Trade-Policy Dynamics: Evidence from 60 Years of U.S.-China Trade ∗

We study China’s export growth to the United States from 1950–2008, using a structural model to disentangle the eﬀects of past tariﬀ changes from the eﬀects of changes in expectations of future tariﬀs. We ﬁnd the eﬀects of China’s 1980 Normal Trade Relations (NTR) grant lasted past its 2001 accession to the World Trade Organization (WTO), and the likelihood of losing NTR status decreased signiﬁcantly during 1986– 1992 but changed little thereafter. U.S. manufacturing employment trends support our ﬁndings: industries more exposed to the 1980 reform have shed workers steadily since then without acceleration around China’s WTO accession.


Introduction
International trade depends on past, present, and future trade policy, but the three are rarely studied together.Many papers study the contemporaneous relationship between trade flows and trade policy while largely ignoring the effects of changes in trade policy that occurred in the past or may occur in the future.One recent literature shows trade responds gradually to past policy changes, whereas another shows uncertainty about future policy can affect trade in the present.We argue the effects of past and future policy are tightly intertwined.We then develop a method to disentangle these effects and use it to study the growth of Chinese exports to the United States.
Our objective is to estimate how expectations of U.S. trade policy on China evolved and to measure how these expectations, together with changes in tariffs, shaped Chinese export growth.Different from previous studies that focus on the 1990s and 2000s, we take a longerterm view that begins when the United States lifted its embargo on China in 1971.We find in the 1970s, when the United States levied high Non-Normal Trade Relations (NNTR) tariffs on China, the probability that China would gain Normal Trade Relations (NTR), and face lower NTR tariffs, was about 30 percent.This uncertainty increased exports of goods with large gaps between the two tariff schedules, which we refer to as high-gap goods.
After China gained NTR status in 1980, the probability that this status would be revoked was high, which depressed exports of these same high-gap goods.This reform became more credible in the late 1980s and early 1990s, and the change in expectations during this period led to sustained growth in Chinese exports to the United States.
Our key findings are that trade-policy uncertainty (TPU) played a larger role in Chinese export growth during the 1980s than during the 1990s and 2000s, and that China's 2001 WTO accession had little impact on policy expectations or trade flows.Thus, we offer a different narrative than Pierce and Schott (2016) and Handley and Limão (2017), who interpret the faster growth of exports of high-gap goods relative to exports of low-gap goods following WTO accession as evidence that this event significantly reduced policy uncertainty.
We offer two new perspectives on this evidence.First, post-WTO high-gap export growth wasn't actually that fast: high-gap exports grew six times faster than low-gap exports during 1985-1993 than during 2000-2006.Second, we find much of the growth during the later period was a gradual adjustment to the reductions in policy uncertainty that occurred during the earlier period and to the tariff liberalizations in 1971 and 1980.This new narrative highlights the importance of accounting for the interaction between expectations about future reforms and gradual adjustments, both to past reforms and to changes in expectations.
Two aspects of U.S. trade policy on China make it ideal for studying the dynamics of TPU.First, the United States has a dual-tariff scheme wherein all of a country's exports are subject to the same tariff schedule (NTR or NNTR) at a given point in time, but tariffs under each schedule differ across goods.Thus, the possibility of switching between schedules affects some goods-those with large gaps between NTR and NNTR tariffs-more than others.Second, the United States imposed a trade embargo on China from 1950-1971.Every good started with zero trade, eliminating concerns about pretrends and allowing us to study disaggregated trade flows over the entire trade relationship.
Our methodology requires two empirical measures as inputs into a structural model.The first is a measure of the gradual adjustment of trade to a change in tariffs.Using an errorcorrection model (Johnson and Oksanen, 1977) and a local-projections specification (Jordà, 2005), we find the long-run response of Chinese exports to U.S. tariffs is almost four times the short-run response and that completing 90 percent of the adjustment takes as long as 20 years.The second measurement is an estimate of how trade responds to TPU.Building on Pierce and Schott (2016), we measure the response of trade in goods with large differences between NNTR and NTR tariffs relative to the response of goods with small differences.The larger the chance of losing this status, the lower exports of high-gap goods will be relative to exports of low-gap goods.We measure the elasticity of Chinese exports to the NTR gap for each year from 1974-2007.These results indicate the effects of policy uncertainty were the largest in the 1970s and early 1980s and had largely dissipated before China joined the WTO. 1n their own, these reduced-form estimates do not identify causal effects or structural parameters.Our elasticities of trade to past policy are biased by uncertainty about future changes.If the risk of losing NTR status depressed trade prior to China's WTO accession, the measured response of trade to the initial 1980 liberalization would be smaller than in the absence of this risk.The NTR-gap elasticities are biased by the slow adjustment to this liberalization.Goods with the largest NTR gaps are most sensitive to the risk of losing NTR status, but these goods experienced the largest tariff reductions when NTR status was first granted, and thus, they took the longest to converge to their new levels of trade.We overcome these identification challenges using indirect inference to estimate the time-varying transition probabilities between the two policy regimes in a dynamic exporting model.
Our model is a multi-industry version of the heterogeneous-firm model with sunk export costs and new exporter dynamics developed by Alessandria et al. (2021).It is a generalization of the sunk-cost exporting model of Das et al. (2007) that captures the key features of marginal exporter dynamics.Firms in each industry differ in productivity and variable export costs, which they reduce gradually through a risky investment. 2 The export-entry decision and gradual reduction in export costs cause trade volumes to adjust slowly to changes in tariffs.Thus, past policy can affect trade long after its implementation.The model features two trade-policy regimes, NNTR and NTR, and the probability of switching between regimes varies over time.This uncertainty depresses export participation and reduces trade volumes when the economy is in the NTR regime.
The model is calibrated to match our estimates of the adjustment process and the yearby-year elasticities of trade to the NTR gap.Firms in the model understand the tariff regime can change, but the realized path of trade policy is identical to the historical experience: the model begins in 1971 in the NNTR regime and switches to the NTR regime in 1980.We choose the probabilities of switching between trade-policy regimes so that the transition to the steady state replicates our estimated path of the elasticities of trade to the NTR gap.
Our identification works as follows.A higher likelihood of reverting from NTR tariffs to NNTR tariffs raises the expected value of future tariffs, which lowers the expected return to exporting, and thus reduces exporter entry and survival.This effect is stronger for high-gap industries than low-gap industries, reducing exports of the former relative to the latter.
The main output of our calibration is a time-varying path of transition probabilities between NTR and NNTR status.We find the annual probability of China gaining NTR status during the 1970s was about 30 percent.Once China gained NTR status in 1980, the probability of losing it was initially high, peaking at 62 percent in 1981.This observation reflects our empirical finding that trade in high-gap goods stagnated relative to trade in other goods for several years after the 1980 reform.Starting in 1986, when China applied to join the agreement that would become the WTO, the probability of losing NTR status fell rapidly.It temporarily rose again in the early to mid 1990s, but by the late 1990s, it had fallen to 5-10 percent.Joining the WTO had a minor effect on the probability of losing access to NTR tariff rates; this probability fell by less than 2 percentage points between 1999 and 2007.
We isolate the roles of TPU and gradual adjustment to tariff changes in a model without uncertainty about trade policy.In this counterfactual, aggregate trade grows faster, particularly in high-gap industries, so the elasticity of trade to the NTR gap shrinks faster than in the benchmark model (and in the data).However, the gradual adjustment to the liberalizations in the counterfactual model is ongoing even after China's 2001 WTO accession.We find that gradual adjustment accounts for almost one third of the overall change in the NTR-gap elasticity documented by Pierce and Schott (2016), which the literature has attributed entirely to a reduction in TPU caused by PNTR access.
Our model highlights a subtle yet important aspect of trade-adjustment dynamics: trade adjusts slowly to changes in expectations about future policy and past policy changes.To illustrate this point, we construct a counterfactual model in which the probability of losing NTR status is constant until China joined the WTO.The single estimated probability of losing NTR status-and the extent to which WTO accession reduced this probability-is substantially higher in this experiment than in our benchmark model.Thus, time-varying policy uncertainty is a key factor in explaining the path of China's integration into the U.S. market.Much of the growth in high-gap good exports after the turn of the century was a delayed adjustment to the increase in the credibility of U.S. policy toward China during the 1980s and 1990s, rather than a reduction in tariff risk associated with WTO accession.
Finally, we revisit the effects of TPU on U.S. labor markets.Pierce and Schott (2016) document large declines in employment in U.S. industries with high NTR gaps after China joined the WTO.On the surface, these findings seem at odds with our new narrative.Using a simple model, we illustrate how differential growth of imports across products from China caused by changes in trade policy (or expectations about future policy) affects domestic employment across industries.Two key channels modulate this effect: the share of domestic absorption that is imported from China (import exposure) and the share of U.S. domestic production that is exported to world markets (export exposure).The same change in imports has a larger effect on employment in industries that are initially more exposed to Chinese imports and less exposed by exporting.We develop an estimating equation in which the effect of the NTR gap is interacted with these exposure terms.Like Pierce and Schott (2016), we find U.S. employment has declined as a result of changes in expectations about U.S. trade policy toward China.By contrast, we find most of this effect occurred long before China joined the WTO, consistent with our analysis of Chinese exports.When we restrict the effect of the NTR gap on employment to be the same across industries, we recover the same patterns as Pierce and Schott (2016).Accounting for heterogeneity in import and export exposure is crucial to getting the timing of the employment effects right.This paper contributes to three strands of literature.The first studies the dynamics of trade after changes in trade policy.Baier and Bergstrand (2007) and Baier et al. (2014) show trade grows slowly following the creation of a free trade area.Anderson and Yotov (2020), Khan andKhederlarian (2021), andBoehm et al. (2023) estimate long-run tariff elasticities of trade that are three to four times the short-run tariff elasticities.We contribute by studying the dynamic response to a single exogenous, immediate tariff reduction over a multi-decade span using disaggregated data.Different from these studies, we do not interpret our results causally or structurally.Instead, we use these results as inputs to our indirect-inference exercise, which uses a model designed to capture the main potential sources of bias in the data.
The second strand studies how expectations about future trade reforms affect trade in the present.Early work focuses on the aggregate effects of temporary reforms (Calvo, 1987) or the credibility of reforms (Staiger and Tabellini, 1987;McLaren, 1997).More recent work uses firm-and industry-level data to identify the effects of TPU.This literature largely focuses on U.S. trade policy toward China. 3Pierce and Schott (2016), Feng et al. (2017), Handley andLimão (2017), andBianconi et al. (2021) measure the growth in trade, employment, and other outcomes that resulted from the elimination of uncertainty when China was granted PNTR status.Our contribution is to study how these tariff gaps, which also capture the size of the initial 1980 liberalization, influenced outcomes from the beginning of the U.S.-China trade relationship.Again, we use these results as inputs to our model, rather than interpreting them causally.
The third strand uses models to estimate trade-policy expectations.Ruhl (2011) estimates the probability of ending the ban on Canadian beef after an outbreak of "mad cow disease."Like us, Handley and Limão (2017) use a dynamic exporting model to estimate the probability of NNTR reversal.We estimate a time-varying probability over a longer interval using a richer model in which tariff changes have persistent effects.Our analysis highlights the importance of earlier changes in trade-policy expectations during the late 1980s and early 1990s in explaining the growth of Chinese exports to the United States around the turn of the century.We find ignoring these changes leads to an overstatement of the effect of PNTR access on tariff risk.Alessandria et al. (2017) estimate the expected path of inward and outward trade policy for China from macroeconomic time series.Complementary to our approach, Alessandria et al. (2024c) estimate a time-varying probability of NNTR reversal from 1990-2005 using within-year variation in trade flows and trade-policy risk in an s-S inventory model, obtaining similar results for this later period.More generally, our work is related to the classic "Peso problem" of estimating the likelihood of discrete events that are unobserved for long periods of time.
Section 2 describes our dataset and presents the results of our empirical analyses.Section 3 lays out our model, and section 4 discusses our calibration strategy.Section 5 presents the results of our quantitative analysis.Section 6 relates our findings about export growth to previous findings about the impact of this growth on U.S. labor markets.Section 7 concludes.

An empirical history of U.S.-China trade
We take a two-pronged approach to analyzing the joint dynamics of U.S. trade policy toward China and imports of Chinese goods.First, we estimate short-and long-run elasticities of trade to the 1980 tariff reduction and the speed of adjustment between the two horizons.
Second, we study the elasticity of trade to the risk of reversing the tariff reduction and its evolution.Neither of these approaches directly identifies structural parameters or causal effects, because they cannot disentangle the effects of slow adjustment to past policy changes from uncertainty about future policy.However, they provide reduced-form evidence that these margins are important.They also produce crucial inputs to our quantitative analysis.

Data
We use annual data on U.S. imports from 1974-2008, aggregated at the 5-digit level of the Standard International Trade Classification (SITC), revision 2. This level of aggregation provides continuous coverage of almost the entire history of U.S.-China trade. 4We refer to this level of aggregation as a good and denote it by g.Our sample contains 1,742 goods and includes applied duties, cost-insurance-and-freight (CIF) charges, and the free-on-board (FOB) import value.The log FOB import value is denoted by v gjt , where j indexes the exporting country and t indexes time.
We use two measures of trade policy: applied and statutory tariff rates.Applied tariffs, denoted τ jgt , are applied duties divided by FOB import values.Ad-valorem-equivalent NNTR and NTR statutory tariffs, from Feenstra et al. (2002), at the 8-digit level of the Harmonized Tariff Schedule (HS), are mapped to the 5-digit SITC classification.The SITC-level NNTR and NTR tariffs (τ N N T R g and τ N T R gt , respectively) are the median 8-digit product-level tariffs within each SITC good.Both statutory tariff schedules are exogenous to China's growth and trade integration.NNTR tariffs were established by the Smoot-Hawley Act of 1930, long before the United States began trading with China, and NTR tariffs apply to all WTO members (and non-members that have been granted conditional NTR status).
Our baseline sample includes U.S. imports from China and every other country that had NTR status throughout the entire period and were not part of preferential trade agreements with the United States, excluding Canada, Mexico, and other communist countries. 5A key feature of our sample is that all the countries, including China, faced approximately the same tariffs after 1980.6Thus, most tariff changes in our sample are explained by good-year fixed effects, and the main source of variation in tariffs applied to China is the 1980 liberalization.
Moreover, the inclusion of imports by non-China NTR countries allows us to control for good-specific U.S. demand shocks.We also exclude goods that include products covered by the Multi Fiber Arrangement (MFA).As documented by Bambrilla et al. (2010), China's accession to the WTO triggered the removal of import quotas on these goods, and our tariff measures do not capture this material change in applied trade policy.In the appendix, we show our results are robust to alternative sample designs.from WTO members (and non-members that, like China, have been unilaterally granted NTR status).In the appendix, we summarize the NNTR and NTR tariff schedules at the 2-digit level of the Chinese Industrial Classification System. 7The mean NNTR rate is 28 percent with a standard deviation of 18 percent.The average applied tariff for non-China NTR countries was five in 1979 and two in 2001.For China, the average applied rate was considerably higher in 1979 (20 vs. five), but similar by 2001 (three vs. two).Figure 1 shows the evolution of the distribution of applied tariffs on Chinese goods.The median tariff fell from 30 percent to about 8 percent.The vast majority of this decline occurred in 1980.Subsequent tariff reductions in NTR tariffs were related to gradual phaseouts from successive rounds of the General Agreement on Tariffs and Trade (GATT).

Policy dynamics
The end of the embargo and the 1980 liberalization were abrupt events, unlike the GATT rounds, which featured gradual tariff phaseouts that were agreed upon in advance.Figure 2 plots the distribution of the residuals from regressing annual tariff changes on country-year, good-year, and country-good fixed effects.Virtually all the variation in tariff changes over 1975 1980 1985 1990 1995 1951, 1962, and 1974 required imports from non-market economies to face NNTR rates.Exceptions to this requirement were rare, typically contingent on substantial reforms, and could be removed quickly (or withdrawn before being implemented), eliminating this requirement was discussed periodically.9Further uncertainty arose from the lack of diplomatic relations between China and the United States.

Slow adjustment to the 1980 granting of NTR status
We begin by studying how U.S. imports from China adjusted after the 1980 granting of NTR status.Trade is known to adjust gradually to trade liberalizations.Baier and Bergstrand (2007) find trade doubles in the long run after the creation of a free trade area, but only one third of the response occurs on impact.Anderson and Yotov (2020), Khan and Khederlarian (2021), and Boehm et al. (2023) find similar differences between short-and long-run trade responses.We use two approaches to study the dynamic response of U.S. imports from China to the 1980 reform: an error correction model (ECM), which recovers short-and long-run trade elasticities while imposing a parametric path of adjustment (Johnson and Oksanen, 1977), and local projections, which recover non-parametric impulse responses (Jordà, 2005).
Both approaches show the growth in trade that followed the 1980 reform was gradual.
Our first approach is an ECM specification: (1) The dependent variable is the one-year log difference in import value.The right-hand side includes the one-year change in applied tariffs, lagged tariffs, lagged log imports, and a set of fixed effects.We interact the first three variables with an indicator variable for China to estimate China-specific elasticities.The short-run trade elasticity, σ SR , is the coefficient on the one-year change in tariffs.The long-run elasticity, σ LR , is determined by the response to lagged tariffs and the autocorrelation of imports.Country-year (δ jt ) fixed effects capture aggregate shocks to exporting countries; country-good fixed effects (δ jg ) capture the average level of exports and time-invariant bilateral trade barriers; and good-year fixed effects (δ gt ) capture good-level U.S. demand shocks and good-specific trade barriers common to all exporters.12Because our sample excludes countries, other than China, that did not receive NTR status during the sample, the good-year fixed effects absorb the effects of multilateral changes in NTR tariffs on trade; thus, σ SR and σ LR measure how U.S. imports responded to changes in bilateral tariffs above and beyond multilateral changes.For the China-specific elasticities σ SR China and σ LR China , given that the vast majority of the identifying tariff variation occurs in 1979-1981, these elasticities largely capture how Chinese exports responded to the 1980 granting of NTR status.
The solid line in Figure 2 shows the path of adjustment to a one-time tariff change implied by our ECM estimates; the estimated parameter values are reported in the appendix.
The short-run trade elasticity is −2.29 and the long-run elasticity is −7.96.The former is consistent with other estimates in the literature, and the latter, although large, is similar to the documented effects of other major liberalizations. 13The large gap between the shortand long-run responses indicates the adjustment of U.S. imports of Chinese goods to tariff changes has been gradual.Our estimates imply U.S. imports from China take seven years to complete 90 percent of the total long-run adjustment to a tariff change.We show in the appendix that these results are robust to a range of alternative specifications with additional controls and different samples of countries and goods.
Our second approach is a local-projection specification: where The dashed line in Figure 2 shows the path of adjustment to a tariff change implied by our local-projections estimation.Whereas the short-and long-run elasticities obtained by the local projections are very close to those from the ECM, the non-parametric estimation displays a slower transition.Our local-projections estimates imply completing 50 percent of the total adjustment takes 10 years and completing 90 percent takes 20 years.In the appendix, we show these results, too, are robust to a wide range of alternative specifications.
Importantly, these estimates are likely confounded by the effects of uncertainty about the expected persistence of the reform.Our specifications (1) and ( 2) include only changes in current applied tariffs, but, as discussed in section 2.2, changes in expectations about future tariffs likely occurred.If the 1980 reform was initially viewed as unlikely to be permanent, as we find in our quantitative analysis, the initial response to this reform would have been smaller-and the adjustment process longer-than it would have been in the absence of uncertainty. 16Thus, we do not interpret these estimates as structural parameters or as causal effects.Instead, we use them to discipline a structural model via indirect inference.

Effects of the risk of losing NTR status
Our second approach draws from the TPU literature, particularly Pierce and Schott (2016) and Handley and Limão (2017).These studies document that the growth in U.S. imports from China around China's WTO accession was strongly correlated with the gap between the NNTR and NTR rate, even though U.S. tariffs on Chinese goods did not change relative to tariffs on other WTO members.When China joined the WTO, the United States removed the annual renewal process, and imports of goods that had faced the largest tariff risk grew fastest.This observatoin is taken as evidence that the risk of future tariff increases depressed trade in those products and that eliminating this risk stimulated trade growth in these products.Our contribution lies in showing how the effect of tariff risk changed over 16 Another potential source of bias is the end of the embargo in 1971.The adjustment to this reform was ongoing when China was granted conditional NTR status in 1980.It also had heterogeneous effects across goods that are correlated with the effects of the 1980 reform.Specifically, goods with lower (higher) NNTR tariffs experienced larger (smaller) liberalizations in 1971 and smaller (larger) liberalizations in 1980.
the history of U.S.-China trade, going back to 1974, before China was granted NTR.
The empirical strategy in the TPU literature is often a difference-in-differences regression that compares goods that were more exposed to future policy risk with goods that were less exposed.In the U.S.-China context, exposure is typically measured by the NTR gap, which is the difference between NNTR and NTR tariffs.We follow Pierce and Schott (2016) and use the NTR gap in 1999 as a time-invariant measure of the NTR gap: g,1999 ).We include the same set of fixed effects as in section 2.3.Our estimating equation is (3)  When China gained NTR status in 1980, the NTR-gap elasticity rose sharply and then leveled off for several years.It did not begin to grow steadily until 1986.Our interpretation of this finding is that gaining NTR status initially caused high-gap imports to increase because tariffs on these goods fell relative to tariffs on other goods, but this reform was initially perceived as likely to be reversed.Then, in the late 1980s, the credibility of China's NTR status began to rise, leading to sustained growth in high-gap imports, despite no material change in tariffs.This interpretation is confirmed by our quantitative analysis in section 3 and is consistent with the finding of Bianconi et al. ( 2021) that stock returns of U.S. firms in industries with high NTR gaps fell during this period.
The NTR-gap elasticity again leveled off from 1992 until 1998, before rising in the leadup to WTO accession and PNTR status.This second slowdown in high-gap import growth began shortly after the U.S. Congress started voting annually on China's NTR status in the wake of the 1989 Tiananmen Square incident, which is widely cited as a key event in the TPU literature.The effect of this event on the NTR-gap elasticity, however, was relatively small in comparison to the changes that occurred during the 1980s.This finding suggests the changes in the risk of losing NTR status played a more important role in the growth of U.S.-China trade immediately after China was granted NTR status in 1980 than in the period surrounding WTO accession.The NTR-gap elasticity between the late 1990s and early 2000s is statistically indistinguishable from zero.
In the appendix, we show these results are robust to alternative specifications.Most importantly, we estimate the NTR-gap elasticities using more-aggregated global bilateral imports and exports to consider the role of good-specific Chinese supply factors.This approach controls for spurious correlation between the NTR gap and differences across goods in, for example, export licenses, state-owned enterprises, import quotas, and industry growth.
Just as our estimates of the pace of adjustment to the 1980 granting of NTR status in section 2.3 are confounded by the effects of the risk that this grant could be reversed, our estimates of the effect of this risk are confounded by the slow adjustment process.The NTR gap captures the effects of the original tariff reduction that occurred in 1980 as well as the risk that this reduction would be reversed later on.The extent to which the NTR gap captures the lagged effect of the granting of NTR status will diminish in time.Thus, we do not interpret these estimates causally either; instead, they are a means to discipline our model.

Model of trade-policy dynamics
We use a structural model to isolate the roles of gradual adjustment and policy uncertainty on the growth of U.S. imports from China.Our model builds on Handley and Limão (2017) and Alessandria et al. (2021).G goods correspond to the 5-digit SITC goods in our empirical analysis.Within each good g, a continuum of heterogeneous Chinese firms produce differentiated varieties.Firms are characterized by their productivity (z) and variable trade cost (ξ).Firms die exogenously at rate 1 − δ(z), where firms with higher productivity have a lower probability of death.The mass of firms in each good is fixed: when a firm that produces good g dies, a new firm replaces it exogenously.To export, a firm pays a fixed cost that depends on whether it exported in the previous period.Two trade-policy regimes exist: NNTR and NTR.The probability of switching between regimes varies over time, generating time-varying tariff risk.
Trade policy.Tariffs, τ gt (s), depend on the current trade-policy regime, s, an aggregate state variable that takes two values: NTR (s = 1) or NNTR (s = 2).17The tariff regime follows a time-varying Markov process with transition probabilities ω t (s, s ).Firms know the entire path of regime-switching probabilities, {ω t (s, s )} ∞ t=0 .We consider alternative information structures in section 5 and the appendix.Technological trade costs.Firms face two types of technological costs that do not depend on trade policy.One is a stochastic iceberg cost, ξ, that can take three values (∞ > ξ gH > ξ gL ) and follows a stationary, first-order Markov process.When ξ = ∞, the firm is a nonexporter.When ξ is finite, some firms will choose to export.When a nonexporter chooses to export, it begins with ξ gH in the next period.Exporters with ξ < ∞ retain their current iceberg costs with probability ρ ξ and switch with probability 1 − ρ ξ .This cost structure implies exporters start exporting small quantities, but with some luck (and repeated investments) grow to export larger quantities.The second technological trade cost is a fixed cost, f , that the firm pays to export in the next period.The fixed costs are identical across firms within a good, but depend on the firm's export history.A nonexporter pays f g0 to start exporting the next period.An exporter pays f g1 to continue exporting.We summarize the fixed-cost structure in a function, f g (ξ), where This model generalizes the sunk-cost model of Das et al. (2007) to capture the exporter life cycle (Ruhl and Willis, 2017).Both types of technological trade costs differ across goods, allowing for heterogeneity in export participation dynamics across sectors in our calibration.
The probability of switching variable trade costs (ρ ξ ) is constant across goods because this parameter primarily governs the aggregate long-run trade elasticity.
Firm optimization.Given the firm's export status, it maximizes current-period profits by choosing its price, taking as given its residual demand and the wage, w, The values of exporting and not exporting at t + 1, respectively, are where r is the interest rate.The value of a firm is The break-even exporter has productivity zgt (ξ, s), such that V 1 gt (z gt (ξ, s), ξ, s) = V 0 gt (z gt (ξ, s), ξ, s), which can be rewritten as For firms at the margin, the fixed cost of exporting equals the expected present value of the gain in firm value from exporting in the future.The gain in firm value depends on the entire expected path of future tariffs, not the current applied tariff rate.
Aggregation.The decision rules, zgt (ξ, s), determine how the distribution of productivity and variable trade costs across firms, ϕ gt (z, ξ), evolves over time for a sequence of realizations of the aggregate state, {s t } ∞ t=0 .The law of motion for this distribution is where Z is a typical subset of R ++ , h g (Z, z) is the probability of surviving and drawing a new productivity in Z conditional on today's productivity z, hg (Z) is the probability of dying and being replaced by a new firm with productivity in Z, and Q gt (Z, z, ξ) = h g (Z, z)ϕ gt (z, ξ).
Although the decision rules, zgt (ξ, s), respond immediately to trade-policy changes, the stock of exporters across trade costs adjusts gradually.Consequently, aggregate trade volumes, respond slowly to policy changes.The slow adjustment makes our model well suited to measuring the roles of gradual adjustment and policy uncertainty in accounting for the growth of U.S. trade with China.

Calibration
Our calibration has four stages.First, we group our 5-digit SITC goods into 15 sectors and use Chinese firm-level data to compute sector-level statistics about exporter dynamics from 2004-2007.Second, we assign several parameters to standard values from the literature and make some common functional-form assumptions.Third, we calibrate the sector-specific parameters so that the model's terminal steady state matches the moments from the first stage.Fourth, we calibrate the probabilities of switching iceberg costs and trade-policy regimes so that the model's transition matches our estimates of the long-run trade elasticity in section 2.3 and the time-varying NTR-gap elasticity in section 2.4.

Chinese firm-level data and sectoral heterogeneity
Following the trade-dynamics literature, we calibrate the model to match micro-level facts about exporter life cycles and macro-level facts about trade dynamics.The micro-level facts come from an annual survey of manufacturing enterprises collected by the Chinese National Bureau of Statistics. 18We compute four statistics that summarize the distribution and dynamics of Chinese firms that export to the United States: the dispersion in export sales (the coefficient of variation of log exports); the fraction of firms that export (the export participation rate); the fraction of exporters who stop exporting each period (the exit rate); and the average exports of incumbent exporters divided by the average exports of new exporters (the incumbent premium).
Aggregation bias is a potential concern.Exporter dynamics could vary across sectors, reflecting sectoral heterogeneity in non-tariff trade costs and other technological primitives.
If this heterogeneity were correlated with the NTR gap, the evolution of NTR-gap elasticity (Figure 3) could be driven by changes in the sectoral composition of Chinese exports to the United States rather than changes in expectations about U.S. trade policy toward China. 19  To ensure our results are not driven by aggregation bias, we compute statistics for each sector in the 2-digit China Industry Classification System (Table 1).We map the 5-digit SITC goods in our data to this system using the ISIC Revision 4 concordance.Heterogeneity exists in exporter behavior across sectors.The coefficient of variation of log exports ranges from 0.85 to 1.94, the export participation rate from 12 percent to 59 percent, the exit rate from 7 percent to 21 percent, and the incumbent premium from 1.76 to 4.82.We find a positive relationship between the NTR gap and the export participation rate (correlation 0.67) but no clear relationship with the exit rate (-0.18), the coefficient of variation of log exports (0.11), and the incumbent premium (-0.18).

Assigned parameters and functional forms
A period is one year.The wage is normalized to one and the interest rate used to discount future profits is four percent.We take the time series for NTR and NNTR tariffs, τ gt (1) and τ gt (2), directly from the data described in section 2.
The functional forms for the productivity process and death probability are taken from Alessandria et al. (2021).Firm productivity follows log a = ρ z ln a + ε, with ε normally distributed with mean zero and standard deviation σ gz , and z = 1 θg−1 log a.This specification eliminates the role of the demand elasticity, θ g , in the size distribution of firms, which facilitates computation.We assume the persistence parameter, ρ z , is common across goods, 19 We thank an anonymous referee for raising this point.while the variance of the innovations, σ gz , varies. 20The probability of death is 1 − δ (a) = max 0, min e −δ 0 a + δ 1 , 1 .We set ρ z , δ 0 , and δ 1 to the values reported in Alessandria et al. (2021).In the next section, we calibrate σ gz .
We use estimates of U.S. import demand elasticities in Soderbery (2018) to set the analogous elasticities in our model, θ g .21θ g is the same for all goods within a sector but varies across sectors.We concord Soderbery's (2018) estimates, which are reported at the HS4 level, to our 5-digit goods by taking the median within each good and aggregating these good-level elasticities to our 15 sectors by taking the average.

Calibrating the transition to aggregate trade dynamics
We calibrate the idiosyncratic probability of switching variable trade costs, ρ ξ , and the probabilities of switching trade-policy regimes, {ω t (s, s )} ∞ t=0 , to match our empirical history of  from 1971from -1979from and NTR from 1980 onward) onward), update the distributions ϕ g,t using the laws of motion ( 9)-( 11), and compute aggregate exports using ( 12).We then estimate equations ( 1) and ( 3) on the simulated data.
The parameters calibrated in this stage are exactly identified: the number of parameters is the same as the number of target coefficients.The probability of switching trade costs, ρ ξ , is primarily identified by the long-run aggregate trade elasticity. 23This parameter governs the measure of high-capacity exporters (firms with ξ = ξ gL ) in the long run and plays a key role in determining the long-run response to trade reforms.We find ρ ξ = 0.91.
The probability of switching from NNTR to NTR, ω t (2, 1), is identified by the NTR-gap elasticity during the 1970s, when China was in the NNTR regime.A higher probability of gaining NTR status boosts exports more in high-gap industries than in low-gap industries because the former gain more from this status.Given the relatively short time China is in the NNTR regime, and the relatively flat NTR-gap elasticity during this period, we assume ω t (2, 1) is constant and target the average NTR-gap elasticity in 1974-1979.
The probability of switching from NTR to NNTR, ω t (1, 2), is identified by the NTR-gap elasticity from 1981 onward.The probability of losing NTR status in period t is identified by the NTR-gap elasticity in period t + 1.As in Handley and Limão (2017), a higher probability of losing NTR status reduces export participation more in high-gap industries than in low-gap industries, but this finding does not affect trade volumes until the following period.24 Note this stage of the calibration procedure is an indirect-inference exercise in the spirit of Gourieroux et al. (1993).The ECM and NTR-gap specifications, (1) and (3), are misspecified: the former is confounded by changes in expectations about future policy, whereas the latter is confounded by gradual adjustments to past changes in applied tariffs.These issues apply to the model as well.Indirect inference allows us to use the estimates from these specifications to recover our model's structural parameters.

Results
First, we discuss how trade-policy expectations have evolved since 1980.Second, we study the contribution of TPU to the growth of Chinese exports to the United States.Third, we study the role of slow adjustment to the 1980 reform in explaining trade growth in subsequent decades.Last, we explore the importance of time variation in policy uncertainty and slow adjustments to earlier changes in expectations in explaining later patterns in trade growth.

Estimates of trade-policy expectations
We begin with the main result of our calibration: the annual probability of switching between policy regimes (Figure 5).The probability of switching from the NNTR to the NTR regime was about 29 percent.The probability of switching back to the NNTR regime was initially Regarding the likelihood of losing NTR status after 1980, the jump between 1980 and 1981 lines up with the change in U.S. leadership from Carter to Reagan; the latter was decidedly more hawkish on China than his predecessor, particularly concerning Taiwan and China's 25 That the probability does not fall to zero implies trade is permanently depressed, albeit slightly, by the possibility of losing NTR status.This positive probability is consistent with evidence from the U.S.-China trade war, where trade in high-NTR-gap goods rose relative to trade in low-NTR-gap goods when new tariffs on Chinese goods were introduced in late 2018.These tariffs were orthogonal to the NTR gap, so the change in the NTR-gap elasticity during this period suggests a reduction in the probability of losing NTR status.We study policy uncertainty during the trade war in Alessandria et al. (2024b).
26 Much of this discussion is based on a series of reports that provide summaries of key changes in trade and trade policy (USITC, 1970(USITC, -1990)).For additional reading, see the appendix.One way to understand our trade-policy probability estimates is to compare the realized path of tariffs with the mean discounted expected tariff that Chinese exporters faced each year.Figure 5 plots the discounted expected tariff across goods in the model, and the mean applied tariff.Whereas the realized path of applied tariffs fell sharply in 1980, and then fell slightly throughout the 1980s and 1990s from reforms to U.S. NTR tariff rates, the discounted expected tariff fell gradually throughout the entire period.The discounted expected tariff exceeded the applied NTR rate even after China joined the WTO in 2001.
The dynamics of the discounted mean expected tariff help us understand the gradual adjustment of export volumes to the abrupt decrease in the current tariff.The intensive margin of trade, exports per exporter, is mostly determined by the current tariff and the distribution of variable trade costs, whereas the extensive margin, through entry and exit, is determined by the path of future tariffs.The slower-to-decrease discounted expected tariff suppressed the participation of Chinese firms in the export market.As the discounted mean expected tariff fell, export participation increased and aggregate trade volumes grew.

The effects of policy uncertainty on trade
To measure how changes in policy expectations have affected trade flows, we compare our benchmark model with a counterfactual one in which firms believe the current trade-policy regime is permanent (equivalent to setting ω(2, 1) and ω t (1, 2) to zero).In this no-TPU counterfactual, firms believe during 1971-1979 the NNTR regime will last forever.In 1980, firms are surprised by the shift to the NTR regime, but thereafter, they believe the NTR regime will last forever.Because the realized path of tariffs in this model is the same as in the benchmark, differences in trade growth are due solely to differences in the expected path of tariffs.27The no-TPU counterfactual also allows us to assess the impact of TPU on aggregate trade.Figure 5 plots aggregate exports in the counterfactual and the benchmark models.
Again, the vertical distance between the two lines measures the effect of TPU.A material difference remains in aggregate trade between the counterfactual and the benchmark after China joins the WTO in 2001.The reason is that the probability of losing NTR status is positive (albeit small) even in the long run.The long-run discounted expected tariff in the benchmark model is higher than the applied tariff, which permanently reduces the number of exporters in high-gap industries.This finding is consistent with Alessandria et al. (2024b), who find exports of high-gap goods grew relative to exports of low-gap goods after the onset of the U.S.-China trade war in 2018, even though the "trade-war gap" (the difference between the trade-war tariffs and NTR tariffs) is orthogonal to the NTR gap.

The role of slow adjustment
The no-TPU counterfactual also allows us to measure the role of slow adjustment to the 1980 granting of NTR status (and the 1971 lifting of the embargo) in explaining trade growth, particularly the patterns in the 1990s and 2000s that are commonly attributed to a reduction in TPU caused by PNTR access.
To do so, we estimate the pre-PNTR elasticity of trade to the NTR gap using the same specification and 1992-2007 observation period as Pierce and Schott (2016): When we estimate this regression using the observed data, we find β = −0.92,and we obtain essentially the same estimate using simulated data from our benchmark model with policy uncertainty. 28When we estimate this regression on simulated data from the no-TPU counterfactual, we find β = −0.26,which is smaller than the estimate from the data but still statistically significant.This finding shows that even if the permanence of China's NTR status had never been in doubt, exports of high-gap goods still would have grown faster than imports of low-gap goods after China gained PNTR status in 2001.Quantitatively, it indicates gradual adjustment to the earlier reform accounts for more than one quarter of the overall effect of PNTR on trade as documented by Pierce and Schott (2016).

The role of time-varying policy uncertainty
We find that changes in expectations about U.S. trade policy toward China mostly occurred in the late 1980s and early 1990s, rather than, as others have argued, at the turn of the century.Here, we study how U.S. imports from China would have grown if only one or two changes in expectations occurred at key geopolitical moments.
First, we study a version of our model in which the probability of losing NTR status is constant between 1980 and 2000 before falling to zero in 2001. 29We calibrate the probability of losing NTR status during 1980-2000 to match the single NTR-gap elasticity estimated by Pierce and Schott (2016), over 1992-2007, from (14).

Employment effects
Changes in policy uncertainty played the largest role in export growth during 1986-1993.
At first glance, this narrative is inconsistent with Pierce and Schott (2016), who document a large decline in U.S. employment in high-gap industries after China joins the WTO.We revisit these employment effects over our longer period.Once we introduce the industry controls suggested by theory, the decline in employment from trade policy on Chinese imports starts earlier and does not accelerate when China joins the WTO.Instead, most of the drop in employment in the period around China's WTO accession is related to industry-specific factors that are correlated with the NTR gap, rather than import growth caused by a change in the credibility of U.S. trade policy on China.

Conceptual framework
To set ideas, consider an Armington model of U.S. demand31 with an aggregate consumption good, Q t , that is a bundle of industry-level goods, Q gt , with elasticity of substitution α, Each good g is a combination of U.S. domestically produced goods, Q Dgt , and Chinese imports, Q M gt , with elasticity of substitution θ g , The demand function for the domestic good and the aggregate price of good g are where P Dgt is the price of the domestically produced good g, P M gt is the price of Chinese exports, τ M gt is the tariff on Chinese exports, and P gt is the price of good g.

Estimation results
Our baseline specification and alternatives are in Figure 7.We estimate one set of parameters for each industry and report results for the industry in the 90th percentile of Chinese import share and the 50th percentile export share.34Plotted in Figure 7 is β t (1 − ω Xg )ω M g , the elasticity of employment to the NTR gap.Employment falls more in industries that are more exposed to the NTR gap, but most of the decline occurs before China joins the WTO.
To compare our estimates with Pierce and Schott (2016), we estimate Relative to (20), this specification forces the employment elasticity to be constant across industries and drops the industry controls for domestic expenditures, exports, and TFP.
Figure 7 shows that, without these controls, employment dynamics are very different: employment is stable during 1990-1997, contracts gradually through 2001, and then declines sharply.We also find robust growth in employment that is correlated with the NTR gap from 1958-1980, which is counterintuitive, given that China did not trade with the U.S. then.
The large differences in moving from the theoretical regression in (20) to the reduced-form regression in (21) suggests the decline in employment in high-gap industries around the time that China joined the WTO may not reflect a change in TPU.
We gain some insight into the importance of the theory-motivated controls by considering alternative versions of (20) in Figure 7. Removing TFP changes our results little.Removing TFP and the controls for export and domestic demand leads to a slightly smaller long-run effect on employment, but by 1994, the effects are almost identical to the baseline model.
Dropping the industry shares, TFP, and export and domestic demand, leaves us with (21), which is very different from the baseline.Thus, heterogeneity across industries in import and export exposure, and the way this heterogeneity modulates the effect of import growth on employment, reconciles our findings with those of Pierce and Schott (2016).
The difference between our specification and ( 21) can be further understood by studying the components of the employment elasticity, β t (1−ω Xg )ω M g .Our results in Figure 7 change the most when we do not control for heterogeneous import and export exposure through ω Xg and ω M g .As we show in the appendix, industries with higher Chinese import shares tend to have larger NTR gaps, rather than smaller gaps as one might expect, which suggests China has a comparative advantage in these industries.Allowing the elasticity of employment to the NTR gap to vary with import and export exposure is important, lest we attribute employment declines in high-gap industries to multilateral China supply factors.
The NTR-gap elasticities, β t , estimated with employment data should, in theory, be the same as the elasticities (with the opposite sign) estimated with the import data from (3).
Absent issues of aggregation, the main differences are (i) (20) lacks the rich controls available with the import data, and (ii) the substitution identified is between imports and domestic sales, rather than across source countries.To gauge the importance of these considerations, in Figure 7, we plot β t (1 − ω Xg )ω M g where we use the estimates of β t from the import regression (3) ("trade coefficients" in the figure) instead of the estimates from the employment regression (20).The effects on employment are half as big as those in our baseline results using employment data.

Conclusions
We study, empirically and quantitatively, the growth of China's exports to the United States since the embargo on Chinese goods was lifted in 1971.We find the dynamics of this integration are consistent with substantial uncertainty about the future path of tariffs, particularly during its initial phase.During the late 1970s, the likelihood of gaining access to U.S. markets at NTR rates was perceived to be low, and once this access was granted in 1980, it was perceived as likely to be revoked.During the mid 1980s, the probability of losing NTR access fell dramatically, and it remained low through the late 1990s in the lead-up to China attaining PNTR status in 2001.This observation suggests much of the growth in trade in products with high NTR gaps in the 1990s and 2000s was a delayed effect of earlier liberalizations-and earlier increases in their perceived credibility.It also indicates the initial lack of credibility about the 1980 granting of NTR status depressed trade much more than later concerns about NTR status renewal that were eliminated when China gained PNTR status in 2001.
Our approach to estimating trade-policy expectations leverages unique aspects of U.S.
policy toward China in which potential changes in future trade policy are known and heterogeneous across products, whereas the likelihood of this change is unknown and common across products.analysis could be extended to consider other events such as Brexit, the U.S.-China trade war, safeguards, and domestic content requirements, as well as traditional protectionist measures such as antidumping duties.In these cases, the size and timing of the reforms are uncertain, but, by interpreting trade flows through a dynamic model, one could discipline the process for these possible trade-policy outcomes.
Our estimates of the dynamics of U.S. trade policy toward China should be useful in disciplining general-equilibrium models of trade dynamics.Reconsidering the aggregate effects of China's global integration, taking into account the dynamics of trade policy we have identified, would be particularly interesting.
Finally, that trade simultaneously depends on past, present, and future changes in trade policy suggests we need to rethink our approach to measuring the response of trade to these changes.Alessandria et al. (2024a) build on our findings here to show how to measure the response of trade to unanticipated versus anticipated changes in trade policy as well as policy changes that feature several forms of uncertainty.
Between 1950 and 2018, three key reforms to U.S. tariffs on Chinese goods were enacted: lifting the embargo in 1971, granting conditional NTR status in 1980, and granting permanent NTR status in 2001.The 1971 and 1980 reforms changed import tariffs dramatically.Before 1971, imports from China faced effectively infinite tariffs.Between 1971 and 1979, Chinese imports faced the relatively high NNTR tariff rates set by the Smoot-Hawley Act of 1930.From 1980 until the 2018 trade war, Chinese goods faced the much lower NTR tariffs applied to imports

Fig. 1 -
Fig. 1 -Growth of aggregate imports from China.Solid line: China's log share of total U.S. imports.Dashed line: median tariff across goods.Dotted lines: 25 th and 75 th percentiles.

Figure 3 Fig. 4 -
Figure3shows that between 1974 and 1979, the NTR-gap elasticity was stable around at −10, indicating imports of high-gap goods were significantly depressed relative to imports Production and demand.Firms use labor to produce, y = z .Productivity, z, is independent across firms and follows a good-specific, stationary Markov process with transition probabilities h g (z, z ).U.S. demand for a firm's good, d gt , is a function of the tariff and the price, p, d gt (p, s) = (pτ gt (s)) −θg D gt .D gt is an aggregate demand shifter and θ g is the good-specific price elasticity of demand.Note the aggregate trade elasticity is determined by the export participation response to a tariff change and the demand elasticity.

U
.S.-China trade.We target the long-run trade elasticity of −7.96 from the error-correction model and the annual NTR-gap elasticities shown in Figure 3. 22 To simulate the history of U.S.-China trade, we initialize our model so that all firms are non-nonexporters in 1970 (i.e., all firms have ξ = ∞), feed in the realized sequence of trade-policy regimes (NNTR

22. 1
percent in 1980, rose sharply to 62.6 percent in 1981, and fell throughout the mid 1980s and early 1990s.A temporary increase occurred in 1994-1996 and a smaller increase in the early 2000s, but the overall trend continued downward.By 2008, the end of our observation period, the probability of moving back to the NNTR regime had fallen to 1.1 percent. 25The historical context supports our estimates of trade-policy expectations in the years surrounding the 1980 reform. 26Regarding the relatively low probability of gaining NTR status during the 1970s, although a few non-market economies had already gained NTR status, the Chinese case was complicated by the lack of formal diplomatic relations and political turnover in both the United States and China.The U.S. Presidency passed from Nixon to Ford and then to Carter during this period.In China, Hua Guofeng was appointed premier following the death of Zhou Enlai and Mao Zedong in 1976, and then Deng Xiaoping consolidated power in 1978.The United States established diplomatic relations with China in 1979, but many additional steps to NTR still remained involving Congress and the key question of Taiwan.

Fig. 5 -
Fig. 5 -Model results.Top left: NTR-gap elasticities.Top right: policy transition probabilities.Bottom left: discounted expected value of tariffs.Bottom right: aggregate trade.

Figure 5
Figure 5 plots the NTR-gap elasticities obtained by estimating (3) on simulated data from the no-TPU counterfactual.During the 1970s, the elasticities in the counterfactual are lower than in the benchmark, where the possibility of gaining NTR status boosted trade in high-gap goods during this period.After 1980, the elasticity in the counterfactual rises faster than in the benchmark, as more firms in high-gap industries enter in response to the perfectly credible reform.The difference between the counterfactual elasticity and the actual elasticity at each point in time measures the contribution of policy uncertainty.This contribution was about 50-70 percent of the elasticity in the data during the 1980s, 50-60 percent during the 1990s, and 65-80 percent during the 2000s.Note policy uncertainty actually accounted for a smaller portion of the NTR-gap elasticity during the periods when NTR reversal was most likely (the late 1980s), and a larger portion of the gap when reversal was least likely (the 2000s).The reason is that delayed adjustment to the 1980 reform played a more important role in the earlier period, when the liberalization was newer.

Fig. 7 -
Fig. 7 -Elasticity of U.S. employment to NTR gap.Solid line: estimates from (20) for industry with median domestic sales share and 90 th percentile Chinese import share.Shaded area: 95percent confidence interval.Dashed line: drop TFP control.Dotted line: drop all controls.Circles: drop all controls and remove interactions with industry shares.

10
When China was granted temporary NTR status in 1980, how long this status would last was uncertain. 11h year, the U.S. president had to renew China's NTR status by July, subject to Congressional approval.The first renewal was granted by President Reagan.From 1990 onward, the U.S. Congress voted on this renewal.The U.S. House of Representatives voted to revokeChina's NTR status in 1990, 1991, and 1992, although the Senate did not.In October 2000, Congress granted China permanent NTR status contingent on joining the WTO, and this grant came into effect in December 2001 upon China's formal WTO accession.The Trump tariffs of 2018, however, show that gaining PNTR status did not entirely eliminate the risk of further tariff changes.

Table 2 :
Sector-level model parameters These parameters are not individually identified, but each target influences the identification of one parameter more than the others.Productivity dispersion, σ gz , is primarily identified by the coefficient of variation of log exports.The entry cost, f g0 , is largely determined by the export participation rate.The continuation cost, f g1 , is mostly governed by the exit rate.The high variable export We calibrate productivity dispersion, σ gz , and non-tariff trade costs, f g0 , f g1 , ξ gH , and ξ gL , so that the model's terminal steady state matches the Chinese exporter-dynamics statistics in the 2004-2007 data (Table1).Our empirical results show the transition of Chinese exports to the United States was largely complete by 2004-2007, so we view these statistics as reflecting technological primitives rather than adjustments to policy changes (or changes in expectations about future policy).This perspective allows us to calibrate the parameters that are identified by these statistics separately from the parameters that govern the transition.We normalize the low variable trade cost, ξ gL , to one in all sectors.We have 15 × 4 = 60 parameters to calibrate at this stage, but the partial-equilibrium structure of our model allows us to calibrate each sector's parameters independently.cost, ξ gH , is pinned down by the incumbent premium.Table 2 lists the calibrated values of these parameters for each sector.

Table 3 :
Calibration summary The price of Q t is normalized to one.Sales by domestic producers are P Dgt Y gt = P Dgt Q Dgt + P Dgt Q * M gt , where Q * M gt is the quantity demanded in China and we have assumed the export price and resulting from gradual adjustment to the 1980 reform, we replace d ln P M jt τ M jt − d ln P Djt by the NTR gap interacted with an annual indicator variable as in (3): GAP g + d ln(P gt Q gt ) − d ln P Dgt − d ln P Dgt ) − d ln Z gt + δ g + δ t + gt , where we have further included industry (δ g ) and time (δ t ) fixed effects. 32Note the shares (ω Xg , ω M g ) are time invariant.These shares are measured in the base period around which we linearize.We use the average shares over 1995-1999 for ω Xg and ω M g . 33Standard errors are clustered at the 4-digit SIC industry level.