2. Preceded (followed) by expansions (contractions) in domestic. 3. Capital, labor account for small fraction of output drop,

Transcription

1 Mendoza (AER) Sudden Stop facts 1. Large, abrupt reversals in capital flows 2. Preceded (followed) by expansions (contractions) in domestic production, absorption, asset prices, credit & leverage 3. Capital, labor account for small fraction of output drop, compared dto imported dinputs, capacity utilization, and dtfp 4. Low-probability events nested with regular business cycles

2 Mendoza (AER) Cross-country event analysis Classification of systemic SS events from Calvo et al. (06) Capital flows criterion: fall in capital flows exceeding 2sd s Spread criterion: spike in aggregate EMBI spread exceeding 2sd s s 33 SS events in sample of EMs (including large and mild output collapse cases) Event windows based on medians of HP detrended data using sample (different from Calvo et al. (06))

3 Mendoza (AER) Current account reversals in Sudden Stop events 3.00% Current Account GDP ratio 2.00% 1.00% 0.00% 1.00% 2.00% 3.00% t 2 t 1 t t+1 t+2

4 Mendoza (AER) Recessions in Sudden Stop events Gross Domestic Product Private Consumption 6.00% 6.00% 4.00% 4.00% 2.00% 2.00% 0.00% 0.00% 2.00% 2.00% 4.00% 4.00% 6.00% t 2 t 1 t t+1 t % t 2 t 1 t t+1 t+2

5 Mendoza (AER) Recessions in Sudden Stop events Investment Tobin Q 20.00% % 10.00% % 0.00% 5.00% % 15.00% % t 2 t 1 t t+1 t t 2 t 1 t t+1 t+2

6 Mendoza (AER) Leverage ratios in Sudden Stop events (listed corporations in Indonesia, Korea, Malaysia & Thailand) debt to market value of equity (right axis) debt to book value of equity (left axis) debt to sales (left axis) Note: Cross-country arithmetic average of median leverage ratios across all publicly listed corporations in each country. Data from Worldscope database.

7 Mendoza (AER) Limitations of Sudden Stop literature Sudden stops as large unexpected shocks Constraints always bind Solutions using local perturbation methods. No non-linearities. Cannot generate crisis events within normal cycles.

8 Propose nonlinear DSGE model of financial crises (Sudden Stops) Show that its quantitative predictions are in line with the facts (except smaller asset price collapse) Leverage rises during expansions, and when it rises enough it triggers a collateral constraint Fisherian deflation causes spiraling decline in price and quantity of collateral assets, and in access to debt and working capital Working capital crunch lowers output and factor allocations

9 Amplification and asymmetry in response to standard size shocks Financial crises are low-probability events nested within regular business cycles Precautionary savings lowers prob. of crisis Long-run business cycle moments not affected by financial frictions

10 Model Households own firms, produce, consume and save/borrow. Households utility function ] E 0 β t U(c t, l t ) t=0 β t : endogenous discount factor that depends on lagged consumption and labor. Quasilinear/GHH preferences. No wealth effects on labor supply.

11 Household s own firms that produce a homogenous good. ν : foreign intermediate inputs y t = exp(ε A t )F (k t, l t, ν t ) Output sold at exogenous world price set to 1. They make capital investment decisions that are subject to adjustment costs: Capital accumulation equation z t is net investment k t+1 = k t + z t

12 Adjustment costs in investment: To change the capital stock by z t must pay an installation cost above the cost of purchasing new capital goods. z t Ψ( z t k t ) Ψ = a 2 k t Capital stock depreciates at the rate δ Household save/borrow in risk free one period bonds qt b = 1 R t : Price of bonds, exogenous z t

13 Working Capital Loans on labor and intermediate inputs Pay in advance: Need to borrow fraction φ of labor bill and intermediate input bill. Total cost of labor w t l t + (R t 1)φw t l t Total cost of intermediate inputs p t v t + (R t 1)φp t v t Price takers in the market for labor and inputs.

14 Household s budget constraint c t + i t + q b t b t+1 = y t p t v t (R t+1 1) φ (w t l t + p t v t ) + b t i t = δk t + z t + z t Ψ( z t k t )

15 Collateral Constraint q b t b t+1 φr t+1 (w t l t + p t ν t ) κq t k t+1 Total debt, including both debt in one-period bonds and working capital loans, cannot exceed a fraction κ of the marked-to-market value of capital. Can arise from costly enforcement / costly state verification. q t : price of domestic capital

16 Competitive equilibrium is inefficient: agent ignores the implications of its actions on the prices. Has a suboptimally low level of precautionary savings, and hence is exposed to Sudden Stops

17 Households problem L = E 0 t=0 β t λ t U(c t, l t )+ y t p t v t (R t 1) φ (w t L t + p t v t ) + ( ) b t c t δk t + z t + z t Ψ( zt k t ) qt b b t+1 +q t z t + k t k t+1 ] ] +µ t q b t b t+1 φr t (w t l t + p t ν t ) + κq t k t+1

18 Bond Euler equation: L b t+1 b t+1 ] λ t qt b µ t qt b 1 µ ] t λ t = βe t (λ t+1 ) = β q b t E t (λ t+1 ) λ t Define Rt h λt E t(λ t+1 ) External finance premium on debt If the constraint does not bind R h t R t = λ t λ t µ t If the constraint binds R h t R t = 1 R h t R t > 1

19 Working Capital Wedge FOC w.r.t l t, L l t U l,t + λ t ( yt l t (R t 1) φw t ) + µ t ( φr t w t ) = 0 U l,t λ t = U l,t U c,t = w t y t l t = 1 + (R t 1) φw t + µ t = w t 1 + φ ] (φr t w t ) λ t )] ( (R t 1) + µ t λ t R t FOC wrt ν t, L v t ( ) ( yt = p t 1 + φ (R t 1) + µ )] t R t ν t λ t

20 Asset Pricing Wedge FOC wrt z t, L z t q t = = ( ) z t Ψ( zt k t ) 1 + z t 1 + Ψ( z t ) + z t Ψ ( z ] t ) k t k t k t Shadow price of capital = Marginal cost of investment

21 Asset Pricing Wedge Euler equation for Capital, L K t+1 ( yt+1 q t (λ t µκ) = βe t λ t+1 + z t+1 Ψ ( z t+1 )( z )] t+1 ) δ + q t+1 k t+1 k t+1 k 2 t+1 When the collateral constraint does not bind, µ = 0 ( λt+1 yt+1 q t = βe t + z t+1 Ψ ( z t+1 )( z )] t+1 ) δ + q t+1 λ t k t+1 k t+1 When the collateral constraint binds, µ > 0 q t = βe t λ t+1 (λ t µκ) k 2 t+1 ( yt+1 + z t+1 Ψ ( z t+1 )( z )] t+1 ) δ + q t+1 k t+1 k t+1 k 2 t+1

22 Euler equation for capital d t+1 y t+1 + z t+1 Ψ ( z t+1 )( z t+1 ) δ k t+1 k t+1 k 2 t+1 ] λ t+1 q t = βe t (λ t µκ) (d t+1 + q t+1 ) ] λ t+1 (d t+1 + q t+1 ) 1 = βe t (λ t µ t κ) q t ] λ t+1 = βe t (λ t µ t κ) Rq t+1 R q t+1 = (d t+1+q t+1 ) q t ] ( ) λ t+1 λt+1 1 = βcov t (λ t µκ) Rq t+1 + βe t E t R q t+1 (λ t µ t κ)

23 1 = βcov t λ t+1 (λ t µκ) Rq t+1 From the bond Euler equation 1 µ ] t = β λ t qt b λ t+1 1 = βcov t (λ t µκ) Rq t+1 λ t+1 1 = βcov t (λ t µκ) Rq t+1 ] ( ) λt+1 + βe t E t R q t+1 (λ t µ t κ) E t (λ t+1 ) λ t ] ( + βqt b λt µ t (λ t µ t κ) ] + ( λt µ t (λ t µ t κ) ) E t R q t+1 ) Et R q t+1 E t R q t+1 R t ] = (1 κ)µ t + Cov t λt+1 R q t+1 ] E t λ t+1 R t

24 E t R q t+1 R ] (1 κ)µ t + Cov t λt+1 R q ] t = t+1 E t λ t+1 If µ = 0 have the standard equity premium equation. If µ > 0, increases the equity premium by (1 κ). Can borrow more when have an additional unit of capital.

25 Equity Prices E t R q t+1 = E t Recursive substitutions ( q t = E t ( ) (dt+1 + q t+1 ) q t q t = E t ((d t+1 + q t+1 )) E t R q t+1 j=0 Π j i=0 ( 1 E t R q t+1+i )) d t+1+j Higher expected returns when the collateral constraint binds at present, or is expected to bind in the future, increase the discount rate of dividends and lower asset prices at present. Even if collateral constraint binds only occasionally in the stochastic steady state, the entire equilibrium asset pricing function is distorted by the collateral constraint.

26 Fisherian Debt Deflation Mechanism When constraint binds, q declines. Constraint binds more Increase in working capital costs Less demand for investment q declines further and so on...

27 Fisherian Debt Deflation Mechanism If κ = 0, no debt deflation mechanism Constraint is independent of asset values When κ = 1, the direct effect on equity premium goes to 0. For debt-deflation mechanism to be relevant, borrowers must be able to leverage their assets but only to a limited degree.

28 Calibrate Solve using discrete state space methods. Long-run business cycles unaffected by collateral constraints Precautionary savings Relatively rare Sudden Stops (3%) coexist with the more frequent, normal business cycles Debt to GDP lower with collateral constraints

29 Table 3. Long-Run Business Cycle Moments Standard Standard Correlation First-order Variable Mean deviation deviation with autocorrelation (in percent) relative to GDP GDP 1. Economy without Collateral Constraint gdp c i nx/gdp k b/gdp q leverage ratio v working capital Savings-investment correlation GDP-world interest rate correlation GDP-int. goods price correlation Economy with 30 Percent Collateral Coefficient (κ = 0.30) gdp c i nx/gdp k b/gdp q leverage ratio v working capital Savings-investment correlation GDP-world interest rate correlation GDP-int. goods price correlation

30 Table 4. Amplification and Asymmetry Features of Sudden Stop Events (mean differences relative to frictionless economy in percent of frictionless averages) (1) (2) (3) (4) (5) Baseline economy Weaker collateral constraint Tighter collateral constraint Zero net exports No working capital κ =0.20 κ =0.30 κ =0.15 threshold φ =0 S.S. non S.S. S.S. non S.S. S.S. non S.S. S.S non S.S S.S non S.S states states states states states states states states states states gdp c i q nx/gdp b/gdp lev. ratio L v w. cap na na prob. of SS events percent 1.07 percent 3.92 percent 9.54 percent 0.07 percent b/gdp in SS events Note: Sudden Stop (S.S.) states are defined as states in which the collateral constraint binds with positive long-run probability and the net exports-gdp ratio is at least 2 percentage points above its mean.

31 Gross Domestic Product Private Consumption 6.00% 6.00% 4.00% 4.00% 2.00% 2.00% 0.00% 0.00% 2.00% 2.00% 4.00% 4.00% 6.00% t 2 t 1 t t+1 t % t 2 t 1 t t+1 t % 15.00% Investment 3.00% 2.00% Net exports GDP ratio 10.00% 5.00% 0.00% 1.00% 0.00% 5.00% 10.00% 15.00% 1.00% 2.00% 20.00% t 2 t 1 t t+1 t % t 2 t 1 t t+1 t+2 Tobin Q 1.050

32 t 2 t 1 t t+1 t % t 2 t 1 t t+1 t+2 Tobin Q t 2 t 1 t t+1 t+2 Figure 1: Macroeconomic Dynamics around Sudden Stop Events in Emerging Economies (cross-country medians of deviations from HP trends) ication of Sudden Stop events in the emerging markets data is taken from Calvo et al. (2006). They define systemic sudden s mild and large output collapses that coincide with large spikes in the EMBI spread and large reversals in capital flows. Tobin lue of equity and debt outstanding over book value of equiy, and it is shown in levels instead of deviation from HP trend