JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.1 (1-20)

Review of Economic Dynamics ••• (••••) •••–•••

Contents lists available at SciVerse ScienceDirect

Review of Economic Dynamics www.elsevier.com/locate/red

Accounting for global dispersion of current accounts ✩ Yongsung Chang a,b,∗ , Sun-Bin Kim b , Jaewoo Lee c a b c

University of Rochester, United States Yonsei University, Republic of Korea International Monetary Fund, United States

a r t i c l e

i n f o

Article history: Received 29 August 2010 Revised 20 September 2012 Available online xxxx JEL classification: F32 F34 F44

a b s t r a c t We develop a multi-country quantitative model of the global distribution of current account and external balances. Countries accumulate domestic capital and foreign assets to smooth consumption over time against exogenous productivity shocks in the presence of liquidity constraints. In equilibrium, optimal consumption and investment responses to persistent productivity shocks imply a degree of intertemporal substitution across countries that can explain up to one-third of the current account dispersion in the data. © 2012 Elsevier Inc. All rights reserved.

Keywords: Dispersion of current accounts Incomplete markets Frictions

1. Introduction Large current account imbalances often become a source of concern, especially when they involve large deficits. The large current account deficit of the U.S. since 2002 has generated much debate about its causes and the need for eventual adjustment. (See Obstfeld and Rogoff, 2005; Engel and Rogers, 2006; Caballero et al., 2008 and Blanchard and Milesi-Ferretti, 2009 for different views on the matter.) Indeed, in many other countries, large current account deficits have often preceded an external crisis, thus stoking fears, especially when the deficits appear on the balance of payments accounts of emerging markets.1 In contrast to this common view that regards large imbalances as a cause for concern, others see a sign of progress in large current account imbalances. Some interpreted the U.S. current account deficit as an outgrowth of an integrated financial market among high-saving countries—e.g., the savings glut view of Bernanke (2005). In this vein, large current

✩ We are grateful for comments by Mark Bils, Martin Boileau, Jay Hong, Gian Maria Milesi-Ferretti, Fabrizio Perri, David Romer, an anonymous referee, and participants at various seminars and conferences. We also thank Jinhee Woo for his excellent research assistance. Chang acknowledges support from the WCU Program through the Korea Research Foundation (WCU-R33-10005). Kim acknowledges support from the Korea Research Foundation (KRF-2009327-B00119). The views expressed are those of the authors and do not necessarily represent those of the IMF or IMF policy. Corresponding author at: Department of Economics, University of Rochester, Rochester, NY 14627, United States. Fax: +1 585 256 2309. E-mail address: [email protected] (Y. Chang). 1 Since 2009, during the ‘Great Recession’, a sharp adjustment has again been forced on many countries with large current account deficits, not only in emerging markets but also in advanced economies. In particular, the developments in Greece had far-reaching effects on many countries in the euro area. For example, see “The euro-zone crisis: Europe’s three great delusions”, The Economist, May 22nd–28th, 2010, p. 12.

*

1094-2025/$ – see front matter © 2012 Elsevier Inc. All rights reserved. http://dx.doi.org/10.1016/j.red.2012.09.007

JID:YREDY AID:599 /FLA

2

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.2 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

account imbalances are a welcome development to the extent that they are outcomes of a rising global economic integration (in financial and trade accounts).2 We develop a multi-country quantitative model of the global distribution of current account and external balances. The main objective is to assess how much of current account dispersion can be accounted for by a simple intertemporal substitution of resources in the face of uninsurable shocks to productivity. This should help the discussion by establishing a clear benchmark distribution of external balances that arises from pure intertemporal substitution. Our model is an open-economy version of the incomplete-markets model of Bewley (1986), Aiyagari (1994), and Huggett (1996). While this model has been widely used to explain income and wealth distributions across households, it has not been applied to study the distribution of current accounts and its evolution over time. Clarida (1990), Castro (2005) and Bai and Zhang (2010) develop multi-country models of global equilibrium under incomplete markets. The world economy comprises a continuum of countries, each of which is populated by a representative household. Countries trade goods subject to an iceberg cost of trade and have access to the world capital market, which is incomplete and subject to several frictions.3 Each country adjusts its consumption, investment, and external assets in response to stochastic shifts in productivity. With plausible parameter values, the model economy generates a pattern of business cycles that is comparable to that in the post-war data documented in the literature: (i) The volatilities and correlations among key aggregate variables are in line with those among advanced countries (e.g., Backus and Kehoe, 1992 and Backus et al., 1994); (ii) the model exhibits a counter-cyclical trade balance in response to a productivity shock as in the data (e.g., Backus et al., 1994). We find that the model is capable of accounting for up to one-third of the global dispersion of current accounts as an equilibrium outcome from intertemporal substitution in response to productivity variations that are comparable to the observed TFP movement across countries. The model is also capable of explaining the historical trend in the dispersion of current accounts by the reduction in frictions. Finally, we find that the easing of financial frictions has a greater effect on the dispersion of current accounts than the easing of trade frictions. A couple of caveats are necessary to judge the quantitative results of our analysis. First, the model fails to match the dispersions of stocks (external balances) and flows (current account) at the same time—while the model matches the dispersion of net foreign assets in the data, it accounts for only one-third of current account dispersion in the data. In our model, the only source of dispersion is the heterogeneity in (uninsurable) productivity, measured relative to each country’s trend growth. This does not necessarily reflect our view of the world. Many features we abstract from in our model should be important for the current account dynamics. Countries differ not only in size but also with respect to the structure of domestic financial markets (Mendoza et al., 2009; Caballero et al., 2008), the degree of moderation in macro volatility (Fogli and Perri, 2006), and the structure of portfolios (Gourinchas and Rey, 2007). Second, in order to simplify the equilibrium construct, we also abstract from terms of trade movements, potentially a strong insurance mechanism against productivity risk (Cole and Obstfeld, 1991). Moreover, we abstract from the valuation channel, which has proven to make a striking difference between the movement in the net foreign assets and current accounts, most famously in the case of the U.S. where the valuation channel led its net foreign assets position to decline much less than the cumulated amount of its current account deficits over the past decades (e.g. Gourinchas and Rey, 2007 among many). Theoretical progress on the valuation channel in full-fledged international macroeconomic models is still in its infancy, despite some progress made (Devereux and Sutherland, 2010), thereby limiting our ability to incorporate it. Thus, our results should be viewed with a limited scope—how much a simple model of intertemporal substitution against productivity shocks can account for the global dispersion of current accounts. The paper is organized as follows. Section 2 documents strong trends in the global dispersion of current accounts, net foreign assets, and trade balances over the past four decades. Section 3 lays out our benchmark model of a world economy where countries engage in international trade and financial transactions subject to frictions. In Section 4, we calibrate the model economy to match the observed pattern of business cycles. We also compare the equilibrium dispersion of the model to that in the data. We then ask whether a decrease in frictions can account for the observed trends in the world distribution of current accounts documented in Section 2. Section 5 concludes.

2. Global dispersion of current accounts

The dispersion of current account balances has been increasing over the past several decades. Fig. 1 shows, for each year from 1960 to 2004, the 80% range that comprises the current account as a percent of annual GDP except for the top

2 This view is closely related to the Feldstein–Horioka (1980) puzzle, which implies that observed current account imbalances are too small to be the result of a fully integrated world financial market. See Bai and Zhang (2010). 3 We consider frictions in both goods and financial markets, partly motivated by the apparent decline in trade costs over time as well as the thesis of Obstfeld and Rogoff (2000) that trade costs can be the main driver of several anomalies in international economics.

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.3 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

3

Fig. 1. Current account to GDP. Note: The 80 percent range (from top to bottom deciles) of current account to GDP ratios. See Appendix A for a detailed description of the data.

and bottom deciles (thus, from 10% to 90%, when ranked numerically). The top panel illustrates the near doubling in the width of the 80% range of current account balances. Table 1 shows that between 1970 and 2000 the cross-sectional standard deviation of the current account to GDP ratios increased from 4.9% to 6.9%.4 This upper panel is based on the sample that rose from 70 countries in 1970 to about 120 countries in 2004 (after having started with 50 countries in 1960). The same pattern is seen in the bottom panel, which is based on the advanced-country sample that started with 18 countries in 1960 and 1970, adding three countries to comprise 21 countries in 2004. The 80% range has widened visibly in this graph as well, and the particularly rapid widening in the 2000s reflects the deepening of global current account imbalances. The standard deviation of current account to GDP ratios has increased at an even higher pace among advanced countries, from 1.9% to 6.7% (Table 1). A similar widening in global dispersion is found for net foreign asset (NFA) positions and trade balances, both measured as a percent of annual GDP. Figs. 2 and 3 show the 80% range for net foreign assets and trade balances, both for the larger sample of about 120 countries as of 2004 and for the more balanced sample of about 20 advanced countries. The dispersion of net foreign assets has increased rather dramatically, more than the dispersion in both current accounts and trade balances.5 According to Table 1, the cross-sectional standard deviation of the net foreign assets to GDP ratio increased

4 We choose 1970 for the first period of data because the sample size was substantial by that time and because the world economy had moved sufficiently close to the breakdown of the Bretton Woods regime that regulated international capital flows much more tightly than later (Obstfeld and Taylor, 2004). 5 In both current accounts and net foreign assets, the impressive rise has been well documented for gross external asset and liability positions (e.g., Lane and Milesi-Ferretti, 2007).

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.4 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

4

Table 1 Distributions of current account, net foreign assets, and trade balance. All

Advanced

1970

2000

1970

2000

−2.4 (%) − 2 .1 11.6 −30.2 4. 9

−1.0 −2.5 19.6 −18.3 6.9

−1.9 −2.3 1 .7 −4.8 1 .9

0.8 −0.5 14.8 −10.3 6 .7

CA GDP

Mean Median Max Min SD

NFA GDP

Mean Median Max Min SD

−16.7 −13.4 77.6 −136.2 29.3

−40.2 −36.9 156.6 −236.1 55.4

−6.3 −8.5 73.2 −34.2 24.3

−11.1 −8.5 104.5 −149.1 51.2

TB GDP

Mean Median Max Min SD

− 1 .7 − 1 .5 54.0 −31.6 9 .8

−1.9 −2.9 36.2 −45.1 11.6

−1.5 − 0.9 5 .5 −11.1 3 .3

2 .4 1 .0 21.1 −11.1 7 .6

Note: See Appendix A for the detailed description of data sources.

Fig. 2. Net foreign assets to GDP. Note: The 80 percent range (from top to bottom deciles) of net foreign assets to annual GDP ratios. See Appendix A for a detailed description of the data.

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.5 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

5

Fig. 3. Trade balance to GDP. Note: The 80 percent range (from top to bottom deciles) of trade balance to GDP ratios. See Appendix A for a detailed description of the data.

from 29.3% to 55.4% between 1970 and 2000. The dispersion in trade balances has increased also, although somewhat less than the dispersion in net foreign assets or current accounts. Between 1970 and 2000, the cross-sectional standard deviation of the trade balance to GDP ratio increased from 9.8% to 11.6%. The same pattern is observed among advanced countries. The cross-sectional standard deviation of NFA to annual GDP ratios increased from 24.3% to 51.2%, and that of trade balance to GDP ratios increased from 3.3% to 7.6%. Fig. 4 depicts the evolution of current account and net foreign asset distributions (both relative to annual GDP) between 1960 and 2000. Each graph represents the kernel density estimate of the cross-sectional distribution. It is clear from these figures that there has been a continuous increase in the dispersion in both distributions. The only notable exception is the current account to GDP ratio in 1980, when presumably the effects of oil shocks temporarily widened the dispersion of current accounts beyond that seen in later years. The rising dispersion of current accounts over the past several decades has been highlighted in several earlier papers. Blanchard and Giavazzi (2002) documented the rising dispersion of current accounts in European countries and associated it with improving financial integration, including the launch of the euro area. Faruquee and Lee (2009) examined a sample of nearly 100 countries and found an underlying trend increase in the dispersion of current accounts. They also found evidence in support of financial integration as the main contributing factor to the rising dispersion while finding little support for trade openness as a contributing factor. Obstfeld and Taylor (2004) have reported the evolution in the dispersion of current accounts since the late 1800s. They attribute this trend movement to underlying financial integration, intertwined with the trilemma of international economics. In particular, they find that the standard deviation of current accounts among 15 sample countries was highest in the

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.6 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

6

Fig. 4. Evolution of current account distribution over time. Note: Kernel density estimates of current account to GDP ratios (top) and net foreign assets to GDP ratios (bottom) for each year. See Appendix A for a detailed description of the data.

early 1900s (prior to the First World War), which they view to be a period with a highly integrated world capital market, comparable to the 2000s.6 3. Theory 3.1. Motivation Since the theory of distribution requires us to go beyond a typical two-country framework to a multi-country model, we turn to a standard incomplete insurance model with multiple (infinitely many) agents that originated with Bewley (1986). This model was further developed by Clarida (1990) in an international context and by Aiyagari (1994) and Huggett (1996) in a domestic context, among others. Faced with incomplete insurance and a limit to borrowing, each country (agent) accumulates domestic capital or foreign assets as a way to smooth consumption in the face of stochastic movements in its productivity. In equilibrium, a stationary distribution emerges for endogenous variables, including current accounts and external balances. This model captures intertemporal substitution for consumption smoothing in the presence of liquidity constraints, although the liquidity constraint itself is not derived from first principles (the same interpretation as in the papers just cited).7

6 7

For evidence of the high international integration of capital markets in the pre-war period based on an interest rate spread, see Mauro et al. (2006). For papers that focus on modeling liquidity constraints in two-country settings, see Aguiar and Gopinath (2006) or Mendoza et al. (2009).

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.7 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

7

Because countries are limited in the amount they can borrow in certain states of nature, they accumulate assets (in the form of domestic physical capital or foreign assets) as a precaution against such events.8 One distinguishing feature of our model, compared with the conventional incomplete insurance model, is the introduction of the spread between the lending and borrowing interest rates, which we interpret as reflecting the cost of financial intermediation. Without the spread, the model generates a very skewed equilibrium distribution of net foreign assets. For a wealth (or income) distribution across households within a country, this skewness (i.e., a long right tail) is a desirable feature (e.g., Díaz-Giménez et al., 1997). However, we do not see such skewness in the NFA distribution in the data. To tame this skewness, we introduce a spread between lending and borrowing rates. The spread in interest rate discourages countries from borrowing too frequently. It also makes lending less profitable, taming the right tail in external balances. As a result, the spread helps us to match the overall shape of the distribution of external balances (more about this in the quantitative analysis in Section 4). Besides constructing the most compact model of dispersion, the modeling choice is motivated by the debate on incomplete risk sharing in the international economics literature. Financial market frictions have been viewed as a primary cause of several well-known phenomena of incomplete risk sharing across countries, including a low international correlation of consumption and home bias in the international allocation of equity. More recently, the phenomenal accumulation of international reserves in emerging markets has been attributed to the self-insurance motive, in the absence of a fully developed market for insurance.9 Compared with earlier works by Clarida (1990), our model forms the basis of a quantitative analysis of the global dispersion of current accounts. We also focus on the effect of various frictions on the global dispersion of current accounts, where relative productivity shocks are the only source of heterogeneity. Clarida (1990) explored the current account level effects of high and low levels of discount rates, in qualitative terms. Without focusing on the evolution of the current account dispersion, two recent papers have developed quantitative models of global equilibrium that build on Clarida’s work. Castro (2005) investigates whether technological shocks can explain income dispersions, and Bai and Zhang (2010) explore the role of financial frictions in explaining the Feldstein–Horioka puzzle. 3.2. Model The world economy consists of a continuum of countries, each of which in turn is populated by a representative agent. The representative agent has access to a production technology, yt = xt ktα , where kt denotes physical capital. A country’s productivity is denoted by xt , which varies exogenously according to a stochastic process with a transition probability distribution function πx (x |x) = Pr(xt +1  x |xt = x). As observed by Glick and Rogoff (1995), current accounts are driven by country-specific shocks rather than global shocks. Accordingly, we focus on a persistent idiosyncratic productivity shock and the uncertainty thereof while abstracting from global uncertainty. A country maximizes the following utility:

E0

∞ 

1 −γ

βt

ct

t =0

−1

1−γ

subject to:

at +1 = xt ktα + (1 + rt )at − (cdt + idt ) − (1 + τ )(c f t + i f t ) − kt +1 = (1 − δ)kt + it ,



1− η1

ct = φ cdt



1− η1

it = φ idt

η 1− η1  η−1

+ (1 − φ)c f t

1− η1  η−1

θ 2



kt +1 − kt kt

2 kt ,

,

η

+ (1 − φ)i f t

.

Each country accumulates two types of assets: foreign bonds (at ) and physical capital (kt ). Countries have access to a world bond market where they trade one-period consumption loans, which play a role as an insurance device against idiosyncratic income fluctuations. A country faces an exogenously imposed borrowing constraint, a¯ , which is set at a level higher than the natural limit. We assume that there is a spread between the lending rate (r L ) and the borrowing rate (r B ) so that r L < r B : that is, r = r L when at > 0 and r = r B otherwise. This spread in interest rates, reflecting the cost of financial intermediation, reinforces a country’s incentive to accumulate foreign bonds or production capital for consumption smoothing in the face of borrowing constraints (more in Section 4).

8 This precautionary motive does not require and is independent of the convexity of marginal utility that is postulated as the basis of precautionary savings in small open-economy models (Obstfeld and Rogoff, 1995 and references therein). 9 See Caballero and Panageas (2008), Lee (2009), and Obstfeld et al. (2008).

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.8 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

8

Physical capital is needed for production and depreciates at rate δ . Investment is irreversible, i.e., kt +1  (1 − δ)kt , and thus cannot be used for consumption. Nor can physical capital be traded internationally, unlike foreign bonds. Investment k −k requires quadratic adjustment costs: θ2 ( t +k1 t )2 kt . t Both domestic consumption and investment composites combine domestic and foreign goods with a substitution elasticity η : domestic consumption (cdt ) and foreign consumption (c f t ) for consumption composite ct , and domestic investment (i dt ) and foreign investment (i f t ) for investment composite i t . Domestic consumption and investment are restricted by domestic production: cdt + i dt  xt ktα . The importation of foreign goods c f t requires an import cost denoted by τ (the familiar iceberg cost of trade, reflecting a transportation cost or trade restrictions). For simplicity, we assume that both domestic and foreign goods are treated identically in the world goods market (thus the relative price of foreign goods in the domestic market is just 1 + τ always and everywhere).10 A country’s trade balance tbt and current account cat are then:

tbt = xt ktα −

θ



kt +1 − kt

2

kt

2 kt − (cdt + idt ) − (1 + τ )(c f t + i f t ),









cat = at +1 − at = tbt + r B + r L − r B 1{at >0} at . It is convenient to express the country optimization problem in a recursive form:







V a, k, x; r L , r B = max

c 1 −γ − 1 1−γ

  + β E V a , k , x ; r L , r B x

 (1)

subject to



θ a = xkα + (1 + r )a − (cd + id ) − (1 + τ )(c f + i f ) − 

2

k = (1 − δ)k + i ,



1− η1

c = φ cd



1− η1

i = φ id

η 1− η1  η−1

+ (1 − φ)c f

η 1− η1  η−1

+ (1 − φ)i f

k − k k

2 k,

> 0,

 0,

xkα  cd + id , a  a¯ ,



r=

rL rB

if a  0, otherwise.

Each country’s optimal decision rules for consumption, investment, bond holding and capital stock can be derived as functions of three state variables a, k and x: cd (a, k, x), c f (a, k, x), i d (a, k, x), i f (a, k, x), a (a, k, x) and k (a, k, x), under a given set of interest rates r L and r B . The recursive competitive equilibrium for the world economy consists of these decision rules for consumption and investment, value function, interest rates, and the invariant distribution μ(a, k, x)11 that satisfy the following conditions. 1. Individual countries optimize: Given r B and r L , the individual country’s decision rules, cd (a, k, x), c f (a, k, x), i d (a, k, x), i f (a, k, x), a (a, k, x) and k (a, k, x), and the value function, V (a, k, x), solve the Bellman equation (1). 2. The world goods market clears:



 α

xk − cd (a, k, x) − id (a, k, x) dμ = (1 + τ )







c f (a, k, x) + i f (a, k, x) dμ.

3. The world bond market clears:



a (a, k, x) dμ = 0.

10 We thus distinguish between home and foreign goods by labels only. This is the simplest step of introducing domestic and foreign goods for each country and of considering the role of trade frictions. Next steps involve the introduction of endogenous fluctuations in the terms of trade and are left for future research. 11 Let A, K and X denote sets of all possible realizations of a, k and x, respectively. The distribution μ(a, k, x) is the probability measure defined over the σ -algebra of A × K × X .

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.9 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

9

μ is time invariant: for any A 0 ⊂ A, K 0 ⊂ K and X 0 ⊂ X ,      μ A0, K 0, X 0 = 1{a =a (a,k,x)} × 1{k =k (a,k,x)} dπ x x da dk dx dμ.

4. The distribution

A×K×X

A0 ,K 0 , X 0

Each country’s optimal decision rules and the market clearing condition in goods and capital markets are the same as in any equilibrium model. A distinguishing point is the fourth condition on the time-invariant measure, the equilibrium distribution of net foreign assets that is endogenously determined in our model. Combining the equilibrium distribution μ(a, k, x) with other optimal decision rules, we can derive the global (equilibrium) distribution of other endogenous variables, including the current account and trade balance. 4. Quantitative analysis 4.1. Calibration For most parameters (e.g., preferences and technology), we adopt values commonly used in the literature. For the parameters that are either controversial or difficult to measure, such as financial frictions and productivity shocks, we consider a range of values based on some indirect evidence and discuss their quantitative impacts on the equilibrium dispersion. The unit of time is a quarter. The discount factor, β , is assumed to be 0.99. We use log utility in consumption (γ = 1) as in a typical business cycle model. Following Obstfeld and Rogoff (2000), the elasticity of substitution between consumption of domestic and foreign goods, η , is 6. According to Anderson and van Wincoop’s (2004) survey article, trade costs (inclusive of tariffs and other factors) are estimated at 48–63%. We set τ = 0.5. Given τ and η , we set the relative weight on domestic goods in the CES utility function (φ = 0.475) to match the average ratio of expenditures on domestic to foreign goods, 4.2, in Obstfeld and Rogoff (2000).12 With these values the model generates an average import-GDP ratio of 19% in the steady state, close to what we observed in 2000. We assume that the log of a country-specific productivity xt follows a stationary but persistent AR(1) process: ln xt = ρx ln xt −1 + t , where t ∼ N (0, σx2 ). While it is well known that shocks to trends or global shocks often trigger big swings in external balances (e.g., Gourinchas and Jeanne, 2009), unfortunately, we cannot incorporate them into our analysis for technical reasons. A stationary equilibrium requires a time-invariant distribution of μ(a, k, x), precluding permanent (or trend) shocks in the model. Incorporating global shocks (or shocks correlated across countries) would make μ(a, k, x) time-varying. In order to compute the equilibrium, we have to keep track of μ(a, k, x), an infinite dimensional object, over time, which is not feasible.13 The typical value in the real business cycle literature is ρx = 0.95 and σx = 0.7% based on Kydland and Prescott (1982), which is estimated from linearly detrended total factor productivity (TFP) for the post-war U.S. economy. Similar values are adopted for the two-country version of international business cycle models (e.g., Backus et al., 1994), estimated from TFP pairs of advanced countries. However, the estimates based on the U.S. (or advanced countries) may significantly understate the uncertainty that a typical country in the world faces because many developing economies exhibit much more volatile TFP. For example, when we estimate the AR(1) process using linearly detrended TFPs, as in Kydland and Prescott (1982), for 29 countries (for which we have reliable data) for the period 1961–2003, we obtain ρx = 0.96 and σx = 2.2%, on average.14 While the average persistence is similar to that of the U.S., the average standard deviation of innovation is more than 3 times larger than that of the U.S. On the one hand, even this large estimate (σx = 2.2%) may be a conservative estimate for the uncertainty that a developing economy faces, because those 29 countries (whose data quality is ‘B’ or higher according to the Penn World Tables) are mostly developed and have relatively stable economies (see Appendix A for the list of countries). In fact, with the larger set of 69 countries for which we have available time series of both national income accounts and external balances (see Appendix A for the list), the average estimate is ρx = 0.95 and σx = 3.8%, more than 5 times larger than that of the U.S. On the other hand, linear detrending may overstate the magnitude of short-run fluctuations (i.e., deviations from trends) of developing economies by omitting non-linear components in productivity trends (e.g., stochastic trends, structural breaks, etc.) as well as transition dynamics.

12

The share of home-traded goods in total traded goods is 0.5 (Stockman and Tesar, 1995) and 0.72 (Corsetti et al., 2008), and the share of non-traded

goods is usually put at 0.5 in the literature (an exception being 0.45 used by Corsetti et al.). The ratio of domestic to foreign expenditure will be

0.75 0.25

=3

0.55×0.28 = 5.5 (Corsetti et al.), with (combining the Stockman and Tesar with the usual ratio between tradable goods and non-tradable goods), or 1− 0.55×0.28 Obstfeld and Rogoff’s (2000) number of 4.2 in the middle. 13 One can rely on an approximate equilibrium concept (such as the ‘bounded rationality’ of Krusell and Smith (1998), which approximates μ(a, x, k) by a limited set of moments). While this is an unexplored (and challenging) area of research, it is beyond the scope of this paper. 14 Our estimation is based on annual data from the Penn World Tables (PWT v6.2). We convert the annual estimates to quarterly values. In calculating TFP, we compute the capital stock from the investment series using the perpetual inventory method. Since the TFP measure is inherently subject to large measurement errors, we restrict the data sample to countries whose data quality is ‘B’ or higher, according to the PWT. The estimation allows for annual time dummies, country dummies, and country-specific linear trends to control for, respectively, global shocks, country fixed effects, and a country-specific trend growth.

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.10 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

10

Table 2 Parameters of the benchmark model economy. Parameter

Description

β = 0.99 γ =1 η=6 φ = 0.475

Discount factor Relative risk aversion Subst. elast. b/w domestic and foreign consumption Weight on domestic goods in CES utility function

α = 0.36

Capital’s share in output production Capital depreciation rate Adjustment cost of investment in physical capital Persistence of productivity shock Standard deviation of innovation to productivity shock

τ = 0.5

Trade friction Interest rate spread Borrowing constraint

δ = 0.025 θ =6 ρx = 0.95 σx = 0.014 ψ = r B − r L = 0.05% a¯ = −40

Table 3 Business cycle moments. Data

Models

BK

BKK

Benchmark (σx = 1.4%)

Small shocks (σx = 0.7%)

σy

2.05 (%) [1.45, 3.11]

1.50 [0.90, 1.92]

1.82 [1.34, 2.30]

0.98

3.09

[0.72, 1.24]

[2.28, 3.91]

σc /σ y

1.17 [0.65, 2.9]

0.85

[0.66, 1.14]

0.34 [0.23, 0.43]

0.42 [0.29, 0.51]

0.29 [0.21, 0.47]

σi /σ y

2.60 [2.10, 5.50]

2.78 [1.14, 3.27]

3.63 [3.22, 3.94]

3.56 [3.13, 3.87]

3.71 [3.08, 4.18]

σnx /σ y

1.03 [0.43, 3.47]

0.68 [0.27, 0.91]

0.29 [0.13, 0.39]

0.30 [0.20, 0.41]

0.28 [0.11, 0.41]

0.76

0.80 [0.57, 0.90]

0.99 [0, 97, 0.99]

0.98 [0.92, 0.99]

0.99 [0.97, 0.99]

0.79 [0.52, 0.94]

0.95 [0.89, 0.99]

0.95 [0.89, 0.99]

0.94 [0.85, 0.99]

−0.26 [−0.68, −0.01]

−0.42 [−0.88, 0.05]

−0.59 [−0.97, −0.0]

−0.29 [−0.97, 0.96]

cor( y , y −1 )

0.78 [0.57, 0.90]

0.71 [0.45, 0.83]

0.71 [0.45, 0.83]

0.71 [0.45, 0.83]

cor(nx, nx−1 )

0.71 [0.29, 0.90]

0.75 [0.55, 0.89]

0.72 [0.38, 0.87]

0.78 [0.59, 0.92]

cor(c , y )

[0.65, 0.96] cor(i , y )

0.78

cor(nx, y )

[0.42, 0.86] −0.20 [−0.43, 0.11]

Large shocks (σx = 2.2%)

Notes: The data statistics under ‘BK’ represent the median, minimum and maximum (in parenthesis) of 10 developed countries from Backus and Kehoe (1992, Tables 2 and 3). Those under ‘BKK’ are based on 11 developed countries from Backus et al. (1994, Table 1). The model statistics are based on the mean, minimum, and maximum from the simulated panel of 100 countries for 100 years. All variables are logged and HP filtered with a smoothing parameter of 1600.

Since there is no clear-cut resolution for the size of the idiosyncratic productivity shocks that can be applied to all countries in the world, for our benchmark case, we use ρx = 0.95 and σx = 1.4%, keeping the persistence the same as in the U.S. but doubling the standard deviation of innovation.15 This choice is consistent with the recent finding by Bahng (2011), who reports that the average volatility of detrended GDP of 12 developing countries is at least twice as large as that of developed countries (4.61% vs. 2.26% measured by the standard deviation of annual GDP growth rates; 2.74% vs. 1.3% measured by the standard deviation of HP-filtered log GDP). As shown in Table 3, the average volatility of output generated from our model is well within the range of output volatility reported in the international business cycle studies such as Backus and Kehoe (1992) and Backus et al. (1994). We also report the equilibria of the models under two alternative values of σx : 0.7% (U.S.) and 2.2% (the average of 29 countries estimated from the PWT). For the benchmark model (discussed below), we set the borrowing limit to be very relaxed (a¯ = −40).16 In our model, this value implies an NFA to annual GDP ratio of −5.3: a country can borrow from abroad up to 530% of its average annual GDP. According to our data, the lowest values of the NFA to annual GDP ratio observed since 1960 are −2.36 for the whole sample and −1.49 for the advanced economy sample. With a¯ = −40, a country rarely faces this limit in our simulation.

15

Using a larger value of σx increases the dispersion of net foreign asset and current account distributions. While the natural limit would be a natural choice for this, it is computationally too costly, since such a limit has to be a very large number in absolute value, making a discrete grid space extremely wide. 16

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.11 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

11

Fig. 5. Stationary distribution of no-spread economy (histogram). Note: Histograms are based on the stationary equilibrium distribution of the model.

For example, the probability of a country’s NFA to annual GDP ratio falling below −5 is 1.7 × 10−5 , according to the world stationary equilibrium distribution, μ(a, k, x), in the benchmark economy.17 Next we turn to the spread (ψ ) between borrowing and lending rates. The existence of a spread is necessary for the qualitative shape of the worldwide distribution of net foreign assets. When there is no spread between borrowing and lending rates, the model generates a very dispersed distribution with unrealistic skewness for net foreign assets. As Fig. 5 shows, the equilibrium distribution exhibits an unrealistically long right tail. For a wealth distribution across households within a country, this long tail is a desirable feature to account for a highly concentrated wealth (e.g., Díaz-Giménez et al., 1997). However, as Fig. 6 shows, we do not see such a skewed concentration in external balances in the data for any cross-section between 1960 and 2000. With a spread, borrowing becomes more costly, restraining countries from borrowing frequently, and lending becomes less profitable, reducing the fat right tail. The resulting distribution of net foreign assets comes much closer to the shape of the actual distribution of external balances. (Moreover, the cross-sectional standard deviation of the NFA to annual GDP ratio is 204%, almost 4 times that in the data for 2000.) For the benchmark, we assume that ψ = r B − r L is 0.05%. This small spread enables the model to effectively tame the skewness of the distribution of NFA as well as match the standard deviation. According to the historical spread between borrowing and lending rates in the U.S., which would form the lower end of the spread between lending and borrowing rates faced by many other countries, the spread is between 0.2% to 1% at an annual rate.18 Thus, the spread (annual value of 0.2%) in our benchmark model corresponds to the lower bound of the above range. In this sense, we interpret our results as reflecting an upper bound for the role of international lending as an intertemporal device against income fluctuations.19 When we increase the spread to ψ = 0.25% (5 times our benchmark value), international borrowing and lending is strongly discouraged in our model. The dispersion of NFA to annual GDP ratio decreases to 1.5% (compared to 55.4% and 29.3% in the data, respectively, for 2000 and 1970). Countries rely heavily on an alternative asset (domestic production capital) as a saving device against fluctuations in TFP. As a result, the model generates a dispersion of CA to annual GDP ratios of 0.8% (about 1/8 of the 2000 value). Finally, the adjustment cost in investment (θ = 6) is chosen so that the average standard deviation of the time series of physical investment is about 3.5 times that of output, a typical target in a real business cycle model. Table 2 summarizes the parameters of the model.

17

Thus, the constraint is essentially not binding in our simulation with 100 countries for 100 years. We calculated the U.S. spread as the difference between bank prime loan rates and 6-month CD rates, obtained from the Federal Reserve Board’s web site. Bank prime loan rates are prime rates charged by banks on short-term loans to businesses and were thus compared to 6-month CD rates, which we viewed to have risk and maturity profiles comparable to those of bank prime loans. Between 1976 and 2007, this spread ranged mostly between 0.2% and 1%. See Homer and Sylla (1991) for historical data on spreads. 19 Spreads in international lending (e.g., sovereign spreads on emerging markets) are often much larger, but a significant part of it is attributed to a risk premium rather than to the cost of financial intermediation, which our model abstracts from. 18

JID:YREDY AID:599 /FLA

12

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.12 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

Fig. 6. Distribution of net foreign assets to GDP ratio over time (histogram).

4.2. Benchmark economy ψ

ψ

We numerically find the equilibrium interest rate r˜ (r B = r˜ + 2 and r L = r˜ − 2 ) and invariant distribution of μ(a, k, x) that clears the world capital market. Appendix B provides a detailed description of the numerical algorithm to find the stationary equilibrium. The market clearing rate r˜ is 1.01%, implying a lending rate of r L = 0.985% and borrowing rate of r B = 1.035%. Before we discuss the implications of uninsurable stochastic productivity shocks for the distribution of current accounts and net foreign assets, we first report some business cycle statistics from our model. Since our objective is to quantitatively assess how much of current account dispersion can be accounted for by a simple intertemporal substitution of resources in the face of uninsurable stochastic productivity, it is desirable for our model to generate reasonable patterns of business cycles and trade dynamics. Table 3 reports the selected second moments of the model and the data. The model statistics are computed from the simulated panel data of 100 countries for 100 years. The data statistics under BK are based on 10 developed countries for the post-war period (until 1990) from Backus and Kehoe (1992, Tables 1 and 2). Those under BKK are based on 11 developed countries mostly for 1970–1990 from Backus et al. (1994, Table 1). All variables are HP filtered with a smoothing parameter of 1600. Looking at the first row, the model generates an average output volatility of 1.82%, with a minimum of 1.34% and a maximum of 2.3% out of our simulation of 100 countries for 100 years. These model moments are somewhat smaller than the statistics in BK (where the median, minimum, and maximum are 2.05%, 1.45%, and 3.11%, respectively) but somewhat larger than those in BKK (where the median, minimum, and maximum are 1.5%, 0.90%, and 1.92%, respectively). With a smaller shock (σx = 0.7%), the average standard deviation of output is 0.98%, about half of that in BK and two-thirds of that in BKK. With a large shock (σx = 2.2%), output volatility is 3.1%, about 50% larger than in BK and twice as large as in BKK. Given that productivity is the only source of business cycles in our model, the average volatility of the model should not exceed that of the data. At the same time, as we noted above, the data in BK and BKK consist of 10 and 11 developed countries, respectively, representing relatively stable economies. Considering this, we argue that the benchmark model generates a reasonable volatility for an average country in the world. The relative volatilities and correlations are in line with the data. Consumption is less volatile than output (the relative standard deviation of 0.34 in the benchmark) and investment is more volatile than output (the relative standard deviation of 3.63). Both consumption and investment are highly correlated with output. The volatility of net exports (relative to output) is 0.29 in our model, smaller than that in the data (1.03 in BK and 0.69 BKK). Given that our model abstracts from variations in terms of trade, this discrepancy seems inevitable. In terms of the persistence of output and net exports, all three models (0.71 and 0.75, respectively, for the benchmark) are very close to those in the data (0.78 and 0.71, respectively). To better understand the dynamics of trade balances and current accounts in our model, in Fig. 7 we plot the impulse response of a country to a productivity shock based on the benchmark specification. We present the response of a country with net foreign assets (as well as a current account and trade balance) near zero and its capital stock near the world average level. More specifically, before a persistent AR(1) productivity shock arrives, the country’s productivity remains

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.13 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

13

Fig. 7. Impulse response to a productivity shock. Note: Impulse response of a country with zero net foreign assets to a positive productivity shock.

constant at its long-run average (xt = 1) for 1000 periods. The response is consistent with that identified by Backus et al. (1994). Investment rises immediately. Because the productivity shock is persistent, we also see a rise in consumption. The increase in consumption and investment together is greater than the gain in output, and the economy experiences deficits in trade and current account balances during the period of high output. Net foreign assets become negative in the short run to finance these deficits. Over time, as physical capital accumulates from strong investment, exports exceed imports and the current account and trade balance turn to surplus. As a result, net foreign assets start building up. As the productivity shock fades, the country runs down its net foreign assets and physical capital to finance a smooth consumption path. Thus, the model generates a counter-cyclical trade balance and current accounts, as we see in the data. In sum, we argue that our model generates a reasonable pattern of economic fluctuations. We now investigate how much the dispersion of current account and net foreign asset distributions can be accounted for by this simple intertemporal consumption smoothing against uninsurable country-specific productivity shocks. As we saw from Fig. 5, without the spread the distribution of external balances exhibits an extremely right-skewed distribution. With the spread, the benchmark model exhibits a much more realistic distribution of external balances (see Fig. 8). Current accounts are distributed mostly within the range of 8% of GDP on both sides. Trade balances are distributed mainly within the range of 15% of GDP. Net foreign assets, on the other hand, are distributed over a much wider range, stretching from −250% to 250%, with the bulk of the mass concentrated between −100% and 100%. Note that the borrowing limit is set at −530%. The global dispersion of external balances obtained from the benchmark model is comparable to the actual 2000 data as the standard deviation of the ratio of net foreign assets to GDP is 59% in Table 4, close to the 2000 value of the standard deviation in the data (55%). (Without the spread, the standard deviation of the NFA to annual GDP ratio is 204%, almost 4 times that in the data for 2000.) Given that our model abstracts from other sources of heterogeneity and shocks, we view this as an upper bound of dispersion that a simple intertemporal substitution in response to productivity shocks can generate. The standard deviation of the current account is 2.4%, about one-third of the actual 2000 value (6.8%). The standard deviation of the trade balance is 3.4%, also about one-third of the actual 2000 value. Thus the model fails to match the dispersions of stocks (external balances) and flows (current account) at the same time. The relatively small dispersion of the trade balance and current account in the model is due to the absence of fluctuations in the terms of trade, which would add to the dispersion in the trade balance by increasing the variation in the value of the trade balance for a given movement in trade volume.20 Nor do we incorporate the valuation channel, which has been shown to have caused a striking divergence between net foreign assets movement and current account dynamics, most famously in the case of the United

20 Another possibility is that our TFP shocks might have been too persistent. In fact, with a small persistence, the gap between the stock (external balances) and flow (current account) is smaller. For example, when we lower the persistence to ρx = 0.87, keeping the overall standard deviation of TFP shocks by increasing σx = 2.3%, the dispersion of NFA decreases to 28.9% (which is about a 50% decrease from the benchmark), whereas the dispersion of CA decreases to 2.0% (about a 20% decrease from the benchmark). However, this model economy’s response to a TFP shock is similar to that of an endowment economy where borrowers tend to show a low investment rate and vice versa, inconsistent with what we see in the data (see Section 4.3 Conditional analysis below).

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.14 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

14

Fig. 8. Distributions of benchmark economy (histogram). Note: Histograms based on the stationary equilibrium distribution of the model.

Table 4 Dispersion (standard deviations) of cross-sectional distributions. Data 1970 CA GDP TB GDP NFA GDP

4.9 (%)

Models 2000

No spread (ψ = 0)

Benchmark (ψ = 0.05%)

Small shocks (σx = 0.7%)

Large shocks (σx = 2.2%)

6 .8

3 .1

2.4

1.1

9.8

11.6

8 .5

3.4

1.3

7.6

29.3

55.4

204.5

59.1

16.5

151.4

Note: Each number represents the standard deviation of cross-sectional distribution. The benchmark model is based on ψ = 0.05% and

4.7

σx = 0.13%.

States. Although the United States ran current account deficits over many years, the capital gains on its net asset position limited the decline in its net foreign assets position to about two-thirds of the total current account deficits over the past two decades (Gourinchas and Rey, 2007, and Lane and Milesi-Ferretti, 2009). More generally and beyond the U.S. experience, the valuation channel operates via capital gains and losses on the stock of foreign assets and liabilities and can drive a wedge between stock and flow movements in international macroeconomics. The relevant asset prices here comprise not only the prices of equities and bonds but also the exchange rate. We do not incorporate this channel, not least because the literature has so far made limited progress in modeling the portfolio choice and asset price dynamics involved in the valuation channel (see Devereux and Sutherland, 2010 as one published example). With large shocks, σx = 2.2%, the dispersion of NFA increases to 151.4% (Table 4). We rule out this case as unrealistic because its equilibrium dispersion far exceeds what we see in the data. With small shocks, σx = 0.7%, the dispersion of NFA decreases to 16.5%, about one-third of that in 2000. Dispersions of current account and trade balances also decrease significantly to, respectively, 1.1% (one-sixth of that in the data) and 1.3% (one-ninth of that in the data). To summarize, our model is capable of accounting for up to one-third of the global dispersion of current accounts. Yet, it is important to emphasize again that in our model, the only source of dispersion is the heterogeneity in (uninsurable) productivity, measured relative to each country’s trend growth. Many features we abstract from are proven to be important for current account dynamics. Countries differ not only in size but also with respect to the structure of domestic financial markets (Mendoza et al., 2009; Caballero et al., 2008), the degree of moderation in macro volatility (Fogli and Perri, 2006), and the structure of country portfolios (Gourinchas and Rey, 2007). Thus, our results should be viewed as having a limited scope: how much of the current account dispersion can be accounted for by the simple intertemporal substitution against productivity shocks, subject to some degree of friction in the flow of goods and finance? 4.3. Conditional analysis We have shown that the simple intertemporal substitution can account for up to one-third of current account dispersion in the data. In order to verify this mechanism in the data, we ask whether the countries at the bottom (i.e., heavy borrowers)

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.15 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

15

Table 5 Countries at the bottom and top of current account distribution. Bottom 20%

Top 20%

Data

Model

Data

CA ( ) GDP

Model

−2.5 (%)

TB ) ( GDP

− 0.2

2.4

0.3

−2.2

− 0.2

1.9

0 .3

 I ln ( GDP )

5 .0

1 .2

−4.7

−1.6

 ln TFP

0 .4

0.2

−0.4

− 0.3

 ln GDP

0.4

0.14

−0.4

−0.26

Note: Each number represents the mean percentage deviation from the country-specific HP trend among countries at the bottom (or top) 20% of the world distribution of current accounts. The data statistics are based on the annual time series of 69 countries for 1960–2004 (with a smoothing parameter of 100 in the HP trend). The model statistics are based on the simulated panel of 200 countries for 100 years of quarterly data (with a smoothing parameter of 1600).

of the current account distribution in fact exhibit a high investment induced by high productivity. As we look at the statistics of countries that belong to the tail of the current account distribution, it is desirable to have a large number of countries. Thus, instead of restricting the sample to those with data quality of B or higher, we impose much less stringent criteria (as explained in Appendix A.3) in selecting countries and obtain the larger data set that consists of external balances and national incomes of 69 countries for 1960–2003. Each year we identify heavy borrowers and lenders, respectively, based on the bottom and top 20% of the distribution of the current account to GDP ratio (CA/Y ). We then compute the average deviations from the country-specific HP trend (with a smoothing parameter of 100) of the following variables: current account to GDP, trade balances to GDP (TB/Y ), investment rate (ln( I /Y )), productivity, (log TFP), and GDP (log Y ). We compute the same statistics based on the model-simulated panel of 200 countries for 400 quarters (with a smoothing parameter of 1600 for the country-specific HP trend). According to Table 5, on average, the countries at the bottom 20% of the current account distribution (i.e., borrowers) show their current account to annual GDP ratio falling below trend by 2.5%. The trade balance is also below trend by 2.2% on average. These countries experience an investment boom as the investment rate is above trend by 5%. At the same time, the average TFP (as well as GDP) of these economies is above trend by 0.4% on average. The model exhibits a similar pattern. Countries at the bottom 20% of the current account distribution have a current account and trade balance below trend by 0.2%. These countries experience investment booms as the investment rate is above trend by 1.2%. These countries also experience TFP that is higher than trend by 0.2%. The GDP is above trend by 0.14%. While the magnitude of the variables is much smaller than what we see in the data, the model matches the data qualitatively. The statistics for the countries at the top 20% of the current account distribution are the mirror images of the bottom 20%. In the data, these countries (i.e., lenders) have an investment rate below trend (by 4.7%) as well as TFP (by 0.4%) and GDP (by 0.4%). Lenders in the model show similar patterns. The investment rate is below trend by 1.6%. The TFP and GDP are also below trend by 0.3% and 0.24%, respectively. To summarize, we see both in the data and in the model that borrowers experience high investment, TFP, and GDP, whereas lenders experience a weak investment, TFP and GDP, confirming the basic mechanism of intertemporal substitution. 4.4. Economies under greater frictions Returning to the rising dispersion in current accounts discussed in Section 2, we ask what factors lie behind the rise in dispersion between 1970 and 2000. We do it in reverse, by considering three cases with greater frictions (namely, tighter constraints) in the economy. We first consider frictions in the goods market, by increasing the trade cost (τ ) to 0.7, which lowers the average importGDP ratio from 19% to 11%. This decline is consistent with the observed change in the import-GDP ratio between 1970 and 2000 (assuming that intermediate imports are about half of gross imports, or they remain a constant percentage of gross imports). According to Table 6, the change in the trade cost brings about little change in the dispersion of external balances. While the shares of both exports and imports decrease, there is little change in the standard deviation of current accounts, net foreign assets, and trade balances since the trade cost affects exports as well as imports. This is because the trading cost has an effect primarily on the intratemporal choice, whereas the current account reflects intertemporal consumption smoothing in this environment. Next, we consider capital market frictions, in two separate directions. First, we consider the case when the borrowing constraint is tightened to a¯ = −4 from −40 in the benchmark model. This new value for the borrowing limit implies that a country can borrow up to 53% of its average annual GDP. This value corresponds to the 90% lower bound of the NFA to annual GDP ratio of the whole sample, including developing countries. This is also close to the lowest value we see in the early periods of our sample. For example, for the 1970 data, the smallest NFA to annual GDP ratio is −0.35 for the advanced economy sample. Second, we consider an increase in financial friction in terms of an increase in the interest rate spread

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.16 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

16

Table 6 Economies with greater frictions. Data 1970 CA GDP TB GDP NFA GDP

4.9 (%)

Models 2000

Benchmark

τ = 0.7

a¯ = −4

ψ = 0.1%

6 .8

2.4

2 .4

2 .0

9 .8

11.6

3.4

3 .4

2 .4

2 .1

29.3

55.4

59.1

58.8

36.3

26.8

Note: Each number represents the standard deviation of cross-sectional distribution. The benchmark model is based on

1 .8

τ = 0.5, a¯ = −40, and ψ = 0.05%.

Fig. 9. Model comparison: current account dispersion. Note: Each graph represents the estimated kernel density based on the simulated panel data of 100 countries for 100 years. The benchmark model is based on τ = 0.5, a¯ = −40, and ψ = 0.05%.

to ψ = 0.1% from 0.05% in the benchmark model. As we saw from the equilibrium dispersion of external balances in the model without a spread, the spread effectively reduces the dispersion of external balances. Under this spread ψ = 0.1%, the dispersion of NFA to annual GDP ratios falls by 50%, which is comparable to the change in the data between 1970 and 2000 (Table 6). While both financial frictions reduce the dispersion of external balances, under our parameter choices, the decline is starker and closer to the data when the spread is increased than when the borrowing limit is tightened. To be more concrete, Table 6 shows that, between 1970 and 2000 in the data, the dispersions of net foreign assets and current accounts declined by 47% and 30%, respectively. We compare these historical changes with the model-implied changes in dispersion. With a tighter borrowing constraint, the dispersions of net foreign assets and current accounts decrease by 38% and 17%, respectively. With a larger spread between borrowing and lending rates, the dispersions of net foreign assets and current accounts decrease by 54% and 25%, respectively, comparable to the change in the data. Fig. 9 shows the distribution of current account balances for each model specification: benchmark, a larger trade friction (τ = 0.7), a tighter borrowing constraint (a¯ = −4), and a larger spread (ψ = 0.1%). Each graph represents the estimated kernel density based on the simulated panel of 100 countries for 100 years. The change in the cost and availability of borrowing and lending is found to have a direct and visible effect on the consumption/saving decision. In contrast, trade frictions appear to have only a secondary effect on the intertemporal choice between consumption and saving while having a primary effect on the intratemporal choice between home- and foreign-good consumption. These results are consistent with those in existing papers (discussed in Section 2), in that international financial integration has likely been one of the major driving forces behind the increase in the dispersion of current accounts. The limited role of trade costs contrasts with Obstfeld and Rogoff’s (2000) proposal that trade costs could be the main driver of the spread between lending and borrowing rates, but this contrast is more apparent than real. Our model agrees with Obstfeld and Rogoff’s analysis in indicating that the spread between lending and borrowing rates has a powerful effect on international financial flows. However, our model does not allow the “reversal” of imports that is critical for significantly restraining the current account imbalances by altering the interest rate spread in the Obstfeld and Rogoff analysis. Nor does our model incorporate the incremental linkage between the spread and endogenous tradability.21 It is left for future

21 See Bergin and Glick (2010) for the analysis of this incremental linkage in a model with a continuum of goods. As for the effect of tradability on current account imbalances, however, they find that the incremental linkage makes it less likely for the trade-induced spread to discourage large current

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.17 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

17

research to enrich the interaction between trade frictions and the interest rate spread and to deepen our understanding of the quantitative importance of trade frictions in determining, via the interest rate spread, the dispersion of current account imbalances. Our result also speaks to the Feldstein–Horioka (1980) puzzle, which can be interpreted as saying that the dispersion of current accounts is too small. While it is not the main purpose of our exercise, we provided a first pass to this aspect of the Feldstein–Horioka puzzle and tentatively concluded that the dispersion is small compared to full risk sharing, and that the even smaller dispersions of the past can be explained by a model with tighter financial market frictions. In this regard, our results complement those studies that seek an answer to the Feldstein–Horioka puzzle in financial markets. As Obstfeld and Rogoff (2000) noted, there has been no dearth of explanations, although financial market causes have long been suspected to be important ones. Bai and Zhang (2010) provided a quantitative study of this explanation of the Feldstein–Horioka puzzle, also in a multi-country equilibrium model. From a historical perspective, the importance of financial frictions in accounting for current account dispersion is consistent with several existing historical studies of international financial markets. As mentioned earlier, Obstfeld and Taylor (2004) find that the dispersion of current accounts—measured as the mean absolute value and the standard deviation of the current account to GDP ratios of 15 countries—was at its largest in the period leading up to the First World War, which is viewed as the period of highest international financial integration. Mauro et al. (2006) provide corroborating evidence that London’s sovereign debt market was indeed highly liquid in the pre-war years, probably more so than today’s market. 5. Conclusion We develop a simple quantitative multi-country model of the global distribution of current account balances. In the presence of liquidity constraints, countries invest in physical capital and foreign assets in the face of persistent productivity shocks. Combined with the diversity in shocks to each country’s income, this intertemporal substitution leads countries to display a well-defined distribution of current account surpluses and deficits. According to our model, optimal consumption and investment responses to persistent productivity shocks imply a degree of intertemporal substitution across countries that can explain up to one-third of the current account dispersion in the data. We show that countries that are at the bottom of the current account distribution (i.e., heavy borrowers) exhibit strong investment and TFP on average and vice versa for those at the top of the distribution. We also find that tighter frictions in financial or trade transactions tend to narrow the dispersion of current accounts, offering an explanation for the smaller dispersion in the past. In particular, financial frictions have a substantial effect on the dispersion, greater than trade frictions. The results of this paper are obtained on the basis of the heterogeneity in productivity alone, while actual current accounts would be influenced by several other heterogeneities. In particular, the heterogeneity in demographic trends has been much debated as the driver of current accounts. Other drivers of current accounts include fluctuations in the terms of trade and alternative forms of financial instruments. While we assume that each country is ex ante of equal size, the real world economy consists of a finite number of countries of different sizes, implying that an idiosyncratic shock to a large economy can have a general equilibrium effect. This makes it difficult to empirically distinguish aggregate shocks from idiosyncratic shocks. Moreover, the optimal policy (from the perspective of the world social planner) may be different depending on whether an idiosyncratic shock stems from a small or large economy. It is left for future work to incorporate these factors into a multi-country equilibrium analysis. Appendix A. Data appendix A.1. Current accounts Current account, trade balance, and GDP data are obtained from the various issues of the International Financial Statistics and the World Economic Outlook database. Net foreign assets data are from Lane and Milesi-Ferretti’s (2007) data set for the 1970–2004 period and obtained by backward adjustment (also earlier working data) for the 1960s. Advanced countries used in the figures are the U.S.A., the United Kingdom, Austria, Belgium, Denmark, France, Germany, Italy, Luxembourg, the Netherlands, Norway, Sweden, Switzerland, Canada, Japan, Finland, Greece, Portugal, Spain, Australia, and New Zealand. A.2. National incomes In estimating the AR(1) process for the country-specific TFP, we use output and investment data from the Penn World Tables. The national income accounts (NIA) data are from the PWT v6.2 (2006); PWT mnemonics are in parenthesis. The

account deficits by smoothing out the sharp non-linearity in the original Obstfeld–Rogoff analysis. For those interested, the following is the original insight of Obstfeld and Rogoff: if a country imports home-producible goods when income and savings are high, at a price higher than the price at which the country will export the same goods when its income is low, then the country’s real interest rate on lending can be lower than its real interest rate on borrowing. While the reversal of imports (importing a good in one period and exporting it in another period) is critical for this channel to discourage large current account deficits, our model precludes this channel by construction.

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.18 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

18

PWT provide two types of price and quantity indices: (1) ‘current price’ estimates based on Geary aggregation of international current prices for each year, and (2) ‘constant price’ estimates based on Geary aggregation of international current prices for benchmark years and interpolation of country-specific constant price NIA data for in-between years. For most of our work we use the ‘constant price’ data. Output, y, is real per capita GDP at constant prices constructed as a Laspeyres index (RGDPL). To avoid extreme measurement errors, we first restrict it to the countries with data quality of B or higher. For conditional analysis, we use a larger set of countries as explained below in Appendix A.3. Per capita capital stock is computed from the time series of per capita investment using the perpetual inventory method. For each country’s initial capital stock, we use the steady-state replacement investment formula: K 0 = I 0 /(δ + g 0 ), where the annual depreciation rate δ is 6% and the average growth rate (g 0 ) is computed from the first 10 years of the sample. For labor input, per capita employment is used. The list of countries with high quality data we use are the U.S.A., Canada, Chile, Uruguay, Argentina, Portugal, Norway, Greece, Ireland, the Netherlands, Belgium, France, Italy, Spain, Sweden, Denmark, Finland, Switzerland, Austria, Iceland, the United Kingdom, Japan, Korea, Singapore, Hong Kong, and Israel. A.3. Data for conditional analysis As we look at the statistics of countries that belong to the tail of (bottom or top 20%) of the current account distribution, it is desirable to have a large number of countries for conditional analysis. Instead of restricting the sample to those with data quality of B or higher, we impose less stringent criteria as follows. By simply merging two data sets (external balances from the IMF and national incomes from PWT) we end up with 73 countries for the 1960–2003 years of current account to GDP (CA/Y ), net foreign asset to GDP (NFA/Y ), trade balance to GDP (TB/Y ), investment to GDP (I /Y ), and TFP. From these 73 countries we excluded countries (to avoid extreme cases) using the following criteria. First, we categorize pooled series of absolute value of CA/Y and NFA/Y into 200 quantiles. Then, if a country’s time series of absolute value of CA/Y or NFA/Y belong to the 200th quantile more than 8 times, we exclude these countries (Ecuador, Nicaragua and Republic of Congo). Also, if a country’s absolute value of NFA/Y is larger than 20 (i.e. the net foreign asset is 20 times larger than GDP) more than 4 times, we exclude this country from the sample (Uruguay). With these criteria, we end up with a 69-country sample for our conditional analysis. For each year, we construct the empirical distribution of CA/Y . Based on this cross-sectional distribution, we identify the bottom and top 20% countries. We then compute the mean percentage deviations from the country-specific trend (HP filtered with smoothing parameter = 100) of CA/Y , TB/Y , I /Y , ln TFP, and ln Y for the countries at both tails. The list of 69 countries we considered for this analysis are the U.S.A., Canada, United Kingdom, Japan, Korea, Singapore, Indonesia, Malaysia, Thailand, Hong Kong, Philippines, India, Sri Lanka, Bangladesh, Fiji, Nepal, Pakistan, Portugal, Norway, Greece, Ireland, Netherlands, France, Italy, Spain, Sweden, Denmark, Finland, Switzerland, Germany, Austria, Iceland, Turkey, Australia, New Zealand, Bolivia, Chile, Colombia, Costa Rica, El Salvador, Jamaica, Mexico, Panama, Paraguay, Trinidad & Tobago, Peru, Venezuela, Guatemala, Honduras, Botswana, Mauritius, South Africa, Tunisia, Benin, Cameroon, Kenya, Ghana, Mali, Malawi, Rwanda, Senegal, Swaziland, Zambia, Egypt, Israel, Jordan, Bahrain, Iran, and Syria. Appendix B. Computational appendix Finding the value function, V (a, k, x), and decision rules, cd (a, k, x), c f (a, k, x), i d (a, k, x) and i f (a, k, x), which satisfy the Bellman equation in (1), is the central step in computing the steady-state equilibrium of the model. This appendix describes the detailed procedure for approximating these objects numerically on the discrete state space of A × K × X . The stochastic process for idiosyncratic productivity is approximated by the first-order Markov process whose transition probability matrix is computed using Tauchen’s (1986) algorithm. The well-known dynamic programming algorithm is employed to find the value function in the Bellman equation. Updating the value function over iterations involves solving the maximization problem on the right-hand side of the Bellman equation. This can be cumbersome, since there are four endogenous variables. We solve the maximization problem by applying an algorithm that can reduce the number of choice variables as follows. 1. First, compute cd (a, k, x), c f (a, k, x), i d (a, k, x) and i f (a, k, x) assuming they are all interior and satisfy the domestic resource constraint, i.e., cd + i d  xkα at the optimum. In this case, these endogenous variables satisfy the following relationship with their CES aggregators:



cd cf

id if



 =

η



η

η 1−η 1−η ωd = φ 1−η [1 + ( 1−φ ] φ ) (1 + τ ) η

η

−η η−1 ] 1−η ω f = (1 − φ) 1−η [1 + ( 1−φ φ ) (1 + τ )

(c i ).

(B.1)

Having substituted the relationship in (B.1), update the value function as follows:

V 1 (a, k, x) = max a ,k

subject to

c 1 −γ − 1 1−γ



  + β E V 0 a , k , x x

(B.2)

JID:YREDY AID:599 /FLA

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.19 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

a = xkα + (1 + r )a − p (c + i ) −

θ



k − k

2

k

19

2 k,

k = (1 − δ)k + i , a  a¯ ,



r=

r¯ − 0.5ψ r¯ + 0.5ψ

if a  0, otherwise,

where p = ωd + (1 + τ )ω f denotes the effective price of the CES aggregator of consumption and investment. The Bellman equation (B.2) is approximated by solving the following:

V 1 (a, k, x) = max k ∈I

where  V 0 (a , k , x) =

N x

max

a (k )∈B(k )

j =1

c 1 −γ − 1 1−γ

 + β V 0 a , k , x

 ,

(B.3)

V 0 (a , k , xj )π (x, xj ) is the conditional expectation of the value function with the current

idiosyncratic productivity being x,

π (x, xj ) = Pr(xt +1 = xj |xt = x) is the transitional probability, B(k ) = {a | a¯  a 

 xkα + (1 + r )a − p (k − (1 − δ)k) − θ2 ( k k−k )2 k} is the feasible set for a given the choice of k , whose feasible set is

I = {k | (1 − δ)k  k  (1 − δ)k + i max }, where i max denotes the maximum possible CES aggregator of domestic and foreign investments for a given (a, k, x) such that:  −( p − θδ) + ( p − θδ)2 − θ 2 δ 2 + 2(θ/k)(xkα + (1 + r )a − a¯ ) max i = . θ/k

We search for the optimal a and k in the corresponding feasible sets using the Brent algorithm, and the conditional expectations of the value function not on the grid points are computed using cubic spline interpolations. Once the Bellman equation in (B.3) is solved, the optimal CES aggregators, c and i, for a given (a, k, x) are obtained. Then the optimal cd , c f , i d and i f for a given (a, k, x) can be computed using these optimal CES aggregators and the interior relationships in (B.1). 2. If cd , c f , i d and i f found above satisfy the domestic resource constraint, the optimal decisions, cd , c f , i d and i f , for a given (a, k, x) are found, and move on to the optimization for another combination of (a, k, x). 3. If cd , c f , i d and i f found from (B.3) violate the domestic resource constraint, they must be solved for from the maximization problem in (B.3) with further restrictions such that (1) cd + i d = xkα , (2) i d = ωd i and i f = ω f i. In this case,  the feasible set for a turns out to be B (k ) = {a | a¯  a  (1 + r )a − (1 + τ )c f − (1 + τ )ω f (k − (1 − δ)k) − θ2 ( k k−k )2 k}.

The value function is iterated through the above steps until V 1 (a, k, x) is close enough to V 0 (a, k, x) for all grids of

(a, k, x). References Aguiar, M., Gopinath, Gita, 2006. Defaultable debt, interest rates, and current account. Journal of International Economics 69 (1), 64–83. Aiyagari, R., 1994. Uninsured idiosyncratic risk and aggregate saving. Quarterly Journal of Economics 109 (3), 659–684. Anderson, James E., van Wincoop, Eric, 2004. Trade costs. Journal of Economic Literature 42 (3), 691–751. Backus, D., Kehoe, P., 1992. International evidence on the historical properties of business cycles. American Economic Review 82 (4), 864–888. Backus, D., Kehoe, P., Kydland, F., 1994. Dynamics of the trade balance and the terms of trade: The J-curve? American Economic Review 84 (1), 84–103. Bahng, Hong Kee, 2011. Accounting for business cycle regularities in emerging economies. Working Paper, University of Rochester. Bai, Yan, Zhang, Jing, 2010. Solving the Feldstein–Horioka puzzle with financial frictions. Econometrica 78 (2), 603–632. Bergin, Paul, Glick, Reuven, 2010. Endogenous tradability and some macroeconomic implications. Journal of Monetary Economics 56, 1086–1095. Bernanke, B., 2005. The global saving glut and the U.S. current account deficit. Remarks at the Sandridge Lecture, March 19. Bewley, Truman, 1986. Stationary monetary equilibrium with a continuum of independently fluctuating consumers. In: Contributions to Mathematical Economics in Honor of Gérard Debreu. North-Holland. Blanchard, Olivier J., Giavazzi, Francesco, 2002. Current account deficits in the euro area: The end of the Feldstein–Horioka puzzle? Brookings Papers on Economic Activity 2002 (2), 147–209. Blanchard, Olivier J., Milesi-Ferretti, Gian Maria, 2009. Global imbalances: in midstream? IMF Staff Position Note SPN/09/29, http://www.imf.org/external/ pubs/ft/spn/2009/spn0929.pdf. Caballero, Ricardo, Panageas, Stavros, 2008. Hedging sudden stops and precautionary contractions: A quantitative framework. Journal of Development Economics 85 (1–2), 28–57. Caballero, Ricardo, Farhi, Emmanuel, Gourinchas, Pierre-Olivier, 2008. Financial crash, commodity prices and global imbalances. American Economic Review 98 (1), 358–393. Castro, Rui, 2005. Economic development and growth in the world economy. Review of Economic Dynamics 8 (1), 195–230. Clarida, Richard, 1990. International borrowing and lending in a stochastic stationary equilibrium. International Economic Review 31, 543–558. Cole, Harold L., Obstfeld, Maurice, 1991. Commodity trade and international risk sharing. Journal of Monetary Economics 28, 3–24. Corsetti, Giancarlo, Dedola, Luca, Leduc, Sylvain, 2008. International risk sharing and the transmission of productivity shocks. Review of Economic Studies 75, 443–473. Devereux, M.B., Sutherland, A., 2010. Valuation effects and the dynamics of net external assets. Journal of International Economics 80 (1), 129–143. Díaz-Giménez, J., Quadrini, V., Ríos-Rull, J.-V., 1997. Dimensions of inequality: Facts on the U.S. distributions of earnings, income, and wealth. Federal Reserve Bank of Minneapolis Quarterly Review 21, 3–21.

JID:YREDY AID:599 /FLA

20

[m3G; v 1.83; Prn:10/10/2012; 9:36] P.20 (1-20)

Y. Chang et al. / Review of Economic Dynamics ••• (••••) •••–•••

Engel, Charles, Rogers, John H., 2006. The U.S. current account deficit and the expected share of world output. Journal of Monetary Economics 53, 1063– 1093. Faruquee, Hamid, Lee, Jaewoo, 2009. Global dispersion of current accounts: Is the Universe expanding? IMF Staff Papers 56, 574–595. Feldstein, Martin, Horioka, Charles, 1980. Domestic saving and international capital flows. Economic Journal 90, 314–329. Fogli, Alessandr, Perri, Fabrizio, 2006. The great moderation and the U.S. external imbalance. Monetary and Economic Studies 24 (S1), 209–225. Glick, Reuven, Rogoff, Kenneth, 1995. Global versus country-specific productivity shocks and the current account. Journal of Monetary Economics 35 (1), 159–192. Gourinchas, Pierre-Olivier, Jeanne, Olivier, 2009. Capital flows to developing countries: The allocation puzzle. Manuscript, University of California at Berkeley. Gourinchas, Pierre-Olivier, Rey, Helene, 2007. From world banker to world venture capitalist: U.S. external adjustment and the exorbitant privilege, in: G7 Current Account Imbalances: Sustainability and Adjustment, National Bureau of Economic Research, pp. 11–66. Homer, Sydney, Sylla, Richard, 1991. A History of Interest Rates, 3rd edition. Rutgers University Press, New Brunswick. Huggett, M., 1996. Wealth distribution in life-cycle economies. Journal of Monetary Economics 38, 469–494. Krusell, Per, Smith, Anthony A., 1998. Income and wealth heterogeneity in the macroeconomy. Journal of Political Economy 106 (5), 867–896. Kydland, Finn, Prescott, Edward, 1982. Time to build and aggregate fluctuations. Econometrica 50 (6), 1345–1370. Lane, Philip, Milesi-Ferretti, Gian Maria, 2007. The external wealth of nations mark II: Revised and extended estimates of foreign assets and liabilities. Journal of International Economics 73, 223–250. Lane, P.R., Milesi-Ferretti, G.M., 2009. Where did all the borrowing go? A forensic analysis of the U.S. external position. Journal of the Japanese and International Economies 23 (2), 177–199. Lee, Jaewoo, 2009. Option pricing approach to international reserves. Review of International Economics 17 (4), 844–860. Mauro, Paolo, Sussman, Nathan, Yafeh, Yishay, 2006. Emerging Markets and Financial Globalization. Oxford University Press, Oxford. Mendoza, Enrique, Quadrini, Vincenzo, Ríos-Rull, Jose Victor, 2009. Financial integration, financial deepness and global imbalances. Journal of Political Economy 117 (3), 371–416. Obstfeld, Maurice, Rogoff, Ken, 1995. Foundations of International Macroeconomics. MIT Press, Cambridge. Obstfeld, Maurice, Rogoff, Ken, 2000. The six major puzzles in international macroeconomics: Is there a common cause? In: NBER Macroeconomics Annual 2000. Obstfeld, Maurice, Rogoff, Ken, 2005. Global current account imbalances and exchange rate adjustments. Mimeo, Harvard University. Obstfeld, Maurice, Taylor, Alan M., 2004. Global Capital Markets: Integration, Crisis, and Growth. Cambridge University Press, New York. Obstfeld, Maurice, Shambaugh, Jay C., Taylor, Alan M., 2008. Financial stability, the trilemma, and international reserves. NBER Working Paper. Stockman, Alan C., Tesar, Linda L., 1995. Tastes and technology in a two-country model of the business cycle: Explaining international comovements. American Economic Review 85 (1), 168–185. Tauchen, George, 1986. Finite state Markov-chain approximations to univariate and vector autoregressions. Economics Letters 20, 177–181.

Accounting for global dispersion of current accounts -

that can explain up to one-third of the current account dispersion in the data. ... (See Obstfeld and Rogoff, 2005; Engel and Rogers, 2006; Caballero et al., 2008 and Blanchard and Milesi-Ferretti .... model economy to match the observed pattern of business cycles. ..... Obstfeld and Rogoff's (2000) number of 4.2 in the middle.

949KB Sizes 1 Downloads 133 Views

Recommend Documents

Accounting for global dispersion of current accounts -
that can explain up to one-third of the current account dispersion in the data. ..... savings in small open-economy models (Obstfeld and Rogoff, 1995 and references ... Nor can physical capital be traded internationally, unlike foreign bonds. ......

Accounting for global dispersion of current accounts
copy is furnished to the author for internal non-commercial research ... the WCU Program through the Korea Research Foundation (WCU-R33-10005). ..... savings in small open-economy models (Obstfeld and Rogoff, 1995 and references therein). .... TFP, w

Trending Current Accounts!
Thus it is puzzling that since 1970, except for a brief recovery between ... fluctuations and does not match the turning points observed in the data. ... of the exogenous state variables, Americans rationally choose to be chronically low savers.

Towards a Theory of Current Accounts
The current accounts data of industrial countries exhibits some strong patterns .... all together, transitory income shocks provide a first source of cross-country ..... collective data mining effort. ...... the Open Economy (Princeton University Pre

Compensating for chromatic dispersion in optical fibers
Mar 28, 2011 - optical ?ber (30). The collimating means (61) converts the spatially diverging beam into a mainly collimated beam that is emitted therefrom.

Compensating for chromatic dispersion in optical fibers
Mar 28, 2011 - See application ?le for complete search history. (56). References Cited .... original patent but forms no part of this reissue speci?ca tion; matter ...

CFP Current Issues of Agricultural Law in a Global Perspective.pdf ...
Page 1 of 2. CURRENT ISSUES OF AGRICULTURAL LAW IN A GLOBAL PERSPECTIVE. Colloquium. When: 17-18 September 2015. Where: Pisa, Italy. Deadline for abstract: 3rd April 2015. Deadline for draft paper: 3rd July 2015. CALL FOR PAPERS. The Scuola Superiore

PDF-Download Business Accounts (Accounting & Finance) Online ...
Book synopsis. This essential introduction to bookkeeping and financial accounting is an easy-to-understand text with clear explanations, worked examples, case studies, questions and selected answers. Perfect for the complete beginner, yet suitable f

[PDF-Download] Business Accounts (Accounting ...
[PDF-Download] Business Accounts (Accounting ... beginner, yet suitable for A level and degree courses, this comprehensive text is supported by free online.