The Impact of Financial Frictions on a Small Open Economy: When Current Account Borrowing Hits a Limit Diego Valderrama Economic Research Department Federal Reserve Bank of San Francisco http://www.frbsf.org/economics/economists/dvalderrama.html Spring 2004
The Impact of Flow Credit Constraints on a Small Open Economy
Structure of Talk
1. Stylized facts 2. Related Literature 3. Small open economy model with financial frictions 4. Model evaluation (Statistical evaluation of data and simulation) 5. Concluding remarks
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The Impact of Flow Credit Constraints on a Small Open Economy
1. Stylized Facts Current account reversal and “excess volatility” in consumption and output
• “Twin Crises” (Kaminsky and Reinhart, 1998, 1999), Current account reversals (MilessiFerretti and Razin, 1997, 1998; Hutchinson and Noy, 2002) • Capital mobility (Taylor, 1997; Lewis, 1997) • Sudden stops and “excess volatility” (Calvo, 1998; Mendoza, 2002; Mendoza and Smith, 2002)
2
The Impact of Flow Credit Constraints on a Small Open Economy
Mexico Figure 1: Gross Domestic Product: Large falls in output in 1982 and 1994
2.7
2.65
2.6
2.55
1984
1992
2000
GDP
Figure 2: Leading to CA reversal and fall in consumption 0.1
0
2.3
CA −0.1
C 1984
1992
Private Consumption
Current Account
2.4
2.2
2000
3
The Impact of Flow Credit Constraints on a Small Open Economy
Histograms show resulting Asymmetry
Figure 3: Gross Domestic Product: Negative skewness 20
18
16
14
12
10
8
6
4
2
0 2.55
2.6
2.65 GDP
2.7
2.75
Figure 4: Current Account: Slight positive skewness 20
18
16
14
12
10
8
6
4
2
0 −0.1
−0.08
−0.06
−0.04 −0.02 Current Account
0
0.02
0.04
4
The Impact of Flow Credit Constraints on a Small Open Economy
Figure 5: Private Consumption: Negative skewness 30
25
20
15
10
5
0 2.2
2.22
2.24
2.26
2.28 2.3 2.32 Private Consumption
2.34
2.36
2.38
2.4
5
The Impact of Flow Credit Constraints on a Small Open Economy
Periods of “Excess Volatility” Figure 6: Conditional Volatility: Gross Domestic Product −4
1
x 10
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 1984
1992 GDP cond. vol.
2000
Figure 7: Conditional Volatility: Current Account −4
1
x 10
0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0 1984
1992 CA cond. vol.
2000
6
The Impact of Flow Credit Constraints on a Small Open Economy
Table 1: Gross Domestic Product COUNTRY
AR Order 6 5 3 5 6
Conditional Vol. ARCH GARCH ∗∗∗ 1 ∗∗ 3 ∗∗ 1 ∗∗∗ 1 ∗∗∗ 1
Higher Order Terms Kz = 5∗∗∗ Kz = 3∗∗ Kz = 4∗ Kz = 3∗∗
BIC-preferred
Japan Kz = 4 Mexico Kz = 0 South Korea Kz = 5 United Kingdom Kz = 0 United States Source: Valderrama (2002). ∗ Significant at the 10% confidence level (CL). ∗∗ Significant at the 5% CL. ∗∗∗ Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. VAR order column gives highest significant VAR lag. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. GDP in real, log, per capita terms, detrended using BP filter. Span: Japan 1955Q2–2000Q2 (181 observations), Mexico 1980Q1–2001Q3 (87), South Korea 1970Q1–2001Q3 (127), United Kingdom 1955Q1–2001Q3 (186), United States 1959Q1–2001Q4 (172). First 8 observations are reserved for model selection.
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The Impact of Flow Credit Constraints on a Small Open Economy
Table 2: Private Consumption COUNTRY Series C Y C Y C Y C Y C Y
VAR Order
Conditional Vol. ARCH GARCH ∗∗∗ 1 1∗∗∗ ∗∗∗ 1 1∗∗∗
Higher Order Terms ∗∗ 4 § 4 3∗ 3 4∗∗∗ 4∗∗∗ 4∗∗∗ , Kx = 4∗∗∗ , Kx = 4∗∗∗ 4
BIC-preferred
Kz = Kz = Kz = Kz = 0 Mexico 3 Kz = 1∗∗∗ Kz = South Korea 3 ∗ 1 Kz = ∗∗∗ 1 Kz = 1∗∗∗ Kz = 0 United Kingdom 5 ∗∗∗ ∗∗∗ 1 Kz = 1 1∗∗∗ Kz = United States 6 1 Kz = Source: Valderrama (2002). ∗ Significant at the 10% confidence level (CL). ∗∗ Significant at the 5% CL. ∗∗∗ Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. §Quadratic term highest order term significant at the 5% level. VAR order column gives highest significant VAR lag. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. Y is GDP in real, log, per capita terms, detrended using BP filter. C is private consumption is in real, log, per capita terms, detrended using BP filter. Private consumption does not include purchases of durables, except for Japan and South Korea. Span: Japan 1955Q2–2000Q2 (181 observations), Mexico 1980Q1–2001Q3 (87), South Korea 1970Q1–2001Q3 (127), United Kingdom 1955Q1–2001Q3 (186), United States 1959Q1–2001Q4 (172). First 8 observations are reserved for model selection. Japan
5
8
The Impact of Flow Credit Constraints on a Small Open Economy
Table 3: Private Investment COUNTRY Series I Y I Y I Y I Y I Y
VAR Order
Conditional Vol. ARCH GARCH ∗∗∗ 1 1∗∗∗ 1∗∗ 1∗∗∗ 1∗∗∗ 1 1∗∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗ ∗ 1 1∗∗∗
Higher Order Terms =4 = 4∗∗ § = 4∗∗∗ , Y, I int. =4 = 4∗∗∗ = 4∗∗∗ =4 = 4∗∗∗ =4 = 4∗∗∗ §§
BIC-preferred
Kz Kz Kz Mexico 4 Kz Kz South Korea 3 Kz Kz United Kingdom 5 Kz Kz United States 4 Kz ∗ Source: Valderrama (2002). Significant at the 10% confidence level (CL). ∗∗ Significant at the 5% CL. ∗∗∗ Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. §Quadratic term highest order term significant at the 5% level. §§Quadratic term highest order term significant at the 1% level. Y, I int. represents an interaction term in the hermite polynomial (Kz = 4, Iz = 2). VAR order column gives highest significant VAR lag. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. Y is GDP in real, log, per capita terms, detrended using BP filter. I is private investment is in real, log, per capita terms, detrended using BP filter. Private investment is the sum of gross fixed capital formation, changes in inventories, and purchases of consumer durables. Consumer durables are not included in Japan and South Korea. Span: Japan 1955Q2–2000Q2 (181 observations), Mexico 1980Q1–2001Q3 (87), South Korea 1970Q1–2001Q3 (127), United Kingdom 1955Q1–2001Q3 (186), United States 1959Q1–2001Q4 (172). First 8 observations are reserved for model selection. Japan
6
9
The Impact of Flow Credit Constraints on a Small Open Economy
Table 4: Net Exports COUNTRY
VAR Order
Conditional Vol. ARCH GARCH 1 1∗∗∗ ∗∗∗ 1 1∗∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗ 1∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗
Higher Order BIC-preferred Series Terms NX Kz = 4∗∗∗ Japan 5 Y Kz = 4∗∗∗ NX Kz = 4∗∗∗ Mexico 6 Y Kz = 4∗∗∗ NX Kz = 4∗∗ South Korea 6 Y Kz = 4∗∗∗ NX Kz = 4 Kz = 0 United Kingdom 5 ∗∗ Y Kz = 4 ARCH(2) ∗ NX Kz = 4 Kz = 0 United States 5 Y Kz = 4∗∗∗ Source: Valderrama (2002). ∗ Significant at the 10% confidence level (CL). ∗∗ Significant at the 5% CL. ∗∗∗ Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. §Quadratic term highest order term significant at the 10% level. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. Y is GDP in real, log, per capita terms, detrended using BP filter. NX is net exports, the difference of exports minus imports; each is in real, log, per capita terms, detrended using BP filter. Span: Japan 1955Q2–2000Q2 (181 observations), Mexico 1980Q1–2001Q3 (87), South Korea 1970Q1–2001Q3 (127), United Kingdom 1955Q1–2001Q3 (186), United States 1959Q1–2001Q4 (172). First 8 observations are reserved for model selection.
10
The Impact of Flow Credit Constraints on a Small Open Economy
Table 5: Current Account, GDP COUNTRY Japan Mexico South Korea
Series CA Y CA Y CA Y CA Y CA Y
VAR Order
4 3 3
Conditional Vol. ARCH GARCH ∗∗ 2 2∗∗ 1∗∗∗ 1 1∗∗∗ 1∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗ 1∗∗∗
Kz Kz Kz Kz
Higher Order Terms = 3, Y, CA int. = 3∗∗ = 3∗∗∗ =3
BIC-preferred
Kz = 4, Iz = 4 Kz = 0
Kz = 4∗∗ Kz = 4∗∗∗ Kz = 4∗∗∗ VAR(6), United States 5 Kz = 4 Kz = 0 ∗ ∗∗ ∗∗∗ Source: Valderrama (2002). Significant at the 10% confidence level (CL). Significant at the 5% CL. Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. §Quadratic term highest order term significant at the 10% level. Y, CA int. represents an interaction term in the hermite polynomial (Kz = 4, Iz = 2). VAR order column gives highest significant VAR lag. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. Y is GDP in real, log, per capita terms, detrended using BP filter. CA is the current account, expressed as a percent of GDP and then filtered using BP filter. United Kingdom
5
11
The Impact of Flow Credit Constraints on a Small Open Economy
Table 6: Current Account, Private Consumption COUNTRY
VAR Order
Conditional Vol. Higher Order BIC-preferred Series ARCH GARCH Terms ∗∗ CA 1 Kz = 4∗ Japan 6 ∗∗∗ C 1 Kz = 4∗∗∗ CA 1∗∗∗ Kz = 4∗∗∗ Mexico 5 C 1 Kz = 4 ∗∗ CA 1 South Korea 6 C 1∗∗∗ CA 1∗∗∗ Kz = 4 Kz = 0 United Kingdom 5 ∗∗∗ ∗∗ C 1 Kz = 4 CA 1∗∗ Kz = 4∗ /S Kz = 0 United States 3 ∗∗∗ C 1 Kz = 4 Source: Valderrama (2002). ∗ Significant at the 10% confidence level (CL). ∗∗ Significant at the 5% CL. ∗∗∗ Significant at the 1% CL. Significance refers to highest order term, unless otherwise specified. §Quadratic term highest order term significant at the 10% level. VAR order column gives highest significant VAR lag. ARCH column gives highest order ARCH term at the 10% significance level or above. GARCH column gives highest order GARCH term at the 10% significance level or above. Higher Order Terms column gives order of Hermite polynomial. BIC-preferred column gives the BIC-preferred model if it is not the overall preferred model. CA is the current account, expressed as a percent of GDP and then filtered using BP filter. C is private consumption is in real, log, per capita terms, detrended using BP filter. Private consumption does not include purchases of durables, except for Japan and South Korea.
12
The Impact of Flow Credit Constraints on a Small Open Economy
2. Related Literature • Financial frictions literature – Calvo (1998) “The Simple Economics of Sudden Stops”. – Arellano and Mendoza (2002) literature survey. – Mendoza (2002): Income requirement to acquire new debt. Constraint is more binding in bad states of the world. It is occasionally binding, resulting in periods of excess volatility. Agents can self insure against constraint and so crises are rare in long run. • Measuring the impact of emerging market crises – “Twin Crises” (Kaminsky and Reinhart, 1998, 1999), Current account reversals (MilessiFerretti and Razin, 1997, 1998) – Current account reversals are often associated with fall in output (Hutchinson and Noy, 2002)
13
The Impact of Flow Credit Constraints on a Small Open Economy
3. Model of Small Open Economy Small open economy (SOE) with endowment of capital. Flow borrowing constraint: Current account cannot exceed a certain fraction of GDP. Constraint can be rationalized by:
• International lending institutions may have a “critical level” that indicates maximum level of current account that is sustainable for indebted countries (Milessi-Ferretti and Razin, 1996b). Large current account deficits were behind the Mexican crisis of 1982, the Mexican crisis of 1994 and the Asia crisis of 1997 (Milessi-Ferretti and Razin, 1996a; Edwards, 2002). IMF includes targets for current account/GDP ratio as part of programs. • Large current account/GDP ratio may be a predictor of financial crises (Kaminsky et al., 1997). • Government policy that aims to reduce volatility of international capital flows (e.g., Brazil (Cardoso and Goldfajn, 1998), Chile (Edwards, 1999), Indonesia (McLeod, 1997), (Reinhart and Smith, 2002)). Capital controls as part of liberalization program (Williamson, 1997b,a).
14
The Impact of Flow Credit Constraints on a Small Open Economy
International Sector
The current account is defined by:
CAt ≡ Bt+1 − Bt = Yt + rt∗Bt − Ct
(1)
• CAt is the current account in period t. • Bt is the net holding of international assets. • Yt = F (K, Lt , zt), domestic product, depends on the capital stock, which is time invariant, and the labor supply this period. • There are two shocks, one to the internationally given interest rate, ηt ( rt∗ = r ∗ ∗exp(ηt )), and one to the domestic product, zt.
15
The Impact of Flow Credit Constraints on a Small Open Economy
Financial friction is on the flow of assets
The flow borrowing constraint faced by domestic agents is given by:
CAt ≥ −κ Yt
(2)
where κ is usually a small positive number so that the current account is allowed to be in deficit. If κ = 0 the country is not allowed to accumulate any debt but it pays the interest on its debt. Rearranging (2), we obtain:
Bt+1 ≥ −κYt + Bt
(3)
• Constraint reflects ability to pay: it is more binding in bad states of nature. • It is occasionally binding, so it has the potential generate excess volatility • Is a constraint on the flow of assets, thus agents cannot completely self-insure. 16
The Impact of Flow Credit Constraints on a Small Open Economy
Supply side Production Yt is given by the following technology:
Yt = F (K, Lt ), α
(4a) (1−α)
F (K, Lt ) = exp(zt)K Lt
(4b)
The aggregate resource constraint of the economy is given by:
Ct = Yt + r ∗ ∗ exp(ηt )Bt − Bt+1 + Bt
(5)
17
The Impact of Flow Credit Constraints on a Small Open Economy
Utility maximization Given the interest rate determined by the rest of the world, and the presence of two shocks, the markets are incomplete. The agent maximizes a Stationary Cardinal Utility (SCU) (Epstein, 1983) that exhibits a time varying discount factor. SCU determines a well-defined stationary distribution of international assets (Mendoza, 1991).
( U=
max
{Ct ,Lt ,Bt+1 }
E0
∞ X
" u(Ct , Lt) exp
−
t=0
t−1 X
!#) v(Cτ , Lτ )
(6a)
τ =0
where:
Ct −
u(Ct , Lt ) =
(1−θ)
−1
1−θ
v(Ct , Lt) = β ln
Lω t ω
Lω 1 + Ct − t ω
(6b)
(6c)
subject to the borrowing constraint, (3),and the resource constraint, (5). 18
The Impact of Flow Credit Constraints on a Small Open Economy
Optimality Conditions & Euler Equations The First Order Conditions (FOC) of the problem (6) are given by:
Ct :
0 = UC (t) − λt
(7a)
Lt :
0 = UL(t) + λtFL(t) + µt κFL(t)
(7b)
0 = −λt + µt + E {λt+1 (1 + rt+1 ) − µt+1 }
(7c)
Bt+1 :
where µt is the non-negative lagrange multiplier on the borrowing constraint and λ is the lagrange multiplier on the resource constraint. Combining these equations yields two euler equations:
Labor: [(6), (7a) & (7b)] Bonds: [(7a) and (7c)]
ω−1
Lt
µt = FL(t) 1 + κ , UC (t)
UC (t) − µt = Et UC (t + 1)(1 +
rt∗)
(8a)
− µt+1 .
(8b)
19
The Impact of Flow Credit Constraints on a Small Open Economy
Intuition
• If the Borrowing Constraint binds today (i.e. µt > 0) then consumption unambiguously decreases today (8b). Similarly, by (8a) labor increases today. The constraint binding today increases the implicit interest rate that the country faces today. • If the Borrowing Constraint binds tomorrow (i.e. µt+1 > 0) then the effect on consumption increases today. (8b) implies that consumption today will increase! The net benefit of saving today is less. Thus consumption increases today. Thus, the net effect on consumption today will depend on the relative strength of the two effects. • If the borrowing constraint binds today and also binds tomorrow, the effect of a binding constraint tomorrow will have an effect on labor today (8a). However, if the borrowing constraint does not bind tomorrow, then labor is independent of the path of consumption.
20
The Impact of Flow Credit Constraints on a Small Open Economy
Stochastic Structure
The two stochastic shocks are assumed to follow a VAR(1) process. That is:
ζt ≡ where
εt =
zt ηt ǫ zt ǫηt
=
ρz 0
0 ρη
"
∼N
0,
ζt−1 +
σǫ2z σǫz ,ǫη
ǫ zt ǫηt
σǫz ,ǫη σǫ2η
(9)
#! (10)
21
The Impact of Flow Credit Constraints on a Small Open Economy
Dynamic programming problem
( V(Bt , ζt) = max
Lt ,Bt+1
u(Ct , Lt )+
exp −β log
1 + Ct −
Lω t ω
) × Et [V(Bt+1 , ζt+1 )]
(11)
subject to the borrowing constraint, Bt+1 ≥ −κYt + Bt, the resource constraint, Ct = Yt + r ∗ ∗ exp(ηt )Bt − Bt+1 + Bt, and the exogenous stochastic process, ζt.
22
The Impact of Flow Credit Constraints on a Small Open Economy
Choice of Solution Method
Discretize state space and iterate on value function:
• International asset position is given by an equi-distanced grid (501 points) • Center international asset grid around deterministic steady state • Quadrature rule (Tauchen and Hussey, 1991) for ζt (5 points for zt, 4 points for ηt )
23
The Impact of Flow Credit Constraints on a Small Open Economy
4. Model Evaluation
• Efficient Method of Moments (EMM) – Minimum Chi-Squared Estimator (GMM) – Simulated Method of Moments (SMM) • First: Obtain a statistical representation of the Mexican data using a Seminonparametric (SNP) Moment Generator – Statistical Model of Data – Quasi-Maximum Likelihood Estimation – Flexible (Allows for ARCH/GARCH and Non-Normal Innovations) – Serves as Moment Generator for for EMM • Second: Simulate the SOE model for a candidate set of parameters until statistical properties of the simulated data are “closest” to the statistical properties of the observed data.
24
The Impact of Flow Credit Constraints on a Small Open Economy
First Step: Statistical Model of Data
The key to the first step is to take a flexible approach to characterize the properties of the observed data. Suppose that p(·) is the “true” transition density function of the data. To approximate the properties of the data use a seminonparametric (SNP) estimator, f (·). The SNP estimator nests a traditional VAR to summarize the conditional mean of the data. It also allows for conditional volatility (ARCH, GARCH), non-Normality (asymmetry, kurtosis), and a time varying conditional distribution (conditional heterogeneity). Choose amongst different candidate statistical models with the help of BIC.
25
The Impact of Flow Credit Constraints on a Small Open Economy
Notation
• • • • • •
yt is the true stochastic process y˜t is the observed stochastic process yˆt(Θ) is the simulated data process from the parameters Θ p(· | Θ) is the (Long-Run) transition probability for the true stochastic process f (yt | yt−L, . . . , yt−1, Ω) is the (SNP) statistical model that describes the observed data. xt−1 ≡ (yt−L, . . . , yt−1)′ is the vector of lagged variables.
26
The Impact of Flow Credit Constraints on a Small Open Economy
Statistical Description of Mexican Data
You want to obtain the (Markovian) transitional density function:
1 yt − µt−1 h f (yt | yt−L, . . . , yt−1, Ω) ∝ Rt−1 Rt−1 Conditional Mean (Location) Linear error Variance (Scale) Normalized innovation
(12)
µt−1 et = yt − µt−1 ′
Σxt−1 = Rxt−1 Rxt−1 ≡ [V ARt−1 (et )] zt =
yt − µt−1 |Rt−1|
27
The Impact of Flow Credit Constraints on a Small Open Economy
Parametric Assumptions • Mean (Location): µt−1
=
b0 + B1yt−1 + B2yt−2 + · · · + BLµ yt−Lµ
(13)
µt−1
=
b0 + Bxt−1
(14)
• Conditional Variance (Scale):
vech Rxt−1
= ρo +
Lr X
P(i) yt−1−Lr +i − µxt−2−Lr +i +
i=1 Lg X
diag G(i) vech Rxt−2−Lg +i . (15)
i=1
28
The Impact of Flow Credit Constraints on a Small Open Economy
• Heterogeneity:
yt − µt−1 h Rt−1
2
= [P (z, x)] φ(t | µ, R)
PK (z, x) =
Kx Kz X X
β
(aβα x )z
α
(16) (17)
α=0 β=0
29
The Impact of Flow Credit Constraints on a Small Open Economy
Results
Using Mexican GDP and Current Account quarterly data (1980–2000) we obtain a statistical model with the following characteristics:
• Vector Autoregressive model of third order (VAR(3)) • Conditional Volatility in both Output and the Current Account • Output is not distributed normally, while one cannot reject Normality for the Current Account.
30
The Impact of Flow Credit Constraints on a Small Open Economy
Table 7: SNP Summary Parameters Estimate VAR Intercept b(y) b(ca) Lµ = 3 B(y, yt−3 ) B(y, cat−3 ) B(ca, yt−3 ) B(ca, cat−3 ) Lµ = 2 B(y, yt−2 ) B(y, cat−2 ) B(ca, yt−2 ) B(ca, cat−2 ) Lµ = 1 B(y, yt−1 ) B(y, cat−1 ) B(ca, yt−1 ) B(ca, cat−1 ) Variance Σy Σy,ca Σca ARCH P (y) P (ca) Hermite A(00) A(ca) A(y) A(ca2 ) A(y 2 ) A(ca3 ) A(y 3 )
Standard Error
t-statistic
−0.1106 0.0480
0.0086 0.0091
−12.917 5.269
0.9017 −0.1197 0.1830 0.6684
0.0413 0.0629 0.0339 0.0439
21.842 −1.902 5.400 15.240
−2.2595 0.2028 −0.1532 −1.9698
0.0703 0.0978 0.0535 0.0778
−32.149 2.073 −2.863 −25.334
2.4013 −0.1940 0.0970 2.1191
0.0456 0.0589 0.0321 0.0478
52.649 −3.292 3.025 44.381
0.0132 −0.0592 0.0467
0.0035 0.0126 0.0117
3.764 −4.704 4.007
0.3414 0.8057
0.0439 0.2286
7.784✔ 3.524✔
1.0000 −1.0344 −0.1148 −0.3080 1.5275 0.0544 0.4306
0.0000 0.9637 0.4697 0.2852 0.7812 0.3465 0.2128
0.000 −1.073 −0.244 −1.080 1.955 0.157 2.024✔
31
The Impact of Flow Credit Constraints on a Small Open Economy
Second Step: Simulation • Likelihood of the underlying process p(· | Θ) is not available in closed form. • The EMM methodology works by approximating the transition density of the data generating process yt using the observed data, y˜t : f (yt | yt−L, . . . , yt−1, Ω)
(18)
• Use the score function from SNP to define the GMM Objective Function: ˜ ≈0 (∂/∂Ω)log[f (˜ yt | y˜t−L, . . . , y˜t−1, Ω)]
(19)
• Use the GMM criterion to evaluate the simulated time series yˆt (Θ) obtained from the value ˆ , the estimated economic model parameters. function procedure, to get Θ • Test of over-identifying restrictions: The GMM objective function is distributed χ2 with degrees of freedom equal to the difference between the number of parameters in the score generator and the number of parameters being estimated. 32
The Impact of Flow Credit Constraints on a Small Open Economy
Results
Two sets of estimates are given: Unconstrained and Low κ (=8%).
• Low κ model is better at capturing nonlinearities found in Mexican data. • Low κ is a local optimum. • SOE model is rejected as the true data generating mechanism: Both models miss VAR structure of the conditional mean for GDP and the Current Account. • Estimates are “reasonable”.
33
The Impact of Flow Credit Constraints on a Small Open Economy
Table 8: Summary Parameters: EMM Parameter Estimates and Standard Calibration Parameters σ ǫz ρz σ ǫη ρη σǫz ,ǫη α A ω β θ r∗ κ χ2 DOF
Benchmark 3.250% 0.82493 0.861% 0.14998 -0.00073 0.36574 0.98405 1.94074 0.00736 1.02165 1.586% 511%
Constrained 3.250% 0.82500 0.875% 0.14999 -0.00118 0.36402 0.95030 1.95479 0.00736 1.02159 1.586% 8.000%
1.17E+06 14
3.50E+06 16
Standard Calibration 3.250% 0.8250 0.360% 0.1500 -0.1100 0.3640 1.0000 2.0000 0.0076 1.0000 1.586% 9.00E+33
Low κ Calibration 3.250% 0.8250 0.360% 0.1500 -0.1100 0.3640 1.0000 2.0000 0.0076 1.0000 1.586% 8%
Benchmark Model (VAR(3),ARCH(1), Kx =3). χ2 row represents value of EMM objective function, which is distributed χ2 with degrees of freedom (DOF row) equal to the number of statistical parameters (moments) minus the number of SOE model parameters being estimated. Last two columns represent standard calibration parameters for economic model described in text.
34
The Impact of Flow Credit Constraints on a Small Open Economy
Table 9: Simulation Statistics: EMM and Standard Calibration GDP Data Calibrated Constrained Calib. Benchmark Constrained
Mean
Std. Dev.
Skewness
Kurtosis
J-B
p-value
obs.
2.660 2.972 2.972 3.196 3.033
2.19% 7.72% 7.72% 7.59% 7.57%
-0.405 -0.006 -0.006 0.000 0.000
4.074 2.380 2.380 2.379 2.377
6.336 320.961 320.961 321.467 323.142
0.042 2.01E-70 2.01E-70 1.56E-70 6.77E-71
84 20000 20000 20000 20000
Current Account Data -2.320% 2.00% 0.204 2.955 0.588 0.745 84 Calibrated -0.379% 4.80% -0.146 2.495 283.590 2.63E-62 20000 Constrained Calib. -0.350% 4.41% 0.180 2.140 724.737 4.22E-158 20000 Benchmark -0.331% 4.71% -0.173 2.463 339.969 1.50E-74 20000 Constrained -0.312% 4.31% 0.136 2.117 711.671 2.90E-155 20000 Statistical model (VAR(3),ARCH(1), Kx =3). J-B is the Jarque-Bera (1987) statistic, a Wald Test of Normality, distributed χ2 (2). The 90% χ2 (2) critical value is 4.61 and the 95% critical value is 5.99. Each simulation has 20000 periods, after dropping the initial 5000 to eliminate the impact of starting conditions.
35
The Impact of Flow Credit Constraints on a Small Open Economy
Table 10: EMM Mean Scores (1)
(2)
(3)
(4)
Benchmark Variance Σy Σy,ca Σca ARCH P (y) P (ca) Hermite A(00) A(ca) A(y) A(ca2 ) A(y 2 ) A(ca3 ) A(y 3 )
Mean Score
S.E.
−151368.30 −10752.32 −4614.92
175228.93 30368.82 19344.38
−8298.54 −1181.86
4477.30 1596.29
2.72 6.11 6.07 −3.45 21.10 16.42
1.81 1.02 7.75 1.91 54.41 6.95
(5)
(6)
Constrained Mean Score
S.E.
−56101.07 −6807.34 −14114.57
175235.00 30368.65 19344.58
−1.85✖ −0.74✔
−4854.59 −1285.09
4477.45 1596.28
−1.08✔ −0.81✔
1.50 5.98 0.78 −1.81 0.38✔ 2.36✖
−3.65 3.73 3.94 1.86 14.96 −9.82
1.95 1.22 8.30 2.78 54.76 9.93
−1.87 3.07 0.47 0.67 0.27✔ −0.99✔
t-stat
−0.86 −0.35 −0.24
t-stat
−0.32 −0.22 −0.73
36
The Impact of Flow Credit Constraints on a Small Open Economy
15
0.25 U: Best U: Worst C: Best C: Worst
Change in Decison of CA/GDP Ratio
10
(%)
5
0
−5
−10
−15
Standard Low κ
−80
−60
−40
−20
0
20
40
Foreign Asset Position
(a) Impact Effect
60
80
100
0.2
0.15
0.1
0.05
0
−80
−60
−40
−20
0
20
40
60
80
100
Foreign Asset Position
(b) Difference
Figure 8: Decision Rules: CA/GDP Ratio Current account/GDP decision rule in response to two shocks, Best and Worst. The Worst shock is a low productivity, high interest rate shock while the Best shock is a high productivity, low interest rate shock. The top panel shows the desired current account/GDP ratio at each given foreign asset position shown on the horizontal axis for a given shock. U refers to the Benchmark calibration, C refers to the Low κ calibration. The bottom panel shows the distance between of the foreign asset position decision for the Best shock and the foreign asset position decision for the Worst Shock
37
The Impact of Flow Credit Constraints on a Small Open Economy
Standard Low κ
5000 4500 4000 3500 3000 2500 2000 1500 1000 500 0 −15
−10
−5
0
5
10
15
Current Account/GDP (%)
Figure 9: Current Account/GDP (%) Histogram produced by simulating the SOE model for the Standard calibration and the Low κ calibration. The length of the simulation is 20,000 periods, after discarding the first 5,000 periods to remove the impact of initial conditions.
38
The Impact of Flow Credit Constraints on a Small Open Economy
1400
Standard Low κ
1200
1000
800
600
400
200
0
−80
−60
−40
−20
0
20
40
60
80
100
Foreign Asset Position
Figure 10: Foreign Asset Position Histogram produced by simulating the SOE model for the Standard calibration and the Low κ calibration. The length of the simulation is 20,000 periods, after discarding the first 5,000 periods to remove the impact of initial conditions.
39
The Impact of Flow Credit Constraints on a Small Open Economy
Alternative Borrowing Constraint
Suppose agents did not face a constraint on the flow of assets:
CAt ≥ −κ Yt
(20)
but instead faced a constraint on the level of assets (Mendoza, 2002):
Bt+1 ≥ −κ Yt
(21)
• New constraint still reflects ability to pay: it is more binding in bad states of nature. • It is still occasionally binding, so it has the potential generate excess volatility. • However agents now can self-insure.
40
The Impact of Flow Credit Constraints on a Small Open Economy
15
0.25 B: Best B: Worst C: Best C: Worst
Change in Decison of CA/GDP Ratio
10
(%)
5
0
−5
−10
−15
Debt Constrained Low κ 0.2
0.15
0.1
0.05
0
−0.05
0
20
40
60
Foreign Asset Position
(a) Impact Effect
80
100
−0.1
0
20
40
60
80
100
Foreign Asset Position
(b) Difference
Figure 11: Decision Rules: CA/GDP Ratio Current account/GDP decision rule in response to two shocks, Best and Worst. The Worst shock is a low productivity, high interest rate shock while the Best shock is a high productivity, low interest rate shock. The top panel shows the desired current account/GDP ratio at each given foreign asset position shown on the horizontal axis for a given shock. B refers to a debt constrained economy, C refers to the Low κ calibration. The bottom panel shows the distance between of the foreign asset position decision for the Best shock and the foreign asset position decision for the Worst Shock
41
The Impact of Flow Credit Constraints on a Small Open Economy
5000 Debt Constrained Low κ 4500
4000
3500
3000
2500
2000
1500
1000
500
0 −15
−10
−5
0
5
10
15
Current Account/GDP (%)
Figure 12: Current Account/GDP (%) Histogram produced by simulating the SOE model for a debt constrained economy and the Low κ calibration. The length of the simulation is 20,000 periods, after discarding the first 5,000 periods to remove the impact of initial conditions.
42
The Impact of Flow Credit Constraints on a Small Open Economy
1500
Debt Constrained Low κ
1000
500
0
−80
−60
−40
−20
0
20
40
60
80
100
Foreign Asset Position
Figure 13: Foreign Asset Position Histogram produced by simulating the SOE model for a debt constrained economy and the Low κ calibration. The length of the simulation is 20,000 periods, after discarding the first 5,000 periods to remove the impact of initial conditions.
43
The Impact of Flow Credit Constraints on a Small Open Economy
5. Conclusions
• Model with financial frictions can generate excess volatility and non-linearity. • Model has problems generating VAR structure of data. • Extensions: Need to incorporate a more realistic production side to fully account for VAR structure of data. This will allows the test of whether a SOE model with financial frictions can explain the joint behavior of consumption and investment. • Statistical tools that can be used to evaluate alternative explanations of excess volatility against the data.
44
The Impact of Flow Credit Constraints on a Small Open Economy
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The Impact of Flow Credit Constraints on a Small Open Economy
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The Impact of Flow Credit Constraints on a Small Open Economy
, “Credit, Prices, and Crashes: Business Cycles with a Sudden Stop.” In Edwards and Frankel, eds (2002) chapter 7, pp. 335–383. and Katherine A. Smith, “Margin Calls, Trading Costs and Sudden Stops of Capital Inflows into Emerging Markets,” Working Paper 9286, National Bureau of Economic Research, Cambridge, MA October 2002. Milessi-Ferretti, Gian Maria and Assaf Razin, “Current Account Sustainability: Selected East Asian and Latin American Experiences,” Working Paper 5791, National Bureau of Economic Research, Cambridge, MA October 1996. and , “Sustainability of Persistent Current Account Deficits,” Working Paper 5467, National Bureau of Economic Research, Cambridge, MA February 1996. and , “Sharp Reduction in Current Account Deficits: An Empirical Analysis,” Working Paper 97/168, IMF December 1997. and , “Current Account Reversals and Currency Crises: Empirical Regularities,” Working Paper 98/89, IMF 1998. Reinhart, Carmen M. and R. Todd Smith, “Temporary Controls on Capital Inflows,” Journal of International Economics, August 2002, 57 (2), 327–351. 47
The Impact of Flow Credit Constraints on a Small Open Economy
Tauchen, George and Robert Hussey, “Quadrature-Based Methods for Obtaining Approximate Solutions to Nonlinear Asset Pricing Models,” Econometrica, 1991, 59, 371–396. Taylor, Alan M., “Argentina and the World Capital Market: Saving, Investment, and International Capital Mobility in the Twentieth Century,” December 1997. Working Paper No. 6302: NBER, Cambridge, MA. Valderrama, Diego, “Nonlinearities in International Business Cycles,” Working Paper 2002-23, Federal Reserve Bank of San Francisco December 2002. Williamson, John, “Capital Controls in Emerging Economies,” in Christine P. Ries and Richard J. Sweeney, eds., Orthodoxy Is Right: Liberalize the Capital Account Last, The Political Economy of Global Interdependence, Boulder: Westview Press, 1997, chapter 1, pp. 13–31. , “Public Policy Towards Capital Flows,” in Istvá P. Székely and Richard Sabot, eds., Development Strategy and Management of the Market Economy, 1 ed., Vol. 2, Oxford: Claredon Press, Oxford, 1997, chapter 10, pp. 325–347.
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