Asymmetric Business Cycles and Sovereign Default∗ Grey Gordon†

Pablo A. Guerron-Quintana‡ August 8, 2017

Abstract What accounts for asymmetric (negatively skewed) business cycles in emerging economies? We show the asymmetry is tied to default risk and that a sovereign default model delivers negative skew. Keywords: Skewness, Asymmetry, Business Cycles, Default JEL classification numbers: F34, F41, F44

1

Introduction

Business cycles in emerging economies are characterized by high volatility, output being smoother than consumption, and recurrent default episodes. A lesser known feature is that business cycles in these countries are asymmetric, with recessions being more pronounced and lasting longer than in small developed economies. This asymmetry can be seen in Table 1, which gives the skewness for output, consumption, and investment averaged over five emerging economies that have defaulted in recent history (the data are described in the appendix). The standard skewness measure, Sk1 , finds negative skew in output, consumption, and investment. The other skewness measure, Sk2 , which is more robust to outliers (Kim and White, 2003), still shows negative skew in all three categories.1 The negative skew in the data is closely tied to default risk, and this can be seen in three ways. One way is to look at a subsample where spreads are below-median and thereby exclude periods of high default risk and post-default periods. When doing this, the negative skew essentially disappears as Table 1 shows. A second way is to look at the relationship of spreads and skewness ∗ We thank the referee for helpful comments and Diogo Lima for providing us with the EMBI and EMBI+ data. Any mistakes are our own. † Indiana University, [email protected]. ‡ Boston College and ESPOL, [email protected]. 1 2 This measure is defined as Sk2 = µ−Q σ , where µ is the mean, Q2 is the median, and σ is the standard deviation. Sk2 is bounded between −1, negative skewness, and 1, positive skewness.

1

Below-median spreads Data

Model

Data

Model

Sk1 measure Output Consumption Investment

-0.67 (0.60) -1.09 (1.13) -0.40 (0.85)

-0.62 (0.59) -0.31 (0.58) -0.33 (3.24)

0.04 (0.51) 0.06 (0.47) -0.01 (0.89)

0.12 (0.48) 0.30 (0.46) 0.90 (1.91)

Sk2 measure Output Consumption Investment

-0.03 (0.12) -0.09 (0.03) -0.04 (0.18)

-0.08 (0.11) -0.05 (0.12) -0.01 (0.20)

-0.03 (0.18) 0.04 (0.25) -0.02 (0.17)

0.03 (0.14) 0.06 (0.14) 0.16 (0.31)

Note: Statistics are computed using de-trended series, see the appendix for details; standard deviations are in parentheses; the data here are for Argentina, Ecuador, Mexico, Peru, and the Philippines. Table 1: Skewness Statistics in the Data and Model across countries. Figure 2 does this for eight emerging economies (five high-spread and three lowspread), plotting the data along with best fit lines. There is a clear negative correlation between spreads and skew for every measure. A third way to see the connection between negative skew and default risk is to consider that developed small open economies (SOEs) have small or positive skew. For instance, the average Sk1 (Sk2 ) measure for the five developed SOEs in our sample range from −0.19 to 0.18 (−0.01 to 0.04) depending on whether one looks at output, consumption, or investment. In the next sections, we lay out a SOE real business cycle (RBC) model with default that delivers asymmetric business cycles. Crucially, it does so for normally-distributed productivity shocks, i.e., there is no skewness in the underlying stochastic process. We then show how default and default risk drive the asymmetry. Intuitively, times of average or above-average productivity in the model are as in any other RBC model. However, when productivity falls significantly, economic activity declines for two reasons: the standard RBC reasons and increased debt-service costs. Moreover, if default occurs, default costs lower productivity, which severely depresses consumption, investment, and output. The reduced investment in default also depletes the capital stock, which prolongs the recession. Consequently, the effects of upward movements in productivity have a limited and short-lived impact while downward movements can have a drastic and long-lived impact. This asymmetry results in an endogenous negative skew of consumption, investment, and output.

2

Sk 1 measure

2

Output Consumption Investment

1

Sk1

0 -1 -2 -3 1

2

3

4

5

6

7

8

9

10

8

9

10

Spreads in percentage points Sk 2 measure

0.6 0.4

Sk2

0.2 0 -0.2 -0.4 1

2

3

4

5

6

7

Spreads in percentage points

Figure 1: Skewness and default-risk spreads

2

Model and calibration

We briefly describe our model and calibration. For a more full description, see Gordon and GuerronQuintana (2017).

2.1

Model

In the long tradition of sovereign default models (Eaton and Gersovitz, 1981; Arellano, 2008; Mendoza and Yue, 2012), a sovereign borrows in international markets to maximize the welfare of domestic residents. The residents have consumption c, supply labor l, and rank consumption/labor bundles according to a Greenwood, Hercowitz, and Huffman (1988) period utility function u(c, l) = ω (c − η lω )1−σ /(1 − σ) with discount factor β. The sovereign produces output y using capital k and labor l according to y = Ak α l1−α . Productivity follows log A0 = (1 − ρA ) log µA + ρA log A + ε0A , where εA ∼ N (0, σA2 ). The sovereign has access to long-term debt contracts in which outstanding debt matures at a rate λ. Debt not maturing pays a coupon z. The sovereign’s stock of debt is denoted −b (the literature uses b as assets by convention). New bond issuance is given by −b0 + (1 − λ)b, which is discounted by a price q. A default has four consequences. First, the debt goes away. Second, the economy is excluded

3

from credit markets (i.e., goes to autarky). Third, it remains in autarky with probability 1 − φ. Last, for the duration of autarky, a fraction κ(A) of output is lost. The sovereign’s problem is to solve V (b, k, m, A) = max (1 − d)V nd (b, k, m, A) + dV d (k, A) , d∈{0,1}

where d is the default choice and V d (V nd ) is the value of defaulting (not defaulting). The variable m is an i.i.d. endowment shock that aids computation. The value of not defaulting is V nd (b, k, m, A) =

max

c,l,k0 ≥0,b0 ≤0

u(c, l) + βEm0 ,A0 |A V (b0 , k 0 , m0 , A0 )

s.t. c + i + q(b0 , k 0 , A)(b0 − (1 − λ)b) = Ak α l1−α + m −

Θ 0 2 (k − k) + (λ + (1 − λ)z)b 2

k 0 = i + (1 − δ)k, where i is investment and Θ controls the cost of adjusting capital. The value of defaulting or of being in autarky is   d 0 0 0 0 0 0 ,A0 |A (1 − φ)V V d (k, A) = max u (c, l) + βE (k , A ) + φV (0, k , m , A ) m 0 c,l,k ≥0

s.t. c + i = (1 − κ(A))Ak α l1−α −

Θ 0 (k − k)2 2

k 0 = i + (1 − δ)k. The equilibrium debt prices implied by risk-neutral foreign lenders who make zero profits loan-byloan (in expectation) are given by q(b0 , k 0 , A) = Em0 ,A0 |A (1 − d(b0 , k 0 , m0 , A0 ))

λ + (1 − λ) [z + q (b00 , k 00 , A0 )] , 1 + r∗

where b00 = b0 (b0 , k 0 , m0 , A0 ), k 00 = k 0 (b0 , k 0 , m0 , A0 ), and r∗ is a risk-free international rate on a oneperiod bond. Note that default risk, Em0 ,A0 |A d0 , and spreads—an increasing function of 1/q—are intimately linked.2

2.2

Calibration

We now summarize the calibration, which is the same as in Gordon and Guerron-Quintana (2017). A period is a quarter. The coupon payment is 3% (z = .03) with 5% of debt maturing each period (λ = .05), which nearly matches the Argentinean data’s 20 quarter median maturity of average bonds and 11% value-weighted average coupon rate (Chatterjee and Eyigungor, 2012). Choosing φ = 0.1, the average stay in autarky is 2.5 years. Following Neumeyer and Perri (2005), we We follow Chatterjee and Eyigungor (2012) in defining spreads as (1 + r˜)4 − (1 + r∗ )4 where r˜ is an “internal rate of return” that satisfies q = (λ + (1 − λ)z)/(λ + r˜). 2

4

set ρA = .95, which is a value consistent with Fernandez-Villaverde, Guerron-Quintana, RubioRamirez, and Uribe, 2011 and much of the SOE business-cycle literature. Mean productivity µA , the labor disutility parameter η, and depreciation δ are chosen so that, in the steady state without foreign lending, output, labor, and the investment-GDP ratio equal 1, 1, and 0.05, respectively. The utility curvature σ is set to 2. The remaining parameters are chosen to match six moments from Argentina’s data: the debt-output ratio −Eb/y, the average spread Er, the spread volatility σr , the volatility of investment σi , the volatility of output σy , and relative consumption volatility σc /σy . In Gordon and Guerron-Quintana (2017), we show this calibration delivers simultaneously the business cycles and default properties of emerging economies such as Argentina.

3

Results and the model mechanism

To compute the model’s skewness statistics, we generate 20,000 simulations of length 75, which is roughly the number of periods available for each of our developing SOEs. Of these, we keep only the 14,101 simulations that had at least one default (in agreement with our sample selection for countries).3 After logging and HP-filtering the model data, we compute the average and standard deviation of the skewness measures, and these are reported in Table 1. On average, the model delivers negative skew in output, consumption, and investment in both the Sk1 and Sk2 measures. While the averages are all negative, the large standard deviations reflect it is possible to have positive skew depending on the simulation. This agrees with the positive skew (depending on the statistic) that can be found in Peru and the Philippines (see the appendix for a country-specific breakdown). As we argued in the introduction, the skewness in the data is driven by default risk, and this is also true in the model. This can be seen in Table 1, where—conditioning on below-median spreads and hence low default risk—the negative skew disappears, just as in the data. Another way to see this is that of the 5,899 simulations where a default did not occur, the Sk1 (Sk2 ) measures range from −0.03 to 0.89 (−0.01 to 0.02) and so exhibit little or positive skew. The mechanism producing negative skew can be seen in Figure 2, which shows what happens, on average, before and after a default. In the periods leading to a default, spreads are initially flat but accelerate upwards in the year just before default. Perhaps surprisingly, investment, consumption and output rise on average until a few quarters before default. But when spreads start to increase, this trend is reversed: Investment, consumption, and output begin to fall, gradually at first but accelerating with a sharp collapse at default. The small movements up with larger and faster movements down—the latter occurring in periods of high spreads and default risk—contribute to negative skew. As the protracted recession after default is both an unusual (the average quarterly default rate in the model is 1.3%) and severe period of economic activity, it also generates negative 3

If this number seems small, note the model’s quarterly default rate of 1.3% should produce—if default occurred in an i.i.d. fashion (which it does not)—20, 000 ∗ (1 − (1 − .013)75 ) ≈ 12, 500 simulations without a default.

5

Spreads

Investment

18

10 Data Model

16 14

0

12 10

-10

8 6 -12

-8

-4

-20 -12

-1

Quarters since default Output

5

0

-5

-5

-10

-10

-8

-4

0

4

8

-15 -12

12

Quarters since default

-4

0

4

8

12

8

12

Quarters since default Consumption

5

0

-15 -12

-8

-8

-4

0

4

Quarters since default

Figure 2: Investment Dynamics around Default skew. The recession itself is triggered by low productivity and default costs, but it is protracted because of a depleted capital stock due to investment that is up to 20% below trend. Conditioning on periods where default risk is low, the model generates zero or positive skew. In these periods, increases and decreases in productivity lead to changes in consumption, investment, and output that are relatively small and persist at normal business cycle frequencies. In contrast, when default risk is high, decreases in productivity cause rapid adjustments that—in the case of a default—lead to severe and long-lasting recessions. Hence, default and default risk produce negative skew in the model, just as they seem to in the data.

4

Conclusion

Our analysis shows that default and default risk significantly contribute to the negative skew seen in developing small open economies.

References C. Arellano. Default risk and income fluctuations in emerging economies. American Economic Review, 98(3):690–712, 2008. S. Chatterjee and B. Eyigungor. Maturity, indebtedness, and default risk. American Economic Review, 102(6):2674–2699, 2012. 6

J. Eaton and M. Gersovitz. Debt with potential repudiation: Theoretical and empirical analysis. The Review of Economic Studies, 48(2):289–309, 1981. J. Fernandez-Villaverde, P. Guerron-Quintana, J. Rubio-Ramirez, and M. Uribe. Risk matters: The real effects of volatility shocks. American Economic Review, 101(6):2530–2561, 2011. G. Gordon and P. Guerron-Quintana. Dynamics of investment, debt, and default. Review of Economic Dynamics, Forthcoming, 2017. J. Greenwood, Z. Hercowitz, and G. W. Huffman. Investment, capacity utilization, and the real business cycle. American Economic Review, 78(3):402–417, 1988. T. H. Kim and H. White. On robust estimation of skewness and kurtosis: Simulation and application to the S&P500 index. Mimeo, 2003. E. Mendoza and V. Yue. A general equilibrium model of sovereign default and business cycles. Quarterly Journal of Economics, 127(2):889–946, 2012. A. Neumeyer and F. Perri. Business cycles in emerging economies: The role of interest rates. Journal of Monetary Economics, 52(2):345–380, 2005.

A

Data description and simulation details

National accounts data are collected from the International Financial Statistics and OECD’s statistical database. The national accounts variables are seasonally adjusted, real, logged and HPfiltered with smoothing parameter 1600. Following Arellano (2008), the spreads are returns for EMBI+ and EMBI Blended-Yield Maturity minus the 5-Year Treasury Constant Maturity Rate (GS5 in FRED, averaged by quarter). Table 2 gives the time periods used for each country (for the emerging markets, we required spreads data to be available which restricts the sample somewhat). Figure 2 is reproduced from Gordon and Guerron-Quintana (2017) and uses a slightly different set of countries; see that paper for more details.

7

Sk1 measure Country

Range

Y

Sk2 measure C

I

Spreads

Developing small open economies, high spreads ARG 94Q1:11Q3 -0.52 -0.92 -1.29 -0.21 ECU 95Q2:02Q2 -0.61 -1.02 -0.54 -0.05 MEX 94Q1:11Q3 -0.64 -0.35 -1.08 -0.07 PER 97Q2:11Q3 -1.63 -3.00 0.74 0.10 PHL 99Q2:11Q2 0.03 -0.14 0.15 0.05

-0.14 -0.07 -0.10 -0.05 -0.10

-0.32 0.02 -0.09 0.05 0.15

6.95 9.12 2.95 4.03 4.19

Mean S.d.

-0.03 0.12

-0.09 0.03

-0.04 0.18

5.45 2.53

Developing small open economies, low spreads CHL 99Q2:11Q3 0.08 0.28 0.80 0.06 HRV 97Q1:11Q2 -0.32 -0.40 0.38 0.04 ZAF 94Q4:11Q3 0.54 0.47 1.14 0.11

-0.06 0.16 0.21

0.06 0.01 0.42

1.82 1.96 2.44

Mean S.d.

2.07 0.33

-0.67 0.60

0.10 0.43

C

-1.09 1.13

I

-0.40 0.85

Y

Median

0.12 0.46

0.78 0.38

0.07 0.04

0.10 0.14

0.16 0.22

Developed small open economies AUS 60Q1:17Q1 -0.42 0.13 CAN 81Q2:17Q1 -0.14 0.76 CHE 80Q1:17Q1 0.40 0.15 NZL 88Q1:17Q1 -0.42 -0.13 SWE 60Q1:17Q1 -0.37 -0.01

-0.02 -0.24 -0.05 -0.26 -0.29

-0.05 -0.00 0.07 0.01 -0.02

0.05 0.09 0.08 -0.09 0.09

0.01 -0.06 0.03 0.01 -0.06

Mean S.d.

-0.17 0.13

0.00 0.04

0.04 0.08

-0.01 0.04

-0.19 0.35

0.18 0.34

Note: Y, C, and I are output, consumption, and investment respectively; all data have been logged and HP-filtered; country codes are in ISO 3166-1 alpha-3 format. Table 2: Skewness measures of individual countries by development status

8