the central bank does not control the nominal interest rate and the CIA constraint is binding, the interest rate is residually determined by the consumption growth through the Euler equation.

12 3.2.2 Experiment II: The economy in the liquidity trap The second experiment assesses the money- nanced scal stimulus at the time of the liquidity trap. More speci cally, the money- nanced scal stimulus is announced at t = and implemented at t = h >, but we assume that the economy is initially in the liquidity trap with I t =. We introduce the deterministic adverse demand shock to generate the liquidity trap, following the literature. 6 equation: where t = ln (Z t+ =Z t ). Here the adverse demand shock appears in the log-linearized consumption Euler We assume that the economy for t < implements the discretionary monetary policy. 7 In period t = c t = c t+ (i t t+ t ) ; (6) is in the steady state in which the central bank, t decreases so that the nominal interest rate hits the ZLB. In particular, t < log = log R for t T and t = for t > T. This ensures that the ZLB constraint is binding for policy. The decline in t is unexpected at t = t T under the discretionary monetary, but once the decline is observed, the path of t for t > can fully be known. The value of t is assumed to be constant over t 2 [ ; T ] and is calibrated to generate three-percent decline in output at the time of the decline in t. 8 This adverse demand shock pins down the initial state of the economy for the money- nanced scal stimulus from which the government tries to make the economy recover from the recession. Because we are interested in measuring the puri ed e ect of the money- nanced scal stimulus, we de ne the allocation with no policy change as the reference level. The black dashed line in Figure 3 is the output responses under this allocation with no policy change. This allocation is calculated under the assumption that the central bank continues to implement the discretionary monetary policy for t. Conveniently, this allocation serves as the reference level in measuring the puri ed e ect of the money- nanced scal stimulus. Given no cost-push shock in the model, the discretionary monetary policy can fully stabilize in ation and output at the steady-state level if the ZLB constraint is not binding. If it is binding, the policy e ect may di er from that in the previous experiment. The discretionary monetary policy cannot fully stabilize the output due to the ZLB and the deviations from the steady state generated by the ZLB for earlier periods t T 6 For example, see Jung, Teranishi and Watanabe (25) who investigate the optimal path of the policy interest rate given that a large shock hits the economy. 7 As discussed in Galí (25, 27), the allocation under the discretionary monetary policy with the ZLB constraint is replicated by the Taylor rule, i t = max (; t + t) ;where >. 8 The size of the decline in t does not a ect our results qualitatively as long as t < log. 2

13 may in uence the e ect of the scal stimulus. In the gure, we set T = 5 so that the decreased t causes the liquidity trap during t 5. Due to the ZLB on the nominal interest rate, the reference level of output shown as the dashed black line is lower than the steady state for t 5 and is kept at the steady state level for t > 5. We can see from Figure 3 that output is lower than the reference level when the money- nanced scal stimulus is announced with implementation lag of six quarters. This money- nanced scal stimulus generates a slower recovery from recession than the reference level. The lower level of output also suggests that the money- nanced scal stimulus causes a recession compared to the reference level. Similar to the previous experiment, it is in a sharp contrast with the scal stimulus without implementation lag (h = ). As the blue line shows, output in this case is much higher than the reference level (i.e., a boom compared to the reference level) and this money- nanced scal stimulus achieves a faster recovery from recession than the reference level. Figure 4 shows the responses of other macroeconomic variables to the announcement of the same money- nanced scal stimulus, conditional on the binding ZLB. In the rst row of the gure, in ation is negative until t = 3 due to the adverse demand shock but turns to be positive due to the higher demand in the future. In comparison to the reference level, in ation under the money- nanced scal stimulus is similarly low for the rst few periods after the announcement of the scal stimulus but higher than the reference level near the time of implementation (e.g., t = 6). Consumption is lower than the reference for several periods after the announcement and is not substantially higher than the reference level even after the implementation. The real interest rate is kept high during the announcement periods but the high real interest rate is mainly driven by the adverse demand shock because the real interest rate is equally high in the reference level. Turning to the nominal interest rate, the right panel of the third row indicates that the duration of ZLB spells is one quarter shorter than the reference level. However, the announcement of the scal stimulus per se does not shorten the duration since the weak aggregate demand does not raise in ation and thus prices and low in ation the nominal interest rate is on the ZLB until period 4 and increases up to 4.5 percent in period 5. The debt-to-gdp ratio is positive in both cases of the money- nanced scal stimulus and of no policy changes. However, the positive debt-to-gdp ratio under the money- nanced scal stimulus persists because the real interest rate under the money- nanced scal stimulus is higher than the reference level at the time of implementation. The mechanism behind output lower than reference level is basically the same as that in the previous experiment in which the initial state of the economy is the steady state. In fact, as long 3

14 as I t >, the CIA constraint binds with equality so that the interpretation remain unchanged. By contrast, when the CIA is not binding, the mechanism is slightly di erent. To see this, we denote the variables with superscript r and the hatted variable by the variable relative to the reference level. For example, the output under the money- nanced scal stimulus relative to the reference level can be expressed as ^y t = y t clearing as y r t. With this de nition in mind, we can write the good market 8 < ( ) ^c t + ^g t for I t = ^y t = : ( ) ( ^m s t ^p t ) + ^g t for I t > ; where ^c t is used for I t = because the CIA constraint is not binding and ^c t cannot be substituted out by ^m s t ^p t. We also note that before the implementation of the scal stimulus, ^g t = g t g r t = so that ^y t = ( t ) ^c t for t < h. Therefore, to see whether the announcement of the money- nanced scal stimulus generates a recession relative to the reference level, it su ces to check the sign of ^c t. Taking the example of h = 6, I t = until t = 4 (See the response of the nominal interest rate shown in Figure 4.). Using (6), ^c t for < t 4 is given by (7) ^c t = ^c t+ + ^ t+ ; because ^ t = t r t = for all t and ^{ t = i t i r t = as long as the nominal interest rate is constrained at the ZLB. If ^c t+ < and ^ t+ < are satis ed, today s consumption ^c t is always negative, meaning that the money- nanced scal stimulus with implementation lag is ine ective. In fact, we can recon rm from Figure 4 that ^c t+ < for < t < 5 that includes the periods under the binding ZLB and that ^ t < for < t < 4, again including the periods under the binding ZLB. Therefore, a recession relative to the reference level can take place for the periods under the binding ZLB. 3.3 The role of the implementation lags Due to a lack of broad consensus on the length of implementation lag, it is useful to consider the output responses for di erent values of h. Recall that (4) implies that as long as the policy announcement raises prices, a recession takes place. This suggests that the recession becomes more severe as forward-looking rms have more chances to adjust their nominal prices upward. A higher h gives forward-looking rms more chances to reset prices and makes a deeper recession. To recon rm the above intuition, Figure 5 plots the output responses to the policy announcement for 4

15 h = ; 4; 6, and 8, along with the reference level of output. Overall, the recession relative to the reference level is deeper as h increases. 3.4 The role of the interest semi-elasticity of money demand The ndings in the preceding subsections depend on how we specify the money demand function. More speci cally, our ndings result from the CIA constraint which leads to (4) and (5). When we replace the CIA by the money-in-the-utility (MIU) function, however, the policy implications may di er due to the presence of the interest semi-elasticity of money demand. In this subsection, we explore this possibility. To clarify the motivation of our analysis, let us consider the following log-linearized money demand function (together with the money market equilibrium): m s t p t = c t i t ; (8) where > denotes the interest semi-elasticity of money demand. While we leave the derivation of this money demand function to Appendix, we here assume that the above money demand function can be derived from the MIU with a satiation level of real money balances. 9 Here, as Appendix shows, depends on how much the steady-state consumption velocity deviates from that evaluated at the satiation level of real money balances. Appendix also shows that other log-linearized equations in the system remain unchanged. For simplicity, suppose that I t > at the time of the policy announcement. Using (8), (4) is now changed into y t = ( )(m s t p t ) + ( )i t + g t : (9) Therefore, if i t is positive (similarly to the nominal interest rate shown in the third row of Figure 4) and is large, y t is more likely to be positive than the case of =. In other words, the policymakers could alleviate the recession under the assumption of the MIU, even if the money- 9 As suggested by Eggertson and Woodford (23) and Jung, Teranishi and Watanabe (25), the standard MIU without a satiation level of real money balances is not necessarily consistent with the ZLB on the nominal interest rate. In Appendix, we follow English, Erceg and López-Salido (27) who assume the MIU with a satiation level of real money balances consistent with the ZLB constraint. In deriving (8), they propose a convenient way of modeling the money demand. Under I t =, (9) does not hold. Therefore, our argument cannot directly be applied to the case of the binding ZLB. However, as we will show later, the announcement of a money- nanced scal stimulus under > tends to immediately increase the nominal interest rate and thus to allow the economy to escape from the liquidity trap. As a result, I t > is observed at the time of the policy announcement and the above argument is not always invalid even when the economy is initially in the liquidity trap. 5

16 nanced scal stimulus has implementation lag. A question is how large should be for them to successfully alleviate the recession. Figure 6 plots output response to the announcement of the money- nanced scal stimulus under three values of. In both panels of the gure, we newly introduce the results under = 4 and 7 along with the benchmark result under =. The left panel represents the case of h = 6 while the right panel refers to the case of h = for comparisons. In each panel, the black solid line corresponds to the case of = 4 while the blue solid line points to the case of = 7. The rst parameterization of the interest semi-elasticity ( = 4) is consistent with Christiano, Eichenbaum and Evans (25) who estimate the semi-elasticity in the medium-scale New Keynesian model based on the U.S. data over 965:Q3 995:Q2. The second parameterization ( = 7) comes from Ireland (29) who estimated over 98:Q - 26:Q4. 2 The sample periods in these empirical studies serve for our purpose because the periods under the binding ZLB are not included. In our model, when the ZLB constraint is binding, the real money holdings exceed the level desired by the household. That is, m s t p t > c t i t. Estimates of based on the data including the period under the binding ZLB may not be appropriate if the estimates assume that (8) always hold with equality. The black solid line shown in the left panel of Figure 6 indicates that, when = 4, the output response follows a path similar to the reference level of no policy change (shown as the dashed black line). Over the periods between the announcement and implementation, output under = 4 does not increase beyond the reference level of output. After the implementation, the increase in output is large due to the actual increase in government purchase. However, in comparison to the benchmark case of =, the extent to which the scal stimulus causes a recession relative to the reference level is weaker and the increase in output after government purchase actually increases is not larger under = 4 than =. When increases to 7, the increase in i t in (9) is relatively large. As a result, the output response follows a path beyond the reference level of output. In other words, the money- nanced scal stimulus is e ective even with implementation lag, in a contrast to the case of = and = 4. Nevertheless, in terms of the recovery from the recession due to the adverse demand shock, the money- nanced scal stimulus with implementation lag achieves a much slower recovery to the steady state than that without implementation lag (see the right panel of the same gure for the case of h =.). More precisely, they report that the interest semi-elasticity of money demand to the annualized interest rate is.96. Transforming this annualized interest semi-elasticity to the quarterly interest rate yields = 3:84 ' 4. 2 He estimates the annualized interest semi-elasticity to range between.5 and.9. Translating this range in terms of the quarterly rate, it is between 6. to

17 Responses of other macroeconomic variables to the policy announcement help us understand the intuition behind the qualitative di erence between the cases of = and = 7. As shown in the third row of the gure, the nominal interest rate under = 7 becomes positive at the time of the policy announcement at t = in contrast to the case of = under which it does not turn to be positive until t = 5. In the case of = 7, (8) holds with equality in and after t =. Other thing being constant, a high nominal interest rate incentivizes the household to reduce the money demand. However, given the money supply in the economy, the real money balances becomes abundant in the economy with I t >. Such real money holdings are used for transactions of goods rather than stored as a substitute for the government bond, increasing the household s consumption. In fact, the second row of the gure indicates that consumption under = 7 increases beyond the reference level. This is in a sharp contrast to the case of =. Under =, the nominal interest rate does not immeidately increase one period before the implementation of the scal stimulus. As a result, the real money balances used for transaction continue to be low and the remaining real money balances held by the household is stored only for transferring the wealth into the next period as a perfect substitute of the government bond. As long as the money demand is su ciently sensitive to the nominal interest rate, the strong aggregate demand from the household consumption leads to a boom relative to the reference level. Likewise, in ation under = 7 is also higher than the reference level, as shown in the rst row of Figure 7. In ation is su ciently high to lower the real interest rate to less than the steady state level of two percent at the time of the policy announcement at t =. The low real interest rate immediately contributes to decreasing the interest payment by the government, so the debt-to-gdp ratio strongly declines. The policy implications of our analysis for the implementation of the money- nanced scal stimulus are threefold. First, if the money- nanced scal stimulus has implementation lag, policymakers should possess detailed knowledge on the money demand function. Without this knowledge, they may fail to achieve a fast recovery from the recession in response to the adverse demand shock. Second, if they are faced with the low interest semi-elasticity of money demand, they should activate the money- nanced scal stimulus as immediately as possible. As long as they do not give the private sectors chances to adjust the private sectors decision to the news before the implementation, policymakers can alleviate the slower recovery of output. Finally, if they face di culties in shortening implementation lags, the money- nanced scal stimulus would be a reasonable policy option only when the interest semi-elasticity of money demand is su ciently large. 7

18 4 Concluding remarks Using the standard New Keynesian framework with nominal rigidities, we analyzed the e ect of the money- nanced scal stimulus with implementation lag on output. The introduction of the implementation lags that are speci c to scal policy may have nonnegligible impacts on output response to a shock to government purchase. While the money- nanced scal stimulus has a strongly positive e ect on output without implementation lag, such a scal stimulus may have a weak or even negative e ect on output if a reasonable length of implementation lag is taken account. We showed that the shorter implementation lags make the e ect on output stronger. Therefore, the design of weaker of better automatic scal stabilizer may be important to improve the e cacy of the money- nanced scal stimulus, as discussed by Blanchard, Dell Ariccia, and Mauro (2). Our analysis also indicated that the e ect of the money- nanced scal stimulus varies, depending on the interest semi-elasticity of money demand. 3 An implication for policymakers is that detailed knowledge of the money demand function is important for a better understanding of the e cacy of money- nanced scal stimulus. In this regard, empirical work on the money demand function which explicitly allows for the ZLB constraint would also be an important. 4 Much remain to be done. 3 The importance of the money demand function for the e cacy of scal policy was also pointed out by Holmes and Smyth (972) and Mankiw and Summers (986), based on the old-fashioned Keynesian IS-LM model. However, they emphasize the roles of the scale variable (e.g., consumption vs. income) in the money demand function. 4 Some early examples of research include Bae, Kakkar and Ogaki (26), Bae and de Jong (27) and Nakashima and Saito (22) among others. 8

19 References [] Bae, Y. and R. M. de Jong (27). Money Demand Function Estimation by Nonlinear Cointegration, Journal of Applied Econometrics, 22 (4), [2] Bae, Y., V. Kakkar and M. Ogaki (26). Money Demand in Japan and Nonlinear Cointegration, Journal of Money, Credit, and Banking, 38 (6), [3] Ball, L. (994) Credible Disin ation with Staggered Price-Setting, American Economic Review, 84 (), [4] Blanchard, O., G. Dell Ariccia and P. Mauro (2). Rethinking Macroeconomic Policy, Journal of Money, Credit and Banking, 42 (s), [5] Christiano, L. J., M. Eichenbaum and C. L. Evans (25). Nominal Rigidities and the Dynamic E ects of a Shock to Monetary Policy, Journal of Political Economy, 3 (), 45. [6] Cwik, T. and V. Wieland (2). Keynesian Government Spending Multipliers and Spillovers in the Euro Area, Economic Policy, 26 (67), [7] Eggertsson, G. B. and M. Woodford (23). The Zero Bound on Interest Rates and Optimal Monetary Policy, Brookings Papers on Economic Activity, 23 (), [8] English, W. B., C. J. Erceg and D. López-Salido (27). Money-Financed Fiscal Programs: A Cautionary Tale, Hutchins Center Working Paper No. 3. [9] Fujiwara, I. and Y. Waki (25). Private News and Monetary Policy Forward Guidance or (The Expected Virtue of Ignorance), Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute Working Paper No [] Fujiwara, I. and Y. Waki (26). Fiscal Forward Guidance, unpublished manuscript. [] Galí, J. (24). The E ects of a Money-Financed Fiscal Stimulus, CEPR Discussion Paper No. 65. [2] Galí, J. (25). Monetary Policy, In ation, and the Business Cycle, Princeton University Press. [3] Galí, J. (27). The E ects of a Money-Financed Fiscal Stimulus, University of Pompeu Fabra Economic Working Paper Series, Working Paper No

20 [4] Holmes, J. M. and D. J. Smyth (972). The Speci cation of the Demand for Money and the Tax Multiplier, Journal of Political Economy, 8 (), [5] Ireland, P. N. (29). On the Welfare Cost of In ation and the Recent Behavior of Money Demand, American Economic Review, 99 (3), [6] Jung, T., Y. Teranishi and T. Watanabe (25). Optimal Monetary Policy at the Zero- Interest-Rate Bound, Journal of Money, Credit and Banking, 37 (5), [7] Leeper, E. M. A. W. Richter and T. E. Walker (2). Quantitative E ect of Fiscal Foresight, NBER working paper No [8] Mankiw N. G. and L. H. Summers (986). Money Demand and the E ects of Fiscal Policies, Journal of Money, Credit and Banking, 4 (), [9] Mertens, K. and M. O. Ravn (2). Understanding the Aggregate E ects of Anticipated and Unanticipated Tax Policy Shocks, Review of Economic Dynamics, 4 (), [2] Nakashima, K. and M. Saito (22). On the Comparison of Alternative Speci cations for Money Demand: The Case of Extremely Low Interest Rate Regimes in Japan,, Journal of the Japanese and International Economies, 26 (3), [2] Ramey, V. A. (2) Identifying Government Spending Shocks: It s All in the Timing, Quarterly Journal of Economics, 26 (), 5. [22] Romer, C. D. and D. H. Romer (2). The Macroeconomic E ects of Tax Changes: Estimates Based on a New Measure of Fiscal Shocks, American Economic Review, (3), [23] Turner A. (25). The Case for Monetary Finance An Essentially Political Issue, presented at the 6th Jacques Polak Annual Research Conference, the International Monetary Fund, November 5 6, 25. [24] Yang, S. S.-C. (25). Quantifying Tax E ects under Policy Foresight, Journal of Monetary Economics, 52 (8),

21 A The system of linearized equations The system of linearized equations is standard except for the occasionally binding CIA constraint. The other equations in the system basically follows Galí (27). Aggregate consumption of the households follows the consumption Euler equation: c t = c t+ (i t t+ t ) ; (A) as we discussed in the main text. In ation evolves as t = E t t+ t ; (A2) where [( )( )=] [( ) = ( + )]. In the above equation, t is the average price markups given by t = c t + ' y t: (A3) Note that the money demand function is given by the CIA constraint: l t c t ; (A4) where l t = m t p t is the real money holdings of the household. This equation holds with equality if I t >. Under the binding CIA constraint (or under the strictly positive nominal interest rate), we also have the law of motion for real money balances l t = l t + m s t t : (A5) If the CIA constraint is not binding (or I t = ), (A4) is not used for computing the allocation. Instead, we use i t = ln R: (A6) implying that the household passively holds money based on the supply. Other equations are discussed in the main text. The equilibrium condition for the nal goods market is ]where g t is exogenously given by (7). Because government purchase is nanced by seigniorage, the money supply is automatically determined: 2

22 m s t = V g t : (A8) Using the reaction function for the lump-sum tax rule t = b b t and the above money supply process, we can specify the equation for the debt-to-gdp ratio as b t = (R b ) b t + brr t ; (A9) where r t is the real interest rate given by the Fisher equation: r t = i t t : (A) The system of equations consists of the endogenous variables, y t, c t, i t, r t ; t, l t, m s t, b t, and g t. If the ZLB constraint is not binding, the model can be solved by (A) (A5) and (A8) (A) in which (A4) holds with equality. If the ZLB constraint is binding, the CIA constraint is not binding. Therefore, (A4) must be replaced by (A6). Likewise, whether or not the CIA constraint is binding depends on the complementary slackness condition: (l t c t ) (i t ln R) =, l t c t >, and i t ln R >. B The model with the money-in-the-utility function To derive the money demand that is correlated with the nominal interest rate and is compatible with the ZLB on the nominal interest rate, the literature has assumed the MIU with a satiation level of liquidity (See Eggertson and Woodford, 23). This is because, if the marginal utility of real money balances is strictly positive, the standard optimality condition rules out the possibility of I t = in equilibrium (given the nite marginal utility of consumption). In this regard, English, Erceg, and López-Salido (27) propose a convenient way of modeling the money demand. Relying on their approach, we rede ne the representative instantaneous utility function and replace U (C t ; N t ) by ~ U (C t ; M t =P t ; N t ) = U (C t ; N t ) + h (M t =P t ). We specify the function h() as a quadratic utility: h Mt P t = 2 max ; k M t =P 2 t Z t ; (B) C t where k is a satiation level of real money balances and C t is the aggregate consumption that is 22