Borrowing constraints and the trade balance–output comovement

Economic Modelling 32 (2013) 34–41

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Borrowing constraints and the trade balance–output comovement☆ Yan Zhao School of Business, East China University of Science and Technology, China

a r t i c l e

i n f o

Article history: Accepted 14 January 2013 Keywords: Real business cycle Small open economy Borrowing constraints

a b s t r a c t The countercyclical trade balance ratio is among the key stylized facts about open economies. The magnitude of the correlation between the trade balance and output, however, differs from country to country. In particular, the trade balance ratio is more negatively correlated with output in emerging economies than in developed economies, suggesting that the trade balance is more sensitive to output changes in the former than in the latter. This paper explores whether this difference is caused by international borrowing constraints imposed on emerging economies. By modeling borrowing constraints as conditional on macroeconomic performance, this paper shows that when there is a positive shock takes place in an emerging economy, GDP increases and the borrowing constraint becomes less binding, resulting in a decreased incentive to accumulate foreign assets. When there is a negative shock, by contrast, GDP falls, and the representative household must increase the trade balance to avoid possible binding borrowing constraints. © 2013 Elsevier B.V. All rights reserved.

1. Introduction The dynamics of the trade balance is one of the most important research topics in international economics. As the net of exports and imports, the trade balance reflects the terms of trade of a country in a given period. The trade balance has a direct effect on the exchange rate and on the level of the national debt. As world economies become increasingly integrated, the trade balance also has a substantial impact on almost all macroeconomic variables, including economic growth, the level of output, economic fluctuations and the unemployment rate. For this reason, it draws wide public attention and research on it has never waned. Most studies of the trade balance focused on its cyclical behavior, which is a product of two main forces. The first is the insurance effect, which implies a procyclical trade balance: a country should increase its net foreign asset holdings in booms as precautionary savings and decrease its net foreign assets in recessions to smooth consumption. The second is the productivity effect. A country that experiences a positive shock should take advantage of enhanced productivity by importing more capital from abroad. This suggests a countercyclical trade balance. Assuming standard preferences, the insurance effect dominates such that the overall trade balance should be procyclical. This is, however, at odds with the data for most open economies. For this reason, generating a realistic trade balance–output comovement has been one of the major goals in the open economy literature, as in ☆ I would like to thank Paul Gomme, Tatyana Koreshkova, Hafedh Bouakez, the participants at the 46th Annual Conference of the Canadian Economics Association, and an anonymous referee for insightful comments and suggestions. All errors, however, are my own. E-mail address: [email protected]. 0264-9993/$ – see front matter © 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.econmod.2013.01.024

Mendoza (1991), Correia et al. (1995), Blankenau et al. (2001), and Letendre (2004). To more accurately capture the cyclical pattern of the trade balance, one common approach has been to adopt GHH preferences, as proposed in Greenwood et al. (1988). As explained in the next section, GHH preferences minimize the insurance effect, so that the productivity effect dominates, making it possible to generate a countercyclical trade balance. Although the trade balance has been extensively discussed, there remain some properties not yet investigated. Further examination of the trade balance across countries reveals not only that the trade balance is countercyclical in nearly all open economies, but also that it varies significantly from country to country. In particular, the trade balance is more negatively correlated with GDP in emerging economies than in developed ones. As shown in Table 1, Aguiar and Gopinath (2007) document that the average of the correlation coefficient is −0.51 for developing countries, and − 0.17 for developed ones, indicating that the comovement between the trade balance and GDP is stronger in the former group than in the latter. 1 More recently, Boz et al. (2011) also find that the trade balance is more strongly countercyclical in developing economies than in developed ones. Moreover, differences in trade balance–GDP comovements have grown in recent years for some countries. Table 1 covers the period of 1980–2003. Using the newly released Canadian and Mexican data through the year 2009, the correlation coefficients have become 0.0043 and − 0.75, respectively. The small correlation in Canada

1 This table is excerpted from Aguiar and Gopinath (2007). tb1t is the ratio of the t trade balance to GDP, i.e., tb1t ¼ tb y . t

Y. Zhao / Economic Modelling 32 (2013) 34–41 Table 1 corr(tb1t, yt) across countries. Emerging countries

Developed countries

Country

corr(tb1t,yt)

Country

corr(tb1t, yt)

Argentina Brazil Ecuador Israel Korea Malaysia Mexico Peru Philippines Slovak Republic South Africa Thailand Turkey Average = −0.51

−0.70 0.01 −0.79 0.12 −0.70 0.01 −0.79 0.12 −0.70 0.01 −0.79 0.12 0.12

Australia Austria Belgium Canada Denmark Finland Netherlands New Zealand Norway Portugal Spain Sweden Switzerland Average = −0.17

−0.43 0.10 −0.04 −0.20 −0.08 −0.45 −0.19 −0.26 0.11 −0.11 −0.60 0.01 −0.17

implies an almost zero comovement between the trade balance and output. Fig. 1 plots the trade balance ratio and HP filtered real GDP (in logs) for Canada and Mexico. As Fig. 1 suggests, while a negative correlation between the trade balance ratio and output for Mexico is evident, the relationship between the trade balance ratio and output for Canada is more difficult to determine. 2 The larger correlation coefficient (in absolute value) indicates that the trade balance in some countries, especially in some emerging economies, is highly responsive to GDP changes. Along with the fact that the trade balance is countercyclical, which suggests that the trade balance deteriorates more in booms, and improves more in recessions in emerging economies than in developed ones, one possible explanation for this difference in magnitude is that some countries face international borrowing constraints. Insofar as these borrowing constraints depend on GDP, a country may need to increase its trade balance during recessions to avoid a possibly binding borrowing constraint, and may not accumulate foreign assets during booms when the borrowing constraint is less binding. 3 Since their introduction into the literature in Eaton and Gersovitz (1981), borrowing constraints have frequently been used in open economy macroeconomic models to study a wide range of topics, including currency crises, as in Aghion et al. (2001); foreign debt crises, as in Caballero and Krishnamurthy (2001); economic growth, as in De Gregorio (1996); “sudden stops”, as in Mendoza (2001); and abnormally high consumption volatility in emerging economies, as in Resende (2006).4 Arellano and Mendoza (2002) survey the literature on borrowing constraints in small open economy models and illustrate their effects. Their central findings are that borrowing constraints introduce large distortions to relative prices, including wages, the real interest rate, and the terms of trade, which in turn cause abrupt changes in the trade

2

The red line in Fig. 1 is the OLS fitting line. Economies with underdeveloped financial markets are more likely to face borrowing constraints. Taking the financial development index from Love (2003) (which roughly corresponds to the same period as Table 1), the correlation between corr(tb1, y) and the financial development indicator is 0.12, suggesting that the more developed are an economy's financial markets, the smaller is the trade balance ratio– output comovement in absolute value. 4 Eaton and Gersovitz (1981) outline the theory of borrowing ceilings to answer the question of why countries choose not to default even when there is no forcible debt repaying mechanism. According to Eaton and Gersovitz (1981), borrowers refrain from defaulting when the disutility of exclusion from outside capital markets in the future exceeds a certain limit. De Gregorio (1996) investigates the relationship between borrowing constraints and economic growth. De Gregorio (1996) argues that borrowing constraints increase saving, which increases growth; at the same time, borrowing constraints reduce the time devoted to human capital accumulation, which decreases growth. 3

35

balance, even when the borrowing constraint is only “occasionally” binding.5 While the effects of a borrowing constraint on open economy macroeconomic models have been widely discussed, their effects on the correlation of the trade balance with GDP have yet to be investigated, especially for purpose of comparing business cycle statistics with the predictions of the standard model. This paper is concerned with the following question: to what extent can borrowing constraints explain the larger correlation coefficient in emerging economies? As the main purpose of this paper is to illustrate the effect of borrowing constraints on business cycle statistics, I focus on the key question of whether borrowing constraints significantly affect the trade balance ratio–GDP comovement. To this end, the model below is constructed in as standard a way as possible, and the borrowing constraint is modeled in as generally a way as possible. This paper adopts the standard small open economy real business cycle framework, as presented by Schmitt-Grohe and Uribe (2003). In formulating the borrowing constraint, I adopt the “ability-to-pay” approach, following Arellano and Mendoza (2002), and thus optimal default is ruled out for simplicity. That is, the borrower always repays the debt if he has the ability. The lender is assumed to be risk-neutral and charges an interest premium to compensate for the default risk. The interest premium in this paper is modeled as conditional on the borrower's debt holdings. More specifically, the borrowing constraint is modeled as a ceiling limit: existing debt cannot exceed a certain fraction of output. As Arellano and Mendoza (2002) put it, in international capital markets, the lender has incomplete information about the borrower and thus relies on some key economic indicators to assess potential risk. Monitoring output of the borrower serves this purpose well. Moreover, this simple setting reflects the lender's needs for default risk management. In particular, as there hardly exists forcible repayment mechanisms for sovereign debt, the lender is more concerned about the borrower's ability, rather than willingness under the “ability-to-pay” framework. A debt limit reduces the likelihood of overborrowing and falling into a foreign debt crisis trap, in which borrowers typically lose their ability to repay their debt. With the assumption that it is chiefly emerging economies that face borrowing constraints, the methodology of this paper is to study one typical emerging economy and compare predictions of the credit-constrained and credit-unconstrained models. In the small open economy literature, Mexico is frequently chosen as a representative emerging market country. In this paper, Mexico is also chosen as the subject of analysis. By including borrowing constraints in an otherwise standard small open economy real business cycle model, the paper confirms the aforementioned conjecture, i.e., that debt ceiling causes the trade balance to move more closely with output changes, and shows that borrowing constraints generate a more sensitive response of the trade balance to output changes. Whereas the correlation between the trade balance ratio and GDP is − 0.22 for the model without constraints, it rises to −0.59 when a borrowing constraint is applied. Two factors contribute to this result. The first is that output becomes less volatile under borrowing constraints. When there is a negative shock, for example, the quantity of labor supply decreases by less in the constrained than in the unconstrained model and accordingly, output falls by less. A smaller decline in labor and output serves to increase the trade balance, which is also an optimal response to the borrowing constraint. The second factor is that the trade balance is more volatile in the model that includes a borrowing constraint. With a negative shock, the standard model without financial market 5 Arellano and Mendoza (2002) divide the various models into two categories: “ability-to-pay” models and “willingness-to-pay” models. The former rule out the possibility of voluntary default and assume that borrowers always repay whenever they have the ability. The latter permit the borrower to optimally default.

36

Y. Zhao / Economic Modelling 32 (2013) 34–41

(a) Canada

(b) Mexico

0.04 0.03 0.02 0

tb1

tb1

0.01 -0.01 -0.02 -0.03 -0.04 -0.05 -0.03

-0.02

-0.01

0

0.01

0.02

0.03

0.12 0.1 0.08 0.06 0.04 0.02 0 -0.02 -0.04 -0.06 -0.08 -0.06-0.05-0.04-0.03-0.02-0.01 0 0.01 0.02 0.03 0.04

log(gdp)

log(gdp)

Fig. 1. Trade balance ratio and GDP. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

imperfections predicts that the trade balance will increase. In the model with borrowing constraints, the representative household must further increase its trade balance to avoid the borrowing constraint bind. Putting these considerations together, the larger increase in the trade balance and the smaller decrease in output, result in a larger correlation (in absolute value) between the trade balance ratio and output. It is worth noting that both the standard model and the model with borrowing constraints adopt GHH preferences, which weaken the insurance effect. Borrowing constraints further weaken this effect because a country may not be able to borrow as much as it needs when it experiences a negative shock. As stated at the beginning of this paper, the smaller the insurance effect, the easier it is to generate a negative trade balance–output comovement. The model used here is closely related to those used in two other recent papers. One of these papers is by Arellano (2008), which links default to output changes and illustrates that default is more likely in recessions.6 The close link between output performance and default probability supports the assumption of this paper that the lender takes GDP as the borrowing constraints. The other paper is by Bykkarabacak and Gumus (2011). Bykkarabacak and Gumus (2011) distinguishes household credit and business credit in that the former plays a more important role in generating business cycles consistent with data for the Turkish economy. Borrowing constraints in Bykkarabacak and Gumus (2011) take the form of collateral, as a proportion of either household income or business output. 7 In this paper, with the assumption of no optimal default and no enforceable repayment mechanism, the lender knows that limiting the borrower's debt holdings is the only way to reduce the likelihood of default. For this reason, setting an upper limit on debt serves the same risk management purpose for the lender as contracting collateral beforehand. The structure of the paper is as follows. The next section, Section 2, presents the standard small open economy model, as in Schmitt-Grohe and Uribe (2003). Section 3 calibrates the model to the Mexican economy and provides simulation results. It also undertakes an impulse response analysis to identify the mechanism by which the borrowing constraint generates increased comovement between the trade balance and output. Section 4 compares the model with two models, the “trend cycle” and the 6 Arellano (2008) models endogenous default risk in a stochastic dynamic framework that features incomplete markets, where interest rates respond to output fluctuations through time-varying default probabilities. 7 Bykkarabacak and Gumus (2011) argues that an expansion of business credit leads to an increase in both imports and exports, while an expansion of household credit results in a substantial increase in imports. This is why household credit is more crucial than business credit in generating the negative comovement between the trade balance and output.

“country premium cycle” in the existing literature on emerging economies. Section 5 concludes, and suggests directions for future research. 2. The economic environment 2.1. Preferences In a small open economy, the infinitely lived representative agent derives utility from a consumption stream, ct, and disutility from work, nt. The agent's preferences are summarized as E0

∞ X

t

β U ðct ; nt Þ;

ð1Þ

t¼0

where β is the discount factor. In the small open economy literature, the functional form for preferences receives particular attention because standard preferences, normally assumed in standard business cycle models, fail to generate a counter-cyclical trade balance ratio. The counter-cyclical behavior is in contradiction with standard business cycle models. The usual intuition is that the individual should increase her asset holdings in booms so that she may also consume more in the future, as implied by consumption smoothing. To explain the countercyclical trade balance, researchers have proposed various theories, of which two are widely accepted. The first is that technological change, and accordingly the change in real income may contain two components: a long-term trend and a transitory fluctuation, as Aguiar and Gopinath (2007) argue. When changes in the long-term trend component dominate, consumption will increase enough to crowd out the trade balance, as the permanent income hypothesis suggests. The second explanation is that preferences may not be standard. In particular, if preferences are GHH, the trade balance could be countercyclical. GHH preferences take the form h uðct ; nt Þ ¼

ω

ct −μ nωt

i1−γ

1−γ

;

ð2Þ

where μ in Eq. (2) is the preferences weight on labor supply, ω is the elasticity of labor supply, and γ denotes risk aversion. GHH preferences have the property that the marginal rate of substitution between consumption and leisure is independent of the consumption level, MRS = − ntω − 1. Suppose that the production function is Cobb–Douglas. That is, yt = ztktαnt1 − α. Utility maximization requires that the relative marginal utility between leisure and consumption

Y. Zhao / Economic Modelling 32 (2013) 34–41

equates their relative price, wage, or marginal productivity of labor, suggesting the following equation: ω

nt ¼ ð1−α Þyt :

ð3Þ

This equation suggests that the wealth effect (on leisure) is eliminated and that the supply of labor is solely determined by the current wage. As a result, the supply of labor displays strong cyclicality, and this induces strongly procyclical consumption as well, because of the ease of substitution between leisure and consumption. Therefore, the consumption smoothing motive or the insurance effect is mitigated. As stated earlier, preferences characterized by a smaller insurance effect help generate the countercyclical trade balance ratio. For this reason, GHH preferences have been a popular approach in the open economy literature, as in Mendoza (1991), Correia et al. (1995), and Schmitt-Grohe and Uribe (2003), among others. To focus on the trade balance, in this paper, preference also takes GHH form.

This economy produces a single tradable goods according to yt ¼

ð4Þ

where kt is the capital stock, nt is the labor supply, α is capital share in output and zt is the productivity shock. The productivity shock zt evolves according to, zt ¼ ρzt−1 þ t ;

ð5Þ

where the disturbance t is distributed normally with variance σ2. The law of motion for capital is ktþ1 ¼ ð1−δÞkt þ xt ;

ð6Þ

where δ is the capital depreciation rate, and xt is investment. It is also assumed that a cost occurs to capital adjustment: the more rapid is adjustment, the greater this cost. The capital adjustment cost is modeled as  2 ϕ 2 ktþ1 −kt , where ϕ is the capital adjustment cost parameter. 2.3. Linkage to international markets In this small open economy, the representative consumer can export goods to accumulate foreign asset holdings, or import goods to finance domestic spending. Let tbt denote the trade balance in period t, and dt stand for the foreign debt level, then dtþ1 ¼ ð1 þ r t Þdt −tbt ;

ð7Þ

where rt is the real interest rate for this small open economy. It is further assumed that whenever borrowing or lending, this consumer faces a country-specific interest rate rt    d −d r t ¼ r þ ψ eð t Þ −1 ;

Finally, it is assumed that debtors face borrowing constraints. The borrowing constraint depends on the performance of its GDP. When GDP increases, lenders take this as an indicator that borrowers have more resources; accordingly, they are less likely to default. Specifically, it is assumed that its debt cannot exceed ξ% of GDP, i.e., dt ≤ ξ %yt :

ð9Þ

This borrowing constraint differs from that assumed by Mendoza (2001) and Uribe (2006). Mendoza (2001)'s model stipulates that some fraction of output must be used as collateral before contracting any new borrowing. Uribe (2006) sets the upper limit as a constant. Here, this borrowing constraint is not collateral, since there hardly exist forcible repaying mechanisms in international financial markets. 9 Accordingly, the resource constraint for the representative household is, ct þ tbt þ xt ¼ yt −

2.2. Technology and investment

z α 1−α e t kt n t ;

37

ð8Þ

where r ∗ is the world risk free real interest rate, ψ is a constant, and d is the long-run foreign debt level. It is worth noting that the parameter ψ usually serves two purposes. On the one hand, it affects the borrowing cost: the more the country borrows, the higher is interest rate the country has to pay. On the other hand, it serves to introduce stationarity in the model, as discussed in Schmitt-Grohe and Uribe (2003). 8 8 Schmitt-Grohe and Uribe (2003) introduce five settings to induce stationarity and illustrates that all settings deliver identical dynamics at business-cycle frequencies. In this paper, the debt elastic interest rate setting is preferred to compare with the “country premium cycle” model as discussed later.

2 ϕ k −kt : 2 tþ1

ð10Þ

Finally, neither the home country nor the foreign country can play a Ponzi-game, which implies: −T

limT→∞ ð1 þ r t Þ

dtþT ¼ 0:

ð11Þ

3. Parameter values and simulation 3.1. Calibration As Table 1 shows, the trade balance ratios vary greatly even for countries at similar development stages. For example, in emerging economies, this coefficient varies from −0.79 (Ecuador, Mexico and South Africa) to 0.12 (Thailand, Turkey, Israel and Peru); in developed economies, it ranges from −0.60 (Spain) to 0.11 (Norway). The methodology of this paper is to study one emerging economy and test whether borrowing constraints predict a stronger trade balance–output comovement. Mexico is chosen as the subject economy for three reasons. The first is data convenience. Mexico is one of the a few emerging countries that has a consistent data set. For this reason, Mexico has been frequently studied, e.g., in Cole and Kehoe (1996), Durdu et al. (2009) and Gelos (2003), among others. Second, Mexico has the largest negative comovement between the trade balance and output, as Table 1 shows, and therefore serves the purpose of this paper well. Third, Mexico has experienced borrowing constraints, for example, during the period of 1994–1995. Apart from the borrowing constraint, the model in this paper is the same as that in Schmitt-Grohe and Uribe (2003). Schmitt-Grohe and Uribe (2003) calibrate their model to the Canadian economy. Here the parameters are re-calibrated, except for those that are impossible to set owing to unavailability of data. For example, there is no labor income report in the national accounts of Mexico; therefore, the parameter α is set to 0.32, the same value as in Canada. The discount factor β is set to 0.93, implying an average annual real interest rate of 8%, which is consistent with interest rates in the Mexican economy from 1970 to 2009. The capital depreciation rate δ is calibrated as 0.08, to match the average Mexican investment– output ratio (12.7%) over the sample period. The risk aversion parameter γ takes the value of 2, a commonly used number in the real business cycle literature. As suggested by Garcia-Cicco et al. (2010), ω is set to 1.6, implying a labor supply elas1 ticity of ω−1 ¼ 1:7 in Mexico. The preference parameter μ is assigned a 9 Uribe (2006) argues that it is costly for creditors to monitor the individual projects and instead, creditors make their lending decision on a few macroeconomic indicators.

38

Y. Zhao / Economic Modelling 32 (2013) 34–41

Table 2 Parameter values. Parameter

Value

Parameter

Value

γ α δ σ r∗ ξ

2 0.32 0.08 0.0262 0.08 37

ω ϕ ρ z ψ μ

1.6 0.017 0.93 0 0.00004 2

value of 2 to ensure that the household allocates around 30% of its time to labor in steady state. The degree of capital adjustment cost ϕ is set to match the volatility of investment. It is worth noting that the debt elastic interest rate parameter, ψ, also represents the international borrowing cost. To focus on the borrowing constraint and to eliminate the noise introduced by borrowing costs, the debt elastic interest rate parameter is set to the smallest possible value that induces stationarity in the model. The AR(1) parameter for the productivity shock process, ρ, and its standard deviation, σ, are estimated from the Solow residual for these data. Because capital stock data are not available for Mexico, the Solow residual is computed without capital. As shown by Gomme and Rupert (2007), omitting capital will not change the time series property of the Solow residual. Finally, the borrowing constraint parameter ξ is set at 37, so that the probability that the debt constraint will bind is 8%, as in Benigno et al. (2010). The parameter values are summarized in Table 2. 3.2. Model solution and simulation The model can be solved through a variety of dynamic programming methods. As argued in Arellano and Mendoza (2002) however, value function iteration is preferred to policy function iteration as the latter involves linear approximation or continuous differentiable iterations owing to the non-linearity implied by the occasionally binding constraint. In this paper, the model is therefore solved through value function iteration. Let zl, zm, and zh denote a “low”, “middle”, and “high” state of total factor productivity, respectively. The three-state Markov chain z = [zl, zm,zh], and the associated transition probability matrix, π, are specified 2 3 0:6642 0:3016 0:0342 as: z = [−0.0477, 0, 0.0477], and π ¼ 4 0:1508 0:6985 0:1508 5, 0:0342 0:3016 0:6642 where   πi; j ¼ prob zt ¼ zj jzt−1 ¼ zi

ð12Þ

is the transition probability from state i to j. 10 Let s denote the state vector. It consists of one exogenous state variable, the technology shock z, and two endogenous state variables, the capital stock k and the level of foreign debt d. The control vectors include the labor input n, next period's capital stock k′, next period's foreign debt d′, and finally consumption c. Accordingly, the dynamic programming problem as follows: V ðz; k; dÞ ¼ maxfuðc; nÞ þ βE½V ðz′; k′; d′g

ð13Þ

subject to the international interest rate Eq. (8), the borrowing constraint Eq. (9) and the budget constraint Eq. (10). 10

Here, the process zt is approximated by a three-state Markov chain using the method of Rouwenhorst (1995). Galindev and Lkhagvasuren (2010) show that for highly persistent autoregressive processes, the method of Rouwenhorst (1995) outperforms other commonly-used discretization methods.

For purposes of comparison, the model without a borrowing constraint, which is obtained by setting ξ to an arbitrarily large number, is also solved through value function iteration. The model with ξ → + ∞ is referred to as the “unconstrained model”, in contrast to the “constrained model” with ξ = 37. Table 3 displays the simulation results together with the second moments of the data. The question of whether adding a borrowing constraint explains the countercyclicality of the trade balance ratio in some countries can be answered by comparing corr(tb1t, yt) in the constrained and unconstrained models. Absent the borrowing constraint, the correlation is − 0.22. With a borrowing that is conditional on GDP, the correlation coefficient increases in absolute value, to − 0.59. Because corr(tb1t, yt) = − 0.73 in the data, the borrowing constraint brings the model much closer to the data. Unfortunately, the borrowing constraint causes the model to match poorly with other moments, especially trade balance volatility, and its serial correlation. The volatility of the trade balance decreases in the constrained model. This is because some levels of foreign debt are ruled out by the borrowing constraint. The lower serial correlation could be corrected by introducing a country premium, which can be obtained by increasing the debt elastic real interest rate parameter, ψ, as demonstrated by Garcia-Cicco et al. (2010). The country premium model, however, is not preferred here because it fails to capture the excess volatility of consumption, as detailed in the next section. As summarized by Arellano and Mendoza (2002), the small open economy real business cycle framework with occasionally binding borrowing constraints is endowed with a self-adjustment mechanism that can mitigate the negative effects of financial frictions. The mechanism here is that debtors will respond to changes in GDP by adjusting the foreign debt level to decrease the probability that the constraint will bind. When the economy is in an upturn, the borrowing constraint will be less likely to bind, and the representative household will decrease its trade balance more than it would otherwise, and in turn, increase its consumption by more than it would otherwise; when the economy is in a downturn, the borrowing constraint tightens, and the household must save more by increasing its trade balance to avoid the borrowing limit. An impulse response analysis can help to illustrate the effect of the borrowing constraint. Suppose that the economy is in the steady state,

Table 3 Observed and simulated moments. Variable

Data

Volatility of GDP Std(yt) 3.60 Volatilities relative to GDP Std(ct) 1.21 Std(xt) 3.28 Std(nt) 0.40 Std(tb1t) 0.56 Serial correlations corr(ct,ct−1) 0.60 corr(xt,xt−1) 0.41 corr(ht,ht−1) 0.38 corr(tb1t, tb1t−1) 0.55 corr(yt,yt −1) 0.57 Correlations with GDP corr(ct,yt) 0.93 corr(xt,yt) 0.93 corr(ht,yt) 0.03 corr(tb1t, yt) −0.73

Model with ξ→+∞

Model with ξ= 37

Model with unit-root trend

Model with country premium

3.36

3.13

3.27

3.40

0.97 3.68 0.38 0.30

1.10 3.28 0.62 0.26

2.10 3.11 0.12 0.23

0.80 3.43 0.35 0.29

0.46 0.38 0.19 0.25 0.43

0.47 0.55 0.25 0.21 0.60

0.49 0.51 0.27 0.33 0.58

0.51 0.43 0.20 0.46 0.62

0.97 0.88 0.98 −0.22

0.88 0.87 0.99 −0.59

0.87 0.89 1.00 −0.98

0.95 0.84 0.99 −0.17

Notes: t 1. tb1t is the trade balance ratio over GDP, i.e. tb1t ¼ tb y . t

2. In the data, labor input is only available from year 1991. 3. Each model is simulated with 1000 replications with 39 periods each. All variables except tb1t are first logged, then applied with HP filter with the smoothing parameter λ=100.

Y. Zhao / Economic Modelling 32 (2013) 34–41

and that productivity moves from the “middle” to the “low” state in the next period, which means that z moves from 0 to −0.0477. The average changes of the variables of interest from the 1000 simulated paths are plotted. Fig. 2 displays the movement of these economic variables in the unconstrained and constrained models, respectively. As Fig. 2 shows, when productivity falls to the “low” state, the labor supply decreases less in the constrained model than in the unconstrained model. Accordingly, the output drop is larger in the unconstrained model. These smaller decreases in labor and output are optimal responses, given the borrowing constraint: they are undertaken to avoid the tighter constraint in the “low” state. Not surprisingly, the trade balance in the constrained model increases by more than it does in the unconstrained model. The larger increase in the constrained model serves to decrease the level of debt to avoid the binding constraint. As a result, there is a larger trade balance adjustment along with a smaller output change in the model with the borrowing constraint, leading to a larger correlation between the trade balance ratio and output. Additionally, the consumption adjustment is larger in the constrained model, implying that the insurance motive is weaker, and this is consistent with the hypothesis that borrowing constraints limits the ability of consumption smoothing. 4. Further discussion: the “trend cycle”, “country premium cycle”, or the “borrowing cycle”? The success of the borrowing constraint in this paper strongly suggests borrowing constraints accounts most of the trade balance–output difference across countries. This section will compare the “borrowing cycle” model with the mainstream of existing literature on emerging

39

economies: the “trend cycle” model and the “country premium cycle” model. One common motivation for these two models is that some macroeconomics variables, especially consumption, are more volatile in emerging countries. More volatile consumption violates the theory of consumption smoothing and stands in sharp contrast with developed economies. It is also in contradiction with the predictions of standard real business cycle model and thus makes it a challenging task to match with the data for research on emerging economies. The “trend cycle” model attributes the excess volatility in consumption to the permanent component of productivity shocks. Also known as “the cycle is the trend”, Aguiar and Gopinath (2007) argue that the productivity shock is more trend-growth related rather than transitory fluctuations around a stable trend in emerging countries, as it is for most developed economies. When there is a shock on an economy, the representative agent in developed countries will not adjust consumption much because the agent knows that the shock is not permanent, with the expectation that output will return to the long-run trend. In contrast, in developing counties, the agent will adjust consumption accordingly because the shock implies a permanent change in output. The “country premium cycle” model, as proposed by Garcia-Cicco et al. (2010), argue that the real interest rate is not fixed and is dependent on the foreign debt level: when the debt level is above the long-run trend, the country has to pay a premium in the interest rate. It is the change in the “country premium” that drives the business cycles in emerging economies. Garcia-Cicco et al. (2010) show that permanent movements in productivity, explain little excess volatility in consumption using the historical data for emerging economies. Instead, the

(a) Labor

(b) Output

0.286 0.285

0.283

yt

nt

0.284

0.282 0.281 0.28 1

2

3

4

5

0.4 0.395 0.39 0.385 0.38 0.375 0.37 0.365 0.36 0.355 0.35

6

1

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(d) TradeBalance 0.007

Constrained Unconstrained

0.0065 0.006 0.0055 tbt

ct

(c) Consumption 0.33 0.325 0.32 0.315 0.31 0.305 0.3 0.295 0.29 0.285 0.28

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years

0.005 0.0045 0.004 0.0035 1

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years

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Fig. 2. Impulse responses.

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Y. Zhao / Economic Modelling 32 (2013) 34–41

authors find that the country premium model matches with the data better. By emphasizing different factors that drives the business cycle in emerging economies, these two hypotheses divide the small open economy models into two distinct categories. Each hypothesis, however, has its own limitations. For “trend cycle” hypothesis, as criticized by Garcia-Cicco et al. (2010), it is problematic to use short sample data to identify the permanent component of productivity shocks because the productivity shock in the pre-war period is significantly different from data afterwards. More importantly, the “trend cycle” hypothesis results in a too strong trade balance ratio–output comovement. This can be seen by setting the AR(1) coefficient ρ=1 in the productivity shock process zt =ρ∗zt−1 +t. By setting ρ=1, the productivity shock becomes non-stationary, and any innovation t has permanent effect on zt and output yt. As implied by permanent income hypothesis, the movement in consumption is larger than that of output. Accordingly, trade balance is crowded out and becomes strongly counter-cyclical. As shown in Table 3, the trade balance ratio–output comovement, corr(tb1t, yt) becomes −0.98, and the relative volatility of consumption is 2.1. In short, matching the excess volatility in consumption in “trend cycle” model is at the cost of overshooting the comovement between the trade balance ratio and output. For the “country premium” hypothesis, it is worth noting that in Garcia-Cicco et al. (2010), the country premium alone cannot generate the excess volatility in consumption. It is the preference shock together with stationary productivity shock that explains most excess volatility. The predictions of the “country premium” model can be obtained by increasing the debt elastic real interest rate parameter, ψ, to 2.8, as adopted by Garcia-Cicco et al. (2010). The simulation exercise shows that the “country premium” alone fails to produce the high consumption–output volatility ratio in the data. The borrowing constraint generates a relative volatility 1.10, while the country premium model generates the relative volatility as 0.80. The reason for consumption to be more volatile in the model with borrowing constraint is that relatively radical changes in the trade balance results in larger adjustments in consumption as well. As plotted in Fig. 2, when the economy transits from the “median” to the “low” state, for instance, the trade balance experiences a larger increase to avoid the binding constraint, and this larger increase causes a larger decrease in consumption as well, compared with the unconstrained model and the country premium model. This result is in line with the idea that borrowing constraints imposed on emerging countries limits their ability to smooth consumption, as discussed in Resende (2006). In summary, in matching with the trade balance ratio–output comovement and excess volatility in consumption, two typical phenomena in emerging economies, the model with explicit borrowing constraint outperforms both the “trend cycle” and the “country premium” hypothesis. This suggests that the “borrowing cycle” should not be overlooked in studying emerging economies. 5. Conclusion The trade balance is subject to various forces, and it is no wonder that its correlation with output varies from country to country. There is, however, a noticeable difference between developing and developed economies: the trade balance ratio in emerging economies is more responsive to output changes. Here, it is argued that this is not a random phenomenon, and that the driving factor behind it is imperfections in international financial markets. The author conjectures that the borrowing constraint, mainly for emerging economies, can cause the trade balance and output to move together more closely. The borrowing constraint here is simply modeled as an upper limit on borrowing, stipulated as a fraction of output. With the borrowing constraint conditional on aggregate economic activity, the representative household must save more by accumulating more

foreign assets (or decreasing foreign debt) in “low” states to avoid hitting the borrowing constraint. The crucial point is that borrowing constraints further weaken the insurance motive, making consumption and the trade balance more sensitive to changes in output. By including the borrowing constraint in an otherwise standard small open economy real business cycle model, the paper finds that the borrowing constraint explains around 70% of the trade balance correlation difference. In addition, the model with the borrowing constraint outperforms existing models, in particular, the “trend cycle” and the “country premium” models, in its ability to capture the excess volatility of consumption, the other stylized fact about emerging economies. The borrowing constraint model generates realistic trade balance ratio–output comovements, compared with the “trend cycle” model. In comparison with the “country premium” model, it easily generates the excess volatility of consumption without using preference shocks. In successfully capturing the typical characteristics of emerging economies, this paper strongly suggests that the borrowing constraint may be an important factor in studying emerging economies. As the main purpose is to illustrate the effect of borrowing constraints on business cycle statistics, this paper has focused specifically on the effects of borrowing constraints to the exclusion of other aspects of the trade balance–output relationship. For example, this paper does not take “willingness-to-pay” into consideration, i.e., the voluntary default case. Additionally, the paper assumes that the borrowing constraint is one-sided: it only sets a maximum for foreign debt, not a minimum. This is of particular interest in view of global trade imbalances, which correspond to persistent surpluses for some countries. Adding these features to the analysis and assessing their quantitative effects on the trade balance correlation will be of interest in further research.

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