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Dynamics of Open Economy Business Cycle Models: "Understanding the Role of the Discount Factor"

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This paper examines the dynamic implications of different preference formulations in open economy business cycle models with incomplete asset markets. In particular, we study two preference formulations: a time separable preference formulation with a fixed discount factor, and a time non-separable preference structure with an endogenous discount factor. We analyze the moment implications of two versions of an otherwise identical open economy modelone with a fixed discount factor and the other with an endogenous discount factorand study impulse responses to productivity and world real interest rate shocks. Our results suggest that business cycle implications of the two models are quite similar under conventional parameter values. We also find the approximation errors associated with the solutions of these two models are of the same magnitude.
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Dynamics of Open Economy Business Cycle Models:
“Understanding the Role of the Discount Factor” *




Sunghyun Henry Kim** and M. Ayhan Kose**








Abstract: This paper examines the dynamic implications of different preference
formulations in open economy business cycle models with incomplete asset markets. In
particular, we study two preference formulations: a time separable preference formulation
with a fixed discount factor, and a time non-separable preference structure with an
endogenous discount factor. We analyze the moment implications of two versions of an
otherwise identical open economy modelone with a fixed discount factor and the other
with an endogenous discount factorand study impulse responses to productivity and world
real interest rate shocks. Our results suggest that business cycle implications of the two
models are quite similar under conventional parameter values. We also find the
approximation errors associated with the solutions of these two models are of the same
magnitude.
Keywords: business cycle dynamics, fixed discount factor, endogenous discount factor, nonstationarity.
JEL classification: F4, E3


* We would like to thank William A. Barnett, an anonymous Associate Editor, and two anonymous referees for
providing very detailed and helpful comments which significantly improved the paper. We are grateful to Marianne
Baxter, William Blankenau, Mario Crucini, Narayana Kocherlakota, Robert Kollmann, Jim Nason, Fabrizio Perri, and
Kei-Mu Yi for their helpful suggestions. An earlier version of this paper was presented at Tufts University, 1999
Computing in Economics and Finance Conference at Boston College, 2000 Midwest Macroeconomics Meetings at
University of Iowa. We would like to thank seminar and conference participants for their feedback. The usual
disclaimer applies.
** Graduate School of International Economics and Finance, Brandeis University, Waltham MA, 02454. E-mail (Kim):
hkim@brandeis.edu, e-mail (Kose): akose@brandeis.edu, phone (Kim): (781) 736-2268, phone (Kose): (781) 736-
2266.

1. Introduction
There have been two popular preference formulations employed in infinite-horizon open economy
Real Business Cycle (RBC) models under incomplete asset markets: time separable preferences with a fixed
discount factor, and time non-separable preferences with an endogenous discount factor.1 The former
formulation is the “standard” one that is widely used in closed and open economy RBC models, under
complete and incomplete asset markets. However, it is by now well known that with this formulation, when
the models are solved using the usual linear approximation methods, it is not possible to generate stationary
state variables and a well-defined wealth distribution in an open economy setting under incomplete markets.2
This problem has led several researchers to employ the latter formulation, which generates well-defined
steady state dynamics in these models.
How can we justify the fact that a number of researchers have employed the fixed discount factor
formulation despite the well-known problems associated with steady state dynamics in open economy RBC
models under incomplete asset markets? Three potential reasons emerge for the widespread use of this
formulation. First, while the issue of the existence of a well-defined long-run wealth distribution might be
important for some economic experiments, there might be no reason to believe that these two preference
formulations generate significantly different model dynamics along the dimensions examined by typical
RBC studies. To be more specific, it might be the case that the models with these two preference
formulations produce very similar moments and impulse responses, which are the main interests of these
studies.
Second, considering that most models in this literature are solved using linear approximation
methods, potential additional accuracy gains from employing an endogenous discount factor might be
insignificant. In other words, while the true solution of the fixed discount factor model, which we call FDM
(exact), and the true solution of the endogenous discount factor model, which we call EDM (exact), might
exhibit some differences, it is not clear whether the approximate solutions of these two models, which we
call FDM (approximate) and EDM (approximate), are different under incomplete markets.
Third, some features of the endogenous discount factor formulation might not be desirable in a
representative agent business cycle model. For example, the endogenous discount factor formulation implies
that agents become more impatient as they become wealthier, and there is a steady state utility level that
relies on a predetermined saving target (see Senhadji (1995) and Daniel (1997)). Another undesirable

1 Baxter and Crucini (1995), Baxter (1995), Rebelo and Vegh (1995), Correia, Neves and Rebelo (1992, 1995), Kollman
(1996, 1998, 2000), Crucini (1999), Arvanitis and Mikkola (1996), van Wincoop (1996), van Wincoop and Marrinan
(1999), Kouparitsas (1997), Sadka and Yi (1996), Blankenau, Kose, and Yi (2001), and Kose and Riezman (2001)
employ the standard time separable preferences with a fixed discount factor in their models. Mendoza (1991, 1995),
Karayalcin (1995), Uribe (1997), Schmitt-Grohe (1998), and Cook and Devereux (2000) use the Uzawa-Epstein type
time nonseparable preferences with an endogenous discount factor.
2 As we discuss in detail in section 2, there are some methods to deal with these problems in open economy models
under incomplete markets.

1

property of the EDM is that it is not possible to examine the state dependent steady state level of net foreign
assets because the EDM forces consumption to behave in such a way that the net foreign asset position goes
back to its initial steady state. Moreover, since a number of macroeconomic time series are nonstationary, it
might not be advantageous to have a model generating stationary variables (see Correia, et al. 1995).3
Despite the wide use of these two preference formulations, there has yet been no rigorous
examination of their impact on the cyclical dynamics of open economy RBC models. The objective of this
paper is to provide a comprehensive comparison of the behavior of an open economy RBC model with
incomplete asset markets under the fixed discount factor with that under the endogenous discount factor. In
particular, we consider two versions of an otherwise identical small open economy RBC model, one with a
fixed discount factor (FDM), and the other with an endogenous discount factor (EDM), and study the
moment implications and impulse responses of these models. We provide empirical support for the three
reasons above and argue for the similarity between FDM (exact) and EDM (exact) based on the similarity
between FDM (approximate) and EDM (approximate), which we systematically study in this paper. 4
Section 2 starts with a brief discussion of the problem associated with the steady state dynamics in
open economy RBC models with incomplete asset markets. Then, we present the two models and their
calibration and parameterization. In section 3, we provide empirical support for the three justifications
described above. We analyze the policy functions generated by the two models in section 3.1. Our
discussion in sections 2 and 3.1 makes transparent the arguments regarding the deterministic and stochastic
steady state dynamics of the two models. We find that while the net foreign asset series in the FDM follows
a unit root process, this series exhibits a near unit root behavior in the EDM. More importantly, the
coefficients in the policy functions generated by the two models display minimal differences under
conventional parameter values. In section 3.2, we examine the second moment implications pertaining to
business cycles and find that the two models generate almost identical business cycle moments. Section 3.3
presents the impulse responses to productivity and the world interest rate shocks. While some small
quantitative differences exist between the impulse responses produced by the two models, qualitative
implications are identical. In section 3.4, we compare the distributions of variables produced by the two
models using the Kolmogorov-Smirnov test statistic. The test results suggest that these empirical
distributions are not statistically different. In section 3.5, we evaluate the approximation errors associated

3 Daniel (1997) notes that it is “intuitively unappealing” to have wealthier agents who are more impatient than less
wealthy agents in this utility formulation. Senhadji (1995) criticizes the use of endogenous discount factor since the
representative agent must save enough to reach a saving target in order to attain a fixed utility level determined by the
steady state. Correia, et al. (1995), after noting that consumption, the net exports, and the net foreign assets are
nonstationary in the data, claim that the stationarity of these variables induced by the non-separable preference
formulation is not “necessarily a desirable property.” (p. 1100)
4 To be more specific, our ultimate objective is to argue for the similarity between the exact solutions of these two
models based on the similarity between their approximate solutions. Our findings suggest that the approximation errors
are quite small implying that the results from these approximate solutions can potentially apply to the exact solutions of
these models.

2

with the solutions of these models. We find that while the solution of the FDM results in slightly larger
approximation errors than that of the EDM, the errors are quite small. We provide a brief conclusion in
section 4.

2. The Model
Before getting into the details of the model economies, we provide a brief discussion of the problem
associated with the steady state. Consider the standard time separable preference formulation in an infinite-
horizon open economy model with incomplete asset markets. In a deterministic setting, the steady state or
the long-run wealth depends on the initial conditions of the economy and the steady state is compatible with
any level of net foreign assets.5 In a stochastic environment, since the net foreign asset series follows a unit
root process, the model generates nonstationary variables implying the absence of a well-defined stochastic
steady state.6 In other words, certain model variables do not return to their initial steady state values when
the model is subjected to a temporary shock. Hence, the long-run wealth of the economy changes with the
state of nature, i.e. the long-run wealth distribution is not well defined.
Researchers have developed several methods that can resolve the steady state issues associated with
the fixed discount factor formulation.7 As mentioned above, one popular alternative is to employ the Uzawa-
Epstein type time non-separable preferences with an endogenous discount factor. Unlike the fixed discount
factor model, the endogenous discount factor model generates stationary net foreign asset series and, in turn,
other state variables become stationary. Moreover, the endogenous discount factor model generates a well-
defined stochastic steady state at which, under certain conditions, a unique level of net foreign assets is
attained implying that the long-run wealth distribution of the economy is also well defined.

5 We consider the case when the time preference is equal to the world interest rate. Otherwise, no deterministic steady
state exists. If the world interest rate is greater (smaller) than the time preference rate, agents permanently accumulate
(deplete) foreign assets. These issues are first discussed in Helpman and Razin (1982). Mendoza and Tesar (1998)
provide a detailed discussion of the steady state issues in a deterministic model with incomplete asset markets.
6 The stochastic steady state of a variable is defined as its expected mean. The fact that our approximate solution
features a unit root in asset holdings does not necessarily imply that the exact solution of the model also has a unit root.
The stochastic steady state of the model might be well defined, but it is not possible to capture this steady state by the
approximate solution method. It is not possible to provide an exact solution of the incomplete market models with the
fixed discount factor formulation unless the state space of asset holdings is bounded.
7 Heathcote and Perri (2000) impose a quadratic adjustment cost on bond holdings to produce stationary asset series.
Cardia (1991) uses the uncertain lifetime approach advanced by Blanchard (1985) in her small open economy model.
Harjes (1997) assumes that the world real interest rate depends on the net foreign assets, and Bruno and Portier (1995)
assume that net foreign assets negatively affect the households’ utility in their small open economy models. Senhadji
(1998) considers a set-up with a downward sloping export demand function. It is also possible to produce stationary
equilibria in models with incomplete asset markets by introducing limits on the level of asset holdings (explicit bounds
as in Huggett (1993) or implicit bounds as in Levine and Zame (1996, 1999) and Kubler and Schmedders (2000)), or by
introducing endogenous solvency constraints (see Alvarez and Jermann (1999)), or enforcement constraints (see Kehoe
and Perri (2000)).

3

To evaluate the impact of the discount factor on the dynamics of business cycles, we study a small
open economy RBC model in which agents produce an internationally tradable good using labor and capital.8
There are two shocks in the model: a productivity shock and a world real interest rate shock. Agents have
access to world financial markets in which they can buy and sell one-period risk free bonds at a stochastic
world real interest rate. We solve the model using a linear approximation method and choose the parameter
values that provide both versions of the model have the same steady state. We calibrate the model to
Canada, an economy that has been extensively studied in the small open economy RBC literature. In section
2.1, we present the model with a fixed discount factor. In section 2.2, we analyze the same model with an
endogenous discount factor. Section 2.3 explains the derivation of the steady state and calibration of the
model.
2.1. The Fixed Discount Factor Model
The optimization problem of the representative agent is the following:
1 σ

w


t n
c
t 



w
1
max
U (c , n )
t
=
t
t
0
E
β 

, σ > 1, w >1,
,
,
,

1
t
b
t
n
t
i
t
c
−σ
t =0
(1)
.
s to c
i
b
y
b
r

t + t +
t =
t +
1
(
t
+
),
1

t 1

α

(2)
1
α
y = z k
n ,
t
t
t
t
i
(3)
k + = 1
( − δ )k + φ ( t )k ,
t 1
t
t
kt
in the momentary utility function ct is consumption, nt is labor hours, w is the intertemporal elasticity of
substitution in labor supply, β is the fixed discount factor, and σ is the household’s coefficient of relative risk
aversion. Our momentary utility formulation implies that the elasticity of substitution associated with leisure
is zero.9 In resource constraint (1), it is investment, bt is the net foreign assets at the end of the period t, rt-1 is
the stochastic world real interest rate from period t-1 to period t, and yt is output. kt is the domestic capital
stock at the beginning of the period t, zt is productivity shock, and α governs the share of income accruing to

8 See Baxter (1995) and Backus, Kehoe, and Kydland (1995) for a survey of open economy RBC models and their use
in studying the sources and transmission of international business cycles.
9 This utility function is introduced by Greenwood, Hercowitz, and Huffman (1988) and is widely used in the open
economy RBC models. Correia, et al. (1995) and Crucini (1999) compare the dynamic implications of this utility
function with those of the Cobb-Douglas utility function, both with a fixed discount factor. We do not adopt the Cobb-
Douglas preference structure because as shown by Correia, et al. (1995) a small open economy model with the Cobb-
Douglas utility function is unable to match the volatility of consumption and the countercyclical behavior of net exports
in real data.

4

labor in constraint (2) that describes the production function.10 In constraint (3), δ denotes depreciation rate
and φ (.) represents the standard adjustment cost function with φ (.) > 0 , φ )
(. ′ > 0 , and φ )
(. ′ < 0 (see
Baxter and Crucini (1993)).
Substituting (2) into (1), the first order conditions of this optimization problem are given as
−σ
w

n
(4)
c :
t
c
= λ ,
t
t
t




w


(5)
n : w
n = y
α ,
t
t
t
i
(6)
i : λ = µ φ ( t

),
t
t
t
kt
y
i
(7)
k
: µ
E
β λ
α
µ g

t =
{
1
(
t
t
− ) t 1+ +
( t 1
+ )},
t 1
+
1
+
t 1
+
k
k
t 1
+
t 1
+
i
i
i
i
where g( t 1
+ ) = 1
( − δ ) + φ ( t 1
+ ) − φ ( t 1+

) t 1
+ ,
k
k
k
k
t 1
+
t 1
+
t 1
+
t 1
+
(8)
b : λ = βE λ
1
(
+
+ r ),
t
t
t
t 1
t
where λt and µt are the Lagrange multipliers associated with the constraints (1) and (3).
Since this problem cannot be solved analytically, we find an approximate solution using the
approximation method of King, Plosser and Rebelo (1988).11
2.2. The Endogenous Discount Factor Model
This part describes the same model with a time non-separable preference formulation in which the
discount factor is endogenous.12 The optimization problem of the representative agent is
1 σ

nw
t
 −
ct
− 1





w
max U (c , n )
, σ > 1, w >1,
t
t
= E0 γ 

t
c , n , i , b

t
t
t
t
t =0
1 − σ

10 We do not consider other shocks such as government spending shocks, or net foreign transfers shocks since Correia,
et al. (1995) convincingly argue that these shocks are not able to generate significant business cycle dynamics in a small
open economy model.
11 Detailed derivation of the steady state and the linearized first order conditions of the model are available upon
request.
12 This preference formulation was first introduced by Uzawa (1968), and further developed by Epstein (1983, 1987).
See Obstfeld (1990) for a theoretical analysis of dynamics of this type of small open economy model.

5

subject to the same constraints (1) - (3) above. The endogenous discount factor, γ , is defined as
t
t 1
 −
w
nτ 
(9)
γ
θ
c
θ > 0.
t = exp −
1
ln( + τ −
) ,
 ∑

τ =
w
0


The discount factor depends on the level of consumption and labor input in the previous periods. θ
denotes the elasticity of the discount factor with respect to utility. The functional form of the endogenous
discount factor implies that an increase (decrease) in current consumption (labor input) decreases the weights
assigned to all future utility, and, in turn, the agent becomes more impatient.13
Using (9), we define an auxiliary variable ψ , the time t value of discounted future utility from date
t
t+1 onwards:
w
n
(
k
c
)1 σ

−1

k
w
γ
(10)

k
ψ = E
.


t
t
= +
− σ
γ
k t 1
1
t
The first order conditions of the optimization problem above are:
−σ
1


n w
t


n w
t

(11)
c : c
λ ψ θ

t
= t +
1
t
+ ct
,
t









w

w
(12)
n : w
n = αy ,
t
t
t
i
(13)
i : λ = µ φ ( t

),
t
t
t
kt


θ
w
n
y
i
t

(14)
k
: µ
c
E λ
α
µ g

t =
1 + t
{
1
(
t
t
− ) t 1+ +
( t 1
+ )},
t 1
+
1
+
t 1
+





w
k
k
t 1
+
t 1
+
w
n
−θ
(15)
b : λ = 1
(
t
+ c
)
E λ
1
(
+
+ r ).
t
t
t
t
t 1
t
w
Using equation (10), we write the following law of motion for the auxiliary variable ψ :
t

13 Epstein (1983) shows that under certain conditions this preference formulation generates “a unique invariant limiting
distribution of the state variables.” Our parameterization also meets those conditions.

6


nw
t+1

1 σ

nw
(ct+1 −
)
−1
t
θ
(16)
E
.
t ψ
(
)
1
(
c
)
w
E
t 1
t
ψ
+
= + −
t
t

w

1 − σ





We solve the model using the same approximation method.
2.3. Calibration
We choose the parameter values to ensure that we have the same steady state for both models. The
variables without time subscripts refer to the steady state values of the corresponding variables. The three
important steady state parameters to be discussed here are r, nx/y (net export/output), and θ, since we attain
the same steady state by using the same values for r and nx/y and by endogenously determining the value of
θ in the EDM.
In the FDM, given r, the steady state version of equation (8) determines only the discount factor β.
Therefore, the number of endogenous variables is less than the number of steady state equations by one.
This implies that any level of foreign assets is compatible with the initial steady state of the model.
Following the standard approach in the literature (see for example, Baxter and Crucini (1993), and Correia, et
al. (1995)), we draw the value of nx/y (net exports/output) from data to solve this problem because nfa/y (net
foreign assets/output) is uniquely determined by nx/y and r.
Unlike the FDM, the EDM does not suffer from the indeterminacy problem because the number of
endogenous variables is equal to the number of steady state equations: i.e. the model generates a unique
steady state level of the net foreign assets. However, this hinges on the assumption that the value of θ is
known in advance. Using the value of nx/y, which is drawn from the data, we pin down the value of θ
endogenously using the steady state version of equation (15). This guarantees that all the variables including
the discount rates in the two models have the same steady state values. This is also the standard calibration
method used in the studies employing the endogenous discounting factor.
We calibrate the structural parameters to correspond to the existing RBC literature and to be consistent
with the long-run features of Canadian economy. Table 1 presents the calibrated values of parameters. We
set the quarterly steady state world real interest rate at 1.21 % which is the average rate calculated using the
U.S. 3-month T-Bill rate deflated with the CPI inflation. Following Mendoza (1991), the elasticity of
substitution, w, is set to 1.455. The risk aversion parameter, σ, is set to 1.5, which is an intermediate case
between the commonly used values of 2 and 1 (see Schmitt-Grohe (1998)). Following Mendoza (1991) and
Schmitt-Grohe (1998), the share of labor income in the production, α, is set to 0.68. The quarterly
depreciation rate, δ, is set to 0.025, a widely used value in the RBC literature.

7

Our benchmark value of nx/y is equal to 0.14 To examine the sensitivity of our results, we experiment
with different values of nx/y, which is equal to the interest payments-output ratio (-rb/y), ranging from
-0.05 to 0.05 per quarter.15 Since θ is an increasing function of nx/y at an exponential rate, θ ranges from
0.0074 to 0.0088.16 The corresponding value of θ is 0.008 when nx/y is equal to 0.
The adjustment cost parameters are chosen so that the steady state of the model is same as the one
without adjustment costs. This implies that φ i
( / k ) = i / k and φ '(i / k) = 1. The steady state value of i / k
is equal to the depreciation rate, δ. The elasticity of the marginal adjustment cost function,
1
η = −(φ′/φ )(i / k)−

, is set to 10, to match the volatility of investment in the data (see Baxter and Crucini
(1993)).
The exogenous shocks, zt and rt, follow AR(1) processes with
(17)

z
zˆ = ρ zˆ −

1 + ε
t
z
t
t
(18)

r
rˆ = ρ rˆ −

1 + ε
t
r t
t
where εz and εr are assumed to follow normal distributions with mean 0 and variance σ 2
2
z and σr . We set the
standard deviations of the productivity and interest rate shocks at 0.615 % and 0.1 % to match the volatility
of output in the data. The persistence parameters of shocks, ρy and ρr, are estimated and they are equal to
0.95 and 0.7.

3. Results

We study the dynamic implications of the FDM and the EDM on five dimensions: first, we compare
the policy functions generated by the two models. Second, we study their second moment implications.
Third, we analyze the impulse responses to productivity and interest rate shocks. Fourth, we compare the
distributions of the three variables, which are nonstationary in the FDM, in the two models. We also
formally test whether the distributions produced by these two models are statistically different. Finally, we
estimate the approximation errors generated by the two models considering that the FDM generates
nonstationary variables that might induce larger approximation errors than those in the EDM.
3.1. Policy functions
Table 2 presents the coefficients of policy functions for consumption, asset holdings and the net
exports of the two models. We concentrate on the coefficients of the endogenous state variables considering
that impulse responses in the next section illustrate the differences in the coefficients associated with shocks.

14 The average value of nx/y is near zero (less than 0.3% per quarter) for Canada.
15 This range is wide enough to cover most realistic cases. The observed trade balance rarely exceeds ±5% of output per
quarter for the OECD countries.

8

Asset holdings follow a unit root process in the FDM, i.e. the coefficient of asset holdings, b2, is equal to 1.
The unit root property implies that a shock in the current period has a permanent impact and the long-run
wealth of the economy depends on the shock realizations. This also induces consumption and the net exports
to be nonstationary. While the coefficients of the policy function for consumption (a1 and b1) are always
larger in the EDM than those in the FDM, differences between the coefficients are very small. In other
words, consumption is more responsive to the state variables in the EDM compared to the FDM.
As the elasticity of the endogenous discount factor θ decreases, differences in the coefficients of the
policy functions disappear. As θ decreases, the discount factor in the EDM responds less to the changes in
utility, therefore the variables in the EDM behave as if the discount factor is almost fixed. For example,
when θ is equal to 0.0074 (nx/y = −5%), the policy functions generated by the two models become almost
identical and the net foreign asset series in the EDM follows a near unit root process (b2 = 0.9999 in the
EDM). In other words, our findings suggest that the moments produced by the EDM converge to those
produced by the FDM when the elasticity of the endogenous discount factor, θ, gets arbitrarily small.
The policy functions of output, labor hours, investment, and capital stock generated by the two
models are identical and invariant to the value of θ. These variables do not depend on the asset holdings, i.e.
the coefficients associated with asset holdings are zero in both models. Therefore, even in the FDM, these
four variables, unlike consumption and the net exports that depend on the previous period's net foreign asset
holdings, become stationary. This results from the momentary preference structure where labor hours
depend only on the current output and there is no intertemporal substitution involving labor. This implies
that labor hours become stationary, which induces output, investment, and capital stock to be stationary as
well. We also examine the sensitivity of policy functions’ coefficients to changes in other parameters of the
model such as σ and w. We find that our results are robust to those changes.
3.2. Second Moment Implications

One of the important objectives of the RBC research program is to construct models that are able to
replicate certain moments of the data. In this section, we compare the business cycle moments generated by
each model. If the discrepancies between the moments generated by the two models are small, then this
suggests that the FDM constitutes a reasonable alternative to the EDM for business cycle analysis. We
simulate the model for 100 periods with our benchmark parameterization and report the average moments
over 300 simulations. All results refer to the moments of Hodrick-Prescott (HP(1600)) filtered variables (see
Hodrick and Prescott (1997)).
Panel A in table 3 reports the second moments generated by productivity shocks. The results suggest
that there is no statistically significant difference between the moments produced by the two models. As
expected, investment is the most volatile variable, and output is more volatile than consumption. All model

16 The value of θ used in the literature with the EDM ranges from 0.001 to 0.1 depending on the model specification.

9

Document Outline

  • Dynamics of Open Economy Business Cycle Models:
  • Understanding the Role of the Discount FactorŽ *
  • Sunghyun Henry Kim** and M. Ayhan Kose**
      • Keywords: business cycle dynamics, fixed discount factor, endogenous discount factor, nonstationarity.
      • JEL classification: F4, E3
  • 2.1. The Fixed Discount Factor Model
    • 2.3. Calibration
  • Shocks
  • All cases
    • Business cycle moments
  • Panel A: Productivity shocks
      • Output
      • Output
  • Variable
  • NFA/Y
      • Productivity and interest rate shocks
  • FDM

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