Policy Research Working Paper 9551 Taking Stock of Trade Policy Uncertainty Evidence from China’s Pre-WTO Accession George Alessandria Shafaat Yar Khan Armen Khederlarian East Asia and the Pacific Region Office of the Chief Economist February 2021 Policy Research Working Paper 9551 Abstract This paper studies the effects on international trade from policy changes around the renewal vote and trade flows. the annual tariff uncertainty about China’s Most Favored An (s,S) inventory model generates this behavior and that Nation (MFN) status renewal in the United States prior to variation in the strength of the stockpiling in advance of joining the World Trade Organization. The paper makes the vote is increasing in the storability of goods. Fourth, four main findings. First, in monthly data trade increases the costs associated with within-year trade policy induced significantly in anticipation of uncertain future increases stockpiling reduce entrants’ incentive to operate in a market in tariffs and falls upon renewal. Second, the probability with tariff uncertainty. The results explain why trade may of a tariff increase was perceived to be relatively small, with hold up in advance of a prospective policy change, such as an average annual probability of non-renewal of about 4.5 Brexit or the US-China escalating tariff war of 2018–19, percent. Third, what matters more is the expected future but may fall sharply even if expected tariff increases do not tariff rather than the uncertainty around it. These effects materialize. are identified using within-year variation in the risk of trade This paper is a product of the Office of the Chief Economist, East Asia and the Pacific Region. It is part of a larger effort by the World Bank to provide open access to its research and make a contribution to development policy discussions around the world. Policy Research Working Papers are also posted on the Web at http://www.worldbank.org/prwp. The authors may be contacted at sykhan@worldbank.org. The Policy Research Working Paper Series disseminates the findings of work in progress to encourage the exchange of ideas about development issues. An objective of the series is to get the findings out quickly, even if the presentations are less than fully polished. The papers carry the names of the authors and should be cited accordingly. The findings, interpretations, and conclusions expressed in this paper are entirely those of the authors. They do not necessarily represent the views of the International Bank for Reconstruction and Development/World Bank and its affiliated organizations, or those of the Executive Directors of the World Bank or the governments they represent. Produced by the Research Support Team Taking Stock of Trade Policy Uncertainty: Evidence from China’s Pre-WTO Accession∗ George Alessandria†, Shafaat Yar Khan‡ and Armen Khederlarian§ JEL Classifications: F12, F13, F14 Keywords: Trade policy uncertainty, anticipation, inventories, China shock, Brexit ∗ We are extremely grateful to Costas Arkolakis, Yan Bai, Mark Bils, Dario Caldara, Jeronimo Car- ballo, Doireann Fitzgerald, Zibin Huang, Nuno Limao, Dan Lu, Justin Pierce, Kim Ruhl, Mike Sposi and Joseph Steinberg for numerous comments and suggestions. We also thank seminar participants at the University of Rochester, Johns Hopkins SAIS, SMU, Vanderbilt, virtual International Trade and Macro, the 2019 Federal Reserve Trade Dynamics Workshop, the Spring 2019 Midwest Macroeconomics Meetings, the Spring 2019 Midwest International Trade Meetings, 2019 BOC-Tsinghua PBCSF-UT Con- ference on the Chinese Economy, 2019 Empirical Investigations in International Trade (F.R.E.I.T.), 2020 NBER Summer ITI, and NBER International Trade and Institutions Conference. † george.alessandria@rochester.edu, University of Rochester and NBER ‡ sykhan@worldbank.org, World Bank § akheder2@ur.rochester.edu, University of Rochester 1 Introduction As the world rethinks the benefits of globalization, the path of future trade policy has become increasingly uncertain. This uncertainty requires firms making long-lived decisions to participate in foreign markets to form expectations over the future path of tariffs. Forecasting this path can be challenging as the timing, size, and likelihood of policy changes are all uncertain. Yet firms do form these expectations and move on. In this paper, we show how to estimate the path of expected future tariffs based on the behavior of firms in advance of a possible policy change whose size and timing are known but whose probability is not. We apply these ideas to China’s annual renewal of normal trade relations (NTR) status in the US prior to access to the World Trade Organization (WTO). We have four main findings. First, we find that trade increases significantly in antic- ipation of uncertain future increases in tariffs in monthly data. Second, the probability of a tariff increase is estimated to be relatively small, with an average probability of non- renewal of about 4.5 percent and annual probabilities that range from 2 to 10 percent. Third, the expected future tariff is the primary driver of trade dynamics instead of un- certainty about the path of tariffs. The “wait-and-see” real option force from uncertainty only slightly weakens the incentives to anticipate the future tariff increase. Fourth, we find that costs associated with trade policy induced stockpiling are responsible for a size- able reduction in an entrant’s value and can thus contribute to the finding of relatively low trade in annual data reported in the literature (Pierce and Schott (2016), Handley and Limao (2017), Graziano et al. (2018)). We use the timing of the annual renewal of China’s NTR status and within-year variation in trade flows around this renewal to identify the impact of uncertain future changes in trade policy. Our identification leverages the fact that the NTR status renewal decision was legislated to occur in the summer of each year. Thus, prior to renewal firms faced greater near-term risk about trade policy than immediately after Congress renewed NTR. Using a generalized triple difference approach, we show that trade flows rise when facing a risk of higher tariffs in the months in advance of the renewal decision but then fall off sharply when renewal occurs. Essentially, trade policy risk induced a seasonal component into within-year trade flows that was related to the expected change in trade policy and the ability of products to be stored. This seasonal was eliminated when China joined the WTO. Our findings can be best understood through the lens of an (s,s) inventory model applied to international trade as in Alessandria et al. (2010b). In this model, firms purchase a storable commodity infrequently to economize on a fixed ordering cost and as a buffer in the presence of demand uncertainty. Firms trade off higher inventory costs against lower international transaction costs. Facing an uncertain future increase in 1 tariffs, firms shift the timing of their purchases so they have relatively high purchases and stocks of inventories in advance of the possible tariff increase. Upon a successful renewal and fixed tariffs for the next 12 months, firms already hold large stocks in inventory and hence are less likely to purchase until they have run down their stockpile. These effects are larger for goods for which holding inventories is less costly in the model and the data. When the risk of a tariff increase is eliminated there is no longer an incentive to bunch trade flows in certain times of the year. The finding that prospective future increases in tariffs increase trade stands in contrast to previous findings in the literature because we are using within-year variation in trade flows rather than annual trade flows. Our approach is complementary to other approaches that identify the role of trade policy uncertainty but operates at a different frequency since it is based on within-year variation of firms already active in the export market who are deciding when to send their shipments. This analysis generates a time-varying path of the probability of non-renewal that can then be plugged into models of the export decision. By compounding these probabilities, we find that nearing its access to the WTO in 2001, China’s probability of retaining its MFN status to the US market is much higher than those estimated in other studies such as Handley and Limao (2017). Moreover, equipped with a model that captures the dynamics of trade flows in the presence of uncertainty, we more generally quantify the role of pure uncertainty in the presence of inventory holdings and fixed costs of ordering. In particular, we compare the trade-dampening wait-and-see effect of uncertainty with the trade-boosting effect of an expected tariff hike. We simulate multiple spreads around the same expected tariff increase and decompose the anticipatory growth into the contribution of the first moment and the second moment. The results indicate that the standardized effect of an expected tariff change is 4.4 times the effect of pure uncertainty and almost all the variation in anticipatory import growth is explained by just the expected tariff change. We also show that our new finding about the effect of trade policy uncertainty on within-year trade flows is related to the well-documented fact that annual trade flows - the sum of these monthly trade flows - were relatively low for high tariff gap products before China joined the WTO. Specifically, we use our model to show that the anticipatory de-stocking and stockpiling from TPU entails additional inventory holding costs that increase overall costs and reduce the value of importing from China. In our model, we find that this stockpiling behavior lowers firms’ annual profits by about 3-7 percent for possible tariff hike of 30 percent that would last 1 year. The effects are much larger for smaller firms and suggests the frictions we emphasize could complement the existing explanations on sunk export costs. This paper is most related to early work evaluating the impact of uncertainty on international trade. Starting with Baldwin (1986), Baldwin and Krugman (1989) and Dixit (1989), models with sunk costs of exporting have been employed to argue that 2 uncertainty depresses trade, since entering firms prefer to wait and see how uncertainty resolves. While entry and exit decisions have been shown to be important in interna- tional trade (Roberts and Tybout (1997), Alessandria and Choi (2007)), we focus on the behavior of incumbent firms in the short window before the resolution of uncertainty. More recent work has focused on the impact of Trade Policy Uncertainty (TPU) by considering exporter market participation decisions in the presence of a possible tariff increases.1 In particular, in our model firms stockpile in the months before uncertainty is resolved thereby leading to a rise in trade. We use the rise in trade to study the underlying uncertainty surrounding these events.2 Recent papers have used the structure of models with sunk costs of exporting and found large effects of uncertainty on trade in various episodes of TPU (Crowley et al. (2018), Feng et al. (2017), Handley and Limao (2014)). One of the most studied episode is the one studied in this paper, namely the renewal of China’s MFN status during the 1990s. Although applied tariffs on US imports from China did not change after its accession to the WTO, Pierce and Schott (2016) find that US industries most exposed to the threat of protectionist tariffs experienced large declines in employment and increased imports from China after the threat was eliminated. Handley and Limao (2017), using the structure of a sunk cost model, find that reduced uncertainty accounted for one third of China’s export growth. By comparing trade patterns between 2000 and 2005, their model-implied probability of MFN access reversal is 13%, nearly three times as large as our estimates from within-year trade flows. Our approach is complementary to their approach and instead focuses on high frequency trade patterns, overcoming concerns of confounding long run factors or dynamics. For instance, Alessandria and Choi (2014) find trade grows gradually in the US following a cut in trade costs owing to the slow dynamics of entry, exit, and firm expansion. Our probabilities can be used as inputs to models with an export entry decision. In contrast with this literature, in our framework, pure uncertainty has little impact on trade patterns as anticipation is mostly driven by expected trade cost changes. In this sense, our results are more in line with Steinberg (2019), who finds a minimal impact of trade policy uncertainty on the UK’s aggregate trade due to Brexit. Our framework provides an alternative mechanism to explain why the UK’s trade has not experienced any declines despite the looming threat of Brexit. There is a growing literature that applies inventory models to explain high frequency dynamics of international trade at the producer level or in the propagation of shocks. In Alessandria et al. (2010a), stronger inventory management considerations in interna- tional trade are shown to have contributed to the sudden drop in trade during the Great 1 Caldara et al. (2019) develop a model with sunk export costs but find that any TPU induced trade declines are due to investment adjustments costs and sticky prices. 2 Ruhl (2011) uses a similar framework to determine the expected duration of a worldwide tempo- rary export ban of Canadian beef following the discovery of a cow infected with Bovine Spongiform Encephalopathy. 3 Recession, while in Alessandria et al. (2010b) inventory adjustments explain import and pricing dynamics of retail goods following large devaluations in emerging economies. In Bekes et al. (2017) demand volatility raises the motive for precautionary inventory hold- ings and explains variation in trade lumpiness across French exporter markets. These papers as well as ours build on the non-convexities from fixed ordering or shipment costs, that have been widely documented.3 Our paper is also related to some recent papers that study anticipation of policy changes. Baker et al. (2018) show that households increase their stocks in anticipation of a future sales tax rate increase. Khan and Khederlarian (2019) find de-stocking by US imports from Mexico to upcoming tariff reductions from NAFTA substantially biases estimates of the trade elasticity. Unlike these papers, we study the effects of an uncertain policy change that did not materialize. The rest of the paper is organized as follows. Section 2 lays out a model in which stockpiling in anticipation of a possible tariff rise increases trade before the resolution of uncertainty. We show that the trade boost increases in the probability of the tariff hike. In Section 3 we show that exports from China to the US rose in anticipation of the resolution of China’s MFN status renewal. In Section 4 we simulate the model matching the anticipatory growth of Chinese exports to the US during this episode to determine the probability of MFN status being revoked. In Section 5 we separate the contribution to the anticipatory increase in trade of pure uncertainty (second moment) versus the expected tariff change (first moment). In Section 6 we show how the frictions giving rise to the observed within-year variation in trade flows in higher tariff gap products lower annual profits and provide a complementary explanation for the cross-industry variation in trade flows emphasized elsewhere. In the final section, we conclude. 2 Model: Anticipation to TPU through Inventories While previous work on trade policy uncertainty has focused on firms’ export entry decisions (Handley and Limao (2017), Crowley et al. (2018), Steinberg (2019)), we study how it affects the shipment decisions of incumbent firms. Lumpiness in trade flows is pervasive and there is strong evidence that exporters ship their goods infrequently to economize on the fixed costs of shipments (Alessandria et al. (2010b), Kropf and Saure (2014), Hummels and Schaur (2013), Bekes et al. (2017)). When facing a possible tariff increase, a firm deciding on when to export (import) has strong incentives to expedite their shipments before tariffs might be raised. In this section we describe a model in which imports rise in anticipation of TPU resolution, leading to short-run reversals in 3 See Alessandria et al. (2010b), Kropf and Saure (2014), Blum et al. (2019). 4 trade flows. In particular, we introduce TPU into a standard (s,s) inventory model4 as in Alessandria et al. (2010b), in which firms stockpile before a possible tariff increase. 2.1 Environment We consider a partial equilibrium model of an industry in which goods are storable and a continuum of monopolistically competitive retailers decide whether to import or not every period.5 Ordering entails a fixed shipment cost, causing firms to order infrequent but large shipments. On top of the fixed cost, retailers face demand uncertainty and a one period delivery lag, leading to precautionary inventory holdings. These frictions give rise to a (s,s) policy, where producers run down their inventories to a level s and then replenish it up to s. Retailers are identical except for their history of demand shocks, that determines their current inventory holdings. Let pj,z,t denote the retail prices charged by importer j in industry z and νj,z,t the demand shock in period t. Importers face a CES demand function with the elasticity of substitution σ : cj,z,t = eνj,z,t p− σ j,z,t (1) The variable cost of importing is ωz,t = ω (1 + τz,t ) where τz,t belongs to a finite set of possible tariffs, T . The cost of importing is the same for each firm in an industry and suppliers are assumed to be perfectly competitive, so that the pass-through of the tariff reduction is complete.6 TPU is reflected in the markov process of τt , which has a transition matrix denoted by Πτ . At the beginning of each period retailers observe their inventory holdings, sj,z,t and their demand shock, νj,z,t ∼iid N (0, σν2 ), assumed to 7 be iid across firms and time , and then price their good and decide to import or not. To import, retailers incur a fixed cost8 f . We assume that imported goods cannot be returned, mj,z,t ≥ 0. Because of demand uncertainty, importers will never run down their inventories to zero i.e. sz > 0, and because of the delivery lag, sales can never exceed 4 Other models with durable goods, such as capital or durable consumer goods, display similar antic- ipation effects. We chose an inventory model because inventory dynamics have been proven to be very successful in accounting for the short run dynamics of international trade flows (See Alessandria et al. (2010b), Alessandria et al. (2010a), Charnavoki (2017)). 5 We abstract from general equilibrium considerations since we focus on high frequency dynamics of trade policy. 6 Perfectly competitive suppliers allow us to rule out changes in prices charged by exporters. We test this in the empirical section. 7 The iid demand shock generates variation in the anticipation to a tariff reduction. Without demand shocks the distribution of inventories would be degenerate and the effects would be bigger and lead to permanent oscillations. With perfectly correlated demand shocks all firms would respond equally to the incentives of anticipating the demand shock. 8 We assume that the fixed cost of importing is the same across industries. 5 current inventory holdings: qj,z,t = min[eνj,z,t p− σ j,z,t , sj,z,t ] (2) Assuming the goods in transit (mj,z,t ) depreciate at the same rate, δz , as in the warehouse, the law of motion for the inventories is: sj,z,t+1 = (1 − δz )[sj,z,t + mj,z,t − qj,z,t ] (3) Next, we characterize the optimal policies and the tariff process. To simplify the notation we drop the industry subscript. The firm’s value of adjusting is denoted by V a (s, ν, τ ) and not adjusting by V n (s, ν, τ ). Every period, retailers optimize by choosing V (s, ν, τ ) = max[V a (s, ν, τ ), V n (s, ν, τ )], where: V a (s, ν, τ ) = max q (p, s, ν )p − (1 + τ )ωm − f + (1 + r)−1 EV [s , ν , τ |s, τ ] (4) p,m>0 V n (s, ν, τ ) = max q (p, s, ν )p + (1 + r)−1 EV [s , ν , τ |s, τ ] p are subject to (3) and (2). Solving for the optimal policies generates an (s,s) ordering policy that depends on current inventory holdings and the demand shock, m = m(s, ν, τ ). Similarly, the pricing schedule is characterized by a constant markup over the discounted marginal value of an additional unit of inventory next period, p = σ− σ 1 (1 + r)−1 (1 − δ )Vs (s , ν , τ ). When facing an expected increase in τ , importers trade off importing sooner at the expense of paying the fixed cost today and incurring higher inventory holding costs. In what follows we describe how under different shock processes for tariffs this trade-off leads to different anticipatory dynamics. 2.2 Trade Policy Uncertainty and Stockpiling We introduce TPU into this environment by formulating a non-stationary Markov process in the form of a time-dependent transition matrix, denoted by Πτ t . Allowing importers to anticipate possible tariff changes leads them to stockpile before the resolution of the uncertainty. In line with the empirical application in the next section, we fix the period in which uncertainty is resolved.9 Let mres be the last period before the possible tariff change, so that in period mres + 1 the uncertainty is resolved.   I if t = mres τ Πt = |T | , ˜ τ = (1 − π ) π Π  Π ˜ τ if t = mres 0 1 Conditional on (π, τ ), the key parameters determining anticipation are the fixed cost of ordering and the cost of inventory holding, that is, the interest rate and the depreciation 9 In general, there can be uncertainty about the timing of a possible policy change. However, US Congress voting on the renewal of China’s MFN status took place every year by July and August. For more see section 3.1. Results with an uncertain resolution are presented in the appendix. 6 rate. For now, we calibrate the model with the sole purpose of illustrating its qualitative response to TPU. In Table 1 we describe the parameter values of the model. We set the fixed cost per order to match the Herfindahl-Hirschman (HH) index of 0.32, that is, an average of 3 shipments per year. We calibrate the model at the monthly frequency by √ setting the discount rate equal to 12 0.97 which yields a three percent annual interest rate, close to the average real rate in the US in the 1990s.10 The monthly depreciation rate is set at 2.5% or an annual rate of around 30%. We set the elasticity of substitution equal to 4. Finally, in line with the delivery times between the US and China, the delivery lag is set to be a month and the variance of the taste shock is set at 0.8. These parameters determine a median inventory-sales ratio of 3.64 months. We now show that, conditional on a tariff increase, the magnitude of the anticipatory stockpiling is increasing in the probability of the tariff hike materializing. Initially, trade is tariff-free, i.e. τ1 = 0. In period mres + 1, importers face the possibility of either remaining at 0 or facing a tariff of 10%. Hence, the set of possible set of tariffs is T = {0, 0.10}. Afterwards, the new state is absorbing in the sense that τt = τmres +1 ∀ t > mres + 1 i.e. the tariff level will remain unchanged.11 To study how trade responds to different probabilities of the same tariff increase taking place, we vary transition probabilities in ˜ τ . In particular, importers face either a 20%, 50% or 100% chance of tariffs being Π mres raised to 10%. We assume importers have 12 months to anticipate this event. Figure 1 plots the aggregate industry response of imports. In all cases, the expected tariff increase does not materialize. Imports rise in anticipation of the uncertainty resolu- tion and then drop sharply afterwards. This reversal in trade flows is short-lived. Imports start rising only in the two to three months before the resolution of uncertainty.12 The magnitude of the trade reversals around the time of the uncertainty resolution are clearly increasing in the probability of the tariff rise. However, qualitatively the responses are very similar. Figure 2 illustrates that the anticipatory rise is paralleled by a similarly strong increase in the aggregate inventory-sales ratio. Since importers want to avoid pay- ing possibly higher tariffs, they stockpile so that they begin the possibly high tariff period with a high level of inventory-sales ratio. The inventory sales ratio reaches its peak in the month of uncertainty resolution. With a 50% chance of renewal, the inventory-sales ratio is around 35% above its equilibrium level. Again, the strength of these effects depend on the probability importers assign to the tariff increase. Once, uncertainty is resolved, trade drops temporarily as importers have amassed enough inventories to satisfy their 10 We measure the real interest rate as the gap between the return on a 10-year constant maturity treasury and the CPI inflation rate. From 1990- 2004 this averaged 3.2 percent. Results are robust to a range of interest rates. 11 The results are nearly identical when the tariff is in place for only one year or the firms face repeated annual uncertainty. 12 Before imports start rising, echo-effects lead to temporary drops in imports in month 8. These are due to importers timing their purchases similarly to have enough inventories before the possible increase in tariffs while saving on the fixed ordering cost 7 demand. Finally, note that these dynamics take place in a window of 5 months before and 5 months after the resolution of uncertainty. Figure 3 shows the time-varying (s,s) bands where the firms in the top-left region orders positive quantities. The initial ordering policy is the same as the ordering policy 12 months ahead of the anticipated change. However, there are two notable changes in the ordering policy one month before the anticipated change. First, the s increases indicating an increase in the mass of ordering firms. Secondly, the gap between s and s increases, indicating larger orders.13 Uncertainty over renewal of China’s MFN status was resolved annually for a period of more than 10 years. In this framework, the dynamics driven by anticipation in one year settle before the beginning of next year’s anticipatory dynamics.14 In the next section we show that the high frequency anticipatory dynamics of the US imports from China were similar to those predicted by this model. 3 Seasonal Effects of China’s TPU Episode In this section we show that the annual possibility of tariff hikes during the 1990s induced strong seasonal patterns in China’s exports to the US. Between 1991 and 2000, every year around September, US Congress voted on revoking China’s MFN status. Al- though ex post China’s access to MFN rates was never reversed, especially in the early years, the revocation vote came close to being successful. While previous studies have focused on the long run effects of this episode’s TPU, we exploit the within-year variation of this episode’s tariff risk. Once Congress had voted, MFN rates were secured at least for another 12 months. We find that in the months prior to the voting, exports of products that faced the largest risk spiked. Once the voting had taken place exports plummeted. In section 4 we replicate this seasonal pattern using the model described in section 2 to estimate the probability importers assigned to the event of MFN revocation. 3.1 Background During the 1990s, US imports from China were subject to substantial policy uncer- tainty since China’s MFN status had to be renewed annually (see Handley and Limao (2017), Pierce and Schott (2016), Crowley et al. (2018)).15 In the 1980s the annual re- 13 Ordering policy three months ahead of the change shows that firms economize on the fixed ordering costs by delaying the orders to one month right before the expected increase in tariffs. 14 In Figure 3 we show that the steady state policy functions exactly overlap with the ones 12 months before the anticipated policy change. 15 With the advent of the Cold War, the US applied protectionist non-Normal Trade Relations (NNTR) tariff rates established by the Smoot-Hawley Tariff Act of 1930 to non-market economies. Under the Trade Act of 1974, the US granted MFN access to non-market economies in the presence of (1) a bilateral commercial agreement and (2) the compliance of freedom-of-emigration requirement. The US President 8 newal of China’s MFN status was carried out without any political considerations. But after the events of the Tiananmen Square in 1989, revocation of China’s MFN status gained central attention as a measure of potential sanction. Every year after 1990 and until 2000, the US Congress voted on the disapproval of the President’s renewal of China’s NTR status. Although China’s MFN status was never actually revoked it came close in 1990, 1991 and 1992 when the House passed legislation to revoke it but the Senate failed to sustain the vote. Revocation would have led to the imposition of non-Normal Trade Relations (NNTR) tariff rates, also known as column 2 tariff rates, that on average were 10 times larger than MFN rates. The political process that determined the annual renewal of China’s MFN status was characterized by a relatively fixed calendar. The President renewed China’s status before its expiration on the 3rd of July.16 After the renewal, the Congress had 60 days to consider a disapproval vote on the Presidential renewal. As can be seen in Figure 4 voting would generally take place between the end of July and beginning of August. If such legislation was passed in both the chambers, the President had the right to veto it. In fact, in 1992 President Bush executed this right and the Senate failed to override the veto. Uncertainty resolved only by the end of September and China’s MFN status remained in place. Under the described political process, in any year, uncertainty regarding the renewal of China’s MFN status would be resolved between the months of August and September. 3.2 Empirical Strategy Our identification of the seasonal effects of the uncertainty regarding China’s annual MFN status renewal is based on (1) product specific variation in the tariff risk, and (2) within year variation of the risk. First, we follow the literature and measure the tariff risk as the gap between the prevailing MFN rate and the NNTR rates.17 We define the tariff NNT R MF N risk of a HS-6 product z to be Xz ≡ maxt {ln((1 + τz,t )/(1 + τz,t ))}. We eliminate time variation in Xz,t by taking the maximum over the period to maximize sample size.18 Figure 5 illustrates that the tariff risk was sizeable throughout the entire period. The median deviation from the prevailing MFN rate was above 25 percentage points. However there was little variation over time. Only between 1996 and 1997, when MFN rates fell after the agreements of the Uruguay Round, the gap between NNTR and MFN rates increased. However, Figure 6 illustrates that there was substantial variation in the tariff risk faced across different products. While for a product in the 10th percentile the gap was given authority to waive the second requirement on annual renewable basis, subject to approval by the US Congress. The US and China signed a bilateral commercial agreement in 1980. 16 Only in 1993 there was uncertainty around the execution of the President’s renewal authority. Before being elected, President Bill Clinton announced he would link China’s MFN status to human rights progress, but then went along with the waiver during his presidency. 17 Because NNTR rates were defined in 1930 by the Smoot-Hawley Trade Act, it is argued that product variation in NNTR rates is exogenous to political economy motives in 1990. 18 For some years the NNTR gap is missing. 9 between the MFN and NNTR rate was less than 5pp, applied tariffs of a product in the 90th percentile could have increased by more than 60pp. Second, the fact that the political stages required to revoke China’s MFN status had a fixed calendar presumably allowed importers to anticipate the resolution of uncertainty. Once the process had concluded by September, importers were certain that rates would remain the same at least until the end of July of the following year. Hence, if importers assigned a non-zero probability to the likelihood of revocation, expected tariffs would deviate from the MFN rate only in the months between July and September. In the model of section 2, the possibility of a tariff hike leads importers to anticipate TPU by increasing their imports in the immediacy of the uncertainty resolution. The fixed timing of the uncertainty resolution during this episode provides an excellent laboratory to test the empirical relevance of this effect of TPU. Our empirical strategy follows a triple difference specification that nets out US and China specific seasonality unrelated to the tariff risk by including a reference importer and exporter group of countries and the post-WTO period, when the within year uncer- tainty resolved. As the reference importer we consider the 15 European Union member countries in 1990 (denoted as EU hereafter).19 China’s exports to the EU were granted unconditional MFN status in 1980. As the reference exporter we consider the aggregate exports to the US from the same 15 EU countries, Norway, Switzerland, the Republic of Korea and Japan (denoted as rest of the World - RoW - hereafter). These countries were granted unconditional MFN rates and did not sign a Free Trade Agreement with the US throughout our sample period. The effect of TPU is measured as the treatment effect of a HS-6 product being traded by the US and China relative to the base effect of Xz on the other trade flows not affected by the TPU. Our baseline estimation equation is the following: i,j,z,t ln(vm i,j,z,t −2:m /vm−7:m−5 ) = TPU βm 1{t<2001} 1{i=U S,j =China} 1{m=m } Xz m + P ost βm 1{i=U S,j =China} 1{m=m } Xz m + Others βm 1{m=m } Xz m + γi,t,m + γj,t,m + 1{t<2001} γs,m + εi,j,z,t,m (5) The left hand side of (5) is our baseline dependent variable that captures within year fluctuations in trade flows. We construct a log growth rate of trade for every month m by taking the average of imports of that month and the previous two relative to the monthly average of a previous period, in particular, the average between m − 7 and m − 5. The use of moving averages allows us to smooth out some of the lumpiness in trade flows at 19 These are Austria, Belgium, Denmark, France, Finland, Germany, Greece, Ireland, Italy, Luxem- bourg, the Netherlands, Spain, Sweden, the UK and Portugal. 10 HS-6 level.20 The use of within year growth rates eliminates any confounding factor that varies at annual frequency, such as applied tariff rates. The first term on the right hand TPU side of (5) is our coefficient of interest, βm , namely the treatment effect of TPU on monthly exports from China to the US relative to those in the post-WTO period and other control trade flows. If imports rose in anticipation of TPU resolution, as predicted TPU by the model in section 2, then βm > 0 for the month before Congress voted. The second term of (5) captures the response of exports from China to the US in the post- WTO period relative to the control trade flows. The third term on the right hand side captures the response of the control trade flows, name US imports from ROW and Chinese exports to the EU, to the tariff risk. Finally, we introduce destination-month-year and source-month-year fixed effects, γi,t,m and γj,t,m , to control for source and destination specific seasonality, such as Chinese New Year, that we allow to vary every year. To address concerns of product specific seasonality, such as demand peaks for toys during Christmas, we introduce monthly HS-2 specific fixed effects, γs,m , which we allow to vary in the pre- and post-WTO period. 3.3 Data We use monthly trade flows at the 6-digit level of the Harmonized System (HS) prod- uct classification. US import data is obtained from the Census Bureau and EU import data from Eurostat. Imports are in CIF value of imports for consumption. MFN and NNTR rates at HS-8 product level are from Pierce and Schott (2016). We take the simple mean at the HS-6 level. Our baseline sample period includes the years 1991 to 2000 and 2003 to 2007.21 The baseline sample is restricted to those products that were traded at least once every year between the US and China. We do this because the mechanism we study in this paper abstracts from the entry decision. The balanced sample includes 1,812 HS-6 products. These products account for 95% of the total Chinese exports to the US in 1990, 86% in 2001 and 80% in 2007. In section 3.5 we report the robustness of the baseline results to alternative sample choices. 3.4 Baseline Results In Figure 7 we present the estimates of β ˆT P U for m ∈ {1, 2, ..., 12}.22 There is a distinct pattern in the growth rates of trade flows in response to the tariff risk. By June 20 We take monthly averages because of the lumpiness in trade flows at HS-6 level of aggregation. The results shown in this section are also robust to using a higher level of product aggregation, such as NAICS industry classification. We prefer the HS-6 level since it is standard in the literature. 21 We eliminate 2001 and 2002 from the sample period in our baseline analysis since there seems to be a slight persistence in the seasonal pattern as we show in the robustness section. 22 The precise coefficients are reported in the first column of the different robustness checks reported in Tables 2 to 5. 11 imports start growing significantly with the tariff risk. The effect peaks in July and remains significantly high in August. Growth rates then decline and become significantly negative in November, reaching its trough in January. At its peak (trough), for the median tariff risk (31pp), imports are on average 7% higher (10% lower) than compared to its reference period. The fact that the trough is larger than the peak is consistent with the overall trade dampening effect of the tariff risk documented previously in Pierce and Schott (2016) and Handley and Limao (2017). These results show that throughout the entire year imports from China to the US responded significantly to the threat of facing a tariff hike. US importers anticipated the possibility of a tariff hike by increasing their purchases before the resolution of uncertainty. When the tariff hike didn’t materialize, imports dropped in the beginning of the year. This TPU induced seasonal pattern of US-China trade flows signals that importers indeed assigned a non-zero probability to the non-renewal of China’s MFN status. However, the magnitude of the anticipatory response was rather small.23 P ost others We report the estimates of βm and βm in Figures B.1 and B.2, respectively. In both cases, there is a slightly significant response in some months. While the coefficients Others P ost of βm are suggestive of a certain degree of substitution.; the estimates βm are a little more subtle to interpret. In first place, they indicate that the peak is larger than the trough, again consistent with the relative growth of high risk products after the resolution of uncertainty. Second, the timing is slightly different and does not match the seasonal that would be expected from uncertainty resolution in the months of July and August, since the peak is in October and the trough in April. Finally, it is important to TPU remember that the coefficients on βm are treatment effects of the tariff risk relative to the post-WTO period and identify the seasonal pattern that is exclusive to the period of uncertainty. Next, we show that these results are robust to various choices made. 3.5 Robustness The seasonal pattern induced by TPU documented in our baseline specification is robust to several alternative empirical approaches. Here we document the seasonal pat- tern under alternative choices of references for trade flows, controls form seasonal effects, dependent and independent variables, product samples and sample periods. Alternative Reference Trade Flows. - Table 2 reports the coefficients on exports from China to the US during the uncertainty period under different choices of control trade flows. In column 1 we restrict the sample to US-China trade between 1991 and 2000. Overall the seasonal pattern is very similar to our baseline result. Two main differences stand out. First, coefficients are larger; second, the seasonal pattern is moved forward 23 To provide a comparison, Khan and Khederlarian (2019) estimate short run anticipatory elasticities during the NAFTA phaseouts to be around 4 to 6. Importantly, in the episode studied here tariff changes are uncertain and observed anticipation is the result of underlying expectations. 12 by two months. In column 2 we include Chinese exports to the EU and US imports from the RoW and consider US-China trade relative to those (difference-in-difference). The seasonal pattern is now almost identical in magnitude and timing to our baseline, although the peak is in August instead of July. In the next columns we extend the sample period to include 2003 to 2007. Column 3 considers Chinese exports to the EU and US and column 4 US imports from China and RoW, including the post-WTO difference. While the pattern is present in both cases, it is stronger when considering US imports from China relative to those of EU from China. Column 5 is our baseline result. In column 6 we include the countries that form RoW separately. In column 7 we use all US imports as the reference exporter. Estimates are very similar to our baseline results. Alternative Seasonality Controls. - In Table 3 we relax and strengthen the fixed effects implemented to control for seasonal effects. Column 4 imposes the most restrictive HS6- month fixed effects that are allowed to vary in the pre- and post-WTO period. The coefficient on the peak falls slightly from 0.27 to 0.24 but the trough remains at -0.36. Even under the very restrictive source-year-month-HS2 and source-year-month-HS2 fixed effects in columns 7 and 8, there remains a significant seasonal pattern that aligns well with the response of trade to the within year predicted by the stockpiling mechanism. Alternative Dependent and Independent Variables. - In Table 4 we estimate (5) under alternative dependent variables and formulations of the tariff risk. In columns 2 and 3 we vary the time horizons considered in the calculation of the short run growth rates of imports. In column 4 we consider the rolling growth rate of the last four month relative i,j,t,z i,j,t,z to the previous four months, i.e. ln(vm −3:m /vm−7:m−4 ). In column 5 we introduce a one i,j,t,z i,j,t,z month gap between the two periods, i.e. ln(vm −3:m /vm−8:m−5 ). The seasonal pattern is unchanged, although the size of the coefficients is slightly smaller than our baseline. This suggests that, import growth was more concentrated in a few months before the expected change. In column 4 we address concerns of missing values in the log growth measure, i,j,t,z i,j,t,z 2(vm −2:m −vm−7:m−5 ) using the mid-point growth rate of the same trade flows, i.e. vi,j,t,z i,j,t,z . Results m−2:m +vm−7:m−5 are similar to the baseline, indicating that missing value do not drive our baseline results. In columns 5 and 6 we fix the reference period of the growth measure. In column 5 we take the log of the monthly share of annual imports. The results indicate that the seasonal pattern is driven by significantly smaller imports throughout November to February and a rise in June. Column 7 instead of taking monthly imports uses the 3 month moving average of our baseline dependent variable. The seasonal pattern is unchanged, but the coefficients drop. This is because the reference period is now fixed.24 In column 8 and 9 we estimate (5) using quantities and unit vales instead of value of trade as the dependent variable, respectively.25 In the case of quantities, the trough is slightly smaller and the 24 Importantly when taking the seasonal pattern to the model we will use the same growth measure as in the baseline. 25 Note that the unit values include shipping costs since we do not dispose of EU imports valued at FOB. 13 peak slightly larger than in the case of values, used in the baseline. Consequently, as can be seen in column 9, there is no meaningful response in the unit values. These results indicate that the TPU induced seasonal pattern is driven entirely by changes in quantities traded and that pricing dynamics did not play any role. Finally, in column 10 and 11, we show that the results are robust to using the annual NNTR gap or the NNTR gap in 2001. Alternative Samples. - In columns 2-5 of Table 5 we consider the robustness of the baseline results to different product sample choices. First, in column 2 we exclude HS-6 goods belonging to HS-8 categories that had their MFA quotas lifted before 2005. The coefficients on the trough and peak both drop by around 10%, but remain significant. In column 3 we restrict the sample to be balanced over all years between 1991 and 2007. The coefficient on the trough now increases slightly and the peak remains unchanged. In column 4 we relax the sample selection and include unbalanced goods except in their first and last year throughout the sample. The coefficients drop slightly, but the overall seasonal pattern remains the same. In column 5 we don’t restrict the sample of goods in any way. Although the seasonal remains, it is much attenuated. We interpret this as evidence for new goods being introduced during months when the tariff risk is low, thereby undermining the slump in the trade of incumbent products. Finally, in the last column we extend the sample period to include 2001 and 2002. The seasonal pattern is now smaller in magnitude though still significant. This suggest that the seasonal pattern induced by TPU partially persisted into the early years when uncertainty had already resolved. 3.6 TPU Effects and Product Storability Next we investigate product heterogeneity in the response to the tariff risk and pro- vide evidence for the mechanism that drives anticipation to a possible tariff hike in the model of section 2. In particular, we study the interaction between the TPU-induced seasonality and the degree of storability of a product. Similar to the approach in Khan and Khederlarian (2019), storability is proxied by the observed lumpiness of trade.26 A product specific measure of storability is obtained by predicting the annual inverse HH index of all HS-6 goods the US imported from the 135 RoW countries between 1991 and 2000 net of source-time fixed effects such as distance and source-specific shocks.27 The inverse HH index is the effective number of months in a year with positive orders. More 26 Lumpiness in trade flows can be rationalized by lumpy demand or inventory holdings. As docu- mented by Alessandria et al. (2010b) and Bekes et al. (2017) among others, trade is intensive in inventories and we take the second view. 27 12 The HH index of annual imports of z from i in year t is HHj,z,t = m=1 (vj,z,t,m / vj,z,t,m )2 ∈ [1/12, 1]. Once calculated for all z, t and reference exporter countries, we estimate 1/HHj,t,z = δ0 + δz + δj,t + uj,t,z and then define the degree of storability as 1/HHˆ ˆ ˆ z = δ0 + δz . The source-year fixed effects net out determinants of lumpiness that are unrelated to the product storability. 14 storable products are ordered less frequently and therefore will have fewer months with import flows.28 Through the lens of the model in section 2, more storable products are expected to display stronger responses to TPU. We test this estimating the following equation: i,j,z,t ln(vm i,j,z,t −2:m /vm−7:m−5 ) = TPU βm 1{t<2001} 1{i=U S,j =China} 1{m=m } Xz,t m + HH βm 1{t<2001} 1{i=U S,j =China} 1{m=m } Xz,t × (1/HHz ) m + Others βm 1{m=m } Xz,t m + Others βm 1{m=m } Xz,t × (1/HHz ) m + γi,t,m + γj,t,m + 1{t<2001} γs,m + εi,j,z,t,m (6) Table 6 reports the responses to the tariff risk for the months we identified as the peak and trough response in our baseline estimation. In column three the interaction term is negative in the peak month and positive in the trough, as predicted by the inventory mechanism. Figure 8 further confirms the heterogeneous response throughout the entire year. A product in the 20th percentile of the inverse HH distribution displays a strong response to Xz,t throughout the entire year, larger than the average response from our baseline estimation. For a product in the 80th percentile of the inverse HH distribution the response is small. In the model described in section 2, products that are characterized by monthly inventory-sales ratios close to one display relatively less anticipation to a possible tariff hike. The documented evidence of stronger TPU-induced seasonal dynamics of more storable products is suggestive of the proposed mechanism. 4 Estimation of the Likelihood of MFN Revocation Thus far, we have identified the TPU-induced seasonality in US imports from China during the decade before China’s accession to the WTO. We now use the structure of the model described in section 2 to estimate the likelihood with which importers expected the MFN revocation to take place. In this particular episode, two of the three uncertainty components are observed: (1) the timing of the resolution, and (2) the tariff risk. The probability of revocation is obtained by matching the anticipatory rise and subsequent decline in trade flows before and after the uncertainty resolution while fixing (1) and (2). In contrast with other approaches in the literature, our methodology exploits the within-year variation of the policy risk. This is appealing because it overcomes concerns of confounding long run factors driving trade patterns. In this section we show that (1) 28 In Figure B.3 we report the distribution of our measure of storability over HS-6 products. 15 the probability of revocation was relatively small; (2) it is largest in the early years of the 1990s and drops in the end; and (3) uncertainty played a minor role in driving the anticipatory response relative to the expected downside risk. 4.1 Model Calibration In the model described in section 2, the magnitude of the anticipatory rise and sub- sequent dip in trade depends on the trade-off between two factors. On the one hand, firms want to avoid paying high tariffs in case the MFN status is revoked. On the other hand, firms want to avoid the ordering and holding costs incurred while expediting the purchase order. Higher per shipment costs and lower depreciation rates are associated with more infrequent purchases and a lower inverse HH index. To estimate the likelihood of non reversal we perform simulations of the model under different depreciation rates. Precisely, we classify the 1,812 HS-6 products of our baseline sample into 453 bins of 4 products grouping them according to their mean tariff risk between 1991 and 2000.29 The depreciation rate of each bin is calibrated to match the median inverse HH index of the 4 HS-6 products in the bin.30 More storable goods allow for more stockpiling in anticipation of a possible tariff increase, as documented in section 3.6. We set the fixed ordering cost to be the same in all simulations at the value of 0.095, implying average fixed costs are equal to 7% of average monthly revenues at steady state.31 The rest of the parameters are common across simulations and reported in Table 1. We calibrate the model to the monthly frequency by setting (1 + r)−1 = 0.97(1/12) , to generate mean annual interest rate of 3%, corresponding to the average difference between the 10-year Treasury rate and the realized CPI inflation between 1990 to 2004. By calibrating the model to the monthly frequency we are implicitly setting the delivery lag equal to 1 month. The elasticity of substitution σ is set equal to 4, a standard value in the literature.32 We borrow the value of the variance of the demand shock σν from AKM setting it equal to 0.8. 4.2 Baseline Result The probability of non-renewal of China’s MFN status is obtained by iterating over possible values of π until the seasonal peak-to-trough response to the tariff risk estimated 29 The reason we do not simulate the model for the 1,812 products is computational time. We have also grouped products into bins according to the joint distribution of the tariff risk and their inverse HH index and the results are similar and are available upon request. 30 In section 3.6 we described the calculation of the inverse HH index. Because in each simulation all firms import the same product and face the same tariff risk, we intend the 4 HS-6 products of each bin to be as similar as possible in terms of these two variables. 31 Alternatively, we could have varied the ordering costs across bins and fixed the depreciation rate. Results of this approach are similar to the ones presented here and available upon request. 32 The anticipatory dynamics around the possibility of a tariff hike are almost entirely driven by the costs of ordering and inventory holding and are not sensitive to the elasticity of substitution. 16 in section 3.4 is matched.33 The response is defined as the difference between the antic- ipatory rise and the subsequent slump, i.e. maxm {β ˆT P U }. Our baseline ˆT P U } − minm {β m m estimate of the is estimated to be 0.63 in section 3.4 (column 5 of Table 2). To obtain the model analog of this elasticity we simulate the model for each of the 453 product bins described above. Hence each simulation is characterized by a pair of (X ˜ b , δb ), where b indicates a bin and X ˜ b is the mean tariff risk the bin of HS-6 products faced between 1991 and 2000.34 For each b, we simulate the transition from the steady state without tariffs to an increase in tariffs of Xb that occurs with probability π , common to all bins. The tariff change occurs 12 months from the initial steady state with probability π . After simulating the transition for each bin we generate a dataset with the monthly aggregate trade flows and compute the analog of our baseline dependent variable of section 3, i.e. ln(˜ ˜b,m−5:m−7 ).35,36 We then estimate the model analog of {βm vb,m−2:m /v T P U 12 }m=1 from our 37 baseline estimation equation (5) using the following equation: ln(˜ ˜b,m−5:m−7 ) = vb,m−2:m /v sim βm 1{m=m } X ˜b + b,m (7) m=m We repeat this procedure varying π until we match the response to the tariff risk, that is until maxm {βˆsim } − minm {βˆsim } = 0.63. m m The estimated probability π ˆ that matches the seasonal response to the tariff risk from the model to the one from the empirical analysis is 4.5%. In section A in the Appendix we show that our results are robust to (1) updates or signals about the likelihood of non-renewal as nearing the resolution; and (2) early resolution of the uncertainty. Our baseline estimate is the result of matching the monthly average peak and trough response over the sample period of 1990 and 2000. While uncertainty was resolved mostly between July and August, there was some annual variation. In the next section we estimate the probability of non-renewal for each year between 1991 and 2000 and find a slightly larger average probability of 7% (See Table 7), consistent with the variation in the date of uncertainty resolution.38 In any case, our estimate of the probability of non-renewal is lower than the one obtained by Handley and Limao (2017) in a framework that exploits 33 In previous versions of the paper we matched only the anticipatory rise. While in the model the anticipatory rise and subsequent drop are almost symmetric, in the data the slump is slightly larger than the rise, consistent with the annual trade dampening effect documented in Pierce and Schott (2016) and Handley and Limao (2017). Therefore, we prefer to match both the rise and drop. Results matching only the rise yield a slightly smaller probability and available upon request. 34 In what follows, tildes on top of variables indicate that they are used or from model simulations. 35 This implies that there are no general equilibrium effects through movements of aggregate price indexes and substitution across industries. We believe that at relatively high frequency this assumption is a reasonable simplification. 36 We simulate 24 months, but only keep months 6 to 17 to construct the data set. As can be seen in Figure 1 the trade dynamics generated by a possible tariff hike are sufficiently short lived not to affect the dynamics in successive year of TPU shocks. 37 It is not necessary to control for seasonality since these are absent in the model. 38 The bottom row of Table 7 provides the probability estimate that corresponds to the case when the post-WTO difference is excluded; that is, column 2 of Table 2. 17 the sensitivity of firms’ market entry decision to TPU.39 While incumbents’ ordering decisions and subjective beliefs might not necessarily be the same as those firms deciding to enter a new destination market, in section 6 we show how these results might be reconciled given the loss caused by the TPU-induced seasonality. 4.3 Annual Probabilities The estimated baseline probability of 4.5% reflects the average probability assigned to the non-renewal of China’s MFN over the entire period. However, uncertainty varied over the decade of the 1990s. We estimate annual probabilities by estimating the annual response to the tariff risk and then applying the probability estimation approach from above to the year-specific estimates of the response to the tariff risk. Precisely, we estimate the following equation:40 i,j,z,t ln(vm i,j,z,t −2:m /vm−7:m−5 ) = TPU βm,t 1{i=U S,j =China} 1{m=m } 1{t=t } Xz,t m t + βm 1{m=m } Xz,t + γi,t,m + γj,t,m + γz,m + εi,j,z,t,m (8) m t Columns 1 and 2 of Table 7 reports the months of the peak and trough response in each year. The results how that in 9/11 of years the peak response takes place between June and September, aligning well with the timing of US Congress voting. Similarly, the trough mostly takes place between January and February, aligning well with the timing of the slump predicted by the model given the moving average growth formulation. Column 3 reports the estimates of the annual maxm {β ˆT P U } and column 4 the ˆT P U } − minm {β m m model implied probabilities. There are three major takeaways from the variation in the estimated probabilities. First, in all years except 1992 we find a non-zero probability of non-renewal.41 Second, the probability rises in 1990 and reaches its peak in 1995 and declines in the end of the decade. Third, the annual probabilities of non-renewal are in line with the contemporaneous political developments. The probability jumps up to around 8% in 1990, when the US Congress came closest to reversing the President’s renewal vote. The probability rises again in 1995 to its maximum value of 10.22% coinciding with President Clinton’s administration and Democratic majority in US Senate and House of Representatives. During his Presidential campaign Clinton had announced he would link China’s MFN status to its human rights record. However after being installed he opted to renew the waiver. After 1997 the probability of non-renewal drops and by 2000 is at its second lowest 4.83%. Figure 9, compares our measure of TPU based on 39 Handley and Limao (2017) find the equivalent probability to be around 13%. 40 Note that in this exercise we use the annual tariff risk X )z, t instead of its maximum. 41 In 1992 uncertainty did not resolve by July as in most other years (See Figure 4) as voting continued into October (See Figure 4). In contrast, our approach relies on the resolution being relatively fixed over time. 18 trade patterns from the newspaper article counts measure by Pierce and Schott (2016). Our estimated probability differs from theirs in the relatively higher probability during Clinton’s administration and the drop in probability in 2000, when the US President signed into law China’s permanent MFN status conditional on joining the WTO. Further, we use our estimated annual probabilities to infer the time-varying likelihood of China maintaining MFN status for the years until 2001 when the process of annual renewal ended with China’s WTO accession. We can infer this likelihood by compounding our estimated annual probability of not revoking China’s MFN status in the years prior to 2001. Figure 10 contains the result of this calculation. We see that, because of the ˆ , the probability in 1990 of China enjoying MFN benefits during overall relatively low π the uncertain period was around 50%. This probability grows as China MFN status is renewed annually until its WTO accession. This exercise illustrates that the probability of continued access to MFN rates 2 years before China obtained the PNTR was already around 90%. 4.4 Role of Pure Uncertainty In this section we separate the effects of a change in expected tariffs from the effects of uncertainty about the change. Theoretically, the real options literature suggests that un- certainty about future states of the world acts as a deterrent to irreversible investments.42 Irreversibility of investments in such models necessitates a large gap between expected benefits and costs to incentivize entry which creates action and inaction regions within the state space. However, the importance of pure uncertainty depends on the sensitivity of these cutoffs and the distribution of firms around it. Both of these factors make the role of pure uncertainty dependent on the calibration and the nature of the uncertainty shock. Since the real options models have a similar stopping time formulation as our inventory model, we investigate the role of pure uncertainty by simulating the certainty equivalent of the expected tariff change. Specifically, we give each bin b a change in tariffs equal to πˆX˜ b with certainty and estimate equation (7) with the simulated data. For a certain change of π ˆX ˆsim is 0.82. This is higher than the estimate of ˆsim } − minm {β ˜ b , the maxm {β m m} 0.63 when the tariffs are expected to increase by X ˜ b with a probability of π ˆ . Therefore, when we keep the expected increase in tariffs the same, we find that the uncertainty depresses the seasonal coefficient by 23% on average. The negative effect of uncertainty is in line with the wait-and-see effect widely reported in the literature. It arises because the chance of the tariff rate remaining unchanged makes an advanced payment of the fixed ordering cost sub-optimal. To illustrate the mechanism, consider the ordering cutoffs in the uncertain and certain 42 See Bernanke (1983), Dixit (1989), Pindyck (1991) and more recently Kellogg (2014). 19 case in Figure 11.43 The top-left region is the ordering region i.e. firms order if they have fewer goods in inventories or higher demand shock. The ordering region in the uncertain case is smaller than the inaction region with the same expected but certain tariff change. The region between the two curves is the inaction region due to pure uncertainty. In this example, the expected tariff change is much larger than the ones face by imports from China during the 1990s when the maximum expected tariff increase was around 8%.44 This explains the minor difference in the coefficient of β ˆ of the certainty equivalent. In the next section we study how pure uncertainty affects the response to tariff risk more generally in this setting. 5 Pure Uncertainty in Inventory Models In this section we explore the role of pure uncertainty against the expected tariff more generally in the model. By considering multiple spreads around the same expected tariff changes, two features of the anticipatory response to possible tariff hikes are illus- trated. In the first place, the import growth is increasing in the expected tariffs, that is, for larger expected tariff increases, the anticipatory increase in imports relative to the subsequent dip is larger. Secondly, the variance or the uncertainty component becomes relatively more important in dampening the trade seasonal for larger expected tariff hikes. Because the implied probabilities (expected tariff hikes) we found in 4.4 were low, the findings in this section explain why uncertainty contributed relatively little in driving the anticipatory rise to the NNTR threat. In all simulations, the parameter values are held constant and the same as in Table 1, with exception of the expected tariff change. For the rest of the section, the combina- tion of future tariff and its probability is indexed by n and tilde denotes the simulation counterpart of the data variables in Section 3. We consider multiple expected tariff in- creases ranging from 1pp to 20pp by varying the probabilities, π ˜n and the tariff changes, X˜ n , in order to have multiple spreads around the same expected change. For example, an expected tariff increase of 10pp can occur through a 25% chance of a 40pp increase or through a 50% chance of 20pp increase. We then analyze the anticipatory response through different estimation specifications. The growth for each simulation is plotted in Figure 12. As expected, the response is increasing but is also non-linear over π ˜n. ˜n X Moreover, conditional on an expected tariff change, the import growth is increasing in the probability of the change. We formalize these findings45 through different estimation specification that disentan- 43 For demonstration purpose, Figure 11 plots the ordering cutoffs when the tariff change is 40% in expectation. The solid blue line shows cutoffs when tariffs are scheduled to rise by 40% with certainty. Dashed red line plots the case when with equal chance tariffs stay the same or increase by 80%. 44 ˜ b } = 10% × 80. ˆ × maxz {X π 45 We focus on simulations of a quantitative version of the model rather than on a simplified analytical 20 gle the role of the first, E(X ˜n) = π ˜n) = π ˜ n , and second moment,46 V ar(X ˜n X ˜n (1 − π ˜ 2, ˜ n )X n of the tariff hike. Results are presented in Table 8. In all regression the left hand side variable is the import change around the resolution of uncertainty as defined in previous sections. In the first and third column, we estimate the linear relationship between the expectations-induced seasonal and the expected tariff change. As expected the relation- ship is positive. This is the trade boosting effect of anticipation. Moreover, it explains the majority of the variation as can be seen in a very high R2 . In column 4 we include the square of the expected tariff change. The negative coefficient on the square term indicates that the trade boom is decreasing in the expected tariff change. Further, the R2 increases and explains 87% of the variation, highlighting the importance of the first moment in explaining the anticipatory response. In column two and five we introduce the pure uncertainty or variance term into the estimation. In both cases the coefficient on the variance is negative. This is the trade dampening effect. In column 2, we standardize all variables for ease of interpretation. The effect of the first moment is 2 times larger than that of the second moment. In column 5, including the first moment, the non-linear term and the variance, all the variation in the anticipatory trade response is captured i.e. R2 is 100%. Through the lens of an (s,s) inventory model, in section 4 we found that US importers assigned a relatively low probability to the non-renewal of China’s MFN status. In this section, we demonstrated that in this model and for the relevant expected tariff change uncertainty played a minor role in importers’ behavior and that anticipation was close to linear. However, when expected tariff changes become large stockpiling effects flatten out and uncertainty strongly depresses policy-induced seasonal in trade. 6 Stockpiling Effect on Annual Trade Flows We now show that the forces giving rise to the within-year anticipatory stockpiling from trade policy uncertainty will also contribute to the low volume of annual trade flows, which has been the focus of prior empirical work. We first discuss the evidence that US imports from China of high tariff gap products grew relatively fast with China joining the WTO and shifted to much more stable trade within-year trade flows. We then explain how in our baseline model of section 2, the seasonal stockpiling induced by the TPU raises inventory holding cost and lowers profits, which will ultimately reduce trade. We explore these links by measuring the decline in firm value with the tariff gap and risk. We explicitly consider how various modeling assumptions about firm heterogeneity and model to enhance the understanding of the main results of the paper, namely the probability of non- renewal of China’s NTR status. 46 The formula for variance is determined by considering the tariff change as a Bernouli process where the only two outcomes are a tariff staying zero with probability (1 − π ˜i ) or increasing to Xz with probability π˜z . 21 operating costs increase the elasticity of firm-value to the tariff gap. To set ideas on how the tariff gap is related to Chinese exports to the U.S., we follow Handley and Limao (2017) and Pierce and Schott (2016) by estimating how aggregate annual trade flows depend on the tariff gap. The yearly results from 1992 to 2007 are reported in Figure 13 and the impact from the change from 2000 to 2005 is in Table 9. We see clearly that the coefficient is rising over time suggesting that these tariff gaps are becoming less important as imports of high tariff gap industries grow faster than low tariff gap industries. In the table we report the elasticity of the change in exports to the tariff gap is about 0.48; thus, the volume of exports from China of a product with a 10 percent tariff gap grew 4.8 percent faster than an industry with no tariff gap. Recall, we also found that trade flows of this same product become more stable within the year with trade flows in renewal months falling about 3.0 percent and post-renewal months growing by about 3.3 percent. Combining these two results we find that trade in the post-renewal months would grow about 8.1 percent compared to about 1.8 percent in the renewal months. To show how our model can generate some of the low trade volume over the year, we now show that the value of entering and importing is falling in the tariff gap and risk. To separate the impact of near-term risk from the more distant, and repeated, risks emphasized by Handley and Limao (2017) we consider how being exposed to just one annual cycle of risk affects the firm’s value. Specifically, we calculate the proportional change in firm value between a firm facing risk (τ, π ) and no risk as, EV−12 (0; τ, π ) − EV (0; 1, π ) ∆V (τ, π ) = (1 − β )EV (0; 1, 0) where EV−12 (0; τ, π ) and EV (0; 1, π ) are the values of entering the market with no in- ventories (first state variable), a tariff gap of τ or zero 12 months before the uncertainty, measured by π , resolves, respectively.47 To concentrate on the short-run risk, we assume that any increase in tariff only lasts one year and that after that year there is free trade.48 We scale the difference in firm value by the annual flow value of firm with no tariff risk. The annual discount factor is denoted by β = (1 + r)−1 . In essence, ∆V (τ, π ) is the pro- portional loss in the flow value of the firm facing one year of possible tariff risk relative to the flow value without uncertainty. Figure 14 plots the change in the value of importing, ∆V (τ, π ), against the gross tariff gap, 1 + τ given two non-renewal probabilites, π , for the product with the median storability. The first non-renewal probability of 4.5 percent is from our estimate for the entire pre-WTO period. Going from 0 to a 40 percent tariff lowers firm value by about 2 percent. The second value of the probability is 13.5 percent, quite close to the value 47 With no tariff gap the expected value does not depend on the probability of non-renewal. 48 If the tariff change was permanent then the change in firm value would roughly be 30 times larger than what we report. 22 from Handley and Limao (2017), and lowers firm value up to nearly 7 percent with a 40 percent tariff. Overall, the value from entering is falling with the expected tariff gap. For a fixed probability of non-renewal, the loss in firm value increases with the tariff gap, but a at a decreasing rate as the wait-and-see mechanism becomes stronger with a higher tariff gap. Our analysis so far is likely to understate the reduction in firm value from the increased inventory costs from tariff risk since it ignores both the costs firms face to operate in foreign markets and firm heterogeneity. In terms of operating costs, since Das et al. (2007) nearly all empirical estimates of export participation models find substantial flow operating costs.49 To explore the impact of this margin we introduce a monthly operating cost equal to 10 percent of average sales in a product with no tariff gap. The middle line in Figure 14 shows this makes the value of importing much more elastic. We have also abstracted from any sources of persistent firm heterogeneity. It is well-known that this tariff risk is more of a concern for smaller firms. To capture this effect we explore the change in value for a firm whose demand is on average 25% lower than the size of the average firm and also faces a fixed operating cost. We compare the value of a small firm with tariff risk to a small firm with no tariff risk and find this makes profits around 3 times more elastic. Overall, for a 10 percent tariff gap we find trade is 4.8 percent lower in the data while our model suggests that the value of entering is 1 to 3.5 percent lower. Lower profits will certainly discourage entry, or encourage exit, but the size of the effect will depend on how many firms are at the margin and their characteristics. 7 Conclusion The aim of this paper is four-fold. First, we show that uncertain future changes in tariffs have sizeable effects on trade flows in the interval before and after these proposed policy changes even when no change in tariff is realized. Second, we show how to use these trade dynamics through the lens of a standard (s,s) inventory model to identify the probability distribution of future trade policy. Third, we demonstrate that these frictions give rise to more costly inventory holdings, lowering firm value of importing and accounting for some of the cross-sectional dampening of trade flows. Finally, we show that there is valuable information in high-frequency trade flows that is hidden by the common practice of annual aggregation. China’s annual US NTR renewal provides the ideal setting to achieve these aims. In models with storable goods and fixed ordering costs, incumbent importers anticipate uncertain future trade policy changes by increasing their purchases before a possible policy change. Given two possible policy outcomes, the magnitude of anticipatory dynamics 49 This fixed cost is different from ordering cost as it is paid regardless of the ordering behavior. 23 depend on three components of uncertainty, (1) the size of the policy change, (2) its probability, and (3) the amount of time until the uncertainty resolution. The features of China NTR fixes the timing and size of the policy change good-by-good and allows us to use the model to estimate the probability of the policy change. We find a lower mean probability of non-renewal than elsewhere but year-to-year variations that match up well with some other qualitative measures. Importantly, we show that the increase in trade flows of high tariff gap products documented elsewhere also coincided with a substantial change in the way that those goods were ordered through the year. We also use the model to distinguish between the role of pure uncertainty and the level-effect of the expected tariff change. Even though the “wait-and-see” effect due to pure risk is present in the (s,s) model, its relative contribution is shown to be quite small relative to the first moment of the policy change. A benefit and limitation of our approach to identify the path of future trade policy is that it hinges on a relatively short-run dynamic decision on the timing of purchases. As the frictions from trade and inventory costs lead importers to hold 3-4 months of imported inventories, future trade policy outside this window has almost no effect on ordering behavior. Thus our approach can be applied to numerous other episodes to estimate the near term path of policy. For instance import decisions soon after the Trump election can help identify the expected tariff in 2017. Likewise, trade and inventory flows in Britain and the EU provide insights to the expected date of Brexit. There have been multiple rounds of precautionary stockpiling in advance of key possible exit dates. We can also extract useful information about the expected spread of COVID-19 from trade flows (Alessandria et al. (2020)) or even consumer shopping behavior. To learn about the longer-run path of trade policy, it will be useful to consider more durable investments such as exporting or FDI as in Alessandria and Mix (2018). Ruhl and Willis (2017) find that the expected duration of exporting of a new exporter is only about three years compared to 9 years for a continuing exporter and so perhaps by leveraging these different horizons we can recover a longer path of future trade policy. Of course, these alternative approaches must remain consistent with the information recovered using the approach here. Indeed, our estimates can be used as inputs into models with alternative margins that could be affected by TPU. Fortunately, our model is easily modified to include the decision to enter markets. Finally, our results provide a mechanism to explain why trade has held up fine in advance of a future policy change such as Brexit. Likewise, trade may not fall in the presence of an increase in tariffs provided they are expected to escalate further as in the case of the US-China trade war of 2018-19. Our results suggest that trade could fall off sharply following a possible increase in tariffs that is unrealized owing to an inventory overhang, although general equilibrium considerations could mitigate this effect. Indeed, revisiting these findings in a general equilibrium framework would be useful to explore 24 the effects of trade policy uncertainty on the aggregate economy. 25 References Alessandria, George and Carter Mix, “Trade Policy is Real News: An Analysis of Past, Present, and Future Trade Costs,” 2018. and Horag Choi, “Do Sunk Costs of Exporting Matter for Net Export Dynamics?,” The Quarterly Journal of Economics, 2007, 122(1), 289–336. and , “Do falling iceberg costs explain recent U.S. export growth?,” Journal of International Economics, 2014, 94 (2), 311–325. , Joseph Kaboski, and Virgiliu Midrigan, “The Great Trade Collapse of 2008-09: An Inventory Adjustment?,” IMF Economic Review, 2010, 58, 254–294. , , and , “Inventories, lumpy trade, and large devaluations,” American Economic Review, 2010, 100(5), 2304–2339. , Shafaat Y. Khan, and Armen Khederlarian, “Stockpiling and the Expected Pandemic: China’s Trade of PPE,” 2020. Baker, Scott, Lorenz Keung, and Stephanie Johnson, “Shopping for Lower Sales Tax Rates,” 2018. Baldwin, Richard, “Hysteresis in Trade,” MIT mimeo prepared for 1986 NBER Sum- mer Institute, April 1986, 1986. and Paul Krugman, “Persistent Trade Effects of Large Exchange Rate Shocks,” The Quarterly Journal of Economics, 1989, 104 (4), 635–654. Bekes, Gabor, Lionel Fontagne, Balazs Murakozy, and Vincent Vicard, “Ship- ment Frequency of exporters and demand uncertainty: An inventory management ap- proach,” Review of World Economics, 2017, 153, 779–807. Bernanke, Ben S., “Irreversibility, Uncertainty, and Cyclical Investment,” Quarterly Journal of Economics, 1983, 98(1), 85–106. Blum, Bernardo, Sebastian Claro, Kunal Dasgupta, and Ignatius Horstmann, “Inventory Management, Product Quality, and Cross-Country Income Differences,” American Economic Journal: Macroeconomics, 2019, 11(1). Caldara, Dario, Matteo Iacoviello, Patrick Molligo, Andrea Prestipino, and Andrea Raffo, “The Economic Effects of Trade Policy Uncertainty,” 2019. Charnavoki, Valery, “Retail Sales of Durable Goods, Inventories and Imports after Large Devaluations,” 2017. Crowley, Meredith, Ning Meng, and Huasheng Song, “Tariff scares: Trade pol- icy uncertainty and foreign market entry by Chinese firms,” Journal of International Economics, 2018, 114, 96–115. Das, Sanghamitra, Mark J. Roberts, and James R. Tybout, “Market entry costs, producer heterogeneity, and export dynamics,” Econometrica, 2007, 75 (3), 837–873. 26 Dixit, Avinash, “Entry and Exit Decisions under Uncertainty,” Journal of Political Economy, 1989, 97(3), 620–38. Feng, Ling, Zhiyuan Li, and Deborah Swenson, “Trade Policy Uncertainty and Ex- ports: Evidence from China’s WTO Accession,” Journal of International Economics, 2017, 106, 20–36. Graziano, Alejandro, Kyle Handley, and Nuno Limao, “Brexit uncertainty and trade disintegration,” NBER WP, 2018, 25334. Handley, Kyle and Nuno Limao, “Trade Investment under Policy Uncertainty: The- ory and Firm Evidence,” American Economic Journal: Policy, 2014. and , “Policy uncertainty, trade, and welfare: Theory and evidence for China and the United States,” American Economic Review, 2017, 107(9), 2731–2783. Hummels, David and Georg Schaur, “Time as a Trade Barrier,” American Economic Review, 2013, 103(7), 2935–2959. Kellogg, Ryan, “The Effect of Uncertainty on Investment: Evidence from Texas Oil Drilling,” American Economic Review, 2014, 104(6), 1698–1734. Khan, Shafaat Y. and Armen Khederlarian, “How Does Trade Respond to Antic- ipated Tariff Changes? Evidence from NAFTA,” Working Paper, 2019. Kropf, Andreas and Philip Saure, “Fixed Cost per Shipment,” Journal of Interna- tional Economics, 2014, 92, 166–184. Pierce, Justin and Peter Schott, “The surprisingly swift decline of US manufacturing employment,” American Economic Journal, 2016, 106(7), 1632–1662. Pindyck, Robert S., “Irreversibility, Uncertainty, and Investment,” Journal of Eco- nomic Literature, 1991, 29(3), 1110–48. Roberts, Mark J. and James R. Tybout, “The Decision to Export in Colombia: An Empirical Model of Entry with Sunk Costs,” American Economic Review, 1997, 87(4), 545–64. Ruhl, Kim, “Trade dynamics under policy uncertainty,” American Journal of Agricul- tural Economics: Papers and Proceedings, 2011, 93 (2), 450–456. Ruhl, Kim J. and Jonathan L. Willis, “New Exporter Dynamics,” International Economic Review, 2017, 58 (3), 703–726. Steinberg, Joseph, “Brexit and the macroeconomic impact of trade policy uncertainty,” Journal of International Economics, 2019, 117, 175–195. 27 Table 1: Moments and Parameters for Experiments and Baseline Simulation Parameter Value Source (1 + r)−1 Annual Discounting factor 0.97 U.S. Real interest rate in 90s σ Elasticity of Substitution 4 Literature f Fixed Cost Ordering 0.095 Match HH index σν Std Dev of Taste Shocks 0.8 AKM δ Annual Depreciation Rate 30% AKM Moments HH Index 0.32 75th pctile - Imports from China Median Inventory-Sales 3.64 months Mean(Fixed Cost/Revenue) 6.9% Note: Real interest rate measured as 10-year Treasury Rate minus observed CPI inflation. 28 Table 2: Seasonal Effect of TPU - Control Trade Flows i,j,t,z i,j,t,z Dep. Var. ln(vm −2:m /vm−7:m−5 ) Period 1991-2000 1991-2000,2003-07 Sample Pooled Separate All All except US from China Pooled China to US, EU China, RoW to US (Baseline) RoW Countries countries Baseline RoW (1) (2) (3) (4) (5) (6) (7) (8) 1{m=1} × Xz,max -0.56∗∗∗ 1{U S,China} -0.42∗∗∗ 1{U S } -0.43∗∗∗ 1{China} -0.24∗∗∗ 1{U S,China} -0.36∗∗∗ -0.33∗∗∗ -0.38∗∗∗ -0.42∗∗∗ (0.09) (0.08) (0.09) (0.09) (0.09) (0.09) (0.08) (0.08) 1{m=2} × Xz,max -0.70∗∗∗ 1{U S,China} -0.41∗∗∗ 1{U S } -0.42∗∗∗ 1{China} -0.21∗∗ 1{U S,China} -0.33∗∗∗ -0.27∗∗∗ -0.35∗∗∗ -0.35∗∗∗ (0.10) (0.07) (0.09) (0.10) (0.09) (0.09) (0.09) (0.09) 1{m=3} × Xz,max -0.63∗∗∗ 1{U S,China} -0.35∗∗∗ 1{U S } -0.30∗∗∗ 1{China} -0.12 1{U S,China} -0.21∗∗ -0.21∗∗ -0.22∗∗ -0.19∗∗ (0.10) (0.08) (0.10) (0.10) (0.09) (0.09) (0.09) (0.09) 1{m=4} × Xz,max -0.42∗∗∗ 1{U S,China} -0.17∗∗ 1{U S } -0.06 1{China} 0.01 1{U S,China} -0.01 -0.01 0.01 0.02 (0.09) (0.08) (0.10) (0.10) (0.10) (0.10) (0.09) (0.09) 1{m=5} × Xz,max -0.16∗ 1{U S,China} 0.04 1{U S } 0.09 1{China} 0.08 1{U S,China} 0.12 0.14∗ 0.13 0.14∗ (0.08) (0.08) (0.09) (0.09) (0.09) (0.08) (0.08) (0.08) 1{m=6} × Xz,max 0.16∗∗ 1{U S,China} 0.28∗∗∗ 1{U S } 0.27∗∗∗ 1{China} 0.20∗∗ 1{U S,China} 0.26∗∗∗ 0.22∗∗∗ 0.26∗∗∗ 0.23∗∗∗ (0.07) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) 1{m=7} × Xz,max 0.28∗∗∗ 1{U S,China} 0.28∗∗∗ 1{U S } 0.36∗∗∗ 1{China} 0.18∗∗ 1{U S,China} 0.27∗∗∗ 0.23∗∗∗ 0.28∗∗∗ 0.27∗∗∗ 29 (0.08) (0.08) (0.09) (0.09) (0.08) (0.08) (0.08) (0.08) 1{m=8} × Xz,max 0.42∗∗∗ 1{U S,China} 0.33∗∗∗ 1{U S } 0.29∗∗∗ 1{China} 0.11 1{U S,China} 0.19∗∗ 0.13 0.20∗∗ 0.17∗∗ (0.09) (0.07) (0.09) (0.09) (0.08) (0.08) (0.08) (0.08) 1{m=9} × Xz,max 0.46∗∗∗ 1{U S,China} 0.23∗∗∗ 1{U S } 0.15 1{China} 0.04 1{U S,China} 0.08 0.08 0.08 0.06 (0.10) (0.08) (0.10) (0.10) (0.09) (0.09) (0.09) (0.09) 1{m=10} × Xz,max 0.50∗∗∗ 1{U S,China} 0.19∗∗ 1{U S } 0.01 1{China} -0.10 1{U S,China} -0.06 -0.05 -0.06 -0.07 (0.10) (0.08) (0.09) (0.10) (0.09) (0.09) (0.09) (0.09) 1{m=11} × Xz,max 0.22∗∗∗ 1{U S,China} -0.02 1{U S } -0.11 1{China} -0.17∗ 1{U S,China} -0.18∗∗ -0.17∗ -0.17∗∗ -0.19∗∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{m=12} × Xz,max -0.14∗ 1{U S,China} -0.17∗∗ 1{U S } -0.27∗∗∗ 1{China} -0.22∗∗∗ 1{U S,China} -0.28∗∗∗ -0.26∗∗∗ -0.29∗∗∗ -0.30∗∗∗ (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) Peak-to-Trough 1.20∗∗∗ 0.75∗∗ 0.79∗∗∗ 0.44∗∗∗ 0.63∗∗∗ 0.56∗∗∗ 0.66∗∗∗ 0.69∗∗∗ Observations 185372 586808 579389 599145 892169 1512037 900062 880794 Adjusted R2 0.045 0.061 0.104 0.067 0.087 0.075 0.070 Note: Regressions of column 1 includes δt,m , column includes δs,t,m δi,t,m , δj,t,m , 1{t<2001} × δs,m , regressions of column 2,4 and 5 include δi,t,m , δj,t,m , 1{t<2001} × δs,m . We omit all estimates except the ones of our interest. In our baseline, the RoW countries are the 15 EU coun- tries, Norway, Switzerland, South Korea and Japan. In the last two columns we define the RoW to be all countries and all the non-baseline countries, respectively. The is obtained by taking maxm {β ˆT P U }. Standard errors in parentheses are clustered at HS6, * p < 0.05, ˆT P U } − minm {β m m ** p < 0.01, *** p < 0.001. Table 3: Seasonal Effect of TPU - Different Fixed Effects i,j,t,z i,j,t,z Dep. Var. ln(vm −2:m /vm−7:m−5 ) (1) (2) (3) (4) (5) (6) (7) (8) 1{U S,China} 1{t<2001} 1{m=1} × Xz,max -0.36∗∗∗ -0.36∗∗∗ -0.39∗∗∗ -0.36∗∗∗ -0.33∗∗∗ -0.28∗∗∗ -0.19∗ -0.19∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) (0.11) (0.11) 1{U S,China} 1{t<2001} 1{m=2} × Xz,max -0.33∗∗∗ -0.31∗∗∗ -0.34∗∗∗ -0.35∗∗∗ -0.31∗∗∗ -0.25∗∗∗ -0.21∗ -0.23∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) (0.12) (0.12) 1{U S,China} 1{t<2001} 1{m=3} × Xz,max -0.21∗∗ -0.21∗∗ -0.21∗∗ -0.20∗∗ -0.18∗∗ -0.11 -0.18 -0.19 (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) (0.12) (0.12) 1{U S,China} 1{t<2001} 1{m=4} × Xz,max -0.01 -0.03 -0.02 -0.01 0.01 0.09 -0.03 -0.024 (0.10) (0.10) (0.10) (0.10) (0.09) (0.09) (0.13) (0.13) 1{U S,China} 1{t<2001} 1{m=5} × Xz,max 0.12 0.10 0.09 0.09 0.13 0.19∗∗ -0.04 -0.02 (0.09) (0.09) (0.09) (0.10) (0.09) (0.08) (0.11) (0.11) 1{U S,China} 1{t<2001} 1{m=6} × Xz,max 0.26∗∗∗ 0.25∗∗∗ 0.22∗∗ 0.23∗∗ 0.25∗∗∗ 0.26∗∗∗ 0.13 0.14 (0.08) (0.08) (0.09) (0.09) (0.08) (0.08) (0.10) (0.10) 1{U S,China} 1{t<2001} 1{m=7} × Xz,max 0.27∗∗∗ 0.27∗∗∗ 0.24∗∗∗ 0.24∗∗∗ 0.27∗∗∗ 0.23∗∗∗ 0.22∗∗ 0.23∗∗ (0.08) (0.08) (0.09) (0.09) (0.09) (0.08) (0.11) (0.11) 1{U S,China} 1{t<2001} 1{m=8} × Xz,max 0.19∗∗ 0.19∗∗ 0.16∗ 0.12 0.18∗∗ 0.11 0.21∗ 0.22∗∗ 30 (0.08) (0.09) (0.09) (0.09) (0.09) (0.08) (0.11) (0.11) 1{U S,China} 1{t<2001} 1{m=9} × Xz,max 0.08 0.08 0.10 0.04 0.08 0.03 0.12 0.13 (0.09) (0.09) (0.09) (0.10) (0.09) (0.09) (0.12) (0.12) 1{U S,China} 1{t<2001} 1{m=10} × Xz,max -0.06 -0.06 -0.03 -0.06 -0.044 -0.05 0.05 0.04 (0.09) (0.09) (0.10) (0.10) (0.09) (0.09) (0.11) (0.11) 1{U S,China} 1{t<2001} 1{m=11} × Xz,max -0.18∗∗ -0.17∗ -0.19∗∗ -0.20∗∗ -0.15∗ -0.13 0.02 0.02 (0.09) (0.09) (0.09) (0.10) (0.09) (0.09) (0.10) (0.10) 1{U S,China} 1{t<2001} 1{m=12} × Xz,max -0.28∗∗∗ -0.28∗∗∗ -0.28∗∗∗ -0.25∗∗∗ -0.25∗∗∗ -0.21∗∗∗ -0.076 -0.082 (0.08) (0.08) (0.09) (0.09) (0.08) (0.08) (0.10) (0.10) Peak-to-Trough 0.63∗∗∗ 0.63∗∗∗ 0.63∗∗∗ 0.60∗∗∗ 0.60∗∗∗ 0.54∗∗∗ 0.43∗∗∗ 0.46∗∗∗ Product/Sector Month FE HS2-1{t<2001} HS2-Year HS4-1{t<2001} HS6-1{t<2001} HS Sections-1{t<2001} None δi,s,t,m , δj,s,t,m δi,s,m × 1{t<2001} δj,s,m × 1{t<2001} Observations 892169 891897 892168 892157 892169 892169 887784 892148 Adjusted R2 0.068 0.073 0.141 0.242 0.049 0.037 0.086 0.080 Note: All estimates are obtained from estimating our baseline estimation equation in (5). The is obtained by taking maxm {β ˆT P U }. ˆT P U } − minm {β m m We omit all estimates except the ones of our interest. Standard errors in parentheses are clustered at HS6, * p < 0.05, ** p < 0.01, *** p < 0.001. Table 4: Seasonal Effect of TPU - Alternative Dependent & Independent Variables i,j,t,z i,j,t,z i,j,t,z i,j,t,z ln(vm −3:m ) ln(vm −3:m ) Mid Point ln(vm ) ln(vm −2:m ) Unit Independent Var. i,j,t,z i,j,t,z i,j,t,z i,j,t Baseline − ln(vm −7:m−4 ) − ln(vm −8:m−5 ) Growth − ln( m vm ) − ln( m vm ) Quantities Unit Values xz,t xz,2001 1{U S,China} 1{t<2001} 1{m=1} × Xz,max -0.36∗∗∗ -0.26∗∗∗ -0.28∗∗∗ -0.29∗∗∗ -0.15∗ -0.17∗∗∗ -0.32∗∗ -0.082 -0.37∗∗∗ -0.38∗∗∗ (0.09) (0.08) (0.08) (0.07) (0.09) (0.06) (0.13) (0.08) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=2} × Xz,max -0.33∗∗∗ -0.32∗∗∗ -0.34∗∗∗ -0.25∗∗∗ -0.23∗∗∗ -0.14∗∗ -0.44∗∗∗ 0.06 -0.33∗∗∗ -0.33∗∗∗ (0.09) (0.08) (0.08) (0.08) (0.08) (0.06) (0.12) (0.09) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=3} × Xz,max -0.21∗∗ -0.16∗∗ -0.26∗∗∗ -0.17∗∗ -0.01 -0.11∗ -0.26∗∗ 0.07 -0.21∗∗ -0.21∗∗ (0.09) (0.08) (0.08) (0.07) (0.08) (0.06) (0.12) (0.08) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=4} × Xz,max -0.01 0.01 -0.06 -0.03 -0.00 0.02 -0.13 0.17∗ -0.04 -0.00 (0.10) (0.08) (0.09) (0.08) (0.08) (0.06) (0.12) (0.09) (0.10) (0.10) 1{U S,China} 1{t<2001} 1{m=5} × Xz,max 0.12 0.06 0.01 0.06 0.01 0.07 0.07 0.05 0.12 0.13 (0.09) (0.07) (0.08) (0.07) (0.07) (0.05) (0.12) (0.08) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=6} × Xz,max 0.26∗∗∗ 0.25∗∗∗ 0.19∗∗ 0.20∗∗∗ 0.06 0.07 0.27∗∗ 0.07 0.22∗∗ 0.27∗∗∗ (0.08) (0.07) (0.08) (0.07) (0.07) (0.05) (0.12) (0.08) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=7} × Xz,max 0.27∗∗∗ 0.26∗∗∗ 0.31∗∗∗ 0.22∗∗∗ 0.22∗∗∗ 0.15∗∗∗ 0.33∗∗∗ 0.03 0.20∗∗ 0.28∗∗∗ (0.08) (0.07) (0.08) (0.07) (0.07) (0.05) (0.12) (0.08) (0.09) (0.08) 31 1{U S,China} 1{t<2001} 1{m=8} × Xz,max 0.19∗∗ 0.12∗ 0.19∗∗ 0.13∗ -0.00 0.12∗∗∗ 0.18 0.10 0.15∗ 0.20∗∗ (0.08) (0.07) (0.08) (0.07) (0.08) (0.05) (0.12) (0.07) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=9} × Xz,max 0.08 0.08 0.12 0.04 0.03 0.11∗∗ 0.16 -0.03 0.05 0.08 (0.09) (0.08) (0.08) (0.07) (0.07) (0.05) (0.12) (0.09) (0.10) (0.09) 1{U S,China} 1{t<2001} 1{m=10} × Xz,max -0.06 -0.06 0.04 -0.08 -0.05 0.02 0.00 -0.10 -0.08 -0.08 (0.09) (0.08) (0.08) (0.07) (0.08) (0.05) (0.12) (0.07) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=11} × Xz,max -0.18∗∗ -0.19∗∗ -0.14∗ -0.19∗∗∗ -0.29∗∗∗ -0.072 -0.14 -0.14∗ -0.19∗∗ -0.20∗∗ (0.09) (0.08) (0.08) (0.07) (0.08) (0.05) (0.13) (0.08) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=12} × Xz,max -0.28∗∗∗ -0.20∗∗∗ -0.23∗∗∗ -0.25∗∗∗ -0.19∗∗ -0.13∗∗∗ -0.31∗∗∗ -0.0076 -0.30∗∗∗ -0.30∗∗∗ (0.08) (0.07) (0.08) (0.07) (0.08) (0.05) (0.12) (0.07) (0.08) (0.08) Peak-to-Trough 0.63∗∗∗ 0.58∗∗∗ 0.65∗∗∗ 0.51∗∗∗ 0.45∗∗ 0.32∗∗∗ 0.77∗∗∗ 0.31 0.59∗∗∗ 0.66∗∗∗ Observations 892169 895643 895395 899347 899317 899345 791635 791626 881309 892169 Adjusted R2 0.068 0.064 0.067 0.080 0.052 0.081 0.045 0.007 0.069 0.068 Note: All estimates are obtained from estimating our baseline estimation equation in (5). All regressions include δi,t,m , δj,t,m , 1{t<2001} × δs,m . The is obtained by taking maxm {β ˆT P U }. We omit all estimates except the ones of our interest. Standard errors in parentheses are ˆT P U } − minm {β m m clustered at HS6, * p < 0.05, ** p < 0.01, *** p < 0.001. Table 5: Seasonal Effect of TPU - Alternative Samples Excl. MFA Balanced Rotating Full Incl. i,j,t,z i,j,t,z Dep. Var. ln(vm −2:m /vm−7:m−5 ) Baseline Phase 1-3 1991-2007 Sample Sample 2001,02 1{U S,China} 1{t<2001} 1{m=1} × Xz,max -0.36∗∗∗ -0.32∗∗∗ -0.38∗∗∗ -0.30∗∗∗ -0.22∗∗ -0.29∗∗∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=2} × Xz,max -0.33∗∗∗ -0.31∗∗∗ -0.32∗∗∗ -0.27∗∗∗ -0.19∗∗ -0.28∗∗∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=3} × Xz,max -0.21∗∗ -0.21∗∗ -0.22∗∗ -0.28∗∗∗ -0.17∗ -0.22∗∗∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=4} × Xz,max -0.01 -0.05 -0.03 -0.12 0.01 -0.02 (0.10) (0.10) (0.09) (0.09) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=5} × Xz,max 0.12 0.05 0.12 0.11 0.08 0.07 (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=6} × Xz,max 0.26∗∗∗ 0.19∗∗ 0.26∗∗∗ 0.25∗∗∗ 0.17∗∗ 0.24∗∗∗ (0.08) (0.08) (0.08) (0.08) (0.08) (0.08) 1{U S,China} 1{t<2001} 1{m=7} × Xz,max 0.27∗∗∗ 0.23∗∗∗ 0.27∗∗∗ 0.23∗∗∗ 0.18∗∗ 0.22∗∗∗ (0.08) (0.09) (0.08) (0.08) (0.08) (0.08) 1{U S,China} 1{t<2001} 1{m=8} × Xz,max 0.19∗∗ 0.14 0.18∗∗ 0.15∗ 0.085 0.15∗ (0.08) (0.09) (0.08) (0.08) (0.08) (0.08) 1{U S,China} 1{t<2001} 1{m=9} × Xz,max 0.08 0.04 0.06 0.16∗ 0.04 0.023 (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=10} × Xz,max -0.06 -0.07 -0.08 0.03 -0.07 -0.07 (0.09) (0.09) (0.09) (0.09) (0.09) (0.09) 1{U S,China} 1{t<2001} 1{m=11} × Xz,max -0.18∗∗ -0.12 -0.18∗∗ -0.05 -0.06 -0.15∗ (0.09) (0.09) (0.09) (0.09) (0.09) (0.08) 1{U S,China} 1{t<2001} 1{m=12} × Xz,max -0.28∗∗∗ -0.23∗∗∗ -0.29∗∗∗ -0.22∗∗∗ -0.20∗∗ -0.19∗∗ (0.08) (0.08) (0.08) (0.08) (0.09) (0.08) Peak-to-Trough 0.63∗∗∗ 0.55∗∗∗ 0.65∗∗∗ 0.55∗∗∗ 0.40∗∗ 0.50∗∗ Observations 892169 819278 874998 1204879 1634409 1016887 Adjusted R2 0.068 0.065 0.069 0.053 0.042 0.069 Note: All estimates are obtained from estimating our baseline estimation equation in (5). All regressions include δi,t,m , δj,t,m , 1{t<2001} × δs,m . The is obtained by taking maxm {β ˆT P U }. We omit all estimates except the ones of our interest. ˆT P U } − minm {β m m Standard errors in parentheses are clustered at HS6, * p < 0.05, ** p < 0.01, *** p < 0.001. 32 Table 6: Effect of TPU & Product Storability i,j,t,z i,j,t,z Dep. Var. ln(vm −2:m /vm−7:m−5 ) Indicator for High Storability Continuous Storability Measure (1) (2) (3) (4) 1{U S,China} 1{t<2001} 1{m=1} × Xz,max × 1{(1/HHz ) 1. The red line is the median value, equal to 31pp. HS-6 products included are those from our baseline sample of goods traded at least once a year in all four directions of trade. 40 Figure 7: Seasonal Effect of TPU Note : Crosses are the estimates of β ˆT P U for each month m = [1, 12] from estimating m equation (5). Estimates of β ˆm are the treatment effect of Xz for US-China trade flows. ˆT P U are reported in column 5 of Table 2. Results of the effect of Results of coefficients of β m Xz for the Post-WTO period and for non-US-China trade flows can be seen in Figure B.1 and B.2, respectively. The blue line is the locally weighted scatterplot smoother. Dashed lines are the 90% confidence interval. Standard errors are clustered at HS-6 product level. 41 Figure 8: High vs. Low Storable Good Note : Crosses are the marginal effect of Xz for US-China trade flows from estimating ˆT P U + β ˆm1/HH equation (6), that is, β m × [1/HHz ] for each month m = [1, 12] for the 10th and ˆT P U and β ˆm1/HH 90th percentile of the inverse HH distribution. Estimates of β m correspond to column 4 in Table 6. The red and blue lines are the locally weighted scatterplot smoothers. Dashed lines are the 68% confidence interval or one standard deviation Standard errors are clustered at HS-6 product level. 42 Figure 9: Estimated Annual Probabilities of Revoked Access to MFN Rates Note: On the left y-axis are our model implied probabilities from simulating the model for HS 6-digit products. The exact probabilities and corresponding coefficients of each year are reported in Table 7. On the right y-axis is the percent of news articles of the New York Times, Wall Street Journal, and the Washington Post discussing the uncertainty of China’s NTR status. 43 Figure 10: Estimated Annual Probabilities of China maintaining MFN Access Note: On the y-axis are the model implied probabilities of China maintaining its MFN status till 2001 and years are on the x-axis. To obtain these we simulate the model for HS 6-digit products and match the β ˆT P U coefficient from (5) by changing probability input to 9 the model. We then compound the probability of China maintaining its MFN status for the successive years until 2001. 44 Figure 11: Comparison of Ordering Cutoffs: The Wait-and-See Effect Note : On the y-axis is the level of demand shock and inventory holdings relative to steady- state average sales is on the x-axis. The area towards the top-left side of the curves is ordering region. Blue solid line shows the ordering cutoffs in the case of a 40% tariff change with certainty. Red dashed line shows the ordering cutoffs in the uncertain case of tariff staying the same or increasing by 80% with equal probabilities. 45 Figure 12: Simulation Result with Varying Expected Tariff Change Note : On the y-axis plots the log difference of (P2T) import growth in the months around the expected tariff change. X-axis plots the expected tariff change. We have multiple observations for similar expected tariff change with different spreads around the same tariff change. For example, we can have a expected tariff increase of 10pp through either 100% probability of 10pp increase or 25% probability of 40pp increase. The dashed line shows the maximum expected tariff change faced by China which is obtained by using maximum annual probability of non-renewal (8%) and the maximum spread (80%). 46 Figure 13: Response of Annual Trade Flows to Risk of Profit Loss Note : On the y-axis is the estimate of βt for t = [1990, 2006] from: 2006 ln(Vi,j,z,t ) = βt 1{i=U S } 1{j =Chn} 1{y=t} Xz y =1990 + γist + γjst + γijt + γijz The blues dashed lines are its 90% confidence interval. Standard errors are robust. 47 Figure 14: Change in Entry Value and Tariff Risk Note : This figure plots the gap in the value of entering in an uncertain industry 12 months before and after the uncertainty resolution, respectively. The loss in value is denominated in the flow value in steady state without uncertainty. The line with low demand shows the value with 25% reduction in demand. 48 Appendix A Model Robustness: Signals and Early Resolution In our baseline we assume that the probability of non-renewal was the same in every month before the date of resolution. Here we study two alternative specifications that serve as robustness checks of our approach. First, we consider the case of an updating of the probability of non-renewal; second, we study the case of an early resolution. Both experiments illustrate that the short-lived dynamics from the (s, s) ordering model are well suited to capture the near-term risk in a fairly narrow window around expected resolution of uncertainty. First, we introduce unanticipated signals on the MFN resolution. Specifically, we assume a larger dispersion of outcomes - namely a 15% of MFN reversal - and then update information on the likelihood to 6%, in either 1, 3 or 6 periods before the resolution. Figure B.5 shows the ordering behavior looks quite similar in the three cases. Only in the case of the “Signal 1 period ahead” is the behavior slightly different. When the initial probability is 15%, firms start responding earlier to the possibility of a tariff hike. When the signal (from 15% to 6% probability) is received one period before the resolution, firms have already stockpiled sufficiently and decrease their orders in the last period before the resolution. Again, under our moving average growth measure these differences cancel out yielding almost identical peak growth rates. When the signal is received 3 and 6 periods before the resolution the ordering pattern is almost indistinguishable from the benchmark case. Second, we allow the uncertainty to be resolved earlier than expected. In particular, firms initiate their orderings believing that tariffs might increase with a 6% chance after a year, but then update the likelihood to 0% after period 7. As you can see in Figure B.6, there is no change in imports in period 13. Hence, our approach would imply that there was no uncertainty regarding the non-renewal of China’s MFN status. 49 B Figures Figure B.1: Baseline Result - Post-WTO Coefficients Note : Crosses are the estimates of β ˆP ost for each month m = [1, 12] from estimating m (5). The blue line is the locally weighted scatterplot smoother. Dashed lines are its 90% confidence interval. Standard errors are clustered at HS-6 product level. 50 Figure B.2: Baseline Result - Non US-China Trade Flows Coefficients Note : Crosses are the estimates of β ˆOthers for each month m = [1, 12] from estimating m (5). The blue line is the locally weighted scatterplot smoother. Dashed lines are its 90% confidence interval. Standard errors are clustered at HS-6 product level. 51 Figure B.3: Distribution of Product Storability Note : This Figure plots the distribution of our measure of storability, namely the inverse HH index. Its value can be interpreted as number of months within a year that have shipments. The red line is the median. Goods that are ordered less frequently are presumably more storable. It is calculated as follows. First, we calculate the annual HH index at HS-10 level between 1991 and 2000 of imports by the US from all countries included in the control group (separately). We then take the residual from regressing those on source-year fixed effects. Finally we take the mean at HS-6 level. 52 Figure B.4: Profit Loss Measure and Spreads Note : On the y-axis is the potential profit loss measure from Handley and Limao (2017), MF N τz,t −3 HL z,t Xz,t = 1− NNT R τz,t , and the X-axis contains the spread between NNTR and MFN rates, tauN NT R z,t MF N − τz,t , for t = 2001. 53 Figure B.5: Updated Signal on the Likelihood of Tariff Hike Note : The x-axis are log deviation from the steady state level of imports. The size of the tariff hike is the same for all three cases and the resolution of the uncertainty is set to occur in period 13. Figure B.6: Early Resolution of Uncertainty Note : The x-axis are log deviation from the steady state level of imports. The size of the tariff hike is the same for all three cases. While in the baseline case the uncertainty resolves after period 13, in the other two cases it resolves after the 7th period. 54