ISSN (Print) 0473-453X

Discussion Paper No. 1196

ISSN (Online) 2435-0982

SHOULD THE FISCAL AUTHORITY
AVOID IMPLEMENTATION LAG?
Masataka Eguchi
Hidekazu Niwa
Takayuki Tsuruga

Revised January 2024
November 2022

The Institute of Social and Economic Research
Osaka University
6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan

Should the fiscal authority avoid implementation lag?∗
Masataka Eguchi†, Hidekazu Niwa‡, and Takayuki Tsuruga§
January 9, 2024

Abstract
Implementation lags are a concern of policymakers as they may reduce the efficacy
of fiscal policy. Using a standard New Keynesian model with an effective lower boundon the nominal interest rate, we compare the impacts of fiscal stimulus on output
across various lengths of implementation lag. We show that despite concerns among
policymakers, implementation lags may enhance the efficacy of government purchaseson output when the economy is caught in a liquidity trap.
JEL Classification: E32; E52; E62
Keywords: Fiscal multiplier, Effective lower bound, Government spending, Liquidity trap∗

We thank Mitsuru Katagiri, Kengo Nutahara, Naoyuki Yoshino, Francesco Zanetti, and two anonymousreferees for their valuable comments and discussions. The authors gratefully acknowledge the financial
support of the Joint Usage/Research Centers at the Institute of Social and Economic Research (ISER) andthe Kyoto Institute of Economic Research (KIER), and Grants-in-Aid for Scientific Research (20H05631,
20H05633, 21H00700, and 21H04397).
†
Faculty of Economics, Komazawa University‡
Osaka School of International Public Policy, Osaka University§
Institute of Social and Economic Research, Osaka University; Correspondence to: Institute of Socialand Economic Research, Osaka University 6-1 Mihogaoka, Ibaraki, Osaka 567-0047, Japan. E-mail address:
tsuruga@iser.osaka-u.ac.jp1

1

Introduction

A broad consensus on discretionary fiscal policy is that it involves long implementation lags.
The seminal work by Friedman (1953) highlighted the potential ineffectiveness or destabilizing effects of fiscal policies with implementation lags. This concern about implementation
lags persists among policymakers and economists, even in recent years, when developed countries have faced an effective lower bound (ELB) on nominal interest rates and increased theirreliance on fiscal policy. For example, Blanchard et al. (2009) and Blanchard, Dell’ariccia,
and Mauro (2010) acknowledge the risks associated with the long implementation lags offiscal policy. Christiano, Eichenbaum, and Rebelo (2011) also argue that long implementation lags in discretionary fiscal policy can decrease the fiscal multiplier, emphasizing theimportance of avoiding implementation lags. Therefore, the fiscal authority should avoid
implementation lags.
This note shows that a fiscal authority may not need to avoid implementation lags.
Using a standard New Keynesian model with an ELB, we examine the efficacy of fiscal
policy over various lengths of implementation lags. We find that implementation lags canenhance the efficacy of fiscal stimulus when the ELB is binding. Thus, a certain length of
implementation lag may be desirable for the efficacy of fiscal stimulus. However, we also
show that implementation lags do not always enhance the efficacy of fiscal stimulus if they
are too long. Fiscal stimulus may even reduce output if implemented when the ELB is
no longer binding. In this case, the concerns of policymakers remain valid and the fiscal
authority should avoid implementation lags. Therefore, the desirability of implementation
lags critically depends on in which state of the economy the government implements fiscal
stimulus.1
Implementation lags in the fiscal authority can be interpreted as a variant of fiscal policy’s
1
Our study is related to the vast literature on state-dependent fiscal multipliers. A seminal work is Auerbach and Gorodnichenko (2012), who argue that fiscal multipliers vary between expansions and recessions.
More recently, Ghassibe and Zanetti (2022) provide a theory and related evidence that fiscal multipliers
depend on the source of economic fluctuations, namely, on what types of shocks generate expansions andrecessions.

2forward guidance and compared with that of monetary policy.2 Fiscal policy with implementation lags leads to changes in future real interest rates through anticipation of policy,
similar to monetary policy’s forward guidance. Our findings regarding the desirability of
implementation lags imply that fiscal policy’s forward guidance is effective only when it ispossible to lower future real interest rates under a binding ELB. This contrasts sharply with
monetary policy’s forward guidance, which becomes effective by lowering future real interest
rates under a nonbinding ELB (i.e., real interest rates after the economy recovers from aliquidity trap).

2

The model

The model we consider here is a standard closed-economy New Keynesian model with an
ELB. The model shares various features discussed in Galı́ (2015), consisting of the consumption Euler equation, the New Keynesian Phillips curve (NKPC), and the Taylor rule with an
ELB. Here, we explicitly introduce fiscal policy with implementation lags into this standard
model. For simplicity, we consider the deterministic version of the model because we focus
only on the impulse response functions to the steady state. In what follows, we describe
the key linearized equations of the model and leave the details to the not-for-publication
Appendix A.
The consumption Euler equation in the representative agent model is given by

ct = ct+1 − (rt − πt+1 − %t ) ,(1)

where ct denotes the log-deviation of consumption from the steady state, rt is the deviationof the net nominal interest rate from the steady state, and πt is inflation. Here, we assume
zero inflation in the steady state and an intertemporal elasticity of substitution of one.
2

For monetary policy’s forward guidance, see Eggertsson and Woodford (2003) and Jung, Teranishi, and
Watanabe (2005), among others.

3Following Krugman (1998), Eggertsson and Woodford (2003), and Jung, Teranishi, and
Watanabe (2005), we introduce a deterministic preference “shock” %t into the consumption
Euler equation to generate a liquidity trap in which the nominal interest rate hits the ELB.
The NKPC takes the following form:
α+ψ
πt = κ ct +yt + βπt+1 ,
1−α

(2)

where yt is the log-deviation of output from the steady state, ψ > 0 denotes (the inverseof) the Frisch elasticity of labor supply, and β ∈ (0, 1) is the subjective discount factor ofhouseholds. We assume the firm’s production function with decreasing returns in labor,
where 1 − α is the returns to labor.3 Also, κ ≡ [(1 − θ)(1 − βθ)/θ)][(1 − α)/(1 − α + εα)]represents the slope of the NKPC, where θ is the probability that firms cannot reset theirprices in each period and ε is the elasticity of substitution across differentiated goods. In(2), ct + [(α + ψ)/(1 − α)]yt represents the log-deviation of the average real marginal cost.4
The monetary authority sets the nominal interest rate according to a simple Taylor rule
where rt responds only to inflation: rt = απ πt with απ > 1. Together with the ELB, thenominal interest rate is given by

rt = max (απ πt , ln β) .

(3)

Recall that rt is the deviation of the nominal interest rate. The steady-state nominal interest
rate equals ln(1/β). Thus, the nominal interest rate becomes zero if and only if rt decreasesto − ln(1/β) = ln β.
We are interested in the impact of a fiscal policy shock on the economy. Following Galı́,López-Salido, and Vallés (2007) and Galı́ (2020), denote gt as the deviation of government
3

Following Galı́ (2015), we assume that intermediate good producers produce differentiated goods using
the production function Yt (i) = Nt (i)1−α , where Yt (i) and Nt (i) are the output of firm i and labor demand
for firm i, respectively.
4Here, ct + ψ/(1 − α)yt is the log-deviation of real wages expressed by the marginal rate of substitution
between consumption and labor, and α/(1 − α)yt is the log-deviation of aggregate labor productivity.

4

purchases from the steady-state value expressed as a fraction of steady-state output (i.e.,
gt = (Gt − G)/Y where Gt , G, and Y are government purchases in period t, steady-state
government purchases, and steady-state output, respectively). We also assume that government purchases are financed by the lump-sum tax. Thus, Ricardian equivalence holds andthe equilibrium allocation is independent of the timing of taxation.
The goods market satisfies the following market-clearing condition:yt = (1 − γ)ct + gt ,(4)

where γ is the steady-state government purchases to output ratio G/Y . As discussed in thenext section, gt is exogenously determined.

3

Policy experiments of implementation lags

3.1

Simulations

Our simulations aim to compare the effects of government purchases on output across various
lengths of implementation lag. In simulations, the government makes an announcement at
t = 0 that government purchases are to increase by one percent of steady-state output
relative to steady-state government purchases. The increase in government purchases takes
place in period h ≥ 0, where h represents the length of the implementation lag. Government
purchases gt take the following values:

gt =




0

for t < h,δ t−h gh

for t ≥ h,(5)where δ ∈ [0, 1) measures the persistence of gt because gt+1 = δgt for t > h. Throughout
this paper, we consider fiscal stimulus, meaning that the government purchases in period h
are always positive: gh > 0.
5

We measure the overall effect of fiscal stimulus with implementation lag h on output by
P∞ t
β (Yt − YtR )ϕh = Pt=0.
∞t
t=h β (Gt − G)(6)

The numerator represents the cumulative changes in output from its reference level YtR ,which we define later. It measures output responses from the periods of announcement (i.e.,from period 0 to h−1) as well as the periods after implementation (i.e., from period h to ∞).
The denominator is the cumulative changes in government purchases relative to the steadystate. This measures changes in government purchases from the periods of implementation(i.e., from period h to ∞). Both the numerator and the denominator are expressed as
the present value.5 Thus, ϕh assesses how the cumulative effect of an anticipated shock togovernment purchases varies as the implementation lag h increases.
As we proceed, it is useful to specify YtR in (6) for our two experiments. The firstexperiment (experiment I) investigates the impact of government purchases on the economy
in a normal time in which the ELB is not binding. In particular, we assume that %t = 0 for
all t ≥ 0, and thus the economy is initially in the steady state, where the nominal interest
rate is greater than zero (i.e., rt > ln β). In this sense, the economy is in the normal time.
Because the initial state of the economy is in the steady state, this experiment specifies thereference level of output as YtR = Y for all t.
The next experiment (experiment II) considers the economy under a liquidity trap inwhich the nominal interest rate temporarily hits the ELB. In particular, we assume that anegative preference shock unexpectedly occurs in period 0 and continues to be negative forthe next three years. After three years, the negative shock disappears. More specifically,%t is fixed at a negative value for t = 0, 1, 2, ..., 11 and %t = 0 for t ≥ 12. In response to
the declines in aggregate demand, the government announces the fiscal stimulus in period
0 (the period when the negative preference shock hits the economy) and implements its
P60
P60
We approximate (6) by t=0 β t (Yt − YtR )/[ t=h β t (Gh − G)]. The approximation is valid as long as his small relative to the truncation value.
56

policy in period h. We define the reference level of output YtR in this experiment as theequilibrium output where the preference shock disturbs the economy without fiscal stimulus.
More specifically, YtR is the equilibrium output arising from fluctuations in %t while keeping
Gt at G for all t.
Throughout the paper, we parameterize the size of the preference shock to ensure thatthe weakened aggregate demand generates the liquidity trap for two years.6 By fixing theduration of a liquidity trap, we can clarify the role of the timing of implementation. In
particular, as long as the duration is fixed, we can identify whether the ELB is binding or
no longer binding when fiscal stimulus is implemented with lag h.
The remaining parameterization for the simulations follows Galı́ (2015) or Galı́ (2020)
unless otherwise noted. We set β at 0.995, which implies a steady-state annualized realinterest rate of two percent under zero steady-state inflation. The elasticity of substitution
across differentiated goods ε is set to nine. The Frisch elasticity of labor supply is 1/5 so thatψ = 5 and the return to labor in the production function 1 − α is 3/4. In addition, we set θ
such that the average duration of price changes is four quarters (i.e., θ = 3/4). Following Galı́,López-Salido, and Vallés (2007), we set γ at 0.2. The persistence of government spending δ
is set to 0.5. Finally, we set απ to 1.50.

3.2

Results

3.2.1

Experiment I: The economy in normal times

Figure 1 reports the simulation results of experiment I. The left panel plots ϕh against
h to compare the overall effect of fiscal stimulus on output across various lengths of theimplementation lag h. The right panel chooses the cases of h = 0 and 4 and shows how
output responses to fiscal stimulus differ between the two cases.
6

In our benchmark parameterization, we set the size of a negative shock to -0.3 percent (i.e., %t for
t = 0, 1, ..., 11 to −0.003). We change this value across robustness checks to ensure the liquidity trap for two
years.

7

[Figure 1 about here.]
As shown in the left panel, implementation lags are not desirable in terms of the overall
effect of a fiscal stimulus on output because ϕh reaches its maximum value when h = 0. We
confirm that h = 0 continues to achieve the (global) maximum value of ϕh even if we allow
for a large h sufficiently beyond the value of h shown in the figure. This result suggests that
fiscal stimulus without implementation lags performs best in terms of the overall effect on
output. One important message in experiment I is that the fiscal authority should avoid any
implementation lags when the economy is in normal times. Quantitatively, the decrease inefficacy is nonnegligible in that if a policymaker postpones the implementation of government
purchases by one year after the announcement, the efficacy of the fiscal stimulus falls by about
83 percent, from ϕ0 = 0.70 to ϕ4 = 0.12. This fall in efficacy results from substantial initialdeclines in output between the announcement and the implementation (see the solid linewith circles for the case of h = 4 in the right panel).
Intuitively, the consumption-smoothing motive gives rise to this undesirability of implementation lags. Government purchases with an h-period implementation lag raise the realinterest rate in period h. An increase in the real interest rate decreases consumption in thesame period (i.e., ch < 0). Put differently, government purchases gh crowd out consumption
ch as in the standard New Keynesian model. In period 0, households realize that government
purchases with an h-period implementation lag reduce their consumption in period h. The
h-period implementation lags provide forward-looking households with opportunities to mitigate a large fluctuation in consumption at the time of the implementation of fiscal stimulus.
Namely, they can smooth out their consumption over the periods before h. This consumption
smoothing results in declines in ct over 0 ≤ t ≤ h − 1. As the implementation lag lengthens, households have more opportunities to reduce consumption. Thus, implementation lags
weaken the overall effect of fiscal stimulus on output.

8

3.2.2

Experiment II: The economy in a liquidity trap

We next turn to experiment II. Figure 2 again plots ϕh against h in the left panel and depicts
output responses for the cases of h = 0 and 4 in the right panel.
[Figure 2 about here.]
In contrast to the result of experiment I, the left panel of the figure suggests that acertain length of implementation lag is desirable because ϕh exhibits a hump shape thatpeaks at h = 5. This shape suggests that a fiscal stimulus with no implementation lag
does not necessarily perform best in terms of the efficacy on output. An important message
in experiment II is that the fiscal authority does not always need to avoid implementation
lags when the ELB is binding. Furthermore, the increment in efficacy is substantial. For
example, if a policymaker postpones the fiscal stimulus by one year after the announcement,
the efficacy of the fiscal stimulus will increase by approximately 2.5 times, from ϕ0 = 1.26 to
ϕ4 = 3.19. This surge in efficacy can be confirmed from output responses in the right panel.
This panel shows output responses for h = 0 and h = 4 as well as the responses without
government intervention (i.e., the reference level of output ytR ). Because of the negative
preference shock %t , output drops in all periods after t = 0. In period 0, the government
announces the fiscal stimulus to mitigate the decreases in output. The fiscal stimulus is much
more effective with implementation lags of one year (h = 4) than without them (h = 0).
Our finding on the desirability of implementation lags sharply contrasts with the broadconsensus among policymakers. Since Friedman (1953), lags in implementing fiscal policies
have long been a concern for policymakers. Even in recent studies, this concern remains.
For example, Blanchard et al. (2009) argue for fiscal stimulus during a financial crisis, butalso recognize that implementation lags remain a risk for fiscal stimulus. In contrast tothese previous studies, we point out the desirability of implementation lags when the ELB
is binding.
We note that the overall effect of fiscal stimulus on output ϕh is hump-shaped rather
9than monotonically increasing in h, as shown in the left panel of Figure 2. Thus, a longer
implementation lag does not always enhance the efficacy of fiscal stimulus even if the ELB
is binding at the time of announcement. Indeed, ϕh is even negative for h ≥ 9. In the next
section, we explain in detail the mechanism behind the hump shape in Figure 2, based onmodel responses to shocks.

3.3

Model dynamics of the economy in a liquidity trap

Figure 3 presents the model dynamics of output, consumption, the nominal interest rate, andthe real interest rate in experiment II. These variables are shown in terms of the responses
to an anticipated increase in government purchases. The nominal and real interest rates
are multiplied by four to express them at an annual rate. Here, negative preference shocks
lasting for three years weaken aggregate demand such that the nominal interest rate hits the
ELB during 0 ≤ t ≤ 7. Given a decline in inflation from weakened aggregate demand, thereal interest rate increases strongly when the nominal interest rate hits the ELB.
[Figure 3 about here.]
We are now ready to discuss the effects of fiscal stimulus with implementation lags.
Figure 3 selects two values for the implementation lags: h = 4 (the solid line with circles)
and h = 12 (the solid line with diamonds). The vertical lines in each panel represent theperiod of implementation of the fiscal stimulus. Note that an implementation lag of one year
means that the government implements the fiscal stimulus during a liquidity trap (see thelower-left panel of Figure 3). By contrast, an implementation lag of three years implies thatthe government implements the fiscal stimulus when the ELB is no longer binding. Recall
that, as indicated in the left panel of Figure 2, ϕh almost peaks in h = 4 (ϕ4 = 3.19), but isconsiderably smaller when h = 12 (ϕ12 = −3.39).
Let us first discuss the effect of a fiscal stimulus on output when implemented during aliquidity trap (h = 4). The solid line with circles in Figure 3 details the model responses
10

to both an increase in gt and a decrease in %t . In the upper-left panel, the solid line withcircles (yt ) is located uniformly above the dashed line (ytR ), especially several quarters after
the announcement of a fiscal stimulus in period 0. That is, government purchases with an
implementation lag of one year raise output relative to the reference level.
To obtain the intuition behind the positive effect on output, define the relative consumption Euler equation asc̃t = c̃t+1 − (r̃t − π̃t+1 ) ,(7)

where the variable with a tilde denotes the variable relative to the reference level (i.e.,RRc̃t = ct − cRt , r̃t = rt − rt , and π̃t = πt − πt ). Equation (7) compares two consumption

Euler equations by taking the difference from the reference level. The preference shock %t
disappears in (7) because %t is common to the two consumption Euler equations and thus,
they cancel each other out.
Government purchases with h = 4 increase inflation without affecting the nominal interest
rate because the economy is caught in a liquidity trap (see the solid line with circles for 0 ≤t ≤ 7 in the lower-left panel). Higher (anticipated) inflation caused by the implementation of
the fiscal stimulus then lowers the real interest rate relative to the reference level, as shownin the lower-right panel of Figure 3. This low relative real interest rate, in turn, stimulates
relative consumption in the same period (see the upper-right panel in period t = h). Put
differently, government purchases increase relative consumption because of the crowding-in
effect of government purchases. In terms of (7), gh leads to c̃h > 0 through a lower realinterest rate r̃h − π̃h+1 < 0. This crowding-in effect is well known in the literature (Woodford(2011) and Christiano, Eichenbaum, and Rebelo (2011)).
The consumption-smoothing motive makes implementation lags desirable. In period 0,
households realize that government purchases with an h-period implementation lag crowdin their consumption in period h through the low real interest rate. The h-period implementation lags provide forward-looking households with opportunities to smooth out theirconsumption over the periods before h. This consumption smoothing leads to increases in c̃t
11over 0 ≤ t ≤ h − 1. As the implementation lag lengthens, households have more opportunities to increase consumption before the implementation of the fiscal stimulus. Thus, a long
implementation lag strengthens the overall effect of the fiscal stimulus on output.
We next turn to the case where the fiscal stimulus is implemented after a liquidity trap(h = 12). In contrast to the case of h = 4, government purchases decrease relative consumption because of the crowding-out effect of government purchases. Higher (anticipated)inflation caused by the implementation of the fiscal stimulus (g12 > 0) raises the real interest
rate relative to the reference level, as the ELB is no longer binding in period t = h = 12.
From (7), this high relative real interest rate (r̃h − π̃h+1 > 0) implies low relative consumption
in the same period (c̃h < 0).
When the fiscal stimulus is implemented after a liquidity trap, the implementation lag is
no longer desirable. Not surprisingly, the intuition in experiment I is applicable to this result
because of the crowding-out effect on consumption. Because of the consumption-smoothing
motive, relative consumption decreases from the time of the announcement (t = 0). As
the implementation lag lengthens, households have more opportunities to decrease relative
consumption before the implementation of the fiscal stimulus. As a result, ϕh tends to declinewith the implementation lag. Moreover, more frequent declines in relative consumption makeϕh become increasingly negative.
Before closing this section, three remarks are in order. First, the mechanism behind thedesirability of implementation lags is similar to that behind forward guidance on monetary
policy. In the case of monetary policy’s forward guidance, the central bank can lower future
real interest rates by decreasing nominal interest rates after the ELB does not become binding. Thus, forward guidance in monetary policy becomes effective by announcing that theaccommodative policy will be implemented after the economy has recovered. Conversely, inthe case of fiscal policy’s forward guidance, fiscal authorities can lower future real interest
rates by increasing inflation when the ELB is binding. As a result, forward guidance infiscal policy becomes effective by announcing that the fiscal stimulus will be implemented

12

before the economy recovers. In other words, fiscal policy’s forward guidance can enhancethe efficacy of fiscal policy, but needs to be implemented in a timely manner.
Second, our result is related to the finding of Farhi and Werning (2016). They analyticallydemonstrate that longer duration of fiscal stimulus always leads to a stronger crowding-in effect on consumption.7 Their finding suggests that a long implementation lag always enhances
the efficacy of fiscal policy, which appears inconsistent with our finding. This difference comesfrom the fact that they assume constant nominal interest rates to represent a liquidity trap.
Thus, in Farhi and Werning (2016), the fiscal stimulus is always implemented during a liquidity trap and its efficacy always increases monotonically. In our model, we assume theendogenous nominal interest rate. The fiscal stimulus is not necessarily implemented during
a liquidity trap (e.g., a large h) and its efficacy is hump-shaped.
Third, Christiano, Eichenbaum, and Rebelo (2011) argues against implementation lags,
which again appears inconsistent with our finding. They emphasize that the fiscal multiplierdrops substantially when government spending increases only after a liquidity trap. Theirargument corresponds to our case for h = 12 in Figure 3. Both models have the same
implication for fiscal policy in that the fiscal stimulus should be implemented in a timely
manner. Namely, the fiscal authority should avoid very long implementation lags. However,
our paper goes a step further than theirs: The fiscal authority may not need to avoid
implementation lags if they are not too long.

3.4

Robustness

Our finding on the desirability of implementation lags is robust to a variety of changes inour model’s assumptions and parameters.

Discounting in the consumption Euler equation and the Phillips curve The firstrobustness analysis replaces the consumption Euler equation (1) and the NKPC (2) with7

See their Proposition 1 in Farhi and Werning (2016, p. 2433).

13

those with discounting. The behavioral New Keynesian model of Gabaix (2020) introducescognitive discounting in the consumption Euler equation and the NKPC. He argues thatthe forward guidance puzzle in monetary policy disappears because cognitive discounting
weakens the forward-looking property of the consumption Euler equation and the NKPC.8
Given that our finding arises from the mechanism of forward guidance, the discounting
makes the forward guidance puzzle less pronounced and may reverse the desirability of
implementation lags when the economy is in a liquidity trap. Based on Gabaix (2020), we
replace (1) and (2) with ct = m̄ct+1 − (rt − πt+1 − %t ) and πt = κ{ct + [(α + ψ)/(1 − α)]yt } +βM f πt+1 , respectively. Here m̄ = 0.85 and M f = m̄[θ + (1 − θ)(1 − βθ)/(1 − βθm̄)] = 0.80
in the parameterization of Gabaix (2020).
Panel (a) of Figure 4 reports ϕh for experiment II under the model with discounting.
The dashed line corresponds to the case where both the consumption Euler equation and
the NKPC are “discounted” as in Gabaix (2020) (i.e., m̄ = 0.85 and M f = 0.80). It
indicates that ϕh remains hump-shaped, suggesting the desirability of implementation lags(e.g., ϕ4 = 2.36, larger than ϕ0 = 1.19). The dotted line plots ϕh when m̄ = 0.85 but
M f = 1.0. In this case, we intentionally isolate the effect of discounting in the consumption
Euler equation on ϕh from the model. The dotted line shows that ϕh is again hump-shaped.
The isolated effect of discounting in the consumption Euler equation is substantial because
the dotted line roughly keeps track of the dashed line for the case of m̄ < 0 and M f < 1.
[Figure 4 about here.]

Monetary policy rule Parameters in the monetary policy rule may influence our results
because they directly affect aggregate demand through the nominal interest rate rt in the
consumption Euler equation (1). Panel (b) of Figure 4 indicates how ϕh for experiment
II changes across three values of απ = {1.25, 1.50, 1.75}. In all cases, ϕh is hump-shaped
8

See McKay, Nakamura, and Steinsson (2016) and Del Negro, Giannoni, and Patterson (2023) for theforward guidance puzzle. McKay, Nakamura, and Steinsson (2017) propose a simple (nonbehavioral) New
Keynesian model in which discounting appears only in the consumption Euler equation.

14

against h.9
Monetary policy inertia may also affect our results. As argued by Hills and Nakata (2018),
monetary policy inertia is consistent with the statement by the Federal Open Market Committee and could generate history dependence in rt akin to that of the optimal commitment
policy (Hills and Nakata, 2018, p. 157). Thus, we replace (3) with rt = max(rt∗ , ln β), wherert∗ is the shadow policy rate. We then consider two alternative specifications for rt∗ : (i)∗+ (1 − ρr )απ πt ; (ii) rt∗ = ρr rt−1 + (1 − ρr )απ πt . The former assumes that thert∗ = ρr rt−1

shadow policy rate depends on its lagged value, and the latter assumes that it depends on theactual value. In both specifications, we borrow ρr = 0.7 from the posterior mean estimatedby Gust et al. (2017).
Our results are robust when we introduce inertia into the monetary policy rule. Panel(c) of Figure 4 plots ϕh for two specifications (i) and (ii) along with ϕh for the benchmark
case denoted as “no policy inertia.” The dashed line represents ϕh in specification (i). It
indicates that the desirability of implementation lags is weaker than the benchmark caseshown in the solid line because ϕh is flatter over h than the benchmark case. In the dottedline corresponding to specification (ii), ϕh is more strongly hump-shaped than that in thebenchmark case. While desirability differs between specifications (i) and (ii), ϕh remains
hump-shaped at least under the plausible value of ρr .
Robustness to miscellaneous model parameters We conduct robustness analysis of
miscellaneous model parameters. In particular, we implement robustness analysis for thepersistence of government purchases (δ), the slope of the NKPC (κ), the inverse of the Frishelasticity of labor supply (ψ), the returns to labor in the production function (1 − α), andthe steady-state government purchases to output ratio (γ). In all cases, we observe a hump
9

Recall that the consumption smoothing motive with the crowding-out effect of fiscal stimulus generates
a negative ϕh for a large h. As απ becomes larger, the crowding-out effect is stronger because of the higher
sensitivity of the nominal interest rate to inflation. For this reason, ϕh for a large h is the lowest underαπ = 1.75.

15

shape of ϕh , confirming the desirability of implementation lags in a liquidity trap.10
Here, we report the robustness to δ in Panel (d) of Figure 4. Again, ϕh is hump-shaped,
though the hump shape becomes weaker for larger δ. Interestingly, ϕh under δ = 0.8 islargest among the three parameter values when h is low (e.g., h = 0), but it now becomesthe lowest when h is large. Namely, ϕh is not monotonic in δ. This finding is consistent
with Ngo (2021), who shows that the fiscal multiplier is not monotonic in the persistence ofgovernment purchases when the ELB is binding.
We can interpret the nonmonotonicity in δ from the perspective of implementation lags.
When h is low (e.g., h = 0), increases in government purchases become negligible after aliquidity trap unless δ is extremely large. An increase in δ when h is low implies that fiscal
stimulus implemented during a liquidity trap occurs persistently. Thus, the increase in δ
enhances the overall effect of fiscal stimulus on output.
When h is high (e.g., h = 8), however, increases in government purchases are substantial
even after a liquidity trap, regardless of the value of δ. This case corresponds to a fiscal
stimulus implemented after a liquidity trap. An increase in δ when h is high means that afiscal stimulus implemented after a liquidity trap occurs persistently. Therefore, a larger δlowers the overall effect of fiscal stimulus on output.

Two-agent New Keynesian models It is well known that the standard New Keynesianmodel predicts the crowding-out effect of fiscal stimulus in normal times, but many previous
empirical studies have argued that the prediction is inconsistent with the data.11 It is notclear whether the same qualitative results are obtained even in models that can explain thecrowding-in effect of fiscal stimulus in normal times. These studies also argue that real wages
increase slowly in response to an increase in government purchases.
To address the external validity of the model, we conduct the same experiments in a two10

The not-for-publication Appendix B reports the results of these robustness checks (except for δ, forwhich we discuss its robustness in the main text).
11
Examples of these studies include: Blanchard and Perotti (2002), Perotti (2007), and Galı́, López-Salido,
and Vallés (2007), among others.

16

agent New Keynesian model with nominal wage rigidity.12 This class of models can generatea crowding-in effect of fiscal stimulus because of the presence of the liquidity-constrained
non-Ricardian households. As shown in the not-for-publication Appendix C, our finding isrobust even in this model: In experiment I (i.e., fiscal stimulus in normal times), ϕh reaches
its maximum value when h = 0, but, in experiment II (i.e., fiscal stimulus during a liquidity
trap), ϕh is hump-shaped against h.

4Conclusion

Since Friedman (1953), implementation lags have been a concern of policymakers because
they may reduce the efficacy of fiscal policies. Even recent studies support the conventionalview that the fiscal authority should avoid implementation lags. We showed that implementation lags could enhance the efficacy of fiscal stimulus on output when the ELB is binding.
In this case, the efficacy exhibits a hump shape against the length of implementation lag,thereby suggesting that the desirability of implementation lags depends critically on whether
the ELB is binding.
We are not arguing that the fiscal authority should control implementation lags. The
literature often argues for the automatic built-in stabilizer or fiscal policy rules to avoid
implementation lags.13 Our analysis implies that attempts to shorten implementation lags
may not necessarily maximize the efficacy of fiscal policy when the ELB is binding.

References
Ascari, Guido, Andrea Colciago, and Lorenza Rossi. 2017. “Limited asset market participation, sticky wages, and monetary policy.” Economic Inquiry 55 (2):878–897.
12

See the not-for-publication Appendix C for details of the model. The model is similar to those of Colciago(2011) and Ascari, Colciago, and Rossi (2017).
13
See Blanchard, Dell’ariccia, and Mauro (2010), for example.

17

Auerbach, Alan J. and Yuriy Gorodnichenko. 2012. “Measuring the output responses tofiscal policy.” American Economic Journal: Economic Policy 4 (2):1–27.
Blanchard, Olivier and Roberto Perotti. 2002. “An empirical characterization of the dynamic
effects of changes in government spending and taxes on output.” the Quarterly Journal of
economics 117 (4):1329–1368.
Blanchard, Olivier J., Carlo Cottarelli, Antonio Spilimbergo, and Steven Symansky. 2009.
“Fiscal policy for the crisis.” CEPR Discussion Paper No. DP7130.
Blanchard, Olivier J., Gionvanni Dell’ariccia, and Paolo Mauro. 2010. “Rethinking macroeconomic policy.” Journal of Money, Credit and Banking 42 (s1):199–215.
Christiano, Lawrence J., Martin Eichenbaum, and Sérgio Rebelo. 2011. “When is the government spending multiplier large?” Journal of Political Economy 119 (1):78–121.
Colciago, Andrea. 2011. “Rule-of-thumb consumers meet sticky wages.” Journal of Money,
Credit and Banking 43 (2-3):325–353.
Del Negro, Marco, Marc P Giannoni, and Christina Patterson. 2023. “The forward guidance
puzzle.” Journal of Political Economy Macroeconomics 1 (1):43–79.
Eggertsson, Gauti B. and Michael Woodford. 2003. “Zero bound on interest rates and optimalmonetary policy.” Brookings Papers on Economic Activity 2003 (1):139–233.
Farhi, Emmanuel and Iván Werning. 2016. “Fiscal multipliers: Liquidity traps and currency
unions.” In Handbook of Macroeconomics, vol. 2. Elsevier, 2417–2492.
Friedman, Milton. 1953. “The effects of a full-employment policy on economic stability: A
formal analysis.” In Essays in Positive Economics. University of Chicago Press Chicago,
117–132.
Gabaix, Xavier. 2020. “A behavioral New Keynesian model.” American Economic Review
110 (8):2271–2327.
18

Galı́, Jordi. 2015. Monetary Policy, Inflation, and the Business Cycle: an Introduction to
the New Keynesian Framework and Its Applications. Princeton University Press.
———. 2020. “The effects of a money-financed fiscal stimulus.” Journal of Monetary Economics 115:1–19.
Galı́, Jordi, J. David López-Salido, and Javier Vallés. 2007. “Understanding the effects ofgovernment spending on consumption.” Journal of the European Economic Association
5 (1):227–270.
Ghassibe, Mishel and Francesco Zanetti. 2022. “State dependence of fiscal multipliers: thesource of fluctuations matters.” Journal of Monetary Economics 132:1–23.
Gust, Christopher, Edward Herbst, David López-Salido, and Matthew E Smith. 2017. “Theempirical implications of the interest-rate lower bound.” American Economic Review
107 (7):1971–2006.
Hills, Timothy S and Taisuke Nakata. 2018. “Fiscal multipliers at the zero lower bound: therole of policy inertia.” Journal of Money, Credit and Banking 50 (1):155–172.
Jung, Taehun, Yuki Teranishi, and Tsutomu Watanabe. 2005. “Optimal monetary policy at
the zero-interest-rate bound.” Journal of Money, Credit, and Banking 37 (5):813–835.
Krugman, Paul R. 1998. “It’s baaack: Japan’s slump and the return of the liquidity trap.”
Brookings Papers on Economic Activity 1998 (2):137–205.
McKay, Alisdair, Emi Nakamura, and Jón Steinsson. 2016. “The power of forward guidancerevisited.” American Economic Review 106 (10):3133–3158.
———. 2017. “The discounted euler equation: A note.” Economica 84 (336):820–831.
Ngo, Phuong V. 2021. “Fiscal multipliers at the zero lower bound: The role of government
spending persistence.” Macroeconomic Dynamics 25 (4):970–997.
19Perotti, Roberto. 2007. “In search of the transmission mechanism of fiscal policy.” NBER
Macroeconomics Annual 22:169–226.
Woodford, Michael. 2011. “Simple analytics of the government expenditure multiplier.”
American Economic Journal: Macroeconomics 3 (1):1–35.

20

0.8

8

0.6

6

0.4

4

0.2

2

0

0

-0.2

-2

-0.4

10

-3

-4
0

5

10

15

0

5

10

15

Figure 1: The effect of fiscal stimulus on output in normal times
Note: The left panel shows the overall effect of fiscal stimulus on output and the right panel shows theimpulse response of output to a fiscal stimulus. A fiscal stimulus is represented by an increase ingovernment purchases announced in period 0 and implemented in period h. The increase in government
purchases is normalized to one percent of the steady-state output. At the time of announcement, theeconomy is in the steady state. The unit of time is one quarter.

21

4

0.01

3
0
2
-0.01
1

-0.02

0

-1

-0.03

-2
-0.04
-3
-0.05
-4

-5

-0.06
0

5

10

15

0

5

10

15

Figure 2: The effect of fiscal stimulus on output in a liquidity trap
Note: The left panel shows the overall effect of fiscal stimulus on output and the right panel shows theimpulse response of output to a fiscal stimulus. At the time of announcement, the economy is caught in aliquidity trap. The dashed line in the right panel represents the equilibrium responses without government
intervention (denoted by “no policy change”). For more details, see the footnote of Figure 1.

22

0.02

0.02

0

0

-0.02

-0.02

-0.04

-0.04

-0.06

-0.06

-0.08

-0.08

-0.1

-0.1
0

5

10

15

0

5

10

15

0

5

10

15

0.02
0.1

0.01
0

0.05
-0.01
-0.02
0
-0.03
-0.04
0

5

10

15

Figure 3: Responses of variables to changes in %t and gt
Note: Each panel of the figure compares the model responses to %t and gt for an implementation lag of
between one and three years (h = 4 and h = 12), along with the reference level of the corresponding
variables. The upper-left and upper-right panels refer to output and consumption, respectively. The
lower-left and lower-right panels present the nominal interest rate and the real interest rate, respectively.
The dashed line in each panel represents the equilibrium responses without government intervention(denoted by “no policy change”). The solid lines in each panel refer to the model response to decreases in
the preference shock and increases in government purchases. The solid line with circles indicates model
responses under h = 4, and the solid line with diamonds indicates model responses under h = 12. The
horizontal axis is the quarters after the preference shocks. The vertical lines in each panel represent thetiming of the implementation of the fiscal stimulus. In the figure, ϕh = 3.19 at h = 4 and ϕh = −3.39 at
h = 12.

23

4

4

2

2

0

0

-2

-2

-4

-4

-6

-6
0

5

10

15

5

0

5

10

15

0

5

10

15

4

2

0
0
-2

-4

-5

-6
0

5

10

15

Figure 4: Robustness checks: Overall effect of fiscal stimulus on output in a liquidity trap
Note: Panel (a) plots ϕh against h under the model with discounting in the consumption Euler equationand the NKPC. Panel (b) compares ϕh across three values of απ in the monetary policy. Panel (c)compares ϕh across three monetary policy rules under the ELB. The dashed line represents ϕh when themonetary policy rule depends on the lagged shadow policy rate. The dotted line shows ϕh when themonetary policy rule depends on the lagged actual policy rate. Panel (d) compares ϕh across three valuesof δ in government purchases. In all panels, the solid line corresponds to the benchmark case replicating ϕhshown in the left panel of Figure 2 for comparison.

24