PRI Discussion Paper Series (No.20A-05)

The Cost of Omitting the Credit Channel in DSGE Models:
A Policy Mix Approach

Senior Economist, Policy Research InstituteTakeshi Yagihashi
March 2020

The views expressed in this paper are those of theauthors and not those of the Ministry of Finance or
the Policy Research Institute.

Research Department Policy Research Institute, MOF
3-1-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8940, JapanTEL 03-3581-4111

The Cost of Omitting the Credit Channel in DSGE Models:
A Policy Mix Approach†Takeshi Yagihashi*First draft: October, 2019
This version: March, 2020

Abstract:
This paper examines whether the omission of the credit channel from policy models usedby both monetary and fiscal policymakers would lead to a noticeably “bad” policy outcome
through model simulation. First, we simulate a financial crisis in which the financial market
friction grows and the risk premium becomes more volatile. Next, both monetary and fiscal
policymakers readjust their policy to stabilize the economy using an approximating DSGE modelthat does not feature the credit channel. We show that while the model misspecification does notaffect much how policymakers perceive the crisis, the newly adopted policy based on theapproximating model would cause further destabilization of the economy. We also show that thedestabilization of the economy could be prevented if the fiscal policymaker is equipped with thecorrectly-specified credit channel model and chooses its new policy while taking into account thedecision-making of the monetary policymaker. Finally, under the scenario that the correctlyspecified model is unknown, we show that the destabilization of the economy could still be
prevented if both policymakers can apply judgement to unreasonable parameter estimates during
the crisis period. In sum, prediction of policy outcomes and cautiousness in interpreting
estimation results can help in mitigating the credit channel misspecification.

Keywords: DSGE model, Lucas Critique, Bayesian estimation, Financial Accelerator model,monetary policy, fiscal policy, policy mix†

We thank the session/seminar participants at Macro Model Workshop 2020 (hosted by Policy Research Institute), Hitotsubashi
University, and Senshuu University for providing us with valuable comments and feedbacks. The views expressed here are thoseof the authors and do not necessarily represent the views of Policy Research Institute.
*
Address: Policy Research Institute, Ministry of Finance Japan, 3-1-1 Kasumigaseki, Chiyoda-ku, Tokyo 100-8940, Japan;
email: takeshi.yagihashi@mof.go.jp.

01 Introduction
Lucas (1976) argued that any macroeconomic model should be structural so that the
hypothetical policy shift does not trigger any spurious shift in model parameters. Soon theanalytical tool now known as the Dynamic Stochastic General Equilibrium (DSGE) model wasdeveloped and has become the workhorse for analyzing the aggregate economy among academics.
Unlike previous generations of models, the behavioral equations of the DSGE model were inprinciple derived from an optimizing principle, and were further pinned down by time-invariant
parameters describing preferences and technology of agents. More recently, many
macroeconomists working in the public sector started to use the DSGE model in their forecasting(or projection) and policy analysis, embracing it as a practical solution to overcome the Lucas'
critique.1
The financial crisis in 2008 brought in new criticism to then-existing DSGE models for theircasual treatment of the “credit channel”, which we broadly define as the transmission process ofpolicy through the supply of loanable funds.2 After the crisis many policy institutions formallyincorporated credit channels into their policy models. 3 Recently, Cai et al. (2019) examineddifferent vintages of the DSGE model used by the Federal Reserve Bank of New York (SWFF++)and found that the version that incorporates financial friction performs well in terms of forecasting.

1 According to Yagihashi (2020), there are 82 institution-affiliated DSGE policy models that accompany formal documentation in
the form of academic research papers, institutional discussion papers, or policy notes. Of these models, 54 are developed bycentral banks, 16 by national government, and 12 by international organizations.
2 Prior to the financial crisis, the treatment of the credit channel within the policy institution was ad hoc. For example, Harrison etal. (2005) describe that in the macroeconometric model used by Bank of England (BEQM), the credit channel is represented byseveral non-structural auxiliary equations which “proxies for short-run effects such as credit constraints, house price effects,
confidence and accelerator effects”. Similar approaches were taken for other models that were used in International Monetary Fund,Federal Reserve, and European Central Bank prior to the financial crisis. See also Bayoumi et al. (2004), Christoffel et al. (2008),
Coenen et al. (2008), and Erceg et al. (2006).
3
These institutions include Federal Reserve Board, Federal Reserve Bank of New York, European Central Bank, theBundesbank, Sveriges Riksbank, Bank of Finland, Bank of Canada, and Spanish Ministry of Economic and Finance.

1Other studies also argued that the presence of the credit channel matters in the context ofpolicymaking.4
The credit channel DSGE models used by many policy institutions typically do not feature
the fiscal policymaker. This is not surprising because these models are mainly used by central
banks whose mandate is the monetary policy. However, the fiscal policymaker can affect thefinancial market by changing the tax rate on capital, which could influence how the economy
stabilizes after the financial crisis and hence the effectiveness of monetary policy. If we do not
explicitly consider the possible model misspecification of the fiscal policymaker, we might
misjudge the importance of the credit channel in DSGE models.
This paper aims to examine the cost of omitting the credit channel from DSGE models bytaking a “policy mix approach”, i.e., assuming that both the monetary and fiscal policymakers playa role in stabilizing the economy. The key question is whether the change in policy conducted byboth policymakers during the financial crisis would lead to a noticeably “bad” policy outcome,
had they used a simpler “approximating model” (AM thereafter) that does not feature the credit
channel. We break this question down into three parts. First, we want to know whether thepolicymakers, equipped with the AM, would hold a vastly different view of the economy fromwhat has actually happened in the “data-generating model” (DGM thereafter). Second, we check
whether the policy changes, simultaneously conducted by the monetary and fiscal policymakers,
would lead to a further destabilization of the economy. Third, we examine whether handing thecorrectly-specified model over to one of the two policymakers would be sufficient to prevent thedestabilization caused by the credit channel misspecification, and what policymakers could do to
mitigate the consequences if they do not know the “true” data generating process.

4
See for example, Kolasa and Rubaszek (2014) and Yagihashi (2018). For comprehensive overview on this topic, also see
Christiano et al. (2018).

2

Our method utilizes the idea of model entropy (i.e., Kullback-Leibler information criterion)
as in Cogley and Yagihashi (2010) and Yagihashi (2018). First, we simulate a financial crisis inwhich the exogenous risk premium shock becomes more volatile and the endogenous financial
propagation mechanism strengthens due to the growing financial market friction. Second, both themonetary and fiscal policymakers independently readjust their policy to minimize the social
welfare loss by using an approximating DSGE model that does not feature the credit channel.
To focus on the core issues, we introduce four assumptions that greatly simplify the analysis.
First, we use a medium-scale DSGE model that embeds the financial accelerator model ofBernanke, Gertler, and Gilchrist (1999, hereafter BGG) as the core credit channel mechanism. This
choice is motivated by BGG’s wide use among policy institutions.5 Second, a financial crisis issimulated by employing two sets of model parameters that characterize the “pre-crisis” and “crisis”
periods. Third, the common goal of the monetary and fiscal policymakers is to minimize thequadratic loss function a la Woodford (2003), which involves stabilization of the interest rate.6
Fourth, the policy shift is described as a one-time change in the reaction coefficients of the
feedback rules regarding the risk-free interest rate, capital tax rate, and labor tax rate.
The main findings are as follows. First, we find that the policymakers would not see theeconomy much differently from what happened in the DGM before and after the crisis: changes in
the pseudo-true values estimated via the AM are mostly contained within an economicallyplausible range, while the forecast error variance decomposition in the AM does not suggest that5
In 2008, Federal Reserve governor Mishkin stated that the financial accelerator mechanism describes well the macroeconomicrisk that the monetary policymaker faces (Mishkin, 2008). The features of the BGG model are incorporated in many DSGE
policy models. Examples include BoC-GEM-FIN model (Bank of Canada), Global Integrated Monetary and Fiscal model(International Monetary Fund), MEGA-D (Central Reserve Bank of Peru), PESSOA (Banco de Portugal), RAMSES2 model(Sveriges Riksbank), R.E.M. 2.0 (National Bank of Romania), SWFF++ model (Federal Reserve Bank of New York).
6This means that the fiscal institution can potentially aid monetary policymaker in stabilizing the economy (and vice versa)
without facing any conflict that may arise from having a different policy objective. This assumption necessarily implies that a)
the fiscal policymaker cares as much about the interest rate stabilization as the monetary policymaker does, and b) any additionalrole of the fiscal policy beyond the short-term economic stabilization is ignored. While it is interesting to consider the case of
conflicting objectives among two branches of the government, addressing this issue goes well beyond the scope of this paper.

3the model is doing a poor job. Second, we show that the new policy obtained using the AM would
result in further destabilization of the economy. The destabilization occurs even if thepolicymakers use the unbiased parameter values in designing the policy shift. Third, we show thatproviding one policymaker with the correctly-specified DGM is not sufficient to avoid
destabilization of the economy. To stabilize the model economy, we need to a) equip the fiscal
policymaker with the correctly-specified DGM and b) let the fiscal policymaker predict the policychange of the monetary policymaker who uses the AM as a guide. Finally, under the scenario thatboth policymakers do not know the DGM, we show that the destabilization of the economy could
still be prevented if both policymakers can use their judgement and partially ignore parameter
estimates that seem unreasonable. Overall, we find that prediction of policy outcomes andcautiousness in interpreting estimation results can help in mitigating the credit channel
misspecification.
To our knowledge, this paper is the first to study the consequences of credit channel
misspecification in both monetary and fiscal policy. Previous papers have studied the same topic
in the monetary policy context (e.g., Yagihashi, 2018). The key difference is that we incorporatea pair of stylized fiscal policy rules, which is becoming increasingly popular in the DSGE literature(Kliem and Kriwoluzky, 2014), into the otherwise standard medium-scale credit channel DSGE
model. This paper is also related to the classic literature that examines monetary-fiscal policy
coordination.7 However, to our knowledge, there are no studies in this field that explicitly examine
how model misspecification in one institution could affect the policymaking of the other and7
Using the framework of noncooperative games, Sargent and Wallace (1981) first demonstrated that whether the monetary
policymaker or the fiscal policymaker gets to move first matters in terms of the final policy outcome. Other related studies
include Leeper and Sims (1994), Davig and Leeper (2007), and Schmitt-Grohe and Uribe (2005, 2007).

4

whether policy outcomes would be any different if one institution is equipped with the correctlyspecified model whereas the other is not.
Another contribution of this paper is to demonstrate the importance of the credit channel infiscal policymaking, in particular the capital tax policy. There are only few studies that examine
the importance of the credit channel in fiscal policy. On the theoretical front, Carton et al. (2017)use simulation to examine how the increase of the capital return tax impacts the model economy
with BGG-type of financial friction. They show that the tax increase has a strong contractionary
effect on the economy in the long-run by forcing firms to cut down on investment. On the empirical
front, Bird et al. (2018) find some supporting evidence for the existence of the credit channel infiscal policy by analyzing data from the 2004-2005 U.S. repatriation tax holiday. This paper adds
to the literature by pointing out the importance of the credit channel for fiscal policymakers in thecontext of model misspecification. 8 Our paper emphasizes the effect of the capital tax policy
during a financial crisis of the sort that we experienced in 2008-09.
The next section provides an overview of the simulation design. Third section describes themodel. Fourth section presents the main result and discuss its policy implications. The last section
concludes.

2 Simulation Design
We largely follow the approach of Yagihashi (2018) to study the cost of the credit channel
misspecification: we generate artificial time series data using the data-generating model (“DGM”)
and design the policy shift according to the misspecified approximating model (“AM”). The key

8
Note that there are DSGE models developed by policy institutions that incorporate the capital tax rate. However, most of themtreat the capital tax rate as a constant parameter instead of a policy instrument (e.g., models developed by Bundesbank andSveriges Riksbank).

5difference from Yagihashi (2018) is that we incorporate two policymakers, monetary and fiscal,in this analysis.9 The fiscal policymaker selects policy rule coefficients related to the capital andlabor tax rate after the financial crisis erupts. The capital tax rate is closely tied to the user cost ofcapital in our model and therefore affect the volatility of the rate of return on capital. As such, thefiscal policymaker can influence how the economy stabilizes after the financial crisis through its
policy shift and indirectly influence the effectiveness of the monetary policy.

2.1 Financial Crisis
We define three subsamples that trace the sequence of events that happened during the recent
financial crisis of 2008-09. Each of the three subsamples are named as follows:
1. Pre-crisis period: the financial market condition and policy rules are set to the benchmark
level,
2. Crisis period: the financial market condition deteriorates, while the policy rules remainunchanged from the pre-crisis period, and
3. Policy shift period: policy rules are reoptimized based on the estimated model parameters
and the policy model.
We assume that the financial crisis and the policy shift occur instantly and the economy
immediately converges to a new rational-expectations equilibrium after the events. Between the
pre-crisis and the crisis period, there is a joint shift in the subset of model parameters that represents
the deterioration of the financial market conditions. Policymakers do not observe the parameter
shift directly because their policy models do not feature these model parameters, but they doobserve the change in the moments of the economic variables (e.g., inflation, output, interest rate)

9
More minor changes include making the welfare loss measure cover multiple period as opposed to current period only (Section2.3) and adding non-Ricardian “hand-to-mouth” consumers in addition to the rational forward-looking consumers (Section 2.5).

6caused by the parameter shift. Between the crisis and the policy shift period, policymakers
reoptimize their policy rule coefficients so as to minimize the prespecified welfare loss function
conditional on the re-estimated model parameters in the crisis period. We first explain how model
parameters are estimated by the policymakers (Section 2.2) and then how the policy shift isdesigned (Section 2.3).

2.2 Parameter Estimation
First, DGM is used to generate the three sets of data corresponding to “pre-crisis”, “crisis”,
and “policy shift” periods. Next, AM is used by both policymakers to estimate model parametersand choosing the optimized policy rule coefficients. The process of parameter estimation isequivalent to minimizing the distance metric known as the Kullback-Leibler Information Criterion(a.k.a. “KLIC”)
argmin
where

| ;

log

is the likelihood function,a vector of estimated model parameters, and

|
|

;
;

|

;

,

is a vector of variables common across models,1
isis a vector of policy parameters, which we treat as“known” to policymakers and leave out of estimation.
When the fiscal policymaker estimates the values of
estimates∗

using Equation (1), the resulting

converge in probability to what is known as the “pseudo-true” values. Due to model

misspecification pseudo-true values necessarily differ from the “true” parameter values used in
DGM. Thus our policymakers use the asymptotically-biased parameters in designing the policy
shift. To ensure that∗reaches the pseudo-true values, we generate time series equivalent of

7

3200 quarters (800 years) for each of the three sample periods.10 We then estimate the posterior
parameter mode using the maximum likelihood method in combination with Bayesian priors.11
Observables are output, inflation, nominal interest rate, investment, consumption, labor, wage rate,
which are standard in the literature of Bayesian estimation of medium-scale DSGE models.

2.3 Policy Shift
In this model, there exist two types of policymakers, namely the monetary and fiscal policymakers.
We assume that both policymakers share a common goal of minimizing the quadratic loss function,
which takes the following functional form
min

,

,

where

≡

/

is inflation,is output,

,

1
0
0

0
0

0
0

2

,

3

is the interest rate, and the hat on top of eachvariable denotes deviation from the steady state. The idea of incorporating the interest ratestabilization as part of the quadratic loss function follows Woodford (2003): parametersanddenote the relative importance of output and interest rate stabilization, respectively. We set theperiod that covers the period welfare loss to 16 quarters (4 years). This implies that thepolicymakers care about economic stabilization in both short and medium terms.

10 In practice, we generated 3,520 quarterly time series and treated the first 320 quarters as “burn-in”. This procedure is to ensurethat our sample is not affected by the initial round of shocks that are randomly picked. The adequate length of the sample period
is determined by observing the behavior of the standard error of the parameter estimates. While in principle these should
approach zero in limit, the speed of convergence is not uniform across parameters. Before picking our sample length, we
experimented with different values of T to check how sensitive the parameter estimates are for different sample length.
11
The approach of Bayesian estimation is standard and closely follows An and Schorfheide (2007). We use Chris Sim’s
optimization routine to obtain the posterior mode of each parameter. Bayesian priors introduce curvature into the likelihood
function and facilitate computation.

8

The monetary policymaker in our model chooses the risk-free nominal interest rate
through the Taylor-type feedback rule,
exp
where

,

4

is the monetary policy shock that follows the AR(1) process,

,

,
, ~

with

,

0,

. We treat

,

exp

,

,

5

as the time-invariant preference parameter that represents themonetary policymaker’s general tendency to move the policy rates cautiously. The policy
coefficients that the monetary policymaker can choose are

,

,

.
,

The fiscal policymaker chooses the capital and labor tax rate

through a pair of

feedback rules similar to that of the monetary policymaker,
,

6

,

7

where

is the amount of government bond. The policy rule parameters involving output,) represent the automatic stabilizing component (e.g., see Coenen et al., 2013), while(

those involving output growth (,) represent the responsiveness of the tax rate during,

the business cycle. The policy rule parameter on the government bond () represents how

quickly the fiscal policymaker wants its projected budget balance to adjust towards its long-run
target of debt-to-output ratio. As with the monetary policy rule’s case,,are treated as (time-9

invariant) preference parameters. 12 Thus, the fiscal policymaker reoptimizes
,

,

,

,

,

during the crisis.

We assume that both institutions are granted operational independence when designing andconducting the policy shift. As such, when reoptimizing the policy coefficients, the policy
coefficients of the other institutions are treated as exogenous constraints as with other model
equations and parameters. In our baseline analysis, we assume that each policymaker naively
believes that the other institution keeps its policy the same as the pre-crisis period. We call this“no prediction case” to distinguish with another “predicted outcome case”, in which the policy
institution equipped with the “true” DGM forms a prediction of the response of the other institution
equipped with the AM.

2.4 Financial Accelerator Mechanism
We follow BGG in modeling the financial accelerator mechanism, motivated by its wide use
among policy institutions.13 The key feature of the financial accelerator mechanism, which also
distinguishes our DGM from the AM, is that there is imperfection in the financial market that
results in a time-varying risk premium between the return on capital (Rk) and the risk-free interest
rate. A risk-neutral financial intermediary collects funds from the representative household andlends them out to individual entrepreneurs. Entrepreneurs are subject to a random idiosyncratic
productivity shock, and they would be forced to declare bankruptcy when they are hit by a large
adverse shock. The optimal contract between the financial intermediary and the entrepreneurs

The two parameters ,are somewhat more difficult to interpret economically compared to , because tax rate smoothing
is not empirically supported (a permanent tax change would accompany a that is one). Here, we follow the specification that is
popular in the fiscal policy literature, (e.g., Kliem and Kriwotzky, 2014).
13
Other credit channel models that are popular among policy institutions are Gertler and Karadi (2011) and Gerali et al. (2010).
See Yagihashi (2020) for further details.
1210requires that the entrepreneurs maximize their profit conditional on the financial intermediary's
participation (i.e., nonnegative profit). Solving the contract problem results in an expression forthe supply of loanable funds,
whereis the price of capital (“Tobin’s q”),

8
is theis the quantity of (installed) capital,⁄

represents the leverage ratio of the entrepreneur and the risk premium
as a function of the leverage ratio. The parameter⁄

1. The term

entrepreneur's net worth available at the beginning of periodthus

are expressedis the financial market friction, which shows(the elasticity of) how strongly the risk premium responds to the leverage ratio. When0, therisk premium (in gross terms) becomes one at all times and our AM becomes isomorphic to the
DGM.
Entrepreneurs use the loanable funds to buy capital from producers of physical capital andrent the capital out to intermediate goods producers. The expected gross return from capital
investment can be expressed as
1

where

is the (gross) marginal product of capital andpremium shock

,

, ~

0,

,

,

9

is the depreciation rate. The risk

follows the AR(1) process
,

where

exp

,

exp

,

,

10

. This shock is introduced to capture the large swing in the risk premiumthat occurred during the recent financial crisis.14

14
We note that in the DSGE literature, the expression of the risk premium shock is sometimes reserved for different types ofshocks. For example, the risk premium shock could mean the wedge that perturbates the marginal rate of substitution between

11

In the AM,

0 due to the lack of financial market

is set to zero at all times andfriction. Thus, the demand for loanable funds equation simplifies to
1

,

11

and the supply of loanable funds is simply the consumption Euler equation derived from thehouseholds’ optimization problem.

2.5 The Remaining Parts of the Model
Both the DGM and AM mostly share the same model structure as the conventional mediumscale New Keynesian DSGE model populated by Smets and Wouters (2003) and Christiano et al.
(2005).15 Here we highlight the differences with these workhorse models.
First, our DGM and AM feature a marginal efficiency of investment (MEI) shock as describedin Justiniano et al. (2010, hereafter JPT). More specifically, our law of motion for capital is defined
as follows,1
where

represents the adjustment cost of capital that satisfies

steady state. The MEI shock

, ~

0,

0 and

0 in theis modeled as,
exp

with

,

1

,

,

. According to Justiniano et al. (2011), this shock “proxies for more

fundamental disturbances to the functioning of the financial sector”. Thus, introducing this shockconsumption across different period within the consumption Euler equation (in this paper we name this type of shock as thepreference shock). Alternatively, the risk premium shock could mean the wedge that enters the uncovered interest rate parity
condition.
15
Much of the details of the model is provided in the appendix of Yagihashi (2018).

12to our model could potentially help the policymakers in identifying the occurrence of the financial
crisis.
Second, we introduce non-Ricardian “hand-to-mouth” households as in Gali et al. (2007)
and Forni et al. (2009). The non-Ricardian households have restricted access to the financial
market and thereby cannot adjust their consumption/saving easily in response to the crisis.
Aggregate variables of the entire household sector is defined as the linear combination of thecorresponding variables for each type of household ( for optimizers, andfor restricted) as

follows,
1

,

1

where

is consumption,is labor,

,

1

,

1

,

is saving, and the parameteris the share of non-Ricardian households, which we estimate in later analysis. This modeling strategy is highly
popular among policy institutions because it generates a strong fiscal multiplier effect.16
Finally, since we incorporate capital and labor tax rates in our model, relevant equations
will be slightly modified. With regard to the capital tax rate, the “net” marginal product of capitalthat pins down the value of physical capital is now defined as
,

1

,

16
According to the detailed policy model analysis in Yagihashi (2020), majority of the policy institutions adopt Gali et al-type“hand-to-mouth” households to make households act in a non-Ricardian manner. Few institutions adopt the “perpetual youth”
structure or apply high future discount rate for borrower-type households.

13whereis the (gross) marginal product of capital derived from the cost minimization problem,is the price level, andis the real cost of capital utilization per unit of physical capital. The

budget constraint of the both types of households are
,

1

1
where

,

is the wage rate for worker k.

2.6 Parameters
The parameters values are initialized based on past research. These are reported in Tables 1
to 4 and explained below.
Table 1 summarizes the parameter values estimated by policymakers with the help ofBayesian priors. Most of the prior mean is set equal to the posterior mean estimates obtained by
JPT.17 These parameter values are also used in generating data. This means that any deviation of
the point estimates from the data-generating values arise solely from model misspecification andnot from how the prior mean is set. Likewise, prior standard deviation is set equal to the posterior
standard deviation of JPT. Finally, the distributions of the priors also follow those in JPT.18
Table 2 summarizes the values of the common parameters across DGM and AM, which are
not estimated due to identification issues. Again, most of them follow JPT’s values. The fiscal
policy reaction coefficients ( ,) and policy weight parameters ( ,) that do not appear in

JPT are borrowed from Kliem and Kriwoluzky (2014) and Woodford (2003).

17 JPT estimated parameter values using the pre-crisis U.S. data from 1954Q3 to 2004Q4. The values are largely consistent withthe literature. The parameter value for the share of non-Ricardian households is obtained from Gali et al. (2007).
18
In principle, parameters that are strictly positive follow the gamma distribution. Those constrained between 0 and 1 follow thebeta distribution. The standard deviations of the shock processes follow the inverse-gamma distribution.

14

Table 3 summarizes the parameter values that appear only in the DGM. We prepare two sets
of values, which correspond to the pre-crisis and the crisis period. The uncertainty about borrowers’
investment project

and bankruptcy costare calibrated so that the implied changes ofbankruptcy rate, risk premium, and leverage ratio roughly match those observed during the recent
financial crisis.19 For the survival probability of lenders

and borrowers’ spending share of output

̅ / , we assume the values remain unchanged across periods.20 For the size of the risk premiumshock, we experiment with different values and check how the result of the forecast error

variance decomposition of the key endogenous variables (inflation, output, interest rate, risk
premium) changes before settling to current values.
Table 4 reports the initial set of policy rule parametersand. They are chosen so thatthey jointly minimize the quadratic loss function in Equation (2). Several points are worth noting.
First, the Taylor rule parameter for inflation satisfies the famous Taylor principle (1). Second,

output elasticities of tax rates are positive, meaning that the fiscal policy is countercyclical. Finally,bond elasticities of tax rates are positive, which implies long-run sustainability of the fiscal policy.

2.7 Equilibrium and Summary Statistics
The rational expectations equilibrium is obtained in three steps. First, we solve for the model's
deterministic steady state. Second, the model equations are log-linearized around the steady stateand stacked into a system of linear expectational difference equations. Lastly, the system is solved
to find the approximate equilibrium law of motion.

19
The targeted values are as follows: (1) the implied annualized business failure rate is 3.42% in the pre-crisis period and 5.64%
in the crisis period, (2) the annual risk premium is calibrated to be 100 basis points in the pre-crisis period and 150 basis points inthe crisis period, and (3) the leverage ratio declines from 5 in the pre-crisis period to 4 in the crisis period. Based on the chosen
values, the elasticity of the risk spread with respect to the leverage ratio becomes 0.0126 in the pre-crisis period and 0.0175 in thecrisis period. For more on value choices, see Yagihashi (2018).
20
The values are taken from BGG.

15

To confirm how the above model replicates the financial crisis in our simulation, we
conduct a stochastic simulation in which all economic shocks are activated at once. We generate
two sets of data, one corresponds to the pre-crisis period and the other for the crisis period. Table
5 reports the standard deviations of the ten pre-selected variables in each subsample. The standard
deviations of all variables rise across subsamples, most notably the capital-related variables. The
increase occurs as a result of the increase in the financial market friction and the larger volatilityof the risk premium shock. The increased volatility of the marginal product of capital, the returnon capital, and the risk spread is related to the increased volatility of the risk-free interest rate(+15%), which further causes the increase in the welfare loss (+47.3%).
Table 6 shows the 10-period ahead forecast error variance decomposition in the DGM forselected variables. To save space, we only report the result of the crisis period and the change fromthe pre-crisis period in the parenthesis. During the crisis period, the demand shock plays a largerrole for the key variables compared with the pre-crisis period (+2.6% points for the variance of
inflation, +1.7% points for output, and +4.1% points for interest rate). This primarily comes fromthe heightened role of the risk premium shock. We also see a reduced role of the MEI shock on
key variables, which partially offsets the positive contribution of the risk premium shock within
the demand shock category.

3 Results
3.1 Changes in Pseudo-True Parameters and Variance Decomposition
We first report how the estimated pseudo-true values for the model parameters (∗described in Section 2.1) change from the pre-crisis to the crisis period using the AM. Table 7
shows the result for the subset of parameters. First, among the 23 model parameters estimated, six

16

of them deviated from the pre-crisis values by more than 10% in absolute terms, which areinvestment adjustment cost (-44.3%), size of MEI shock (-28.6%), persistence of MEI shock(+19.1%), persistence of monetary policy shock (-15.1%), price indexation (+16.6%), and wage
indexation (+10.9%). The first four belong to the demand block of the model, while the last two
belongs to the supply block of the model. The most surprising outcome is that the size of the MEI
shock is falling (rather than rising) in the eyes of the policymakers. Since the volatility in key
model variables is rising as seen in Table 5, policymakers are likely to anticipate the size of thedemand shocks to rise. Turning to other model parameters, most of the changes in the pseudo-true
values estimated via the AM are within an economically plausible range. In that regard, there is
not enough evidence suggesting the AM performs poorly as a policy model.
Table 8 reports the forecast error decomposition result using the AM. The lack of the risk
premium shock in the AM means that the demand shocks only consists of the MEI shock, thepreference shock, the monetary policy shock, and the government spending shock. We observethat the contribution of the demand shock to inflation rises by 6.2% points, half of which are
attributed to the rise of the preference shock (+3.5%). The preference shock also plays a larger rolein explaining the overall volatility in output (+3.1%) and the interest rate (+6.2%). The increased
contribution of the preference shock in explaining the volatility of key variables in the AM closely
parallel with the increased contribution of the risk premium shock in explaining the volatility of
key variables in the DGM (see Table 6). In the AM, the preference shock effectively serves as a“stand-in” for the risk premium shock, thereby preventing policymakers from understanding thetrue nature of model misspecification.21

21

Our finding also corroborates with some of the research within the DSGE literature (e.g., Gali et al., 2012) that
calls our preference shock as the risk premium shock.

17

In sum, we argue that the policymaker would not see the economy much differently fromwhat happened in the DGM before and after the crisis. Hence, they would not see any problem tocontinue using the AM as their policy model.

3.2 Did the Policymakers Succeed in Stabilizing the Economy?
The next step is to examine whether policymakers can successfully stabilize the model
economy despite using the misspecified model as a guide. Table 9 summarizes the result. The
column labeled as “DGM outcome” reports the simulation outcome in which both policymakers
jointly choose coefficients

andso as to minimize the pre-specified quadratic welfare loss

function while using the DGM as their policy model. We treat this as our benchmark in evaluating
the other policy outcome.22 We find that under the benchmark, the welfare loss decreases by 6.3%
compared with the crisis period. This means that under the full-information disclosure setting, thepolicy shift results in economic stabilization as intended.
The column labeled as “AM outcome” reports the simulation outcome in which both
policymakers use the misspecified model and shift their policy independently. The measured
welfare loss is now 9.5% higher compared to the crisis period, meaning that the model economy
has destabilized due to the policy shift. The welfare loss is 16.9% higher than what would havebeen achieved under the “DGM outcome”.
To examine what exactly causes the destabilization of the model economy, we examine twomore cases. The first case is when the policy model is misspecified, but the model parameters usedin calculating the optimized policy coefficients are set to the DGM values (“case (a)”). The second

22
Under this scenario, the newly chosen interest rate rule becomes slightly anti-inflationary (higher
period, whereas the capital tax rate rule becomes less responsive to output and bond (lower,
pre-crisis period. The actual values of these policy coefficients are available upon request.

) relative to the pre-crisis, and) relative to the18case is when the policy model is correctly specified but parameters are set to the biased estimates
based on the AM (“case (b)”). Case (a) shows that the welfare loss becomes 26.4% higher
compared with the crisis period, whereas case (b) shows that the welfare loss decreases by 3.1%
relative to the crisis period. While in the latter case the loss is still higher than what would havebeen achieved under the DGM outcome, at least the policymakers are partially successful instabilizing the economy.
In sum, we find that designing a policy shift using a misspecified policy model, as opposed
to using the biased parameters, costs more in the case of credit channel misspecification. This
corroborates with our earlier finding that parameter changes seem inconsequential from thepolicymaker’s standpoint.

3.3 Who Should be More Aware of Model Misspecification?
As we mentioned in the introduction, most of the existing credit channel models used inpractice are those developed by the central banks. Motivated by this observation, we now ask thefollowing question: if either the monetary or the fiscal policy institution uses the DGM while theother continues to use the AM, would the above outcome improve? We examine this question
under both “no prediction case” and “predicted outcome case” as described in Section 2.3. Table
10 shows the result.
First, we examine the case of “no prediction case”. We find that the welfare loss increases
by 0.2% relative to the crisis period when the fiscal policymaker uses the DGM (Table 10 column(1)), whereas the welfare loss increases by 6.2% when the monetary policymaker uses the DGM(Table 10 column (2)). Both outcomes have improved compared with the case in which both
institutions use the AM as their policy model (-8.5% and -3.0%, respectively). Yet, in both cases

19the policy shift results in further destabilization of the model economy from the crisis period. Thismeans that the cost of the credit channel misspecification is smaller but still present.
Next, we examine the case of “predicted outcome case”, i.e. assume that the policy institution
equipped with the DGM can predict how the other institution shifts its policy based on the AM.
When the fiscal policymaker uses the DGM and the monetary policymaker uses the AM, thewelfare loss decreases by 3.1% relative to the crisis period (column (3)). When the monetary
policymaker uses the DGM and the fiscal policymaker uses the AM, the welfare loss increases
slightly by 1.3% relative to the crisis period (column (4)). Both results improve upon the “noprediction case”, which makes sense because the institution that uses the DGM knows exactly how
the other institution would respond to the financial crisis and therefore it can design a better policy
shift of its own. In conclusion, only when the fiscal policy is equipped with the DGM, the policy
shift would stabilize the economy (Table 10, Column (3)).
In reality, it is common that the monetary policymaker uses DSGE models that featurefinancial market friction whereas the fiscal policymaker does not. Our result seems to suggest thatmisspecification in the credit channel is at least as important for the fiscal policymaker as it is forthe monetary policymaker. The result also indicates that when shifting a policy during a financial
crisis, forming a prediction regarding to what the other institution does can be quite beneficial.

4 The Role of Judgement
In practice, policymakers rarely take the model outcome at face value because they are aware of
the fact that DSGE models are approximation to the complicated reality. As such, policymakers

20would first check whether model outcomes are indeed consistent with his/her own knowledge
about the state of the economy and apply further judgment if deemed necessary.23
In this section we examine whether applying judgement to the result of the parameter
estimates could be beneficial for the policy outcome under the credit channel misspecification. In
Section 3.1, we found that six model parameters showed large changes during the crisis (10% andover), which did not actually occur in the data-generating process. Here, we specifically focus on
those related to the MEI shock, which is often interpreted as a proxy for the financial market(Justiniano et al., 2011). According to our earlier estimation, both the size and persistence of the
MEI shock changed notably during the crisis (-28.6%, +19.1%, respectively). Furthermore, theobserved decrease of the size of the MEI shock is counterintuitive, given that the risk premium
shock has increased in our simulation. While Equation (1) tells us that all parameter changes are
simply an artifact arising from the KLIC optimization and therefore have no structuralinterpretation, policymakers who are not aware of the mechanism may be confused by theseemingly inconsistent outcome between the observed increase in the volatility of the financial
market variables and the reduced size of the MEI shock. One practical solution is to partially ignore
the estimation outcome regarding the MEI shock.

4.1 Judgement Exercised by Both Policymakers
Parallel to Section 3, we start our analysis by assuming that both policymakers use the AM
as their policy model. Furthermore, we assume that both policymakers can simultaneously adopt
the same combination of parameter values for the size and persistence of the MEI shock that fall23
For example, Bank of England has its own pre-specified procedure (“misspecification algorithm”) in which bank staff examine
possible ways that their policy model (COMPASS) may mislead them in forming an official forecast (Burgess et al., 2013). An
alternative approach is to introduce a minimax-type robust control approach to the policymaking process, e.g., “slant” the modeloutcome such that the policymaker is best prepared for the worse outcome that could possibly arise from the policy model(Hansen and Sargent, 2008).

21

within the pre-crisis and crisis period estimates. Figure 1 presents the contour map of the welfare
loss in which the size of the shock is on the vertical axis and persistence is on the horizontal axis.
The dot in the lower-right corner represents the combination of the estimates for the pre-crisis
period (10010.29 andthe crisis period (1000.68), whereas the dot in the upper-left corner shows those for7.35 and0.81).

We find that if both policymakers stick to the original estimates (lower-right corner), thewelfare loss would be as high as 3.752. This is much worse than the loss in the crisis period (3.039)
and 13% higher than the welfare loss when the estimates during the crisis period were used indesigning the policy shift (3.327). Within this contour map, the lowest loss is achieved whenpolicymakers adopt the new estimates for the persistence of MEI shock but mostly ignore thechange in the size of the MEI shock (2.967). The loss associated with this judgment is 2% lower
than the crisis period and thus implies economic stabilization through policy shift.
The key finding from this exercise is that policymakers’ judgement of parameter changes
seem to matter greatly in terms of subsequent policy outcome. If judgement is exercised carefully,
it can help policymakers in stabilizing the economy and overcome the credit channel
misspecification.

4.2 Judgement Exercised by One PolicymakerIn this subsection, we repeat the above exercise by first assuming that only the monetary
policymaker uses the misspecified AM while the fiscal policymaker uses the DGM.24 Figure 2
shows the resulting contour map. We notice that the contour map looks much simpler in structurecompared to Figure 1. Also, the loss is not much different whether the crisis estimates or the pre24
We assume that the fiscal policymaker uses the DGM and optimize their policy independently (i.e. no prediction of monetary
policy shift).

22

crisis ones (3.045 as opposed to 3.078) are used. The loss would further reduce if the monetary
policymaker uses the new estimate for the size of the MEI shock while ignoring the persistence ofthe MEI shock. The associated loss (2.963) is very similar to the case when both policymakers use
the AM and apply judgement (2.967, see Figure 1).
Next, we examine the case in which the fiscal policymaker uses the AM and the monetary
policymaker uses the DGM. Figure 3 shows the result. Comparing with Figure 2, the loss varies
more markedly depending on whether the fiscal policymaker uses the crisis period estimates (4.101)
or stick with the pre-crisis estimates (3.226) when choosing the new policy. The loss is minimized
when the fiscal policymaker sticks to the old estimate for the size of the MEI shock while adopting
the new estimate for the persistence of the MEI shock. The associated loss (2.852) is almost
identical to the loss realized when both policymakers use the DGM as the policy model (2.847,
see Table 9).
In sum, we find that judgment regarding to the MEI shock parameters have different policy
implications for each policymaker. The monetary policymaker’s judgment about the MEI shock
estimates had only minor impact on policy outcome as long as the fiscal policymaker used theDGM. In contrast, the fiscal policymaker’s judgement about the MEI shock, when the monetary
policymaker uses the DGM, had a larger impact on policy outcome. This finding seems to point
to the importance of using the correctly-specified credit channel model for fiscal policymaking,consistent with earlier findings in Section 3.3.

5 Conclusion
This paper examined the cost of policymaking in DSGE models when model misspecification
occurs in the credit channel for both the monetary and fiscal policymakers. The financial

23

accelerator model of Bernanke et al. (1999) was chosen as the data generating model and thesimpler approximating model without the financial market friction and the risk premium shock
was used as the policy model. We simulated a financial crisis that involved changes in the degreeof financial market friction and a more volatile risk premium. Following the crisis, both monetaryand fiscal policymakers estimated model parameters and shifted their policy accordingly to combat
the crisis using the approximating model.
Our main findings are as follows. First, while the model misspecification does not affect muchon how policymakers perceives the crisis, the newly adopted policy based on the approximating
model would cause further destabilization of the economy. Second, the destabilization of theeconomy could be prevented if the fiscal policymaker is equipped with the correctly-specified
DSGE model and chooses its new policy while taking into account decision of the monetary
policymaker. Third, we find that the destabilization of the economy could be prevented if both
policymakers can partially ignore the increase in the size of the marginal efficiency of investment
shock that is observed in the approximating model during the crisis period.
While previous literature has studied DSGE model misspecification with the credit channel,
none of them has examined policy implications while explicitly considering the interaction
between monetary and fiscal policymakers. The novelty of our finding is that model
misspecification seems to be more important for the fiscal policymaker than it is for the monetary
policymaker. This finding goes against the common practice that most of the credit channel DSGE
models are used by central banks but not by fiscal policy institutions. Our paper suggests that fiscal
policymakers should consider using a DSGE model that incorporates the credit channel.
The limit of this paper is that we adopted a very simplified optimization process inpolicymaking. One possible extension is to experiment with different policy objectives. For24example, if we were to introduce term structure of the interest rate into our model, we could include
stabilization of the long-term interest rate in policymaking, which is more relevant for public debt
management. Another extension is to add government spending rules such as those used by theEuropean Commission (Albonico et al., 2017). We leave them for future research to explore.

25

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28

Table 1: Estimated Parameters in the New Keynesian Approximating Model
Prior
Mean

Prior
St.Dev.

Preference and Technology Parameters
0.78
0.04
Consumption habit
3.79
0.76
Inverse Frisch elasticity
5.30
1.01
Elast. Of capital utilization
2.85
0.54
Investment adjustment cost ′′
0.84
0.02
Calvo prices
0.24
0.08
Price indexation
0.70
0.05
Calvo wages
0.11
0.03
Wage indexation
0.50
0.10
Share of non-Ricardian household
Shock-related Parameters
0.14
0.06
Persistence of monetary policy shock
0.95
0.01
Persistence of technology shock
0.95
0.01
Persistence of government spending shock
0.72
0.04
Persistence of MEI shock
0.94
0.02
Persistence of price markup shock
0.95
0.01
Persistence of wage markup shock
0.67
0.04
Persistence of preference shock
0.22
inf
Size of monetary policy shock 100
0.88
inf
Size of technology shock 100
0.35
inf
Size of government spending shock 100
6.03
inf
Size of MEI shock 100
0.14
inf
Size of price markup shock 100 ∗0.20
inf
Size of wage markup shock 100 ∗0.04
inf
Size of preference shock 100 ∗Distribution
Beta
Gamma
Gamma
Gamma
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Beta
Inv-Gamma
Inv-Gamma
Inv-Gamma
Inv-Gamma
Inv-Gamma
Inv-Gamma
Inv-Gamma

Note: The MEI shock refers to the marginal efficiency of the investment shock. The prior mean in the second
column is set equal to the parameter values that are used for data generation. All model parameters are basedon quarterly frequency.

29

Table 2: Calibrated Parameters Common to the DGM and AM

Discount factor
Capital share
SS price markup
SS wage markup
MA parameter of price markup shock
MA parameter of wage markup shock
SS work hours (in log)
Government spending share of output ̅ /Depreciation rate
Monetary policy: smoothing
Capital tax policy: smoothing
SS capital tax rate ̅Labor tax policy: smoothing
SS labor tax rate ̅
Policy weight: output
Policy weight: interest rate

Value

Source0.9904
0.17
0.23
0.15
0.77
0.91
0.38
0.21
0.025
0.82
0.81620.35720.85770.2343
0.048
0.236

JPT
JPT
JPT
JPT
JPT
JPT
JPT
JPT
JPT
JPT
KK
KK
KK
KK
Woodford (2003)
Woodford (2003)

Note: DGM refers to the data generating model and AM refers to the approximating model. For thesize of the risk premium shock, we prepare two values that correspond to the pre-crisis period and thecrisis period. In the “Source” column, JPT stands for Justiniano et al. (2010) and KK stands for Kliem
and Kriwoluzky (2014). All parameters are in quarterly frequency.

Table 3: Calibrated Parameters in the DGM

Uncertainty about borrowers’ investment project
Bankruptcy cost
Elasticity of the risk spread w.r.t. leverage ratio
Survival probability of lender
Borrower spending share of output ̅ /Persistence of risk premium shock
Size of risk premium shock 100

Pre-crisis

Crisis0.093
0.039
0.0126
0.9724
0.01
0.50
0.20

0.129
0.043
0.01750.9724
0.01
0.50
1.00

Note: For the uncertainty about borrowers’ investment project, bankruptcy cost, and elasticity of therisk spread with respect to the leverage ratio, we prepare two values that correspond to the pre-crisisand the crisis period. The survival probability of the lender is calibrated based on Bernanke et al.
(1999), while other parameters are calibrated based on Yagihashi (2018). All parameters are inquarterly frequency.

30

Table 4: Initial Policy Coefficients Calculated Under the DGM
ValuesMonetary Policy Rule Parameters
5.75
Monetary policy.: inflation
23.62
Monetary policy.: output
74.19
Monetary policy.: output
Fiscal Policy Rule Parameters392.94
Capital tax policy: output
48.82
Capital tax policy: output
0.38
Capital tax policy: output
953.32
Labor tax policy: output
86.86
Labor tax policy: output
0.05
Labor tax policy: output
Note: The policy parameters are obtained from the data generated by the DGM and calculated using
the same model so as to minimize the quadratic welfare loss function in Equation (2) subject to model
equations.

Table 5: Standard Deviations of the Generated Variables Under the DGM
Precrisis

CrisisChangeInflation Π
OutputInterest rate
Investment
CapitalMarginal product of capital
Return on capital
Risk spread
Labor
Wage

0.316
0.042
1.032
34.0558.811
10.352
4.321
1.009
4.365
3.083

0.324
0.043
1.187
40.02312.05613.157
5.869
1.522
4.675
3.562

+3%
+3%
+15%
+18%
+37%
+27%
+36%
+51%
+7%
+16%

Welfare loss

2.063

3.039

+47.3%

Note: Standard deviations and welfare losses are obtained based on observations in the DGM.

31

Table 6: Share of the 10-period Ahead Forecast Error Variance Explained by Structural Shocks:
DGM Case(1) Demand
shocksInflation Π
OutputInterest rate

MEI

Risk prem. Preference

Policy(2) Supply
shocks

12.7%

5.2%

3.5%

1.4%

2.6%

87.3%

(+2.6%)(-0.6%)(+3.4%)(-0.1%)(-0.1%)(-2.6%)

52.1%

30.4%

4.4%

4.7%

12.5%

47.9%

(+1.7%)(-1.8%)(+4.3%)(-0.2%)(-0.5%)(-1.7%)

73.9%

38.2%

16.9%

5.6%

13.1%

26.1%

(+4.1%)(-8.9%)(+16.3%)(-1.0%)(-2.3%)(-4.1%)

Note: The result is based on the 10-period ahead forecast error variance decomposition, measured during thecrisis period. Policy parameters are set to baseline (pre-crisis) values. Demand shocks consist of the MEI
shock, the risk premium shock, the preference shock, and two policy shocks (monetary plus government
spending). Supply shocks consist of technology shock, price markup shock, and wage markup shock.

Table 7: Change of Pseudo-true Values from Pre-Crisis to Crisis Period
Parameters

Changes
Change of 10% or more in absolute value- 44.3%, from 6.91 to 3.85
Inv. adjustment cost ′′- 28.6%, from 10.29 to 7.35
Size of MEI shock 100+19.1%, from 0.68 to 0.81
Persistence of MEI shock+16.6%, from 0.15 to 0.18
Price Indexation- 15.1%, from 0.14 to 0.12
Persistence of m-policy shock+10.9%, from 0.12 to 0.13
Wage indexation
Change of more than 5% and less than 10% in absolute value+7.5%, from 0.69 to 0.74
Persistence of preference shock- 6.0%, from 3.59 to 3.38
Inverse Frisch elasticity

Note: The table is produced based on Appendix Tables A.2 and A.3. Change are in terms of pseudotrue values between pre-crisis and crisis period.

32

Table 8: Share of Variance Explained by Structural Shocks During the Crisis Period: AM Case
(1) Demand
shocksInflation Π
OutputInterest rate

MEI

Preference

Policy(2) Supply
shocks

20.0%

13.4%

5.1%

1.4%

80.0%

(+6.2%)(+3.5%)(+3.5%)(-0.7%)(-6.2%)

52.0%

34.1%

8.4%

9.5%

48.0%

(-1.0%)(-2.0%)(+3.1%)(-2.0%)(+1.0%)

79.7%

57.8%

12.4%

9.5%

20.3%

(+3.3%)(+0.7%)(+6.2%)(-3.6%)(-3.3%)

Note: The result is based on the 10-period ahead forecast error variance decomposition. Policy
parameters are set to baseline (pre-crisis) values. Demand shocks consist of the MEI shock, the risk
premium shock, the monetary policy shock, the government spending shock, and the preference
shock. Supply shocks consist of the technology shock, the price markup shock, and the wage markup
shock.

Table 9: The Effect of Policy Shift When Both Policy Institutions Use the Same Policy Model(1) Model(2) Parameters

Welfare loss WL(relative to crisis period)(relative to DGM outcome)(1) DGM
outcome(2) AMoutcomeCase (a)Case (b)

DGM
DGM

AM
AM

AM
DGM

DGM
AM

2.847

3.327

3.841

2.945

(-6.3%)(0.0%)(+9.5%)(+16.9%)(+26.4%)(+34.9%)(-3.1%)(+3.4%)

Note: Column (1) shows the case in which both policy institutions use the DGM as their policy modeland jointly shift the policy coefficients so as to minimize the welfare loss. Column (2) shows the casein which both policy institutions use the AM as their policy model while adopting the estimatedpseudo-true values as the model parameter. Case (a) is when both institutions use the AM as theirpolicy model while adopting the true parameter values when designing the policy shift. Case (b) iswhen both institutions use the DGM as their policy model while adopting the estimated pseudo-true
values for the model parameters.

33

Table 10: The Effect of the Policy Shift When One Policy Institution Uses the AM and the Other
Uses the DGM, with and without prediction(1) Monetary policymaker(2) Fiscal policymaker(3) Prediction of AM outcome

Welfare loss WL(relative to crisis outcome)(relative to both-AM outcome)(relative to DGM outcome)

(1)

(2)

(3)

(4)

AM
DGM
no

DGM
AM
no

AM
DGM
yes

DGM
AM
yes

3.045

3.226

2.943

3.079

(+0.2%)(-8.5%)(+6.9%)(+6.2%)(-3.0%)(+13.3%)(-3.1%)(-11.5%)(+3.4%)(+1.3%)(-7.5%)(+8.1%)

Note: Columns (1) and (2) show the cases in which one of the policy institutions uses the DGM as their policy
model and shifts the policy while assuming that the other institution keeps the policy coefficients the same asin the pre-crisis period. Columns (3) and (4) repeat the same exercise, with the additional assumption that thepolicy institution that uses the DGM forms a prediction of the policy shift of the other institution that uses theAM when designing its own policy shift.

34Figure 1 Contour Map of Welfare Loss: Both Institutions Distrust the Parameter Estimates

Note: Each line in the figure represents the level of welfare loss associated with the combination ofparameter values for the size and persistence of the MEI shock adopted by the policymaker that uses
the AM. The dot described as “minimum” represents the combination of parameter values that achieve
the lowest welfare loss in the entire parameter space considered.

35

Figure 2 Contour Map of Welfare Loss: Monetary Policymaker Uses AM and Distrusts theParameter Estimates, Fiscal Policymaker Uses DGM

Note: Each line in the figure represents the level of welfare loss associated with the combination ofparameter values for the size and persistence of the MEI shock that is adopted by the policymaker thatuses the AM. The dot described as “minimum” represents the combination of parameter values that
achieve the lowest welfare loss in the entire parameter space considered.

36

Figure 3 Contour Map of Welfare Loss: Fiscal Policymaker Uses AM and Distrusts theParameter Estimates, Monetary Policymaker Uses DGM

Note: Each line in the figure represents the level of welfare loss associated with the combination ofparameter values for the size and persistence of the MEI shock that is adopted by the policymaker thatuses the AM. The dot described as “minimum” represents the combination of parameter values that
achieve the lowest welfare loss in the entire parameter space considered.

37

Appendix
Table A.1: Pseudo-true Values of Parameters Under Misspecified New KeynesianApproximating Model (AM)(a) Preference/technology Parameters

Consumption habit
Inverse Frisch elasticity
Elast. Of capital utilization
Investment adjustment cost ′′Calvo prices
Price indexation
Calvo wages
Wage indexation
Share of non-Ricardian HH(1)
Precrisis(2)
CrisisChange0.85(0.01)
3.59(0.16)
5.56(0.11)
6.91(0.47)
0.85(0.00)
0.15(0.02)
0.72(0.01)
0.12(0.02)
0.48(0.01)

0.84(0.01)
3.38(0.16)
5.68(0.13)
3.85(0.34)
0.84(0.00)
0.18(0.02)
0.74(0.01)
0.13(0.03)
0.48(0.01)

-1.0%
-6.0%
+2.1%
-44.3%-1.1%+16.6%+2.9%+10.9%+1.4%

38

Table A.2: Pseudo-true Values of Parameters Under Misspecified New KeynesianApproximating Model (AM), continued(b) Shock-related Parameters

Persistence of monetary policy shock
Persistence of technology shock
Persistence of government spending shock
Persistence of MEI shock
Persistence of price markup shock
Persistence of wage markup shock
Persistence of preference shock
Size of monetary policy shock 100
Size of technology shock 100
Size of government spending shock 100
Size of MEI shock 100
Size of price markup shock 100∗

Size of wage markup shock 100∗

Size of preference shock 100∗(1)
Precrisis(2)
CrisisChange0.14(0.02)
0.97(0.00)
0.95(0.00)
0.68(0.01)
0.99(0.00)
0.95(0.00)
0.69(0.01)
0.21(0.00)
0.95(0.01)
0.35(0.00)
10.29(0.61)
0.12(0.00)
0.20(0.00)
0.04(0.00)

0.12(0.02)
0.97(0.00)
0.95(0.00)
0.81(0.01)
0.98(0.00)
0.95(0.00)
0.74(0.01)
0.22(0.00)
0.97(0.01)
0.34(0.00)
7.35(0.38)
0.12(0.00)
0.20(0.00)
0.03(0.00)-15.1%-0.4%-0.5%+19.1%
-0.5%
-0.3%
+7.5%
+3.9%
+1.5%
-0.5%
-28.6%
+1.6%
+2.0%
-1.0%

Note: The estimates in each column are obtained from the data generated by the financial accelerator data
generating model (DGM) and estimated using the New Keynesian approximating model (AM). Numbers in theparenthesis are standard errors. The MEI shock refers to the marginal efficiency of the investment shock.

39