The Role of Collateral in Sudden Stop Models

• Published date: 01 November 2023
• Author: Bingbing Dong,Jieran Wu,Eric Young
• Date: 01 November 2023
• DOI: http://doi.org/10.1111/cwe.12510

©2023 Institute of World Economics and Politics, Chinese Academy of Social Sciences

China & World Economy / 79–110, Vol. 31, No. 6, 202379

The Role of Collateral in Sudden Stop Models

Bingbing Dong, Jieran Wu, Eric Young*

Abstract

This paper examines the role of collateral in sudden stop models that feature occasionally

binding constraints and endogenous growth. It shows how different assumptions

regarding the nature and valuation of collateral alter the dynamics of crisis episodes

and the welfare costs of pecuniary externalities. For example, in a model with land

as collateral, valuing collateral at the “expected future price” leads to substantially

weaker Fisherian defl ation eff ects than the case with collateral valued at the “current

price.” However, the average size of sudden stops in the two economies are similar

because households endogenously avoid the region where large sudden stops would

occur. The differences between different collateral valuations and the size of sudden

stops are amplified when we abstract from endogenous growth. In another case,

assuming collateral is income rather than land leads to smaller sudden stops as income

is less volatile than asset prices. Finally, we show that some choices lead to constrained

or conditionally effi cient allocations whereas others generate ineffi ciencies, but these

ineffi ciencies are small.

Keywords: collateral, Fisherian deflation effect, pecuniary externalities, sudden stops

JEL codes: C61, E21, F34, F41, G01

I. Introduction

In models of sudden stops, the collateral constraint is generally simply assumed into

existence, rather than being derived explicitly from an underlying friction.1 As a result,

*Bingbing Dong, Assistant Professor, Shanghai Advanced Institute of Finance (SAIF), Shanghai Jiao Tong

University, China. Email: bbdong@saif.sjtu.edu.cn; Jieran Wu (corresponding author), Professor, School of

Economics, Academy of Financial Research, and Innovation Center of Yangtze River Delta, Zhejiang University,

China. Email: jw5ya@zju.edu.cn; Eric Young, Professor, Economics Department, University of Virginia and

Research Department, Federal Reserve Bank of Cleveland, USA. Email: ey2d@virginia.edu. The authors are

grateful for support from the National Natural Science Foundation of China (No. 72063030, 72141305), the

Ministry of Education Social Sciences Foundation for Youths (No. 20YJC790018), and the Bankard Fund for

Political Economy at the University of Virginia. The views expressed in this paper are those of the authors and do

not represent the views of the Federal Reserve Bank of Cleveland or the Federal Reserve System.

1Some papers provide an informal discussion, such as Bianchi (2011), Jeanne and Korinek (2019), and Bianchi

and Mendoza (2018).

Bingbing Dong et al. / 79–110, Vol. 31, No. 6, 2023

©2023 Institute of World Economics and Politics, Chinese Academy of Social Sciences

80

a number of plausible choices exist regarding what serves as collateral and how that

collateral is valued. To be specific, suppose that the occupants of a small open economy can

pledge land in return for international debt. Examples in the literature suppose that either

individual land holdings or aggregate land holdings serve as collateral. In addition, the

valuation of this collateral can be based on (i) the current price or (ii) the expected future

price, or (iii) the worst possible future price. Furthermore, the collateralization can involve

either current land or future land. All of these assumptions can be found in the literature –

see Jeanne and Korinek (2013), Korinek and Mendoza (2014), Bianchi and Mendoza

(2018), Devereux et al. (2018), and Ma (2020). Another strand of literature views

collateral as arising from current income, including Bianchi (2011) and Benigno et al.

(2013, 2016, 2023), in which some type of terms-of-trade price appears.

In this paper we characterize how the behavior of a small open economy model

with endogenous growth and collateral constraints (a sudden stop model) changes

across different model specifications. Specifically, we consider alternative assumptions

regarding (i) elastic versus inelastic labor; (ii) endogenous versus exogenous growth;

(iii) collateral valuation at current versus expected future prices; (iv) current versus future

land as collateral; (v) income versus land as collateral; and (vi) aggregate versus individual

collateral. The above assumptions correspond to various modeling choices in terms of the

model environment (i and ii), collateral valuation (iii), and nature of collateral (iv, v, and vi).

We find that some of these choices change the behavior of the model and the welfare losses

associated with pecuniary externalities substantially, whereas others make no quantitative

difference. We concentrate here on presenting the key choices and the mechanisms that

underlie the resulting differences, and relegate discussions of other choices to Section VI.2

The first set of key choices that we investigate are related to the valuation of

collateral in a model with endogenous growth and inelastic labor. Let land nt serve

as collateral and be valued at either the current price qt or the expected future price

Et[qt + 1]. In the first case, the sudden stop displays a strong “Fisherian deflation” effect –

a negative shock that causes the collateral constraint to bind forces consumption to fall,

which in turn reduces asset values today (because land is productive) and thus further

tightens the constraint, necessitating further reductions in consumption. The result is a

nonmonotonic debt function; debt decreases rather than increases in the binding region.

In contrast, this feedback mechanism is substantially weaker if land is valued at the

next period’s price – we find a flat spot in the debt accumulation rule in the binding

region. The result is that a typical sudden stop will be smaller. The collateral value is

2Our positive results are broadly consistent with Ottonello et al. (2022), which focuses on the implication of

collateral constraints on macro-prudential policy design.

©2023 Institute of World Economics and Politics, Chinese Academy of Social Sciences

The Role of Collateral in Sudden Stop Models81

less vulnerable to bad shocks in the expected price case, so agents reduce precautionary

saving and accumulate higher debt on average, causing the crisis probability to increase.

Quantitatively, however, we find only small differences because agents endogenously

avoid the regions of the state space where large sudden stops would occur.

The reduced severity of sudden stops is partially due to the presence of endogenous

growth. Introducing endogenous growth affects the model dynamics through two channels.

First, households have an extra tool to smooth consumption by changing the research and

development (R&D) investment, which generates endogenous variations in the stochastic

discount factor that offsets the changes in the intertemporal marginal rate of substitution

(IMRS). We term this effect the “discount rate” channel, as it effectively changes the

relative patience of agents. Second, the dividend stream is augmented with an additional

growth term, which in turn affects the collateral asset (land) value; we call this effect the

“dividend” channel. Using a special analytical example with no “discount rate” channel,

we illustrate that compared with the no-growth economy, the collateral value is higher and

less sensitive to changes in productivity with endogenous growth. When a sudden stop

happens, agents reduce R&D investment and the growth rate. In comparison with normal

times, the decline in the growth rate causes agents to behave as if they are more patient,

increasing asset (land) demand and reducing borrowing. Although a drop in growth rate

affects the land’s valuation through future dividends, the effect is short lived. The drop in

asset/collateral value during a crisis is therefore mitigated, and this force is stronger if the

collateral is valued at the future expected price rather than the current price.

The second set of key choices we investigate regards the nature of collateral with

elastic labor. We consider both land and income as collateral, valued at current prices.

In either case, we find smaller sudden stops. The reason is that, given the current state,

the deflation spiral is weaker because agents can increase labor effort during a sudden

stop; increasing labor effort both raises the value of land (due to complementarity in the

production function) and raises income (as production is decreasing returns to scale in

labor). As a result, the decision rule for debt does not “turn upward” but rather only falls

at a slower rate (that is, agents always borrow more if their debt is higher).3

Finally, we consider the implications of our experiments for the measurement

of pecuniary externalities; that is, how different would outcomes be if private agents

internalized their effect on collateral values (as a constrained planner would do)? We

define two types of efficient allocations. The “conditionally efficient allocation” (see

Benigno et al., 2013) has the planner take as given the collateral pricing function (that is,

3We do not consider future price valuations here because the presence of future controls in the current set of

constraints raises time consistency issues.