A. The Emerging Economy

The representative firm inside the SOE produces a tradable commodity by combining labor (n) and a time-invariant stock of physical capital (k) using a Cobb-Douglas technology: exp(ε_t)F(k, n), where ε is a Markov productivity shock. This firm participates in competitive factor and goods markets taking the real wage (w) as given. Thus, the choice of labor input consistent with profit maximization yields standard marginal productivity conditions for labor demand and the rate of dividend payments (d):

Households choose stochastic sequences of consumption (c), labor supply (n), equity holdings (α), and foreign bond holdings (b) so as to maximize the following utility function:

This utility function is a time-recursive, intertemporal utility index with an endogenous rate of time preference that introduces an “impatience effect” on the marginal utility of consumption (i.e., changes in c_t alter the subjective discount rate applied to future utility flows). Utility functions with this feature are commonly used in small open economy models to obtain well-defined long-run equilibria for holdings of foreign assets.⁵ As Section III shows, in models with credit constraints these preferences are also critical for supporting long-run equilibria in which credit constraints can bind.

The period utility function u(⋅) is a standard, concave, twice-continuously differentiable utility function. The function v(⋅) is the time preference function, which is also concave and twice-continuously differentiable. The argument of both functions is a composite good defined by consumption minus the disutility of labor c-h(n), where h(⋅) is an increasing, convex, continuously-differentiable function. Greenwood, Hercowitz and Huffman (1988), GHH, introduced this composite good as a way to eliminate the wealth effect on labor supply. As in Mendoza and Smith (2006), this property of preferences, together with conditions (1) and (2), separates the determination of equilibrium wages, dividends, labor and output from the equilibrium allocations of consumption, saving and portfolio choice.

The household maximizes lifetime utility subject to the following budget constraint:

where α_t and α_t+1 are beginning-and end-of-period shares of capital owned by households, q_t is the price of equity, and R is the world real interest rate, which is kept constant for simplicity.

Foreign debt contracts feature a collateral constraint in the form of a margin clause that limits the debt not to exceed the fraction κ of the market value of the SOE’s equity holdings:

Margin clauses of this form are widely used in international capital markets. In some instances they are imposed by regulators with the aim of limiting the exposure of financial intermediaries to idiosyncratic risk in lending portfolios, but they are also widely used by investment banks and other lenders to manage default risk (either in the form of explicit margin clauses attached to specific securities offered as collateral, or as implicit margin requirements linked to the volatility of returns of an asset class like those implied by value-at-risk collateralization). Margin clauses are a particularly effective collateral constraint (compared to the classic constraint of Kiyotaki and Moore, 1997, that limits debt to the discounted liquidation value of assets one period ahead) because: (a) custody of the securities offered as collateral is surrendered at the time the credit contract is entered and (b) margin calls to make up for shortfalls in the market value of the collateral are automatic once the value of the securities falls below the contracted value.

Households in the small open economy also face a short-selling constraint in the equity market: α_t+1 ≥_χ with -∞<_χ<1 for all t. This constraint is necessary in order to make the margin constraint non-trivial. Otherwise, any borrowing limit in the bond market implied by a binding margin constraint could always be undone by taking a sufficiently short equity position.

B. The Foreign Securities Firm, IFO & the Price Guarantees

The representative foreign securities firm obtains funds from international investors and specializes in investing them in the SOE’s equity. This firm maximizes its net present value discounted at the discount factor of its international clients (i.e., the world interest rate). Thus, the foreign traders’ problem is to choose α_t+1^*, for t = 1,…, ∞, so as to maximize:

The total net return of the foreign securities firm (π_t) is the sum of: (a) dividend earnings on current equity holdings $({{k\alpha }_t}^{*}{d}_t)$, minus (b) the value of equity trades, which is the difference between equity purchases q_t k α _t+1^* and equity sales ${max}(q_t,{\tilde{q}}_t){{k\alpha }_t}^{*}$ executed at either the market price q_t or the guaranteed price ${\tilde{q}}_t$, whichever is greater, minus (c) trading costs, which include a term that depends on the size of trades $({{\alpha }_{t+1}}^{*}-{{\alpha }_t}^{*})$ and a recurrent trading cost (θ), minus (d) lump sum taxes paid to the IFO $({{kT}_t}^{*})$. Trading costs are specified in quadratic form, so a is a standard adjustment-cost coefficient.

The IFO buys equity from the foreign traders at the guaranteed price and sells it at the equilibrium price. Thus, the IFO’s budget constraint is:

If the guarantee is not executed, the tax is zero. If the guarantee is executed, the IFO sets the lump-sum tax to match the value of the executed guarantee (i.e., the extra income that foreign traders earn by selling equity to the IFO instead of selling it in the equity market). Since the return on equity is $R_t^q\mathit{\equiv }\mathit{[}{d}_t+q_t\mathit{]}/q_{t-\mathit{1}}$, the IFO’s offer to guarantee the date-t price implies a guaranteed return on the emerging economy’s equity ${\tilde{R}}_t^q=[{\tilde{q}}_t+d_t]/q_{t-1}$.

C. Equilibrium

A competitive equilibrium is given by stochastic sequences of prices ${[w_t,d_t,q_t]}_{t=0}^{\infty }$ and allocations ${[c_t,n_t,b_{t+1},{\alpha }_{t+1},{\alpha }_{t+1}^{*},T_t^{*}]}_{t=0}^{\infty }$ such that: (a) households maximize the utility function (3) subject to the constraints (4) and (5) and the short-selling constraint, taking prices, wages and dividends as given, (b) domestic firms maximize profits so that equations (1) and (2) hold, taking wages and dividends as given, (c) foreign traders maximize (6) taking the price of equity, the price guarantees and lump-sum taxes as given, (d) the budget constraint of the IFO in equation (7), holds and (e) the equity market clears (i.e., α_t + α_t^* = 1 for all t).

A. Recursive Equilibrium and Solution Method

In the recursive representation of the equilibrium, the state variables are the current holdings of assets and bonds in the emerging economy, α and b, and the realization of the productivity shock ε. The state space of asset positions spans the discrete grid of NA nodes A={α₁<α₂<…<α_NA} with α₁=χ, and the state space of bonds spans the discrete grid of NB nodes B={b₁<b₂<…<b_NB}. The endogenous state space is defined by the discrete set Z = A × B of NA ×NB elements. Productivity shocks follow a stationary, two-point Markov chain with realizations E={ε_L < ε_H}. Equilibrium wages, dividends, labor and output are determined by solving the supply-side system given by equations (1), (2), (9) and the production function. The solutions are given by functions that depend only on ε: w(ε), d(ε), n(ε) and F(ε).

The numerical solution of the recursive equilibrium is obtained using a modified version of Mendoza and Smith’s (2006) quasi-planning problem algorithm. The algorithm starts with a conjecture for the function Ĝ(α, b, ε): E × Z → R⁺, which returns the expected present discounted value of “excess prices” for any triple (α, b, ε) in the state space. Given this conjecture, the optimal decision rules for equity and bond holdings of domestic agents, α′ (α, b, ε),b′ (α, b, ε): E × Z → R, are obtained by solving the following dynamic programming problem:

subject to:

Note that equity prices in (17) and (18) were replaced with the prices along the demand curve of foreign traders by imposing equity market clearing and solving for equity prices using (15).

The decision rule for equity holdings is plugged into equation 15) to derive an “actual” asset pricing function (for the given conjecture Ĝ(α, b, ε)). The decision rules for bonds and equity, the guaranteed prices, and this “actual” pricing function are then used to solve for the “actual” G(α, b, ε) function. The conjectured and actual G functions are then combined to create a new conjecture using a Gauss-Siedel rule, and the procedure starts again with the Bellman equation (18). The process is repeated until Ĝ(•) and G(•) converge, so that the function Ĝ(α, b, ε) that is taken as given in the dynamic programming problem is consistent with the function G(α, b, ε) implied by the asset pricing function and decision rules that are endogenous outcomes of that problem.

The drawback of this method is that it assumes that the emerging economy internalizes the demand function of foreign traders. As a result, the equilibrium of problem (18) is equivalent to a competitive equilibrium for a variant of the model with a proportional tax or subsidy on asset returns, with tax revenues rebated as a lump-sum transfer. In the simulations we discuss below, however, the implied taxes are negligible: The maximum taxes in absolute values range between 0.08 (0.4) and 0.2 (0.8) percent when a =0.2 (2). The average tax in absolute value is 0.03 (0.3) percent in the simulations with a =0.2 (2).

B. Deterministic Steady State and Calibration

The functional forms that represent preferences and technology are the following:

γ is the labor income share, σ is the coefficient of relative risk aversion, β is the elasticity of the rate of time preference with respect to 1+c_t - h(n_t), and δ sets the wage elasticity of labor supply (which is equal to 1/(δ-1)). The condition 0<β≤σ is required to limit impatience effects and obtain a well-defined limiting distribution of foreign bonds (see Arellano and Mendoza (2003) for details).

The calibration strategy differs markedly from the one in Mendoza and Smith (2006). They normalize the capital stock to k=1 and let the steady-state equity price adjust to the value implied by the asset pricing condition, given a set of parameter values taken directly from the data or set to enable the model to match ratios of national accounts statistics. Here, we normalize instead the steady-state equity price so that the capital stock matches the deterministic, steady-state capital stock of a typical RBC-SOE model calibrated to Mexican data (see Mendoza (2006)). The steady state of this RBC-SOE model is a frictionless, neoclassical stationary equilibrium. Calibrating to this frictionless equilibrium helps focus the analysis on the use of price guarantees to prevent Sudden Stops triggered by margin calls that hit the economy only when it is highly leveraged (and hence off the long-run equilibrium).

The risk aversion parameter is set at σ =2 in line with values often used in RBC-SOE studies. The parameter values that enter into the supply-side system are determined as follows. The labor share is set at γ =0.65, in line with international evidence on labor income shares. The Mexican average share of labor income in value added in an annual sample for 1988–2001 is 0.34, but values around 0.65 are the norm in several countries and there is concern that the Mexican data may measure inaccurately proprietors income and other forms of labor income (see Mendoza (2006) for details). The real interest rate is set at 6.5 percent, which is also a value widely used in the RBC literature. Since the model is set to a quarterly frequency, this implies R=1.065^1/4. The labor disutility coefficient is set to the same value as in Mendoza and Smith (2006), δ =2, which implies a unitary wage elasticity of labor supply.

As in a typical RBC calibration exercise, the calibration is designed to yield a set of parameter values such that the model’s deterministic steady state matches actual averages of the GDP shares of consumption (sc), investment (si), government purchases (sg) and net exports (snx). In the Mexican data, these shares are sc=0.684, si=0.19, sg=0.092, and snx=0.034. Since the model does not have investment or government purchases, their combined share (0.282) is treated as exogenous absorption of output equivalent to 28.2 percent of steady-state GDP. In the stochastic simulations we keep the corresponding level of these expenditures constant at 28.2 percent of the value obtained for steady-state output in the calibration.

The typical RBC-SOE model features a standard steady-state optimality condition that equates the marginal product of capital net of depreciation with the world interest rate, and a standard law of motion of the capital stock that relates the steady-state investment rate to the steady-state capital-output ratio. Given the values of si, γ, δ and R, these two steady-state conditions yield values of the depreciation rate (dep) and the capital-output ratio (sk). On an annual basis, the resulting depreciation rate is 7.75 percent and sk is about 2.5.

In a deterministic steady state of the model of Section II in which the credit constraint does not bind and there are no price guarantees, the equity price is q = q ^f = d/(R-1). Given the RBC-SOE calibration criterion that the steady-state marginal product of capital net of depreciation equals the net world interest rate, q^f can be re-written as F_k (k, n)/(Fk (k, n)-dep). With the Cobb-Douglas production function this reduces to q ^f = (1-γ)/(1-γ -si). Thus, the requirement that the model’s dividend rate must match a typical RBC-SOE calibration implies that the steady-state equity price is determined by si and γ. With the parameter values set above we obtain q ^f=2.19.

Given the values of γ, δ, R, and q^f the steady-state solutions for n, w, k, and F(k, n) follow from solving the supply-side system conformed by (1), (2), (9) and (21). The resulting steady-state capital stock is k =79. By construction, this capital stock is also consistent with the estimated capital-output ratio of 2.5 and the observed Mexican investment rate of 0.19.

The parameters that remain to be calibrated are the time-preference elasticity coefficient β and the financial frictions parameters a, θ and к. The value of β is derived from the consumption Euler equation as follows. In the deterministic stationary state of the model there are no credit constraints and hence the endogenous rate of time preference equals the real interest rate:

Given the values of R, δ, n, F(k, n) and sc, this condition can be solved for the required value of β. The solution yields β =0.0118. The total stock of domestic savings at steady state follows then from the resource constraint as s = [c-F(k, n)(si+sg)-wn]/(R-1)= αq ^fk + b.

Up to this point the calibration followed the typical RBC-SOE deterministic calibration exercise. A problem emerges, however, when we try to determine the composition of the savings portfolio because the allocation of savings across bonds and equity is undetermined. Any portfolio (α, b)∈A×B is consistent with the RBC-SOE deterministic steady state as long as it supports the unique steady-state level of savings (i.e., αq ^fk + b = s) and the margin and short-selling constraints do not bind (b> -кαq ^fk and α > χ). Moreover, given the values of s, q^f and k implied by the calibration, it follows from the definition of savings that there is only a small subset of portfolios in which the economy borrows in the bond market (i.e., portfolios with b<0) in the set of multiple steady-state portfolios. Debt portfolios require α > 0.9. If domestic agents own less than 90 percent of k, their steady-state bond position is positive and grows larger the smaller is α. This also implies that it will take low values of к to make the margin constraint bind. In particular, setting the upper bound of α at 100 percent, it takes к ≤ 0.10 for the margin constraint to bind for at least some of the multiple steady-state pairs of (α, b). These low values of к can be justified by considering that the margin constraint represents the fraction of domestic capital that is useful collateral for external debt. Several studies in the Sudden Stops literature provide arguments to suggest that this fraction is small (see, for example, Caballero and Krishnamurty (2001)).

The stochastic RBC-SOE without credit constraints has the additional unappealing feature that it can lead to degenerate long-run distributions of equity and bonds in which domestic agents hold the smallest equity position (χ) and use bonds to engage in consumption smoothing and precautionary saving. The reason is that, without credit constraints and zero recurrent trading costs, risk-averse domestic agents demand a risk premium to hold equity while risk-neutral foreign traders do not.⁶ Hence, domestic agents end up selling all the equity they can to foreign traders, although the process takes time because of the trading costs that foreign traders pay.

To circumvent the problems of portfolio determination in the deterministic and stochastic RBC-SOE steady states, we calibrate the values of the financial frictions parameters (a, θ and к) so that the allocations and prices obtained with the deterministic RBC-SOE steady state can be closely approximated as the deterministic steady state of an economy with negligible (but positive) recurrent trading costs and a margin constraint that is just slightly binding. This calibration scenario is labeled the “nearly frictionless economy”(NFE).

The deterministic steady state of the NFE has well-defined, unique solutions for bond and equity positions. In particular, foreign traders hold a stationary equity position at the price q = q^f/(1+aθ). Since this price is less than q^f, which is the price at which the return on domestic equity equals R, it follows that at this lower price R^q > R. Thus, foreign traders now require an equity premium to hold a stationary equity position. The ratio of the Lagrange multipliers of the domestic agent’s margin constraint and budget constraint can then be found to be η/λ = (R^q-R)/(R^q -Rк). In addition, since the margin constraint binds, bond holdings must satisfy b = -кα q k, and hence a unique stationary domestic equity position can be obtained from the steady-state consumption Euler equation. This is the value of α that solves the following expression:

Equation (24) illustrates the key role of the endogenous rate of time preference in supporting deterministic stationary equilibria with binding credit limits: it allows the rate of time preference to adjust so as to make the higher long-run consumption level, implied by the fact that the credit constraint prevents domestic agents from borrowing as they desire in the transition to steady state, to be consistent with the higher effective long-run real interest rate also implied by the credit constraint. The recurrent trading cost is also critical. With θ=0, a stationary equity position for foreign traders requires a price equal to q^f and a return on equity equal to R, but the latter implies that η/λ=0, so the borrowing constraint could not bind.

In the NFE steady state, the values of a, θ and к are set to support a deterministic steady state with a binding borrowing constraint that satisfies the following conditions: (1) the debt-GDP ratio is in line with Mexican data, (2) the allocations, factor payment rates and the equity price are nearly identical to those obtained for the frictionless RBC-SOE deterministic steady state, and (3) the elasticity of the foreign trader’s demand curve is relatively high. The values of the financial frictions parameters are: a = 0.2, θ = 0.001 and к = 0.03. With these parameter values, and the values set earlier for γ, δ, β, and R, the NFE steady state yields values of c, s, n, w, d, q, and R^q nearly identical to those of the RBC-SOE deterministic steady state, but the NFE also has unique portfolio allocations of α = 0.931 and b = -4.825 (which implies a debt-GDP ratio of about 0.62).

C. Stochastic Simulation Framework

The stochastic simulations are solved over a discrete state space with 78 evenly-spaced nodes in the equity grid and 120 evenly-spaced nodes in the bonds grid. The lower bound for equity is set at χ=0.84, so the equity grid spans the interval [0.84,1]. These equity bounds, together with the maximum equity price supported by (15) and the margin constraint, set the lower bound for bonds as -к q^maxk = -5.2. This is the largest debt that the SOE could leverage by holding the largest possible equity position at the highest possible price. The upper bound of bonds is found by solving the model repeatedly starting with an upper bound that supports steady state savings with the equity position at its lowest, and then increasing the upper bound until the grid captures the support of the ergodic distribution of bonds. The resulting grid spans the interval [-5.2,25.7]. The segment of debt positions inside this interval is relatively small, reflecting the fact that, despite the frictions induced by asset trading costs, domestic agents still have a preference for riskless bonds as a vehicle to smooth consumption and build a buffer stock of savings.

A lower bound on domestic equity holdings of 84 percent seems much higher than the conventional short-selling limit set at 0 but it is consistent with the national aggregates targeted in the calibration. In Mexico, the 1988–2000 average ratio of stock market capitalization to GDP was 27.6 percent. Since the calibration produced an estimate of the capital-output ratio of about 2.5, the shares of publicly traded firms constitute just 11 percent of the capital stock. A large fraction of Mexico’s capital is owned by non-publicly-traded firms and by owners of residential property, and thus does not have a liquid market in which shares are traded with foreign residents. In general, it is hard to argue that a large fraction of the physical capital of most emerging economies has a liquid international market. Moreover, the result from the calibration showing that bond positions become positive and unrealistically large for α<0.9 also argues for a high value of χ.

Productivity shocks are modeled as a two-point, symmetric Markov process that follows the “simple persistence” rule. The two points of the Markov chain and the transition probability matrix are set so that the model mimics the standard deviation and first-order autocorrelation of the quarterly cyclical components of Mexico’s GDP reported in Mendoza (2006)—2.64 percent and 0.683 respectively. This requires a Markov process of productivity shocks with a standard deviation (σ_ε) of 1.79 percent and a first-order autocorrelation coefficient (ρ_ε) of 0.683. The simple persistence rule implies then that the two points of the Markov chain are -ε_L = ε_H = 0.0179 and these two states have a long-run probability of ½. The transition probability of remaining in either state is given by ½(1-(ρ_ε)+ρ_ε = 0.8415 and the transition probability of shifting across states is ½(1-ρ_ε) = 0.1585.

D. Baseline Results: Globalization Hazard and Sudden Stops Without Price Guarantees

The baseline results include four simulations: (1) the NFE case, (2) the economy with binding margin requirements (BMR), which uses a margin coefficient set at к =0.005, (3) a simple price-guarantees policy that sets a single, non-state-contingent guaranteed price (NSCG) for all dates and states, and (4) an economy with the same guaranteed price but as a state-contingent guarantee (SCG) that applies only in a subset of the state space.

The key result that emerges from comparing the NFE and BMR economies is that the financial frictions representing globalization hazard in the model do cause Sudden Stops when the ratio of debt to the market value of equity is high and the equity market has enough liquidity (i.e., domestic agents are not at their short-selling limit). Since this result echoes findings from Mendoza and Smith (2006), we keep the presentation short and refer the reader to their article for details.

Figures 2 shows the long run distributions of equity and bonds for the four simulations. Comparing the bond distributions of the NFE and BMR simulations, the effect of the margin constraint is evident. The distribution is biased to the left in the two economies but it shifts markedly to the right in the BMR case. The opposite occurs with the distribution of equity. The bias to the left in the distribution of equity reflects the incentive that risk-averse domestic agents have to sell equity to risk-neutral foreign traders. Binding margin constraints shift the equity distribution further to the left because of the equity fire sales triggered by margin calls. These shifts in the distributions of equity and bonds also reflect the outcome of precautionary saving. Domestic agents, aware of the imperfections of financial markets, have an incentive to build up a buffer stock of savings so as to minimize the risk of large declines in consumption, and in doing so they also lower the risk of facing states in which margin constraints bind in the long run (Figure 2 shows that the long run distribution of bonds of the BMR economy rules out states with very large debt positions). Still, Table 1 shows that the long-run probability of binding margin constraints is about 4 percent. Sudden Stops are therefore rare but non-zero probability events in the stochastic steady state (although many of the states in which margin constraints bind in the long run do not trigger Sudden Stops, as explained below). Note also that margin constraints cause a portfolio reallocation of savings from equity into bonds. Table 1 shows that the long-run average of the bonds-output ratio increases from 18 percent in the NFE to 50 percent in the BMR economy.

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Ergodic Distributions of Domestic Equity and Bond Holdings

Citation: IMF Working Papers 2006, 073; 10.5089/9781451863338.001.A001

Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements, NSCG is economy with be margin requirements and non-state-contingent guarantees, and SCG is economy with binding margin requirements and stag contingent guarantees.

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Table 1.

Long Run Business Cycle Moments

Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements, NSCG is economy with binding margin requirements and non-state-contingent guarantees, and SCG is economy with binding margin requirements and state-contingent guarantees.

Table 1.

Long Run Business Cycle Moments

Variable	mean	std. dev. (in %)	std. dev. relative to GDP	Correlation w/GDP	first-order auto- correlation
I. NFE Economy
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.366	2.185	0.826	0.853	0.770
current account-GDP ratio	0.000	1.347	0.509	0.979	0.660
trade balance-GDP ratio	0.315	0.948	0.358	0.564	0.811
equity price	2.187	0.121	0.046	0.961	0.606
foreign debt-GDP ratio	0.177	56.694	21.442	-0.076	0.997
debt-equity ratio	0.010	2.888	1.092	0.000	0.001
II. BMR Economy (probability of binding margin constraints = 3.973%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.365	2.186	0.827	0.856	0.771
current account-GDP ratio	0.000	1.324	0.501	0.982	0.664
trade balance-GDP ratio	0.315	0.940	0.355	0.565	0.823
equity price	2.187	0.121	0.046	0.962	0.609
foreign debt-GDP ratio	0.499	37.964	14.358	-0.118	0.994
debt-equity ratio	0.026	2.007	0.759	0.000	0.001
III. NSCG Economy (probability of binding margin constraints = 0.001%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.362	2.052	0.776	0.790	0.724
current account-GDP ratio	0.000	1.487	0.562	0.968	0.660
trade balance-GDP ratio	0.315	1.111	0.420	0.631	0.750
equity price	2.198	0.099	0.037	0.891	0.384
foreign debt-GDP ratio	1.336	41.053	15.526	0.001	0.992
debt-equity ratio	0.071	2.186	0.827	0.000	0.006
IV. SCG Economy (probability of binding margin constraints = 0.001%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.364	2.121	0.802	0.834	0.765
current account-GDP ratio	0.000	1.380	0.522	0.974	0.660
trade balance-GDP ratio	0.315	1.000	0.378	0.599	0.788
equity price	2.188	0.121	0.046	0.903	0.630
foreign debt-GDP ratio	1.114	34.141	12.912	-0.067	0.991
debt-equity ratio	0.059	1.810	0.685	0.000	0.004

Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements, NSCG is economy with binding margin requirements and non-state-contingent guarantees, and SCG is economy with binding margin requirements and state-contingent guarantees.

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Table 1.

Long Run Business Cycle Moments

Variable	mean	std. dev. (in %)	std. dev. relative to GDP	Correlation w/GDP	first-order auto- correlation
I. NFE Economy
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.366	2.185	0.826	0.853	0.770
current account-GDP ratio	0.000	1.347	0.509	0.979	0.660
trade balance-GDP ratio	0.315	0.948	0.358	0.564	0.811
equity price	2.187	0.121	0.046	0.961	0.606
foreign debt-GDP ratio	0.177	56.694	21.442	-0.076	0.997
debt-equity ratio	0.010	2.888	1.092	0.000	0.001
II. BMR Economy (probability of binding margin constraints = 3.973%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.365	2.186	0.827	0.856	0.771
current account-GDP ratio	0.000	1.324	0.501	0.982	0.664
trade balance-GDP ratio	0.315	0.940	0.355	0.565	0.823
equity price	2.187	0.121	0.046	0.962	0.609
foreign debt-GDP ratio	0.499	37.964	14.358	-0.118	0.994
debt-equity ratio	0.026	2.007	0.759	0.000	0.001
III. NSCG Economy (probability of binding margin constraints = 0.001%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.362	2.052	0.776	0.790	0.724
current account-GDP ratio	0.000	1.487	0.562	0.968	0.660
trade balance-GDP ratio	0.315	1.111	0.420	0.631	0.750
equity price	2.198	0.099	0.037	0.891	0.384
foreign debt-GDP ratio	1.336	41.053	15.526	0.001	0.992
debt-equity ratio	0.071	2.186	0.827	0.000	0.006
IV. SCG Economy (probability of binding margin constraints = 0.001%)
GDP	7.833	2.644	1.000	1.000	0.683
Consumption	5.364	2.121	0.802	0.834	0.765
current account-GDP ratio	0.000	1.380	0.522	0.974	0.660
trade balance-GDP ratio	0.315	1.000	0.378	0.599	0.788
equity price	2.188	0.121	0.046	0.903	0.630
foreign debt-GDP ratio	1.114	34.141	12.912	-0.067	0.991
debt-equity ratio	0.059	1.810	0.685	0.000	0.004

Note: NFE is nearly frictionless economy, BMR is economy with binding margin requirements, NSCG is economy with binding margin requirements and non-state-contingent guarantees, and SCG is economy with binding margin requirements and state-contingent guarantees.

Financial frictions have negligible effects on business cycle moments (see Table 1). Hence, as in Mendoza and Smith (2006), we study Sudden Stops by examining the model’s dynamics in the high-debt region of the state space in which the margin constraint binds (i.e., the “Sudden Stop region”). Figure 3 shows the date-0 responses (or impact effects) of consumption and the current account-GDP ratio (ca/y) to a negative, one-standard-deviation productivity shock for (α, b) pairs in the Sudden Stop region, measured in percent of the long-run mean of each variable. The Sudden Stop region includes the first 25 nodes of the B grid and all 72 nodes of the A grid.

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Consumption & Current Account-GDP Ratio Impact Effects of a Negative Productivity Shock in the Sudden Stop Region of Equity & Bonds

Citation: IMF Working Papers 2006, 073; 10.5089/9781451863338.001.A001

Note: The values are in percent deviations from long run average for consumption impact effects, and percentage point difference for current account-GDP ratio impact effects.

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Figure 3 suggests that there are two key factors driving impact effects in the Sudden Stop region: (1) The leverage ratio, defined as the ratio of debt to the market value of equity, and (2) The liquidity of the equity market, defined as the difference between α and χ. Sudden Stops with large reversals in c and ca/y occur when the leverage ratio is high, but given high leverage the impact on asset prices is different depending on asset market liquidity. If the asset market is illiquid, the Sudden Stop can feature negligible asset price declines because domestic agents are close to χ and hence have little equity to sell (see Figure 5a), but if there is some liquidity in the asset market, the Sudden Stop in c and ca/y is accompanied by a fall in q. In contrast, when the leverage ratio is sufficiently low and the asset market is sufficiently liquid, the drop in consumption and the current account reversal are small (nearly as small as in the NFE case) but the drop in asset prices is larger. In this case, domestic agents liquidate more equity and trigger larger asset price collapses, but they do so in order to swap their limited borrowing ability via bonds for equity sales so as to minimize the drop in consumption. This pattern of larger current account corrections coinciding with smaller asset price collapses fits the observations of some emerging markets crises. The current account reversal in the first quarter of 1995 in Mexico was 5.2 percent of GDP but the drop in real equity prices was nearly 29 percent. In contrast, in Korea the current account reversal in the first quarter of 1998 was twice as large but the asset price drop was just 10 percent.

Figure 4 illustrates Sudden Stop dynamics using the conditional forecasting functions of c, q and ca/y. The first two are shown as percentages of their long-run averages in the NFE and the last is shown as the percentage points difference relative to the long-run average in the NFE. These forecasting functions represent non-linear impulse response functions to a negative, one-standard-deviation productivity shock conditional on initial positions of equity and bonds inside the Sudden Stop region. The Figures plot two sets of forecasting functions, one for a high leverage initial state, at which α = 0.938 and b = -4.68 (with debt ratio of 60 percent of GDP and a leverage ratio of 3 percent of GDP), and one for a low leverage state with the same α but b = -3.38 (with a debt ratio of 43 percent of GDP and a leverage ratio of 2 percent of GDP). Since these initial states are distant from the corresponding long-run averages, the data in the Figures were adjusted to remove low-frequency transitional dynamics driven by the convergence of bonds and equity to their long-run means. Given that c, q and ca/y have nearly identical long-run averages in the four baseline experiments (except for the mean of q in the NSCG economy, which is higher), the forecasting functions were detrended by taking differences relative to the NFE forecasting functions.

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Conditional Responses to a Negative, One-Standard-Deviation Productivity Shock

Citation: IMF Working Papers 2006, 073; 10.5089/9781451863338.001.A001

1/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states α=0.938 and b=-4.68, which imply a leverage ratio of 0.029 and a debt/GDP ratio of 0.597.2/ Forecasting functions of each variable’s equilibrium Markov process conditional on initial states α=0.938 and b=-3.38, which imply a leverage ratio of 0.021 and a debt/GDP ratio of 0.434.

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Equity Pricing Function in the Low Productivity State

Citation: IMF Working Papers 2006, 073; 10.5089/9781451863338.001.A001

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The impact effects in the initial date of the forecasting functions of the BMR economy differ sharply across the high and low leverage states, and those of the high leverage state deviate significantly from those of the NFE (or from zero in terms of Figure 4, since the data are plotted as differences relative to the NFE). In the high leverage state of the BMR economy, the negative shock triggers a Sudden Stop driven by the mechanisms described in Section 3: Domestic agents sell equity to meet margin calls and trigger a Fisherian deflation that reduces further their ability to borrow. The net result is that, on impact, a one-standard-deviation shock to productivity causes c and q to drop by 1.5 and 0.4 percent more than in the NFE respectively and ca/y to rise by about 1 percentage point of GDP. In the low leverage state, domestic agents are better positioned to smooth consumption by substituting debt for equity to finance a current account deficit. As a result, the responses of c and ca/y in the BMR economy are nearly identical to those in the NFE, so their detrended forecasting functions hover around zero. This occurs even though the sales of equity still make q fall by about the same amount as in the high leverage scenario. Notice also that the drop in asset prices is small relative to observed Sudden Stops, but very large relative to the standard deviation of asset prices in the NFE.

One caveat about the plots in Figure 4: The initial bond and equity positions used to generate them yield outcomes consistent with Sudden Stops, but the set of impact effects that the model predicts for all initial conditions inside the Sudden Stop region are shown in Figures 3. As these Figures show, the Sudden Stop region includes scenarios with much larger consumption and current-account reversals than those shown in Figure 4, as well as scenarios in which there is little difference between the BMR and NFE because the asset market is sufficiently liquid to maintain a similar current account deficit by selling equity when the margin constraint binds. Precautionary saving implies, however, that all the scenarios with very large reversals in consumption have zero probability in the long run. Notice also that, since the Sudden Stop region includes instances in which the margin constraint binds but fire sales of assets prevent a sharp current account reversal, the probability of binding margin constraints is not identical to the probability of Sudden Stops.

Figure 4 suggests that Sudden Stops in the model are short-lived. The responses of the BMR economy converge to those of the NFE in about 4 quarters. Mendoza and Smith (2006) obtained Sudden Stops with more persistence using higher per-trade costs, which hamper the foreign traders’ ability to adjust equity holdings.

E. Baseline Results: State-Contingent and Non-State-Contingent Price Guarantees

The price guarantees are set above the fundamentals price in the low productivity state.⁷ This is motivated by a theoretical result that holds for stationary decision rules (i.e., α_t+1=α_t, b_t+1=b_t) and equilibrium equity prices in the high productivity state that exceed a time-and state-invariant guaranteed price. Under these assumptions, we can show that $G(\alpha ,b,{\epsilon }_L)=z\left(\tilde{q}-\frac{q^f({\epsilon }_L)}{1+a\theta }\right)$, where z is a positive fraction that depends on R, a, θ and the transition probabilities of the shocks. Hence, $\tilde{q}>\frac{q^f({\epsilon }_L)}{1+a\theta }$ is a necessary condition for the guarantees to be executed at least in some states.

The non-state-contingent price guarantee is set ½ of a percentage point above the fundamentals price in the low productivity state (2.185). Hence, the guaranteed price is 2.196. This guarantee is offered in all states (α,b, ε) in the NSCG economy. In contrast, the SCG economy provides the same guaranteed price only for (α,b) pairs inside the Sudden Stop region.

Figure 2 shows that, relative to the BMR case, the non-state-contingent guarantee shifts the distribution of equity (bonds) markedly to the left (right). The long-run average of the expected present value of excess prices (i.e., the long-run average of G) is 0.01, which is about ½ of a percent above the mean equity price in the stochastic stationary state. Comparing long-run moments across Panels I, II and III of Table 1, the main change in the NSCG simulation is the reduction in the probability of binding margin constraints. The probability is almost zero with price guarantees, compared with 4 percent in the BMR economy. The long-run moments of the model’s endogenous variables vary slightly with the non-state-contingent guarantee. Asset-price fluctuations display less variability, persistence and comovement with output in the NSCG economy relative to the NFE and BMR cases. The mean equity price increases by 0.053 percent, slightly more than the percent difference between the guaranteed price and the fundamentals price of the low productivity state. The coefficient of variation of consumption falls by about 1/5 of a percentage point and the variability of the current account and the trade balance increase slightly. Consumption also becomes less correlated with GDP.

The effects of the price guarantee on Sudden Stop dynamics are shown in Figure 4. Price guarantees are an effective policy for containing Sudden Stops. Comparing the NSCG and BMR economies in the high leverage state, the initial consumption and current account reversals are smaller in the NSCG economy, and the drop in equity prices turns into an increase of about ¼ of a percentage point. In the low leverage state, the increase in equity prices in the NSCG economy is slightly larger than in the high leverage state, and we now obtain an increase in consumption and a widening of the current account deficit at date 0. The price guarantee results in a price of equity at date 0 that is 2/3 of a percentage point higher in the NSCG than in the BMR economy in both the high and low leverage states. The price guarantee is executed in both states of the NSCG economy.

Figure 5 plots the levels of equity prices in the low productivity state of the NFE, BMR and NSCG economies for all equity and bond positions. The plots show that the non-state-contingent guarantee not only results in higher prices in the Sudden Stop region, but it actually increases prices in all states. In fact, the guarantee produces significantly higher asset prices in the NSCG economy than in either the NFE or BMR economies in states well outside the Sudden Stop region. This is a potentially important drawback of non-state-contingent price guarantees: they distort asset prices even when the economy is in states where it is far from vulnerable to Sudden Stops.

One alternative to remedy the drawbacks of non-state-contingent price guarantees is to consider state-contingent guarantees. Figure 2 shows that the SCG economy yields a long-run distribution of equity (bonds) that is less skewed to the left (right) than in the NSCG economy. Table 1 shows that the changes in the long-run business cycle moments of the SCG economy relative to the NFE and BMR cases are qualitatively similar to those noted for the NSCG economy but the magnitude of the changes is smaller. The SCG economy still features near-zero percent probability of observing states of nature in which the margin constraint binds. Hence, the state-contingent guarantee is as effective as the non-state-contingent guarantee at eliminating the possibility of hitting states with binding margin requirements in the long run.

Figure 4 shows that, in both the high and low leverage states, the SCG economy features nearly identical date-0 responses in consumption and the current account as the NSCG economy and a slightly smaller recovery in asset prices. After date 0, the SCG economy converges faster to the dynamic paths of the NFE economy. Finally, a comparison of the middle and bottom plots of Figure 5 shows that the SCG economy yields higher asset prices mainly in the Sudden Stop region of the state space. Thus, state contingent guarantees induce smaller distortions on asset demand and asset prices than the non-state-contingent guarantees, particularly outside the Sudden Stop region, yet they have similar effects in terms of their ability to prevent Sudden Stops.

A. Normative Implications of the Baseline Simulations

We study next the normative implications of the baseline simulations by examining how domestic welfare and the value of foreign securities firms varies across the NFE, BMR, NSCG and SCG simulations. Welfare costs, W(α, b, ε), are measured by computing compensating variations in date-0 consumption that equate expected lifetime utility in the BMR, NSCG and SCG economies with that of the NFE for any triple (α, b, ε) in the state space. Welfare effects are typically computed as compensating variations that apply to consumption at all dates, but in principle both measures are useful for converting ordinal units of utility into the cardinal units needed for quantitative welfare comparisons. The two measures yield identical welfare rankings for the four experiments, but the measure based on date-0 consumption highlights better the welfare costs of Sudden Stops and the potential benefits of price guarantees because large deviations from the consumption dynamics of the NFE occur only in Sudden Stop states (in which bond and equity positions are distant from their long-run averages).

The model belongs to the class of models in which capital markets are used to smooth consumption over the business cycle. Hence, since it is well-known that the welfare cost of “typical” consumption fluctuations is small in these models, the mean welfare costs of deviating from the NFE (E[W(α, b, ε)] computed with the ergodic distribution) should be small. As Table 2 shows, welfare comparisons based on date-0 consumption preserve this result. Agents in the BMR, NSCG and SCG economies incur average welfare losses relative to the NFE equivalent to cuts of less than 0.07 percent in c₀. This is also in line with Mendoza’s (1991) results showing trivial welfare costs for giving up access to world capital markets in an RBC-SOE model.

Table 2.

Payoffs of Domestic Agents and Foreign Traders in Baseline Simulations

^1/Compensating variation in date-0 consumption that equates expected lifetime utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^2/Compensating variation in date-0 consumption that equates date-0 period utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^3/Difference of total welfare cost minus short-run cost.

Table 2.

Payoffs of Domestic Agents and Foreign Traders in Baseline Simulations

			NFE	BMR	NSCG	SCG
I. Long-run averages
Domestic Agents
Welfare cost 1/				0.017	0.062	0.057
Foreign Traders
	Present value of traders’ returns		17.920	20.519	27.350	25.529
		percent change w.r.t. NFE		14.499	52.621	42.460
	Returns		0.280	0.321	0.427	0.399
		(a) dividend earnings	0.280	0.320	0.427	0.399
		(b) trading costs	1.1E-05	2.3E-05	8.8E-05	1.6E-04
VI. II. High Leverage Sudden Stop State
Domestic Agents
	Welfare cost 1/			0.367	-1.036	-0.317
		(a) short-run cost 2/		1.376	0.862	0.978
		(b) long-run cost 3/		-1.010	-1.899	-1.295
	Date-1 rate of time preference		1.58	1.56	1.57	1.57
Foreign Traders
	Present value of traders’ returns		10.931	10.940	10.858	10.901
		percent change w.r.t. NFE		0.082	-0.670	-0.276
	Returns at date 0		-0.192	-3.770	-3.796	-3.791
		(a) dividend earnings	0.166	0.166	0.166	0.166
		(b) value of trades	0.359	3.927	3.953	3.948
		(c) trading costs	1.6E-04	9.8E-03	9.8E-03	9.8E-03
VII. III. Low leverage Sudden Stop State
Domestic Agents
	Welfare cost 1/			0.215	-1.194	-0.393
		(a) short-run cost 2/		0.055	-0.356	-0.293
		(b) long-run cost 3/		0.160	-0.838	-0.100
	Date-1 rate of time preference		1.59	1.59	1.59	1.59
Foreign Traders
	Present value of traders’ returns		10.931	10.937	10.854	10.901
		percent change w.r.t. NFE		0.055	-0.707	-0.272
	Returns at date 0		-0.192	-3.056	-3.077	-3.074
		(a) dividend earnings	0.166	0.166	0.166	0.166
		(b) value of trades	0.359	3.215	3.237	3.234
		(c) trading costs	1.6E-04	6.7E-03	6.7E-03	6.7E-03

^1/Compensating variation in date-0 consumption that equates expected lifetime utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^2/Compensating variation in date-0 consumption that equates date-0 period utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^3/Difference of total welfare cost minus short-run cost.

View Table

Table 2.

Payoffs of Domestic Agents and Foreign Traders in Baseline Simulations

			NFE	BMR	NSCG	SCG
I. Long-run averages
Domestic Agents
Welfare cost 1/				0.017	0.062	0.057
Foreign Traders
	Present value of traders’ returns		17.920	20.519	27.350	25.529
		percent change w.r.t. NFE		14.499	52.621	42.460
	Returns		0.280	0.321	0.427	0.399
		(a) dividend earnings	0.280	0.320	0.427	0.399
		(b) trading costs	1.1E-05	2.3E-05	8.8E-05	1.6E-04
VI. II. High Leverage Sudden Stop State
Domestic Agents
	Welfare cost 1/			0.367	-1.036	-0.317
		(a) short-run cost 2/		1.376	0.862	0.978
		(b) long-run cost 3/		-1.010	-1.899	-1.295
	Date-1 rate of time preference		1.58	1.56	1.57	1.57
Foreign Traders
	Present value of traders’ returns		10.931	10.940	10.858	10.901
		percent change w.r.t. NFE		0.082	-0.670	-0.276
	Returns at date 0		-0.192	-3.770	-3.796	-3.791
		(a) dividend earnings	0.166	0.166	0.166	0.166
		(b) value of trades	0.359	3.927	3.953	3.948
		(c) trading costs	1.6E-04	9.8E-03	9.8E-03	9.8E-03
VII. III. Low leverage Sudden Stop State
Domestic Agents
	Welfare cost 1/			0.215	-1.194	-0.393
		(a) short-run cost 2/		0.055	-0.356	-0.293
		(b) long-run cost 3/		0.160	-0.838	-0.100
	Date-1 rate of time preference		1.59	1.59	1.59	1.59
Foreign Traders
	Present value of traders’ returns		10.931	10.937	10.854	10.901
		percent change w.r.t. NFE		0.055	-0.707	-0.272
	Returns at date 0		-0.192	-3.056	-3.077	-3.074
		(a) dividend earnings	0.166	0.166	0.166	0.166
		(b) value of trades	0.359	3.215	3.237	3.234
		(c) trading costs	1.6E-04	6.7E-03	6.7E-03	6.7E-03

^1/Compensating variation in date-0 consumption that equates expected lifetime utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^2/Compensating variation in date-0 consumption that equates date-0 period utility obtained in the BMR, NSCG and SCG economies with that of the NFE.

^3/Difference of total welfare cost minus short-run cost.

The situation is very different when comparing welfare conditional on Sudden Stop states. Since the Bellman equation implies that lifetime utility as of date 0 can be expressed as V(t) = u(t) + exp(-v(t))E_t[V(t+1)], Table 2 decomposes the total welfare cost into a short-run cost (i.e., the percent change in c₀ that equates u(0) in the distorted economies with that of the NFE) and a long-run cost (i.e., the percent change in c₀ that equates exp(-v(0))E₀[V(1)] in the distorted economies with that of the NFE). The Table also lists the rate of time preference, exp(-v(0)), to show that changes in the endogenous subjective discount are irrelevant for the welfare analysis.

In the high leverage Sudden Stop state, which is the one that in the BMR economy produces dynamics closer to those of observed Sudden Stops, the short-run welfare costs show that domestic agents are worse off in the BMR, NSCG and SCG economies than in the NFE. The welfare cost is 1.4 percent for the BMR economy and 0.9 and 1 percent for the NSCG and SCG economies respectively. This ranking reflects the fact that declines in date-0 consumption, and hence u(0), are smallest in the NFE because it provides the best environment for consumption smoothing, followed by the economies in which price guarantees help contain Sudden Stops.

The long-run costs are negative (i.e., domestic agents make welfare gains) because consumption after date 0 increases at least temporarily in the BMR, NSCG and SCG economies. In the high leverage case of the BMR economy, the binding credit constraint tilts the consumption profile by reducing consumption at date 0 and increasing it later, resulting in a long-run welfare gain of about 1 percent. Consumption tilting is also at work in the NSCG and SCG economies, but in addition the higher (distorted) asset prices lead to higher consumption relative to both the BMR and the NFE for three quarters beyond the initial date (see Figure 4). This expansion of consumption in the economies with price guarantees is driven in turn by larger current account deficits, which are financed by equity sales at higher prices.

After date 0, domestic agents set to rebalance their portfolios from equity into bonds gradually, but in economies with price guarantees the capital inflows from equity sales exceed the outflows from bond purchases in the early periods of transition thus producing larger external deficits. This leads to long-run welfare gains in the high leverage NSCG and SCG economies (1.9 and 1.3 percent respectively) that are large enough to offset the short-run costs, so that domestic agents obtain total welfare gains of 1 percent in the NSCG and 0.3 percent in the SCG.

These results show that the asset price changes induced by price guarantees represent nontrivial distortions relative to the NFE. Moreover, as we show below, the same distortions that increase domestic welfare in the high leverage Sudden Stop states of the NSCG and SCG economies reduce the value of foreign traders’ firms in those states.

At equilibrium, the foreign traders’ net returns can be written as:

The three terms in square brackets in the right-hand-side of this expression represent the foreign traders’ dividend earnings, the net value of their trades, and the trading costs they incur. Notice that, since the budget constraint of the IFO holds, the lump sum taxes paid by foreign traders cancel with the value of the executed guarantees. Thus, price guarantees distort the traders’ optimality condition with the moral hazard effect identified in (15) without direct income effects.

The payoff of foreign traders D is the expected present discounted value of the stream of net returns. In the recursive representation of the equilibrium, this present value of returns is a function D(α, b, ε), and hence we can compute long-run averages of net returns, E[D(α, b, ε)], and values of D(α, b, ε) conditional on Sudden Stop states. Since the model has a well-defined stochastic steady state, the long-run mean of net returns is given by $E[D]=\mathit{\text{kE}}[\widehat{\pi }]R{(R-1)}^{-1}$.

Table 2 shows that, relative to the NFE, E[D] and $E[\widehat{\pi }]$ are 14.5 percent higher in the BMR economy and 52.6 and 42.5 percent higher in the NSCG and SCG economies respectively. Thus, from the perspective of the long-run average of the value of their firms, foreign traders are better off in the BMR economy and significantly better off in the economies with price guarantees than in the NFE. Table 2 also shows that this is the case mainly because of the increased average equity holdings of foreign traders in the BMR, NSCG and SCG economies, and the corresponding increase in their average dividend earnings. The contribution of changes in the value of trades to changes in E[D] and $E[\widehat{\pi }]$ is zero by definition (since the unconditional means of α_t and α_t+1 are identical) and the contribution of changes in trading costs is negligible. Foreign traders build up a larger equity position in the BMR economy as a result of the rebalancing of the portfolio of domestic agents from equity into bonds shown in Figure 2, and also because in some states foreign traders buy assets at crash prices (i.e., when domestic agents fire sale assets to meet margin calls). Foreign traders are much better off when price guarantees are in place because the price guarantees are equivalent to a guaranteed minimum return, which reduces sharply the downside risk of holding equity and results in even larger domestic portfolio reallocations from equity into bonds.

The result that the payoff of foreign traders is significantly higher on average in the long run with price guarantees hides the fact that, when evaluated conditional on a Sudden Stop state, the payoff of foreign traders is lower in economies with price guarantees. Table 2 shows that the ranking of foreign traders’ payoffs obtained by comparing D(α, b, ε) across Sudden Stop states with low or high leverage is the opposite from the one obtained by comparing E[D]. Relative to the NFE, the present value of profits is nearly unchanged in the BMR economy and it falls in the high and low leverage states of the economies with price guarantees (by about 0.7 and 0.3 percent in the NSCG and SCG economies respectively). The latter occurs because in the NSCG and SCG economies the increase in the long-run average of net returns $(E[\widehat{\pi }])$ is not sufficient to offset the short-run decline in returns $(\widehat{\pi }(\alpha ,b,\epsilon ))$ that occurs at date 0 when a Sudden Stop hits (see Table 2). In turn, this decline in net returns at date 0 is almost entirely driven by changes in the value of trades. The value of trades in the high (low) leverage state rises from 0.36 in the NFE to 3.93 (3.22) in the BMR economy and to about 3.95 (3.24) in the NSCG and SCG economies. In the BMR economy, the increase reflects the domestic agents’ fire sales of equity to meet margin calls. The equity price falls, and when it falls foreign traders demand more equity and the value of their trades increases. In the economies with price guarantees, the moral hazard distortion exacerbates this effect by increasing the foreign traders’ equity demand and producing equilibrium prices higher than in the BMR economy.

In line with the increase in trading values, trading costs rise sharply from the NFE economy to the other economies, but their absolute amounts remain small. Dividend earnings do not change because date-0 equity holdings are the same in all four economies and the dividends of domestic firms are independent of financial frictions and price guarantees.

In principle, the present value of foreign traders’ net returns conditional on a Sudden Stop state could be higher or lower with price guarantees than without depending on whether the short-run effect lowering date-0 net returns is weaker or stronger than the long-run effect increasing average net returns. The strength of these effects depends in turn on how much and how fast equilibrium equity positions and equity prices move, which depends on the parameters driving the demand for equity of domestic agents and foreign traders. According to Table 2, however, the substantial increases in the average payoff of foreign traders (E[D]) in the NSCG and SCG economies exceed by large margins the small reductions in D(α, b, ε) to which foreign traders are exposed with very low probability in the long run.

To analyze the distributional implications of price guarantees, consider the “resource constraint” implied by the households’ budget constraint and the traders’ net returns:

As noted earlier, the long-run averages of consumption in the NFE, BMR, NSCG and SCG economies are nearly identical (see Table 1). On the other hand, Table 2 shows that the long-run average of the foreign traders’ dividend earnings is higher in the latter three than in the NFE. Taking the long-run average of equation (26), it follows from these two observations that domestic agents can sustain similar long-run average consumption levels because their average savings remain nearly unchanged: The drop in dividend earnings on equity is nearly offset by increased interest income from bonds. Thus, the baseline results suggest that globalization hazard and price guarantees, as modeled in this paper, do not alter the long-run average shares of global income and wealth across the small open economy and the rest of the world. Foreign traders receive a larger share of domestic GDP but GNP is unaffected because domestic agents increase bond holdings and thus collect more interest income from abroad. The independence of GDP from financial frictions and price guarantees is a strong assumption that plays a key role in this result. The SOE assumption also plays a role because it allows the domestic portfolio swap of equity for bonds to occur without increasing the price of these bonds, which would lower the world interest rate.

Short-run distributional effects at a Sudden Stop state are different. GNP and GDP are unchanged across the four simulations, but there is a redistribution of world income via the current account. Relative to the NFE, foreign traders transfer income to domestic households in the BMR, NSCG and SCG economies, as the value of trades in the third term of the right-hand-side of (26) increases because domestic agents fire-sale equity to meet margin calls. But whether the domestic economy receives more or less income from the rest of the world as a whole depends on whether the fire sale of assets can prevent the current account reversal, which in turn depends on the leverage ratio and the liquidity of the asset market. Table 2 shows that $\widehat{\pi }(\alpha ,b,\epsilon )$ falls at date 0 in the high and low leverage states, but Figure 4 shows that the reversal in ca/y is larger in the former. Thus, the high leverage state features a redistribution of income from foreign traders to domestic agents via the equity market, but the larger current account reversal indicates that this redistribution is more than offset by the loss of access to the credit market, so that the domestic economy reduces the share of world output that it absorbs. In contrast, in the low leverage state the current account deficit remains close to the level of the NFE and hence the domestic economy maintains its share of world output. These results hold across the BMR, NSCG and SCG economies compared to the NFE but the effects are stronger in the economies with price guarantees.

The above results show that, comparing long-run averages of the payoffs of domestic agents and foreign traders, foreign traders are significantly better off in the economies with price guarantees than in the NFE or BMR economies, while domestic agents are nearly indifferent. This suggests that price guarantees could be close to a win-win situation, but this result has some caveats. In particular, domestic agents are nearly indifferent between the long-run outcomes of the four economies because of the trivial cost of consumption fluctuations in models of the class examined here, and foreign traders make large gains in the BMR, NSCG and SCG economies because their dividend earnings are unaffected by financial frictions. Interestingly, in the short run and starting at a Sudden Stop state, the moral hazard distortion of economies with price guarantees yields persistently higher asset prices that redistribute income from foreign traders to domestic agents by more than is needed if the aim were just to recover the outcome of the NFE (hence making domestic agents better off and foreign traders worse off). Still, foreign traders are much better off in the long run because the large increase in E[D] in the NSCG and SCG economies dwarfs the small, near-zero-probability reduction in D(α, b, ε) for Sudden Stop states.

B. Sensitivity Analysis

Table 3 reports the results of a sensitivity analysis that evaluates the robustness of the baseline results to the following parameter changes: Columns (II) and (III), larger and more persistent productivity shocks (σ_ε=0.024 and ρ_ε=0.8), Column (IV), higher price guarantees (1 percent above q ^f(ε_L)), Column (V), higher recurrent trading costs (θ=0.01), and Column (VI), higher per-trade costs (a =2). Column (I) reproduces the baseline results. The Table shows panels with results for the BMR, NSCG and SCG economies for all six scenarios. In each case, three sets of results are listed: (a) Sudden Stop effects as measured by the detrended, date-0 forecasting functions conditional on the high leverage state, (b) key moments of the ergodic distribution, and (c) changes in the payoffs of domestic agents and foreign traders, relative to the corresponding NFE simulation, for the high leverage Sudden Stop state and in the long-run averages.

Table 3.

Sensitivity Analysis

Note: The guaranteed price is 0.5 percent (1 percent for column (IV)) above the fundamentals price in the low productivity state of the baseline simulation. Welfare costs are compensating variations in initial consumption that equalize lifetime utility in each simulation with that of the corresponding NFE. Initial responses are in percent of the corresponding NFE and detrended as described in the text (except the response for traders’ returns which is in percent of the capital stock and the response for the current account-output ratio which is the difference in percentage points relative to the corresponding NFE).

^1/Percentage change relative to NFE

Table 3.

Sensitivity Analysis

		Baseline	Productivity Shocks		Guarantees	Trading Costs
		(I)	(II) ρ = 0.8	(III) σε = 2.4%	(IV) 1% above qf	(V) θ = 0.01	(VI) a = 2
I. BMR Economy
Initial responses in high leverage state
	consumption	-1.335	-1.380	-1.404	n.a.	-1.453	-3.059
	current account-GDP ratio	0.939	0.972	0.997	n.a.	1.023	2.157
	equity price	-0.413	-0.413	-0.413	n.a.	-0.412	-4.324
	traders’ returns	-4.529	-4.526	-4.526	n.a.	-4.522	-4.866
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		3.973	4.200	2.331	n.a.	16.740	19.444
Averages					n.a.
	consumption	5.365	5.369	5.366		5.369	5.378
	equity price	2.187	2.187	2.187	n.a.	2.183	2.183
	equity holdings	0.883	0.885	0.861	n.a.	0.906	0.907
Standard deviations (%)					n.a.
	consumption	2.186	2.382	2.721	n.a.	2.169	2.454
	current account-GDP ratio	1.324	1.325	2.020		1.432	1.428
	equity price	0.121	0.184	0.100	n.a.	0.114	0.463
Domestic welfare loss1/					n.a.
	high leverage state	0.367	0.361	0.389	n.a.	0.490	4.074
	long-run average	0.017	0.013	0.012	n.a.	0.099	0.110
Change in PDV of traders’ returns1/
	high leverage state	0.083	0.082	0.095	n.a.	3.448	0.924
	long-run average	14.502	12.163	4.354	n.a.	34.519	27.531
II. NSCG Economy
Initial responses in high leverage state
	consumption	-0.840	-0.875	-0.901	-0.503	-0.885	-2.205
	current account-GDP ratio	0.591	0.616	0.640	0.354	0.623	1.554
	equity price	0.259	0.274	0.214	0.718	0.362	-3.256
	traders’ returns	-4.562	-4.560	-4.561	-4.586	-4.561	-4.926
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		0.001	0.017	0.024	0.002	0.002	0.000
Prob. of executing guarantee (%)		34.290	32.892	15.434	29.650	34.068	28.925
Averages
	consumption	5.362	5.365	5.360	5.361	5.362	5.362
	equity price	2.198	2.199	2.198	2.208	2.198	2.206
	equity holdings	0.844	0.844	0.844	0.842	0.844	0.842
	expected PDV of excess prices	0.012	0.013	0.011	0.022	0.015	0.023
Standard deviations (%)
	consumption	2.052	2.269	2.615	2.014	2.047	2.191
	current account-GDP ratio	1.487	1.473	2.035	1.567	1.490	1.584
	equity price	0.099	0.149	0.104	0.091	0.100	0.429
	expected PDV of excess prices	2.083	3.913	4.235	1.375	1.368	1.466
Domestic welfare loss1/
	high leverage state	-1.036	-1.137	-1.033	-2.359	-1.025	1.506
	long-run average	0.062	0.063	0.132	0.086	0.286	0.332
Change in PDV of traders’ returns1/
	high leverage state	-0.670	-0.732	-0.660	-1.372	2.501	-0.459
	long-run average	52.621	51.867	17.567	54.696	122.862	116.646
III. SCG Economy
Initial responses in high leverage state
	consumption	-0.952	-0.878	-0.988	-0.626	-0.920	-2.182
	current account-GDP ratio	0.670	0.618	0.702	0.440	0.648	1.538
	equity price	0.107	0.270	0.105	0.550	0.313	-3.227
	traders’ returns	-4.555	-4.560	-4.555	-4.586	-4.558	-4.928
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		0.001	0.014	0.042	0.009	0.013	0.000
Prob. of executing guarantee (%)		0.035	0.261	0.391	0.502	6.063	3.245
Averages
	consumption	5.364	5.369	5.363	5.363	5.358	5.355
	equity price	2.188	2.188	2.189	2.190	2.190	2.191
	equity holdings	0.855	0.855	0.855	0.850	0.879	0.874
	expected PDV of excess prices	0.002	0.002	0.011	0.003	0.007	0.009
Standard deviations (%)
	consumption	2.121	2.317	2.709	2.095	2.061	2.298
	current account-GDP ratio	1.380	1.369	2.028	1.420	1.466	1.536
	equity price	0.121	0.187	0.120	0.137	0.154	0.469
	expected PDV of excess prices	42.186	62.894	4.235	52.202	37.543	51.111
Domestic welfare loss1/
	high leverage state	-0.317	-0.481	-0.297	-0.869	-0.385	2.596
	long-run average	0.057	0.053	0.033	0.054	0.086	0.121
Change in PDV of traders’ returns1/
	high leverage state	-0.276	-0.359	-0.246	-0.567	2.985	0.167
	long-run average	42.460	41.196	9.446	47.217	72.049	73.680

Note: The guaranteed price is 0.5 percent (1 percent for column (IV)) above the fundamentals price in the low productivity state of the baseline simulation. Welfare costs are compensating variations in initial consumption that equalize lifetime utility in each simulation with that of the corresponding NFE. Initial responses are in percent of the corresponding NFE and detrended as described in the text (except the response for traders’ returns which is in percent of the capital stock and the response for the current account-output ratio which is the difference in percentage points relative to the corresponding NFE).

^1/Percentage change relative to NFE

View Table

Table 3.

Sensitivity Analysis

		Baseline	Productivity Shocks		Guarantees	Trading Costs
		(I)	(II) ρ = 0.8	(III) σε = 2.4%	(IV) 1% above qf	(V) θ = 0.01	(VI) a = 2
I. BMR Economy
Initial responses in high leverage state
	consumption	-1.335	-1.380	-1.404	n.a.	-1.453	-3.059
	current account-GDP ratio	0.939	0.972	0.997	n.a.	1.023	2.157
	equity price	-0.413	-0.413	-0.413	n.a.	-0.412	-4.324
	traders’ returns	-4.529	-4.526	-4.526	n.a.	-4.522	-4.866
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		3.973	4.200	2.331	n.a.	16.740	19.444
Averages					n.a.
	consumption	5.365	5.369	5.366		5.369	5.378
	equity price	2.187	2.187	2.187	n.a.	2.183	2.183
	equity holdings	0.883	0.885	0.861	n.a.	0.906	0.907
Standard deviations (%)					n.a.
	consumption	2.186	2.382	2.721	n.a.	2.169	2.454
	current account-GDP ratio	1.324	1.325	2.020		1.432	1.428
	equity price	0.121	0.184	0.100	n.a.	0.114	0.463
Domestic welfare loss1/					n.a.
	high leverage state	0.367	0.361	0.389	n.a.	0.490	4.074
	long-run average	0.017	0.013	0.012	n.a.	0.099	0.110
Change in PDV of traders’ returns1/
	high leverage state	0.083	0.082	0.095	n.a.	3.448	0.924
	long-run average	14.502	12.163	4.354	n.a.	34.519	27.531
II. NSCG Economy
Initial responses in high leverage state
	consumption	-0.840	-0.875	-0.901	-0.503	-0.885	-2.205
	current account-GDP ratio	0.591	0.616	0.640	0.354	0.623	1.554
	equity price	0.259	0.274	0.214	0.718	0.362	-3.256
	traders’ returns	-4.562	-4.560	-4.561	-4.586	-4.561	-4.926
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		0.001	0.017	0.024	0.002	0.002	0.000
Prob. of executing guarantee (%)		34.290	32.892	15.434	29.650	34.068	28.925
Averages
	consumption	5.362	5.365	5.360	5.361	5.362	5.362
	equity price	2.198	2.199	2.198	2.208	2.198	2.206
	equity holdings	0.844	0.844	0.844	0.842	0.844	0.842
	expected PDV of excess prices	0.012	0.013	0.011	0.022	0.015	0.023
Standard deviations (%)
	consumption	2.052	2.269	2.615	2.014	2.047	2.191
	current account-GDP ratio	1.487	1.473	2.035	1.567	1.490	1.584
	equity price	0.099	0.149	0.104	0.091	0.100	0.429
	expected PDV of excess prices	2.083	3.913	4.235	1.375	1.368	1.466
Domestic welfare loss1/
	high leverage state	-1.036	-1.137	-1.033	-2.359	-1.025	1.506
	long-run average	0.062	0.063	0.132	0.086	0.286	0.332
Change in PDV of traders’ returns1/
	high leverage state	-0.670	-0.732	-0.660	-1.372	2.501	-0.459
	long-run average	52.621	51.867	17.567	54.696	122.862	116.646
III. SCG Economy
Initial responses in high leverage state
	consumption	-0.952	-0.878	-0.988	-0.626	-0.920	-2.182
	current account-GDP ratio	0.670	0.618	0.702	0.440	0.648	1.538
	equity price	0.107	0.270	0.105	0.550	0.313	-3.227
	traders’ returns	-4.555	-4.560	-4.555	-4.586	-4.558	-4.928
Moments of the ergodic distribution
Prob. of binding mar. cons. (%)		0.001	0.014	0.042	0.009	0.013	0.000
Prob. of executing guarantee (%)		0.035	0.261	0.391	0.502	6.063	3.245
Averages
	consumption	5.364	5.369	5.363	5.363	5.358	5.355
	equity price	2.188	2.188	2.189	2.190	2.190	2.191
	equity holdings	0.855	0.855	0.855	0.850	0.879	0.874
	expected PDV of excess prices	0.002	0.002	0.011	0.003	0.007	0.009
Standard deviations (%)
	consumption	2.121	2.317	2.709	2.095	2.061	2.298
	current account-GDP ratio	1.380	1.369	2.028	1.420	1.466	1.536
	equity price	0.121	0.187	0.120	0.137	0.154	0.469
	expected PDV of excess prices	42.186	62.894	4.235	52.202	37.543	51.111
Domestic welfare loss1/
	high leverage state	-0.317	-0.481	-0.297	-0.869	-0.385	2.596
	long-run average	0.057	0.053	0.033	0.054	0.086	0.121
Change in PDV of traders’ returns1/
	high leverage state	-0.276	-0.359	-0.246	-0.567	2.985	0.167
	long-run average	42.460	41.196	9.446	47.217	72.049	73.680

Note: The guaranteed price is 0.5 percent (1 percent for column (IV)) above the fundamentals price in the low productivity state of the baseline simulation. Welfare costs are compensating variations in initial consumption that equalize lifetime utility in each simulation with that of the corresponding NFE. Initial responses are in percent of the corresponding NFE and detrended as described in the text (except the response for traders’ returns which is in percent of the capital stock and the response for the current account-output ratio which is the difference in percentage points relative to the corresponding NFE).

^1/Percentage change relative to NFE