The Dynamics of the U.S. Trade Balance and Real Exchange Rate: The J Curve and Trade Costs? February 2018 First Draft: February 2015
George Alessandria University of Rochester and NBER Horag Choi Monash University
Abstract We study how changes in trade barriers have in‡uenced the US trade balance and real exchange rate since 1980 - a period when trade tripled. Using two dynamic trade models, we decompose ‡uctuations in the trade balance into terms related to trade integration (global and unilateral) and business cycle asymmetries. We …nd four main results. First, the relatively large US trade de…cits as a share of GDP in the 2000s compared to the 1980s mostly re‡ect a rise in the trade share of GDP. Second, controlling for trade, only about 60 percent of net trade ‡ows are due to business cycle asymmetries. And third, about two-thirds of the contribution of business–cycle asymmetries are a lagged response. For instance, the short-run Armington elasticity is about 0.2 while the long-run is closer to 1.12 with only 6.9 percent of the gap closed per quarter. Finally, we identify a substantial slowing, and even a reversal in trade integration that begins in 2006. Using a dynamic GE model of trade integration, we show how permanent and transitory changes in trade policy may a¤ect the trade balance going forward.
JEL classi…cations: E31, F12. Keywords: Trade Balance, Real Exchange Rate, Trade Integration, International Business Cycles.
[email protected];
[email protected]. We thank Yan Bai, Mark Bils, Doireann Fitzgerald, Jonathan Heathcote, Patrick Kehoe, Virgiliu Midrigan, Brent Neiman, Fabrizio Perri, Kim Ruhl, Joe Steinberg, Mike Waugh, and Kei-Mu Yi for helpful discussions. We also thank audiences at the Banque de France, Bu¤alo, ITAM, LSE, Nottingham, Rochester, SED, Toronto, Western Ontario, NBER and Chicago, Dallas, Minneapolis, Philadelphia, and St. Louis Feds for helpful comments.
1. Introduction What leads a country to run a trade de…cit or surplus? This questions has risen in prominence with the large US trade de…cits in the mid to late 2000s and concurrent large surpluses by China and some other Asian economies. The traditional view is that ‡uctuations in the trade balance re‡ect cross-country di¤erences in the business cycle from country-speci…c productivity, monetary, and …scal shocks, or longer-term structural asymmetries related to demographics, social insurance, or wealth. A contrasting view, commonly advanced by politicians, is that di¤erences in trade barriers or trade policy are important drivers of the trade balance. This alternative view has much support in the US administration and is perceived to be shaping US trade policy. The aim of this paper is to evaluate the relative importance of these diverse views for the dynamics of the US’s trade balance. Contrary to the traditional view, trade policy is found to matter for the trade balance, although through di¤erent mechanism from those favored by politicians. To set ideas, …gure 1 plots two salient features of the US economy’s connection with the rest of the world: rising trade de…cits and rising trade. First, since 1980 the US trade balance shows two cycles of increasing amplitude. In the 1980’s cycle, the US trade de…cit as a share of GDP peaked in the third quarter of 1986 at 2.6 percent. Twenty years on, it peaked again but now at 5.6 percent of GDP. In both cases, the maximum trade de…cit lagged the peak real exchange rate by about 6 quarters and the peak real exchange rates were of roughly similar magnitude, suggesting an increased sensitivity of the trade balance to the real exchange rate. Second, the near doubling of the US trade de…cit occurred as trade, measured as the sum of exports and imports, doubled from 12.9 percent of GDP to 26.1 percent.1 The rise in trade is often attributed to reductions in policy and non-policy trade barriers, making trade policy a potential determinant of the trade balance. We emphasize two channels through which changes in trade barriers in‡uence the trade 1
From 1980 to 2015 the real trade share of GDP rose from 11.5 percent to 29.0 percent.
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balance. First, there is a scale e¤ect of trade on the trade balance. As a country becomes more open, perhaps by entering into symmetric bilateral trade agreements that lower trade barriers in both directions, the usual factors - country-speci…c shocks that generate asymmetries in the business cycle - can generate larger swings in the trade balance. Quite simply, a closed economy can not run a trade de…cit or surplus but an open economy can. This explanation would be consistent with real exchange rate ‡uctuations being associated with larger ‡uctuations in the trade balance over time. Second, there is a sequencing e¤ect from a temporary unilateral change in a trade barrier. That is, persistent di¤erences in the pace that countries open up to each other can generate a motive for intertemporal trade. An example of this might be a US trade policy of lowering barriers on imports in return for future reductions on barriers to exports. Similarly, temporary trade barriers such as anti-dumping duties, safeguards, quotas, or voluntary export restraints, perhaps in response to surges from the …rst mechanism or the business cycle, will also generate a temporary gap in bilateral trade cost. Indeed, Bown and Crowley (2013) …nd that temporary trade barriers in the US and its main trading partners appear to rise in recessions, following import surges, and following an appreciation. If this gap in trade policy is expected to be persistent, but not permanent2 then when the cost of importing is relatively low compared to the cost of exporting there is a strong motive for consumption to be relatively high in the US relative to the ROW and sustained trade de…cits. To quantify the relative importance of changes in trade barriers versus other business cycle asymmetries for the US trade balance requires identifying the changes in inward and outward trade barriers. We follow the Gravity literature and use theory to identify these changes. We measure trade costs in both partial and general equilibrium models that allow for trade to respond gradually to aggregate shocks. Both models attribute about two-thirds 2
We don’t consider the role of permanent unilateral changes in trade barriers on the trade balance although in dynamic models of the type considered here these can also lead to intertemporal trade (See Alessandria, Choi and Ruhl, 2014).
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of the ‡uctuations in the US trade balance to changes in trade barriers and yield series for trade barriers that appear consistent with the conventional narrative on the timing of US trade policy. Our …rst, partial equilibrium approach leverages the benchmark Armington trade model, the core trade block in nearly all sticky and ‡exible price models with all asset market structures,3 to decompose the trade balance. It also allows us to consider a quite general lag and lead relationship between relative prices - namely the terms of trade and real exchange - and the trade balance, something we …nd to be quite important, although for di¤erent reasons than those emphasized in the literature. Since Backus, Kehoe, and Kydland (1994) the dynamic relationship between the real exchange rate and the trade balance has been attributed to di¤erences in the timing of investment across countries rather than slow adjustment to relative prices. Our analysis makes clear that is really the slow adjustment of trade ‡ows to international relative prices that gives rise to the dynamic correlation between the real exchange rate and trade balance. A disadvantage of our …rst, partial equilibrium, approach is that it attributes the general equilibrium e¤ects of changes in trade barriers to business cycle shocks. To account for these general equilibrium e¤ects we next build a two country dynamic incomplete markets stochastic general equilibrium model of international business cycles and trade integration with a short-run and long-run trade elasticity coming from the export entry and exit decisions of heterogenous …rms in the spirit of Baldwin and Krugman (1989). This model allows for business cycle shocks to a¤ect measures of trade costs and changes in trade barriers to a¤ect the business cycle. It permits a structural decomposition of the dynamics of the trade balance as well as sources of integration and business cycles. It also allows us to perform 3
Heathcote and Perri (2014) discuss various asset structures. In the international macro models the asset structure relates the movements in relative prices to relative spending and the Armington trade models relates these to the trade balance. Our partial equilibrium approach imposes no asset structure and instead uses the data on relative spending and relative prices.
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counterfactuals for changes in US and ROW trade policies. To bring our main ideas into focus it helps to split the trade balance as a share of GDP into a term related to the level of trade to GDP (TRY) and another term that is the trade balance as a share of trade (TBTR), (1)
T BY =
X +M X M = T RY Y X +M
T BT R:
Figure 2 plots the US trade balance to GDP ratio and a counterfactual US trade balance holding the trade share constant at its level in 1986. This is a simple way to capture the scale e¤ect. Not surprisingly, with this counterfactual the peak trade de…cit in 2006 of only 2.7 percent, is almost the same as in 1986, making the amplitude of the more recent cycle in the trade balance of similar magnitude to the 1980s cycle. This shows that the movements in the trade balance to trade ratio were about the same in 2006 as in 1986. It also may explain why the swings in the real exchange rate were of similar magnitude to the 1980s. Trade integration also contributes to ‡uctuations in the trade balance to trade ratio (TBTR). Using the Armington CES trade model we show how to decompose the ‡uctuations in the trade balance to trade ratio into terms related to uneven trade integration and di¤erences in the business cycle. Our decomposition extends the trade wedge accounting approach of Levchenko, Lewis and Tesar (2010) and Alessandria, Kaboski, and Midrigan (2011, 2013). The business cycle component is determined by cross-country di¤erences in expenditures, international relative prices (both the terms of trade and real exchange rate), and the elasticity of substitution between imported and domestic goods - the Armington elasticity. The gap between the movements predicted from theory and data is our trade wedge. Unlike the earlier work on the trade wedge, we explicitly take into account the well-known idea that the trade balance takes time to respond to movements in the real exchange rate and terms of trade. Indeed, a contribution of this paper is to estimate the short-run and long-run Armington elasticity along with the speed of adjustment to evaluate the role of these di¤erent elasticities 4
on the dynamics of the trade balance. Not accounting for these dynamics exaggerates the importance of changes in trade barriers for the trade balance. Our partial equilibrium decomposition of the trade balance to GDP yields three main results. First, the relatively large trade de…cits as a share of GDP of the US in the 2000s compared to the 1980s mostly re‡ects a rise in the trade share of GDP. Indeed, holding trade constant at the level from the 1980s would have reduced the average trade de…cit in the 2000’s roughly in half. Second, about 40 percent of the ‡uctuations in the ratio of the trade balance to trade re‡ect an uneven pace of trade liberalization. Third, while asymmetries in the business cycle, as re‡ected in movements of relative production and expenditures and relative prices, account for the remaining 60 percent of ‡uctuations in the trade balance over trade, almost 2/3 of the business cycle induced movements in net trade ‡ows are a lagged response to asymmetries in the business cycle. A simple way of seeing this is that the shortrun Armington elasticity is about 0.20 while the long-run is closer to 1.12 with only 6.9 percent of the gap closing each quarter. Ignoring the gradual response of net trade ‡ows to the business cycle would lead one to substantially overstate the importance of uneven changes in trade barriers. Our partial equilibrium decomposition also provides an accounting of the timing of trade integration split between common, bilateral changes in trade barriers and uneven changes in trade barriers. The dynamics of our inferred trade barriers are consistent with a typical narrative on US trade policy. There was substantial reduction in global barriers from the 1980s through the early 2000s. Starting in the mid 2000s trade barriers have held steady and since the Great Recession they have increased. We also …nd substantial di¤erences in inward and outward barriers. Namely, the ROW appears to open up relative to the US starting in the early 80s with the rise in protectionist policies under Reagan, followed by the Canadian and North American free trade agreements. This continues until the late 90s at which point the US starts opening faster to the ROW around the time that it grants permanent normal 5
trade relations to China and China joins the WTO. And …nally, we see that the US has opened up substantially relative to the ROW since the Great Recession. To relate the trade balance to the shocks generating international business cycles we next build on the general equilibrium heterogeneous producer model of Alessandria and Choi (2007). This is a variation of the Backus, Kehoe, and Kydland (1994) international real business cycle model with heterogenous producers subject to idiosyncratic productivity shocks and a sunk and …xed cost of exporting as in Dixit (1989), Baldwin and Krugman (1989), and Das, Roberts and Tybout (2007). These forms of heterogeneity and …xed trade costs have found great support in explaining producer export dynamics and the transition following trade reform, particularly for the US. A key feature of this model is that the heterogeneity and dynamic exporting decision leads exporters to respond gradually to aggregate shocks such as trade costs or productivity and so the model has the potential to capture the dynamic relationships we documented in the data. We extend the model along two dimensions. First, we introduce pricing-to-market by allowing an exporter’s elasticity of demand to vary with the real exchange rate. Pricing-tomarket is crucial to explain the persistent deviations from the law of one price across countries and to get the real exchange rate to ‡uctuate more than the terms of trade as in data (see Engel, 1999, and Alessandria 2009). Second, we introduce shocks to the costs of trade in each country and …nancial shocks that a¤ect country-speci…c discount factors. We model changes in trade barriers as global and unilateral shocks. Global shocks change the cost of imports and exports equally, while unilateral shocks move the costs of imports and exports in opposite directions. In our two country symmetric economy,4 global shocks to trade barriers a¤ect gross trade 4
Building on this paper, Alessandria, Choi and Lu (2016) consider an asymmetric variation of the current model in the context of China’s trade integration and growth. With asymmetric countries, transitory common trade cost shocks also a¤ect intertemporal trade since they have larger e¤ects on the wealth of the smaller, more open economy. Ravikumar, Santacreu, and Sposi (2017) show global trade reforms can generate intertemporal trade in a model with capital accumulation and asymmetric countries.
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‡ows but do not a¤ect net trade ‡ows since they a¤ect spending and production the same in both countries. Unilateral shocks a¤ect net trade ‡ows when they are not expected to be permanent as they temporarily change the relative price of consumption across locations, generating a motive to borrow and lend. The model is estimated on US net and gross trade ‡ows, relative prices, and production using Bayesian methods. The estimated model is used to quantify the general equilibrium e¤ect of changes in trade barriers on international relative prices and relative expenditures, movements that in our partial equilibrium decomposition were attributed to the business cycle. We …nd that now about one quarter of the movements from our empirical decomposition that were attributed to business cycles can be attributed to changes in international trade barriers as these unilateral changes have a small e¤ect on the gap in spending across countries but a big e¤ect on international relative prices. We also …nd that about 15 percent of the growth in US trade that we attributed to changes in trade barriers can be attributed to the growth in productivity in the ROW. Putting these together we …nd that changes in trade barriers once again account for about two-thirds of the ‡uctuations in the trade balance as a share of GDP since 1991. Moreover, our theory suggests that eliminating any changes in trade barriers would have lead the trade de…cit to only be 0.3 percent on average rather than 3 percent since the Great Recession. Our estimated GE model also yields an estimate of the elasticity of substitution between imported and domestic goods. As the model generates movements in trade, relative prices, and relative expenditures consistent with the data it provides some sense of the biases from the estimates in the partial equilibrium model.5 In contrast to the elasticity from our partial equilibrium model of 0.20 and 1.12 we estimate an elasticity of 3.3. Moreover, in response to 5
A large literature estimates the trade elasticity. Similar to Hooper, Marquez, and Johnson (2000), we estimate an error correction model of trade ‡ows, but unlike that paper we focus on net trade ‡ows. Gallaway, McDaniel and Rivera (2003) estimate these at the industry level, and …nd that long-run elasticities are generally two to three times short-run trade elasticities.
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a permanent decline in trade barriers, the model yields a trade elasticity of about 6. Thus our GE model is consistent with what Ruhl (2004) calls the trade elasticity puzzle - the tendency for the trade response to ‡uctuations in the real exchange rate to be quite low over the business cycle, while responses to changes in tari¤s and trade barriers are quite high. In our case, the low short-run elasticity can be attributed to not accounting for how changes in trade barriers in‡uence relative prices and relative expenditures. Our estimated model also generates a path of increased export participation by US producers that closely matches the data. We then use our estimated model to consider the e¤ect on the trade balance of a number of di¤erent scenarios in which US barriers on imports rise more than exports in the future and are expected to remain high temporarily. We show that when these are expected to go into place in the future it will generate a trade de…cit today and in the long-run. When the policy is in place, the US will run a trade surplus and the size of the surplus will depend on the nature of the US’s trading partners response. A trade war will reduce the surplus more with time as trade declines. The impact of these policy changes is shown to be considerably smaller in models that lack the dynamic features of exporting as those alternative models require a much lower elasticity of substitution to …t the data. This paper is organized as follows. In the next section, we discuss the related literature. In section 3 we decompose the source of ‡uctuations in the US trade balance. In section 4, we build a two country general equilibrium model of endogenous trade participation, trade integration, and the business cycle. In section 5, we estimate the model and examine its properties in response to changes in trade costs and productivity. Section 6 concludes.
2. Related Literature Our paper is a joint analysis of US business cycles and trade integration. On the business cycle side, it is closely related to models of international business cycles such as Backus, Kehoe
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and Kydland (1994), Chari, Kehoe and McGrattan (2002), Corsetti, Dedola and Leduc (2008), Heathcote and Perri (2002, 2014), and Croce, Colacito, Ho, and Howard (2012). A number of recent papers extend this framework to allow for a di¤erent short-run and long-run trade response (Alessandria and Choi (2007), Drozd and Nosal (2011), Engel and Wang (2012), Alessandria, Pratap and Yue (2011), and Imura (2013)) but have not considered the role of changes in trade costs in aggregate ‡uctuations. Unlike these papers, which generally focus on the model’s ability to match …rst and second moments of …ltered variables and highlight certain puzzles, we estimate our model to match the data and thus can decompose the source of ‡uctuations in key cross-country variables.6 We also contribute to the recent literature on global imbalances (Caballero, Farhi, and Gourinchas, 2008, Mendoza, Quadrini, and Rios-Rull, 2009) and the adjustment required to close these imbalances (Obstfeld and Rogo¤, 2005, Dekle, Eaton, and Kortum, 2008). Kehoe, Ruhl and Steinberg (2017) also study the dynamics the US trade balance but are focused on its contribution to the decline in manufacturing employment and do not consider the role of changes in trade barriers. A key conclusion of our analysis is that the same theory of trade balance dynamics can explain the 1980’s and 2000’s US trade balance dynamics. Similar to Obstfeld and Rogo¤ (2000), we are interested in the role of trade costs on aggregate ‡uctuations. Unlike that paper, we are interested in how changes in bilateral trade costs may contribute to aggregate ‡uctuations. A few papers have considered the aggregate e¤ects of asymmetric trade barriers.7 Kose and Yi (2006) show that correlation of output across countries depends on the extent of trade. Fitzgerald (2012) shows that heterogeneity in trade costs is important for understanding the extent of observed risk-sharing. Barattieri (2014) also considers the e¤ect of uneven changes in trade integration for trade imbalances 6
In our model analysis, we match the data on relative prices, relative quantities, and trade and thus can speak to a broader range of issues related to comovement, risk sharing, and exchange rate volatility as well as the contribution of trade integration to consumption growth and employment changes. 7 Waugh (2010) studies asymmetries in trade costs in cross-country income di¤erences.
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that arise from symmetric changes in trade barriers across sectors but with countries di¤ering in sectoral comparative advantage. Complementary to our analysis are Eaton, Kortum, and Neiman (2016b) and Reyes-Heroles (2016) who use multi-country multi-industry static trade models to study the role of perfectly anticipated changes in common trade barriers and other aggregates in the distribution of trade imbalances and aggregate ‡uctuations.8 Our estimation of a stochastic model allows us to di¤erentiate between anticipated and unanticipated shocks. We …nd that most movements in trade costs (and productivity) have been asymmetric and unanticipated and that a model with a dynamic trade decision best …ts the data. A recent group of papers motivated by the Great Trade Collapse also identify and measure the change in trade costs to understand their aggregate implications (Levchenko, Lewis, and Tesar, 2010, Alessandria, Kaboski and Midrigan, 2010, 2011, 2013, Eaton, Kortum, Neiman and Romalis, 2016a). Unlike these papers, and the Gravity Literature that inspired them, we allow trade to respond with a lag to aggregate shocks and show that these lags strongly in‡uence estimates of changes in trade barriers. A key …nding is that abstracting from these dynamic considerations exaggerates the importance of trade barriers for the dynamics of the trade balance.
3. Evidence In this section, we propose a decomposition of US net trade ‡ows. We …rst put some theoretical structure to the simple decomposition from equation that allows us to separate the scale and sequencing e¤ects in the data. This structure also allows us to reconsider the source of comovement between the real exchange rate and trade balance emphasized by Backus, Kehoe, and Kydland (1994), hereafter BKK. In contrast to BKK, we show that the lagged response of net trade ‡ows primarily re‡ects di¤erences in short- and long-run response to shocks rather than large asymmetries in investment across countries. We then estimate 8
These models allow for some dynamic interactions in perfect foresight economies but lack any dynamic decisions related to trade.
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the key parameters of the theoretical model determining the trade balance. The estimated model is used to decompose the ‡uctuations in the US trade balance. Finally, we present the inferred changes in trade integration split between bilateral and unilateral changes in trade barriers. We emphasize that ignoring the dynamic relationships in the data exaggerates the importance of changes in trade barriers for net trade ‡ows. A. Theory The simple decomposition of the trade balance in equation 1 is closely related to the Armington trade model common to almost all multi-country trade models of integration and business cycles. In the Armington trade model, home and foreign goods are imperfect substitutes with a constant elasticity of substitution. This yields a CES import demand for imports at home and in the ROW such that the log ratio of exports to imports is described by the following structural relationship (2) where
ln (X=M ) = ln (! =!)
[ln (Px =P )
ln (Pm =P )] + ln (D =D) ;
is the elasticity of substitution between home and foreign goods, !; ! are preferences
for imported goods, ;
> 1 are iceberg trade costs that create a gap between the factory
and consumer price, Px and Pm are the factory export and import prices9 , P; P are the home and foreign price levels, D; D denote home and foreign domestic absorption of tradables.10 It is straightforward to show that the ratio of exports to imports is related to the trade balance to trade ratio as (3)
ln (X=M )
2T BT R = 2
9
X M ; X +M
US import and export prices exclude freight and tari¤. To the extent that these international trade costs are included in import and export prices our empirical approach will understate their importance. 10 This equation also holds in the Eaton-Kortum and Melitz-Chaney trade models.
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so that we can then decompose the trade balance to GDP into a term that depends on the export-import ratio and another term that depends on the trade share of GDP,11 (4)
T BY
0:5 ln (X=M ) T RY;
For our purposes it is useful to combine the changes in trade costs and tastes into a single term that is the trade wedge, T ; T: De…ning the terms of trade and real exchange rate as (5)
T OT = Pm =Px and RER = P =P;
the main equation becomes (6)
ln (X=M ) = ln (T =T ) + [ln T OT + ln RER] + ln (D =D) :
This provides a simple decomposition of the export-import ratio into changes in the di¤erence in trade wedges, substitution from relative prices, and relative expenditures. This equation also sheds light on BKK’s famous "S-curve" result that echoes an earlier literature’s emphasis on the J-curve. They show that the trade balance as a share of GDP is more correlated with past movements in the real exchange rate than current movements12 and that this feature is well-described by a two country dynamic stochastic general equilibrium model with productivity shocks and capital accumulation.13 In that model a positive productivity shock at home leads both to a real exchange rate depreciation and a trade de…cit. The cross country productivity gap lowers the price of the home good yielding a depreciation while creating a large temporary gap in investment between home and foreign leading to a 11
This measure overstates the maximum de…cit by 0.4 percentage points (22.7 percent vs 23.1 percent). BKK focus on the dynamics between the trade balance and the terms of trade rather than the real exchange rate. However, in their framework (and the data) the terms of trade and real exchange rate are perfectly (highly) correlated. 13 BKK focus on the nominal trade balance which is highly correlated with the real trade balance. Ra¤o (2008) points out that in the BKK model that real trade balance to gdp ratio and nominal trade balance to gdp are negatively correlated when investment is constrained to match the observed pattern in the data while in the data they are quite positively correlated. Given our focus on matching trade ‡ows and relative prices these are less of a concern. 12
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trade de…cit. As the gap in investment is relatively short-lived, the trade de…cit is also quite short-lived while the depreciation is quite persistent yielding the cross-correlation in the data. The apparent success of the two country RBC model in explaining the comovement between the trade balance and the real exchange rate is rooted in its two well-known failures: the quantity and price puzzles. The quantity puzzle is the inability of the model to generate business cycles that are synchronized across countries. The price puzzle is the inability of the model to generate large enough relative price movements. Whenever the real exchange rate depreciates, say from an increase in productivity, substitution makes the ratio of exports to imports increase. To generate a trade de…cit with a depreciation then requires the second term, the di¤erence in foreign and domestic expenditures, to respond strongly to o¤set the substitution e¤ect. Taken together the quantity and price puzzles make the expenditure effect quite strong and the substitution e¤ect weak. With a strong but temporary gap in cross country expenditures the ratio of expenditures will move from de…cit to surplus over time explaining the gradual response of the trade balance following the depreciation. Controlling for relative expenditures, the trade-expenditure ratio, (7)
ln (X=M )
ln (D =D) = ln (T =T ) + [ln T OT + ln RER] ;
isolates the substitution e¤ect. A depreciation will always lead to a surplus in this alternative measure of net trade ‡ows in all constant elasticity models. Moreover, correlations of the left hand side with lags of the real exchange rate will equal the autocorrelation of the tradeexpenditure ratio. Of the series in this equation, the only one that requires some discussion is the measure of expenditures. US expenditures are proxied with an equally weighted average of spending on consumer goods and investment goods since this accounts for trade being intensive in durables. For foreign spending, we lack such a good measure of spending and thus use a measure of foreign industrial production that is trade-weighted. Obviously, foreign industrial 13
production will overstate (understate) foreign expenditures when the US is running a de…cit (surplus); however, given the level of openness this tends to be a reactively small bias.14 Figure 3 plots the cross-correlation between the real exchange rate and two measures of the export-import ratio in the data and the benchmark theory of BKK. Panel A shows that the contemporaneous correlation of the export-import ratio with the real exchange rate is positive15 in the data but that the export-import ratio is more strongly correlated with lagged real exchange rate movements with a peak correlation at about 6 quarters. Panel B shows that the cross-correlation is quite similar between the real exchange rate and trade-expenditure ratio. Indeed, there is perhaps a slightly stronger lagged relationship now. This clearly suggests that it is not di¤erences in the timing of expenditures that drive the asymmetry in the data. We next examine the cross-correlation of these variables in the BKK model from productivity shocks. The theory generates an asymmetric cross correlation function although it overpredicts the cross-correlation at all horizons. Moreover the gap between the correlation of the export-import ratio at lags and leads is much smaller than the data. More importantly, panel B demonstrates that controlling for expenditures eliminates any asymmetry in the cross-correlation function.16 This clearly suggests a need to allow for a time varying Armington elasticity and/or shocks to the gap in the trade wedge to capture the dynamic relationship between relative prices and relative quantities. 14
We explore some of the biases from the weighting on expenditures as well as using ROW production rather than expenditures in Appendix 2. We …nd these biases tend to be relatively small when we account for them both in our measure of expenditures and in our GE model. 15 BKK actually emphasize a negative contemporaneous correlation. This correlation is only present when the model and data are HP …ltered. 16 For the US measure of expenditures we use a weighted average of consumption and investment while we proxy foreign expenditures on tradables with foreign industrial production from the Dallas Fed. Using this empirical measure in the BKK model delivers an almost identical result in Figure 3B. See the Data appendix for more details.
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B. Evidence To evaluate the determinants of the ‡uctuations in the export-import ratio we follow the trade wedge literature by measuring the gap between observed net trade ‡ows and predicted trade ‡ows using the observed relative prices and relative spending. Doing so requires a measure of the Armington elasticity. There is much disagreement about this parameter. For instance, Eaton, Kortum, Neiman and Romalis (2016a) set this to 3 in their study of trade in the Great Recession while Heathcote and Perri (2014) advocate for an elasticity closer to 0.4. Given the disagreement about this parameter, and our desire to minimize the importance of the gap in trade barriers on net trade ‡ows, we estimate equation 7, where now ln (T =T ) can be interpreted as a combination of trade integration shocks plus a residual. Table 1 reports the results of three types of regressions, in levels, …rst di¤erences, and …rst di¤erences with an error correction term.17 The error correction regression permits us to distinguish between short-run and long-run relationships and have a long tradition in studies of trade dynamics. All coe¢ cients are quite signi…cant. For the level regression the term on relative expenditures is constrained to be unitary as theory suggests. We consider two regressions in levels. The …rst follows the trade literature and constrains the elasticity of substitution to equal 3. It implies we are only estimating the mean in the data and leads to a very poor …t, supporting our approach to estimate the elasticity of substitution. When we estimate the elasticity separately (column Level 2) we …nd an elasticity of substitution closer to 0.28 which is closer to the value used in the international macro literature, although this elasticity mixes the short-run and long-run e¤ects of relative prices on the export-import ratio. Our regressions in di¤erences separate the short-run and long-run source of movements in net trade ‡ows. Now we …nd that the Armington elasticity is quite low in the short run. The 17
The error correction model is p is the relative price term.
yt =
SR
pt + (yt
15
1
+
LR pt 1 ) + "t
were y is the dependent variable,
error correction model yields a short run elasticity of 0.119 and a long-run elasticity of 1.026 with 6.6 percent of the gap between the current net export ratio of the long-run closed each quarter. If the short-run e¤ect of di¤erences in expenditures is allowed to be di¤erent18 from 1, which generalizes the idea of slow adjustment, we estimate a coe¢ cient on expenditures of 0.608, a short-run price elasticity of 0.18 and a long-run Armington elasticity of 1.09 with only 6.7 percent of the gap closed per quarter. If we follow Alessandria, Kaboski, and Midrigan, (2011 and 2013) by introducing terms accounting for the change in net inventory investment,19;20 we …nd a slightly higher short-run and long-run elasticity of 0.204 and 1.124 and slightly faster adjustments (6.9 percent), although now the impact response of di¤erences in expenditures is lower (0.58). The coe¢ cients are all quite precisely estimated. The …t, measured by adjusted R2 ; of the empirical model rises from 26.2 percent in di¤erences to 43.7 percent in our short-run/long-run model. The …t of the empirical models suggests there are substantial movements in the export-import ratio that are related to trade integration. These shocks could re‡ect a di¤erent pace of liberalization (contemporaneous and lagged e¤ects) or perhaps inventory type considerations that we haven’t fully accounted for. The improved …t of the error correction model, plus the relatively low short-run price and expenditure coe¢ cients, suggest that a substantial fraction of the e¤ects of relative spending and relative prices occur gradually. Unlike previous work which focus on the slow response to international relative prices we also document a slow response to di¤erences in expenditures. The estimated coe¢ cients from the regression of changes in the trade-expenditure ratio are used to construct a predicted path of the trade-expenditure ratio. Figure 4A plots the 18
This case also helps to capture any di¤erences related to the composition of trade being di¤erent than our measure of expenditures. A sign that this is not overly important is that when we estimate a coe¢ cient on the long-run expenditure term it is not signi…cantly di¤erent than 1. 19 In this regression we only use a measure of the change in net inventory investment in the US as we lack a similar measure in US trading partners. The gain in explanatory power is thus perhaps understated. 20 Alessandria, Kaboski, and Midrigan, (2011 and 2013) show that international trade frictions lead to higher inventory holdings on imported than domestic goods and that periods of rapid trade adjustment are strongly related to inventory adjustments.
16
predicted export-import ratio from the data and our statistical models estimated in di¤erences along with the US real exchange rate. Figure 4B plots the gap in the trade wedge from each empirical model. The error correction model clearly captures the gradual movements in the trade-expenditure ratio to movements in the real exchange rate and relative spending. In particular, the delayed response of the trade-expenditure ratio to the Plaza and Louvre Accords and the depreciation of the dollar in the early 2000’s are quite evident. Table 2 summarizes some measures of the contribution of the gap in the trade wedge to our understanding the export-import ratio. We focus on the R2 and the share of the variance as measures of the contribution of the di¤erence in the pace of trade liberalization. In terms of the R2 ; all three models account for about 70 percent of the growth in the export-import ratio. In terms of a variance decomposition, the single elasticity models account for 57 to 60 percent of the variance while the error correction model accounts for 100 percent of the variance. A conservative reading of the data is that about 2/3 of the ‡uctuations can be explained by the model. We also split the error-correction model into the predicted movements coming from the short-run part of the model in the column SR. Using this decomposition we estimate that about 1/3 to 2/3 of the ‡uctuations in the export-import ratio are the delayed response to the business cycle. We attribute the movements of the export-import ratio that are not explained by the movements in relative prices or relative expenditures as arising from unilateral trade integration shocks. Thus depending on our empirical model, uneven trade liberalization explains between 40 and 73 percent of the ‡uctuations in the export ratio. Table 3 reports the average US trade de…cit in the data since 1991 and a counterfactual holding the share of GDP in trade at its 1986 level. Without trade growth, the average US trade de…cit would have been slightly more than half as big (1.58 percent vs 2.95). Attributing the gap between the data and this counterfactual to trade integration, suggests that just under half of the average US trade de…cit since 1991 was due to bilateral trade integration. 17
We conclude with a variance decomposition of the trade balance into the parts that can be explained by variation in relative prices and relative expenditures. The remainder we attribute to trade.21 First, we note that the trade balance can be split into a part that holds the trade share of GDP constant and a part that is from the changes in trade share. T BYt = 0:5 [T RY0 ln (X=M ) + (T RYt
T RY0 ) ln (X=M )]
Next we note that the change in the export-import ratio can be split between the part from changes in relative expenditures and relative prices and the gap in the trade wedge T BYt = 0:5
h
i h TW + (T RYt + ln (X=M ) T RY0 ln (X=M )BC t t
i T RY0 ) ln (X=M )t :
Since the scale e¤ect is one of the novel mechanisms we emphasize we do not break this out. Next, we decompose this …rst term with respect to initial conditions and use it to construct the business cycle component as T BYtBC = 0:5 T RY0
h
ln (X=M )BC t
ln (X=M )BC + ln (X=M )BC 0 0
i
assuming that there is no initial gap in the trade wedge. Figure 5 plots the trade balance as a share of GDP along with dynamics from the business cycle and the gap remaining from trade barriers (common and di¤erential). Table 4 reports the share of the variance in the trade balance accounted for by our business cycle term. Depending on how we attribute the covariance term, we …nd that business cycle shocks accounted for 31 to 44 percent of the ‡uctuations in the real trade balance over the whole sample The importance of business cycle versus trade shocks varies over time. Looking narrowly at the pre 1991 swing we …nd that trade accounted for only about 30 percent of the variation in the trade balance while in the post 1991 period it accounted for about 69 21
This is a decomposition of the source of ‡uctuations in the trade-balance to gdp coming from an accounting identity. It is in no way attributing the ‡uctuations in the trade balance to particular shocks. We will use the model to decompose the shocks leading to these ‡uctuations.
18
percent. C. Changes in trade barriers We next consider the inferred changes in policy and non-policy trade barriers from our empirical models. So far, our empirical work yields the gap in the ROW and US trade wedge. Each country’s trade wedge is constructed as a residual using the estimated coe¢ cients. Figure 4B plots the export-import ratio and the evolution of the gap in trade wedges from the static and dynamic empirical models. The gap in the wedge from the static model is highly correlated with the data while the gap in the wedge from the dynamic model is much less correlated. Focusing on the gap in the wedge from the dynamic model, there is a substantial swing in trade policy from 1979 to 198322 followed by more gradual change beginning in 1983 with the ROW becoming relatively more open to the US. This year certainly marks a turning point in US trade policy as Voluntary Export Restraints (VERs) on Japanese cars begin to bind quite tightly23 , Steel Quotas are imposed, Congress passes the Buy America Act, and the Reagan administration steps up its push for reciprocity in trade relations. The pace of integration accelerates in the late 1980s at about the time of the Canadian-US Free Trade Agreement and again with NAFTA. Both agreements lowered barriers on US exports much more than barriers on US imports which were already quite low (see Tre‡er 2004). The gradual opening of the ROW relative to the US continues until about 1998 at which point the US begins to become relatively more open to foreign goods. This clearly coincides with US granting China permanent normal trade relations and China joining the WTO. Our dynamic model suggests this is an in‡ection point in relative trade policy while the static 22 These early movements coincide with the second oil shock and in part re‡ect changes in OPEC’s market power. 23 In May 1981 Japanese automakers agreed to limit exports of passenger cars for three years. This VER was initially not very binding given the weakness in auto sales in 1981 and 1982, but became quite binding as the economy took o¤ in 1983. The policy was extended and remained in place through 1994. Berry, Levinsohn, and Pakes, 1999, provide a structural analysis of these policies.
19
model points to quite a large reversal in the direction of opening. Since the Great Recession the US has become substantially more open to the ROW. This may re‡ect the strong home bias inherent in …scal expansions in a number of countries such as China. Absent this change in the gap in trade policy, US net trade ‡ows would have been expected to move strongly to balance as a result of the persistently weak dollar and strong expansion in foreign output. Figure 6 plots the bilateral trade wedge that comes from the empirical dynamic trade model along with the HP trend with a smoothing factor of 1600. A few interesting points are evident. First, trade integration was fairly steady until the late 90s and then was steady through the Great Recession. Second, since the Great Recession trade integration has reversed and has fallen to a level consistent with the early 90s. The timing of the slow-down in the trade wedge is perhaps a bit earlier than one might suspect given the trade data, which was continuing to grow up to the Great Recession and with the Great Trade Rebound. However, our empirical model allows for trade barriers and relative prices to only gradually a¤ect trade and so the continued growth in trade re‡ects the …nal stages of the transition to changes in trade policy.
4. General Equilibrium Model We now develop a dynamic stochastic two country general equilibrium model with heterogenous producers entering and exiting the export market that allows trade to respond gradually to aggregate shocks. We extend the general equilibrium dynamic export participation model of Alessandria and Choi (2007) to include more shocks, variables markups, an endogenous discount factor, and incomplete …nancial markets. This model nests simpler models with a static export decision or no export decision. We use the model to evaluate the impact of symmetric and asymmetric changes in trade costs, productivity, and …nancial shocks on net ‡ows and the aggregate economy. By using a general equilibrium model, we can evaluate how changes in trade costs a¤ect the business cycle. We also introduce a mechanism
20
whereby the business cycle can give rise to "changes" in trade costs from mismeasured prices owing to changes in the extensive margin of export participation (Feenstra, 1994). Essentially, the measured import and export prices do not capture the gains from increased variety and this will be a source of the trade wedge. In each country, consumers consume a non-tradeable good made of a di¤erent mix of tradable intermediates. We normalize home and foreign …nal good prices to 1, Pt = Pt = 1; but de…ne the real exchange rate, qt ; as the relative price of a basket of home to foreign goods:24
Consumers: Consumers maximize the discounted sum of utility. They trade a noncontingent bond with the ROW. max E0
1 X
tU
(Ct ; Lt ) ;
t=0
subject to Ct + Vt Bt = Wt Lt + Bt where U (C; L) = C (1
L)1
1
= (1
);
t
1
+
t;
is the dividend payments from home …rms
and Vt is the discount price of the bond. To ensure stationarity, there is a small bond holding cost of
b
2
Vt Bt YtN
for home with YtN being nominal home GDP and
Vt Bt qt YtN
b
2
for foreign.
The stochastic cumulative discount factor evolves as ln ( where
t+1 =
t)
= ln
is the steady state
t
= (1
b ) ln
+
b
ln
t 1
et ln C
ln C + " =2;
et is the average (aggregate) ; C is the steady state C; and C
consumption in the economy, and " is a shock. The discount factor
t
is external. The
foreign discount factor evolves similarly but with the discount factor shock coming in with a negative sign. Since Uzawa (1968), endogenous discount factors are commonly used in 24
This is like assuming that the price of goods in the US in dollars is 1 and the price of a basket of goods in euros is 1 and that q is the relative price of euros to dollars.
21
international models (see Corsetti, et al. 2008).25 This introduces a channel for aggregate shocks to move the real exchange rate and relative consumption in a way that models with pure time seperable preferences lack. We abstract from capital accumulation in our model since we have already shown this mechanism is not the main determinant of the dynamic relationship between international relative prices and the trade balance. Empirically, capital accumulation is included in our measure of spending and so one should view the consumer as having some preference for a ‡ow for consumption and investment but does not consider how this investment a¤ects future output.
Aggregation Technology or Consumption Index: A competitive retail sector combines a continuum of domestic varieties with the available imported varieties to produce the …nal good. The aggregators are 1
Dt =
1
YHt + a YF t
1
1
; YHt =
Z
1
1
Yhit di
1
; YF t =
Z
i2Et
0
1
t
Yf it di t
!
t t
1
:
where YH ; YF are the composite domestic and imported goods, a denotes the weight on imported goods and
is the Armington elasticity. The elasticity of substitution across imported
varieties is allowed to be time varying,
t
= qt with qt being the real exchange rate in terms
of home aggregate (a rise in q means real depreciation of home): This is a parsimonious way of embedding pricing-to-market into the model. It can be microfounded using search frictions as in Alessandria (2009), Alessandria and Kaboski (2011), or Drozd and Nosal (2013). A key advantage of this form of pricing-to-market, rather than nominal rigidities, is that it can generate quite persistent deviations from the law of one price. The price indices for the 25
As in Kehoe, Ruhl, and Steinberg (2016) the discount factor shock captures aspects outside of the model that a¤ect consumption directly but not trade.
22
aggregates are PHt =
Z
1
1 Phit
1
di
; PF t =
Z
Pf1it
i2Et
t
di
!1 1
t
1 ; Pt = PHt + aPF1 t
1 1
= 1:
In equilibrium Dt = Ct :
Firms: Firm have idiosyncratic and aggregate shocks to productivity. The production function of a …rm is given by Yit = ezt + it Lit ; where zt is the country-wide productivity, N 0;
2
it
is the …rm speci…c productivity with
: The country productivity follows an AR(1) 3 3 2 2 3 2 6 zt 1 7 6 "zt 7 6 zt 7 5; 5+4 5 = Az 4 4 "zt zt 1 zt
process, 3 2 6 "zt 7 iid 5 N (0; 4 "zt
iid it
Z) :
To capture the dynamics of export participation, …xed export costs are Wt f0 for starters and Wt f1 for continuing exporters. The (gross) marginal trade cost is given by exporters, and
t
t
for home
for foreign exporters. The resource constraint for each good equals Yit = Yhit + mit t Yhit ;
where mit is the current export status of …rm i. The marginal trade cost is stochastic with 2 3 2 3 2 3 2 3 6 ln t 7 6 ln t 1 7 6 " t 7 6 " t 7 iid 4 5=A 4 5+4 5; 4 5 N (0; ) ln t ln t 1 "t "t
We abstract from changes in the two types of …xed export costs although these do move around over the cycle as the …rm must hire workers to pay these costs and the real wage does ‡uctuate.26 26
In a related paper, Alessandria and Choi (14), we show that a model of this type can capture US trade integration from the observed changes in the marginal cost of trade and so shocks to the …xed costs of trade are unecessary.
23
The problem of a …rm is then Vt ( ; m) =
max pct (p) + m0 p ct ( p )
Wl
m0 ;p;p ;l
m0 W fm + Qt EVt+1 ( 0 ; m0 ) where m = f0; 1g is an indicator that summarizes past export status and determines the current …xed export cost. It is well known that when the cost of starting to export exceeds the cost of continuing to export, Wt f0 > Wt f1 ; the decision to export is forward looking. It is also well-known that there is a threshold technology for exporters to continue exporting, threshold technology for non-exporters to start exporting,
0t .
1t ;
and a second
Firms will move in and out
of the export market in response to shocks to idiosyncratic and aggregrate shocks. These thresholds satisfy the following equations W t f0
t
(
0t )
= Qt Et Vt+1 ( 0 )
W t f1
t
(
1t )
= Qt Et Vt+1 ( 0 )
Vt ( ) = Vt ( ; 1)
Vt ( ; 0)
The productivity distribution of exporters and non-exporters in each country is a state variable. As in Alessandria and Choi (2007) we assume idiosyncratic shocks are iid so that we only introduce one additional state variable, the stock of past exporters which evolves as Nt = Nt Nt
= Nt
1
Pr (
1t )
+ (1
Nt 1 ) Pr (
0t ) ;
1
Pr (
1t )
+ 1
Nt
0t ) :
1
Pr (
Given the iid nature of idiosyncratic costs, the export decision introduces a way to lower the cost of trade by increasing the mass of low …xed cost exporters. Enriching the model with 24
persistent idiosyncratic shocks or a growth pro…le for new exporters yields somewhat similar propagation of trade cost and aggregate shocks.
Aggregate Variables: Nominal output (GDP) is given by YtN
=
Z
(Phit YHit + qt Phit YHit ) di:
Real GDP is given by YtN : PHt
YtR = The nominal export is given by EXtN
=
Z
qt Phit Yhit di = aqt PHt1 Dt :
The export price index is given by PXt =
qt PHt
:
t
The real export is given by EXtR =
EXtN =a PXt
1
qt PXt Dt :
t
The nominal import is given by IMtN
=
Z
Pf it Yf it di = aPF1 t Dt :
The nominal trade balance to nominal GDP ratio is given by N XYt =
EXtN IMtN : YtN
The import price index is given by PM t =
PF t t
25
:
The real import is given by IMtN =a PM t
IMtR =
1 t
PM t D t :
Consistent with national accounts procedures, we de…ne the terms of trade using factory gate prices (i.e. prior to trade costs). We then assume the price index does not account for the bene…t of increased varieties (Feenstra, 1994)
T OTta =
1 Nt
R
1
i2Et
1 Nt
1
Pf1it t di
R
=
1
P1 i2Et hit
t
di
1
1 t 1
t
t
Nt
PF
1
Nt
t
1
:
PH
So, we have the real export-import ratio is now ln EX R =M R
=
EX N =PX = IM N =PM
= (
t)
t
EX N =PH PH =PX IM N =PF PF =PM
+ (tot + rer) + d
d
where the gap in the trade wedge is equal too t
t
= ln
! !
+(
1) ln
t
+
t
t t
1 Nt ln 1 Nt
and lower case variables denote logs. The trade wedge will vary because of changes to the ratio of trade costs and di¤erences in export participation. Export participation will vary from changes in trade costs and the business cycle and so there is potential for shocks to productivity and preferences to generate a trade wedge.
5. Solution and Estimation We solve the model by linearizing it around the steady state.27 Given that we are dealing with a large model, we …x several parameters to conventional values and estimate the rest using Bayesian techniques. Table 5 reports the parameters. The time period is a quarter and so we set 27
= 0:99: The weight on leisure is set so that
Even though we consider some large shocks to trade costs, trade remains relatively small and so most of the dynamics look similar when we solve the model using global and local methods.
26
hours worked is equal to 1/4. The bond adjustment cost is set to ensure stationarity. The …xed trade costs (f0 ; f1 ), standard deviation of idiosyncratic productivity shocks (
) ; and
the weight in the aggregator are chosen so that in steady state trade is 10 percent, export participation is 20 percent, the quarterly exporter exit rate is 2.5 percent, and exporters are 50 percent larger than non-exporters, which are consistent with US trade and exporter characteristics in the early 90s (see Alessandria and Choi, 2014b). These parameters ensures that marginal exporters are similar to the data. With respect to preferences, we need to estimate four parameters: 1) the Armington elasticity, ; 2) the pricing-to-market parameter, ; 3) the risk-aversion parameter, ; and 4) the weight on external habit in the endogenous discount factor, : For the shocks, productivity, trade cost, and …nancial shocks are independent. We also rewrite the country shocks to include a common 3 2 3 2 6 ln t 7 6 ln ct + ln dt 7 5 and 4 5=4 ln ct ln dt ln t
shock and country speci…c shock. 3 3 2 2 6 ln zt 7 6 ln zct + ln zdt 7 5 5=4 4 ln zct ln zdt ln zt
We then assume that these shocks are persistent 0 1 3 3 2 2 32 3 2 0 C c iid B 0 6 c 0 7 6 ln ct 1 7 6 " c t 7 6 ln ct 7 A; 5; " t N @ ; 5+4 54 5 = 4 4 0 0 " ln 0 ln dt d dt 1 dt d 2 3 2 32 3 2 3 0 1 c 0 C zc iid B 0 6 ln zct 7 6 z 0 7 6 ln zct 1 7 6 "zt 7 = + 4 5 4 54 5 4 5 ; "zt N @ ; A: d 0 0 ln zdt 0 ln zdt 1 "ct zd z
Finally we assume that shocks to the discount factor move it in opposite directions across countries (i.e. "b =
"b ):
We are thus estimating the persistence and variance of 5 shocks. We follow much of the literature on international business cycles and assume there is no spillover in shocks and that the shocks are uncorrelated. Finally, because relative prices and relative production are indices we need to estimate the level of these variables.
27
The …fteen parameters are estimated using …ve time series from the US and the rest of the world: 1) US real trade share of GDP, ((X+M)/Y), 2) the terms of trade plus the real exchange rate (totq), 3) the US real export-import ratio (EXIMR), 4) US detrended industrial production, (IP), and 5) The ratio of foreign to US Industrial Production. For these parameters we have relatively ‡at priors. Figure 7 shows the data and model along with the estimated innovations to productivity and trade costs. A. Estimation results The shocks are estimated to be quite persistent which is not too surprising given this is a period with substantial changes in trade policy towards integration, quite persistent trade imbalances, and quite persistent swings in production. The posterior mean of the common trade cost shock is close to a unit root, is slightly less persistent with with
c
= 0:006 vs
d
d
c
= 0:995 while the di¤erential trade cost
= 0:991. The common trade cost is slightly less volatile
= 0:049: The common productivity shock is slightly less persistent
than the di¤erential productivity shock (0.987 vs 0.989) and slightly more volatile (0.012 vs 0.011). The persistence of the beta shock is 0.947 and the standard deviation of the shock is 0.0006. The Armington elasticity equals
= 3:26 which is quite a bit higher than what we found
in our empirical analysis and provides some sense of the biases arising from not accounting for the extensive margin of trade and the endogeneity of prices and quantities. The risk aversion parameter equals
= 6:57; or only slightly larger than that used by Chari et al. (2002) in
their study of real exchange rate ‡uctuations. The pricing-to-market parameter is found to equal -0.316. Finally, we …nd very little external habit of only 0.27 percent. Figure 8 plots the path of trade costs and productivity along with the path expected at the start of the sample measured as deviations from the steady state. The gap in trade costs was quite large initially and was expected to fall as it did, although there were sizeable
28
‡uctuations over time. The common trade cost was also quite large initially, and expected to fall by one-third. The actual path of trade cost involved a much larger drop than expected (11 percentage points vs. 3 percentage points). In terms of the gap in productivity, the US productivity was 5 percent above the ROW in 1980. This gap was expected to almost completely close by 2015 but we have seen much larger growth in output in the ROW. In terms of average productivity, we infer that productivity was close to the steady state in 1980. B. Variance decomposition We now discuss the source of ‡uctuations in some key variables that determine the trade balance. We consider the contribution of di¤erent shocks over the period of interest as well as longer-term unconditional moments. Figure 9 plots the source of ‡uctuations in the real trade share, export-import ratio, and real trade balance as a share of output split between the initial conditions and the subsequent shocks. The US real trade share as a share of its change by the end of the sample is plotted in the top panel. It shows that about 85 percent of the growth in trade can be attributed to changes in trade cost. The remaining 15 percent re‡ects the growth in productivity in the rest of the world. The shocks to the discount factor have no long-run e¤ect on trade and generate only very minor ‡uctuations. The export-import ratio is plotted in the middle panel. Here we see that the initial conditions, mostly the US net foreign assets and di¤erence in trade costs, could have been expected to generate a de…cit over time and that this de…cit is about half of the data in 2015. There are sizeable swings from the shocks to the di¤erence in productivity and discount factor shocks but by the end of the sample these two together would predict a surplus. Shocks to the gap in trade costs generally contributed to a de…cit. They are about twice as important in the 2000s vs 1980s. By the end of the sample we …nd that the gap in trade costs can
29
account for almost 100 percent of the export-import ratio. The trade balance as a share of output is plotted in the bottom panel. To construct this from the model we use the following accounting identity T BYt = T RY0 ln EXtR =MtR =2 + (T RYt
T RY0 ) ln EXtR =MtR =2;
which permits us to measure the direct and interacted e¤ects of shocks and initial conditions. Given we have 6 possible determinants of each variables it is impractical to separate out each e¤ect. Instead, we plot a few reasonable counterfactuals. First, we plot the dynamics assuming that there are no shocks to either type of trade cost. This substantially reduces what we called the scale e¤ect since about 85 percent of the growth in trade could be attributed to changes in common trade cost. Now the peak trade de…cit in the 80s and 2000s are nearly identical at about 2 percent. Moreover, the US trade balance is roughly in balance from 1990 to 1997 and again since the Great Recession. Compared to our crude accounting for trade integration in Figure 2, our GE model suggests changes in trade barriers are an even more important source of the trade de…cit over the sample. We also plot the dynamics of the trade de…cit from just shocks to the gap in trade cost at the initial and actual trade shares which show a rising importance of asymmetries in trade shocks. Finally, we plot the impact of the asymmetric trade shock plus the common trade cost shock interacted with all the other shocks. This makes it clear that the larger de…cits in the 2000s relatively to the 1980s is almost entirely due to trade policy. Table 6 reports a variance decomposition of the contribution of di¤erent shocks for a variety of variables of interest based on the unconditional moments of the model. In general, relative productivity and relative trade cost shocks are the main drivers of any asymmetries across countries as discount factor shocks have a very small impact. Focusing on the real export-import ratio, the di¤erential productivity and trade costs are now about equally important accounting for 47 percent of the variance. This is a slightly 30
larger role for trade policy than in our short-run-long-run empirical model where trade costs contributed only about 30 percent. Thus, the e¤ect of trade costs on the business cycle, through relative prices and relative expenditures, is more important than the role of the business cycle on trade costs through mismeasurement from the extensive margin and our use of industrial production as a proxy for …nal demand. The variance of real trade ‡ows is almost entirely due to changes in common trade barriers and so the earlier empirical decomposition was correct in attributing the movements in the trade share to trade integration. For the movements in the relative price we emphasized, the sum of the terms of trade and real exchange rate, we …nd that di¤erential trade costs account for about 97.5 percent of the ‡uctuations. Di¤erences in trade costs have a minimal impact on relative spending or production Trade costs have a minor impact on production and consumption, accounting for less than 1 percent of the variance of industrial production and 3 percent of the variation in consumption. Fluctuations in employment are more in‡uenced by trade costs with over 1/3 of the ‡uctuations due to trade costs. Di¤erential trade costs account for over 90 percent of the measured gap in the trade wedge using production or expenditures. This suggests that using production as a proxy for …nal spending will have a minor impact on our measured wedges. It appears that the movements in relative exporting are too small to generate much mismeasurement in the di¤erential trade wedge. C. Additional Predictions and properties of the model Here we consider the …t of the model along some non-targetted dimensions and some features of the model. In particular, we examine the dynamics of export participation in the data and the model, the gradualness predicted by the model, and the impact on the trade balance of di¤erential trade cost shocks and common trade cost shocks.
31
A key feature of our model is the inclusion of a dynamic exporting decision. Models of this sort have been shown to explain the entry and exit decision of …rms in response to changes in trade barriers (Das, Roberts, and Tybout, 03, Alessandria and Choi, 14b). Here we show that our model generates movements in export participation that are quite consistent with time series evidence from the US. Figure 10 plots the log change in US export participation in the model and the data.28 Despite not being targeted, the model captures most, but not all, of the growth in export participation. It does particularly well capturing the dynamics of export participation in between 1980 to 1997, a period of export exit followed by substantial expansion after the Plaza and Louvre Accords. It captures the downturn in export participation after the Asian Crisis, as well as the expansion that starts in 1999 and in the long run. A key feature of our analysis is that trade takes time to adjust to changes in trade barriers. We now consider how quickly trade responds by comparing the ratio of imports to domestic spending at di¤erent horizons for a common shock (with the estimated persistence). The top panel Figure 11 plots the ratio of change in the import ratio to change in trade costs against the same variable in quarter 20. The model generates some gradualness with about 50 percent of the impact is in the …rst quarter, 80 percent in four quarters, and 95 percent in two years. The bottom panel plots the elasticity of the import ratio to various shocks. The trade elasticity which measures the change in the import ratio relative to the change in trade costs rises from 3 to about 6. The elasticity of the import ratio to our relative price measure in response to changes in productivity and di¤erential trade costs. These elasticities are quite low, less than 1 for the response to productivity shocks, and close to zero for the response to di¤erential shocks. Both elasticities are time varying, although they don’t change as much as 28
The data is from a mix of the Annual Survey of Manufactures, Census of Manufactures, Compustat (Lincoln and McCallum, 2015) and Census Report on US Pro…le of Exporters. These are measured at the annual level and spliced together.
32
in the data. The model is consistent with what Ruhl (2004) describes as the trade elasticity puzzle. Next, we consider the dynamics of the trade balance in response to the di¤erent shocks (productivity, trade cost, and discount factor) that each lead to a 1 percent initial trade de…cit (…gure 12). For each shock, the shock is considered with and without a shock that reduces global trade barriers to make clear the scale e¤ect of trade on intertemporal trade.29 Including a trade shock magni…es the initial de…cit. As trade takes time to expand, the de…cit will continue to worsen and so the trade shock introduces some additional persistence into the trade balance dynamics. D. Temporary Trade Protection To more fully highlight the in‡uence of trade policy on the trade balance we consider an explicitly temporary trade policy such as an anti-dumping penalty, safeguard measure,30 or voluntary export restraint. This is modelled as a shock that raises the gap between import and export costs by two standard deviations. As these policies are rarely a surprise the policy is announced to start in two quarters and last for three years. The timing of this policy (pre-announced with a 3 year duration) is meant to mimic the 1981 US policy on Japanese autos. The gap is modelled as arising under four scenarios. First, we consider a Negotiated adjustment with an increase in import costs and reduction in export costs. Second, we consider an immediate Trade War such that common trade costs rise with the gap. Third, we consider a Trade War that escalates gradually and de-escalates gradually. And …nally, we consider a Trade War that gradually escalates and remains in place, much like the dynamics of trade policy in the Great Depression. In the Negotiated adjustment only the sequencing 29
The interaction e¤ects are solved using our linear decision rules. Safeguard measures (Section 201 of 1974 Trade Act) restrict imports temporarily if an industry is injured or threatened with injury. 30
33
e¤ect of trade barriers operates. In the Trade War cases the scale e¤ect also matters. In each case we start from a steady state trade share of GDP of 30 percent. We assume that agent’s know which case they are in and fully anticipate how changes in trade barriers will a¤ect trade ‡ows. Allowing for the policy response to be uncertain would generate more variation in net ‡ows across the observed outcomes. Figure 13 depicts the dynamics of trade barriers, trade, and net trade ‡ows under both policies. In all four cases, as agents know that barriers will be relatively high for trade into the home country in two quarters there is an incentive for the home country to consume in advance (and foreign to delay) and so the home country will run a small trade de…cit initially followed by a surplus for the next 12 quarters. Once the policy is removed the home country will run a persistent trade de…cit. Even though the gap in trade barriers is the same in all the policies, the Negotiated policy leads to larger swings in the trade balance than the Trade Wars since these also lower trade.31 The di¤erence in the trade balance is not monotonic since trade falls gradually with the implementation of the policy and rises gradually in anticipation of the removal, or lack thereof, of the policy. In total, this leads to a surplus that are 75 to 85 percent of the negotiated policy and a smaller de…cit once the policy is removed. E. Observed Trade Policy We next compare the dynamics of trade barriers in our two models. Figure 14 plots the inferred common trade wedge from our partial equilibrium model (PE) and the negative of the common trade cost in our GE model (GE). These two measures of trade frictions move quite similarly although the PE wedge is substantially more volatile, particularly during recessions. The main di¤erence is towards the end of the sample where our PE model suggests trade barriers have increased since the Great Trade Recovery while the GE model suggests trade 31
The e¤ect of the policy on output, consumption, and employement depend on the response. In the negotiated case, US consumption falls and employment rises during the policy.
34
barriers have more or less remained constant from 2006 onwards. Panel B compares the di¤erential trade wedge and negative of the di¤erence in trade costs from the two models. The two models generate quite similar gaps from 1980 to 1997 but since then they tend to move in opposite directions. Indeed, the GE wedge suggests that it is the US that has become more closed relative to the rest of the world since the Great Recession. This may re‡ect an inability of the GE model to capture the gradualness over the business cycle as we see in the data. F. Sensitivity We now examine the sensitivity of our …ndings to a couple modelling assumptions. Specifically, we consider an alternative model in which exporting is a static decision (with and without pricing-to-market) and a variation of the benchmark economy with no asymmetries in trade barriers. Each model is re-estimated on the same data. The estimated parameters are in table 7 and some properties of the models are reported in tables 8. The benchmark economy yields the best …t to the data. The most radical change in …t occurs when we restrict the model to only consider common changes in trade barriers. With only four shocks and …ve series, the model misses out badly on movements in relative prices. Aside from the parameters that are being exogenously changed across variations, the main di¤erence shows up in the estimate of the Armington elasticity. While the benchmark model has a posterior mean of 3.26, in the static exporting models it drops to 2.14 with pricing-tomarket and 1.81 without pricing-to-market. Eliminating uneven trade policy shocks yields an elasticity estimate of 1.82. These alternative models provide some sense of the biases in estimates of the Armington elasticity. With a lower Armington elasticity the changes in trade policy must be 3 to 4 times larger to generate the same changes in trade observed in the data. Turning next to the variance decomposition, and focusing on cross-country ratios, we …nd an important role for di¤erential changes in trade barrier in all the models that allow for
35
them. Indeed, we …nd that our dynamic exporting model actually attributes the smallest role to these shocks to nominal net trade ‡ows (25% in the benchmark versus 34 percent in the static model with no pricing-to-market). This arises because in the benchmark model non-trade related shocks can generate persistent ‡uctuations in net ‡ows and thus account for some of the variation in the asymmetric trade wedge. Indeed, we …nd the static trade models require relative more volatile shocks to the asymmetric trade cost. On a more narrow scale, and through the lens of our decomposition from equation 3, this arises because of con‡icting e¤ects on di¤erential trade costs on relative spending and relative prices. The benchmark dynamic model suggests relative spending is less driven by relative trade barriers than the static models while relative prices are more driven by asymmetric trade costs in the benchmark model. An interesting …nding is that the discount factor shocks do not account for more than 7 percent of all net trade ‡ows. We conclude by comparing the impact of a temporary change in trade policy in the static model to our benchmark model in Figure 13. For simplicity, we focus just on the case of a gradual trade war and put the same shocks through both models. Here we see that the static model predicts that ‡uctuations in the trade balance are about 30-40 percent as large as in our benchmark model and are less a¤ected by the dynamics of trade. This is largely a result of having a much lower trade elasticity. We also see that in the static model that trade ‡ows move nearly perfectly with the trade policies unlike the dynamic model which has some anticipatory and lagged e¤ects.
6. Summary There is little doubt that the near tripling of US trade from 1980 to 2015 is directly attributable to large changes in policy and non-policy trade barriers and that these policies have di¤ered on imports, exports, and over time. There is considerably more doubt about how these policies have in‡uenced the trade balance, although much is at stake in understanding
36
their role. To quantify the role of trade policy for the trade balance, we have undertaken a dynamic analysis that merges research on international business cycles and trade integration. Interpreting the data on business cycles and trade integration through two standard dynamic trade models, we …nd that trade policies were indeed in‡uential for the dynamics of the trade balance, particularly when measured as a share of GDP, as is common. Our analysis shows that the traditional source of movements in the trade balance operating through changes in relative prices or relative expenditure are less important than previously understood, particularly if one focuses solely on their contemporaneous rather than lagged e¤ects. Not accounting for these gradual dynamics overstates the role of changes in trade barriers. Extending standard models of the international business cycle to allow for gradual trade dynamics and changing trade barriers appears to be a necessary direction for understanding the cyclical behavior of the trade balance and the transmission of business cycles. Changes in trade policy are shown to matter for the dynamics of the US trade balance (and relative prices) in a period of substantial trade integration. Whether changes in trade barriers continue to in‡uence the dynamics of the trade balance will depend on future policy developments. There appear con‡icting prospects though. On the one hand, we …nd the common trade barrier has been fairly stable since the early to mid-2000s after steadily falling from the 1980s. As these trade barriers likely re‡ect bilateral changes in trade policy and there are limited prospects for US trade agreements on the horizon this suggests, perhaps unfortunately, trade will be less important for the trade balance going forward. On the other hand, there is strong evidence that US inward and outward barriers have moved apart since the Great Recession. If trade policy is aimed at bringing these back to pre-Great Recession levels, as seems to be the case, then these may strongly in‡uence the trade balance going forward. Finally, we have focused quite narrowly on how changes in trade policy and business 37
cycle shocks a¤ect the trade balance as this is a key variable in many models and a political lightning rod. Since our general equilibrium model has been estimated to be consistent with international relative prices, US and ROW production, net and gross trade ‡ows, there are many other features of international business cycles that our analysis can account for, like the quantity or Backus-Smith puzzles. Our framework is also useful for understanding how much changes in trade barriers may have boosted growth along the transition to a more integrated economy as well as the source of the global slowdown in trade and growth since the Great Recession (see Alessandria and Mix, 2017).
7. Data Appendix Recall that our main equation is ln (X=M ) = ln (! =!)
[ln (Px =P )
ln (Pm =P )] + ln (D =D) ;
D - is an equally weighted average of Real PCE: Goods and Real Gross Private Domestic Investment D - is proxied by a US trade weighted World Economies Industrial Production (Dallas Fed). P/P is measured as the Real Broad Trade-Weighted Exchange Value of the US$ (Mar73=100) (FRB) X -Real Exports of Goods & Services (SAAR, Bil.Chn.2005$) (BEA) M - Real Imports of Goods & Services (SAAR, Bil.Chn.2005$) (BEA) PX Exports of Goods & Services: Chain Price Index (SA, 2005=100) (BEA) PM Imports of Goods & Services: Chain Price Index (SA, 2005=100) (BEA) NII is Real Net Inventory Investment (SAAR, Bil.Chn.2005$) (BEA) To measure the US trade wedge on imports we use the BEA’s consumption price de‡ator (Consumption : Chain Price Index (SA, 2005=100)) Time period 1979q1 to 2015q4.
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41
Table 1: Estimates of US Export-Import Ratio Level1 Level2 Di¤erences Short-run Price
Spending
3
0.283* (2.52)
0.137*** (4.66)
ECM2
ECM3
0.119*** 0.180*** (5.02) (6.57)
0.204*** (7.98)
0.608*** (4.17)
0.576*** (4.01)
1
Adjustment
0.0659*** 0.0667** 0.0687*** (3.54) (3.54) (3.98)
Long-run Price N rmse R2a Inventory
ECM1
148 0.348 -5.82 N
148 0.075 0.682 N
148 0.0215 0.262 N
1.026*** 1.091*** (7.75) (6.36) 148 148 0.0201 0.0192 0.352 0.411 N N
Period: 1979Q1-2015Q4. T-stats based on Newey-West s.e. in parentheses, ECM stands for error correction model.
p < 0:05;
42
p < 0:01;
p < 0:001
1.124*** (5.78) 148 0.0187 0.437 Y
Table 2: Contribution of business cycle to export-import ratio
Whole Sample 2
R Variance Decomposition
Di¤ 72.6 56.6
Levels 68.4 59.5
SR/LR SR* SR/LR 45.8 75.2 31.8 101.5
Since 1991 2
R 79.0 71.6 Variance Decomposition 65.6 69.4 *SR uses coe¢ cient on di¤erence terms
56.2 38.9
73.5 110
Table 3: Avg. Trade balance to gdp since 1991
Levels Contribution Data -2.95 100% Counterfactual* -1.58 53.5% Trade contribution Global -1.37 46.5% *Based on (1986 trade share)
Table 4: Empirical Decomposition of trade balance to gdp
Initial Trade Avg Trade 86 Trade try var(NXYjtry) Whole Sample 11.3 30.3 81.6 42.3 Since 1991 15.7 44.6 91.8 30.6 1986 trade share is 13.0 percent
43
Table 5: Parameters Fixed Parameters
0.99 0.0001
Calibrated Parameters Parameter Value 0.30 a1 0.1551 f0 0.1278 f1 0.0373 0.15 4
Target Labor 25 Trade share 10 Export 20 Exporter stopper rate 2.5 Exporter premium 50 Markup 33
Estimated Parameters prior mean post. mean 90% HPD interval zc zd c d
b c d
zc zd b
Pricing-to-market Habit Armington Elasticity Risk Aversion Mean relative price Mean relative size
0.9 0.9 0.9 0.9 0.95 0.01 0.01 0.01 0.01 0.001 -0.23 0.01 1 2 0 0
0.9869 0.9728 0.9892 0.9836 0.9953 0.9915 0.9910 0.9866 0.9471 0.9376 0.0057 0.0035 0.0492 0.0447 0.0123 0.0111 0.0110 0.0097 0.0006 0.0005 -0.3162 -0.4349 0.0027 0.0019 3.2620 2.8393 6.4523 5.0436 0.5179 0.3477 -0.0848 -0.1664
44
0.9994 0.9937 0.9996 0.9948 0.9559 0.0078 0.0531 0.0132 0.0121 0.0008 -0.1417 0.0035 3.8146 7.8391 0.6819 0.0235
prior pstdev unif unif unif unif norm invg invg invg invg invg norm invg unif norm norm norm
1 1 1 1 0.01 0.2 0.2 0.02 0.02 0.02 0.1 0.1 2.5 2 0.2 0.2
Table 6: Variance Decomposition - Benchmark (%) Zc Real Export-Import ratio 0.0 Real Trade Share 0.0 Relative Price (tot+rer) 0.0 Relative Expenditures 0.0 Relative Production 0.0 Wedge Gap with spending 0.0 Wedge Gap with production 0.0 Nominal Export-Import Ratio 0.0 Labor 0.0 Production 77.8 Discount factor 72.5 Consumption 77.3
Zd c d 47.5 0.0 47.1 5.4 1.3 98.7 0.1 0.0 2.5 0.0 97.5 0.0 96.7 0.0 2.6 0.7 94.6 0.0 4.2 1.3 5.2 0.0 94.4 0.5 7.9 0.0 91.4 0.7 67.5 0.0 25.0 7.5 57.0 15.2 21.6 6.2 20.9 0.1 0.9 0.3 17.4 3.1 0.5 6.5 19.1 2.9 0.5 0.1
Table 7: Alternative Models - Parameter Estimates Benchmark Full Only Common 0.9869 0.9892 zd 0.9953 c 0.9910 d 0.9471 b 0.0057 c 0.0492 d 0.0123 zc 0.0110 zd 0.0006 b Pricing-to-market -0.32 Habit 0.0027 Armington Elasticity 3.26 Risk Aversion 6.45 Mean relative price 0.52 Mean relative size -0.0848
0.9928 0.9905 0.9973
zc
Log Data Density
0.0124 0.0122 0.0006 -0.29 0.0024 1.82 6.31 0.19 -0.239
0.9824 0.9886 0.9982 0.9908 0.9512 0.0173 0.0607 0.0126 0.0111 0.0007 -0.33 0.0029 2.14 6.13 0.49 -0.0783
0.0027 1.81 6.27 0.47 -0.0942
1490.7
1761.7
1758.9
0.9568 0.0217
1772.4
45
Static PTM No PTM 0.9831 0.9914 0.9982 0.993 0.949 0.0258 0.0675 0.0123 0.0111 0.0008
Table 8: Alternative Models - Variance Decomposition Variable/Model
Shock Productivity Trade Discount
Real Export-Import Ratio Benchmark Static Static-NoPTM Benchmark Common
47.5 48.1 47.0 92.9
47.1 46.7 49.2 0.0
5.4 5.2 3.8 7.1
Nominal Export-Import Ratio Benchmark Static Static-NoPTM Benchmark Common
67.5 64.9 60.8 92.8
25.0 28.0 34.0 0.0
7.5 7.1 5.3 7.2
Relative Expenditures Benchmark Static Static-NoPTM Benchmark Common
96.7 93.1 89.1 99.0
2.6 5.9 9.9 0.0
0.7 1.0 1.0 1.0
Relative Prices (TOT+RER) Benchmark Static Static-NoPTM Benchmark Common
2.5 5.8 9.6 95.7
97.5 93.9 90.0 0.0
0.0 0.3 0.4 4.4
Relative Production Benchmark Static Static-NoPTM Benchmark Common
94.6 94.0 94.2 99.3
4.2 4.8 5.0 0.0
1.3 1.2 0.8 0.8
46
Real Trade Balance (% of GDP) -.04 -.02 0 .02
Real Exchange Rate TB/Y
-.06
RER
1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1
-.1 0 .1 .2 .3 Real Trade Weighted U.S. Dollar Index: Broad
Figure 1: US Real Trade Balance
.15 .2 .25 .3 Real Trade Share of GDP (X+M)/Y
TB/Y Trade/Y
.1
-.06
Real Trade Balance (% of GDP) -.04 -.02 0 .02
Trade share
1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1
47
.02
Figure 2: Contribution of Trade Growth to Trade Balance
-.06
-.04
-.02
0
TB/Y TB/Y_86wt
1980q1
1985q1
1990q1
1995q1
2000q1
2005q1
2010q1
2015q1
Figure 3: Comovement of RER t with 1
B. Trade-Expenditure Ratio t+k
1
A. Trade Ratio t+k
Theory
0 -.5
-.5
0
.5
Data
Theory
.5
Data
-12
-8
-4
0 Quarter(k)
4
8
12
-12
Note: Based on US from 1979q1 to 2015q4
-8
-4
0 Quarter(k)
Note: Based on US from 1979q1 to 2015q4
48
4
8
12
Figure 4: Net Trade Flows and Wedges .2
A. Export-Import Ratio Data Static
-.4
-.2
Percent
0
Dynamic
1980q1
1985q1
1990q1
1995q1 2000q1 time
2005q1
2010q1
2015q1
Note: 1979q1 to 2015q4
.2
B. Export-Import Ratio and Wedges Data Static
-.4
-.2
Percent
0
Dynamic
1980q1
1985q1
1990q1
1995q1 2000q1 Quarter
Note: 1979Q1 to 2015Q4
49
2005q1
2010q1
2015q1
-.04
Percent -.02
0
.02
Figure 5: Trade Balance Decomposition
-.06
Data Business Cycle Trade 1980q1
1985q1
1990q1
1995q1 2000q1 Quarter
2005q1
2010q1
2015q1
Note: 1979Q1 to 2015Q4
-.2
Level 0
.2
.4
Figure 6: Common Trade Wedge
-.4
Wedge
1980q1
1985q1
1990q1
Trend (HP1600)
1995q1 2000q1 Quarter
Note: Based on US from 1979q1 to 2015q4.
50
2005q1
2010q1
2015q1
Figure 7: Smoothed Series and Shocks
A. Smoothed Series (Data and Model) US Real Export-Import RatioUS Trade share of GDP 0.2
0.5
0
0.2
US IP
0.1 0
-0.2
0 -0.5
-0.4
-0.1
-0.6 1980 1990 2000 2010
-1 1980 1990 2000 2010
Relative IP (US-ROW)
-0.2 1980 1990 2000 2010
US Relative Price (RER +TOT )
0.2
0.4
0.1
0.2
0 0 -0.1 -0.2
-0.2 -0.3 1980 1990 2000 2010
-0.4 1980 1990 2000 2010
B. Estimated Shocks Common Technology (Zc) 2 0
4
Productivity Gap
2
Beta gap (US - ROW, %) 4 2
0 -2
0 -2
-4 -6 1980 1990 2000 2010
Common Iceberg Cost 4 2
-2
-4 -6 1980 1990 2000 2010
Differential Iceberg Cost
6 4 2
0 0 -2
-4 1980 1990 2000 2010
-2 -4 1980 1990 2000 2010
51
-4 1980 1990 2000 2010
Figure 8: Dynamics of Trade Costs and Productivity: Expected and Actual Differential Trade Cost (
d
)
Common Trade Costs (
1.5
1
c
)
0.15
Initial Actual
0.1
0.05 0.5 0
0
-0.05
Differential Productivity (Z
d
)
Common Productivity (Z ) c
0.1
0.2
0
0.1
-0.1
0
-0.2
-0.1
-0.3 1980 1985 1990 1995 2000 2005 2010 2015
-0.2 1980 1985 1990 1995 2000 2005 2010 2015
52
Figure 9: Decomposition Trade, Export-Import Ratio and Trade Balance
Real Trade Share (% of Long-Run)
Percent (%)
100
50
Data Trade + initial Productivity Discount
0
Real Export-Import Ratio
Percent (%)
20 0 -20
Data Trade Technology Discount Initial
-40 -60
Real Trade-Balance/GDP Percent (%)
0 -2 -4 -6
Data No trade shocks (initial trade) d d d
-8 1980
(actual trade) + c*(all shocks)
1985
1990
1995
2000
53
2005
2010
2015
Figure 10: Change in US Export Participation US Exporters 0.3 0.25 0.2 0.15 0.1 1980
Model Data
1985
1990
1995
2000
2005
2010
2015
Exporters to US 0.25 0.2 0.15 0.1 ROW Exporters to US
0.05 1980
1985
1990
1995
2000
54
2005
2010
2015
Figure 11: Dynamics of import ratio relative to 20 quarter change Export Growth from Common Trade cost Reduction 1
0.9
0.8
0.7
0.6
0.5
0.4
Exports Exporters
0.3 0
2
4
6
8
10
12
14
16
18
20
Trade Elasticity and Armington Elasticity from Different Shocks 7
6
5
4
3
2
1
Comm on trade cos t Productivity Difference trade cost
0
-1 0
2
4
6
8
10
55
12
14
16
18
20
Figure 12: Interaction e¤ects on Trade Balance Productivity
0
Trade cost
0
TB/Y (%)
-0.5 -0.5 -1 -1 -1.5 -2
-1.5 0
20
30
40
0
Discount Factor
0.5
TB/Y (%)
10
6
-0.5
4
-1
2
-1.5
20
30
40
Trade share of GDP %
8
0
10
0 0
10
20
30
40
0
56
10
20
30
40
Figure 13: Temporary Trade Protection Differential Trade costs (
d
)
Common Trade Costs ( 20
10 Negotiated Trade War (TW) Gradual TW Permanent TW
5
c
)
10
0
0
-10
-5 0
10
20
30
40
0
Trade Share of GDP
20
40
Trade Balance of GDP
30
0.8 0.6
20
0.4 0.2
10
0 -0.2
0 0
20
40
0
57
20
40
Figure 14: Trade wedge and Barriers
Common Trade Wedge/Costs ( 0.4 0.3
c
) 0.6
GE(lhs) PE
0.4
0.2 0.2
0.1 0
0
-0.1 -0.2 1980
1988
1996
2004
Differential Trade Wedge/Cost ( 0.4
2012
d
)
0.2
0.3 0.2
0 0.1 -0.2 0
-0.4 -0.6 1980
-0.1 1988
1996
58
2004
2012
Figure 15: Temporary Trade Protection Static vs Dynamic Model Trade Share of GDP
Trade Balance of GDP
30 0.8 0.7
25
0.6 20
0.5 0.4
15
0.3 0.2
10
0.1 0
5
-0.1
Dynam ic Static
-0.2
0 0
20
40
0
59
20
40
Appendix 2 - empirical sensitivity (not for publication) In our estimates of the partial equilibrium model, our use of rest of world industrial production as a proxy for world demand introduces a bias. Here we show the bias is relatively small. The main problem is that industrial production may di¤er from expenditures owing to the ROW trade balance. We can construct a foreign measure of real expenditures by recognizing that the US trade balance will account for the di¤erence between production and spending in the rest of the world. DN = Y N + IM N
EX N
Assuming a steady state with all prices equal to 1 we can rewrite DR = Y R 1 +
IM R
EX R YR
=YR 1
tby U S
Y US YR
Using this equation, we construct a new measure of foreign expenditures. The following table reports our original …ndings along with this alternative measure of foreign demand with various controls. In general, we …nd that price elasticities seem to be slightly lower with this measure while the response to the gap in spending is slightly higher as the gap in spending is now smaller than the gap in production. These regressions explain about 5 percent more of the ‡uctuations in the export-import ratio but our …nding that there is substantial unexplained component and net trade ‡ows respond gradually remain robust. The following …gure shows the pattern of trade wedges, common and the gap, are quite similar to our benchmark case and still di¤er in substantial ways compared to a static trade model.
1
Table 1a: Estimates of US Export-Import Ratio IP
IP
D*
-0.204*** (7.98)
-0.202*** (7.63)
-0.171*** (7.54)
-0.171** (7.43)
-0.168** (7.25)
-0.168** (7.19)
1.351** (4.74)
1.385** (4.84)
1.315** (5.34)
1.334** (5.39)
0.992* (5.74)
0.991* (5.70)
-1.530* (8.45)
-1.513* (8.49)
-1.090 (6.60)
-1.081 (6.58)
-1.145 (7.44)
-1.145 (7.36)
0.576*** (4.01)
0.590*** (4.09)
0.690*** (5.81)
0.698*** (5.89)
0.671*** (4.55)
0.672*** (4.52)
Adjustment 0.0687*** 0.0752*** 0.0775*** 0.0810*** 0.0727*** (3.98) (3.99) (4.51) (4.66) (4.01)
0.0730*** (3.93)
Short-Run Price
NIIY
2
NIIY
1
Spending
Long Run Price
-1.124*** (5.77)
-0.977** (5.63) 1.290*** (12.86)
-0.938*** (5.8)
-0.868** (5.91) 1.145*** (17.58)
9.985** (2.82) 148 0.0187 0.437
10.67** (3.04) 148 0.0188 0.436
9.783** (4.17) 148 0.0178 0.490
10.16** (4.27) 148 0.0179 0.488
Spending
N IIY N rmse Ra2
D*
D*
D*
-0.949** (6.79)
-0.941** (6.56) 1.016*** (15.72)
148 0.0180 0.481
148 0.0181 0.477
Period: 1979Q1-2015Q4. T-stats based on Newey-West s.e. in parentheses, ECM stands for error correction model.* p<0.05** p<0.01*** p<0.001". No LR Spending coe¢ cient implies=1.
2
Common Trade Wedge Trend .4
.4
Wedge Benchmark
Benchmark Foreign Demand
Level 0 -.2 -.4
-.4
-.2
Level 0
.2
No Inventory
Foreign Demand
.2
No Inventory
1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1 Quarter
1980q1 1985q1 1990q1 1995q1 2000q1 2005q1 2010q1 2015q1 Quarter
Note: B as ed on US from 1979q1 to 2015q4.
Note: B as ed on US from 1979q1 to 2015q4.
-.1
Percent 0
.1
.2
Trade Wedge Gap
-.2
Static Demand 1980q1
1985q1
1990q1
1995q1 2000q1 Quarter
Note: 1979Q1 to 2015Q4
3
Benchmark
2005q1
2010q1
2015q1
