Sudden Stops, Financial Crises, and Leverage

Three macroeconomic regularities define a Sudden Stop – a reversal of international capital flows showing up as a jump in net exports and the current account, declines in domestic production and absorption, and corrections in asset prices – and the paper quantifies each with five-year event windows. Using the Calvo, Izquierdo and Talvi (2006) dating and location of events (33 Sudden Stops, with large and mild output collapses, across the 31 countries JP Morgan defines as emerging markets), and cross-country medians of deviations from Hodrick-Prescott trends fitted to 1970-2006 data, the median Sudden Stop shows: a reversal in the cyclical component of the net-exports-to-GDP ratio of about 3 percentage points of GDP, from a deficit of about 2 percent at t-1 to a surplus of 1 percent at t that persists through t+2; GDP and consumption about 4 percentage points below trend at date t; investment collapsing “almost 20 percentage points below trend”; and Tobin’s Q reaching a trough at date t about 13 percentage points below its pre-Sudden-Stop peak, recovering about two-thirds of its value by t+2 (§1, p. 1). Q is measured as the country-median of firm-level ratios of market value of equity plus debt outstanding to book value of equity, from Worldscope, and is not detrended because the data begin only in 1994 (§1, p. 1).

Sudden Stops must be rare events nested inside normal cycles, they must be asymmetric, and a large drop in the Solow residual must account for much of the initial output collapse. The paper lists these explicitly (§1, pp. 1-2). Rarity is partly definitional, since a key identification criterion is that capital flows fall significantly below their mean. Asymmetry is an empirical claim: “symmetric episodes of sudden large drops in trade surpluses accompanied by surges in output and absorption are not observed.” On the Solow residual, the paper notes that part of the drop reflects factors that bias it as a measure of true TFP – imported inputs, capacity utilisation, labour hoarding – and cites its own earlier finding that in Mexico’s 1995 Sudden Stop “a large drop in imported inputs accounts for 3.1 percentage points of the 8.5 percent fall in output per worker between the 94:Q3 and 95:Q2.” These features jointly dictate the modelling strategy: the stochastic steady state must contain both infrequent Sudden Stops and normal cycles, the same exogenous shocks must produce both, and the productivity-measurement wedge must be endogenous.

Because agents in those models retain unrestricted access to a perfect world credit market, so a bad shock produces consumption smoothing via foreign borrowing – the opposite sign of what Sudden Stops show – and rescuing them requires assuming shocks that are both large and unexpected. The paper is direct about this: negative TFP or imported-input-price shocks induce “standard consumption-smoothing and investment-reducing effects,” and while large shocks could produce a big output collapse driven partly by cuts in imported inputs, “this would still fail to explain the current account reversal and the collapse in consumption (since households would borrow from abroad to smooth consumption)” (§1, p. 3). Adding large shocks to the world interest rate or to financing access changes the outcome, but “such a theory of Sudden Stops would hinge entirely on unexplained ’large and unexpected’ shocks” – large by necessity, because the recession must exceed normal recessions, and unexpected because otherwise agents “would self-insure to undo their real effects.” The paper’s claim is precisely that a collateral constraint “can provide an explanation for Sudden Stops that does not hinge on large, unexpected shocks.”

Total debt – one-period international bonds plus within-period working-capital loans, counting both interest and principal – cannot exceed a fraction of the marked-to-market value of the capital stock, which makes the constraint an upper bound on the aggregate leverage ratio. This is the margin requirement of Aiyagari and Gertler (1999), and it is “not derived here from an optimal credit contract. Instead, the constraint is imposed directly as in the models with endogenous credit constraints examined by Kiyotaki and Moore (1997), Aiyagari and Gertler (1999), and Kocherlakota (2000)” (§2.1, p. 8). The paper offers a rationalisation rather than a derivation: such a constraint “could result, for example, from an environment in which limited enforcement prevents lenders to collect more than a fraction of the value of a defaulting debtor’s assets.” Working-capital interest and principal both enter because these are within-period loans, so “lenders consider that the market value of the assets offered as collateral must cover both components.” The paper also argues the mechanism is not specific to literal margin clauses: value-at-risk portfolio management by investment banks and mark-to-market regulatory capital requirements can trigger the same dynamics, and “mechanisms like these played a central role in the Russian/LTCM crisis of 1998 and the U.S. credit crisis of 2007-2008” (§2.2, p. 11).

An endogenous external financing premium that raises the effective cost of bond debt, working-capital loans and equity, and the debt-deflation mechanism itself. The premium arises directly from the multiplier on the collateral constraint in the Euler equation for bonds, with an indirect reinforcement because “a binding credit constraint makes it harder to smooth consumption, and hence the covariance between marginal utility and the world interest rate is likely to increase” (§2.2, pp. 8-9). The premium can be read as “the premium at which the SOE would choose debt amounts that satisfy the collateral constraint with equality in a credit market in which the constraint is not imposed directly.” The same multiplier enters the first-order conditions for labour and imported inputs, raising the effective marginal financing cost of working capital and so cutting factor demands and output contemporaneously (§2.2, p. 10, eqs. 9-10). The equity premium responds similarly but not identically: the direct effect there is offset by a term measuring “the marginal benefit of being able to borrow more by holding an additional unit of capital,” while the covariance between marginal utility and the return on capital becomes more negative when the constraint binds (§2.2, p. 9). Higher expected returns, present or anticipated, raise the discount rate on dividends and so lower the price of capital today – the Aiyagari-Gertler result the paper builds on.

Agents meet margin calls by fire-selling capital, but they face an upward-sloping supply of equity because of Tobin’s Q, so the price of capital falls; the lower price makes the constraint more binding than it was at the notional prices, so another round of margin calls follows. The paper concedes this is “harder to illustrate than the external financing premia because of the lack of closed-form solutions,” but describes it precisely: “if the constraint was binding at the initial (notional) levels of the price of capital and investment, it must be more binding at lower prices and investment levels, so another round of margin calls takes place and Fisher’s debt-deflation mechanism is set in motion. Moreover, the Fisherian deflation causes a sudden increase in the financing cost of working capital, lowering factor allocations and output” (§2.2, pp. 10-11). The contrast with a fixed, exogenous debt limit is the whole point: with a fixed limit, lower equity demand and higher discounting of dividends would exhaust the adjustment.

Because at both extremes it disappears: a zero collateral coefficient makes the constraint unresponsive to asset values, and a coefficient of one removes the direct effect on the equity premium and, under perfect foresight, all distortion of investment and the price of capital. The paper states the non-monotonicity explicitly and draws the conclusion: “for the debt-deflation mechanism to operate, credit markets must allow borrowers to leverage their assets but only to some degree” (§2.2, p. 10-11). This is also how the paper reconciles its results with Kocherlakota’s (2000) finding of small amplification: Kocherlakota’s cases either used a fixed factor such as land as collateral, which “prevents declines in x from compounding with the decline in asset prices in the debt-deflation dynamics,” or used a constraint implying a collateral coefficient of one, “which under perfect foresight removes the debt-deflation mechanism” (§2.2, p. 11). The two sets of results are therefore described as consistent rather than contradictory.

To Mexican data, with the deterministic stationary equilibrium matched to Mexican averages, and with two remaining parameters pinned down by simulated method of moments. Using 1993:Q1-2005:Q2 data, the ratio of GDP to gross output is 0.896 and imported inputs are 0.114 of GDP, giving an imported-input share in gross output of 0.102; combined with a 0.66 labour share on GDP from Garcia (2005) this yields a labour share of 0.592 and a capital share of 0.306 in the gross-output production function (§3.2, p. 12). The depreciation rate is 8.8 percent a year, the 1980:Q1-2005:Q2 average capital-to-gross-output ratio is 1.758, and these imply an investment-to-gross-output ratio of 15.5 percent and an investment-to-GDP ratio of 17.2 percent. The mean relative price of imported inputs is 1.028; the implied mean gross real interest rate is 1.086, which the paper acknowledges is “relatively high” but defends as the rate that, given the other parameters, supports Mexico’s average investment ratio in the deterministic steady state (§3.2, p. 13). The labour-supply exponent is 1.846, implying a labour-supply elasticity of about 1.2. Government purchases of 0.11 of GDP are handled through a time-invariant consumption tax of 0.168 so that private consumption matches 0.65 of GDP. Relative risk aversion is set to 2 and the time-preference semi-elasticity comes out at 0.0166, which the paper reads as meaning “the ‘impatience effects’ introduced by the endogenous rate of time preference have negligible quantitative implications.” The deterministic steady state implies net foreign assets of about -0.86 of GDP. The capital-adjustment-cost coefficient (2.75) and the working-capital coefficient (0.26) are chosen by simulated method of moments to match the ratio of investment to GDP volatility of 3.6 and a mean working-capital-to-GDP ratio of one-fifth, in a simulation where the constraint does not bind (§3.2, pp. 14-15).

It flags several directly, including the working-capital target, the interest-rate and productivity shock measurement, and the shocks attributed to 1995. On working capital: Mexican data on working-capital financing are unavailable, so the 20 percent target approximates the 24.4 percent average ratio of total credit to private nonfinancial firms to GDP over 1994:Q1-2005:Q1, a figure that “includes financing at all maturities and for all uses, so it overestimates actual working capital financing,” while also covering the 1995-2002 bank recapitalisation period during which credit fell for “abnormal” reasons that bias it down (§3.2, pp. 14-15). On the shocks: “typical endogeneity caveats apply to our estimates” of the interest-rate shock, because of the link between country risk and business cycles, and of the TFP shock, because of capacity utilisation and factor hoarding – so “the ’large’ TFP and interest rate shocks reported for the 1995 Sudden Stop probably overestimate the true exogenous shocks that occurred that year” (§3.2, p. 14). The measured autocorrelations are 0.572 for the interest-rate shock and 0.537 for the TFP shock, and the two are negatively correlated at -0.669. The model is solved by a non-linear global method on a discrete grid of 60 capital values, 80 bond values and 8 shock triples (§3.1, p. 12).

Almost not at all, outside the variables the constraint touches directly. Comparing a frictionless economy with economies where the leverage ceiling is 0.3 and 0.2, the paper finds long-run business-cycle moments “very similar,” with large effects confined to the leverage ratio, the foreign-asset ratio and the net-exports ratio: for those three, the means of leverage and foreign assets rise, the mean net-exports ratio falls, all three become less variable and more countercyclical (§4.1, pp. 15-16). The frictionless benchmark itself overestimates GDP volatility (3.9 percent in the model against 2.7 percent in the data) but matches the relative volatilities, the correlations with GDP, and the autocorrelations reasonably; it reproduces consumption being more volatile than GDP, a negative interest-rate-output correlation and countercyclical net exports, and it nearly matches the first-order autocorrelation of the net-exports ratio (0.769 model, 0.797 data). The reason the constrained economy looks so ordinary on average is precautionary saving: even with perfect credit markets and incomplete insurance the average net-foreign-asset ratio is about -33 percent, “almost 53 percentage points higher than in the deterministic steady state,” and with the leverage ceiling at 0.2 it rises further, to about -10 percent (§4.1, p. 16).

In Sudden Stop states, the extra response relative to the frictionless economy at the identical state runs from about 1.1 percent more decline in GDP to almost 12 percentage points more collapse in investment; in non-Sudden-Stop states the two economies respond about the same. Sudden Stop states are defined as states where the collateral constraint binds with positive long-run probability and the net-exports-to-GDP ratio is at least two percentage points above its mean; amplification coefficients are differences in each variable’s response between the constrained and frictionless economies at a common state, averaged over the model’s ergodic distribution (§4.2, p. 16). Scaling by each aggregate’s cyclical variability, the excess responses “imply business cycles that are larger than typical cycles by factors of about 1/3 for GDP to 1.4 for the net exports-GDP ratio.” Two features of the exercise matter for how the result should be read: the shocks are at most one standard deviation in size, and the shocks hitting the constrained and unconstrained economies within each column are identical – so “the model displays significant amplification and asymmetry in response to shocks that are relatively small, and it has the feature that symmetric shocks produce asymmetric responses, the extreme case of which is a Sudden Stop.” The comparison with Kocherlakota (2000) is stark: varying the capital share from 0.1 to 0.3 he found output amplification of 0.15 to 0.35 against 1.13 here, and asset-price amplification of 0.004 to 0.008 against 2.9 here (§4.2, p. 17).

A leverage ceiling of about one-fifth delivers a long-run Sudden Stop probability of 3.3 percent, which matches the observed frequency in the Calvo et al. (2006) cross-country panel. The paper is explicit that precautionary saving is what forces the ceiling to be this tight: “the long-run probability of observing Sudden Stops is reduced by precautionary savings, and hence the model requires an upper bound on the leverage ratio of about 1/5 in order to match the 3.3 percent Sudden Stops probability” (§1, p. 4; §4.2, p. 16). Raising or lowering the ceiling has small effects on the amplification coefficients themselves but moves the amplification of the leverage ratio and the Sudden Stop probability in the opposite direction; lowering the net-exports threshold used to define a Sudden Stop from two percentage points to zero weakens the amplification coefficients somewhat, and raises the event probability sharply (§4.2, p. 17).

Yes for output, consumption, investment and the external accounts; only qualitatively for asset prices. Running a 10,000-period simulation and building five-year event windows around simulated Sudden Stops – identified, to match Calvo et al.’s systemic-event definition, as states where the constraint binds, output is at least one standard deviation below trend, and the net-exports ratio at least one standard deviation above trend – the model “predicts that Sudden Stops are preceded by periods of economic expansion, with GDP, C and I above trend and NXY running deficits at t-2 and t-1,” matches “very closely the magnitude of the declines in GDP, C, and I” at date t, produces a reversal in net exports between t-1 and t “very similar to the one in the data” though at levels the model overstates, and reproduces a slow recovery at t+1 and t+2 (§4.3, p. 18). The exception is asset prices: “the model’s dynamics are qualitatively correct, but quantitatively the decline in asset prices is about 40 percent the size of the actual decline.” The paper notes in mitigation that all of these responses come from one-standard-deviation shocks and that larger shocks would produce larger responses, and that even at this size the model “generates significantly more asset price amplification than in previous studies” (§4.3, p. 19). Against Mexico’s 1995 event specifically, the model matches the GDP and consumption declines well but understates both the pre-crisis boom and the size of the net-exports reversal.

Yes – in Sudden Stop events the model’s Solow residual falls by more than true productivity, overstating it by roughly 30 percent in the baseline – but the paper stresses that true productivity still has to fall. Comparing event windows for the exogenous productivity shock with those for the model’s Solow residual, the two track each other except at the date of Sudden Stops, when the Solow residual falls more (§4.3, p. 18; §1, p. 4). The caveat is stated without hedging: “it is also important to acknowledge that true TFP still has to fall for the output decline to be realistic, and the reason why TFP would fall like this when a Sudden Stop hits remains an open question beyond the scope of this paper.” Raising the imported-input share from 0.1 to 0.2 widens the wedge considerably: an average decline of about 1.2 percent in true productivity translates into a Solow-residual decline almost twice as large (§4.4, pp. 19-20).

The collateral constraint’s bite on working capital: with working capital removed, the model generates no amplification in GDP or factor allocations, the Sudden Stop probability becomes very low, and the pre-crisis expansion disappears. Setting the working-capital coefficient to zero leaves capital predetermined and removes the external financing premium from factor demands, so “factor allocations and output are not affected contemporaneously by the collateral constraint” (§4.2, p. 17). The event-window consequence is more damaging than the missing amplification: without working capital the model “fails to produce periods of economic expansion preceding Sudden Stops, as GDP, C and I are already below trend, and NXY is above trend, before the Sudden Stop hits,” because simulated Sudden Stops are then preceded by low and falling productivity rather than high and rising productivity – investment drops to almost 15 percentage points below trend, consumption and investment about 2 percentage points below trend by t-1, and the trade surplus rises to about 2.5 percentage points of GDP by the same date (§4.4, p. 19). Other aggregates still show amplification and asymmetry, but smaller.

A higher imported-input share improves the fit; a lower labour-supply elasticity worsens it. Raising the imported-input share from 0.1 to 0.2 strengthens the production effects of all three shocks, so the declines in GDP, consumption, working capital, labour and imported inputs are larger while investment and Tobin’s Q are about unchanged, and “the drops in output and consumption at date t are nearly a perfect match to those observed in actual SS events” (§4.4, pp. 19-20). The paper argues this matters because the baseline share “is probably conservative”: Goldberg and Campa (2006) report imported inputs as 14 to 49 percent of total intermediate goods across 17 industrial countries, median 23 percent, with Mexico about one-quarter, and to the extent domestic inputs substitute for imported ones and also require working-capital financing, the higher share is “likely to be closer to the one that is empirically relevant.” Raising the labour-supply exponent to 3, which lowers the labour-supply elasticity from about 1.2 to 0.5, keeps the qualitative shape of the events but shrinks the fluctuations, narrows the productivity-measurement wedge, and – unlike the imported-input exercise – also reduces the declines in investment and asset prices, so “labour supply elasticity of about 1.2, as in the baseline, or higher, is important for the model’s ability to explain observed SS dynamics.”

That the route to fewer Sudden Stops runs through financial development that weakens the contractual frictions behind collateral constraints, that tighter mark-to-market or value-at-risk rules can be counterproductive, and that reserve accumulation is a defensible second best – with the paper explicit that a well-run open economy can still be hit. “The findings of this paper suggest that the key to reducing the probability of Sudden Stops is in promoting the attainment of levels of financial development that weaken the contractual frictions behind collateral constraints,” while, taking the underlying shocks as given, “tighter ‘marked-to-market’ capital requirements or ‘value-at-risk’ targets, designed to manage exposure to idiosyncratic risk, can be counterproductive and raise the probability of observing Sudden Stops” (§5, p. 22). The structural point behind this is that “an economy can have solid domestic policies and competitive, open markets, and still reach a point of high leverage at which a Sudden Stop is caused by a relatively small foreign or domestic shock.” Since waiting for financial development “seems naive” and tighter credit limits “can make things worse,” the paper endorses self-insurance through a sufficiently large stock of reserves, citing Durdu, Mendoza and Terrones (2008) for supporting evidence. It also names its own main unfinished business: a setup with liability dollarisation, in which foreign debt is denominated in tradables but leveraged on non-tradable assets or incomes, so that debt deflation could operate through the relative price of non-tradables rather than through an exogenous devaluation.