RELATIVE PRICES AND HYSTERESIS: EVIDENCE FROM US MANUFACTURING

A central tenet of economics is that prices matter. A corollary is that in a world with sunk costs, historical prices can affect current economic outcomes. There exists a large theoretical literature on exchange rate hysteresis, but recent empirical treatments are scarce. To fill the gap, I employ new measures of real exchange rates (RERs) to study the impact of large, temporary movements in relative prices on the US manufacturing sector. To identify a causal impact of RER movements on manufacturing, I test whether sectors more exposed to international trade respond differently when relative prices appreciate. I also compare the US experience to Canada’s in the mid-2000s, when high oil prices and a falling US dollar led to an equally sharp appreciation of the Canadian dollar. I find that temporary RER shocks have a surprisingly persistent impact on employment, output, and productivity in relatively more open manufacturing sectors. JEL Classification: F10, F16, L60

Recently, with the stated goal of protecting the US manufacturing sector, Donald Trump has launched a trade war, threatening and implementing tariffs, while also following a strong dollar policy. China, a country which has long used an undervalued currency as a tool of development policy, has responded in part by devaluing the renmenbi. Thus, a natural question to ask is what impact an over-or under-valued exchange rate has on the manufacturing sector, and whether the impact is persistent.
While there is a classic literature on the contemporaneous impact of the dollar on US manufacturing for the 1980s, including Branson and Love (1986), Revenga (1992), and Klein et al. (2002), this literature does not study the more recent period of sharp dollar movements from 1997 to 2004 or study how exchange rate movements affect later economic outcomes, a phenomenon known as hysteresis. This is a critical period, as it includes a "surprisingly sudden" collapse in US manufacturing employment, and some economists, including Ben Bernanke, believe that the origins of the growth slowdown date from this time period. The US experience with sharp currency movements in the 1980s, a period in many ways ideally suited to studying the impact of RER movements, also ushered in a large, but mostly theoretical literature on exchange rate hysteresis (e.g., Dixit (1989aDixit ( ), (1989bDixit ( ), (1991Dixit ( ), (1992, Krugman (1987Krugman ( ), (1988, Krugman (1987) (1989), and Baldwin (1988Baldwin ( ), 1990). As US economic growth has slowed since 2000, and as real manufacturing output shrank in the early 2000s and has remained below trend ever since (see Figure 7), now is an appropriate time to revisit the question of the impact of exchange rate movements on US manufacturing, and to test explicitly for exchange rate hysteresis. 1 Exchange rate movements are not generally exogenous. In order to try to identify a causal impact of RER movements on US manufacturing, I use a Bartik-style panel difference-in-difference in which I exploit substantial variation in initial exposure to trade across 360 manufacturing sectors and in real exchange rates over time to assess the impact of currency appreciations on sectors with greater exposure to international trade. I focus on periods in US history with large movements in RERs (important to improve the signal-to-noise ratio) plausibly exogenous from the perspective of moretradable manufacturing sectors, and separately control for potential third factors. Since identifying causal effects from non-experimental data is challenging, I use a variety of 1. We follow Summers and Blanchard here in defining hysteresis in the loose sense that "history matters", and we define "strict hysteresis" as the case when a temporary shock has a permanent impact absent an offsetting shock in the other direction. I find that a temporary RER shock has a suprisingly persistent impact on manufacturing employment (history matters), enough so that I cannot rule out strict hysteresis, but there is not much practical difference between long-run persistence and strict hysteresis in any case. Sources: BEA and Campbell (2016) includes developing countries such as China. I find that this index accurately predicts manufacturing employment declines, but also find robustness to alternative measures, such as the Fed's RER index.
This paper is also closely related to the literature on the China shock as a cause of the decline in US manufacturing in the early 2000s, including Autor et al. (2013), Autor et al. (2014), Acemoglu et al. (2015), and Pierce and Schott (2016). 4 I use similar Bartikstyle identification, with the key difference being that this paper is the first to look at the entire trade shock in the early 2000s (rather than focusing solely on China, or on China's WTO accession, as Pierce and Schott do), and compare it to the similar-in-magnitude shock of the 1980s. I confirm a role for China, and also find that sharp movements in relative prices were also important determinants of manufacturing employment and output during this period as during the 1980s.
There is, of course, already a literature on the impact of RER movements on manufacturing, which tends to find that manufacturing employment is sensitive to currency appreciations, though with some heterogeneity across countries. Ekholm et al. (2012) find that oil price appreciations differentially effect more open sectors in Norway. 5 Klein 4. Other key papers in this literature include Houseman et al. (2015), Houseman (2016), Ebenstein et al. (2014), Autor et al. (2014), Charles et al. (2013), Boehm et al. (2015), and Dauth et al. (2014).
5. Klein et al. (2002) contains an overview of this literature to that point. Other key papers include Gourinchas (1999) and Campa and Goldberg (2001), who find either a small or non-robust impact using US data. Rose (1991) and McKinnon and Schnabl (2006), find no impact of RER movements on trade, while Chinn (2004) finds that a low responsiveness of imports to exchange rate changes. Lastly, in a sequel to this paper,  replicate the same identification strategy as in this et al. (2003), the seminal paper in this literature and also the closest to this study, finds a large effect of the US RER shock in the 1980s on manufacturing, but was originally written before the exchange rate shock in the early 2000s, and was focused on the contemporaneous impact of RERs rather than hysteresis.
One puzzle from the US literature (see Klein et al. (2002)) is that RER appreciations have led to declines in employment in the US, whereas depreciations do not seem to help. The solution to the puzzle is that what matters for employment is the level of US relative unit labor costs, rather than the change. Conceptually, if unit labor costs were the same in the US and in China, then there would be no economic reason to move production, particularly as this could entail substantial fixed costs. On the other hand, when US unit labor costs are 50% higher than for trading partners, there is a clear economic incentive to shift production, and firms already located abroad would have a competitive advantage (assuming all else is equal).
It has been established empirically that history matters for trade patterns (Eichengreen and Irwin (1998), , Head et al. (2010) and Head and Mayer (2013)). The literature on exchange rate hysteresis has been almost entirely theoretical, while the literature on RERs and manufacturing has not addressed hysteresis. 6 Given the persistent US trade deficit following the trade shocks of the early 2000s (see Figure 1), now would seem an appropriate time to revisit the issue.
1 Measurement, Data, and Theory

Measurement of Real Exchange Rate Indices
Trade economists generally regard real exchange rate indices based on unit labor costs as the most reliable indicators of competitiveness for the manufacturing sector. However, the best known of these indices, the IMF's Relative Unit Labor Cost (RULC) index, has a number of glaring conceptual flaws. Namely, (1) the trade weights are fixed, and have become outdated -they do not even include China, and Japan is given a 20% weight, even into the 2000s, (2) it is computed as an index-of-indices, and thus the IMF's index paper using individual-level data from the CPS MORG.
6. Belke et al. (2013) and Belke and Kronen (2016) conclude that German and Greek exports exhibit exchange rate hysteresis, while Parsley and Wei (1993), using US data, find hysteresis to be insignificant and inconsequential. In addition, Alessandria and Choi (2007), (2014b) and (2014a), do calibration exercises they argue are consistent with sunk fixed costs of exporting.  finds evidence of hysteresis in trade patterns. A number of other empirical papers have interpreted persistence in export status as evidence for hysteresis (e.g., Roberts and Tybout (1997), Campa (2004), Bernard and Jensen (2004), and Kaiser and Kongsted (2008)).
does not reflect compositional changes in trade toward countries that have systematically lower unit labor costs, (3) it uses country-specific deflators, which can become biased over time without the benefit of multiple benchmarks. (This last point also afflicted  versions of the Penn World Tables predating version 8.0.) The problem with RER indices computed as index-of-indices was first noted in a brilliant contribution by Thomas et al. (2008), who proposed an alternative Weighted Average Relative Price (WARP) index instead, and found that this version did a better job predicting the US trade balance out-of-sample.  then applied Thomas et al.'s methods to the construction of a RULC index, and found that this, too, did a better job of predicting manufacturing trade balances out-of-sample. This method makes corrections to address the three problems with the IMF's index: (1) it uses variable trade weights updated each year, and includes China, (2) it is computed as a weighted average of levels, and (3) it uses multiple cross-country benchmarks.
The  Weighted-Average Relative Unit Labor Cost index (WARULC) is thus computed as: (1.2) and where Ω i,t are time-varying trade weights (a weighted average of import, export, and third-country competition weights, the same as used by the BIS and very similar to the Fed's weights), and where w i,t are manufacturing wages of country i at time t, e i,t is the local currency price of a dollar, and Y i,t is manufacturing production, converted to dollars at PPP (equal to one for the US). One of the key differences with the IMF's index is that for this index the ULCs are actual unit labor costs rather than indices of unit labor costs. Manufacturing PPP data were computed using ICP data for benchmark years, and then interpolated in between using manufacturing deflators from the OECD, or country-specific sources in the case of China.
It turns out that all three of the adjustments from the IMF's RULC to WARULC are important. For example, changing the indexing method while using fixed trade-weights would yield an index almost identical to the IMF's index, even if China is included. Without the multiple benchmarking, WARULC would still have a more negative slope. I refer readers interested in the differences in these indices when some of these adjustments are left out to .
I also consider alternative measures of relative prices. Figure 2 compares several state-of-the-art measures of relative prices which use PWT v8.0 data and methodology to more commonly used measures provided by the Federal Reserve Board and IMF. Indexing the IMF's RULC series to begin at the same level as the WARULC index in 1975, the IMF's index implies that US ULCs were nearly 40% lower than trading partners by the 2000s, which is implausible. I have also plotted an updated version of Weighted Average Relative Prices (WARP) (from Thomas et al. (2008)) using PWT v8.1, and Penn-Adjusted Weighted Average Relative Prices (PWARP), introduced in Campbell (2016), which controls for Balassa-Samuelson effects. The Federal Reserve's CPI-based Broad Trade-Weighted Real Exchange Index, plotted in yellow, also implies that the dollar tended to depreciate over the period. The three "Weighted Average Relative" (WAR) indices all yield broadly similar results, although there are certainly differences in the details and in the implied degree of overvaluation. I also do exercises in the Online Appendix using different sectoral values of WARULC.

Other Data
Sectoral data on employment, shipments, value-added, wages, hours worked, and capital, and the prices of shipments, materials, and energy are provided by the Census Bureau's Annual Survey of Manufactures, via the NBER-CES Manufacturing Industry Database for the 4-digit SIC data from 1958 to 2009. Data were taken directly from the Census Bureau for the NAICS version of the same variables spanning 1989-2011. Trade data from 1991-2011 are from Comtrade WITS when available, and these data are augmented with trade and the cost of insurance and freight data from Feenstra et al. (2002) from 1972-2005. Sectoral tariff data for 1974-2005come from Schott (2008 via Feenstra et al. (2002), as does data on the increase in tariffs China would have faced had MFN status been revoked (the key control in Pierce and Schott (2016)). Additional data on the tariffs US industries face for 1990-2009 were taken from UNCTAD. Other Chinarelated variables from 2016, such as Chinese production subsidies and export eligibility by sector, are not yet publicly available but were not generally found to be significant predictors of employment changes. International manufacturing data on employment and output at the 3-digit ISIC Rev. 2 and Rev. 3 level for G7 countries comes from UNIDO's INDSTAT database. 7 The summary statistics for the most relevant variables in select years are reported in Table 12 in the Online Appendix. "Openness", a weighted average of import penetration and the export share of shipments, increased from about 7% in 1972 to 24% in 2001 (when China acceded to the WTO) and 27.9% by 2005. It can be seen that labor costs are a large, but declining, share of value-added over the period, declining from 42.6% of value-added to just 32%. The average applied tariff was about 8.2% in 1974, but it fell to just 2.4% by 2005. The last two entries in Table 12, capital-per-worker and the 5-factor TFP index, also come from the NBER-CES manufacturing data set. The details of their creation are described in Bartlesman and Gray (1996). Finally, panel (a) of Figure 12 shows that there was a large variation in the distribution of openness by sector in 1997, and Panel (b) demonstrates the rise in import penetration relative to export shares when the US WARULC index is elevated.

Theoretical Motivation
Given that the theoretical motivation is intuitive ("relative prices matter"), the focus of this paper is on identifying a causal relationship for the impact of RER movements on outcomes in manufacturing using reduced-form empirical exercises. Any model in which prices matter is likely to deliver the result that a shift in the RER will have an impact on outcomes. However, only models with some form of sunk costs will imply that a temporary RER shock will have persistent effects, or, put another way, that current 7. In addition, the classification of broad industrial sectors by markups, used for robustness, is borrowed from Campa and Goldberg (2001), but I do not find that these sectors are more sensitive to RER movements. 8 outcomes will be affected by the history of relative prices. In the online appendix, Section 7.1, I present a slight variation of the Melitz (2003) model with sunk entry costs, and show that this version of the model implies that historical prices matter. The model also helps motivate some of the controls, including controls for demand, trade policy, trade costs, and productivity, which are also intuitive. However, in the end, to what extent RERs, and historical prices matter is an empirical question.

The Research Design (Identification)
The main research design in this paper is a difference-in-difference, where I compare the evolution of employment in more open sectors to less open sectors before and after a RER appreciation. This research design is displayed in a standard treatment-control event-study diagram in Figure  In the panel regressions which follow, I use a continuous measure of openness.) Yet, when the dollar appreciated in the 1980s, the more open sectors lost more than 10% of their employment relative to the least open sectors. Interestingly, after the dollar returned to fundamentals in the late 1980s, this differential impact decayed very modestly, if at all. I would argue that the 1980s episode deserves to be a canonical example of a persistent effect of a temporary exchange rate shock, for several reasons. First, the RER shock (50% appreciation) was large, which increases the signal-to-noise ratio.  it is commonly believed that the strong dollar was a speculative asset bubble divorced from economic fundamentals (see, for example, Krugman (1985)). Third, given that labor costs were 40% of value-added for the typical sector, it would be implausible if profit-maximizing firms did not respond to this large change in relative prices. Fourth, and perhaps most importantly, an employment collapse in more open manufacturing sectors should lead endogenously to an RER depreciation rather than an appreciation. Thus, in this case reverse causality should lead to a bias in the direction of not finding anything. If the large estimated negative impact of RER appreciations on manufacturing employment is in fact a floor, the results in this paper would only be more salient. In addition, exchange rates impact trade and manufacturing employment with a lag. Thus, it is not clear why an employment collapse in more tradable sectors in 1986 should cause a dollar appreciation at all, much less in 1985. However, this logic does not necessarily mitigate against third factor causality. Lastly, in both the 1980s and the early 2000s, the declines in more open sectors occurred at the same time as declines in aggregated "structurally adjusted" manufacturing employment ( Figure 10 in the appendix). 9 This appears to be a case in which the most serious threat to identification is not reverse causality per se, but rather that a third factor could cause both an exchange rate appreciation and a decline in manufacturing. The general solution to this problem is to control for obvious third factors in a panel "difference-in-difference" setting using disaggregated data that tests explicitly whether an appreciation in the RER causes a decline in relatively more open manufacturing sectors (where a continuous measure of openness is defined at a several year lag so that it itself is not endogenous). For example, a primary concern is that high real interest rates (RIRs) could cause an appreciation of the RER and a decline in manufacturing employment. In this case, it is straightforward to include the RIR as a control variable, along with the RIR interacted with sectoral capital intensity and openness, as more capital-intensive or open sectors could potentially be more sensitive to movements in the RIR. However, in fact import-competing sectors tend to be slightly less capital intensive and appear to be less sensitive to movements in the RIR than other sectors. In addition, RIRs were at historic lows during the collapse of manufacturing in the early 2000s. Although RIRs were high in the early 1980s, the timing of the peak in RIRs does not match the 1980s collapse in manufacturing as well as relative prices. In addition, tight monetary policy should lead to trade surpluses as domestic consumption declines, while both RER appreciation episodes in fact led to large trade deficits. Thus, tight monetary policy is in fact not a good candidate explanation for the sharp relative decline in more open sectors in either period.

Panel Regression Approach
The traditional assumption in the literature is that log changes in the RER affect log changes in manufacturing employment (a log-log specification). I begin with this as well, while testing for assymmetric affects. I follow Klein et al. (2002) and define the variable Appreciation to be equal to the log change in the RER when it is increasing, and equal to zero otherwise, and an analogous variable Depreciation to equal the log change in the RER in periods when it is decreasing, and equal to zero otherwise. The full regression is: Openness h,t−3,t−6 + β 2 ∆ln(D ht ) + β 3 ∆ln(T F P ht ) + turing employment on changes in GDP and lagged changes in the Fed's Broad Trade-Weighted RER Index. This index was used because it has data at quarterly intervals. ..., 359, t = 1973, ..., 2009, where L ht is employment in sector h at time t, RER is a measure of the real exchange rate, such as WARULC, D h,t is sectoral domestic demand (defined as shipments plus imports minus exports, and is implied by our model to affect employment), T F P h,t is a measure of TFP (I use 4 and 5-factor measures of productivity in addition to valueadded and shipments divided by production worker or total employment), and the Cs are various other controls. The variables Appreciation h,t−1 and Depreciation h,t−1 (the log changes in the RER in years of appreciations and depreciations, equal to zero otherwise) are lagged one year as in Klein et al. as exchange rate changes are observed to take time to reach their full impact.
However, the puzzle with this specification has been that while appreciations in the US tend to harm employment, depreciations do not tend to help. I propose an intuitive solution to this puzzle: what matters for changes in manufacturing employment is the level of RER, so that a depreciation back to parity should not, in fact, be expected to cause an increase in employment, although a depreciation which leaves a currency undervalued would. An asymmetric impact of appreciations and depreciations is consistent with using the level instead, which implies that a temporary shock will have a persistent effects, unless it is offset later by an equal shock in the opposite direction.
Thus, an alternative specification using the log level of the RER, which implies hysteresis (see a simple proof of this conjecture in Appendix Section 7.3), is: ..., 359, t = 1973, ..., 2009 is an average of openness (defined as in equation 8.3) at 3, 4, 5, and 6 year lags: Openness t−k .

(2.3)
This is done precisely to eliminate any potential feedback from the exchange rate to openness. This ensures that the time series changes in the interaction term will be driven primarily by movements in the exchange rate. The rationale for using a (slowly) evolving measure of openness instead of a fixed measure is that, given the long panel covering four decades, of course the world changed and trade intensities evolved over time. Any sector's exposure to RER movements should depend on its current exposure to trade rather than whatever its trade exposure happened to be at the end of the Bretton Woods period. While openness could theoretically be a function of the RER, in practice more open manufacturing sectors do not lose jobs when WARULC is close to unity (see Figure 16). Thus it is not surprising that the results are robust to using either shorter or longer lags of openness. In fact the results are also robust to using initial period openness (1972) for the entire sample (see Online Appendix Table 15, in addition to Figure 3.) Each regression also includes sectoral fixed effects α h , year fixed effects ν t , and twoway clustered errors (Cameron et al. (2011)), by both industry and by year. All regressions in the benchmark table are weighted by initial period value-added, although later I show that the results are robust to various weighting schemes. Table 1, column (1) runs the specification in equation 2.1, and shows that appreciations in relative unit labor costs are associated with a decline in employment for more open sectors (at 10%), but that depreciations have no significant impact. Column (2), using equation 2.2, includes the log of the level of WARULC instead as a control, and this time the interaction is significant at 1% (indeed, even at .5%), and has a slightly higher Rsquared than column (1) despite one fewer control (.283 vs. .280). Column (3) includes controls for productivity, demand, capital-per-worker and capital-per-worker interacted with the real interest rate, defined as the interest rate on 30-year mortgages less the Core CPI, and lagged log changes in wages and the price of shipments. Once again, appreciations are associated with employment declines for more open sectors, but depreciations are not significantly correlated with job gains. In column (4), I also include the log of the level of WARULC interacted with openness, and find that the RER appreciation and depreciation variables lose significance, while the level of WARULC continues to have a significant impact. Thus, I use the level of WARULC for the remainder of the paper. Since the level of WARULC impacts the log change in employment, this specification by itself implies hysteresis.

Panel Regression Results
The coefficient of -.37 in column (4) suggests that in 2001, when US ULCs were 38% (or 1.38, for a log value of .32) above a weighted average of ULCs of US trading partners, an industry in the 90th percentile of lagged average openness (openness of .58) would have lost an additional 6% of employment from 2001 to 2002 (=exp(-.37*0.32*.58)-1), as compared with a completely closed industry, and 4% more than an industry with median openness (which was .16 in 2001). Over the entire 1997-2005 period, this industry would 13 have lost a cumulative 30% of employment relative to a closed industry, and 19% more than an industry with average openness.
Column (5) adds additional controls, including controls for sectoral input prices (materials, energy, and investment) and sectoral input prices interacted with sectoral input shares lagged one period. I also add in the two China-related controls from Pierce and Schott (2016), the Post-PNTR*NTR gap variable, and a second control for MFA exposure (as described previously), and find that both had significant adverse impacts on employment (the NTR gaps are all negative). I also control for the share of intermediate inputs over shipments, and an interaction of this term with the level of the log of WARULC. Neither are significant in column (5). If we ran a quantile regression instead (which we do in the robustness), we would actually find significance, but with a negative sign. This could be seen as a caveat to the main results, as one might expect that as the dollar appreciates, sectors with substantial imported inputs would not be hurt as badly, as the cost of these inputs would become cheaper. On the other hand, it could be that sectors with more imported intermediates are also sectors in which offshoring is more feasible, and thus may be more likely to take place when domestic production costs rise. In this case we might expect the negative coefficient we only see with a quantile regression. Also, it is worth repeating that the sectoral imported input data are simply estimates made using a proportionality assumption which assumes that a sector's imports of each input, relative to its total demand of that input, are the same as the economy-wide imports relative to total demand. Thus, our lack of a clear result on the impact of intermediate inputs could simply be an artifact of the data.
Lastly, to control for the possibility that more open sectors also may be more sensitive to movements in real interest rates, I include an interaction between openness and the real interest rate, defined as the yield on 30-year mortgages minus the Core CPI. I find that employment in more open sectors is not generally more sensitive to movements in interest rates. *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period . The dependent variable is the log change in sectoral manufacturing employment in the first five columns, and the 5 year log change in the last column. Sectoral changes in the cost of investment, energy, and materials are omitted for space. L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years, and is interacted with the logged lag of WARULC, a measure of the RER. The variable "3-6yr.Avg.MPInp/Ship." is the moving average of imported inputs divided by shipments lagged 3, 4, 5, and 6 years.
Column (6) runs the regression using five year log changes as the dependent variable, and includes two separate RER controls. One is the same interaction between WARULC lagged one year and the three to six year weighted average of openness as in the previous columns, and the second is an interaction between the average of ln(WARULC) lagged two to five years and the average of openness lagged six to nine years -thus this is a measure of historical relative prices. The idea is to directly test the idea that employment today is a function of lagged relative prices. And, indeed, we see that the coefficient on lagged WARULC is only a bit more than half of the coefficient on the average of WARULC the previous four years. Historical prices matter, even after controlling for current prices.

Robustness
How robust are these results? In Table 2, I include 30 different robustness checks (each column within a panel is a separate regression). First, in Panel A, I show that the results are robust to various combinations of year and industry fixed effects, and to excluding the full controls included in Table 1. In column (6), this includes a control for 2-digit SIC*year interactive fixed effects (that is 740 FEs), in addition to 4-digit SIC FEs. In Panel B, I show the results are robust to using quantile regressions, which are less sensitive to outliers than OLS. In Panel C, I show that the key results are insensitive to different choices of weights: initial value-added, no weights, initial employment or shipments, average value-added, or value-added lagged one period. In Panel D, I add and subtract industries which one might want to exclude for various reasons. In the baseline regressions in Table 1, I excluded unbalanced sectors and publishing, as this sector was eventually re-classified out of manufacturing. In the second and third columns of Panel D, I add these sectors back in, and find that the results are little changed. In column (4), I subtract defense-related sectors (as government spending in these sectors boomed in the 1980s and 2000s), and in column (5), I deduct computer-related sectors (given the questions about the official productivity numbers in these sectors), and then add all the sectors back in column (6). The results appear to be robust.
In Panel E, I do an additional functional form test for WARULC. I create five separate indicator bins for the level of WARULC, for every .1 increase between 1 and 1.5, and interact them with openness (I thank Matthew Gentzkow for this suggestion). In the preferred specification in Column A, I find that, for example, when the RER is less than 1.1, there is no correlation between openness and employment changes. Yet, when WARULC is between 1.1 and 1.2, the coefficient is -.048, and borderline significant. This Errors clustered by year and 4-digit SIC sectors. *p < 0.1, **p < 0.05, ***p < 0.01. There are five sets of six regressions, with the same controls as in column (5) of Table I coefficient rises all the way to -.098 when WARULC is between 1.2 and 1.3. While the absolute value of the coefficient increases monotonically, it doesn't necessarily increase proportionally. However, there are not many observations of WARULC greater than 1.4, and in some of the other specifications the decline in more open sectors becomes significantly steeper. It might also be the case that more jobs are lost in the first years of an appreciation episode than in the later years, but we do not really have enough appreciation episodes to test this. On the whole, the log-linear specification looks to be approximately correct. There is not space to list all the myriad robustness exercises I have implemented, so I leave even the summary of these to the Online Appendix. The most important one is that I find that not only output is affected, but so is value-added, shipments, TFP, hours worked, and production worker wages. This is somewhat reassuring that our results for employment are not spurious. Inventory, sectoral output prices, and sectoral input prices are not affected -the latter can be thought of as somewhat of a falsification exercise, as they should not be affected.

Accounting for Employment Changes
The results so far indicate that RER movements seem to have a statistically significant and large impact on the sectors most exposed, but if the sectors that trade the most are small, then the overall impact on employment might not be very large. To estimate the relative number of jobs lost due to trade and RER movements over the 1995-2007 period, I use the panel regression results from Column 5 of Table 1 from regression equation 2.2 (and also compare to the two versions which either exclude demand, or use an IV for demand as in the appendix). The approach is to multiply the coefficient on the interaction term, by the interaction term itself and the lagged level of employment (L), and then to sum across all 395 industries with data in this period. In addition, for any year when the WARULC index is less than one standard deviation above unity (1.12), I simply set the job losses to zero. Certainly, this method relies on a number of assumptions. First, this is the total number of relative jobs lost in more open sectors rather than the overall total. However, this still gives an indication about the overall magnitude of the shock, and, secondly, there is a lot of evidence that sectors with little trade exposure are not adversely helped or hurt during years when the RER is appreciated. Secondly, this method will only pick up the direct effects of the RER shocks, and not indirect effects, such as via local labor market effects or input-output linkages. Third, the Federal Reserve would likely respond to job losses in manufacturing by keeping interest rates lower than it otherwise would have, thus raising overall manufacturing employment, and there also could be other general equilibrium effects as workers move from tradable to non-tradable sectors. I would also stress that these estimates are likely to be approximate, and suggestive rather than conclusive. In any case, choosing the most conservative out of the three panel regressions, the one using a demand IV (impacts are larger when omitting a demand control or when controlling for actual demand) the results suggest that the trade shock was quantitatively large, and directly responsible for roughly 2.5 million jobs lost from 1998 to 2007, with about 1.5 million jobs associated with the appreciation of the WARULC index, and the balance mostly due to China's WTO accession (one million). 10 Another caveat is that the ASM data used in the regressions implies a total manufacturing job loss of 4.1 million vs. just 3 million for the BEA's numbers. Nevertheless, this complete estimate of the toll from trade is substantially larger than the direct estimate of 560,000 provided by Acemoglu et al. (2015). Yet, note that this figure is still substantially lower than the 3.9 million jobs lost implied from using a straightforward, back-of-the-envelope accounting approach (Table 4), which suggests that 2.5 million jobs lost directly due to trade is at least plausible. 11 By contrast, the same method implies that during the 1980s shock, only 923,000 jobs were lost, as the economy was significantly less open then.
Panel (a) of Figure 4 plots a "counterfactual", where I add back the jobs lost due to the dollar appreciation, and then also add back the jobs lost due to China's accession to the WTO and the MFA agreement. However, what is clear is that this counterfactual exercise still implies a substantial fall in manufacturing employment after 2000. What accounts for this decline?
To understand what may be driving this, Figure 4(b) details the impact of changes in demand and productivity on changes in manufacturing employment (using the regression coefficients from Column 5 of Table 1 from regression equation 2.2, only we use actual demand rather than an IV). We then compute the change in employment due to changes    in demand as: Where D is actual domestic demand, equal to shipments plus imports minus exports. We make the same calculation for productivity, multiplying the coefficient on log changes in productivity, by the log change in productivity itself, and then by the lagged level of employment. While the jobs lost due to productivity gains after 2000 look unimpressive, demand growth stands out as being particularly sluggish in this period. While this may have been the result of an exogenous sectoral shift in consumption patterns toward services, another possibility is that the decline in demand was itself caused by trade via input-output linkages. For example, every dollar of output of apparel manufacturing requires 30 cents of output from textile mills. Overall, every dollar of aggregate manufacturing output generally requires about 60 cents worth of additional output from other manufacturing industries (I get a similar estimate using detailed IO data). This would suggest that the direct and indirect impact of trade might be as high as 4.1 million manufacturing jobs, which admittedly sounds implausibly large. Acemoglu et al. (2015) estimate the total input-output linkages from all sectors, including services, and get a full multiplier close to four (which includes local labor market effects, which they find to be close to zero). If correct, this would imply that a direct impact of 2.5 million jobs would result in a stunning toll of 10 million jobs lost overall, easily large enough to lend credibility to the Bernanke hypothesis that trade and the savings glut are the fundamental cause of the low nominal interest rates, the US's slide into a liquidity trap, and the apparent "secular stagnation" experienced in the US since 2000. 12 Of course, these are micro estimates, and do not factor in general equilibrium effects, the jobs gained from the Fed's low interest rates in the mid-2000s, cited as a factor contributing to the housing bubble, and which likely increased employment. Yet, neither do they count the employment impact of the collapse of the housing bubble or the slide into a liquidity trap in 2008. Despite the emphasis that these are rough estimates, to be taken with a grain of salt, they suggest three important conclusions: (1) the RER shock, and trade shocks in general, appear to have been large enough to have had an impact on the macroeconomy, (2) productivity growth does not appear to have been a more significant cause of job loss than it had been in previous decades when manufacturing employment was steady, and (3) slower demand growth also appears to be a significant factor in the decline of the level of manufacturing employment, although the causes of this decline are beyond the scope of this paper.
(Panel (a) of Figure 6). As Canadian unit labor costs have increased sharply relative to trading partners (including the US) since 2003, Canadian manufacturing has lost more than twice as many manufacturing jobs as the US as a share of 2003 employment, with the losses concentrated in the more open Canadian manufacturing sectors ( Figure 6, Panel (b)). Thus, we now estimate:   ..., 29, t = 1978, ...1995, 1998, ..., 2003, The dependent variable is now the log change in sectoral US employment minus the average log change in employment in Canada, France, Germany, Italy and the UK. Since this is a smaller sample of countries than that which comprises the weighted average in the RULC sample, I simply take the ratio of the US WARULC relative to the G5. The manufacturing data are 3-digit ISIC Rev. 2 data from UNIDOs, which does not report data for the US for the year 1996. I include only a single lag instead of the four year moving average lagged three years because there is missing data, and since I have found that using a one year lag instead makes little qualitative difference with the ASM data.
The first column in Table 3 runs the difference-in-difference regression using US data as in previous tables (e.g., regression 2.2) with errors clustered at the ISIC 3 industry level and includes industry and year dummies (a version with quantile regressions for robustness is in the appendix, Table 32). Here, we can add in a control for foreign demand as well since we have this data. The controls for both US demand and foreign demand are computed using the IV strategy as before based on country GDP and sectorspecific elasticities. Foreign demand is then computed as a US export-weighted average of demand in the other five economies. The key interaction term between openness and WARULC is large and highly significant, indicating that more open sectors tend to lose employment when unit labor costs are high relative to less open sectors compared with when WARULC is close to unity. 13 The magnitude suggests that as a sector goes from no openness to 50% openness, employment will decline by an additional 12.2% in a year when WARULC is 1.5 (=exp(-.64*.5*ln(1.5))-1). In the second column, the dependent variable is now the log change in sectoral output, and the key interaction term is once again large and significant. 14 In column 3, the coefficient of -.7 tells us that for a sector with an additional 50% openness, it will lose (=exp(-.7*.5*ln(1.5))-1) = 13.2% of its total employment when WARULC is 1.5 relative to the employment change of the same sector in other major economies. Note that not much happened to the average G5 WARULC index over this period, and if we entered it in separately it would have the "correct sign" but would typically not be significant across specifications. These numbers are larger than those implied by running a directly comparable regression using the ASM data (compared to column 1 of Panel A in Table 2), as the coefficient of -.64 can be compared with a coefficient of -.30. One reason may be that there are only 31 sectors with ISIC data, and thus estimates using this data are more likely to be noisy.
In the third column of Table 3, I estimate the relative difference-in-difference regression in equation (4.1), and find that the magnitude of the results increases compared to column (1), although the estimate also becomes less precise. Given that the previous literature has found heterogeneous effects of exchange rate movements by country dependent on labor market institutions (see, for example, Berman et al. (1998), Nucci and Pozzolo (2010), and Belke et al. (2013)), it is important to show in column (4) that the relative difference-in-difference results hold for output as well as employment. In column (5), I estimate the difference-in-difference estimation as in column (1) for Canada instead of the US, and also find that when Canadian Weighted Average Relative Unit Labor Costs are high, the more open Canadian manufacturing sectors lose employment relative to less open sectors. This is also true for Canadian output. Note that the coefficient for Canada is much smaller than for the US. This could be seen as a caveat to the main results, but keep in mind that the typical Canadian sector is about five times more open than the average US sector, which means that while the elasticity is lower, the impact on employment could actually be roughly the same. A second factor is that 13. I subtract one in the US case rather than taking the log (which is approximately the same), because each country may need a slightly different normalizations, and Canada appears to lose employment in manufacturing as its WARULC goes above .85. Since the WARULC measures here exclude factors such as tariffs, fiscal policy, and various other factors, the break-even point for competitiveness need not be exactly one.
14. In this paper, I do not focus on Europe, in part because it has been done, and in part because it would be deserving of a separate paper. Chen et al. (2013) finds that Euro zone countries with relative price appreciations after the formation of the Euro also experienced worsening trade balances. Ekholm et al. (2012) adopt a similar methodology and finds that oil price appreciations adversely affected the Norwegian manufacturing sector.  Standard errors clustered by sector in parentheses. *p < 0.1, ** p < 0.05, *** p < 0.01. Each column is an OLS regression including year and 3-digit ISIC industry fixed effects. Data for the first four regressions span from 1977 to 1995 and 1998-2003 for 31 sectors, and the last two regressions span 1991-2010 for 104 sectors. The dependent variables in the first two columns are the log change in sectoral manufacturing employment and output. In the 3rd and 4th columns, the dependent variables are the log change in manufacturing employment (and output) relative to the average log change in employment (and output) in the same sectors in other major economies. Data in the last two columns are for Canada. In the 5th column, I normalized WARULC by adding .15. In the last column, oil prices are used as a proxy for Canada's RER. To normalize oil prices, I took the log and of the price of a barrel of crude oil and subtracted three.
other RER indices for Canada, such as WARP and BSWARP, do not show as sharp of an appreciation in the 2000s as WARULC, so estimating with these alternative (yet also appropriate) RER indices would yield a higher elasticity for Canada. For Canada, it appears that the dividing line between faster vs. slower growth for more open sectors is when WARULC is around .85 instead of 1, so I have normalized the Canadian index by adding .15 for Canada (the results are little changed if one adds .1 instead). This could be due to a country-specific bias in the data collection, tariff policy, or any number of other factors. Finally, in the last column, I proxy movements in Canadian relative unit labor costs using the log of oil prices minus three, 15 and again find that when oil prices are high, the more open sectors in Canada tend to lose ground relative to less open sectors.

Conclusion
When nominal exchange rates move, the nominal rigidity of wages leads to large changes in Weighted Average Relative Unit Labor Costs (WARULC), a new measure of competitiveness for the manufacturing sector. I examine periods, such as the 1980s for the US, and the 2000s for the US and Canada, when identifiable exogenous factors were likely to have driven large movements in relative price levels. These exogenous shocks (from the perspective of manufacturing employment) led to overvalued relative unit labor costs, and are correlated with periods of increased imports and decreased manufacturing exports, and to declines in employment, hours worked, TFP, and output concentrated in relatively more open manufacturing industries. The impact of a temporary shock to relative prices is persistent, indicating that current economic relationships are historically dependent, an insight of obvious importance to the field of development economics.
One policy implication is that governments may want to avoid sustained periods of overvaluation, which arose partly due to policies of the US and foreign governments in both the 1980s and the 2000s (deficits, and the Great Reserve Accumulation) and also that after such a period, it may be advisable to follow it up with a sustained period of undervaluation. In addition, given the impact of monetary policy on exchange rates, monetary models should incorporate hysteresis. In addition, I find that the shock to trade in the early 2000s, and the measured elasticity of RER changes on more open manufacturing sectors was large enough for this shock to have played a significant role in the "surprisingly sudden" collapse of US manufacturing employment in this period. As the period of slow growth in the US and other developed economies continues while the debate over "secular stagnation" rages, understanding the fundamental cause of the slow growth performance in the 2000s is as important as ever. This thesis suggests that one would do well to start by studying the recent history of relative prices, and by dusting off the 1980s literature on hysteresis. 16 15. Any measure of the RER or proxy for it have to be transformed somehow so that they vary between zero and positive or negative numbers, otherwise the interaction with openness will be collinear with openness itself.
16. Note that this is in line with the Bernanke (2005)

Appendix
Figure 7: Real American Manufacturing Output Relative to Trend, 1987Trend, -2017 Source: BLS, via FRED. The trend in manufacturing output growth was fit from 1987 to 1998 using the average growth rate, and then extrapolated. I then plot actual output relative to trend.    Sources: Census, Comtrade, and  7 Online Theory Appendix

Main Theoretical Model
In this section, I motivate the empirics using a slight variation of the Chaney (2008) model with sunk costs as in Melitz (2003). I use this approach because I can show analytically that sectoral labor demand depends on the past history of prices (and I can derive an analytical solution for a dynamic gravity equation), and also partly due to the popularity of the Melitz model.
In this model, households in the home country consume from a continuum of goods, ω, from a set of goods in H+1 sectors, Ω h , determined in equilibrium. There is a freely traded homogeneous numeraire good q 0 as in Chaney (2008), with one unit of labor producing w units of the good.
Each period this leads to the solution for variety ω, with total income in the home country, Y t , and the CES price Firms maximize profits each period after paying a sunk fixed cost to receive a productivity draw (output per unit of labor ϕ) and begin producing for the home market, and then choose whether to pay a sunk entry cost to enter the foreign market (for simplicity I assume there are only two countries). Profits per period for an existing firm from sales at home are thus 17 where p is price, q is output sold at home, w is the wage, τ is an iceberg trade cost, f is the per-period overhead cost and ϕ h (ω) is the output per unit of labor, supplied inelastically by households. Firms have an exogenous probability of death δ, yet otherwise will always choose to stay in a market they have previously entered, as expected profits are strictly 17. And similarly for exports: , where q * and p * denote quantities and prices of goods produced at home and sold abroad. positive going forward. Maximizing profits, firms choose prices marked up over marginal cost p h (ω) * t (denotes the price of exports) (7.4) A home firm which has previously paid to receive a productivity draw will pay a sunk fixed cost to export, f x , if it is less than the expected discounted present value of future profits. 18 The baseline empirical approach in the next section will be to use relative price indices to explain the behavior of sectoral manufacturing employment. Thus, we can write sectoral labor demand as: Overhead .
(7.6) Here M e ht is the mass of potential entrants at time t, x ht = 1−G(φ x ) is the share of new firms in sector h with productivity greater than the cutoff productivity for exporting,φ x , and h,t,s = 1 − G(φ f,t,s ) is the share of continuing firms with productivity greater than the maximum cutoff for continuing to produce for the home market,φ f,t,s , in between years t-s and t. The mass of entrants in Chaney (2008) is assumed to be exogenous, and based on country factors (proportional to output).
The cutoff productivity for entering into the export market at time t can be derived from equation (7.5) assuming that firms know the productivity distribution when they decide to invest to receive a productivity draw, and then have perfect foresight of market conditions for the upcoming period when they decide to invest. However, firms make their investment decisions using rules-of-thumb, taking the form of simple expectations about a future they believe will be like today, conditioned on not receiving a "death" 18. Firms will pay a fixed cost to receive a productivity draw and enter the domestic market if the expected profits, home and abroad, are greater than the fixed cost of entry: 37 draw with probability δ. Thus the cutoff productivity for exporting is When wages, trade costs, or the sunk fixed costs of exporting rise, or the foreign market either becomes more competitive or experiences an exogenous reduction in demand in sector h, the cutoff productivity for exporting will rise, meaning that fewer firms will enter.
Additionally, existing firms will exit and stop producing if revenue fails to cover perperiod fixed costs. The cutoff productivity for staying in business for purely domestic firms is 19φ This equation tells us that when labor costs or fixed costs rise, or when the domestic market becomes more competitive or domestic demand in sector h shrinks, fewer firms will be around to employ labor in overhead activities. To the extent that it is the case that more productive firms export (as it is in this model), relative price appreciations, denoted by a rise in wages, or a rise in domestic vs. foreign GDP, would imply that import-competing industries might be more adversely affected than relatively exportintensive industries along the extensive margin, since industries with many firms that do not export may have a more difficult time covering the fixed overhead costs.
The first term in the sectoral labor demand equation (7.6) is the total labor requirement for home production. Plugging in the solutions from above and integrating assuming Pareto-distributed productivity with parameter γ h (the Pareto distribution is 19. The constraint for staying in business for firms which also export isφ f xt = 38 where λ 1 and λ 2 are parameters 20 , ρ = 1 − δ for brevity,φ mh,t,s is the maximum cutoff productivity to remain in the market for a firm that entered s periods previously in the intervening years, and variables with an asterisk denote foreign variables. Thusφ * mxh,t,s is the maximum cutoff productivity for a foreign firm that entered s periods previously to export and remain producing during the intervening years, and variables with an asterisk denote foreign variables. The denominator of this equation is the solution to . Thus, along the intensive margin, labor demand for domestic production depends positively on domestic sectoral demand (µ ht Y t ), negatively on domestic wages, and positively on importing trade costs, τ * ht . The extensive margin operates via current and lagged cutoff productivities, which negatively impact home sectoral labor demand. Higher home wages, a more competitive home market, higher fixed costs or smaller domestic demand will all potentially trigger firm exits (via equation 7.8), which will not necessarily be reversed immediately when these variables return to previous levels. The sole discordant note is that, due to the CES preferences, which serve as a modeling convenience rather than as a statement about the way the world operates, growing productivity in a sector will not imply decreased labor demand as both intuition and data would suggest.
The second term on the right-hand side of equation (7.6) is analogous, as labor devoted to production for exports will be a positive function of foreign demand along the intensive margin, and a negative function of home wages and trade costs for exporting. Additionally, there can be movements along the extensive margin, which will depend on the cutoff productivity for existing firms, equation (7.8). If wages, fixed overhead costs (f ht ), iceberg trade costs, or more foreign firms enter, the cutoff productivity for making a profit will rise, and some existing firms will be forced out of the market: (7.10) While there is no explicit "exchange rate" in this model, one could proxy it in several ways. One is to stipulate that both wages and output are denominated in local dollars, and to then treat an exchange rate appreciation as local wages and output rising relative to foreign. A second approach, used by Nino et al. (2011), is to proxy exchange rate movements using the iceberg trade costs. Either would yield the needed result, although a referee correctly notes that this model, with CES preferences and no relocation decision by firms, should not be expected to yield a realistic elasticity. Also note that since either of these methods imply a constant elasticity of changes in employment in exporting or given movements in wages or iceberg trade costs, that sectors with higher shares of either imports or exports in production will theoretically be impacted more by movements in exchange rates. This intuitive theoretical result will be used to identify the impact of relative price movements on manufacturing employment.

Proposition: Trade is a Function of History
To simplify matters, the fixed overhead costs will now be set to 0. Total exports in industry h at time t are the sum of exports of each cohort of past entrants, where I borrow Chaney's assumption that the mass of entrants in industry h at time t is α ht Y t : Substituting in the solutions for x = pq, plugging in the pricing rules, assuming Pareto-distributed productivity and integrating, I arrive at a dynamic gravity equation: , and where P 1−σ t is the denominator of equation (7.10).
The key underlying insight of this equation is that trade today depends on the history of trade costs, both entry and iceberg, in addition to market sizes and contemporaneous variables. Even with the simplifying assumptions, this equation is still fairly complex, so for purposes of clarity, I have summarized the sign of the impact of key variables on exports (foreign variables denoted by an *) at time t: Note that if we were in a one-period world, then, as in Chaney (2008), the elasticity of substitution would not magnify the impact of iceberg trade costs, but that with multiple periods of firm entry, this result would no longer follow. How general is this dynamic gravity formulation? In the Additional Appendix, I prove that similar transition dynamics arise when moving from autarky to free trade for assumptions similar to those for key models in the new trade theory canon, including Krugman (1980) and Melitz (2003). Recent related research includes Burstein and Melitz (2013), who provide impulse response functions for shocks to trade costs, and Bergin and Lin (2012), who focus on the dynamic impact of future shocks. The large aforementioned literature on hysteresis from the 1980s carried the same core insight, that trade shocks can have persistent effects, as in equation (7.12). This paper is the first to show that the logic of sunk entry costs naturally leads to a "dynamic gravity" equation which can be derived explicitly.
Empirically, incumbent firms dominate most sectors in terms of market share, which means that the current trade relationship could be determined, in part, by historical factors as emphasized by , Eichengreen and Irwin (1998), and Head et al. (2010. 21

Corollary: The Real Wage is a Function of Historical Market Access
A key insight from New Trade Theory is that the real wage is a function of market access. Krugman (1992) argues that new trade theory can help explain higher wages in the northern manufacturing belt of the US, Redding and Venables (2004) argue that market access can explain cross-country variation in per capita income, and Liu and Meissner (2015) show that market access can help explain high living standards in northwest Europe in the early 20th century. An important corollary is that sunk costs imply that the real wage is also a function of historical market access. This follows from the dynamic gravity equation, as utility is increasing in the number of varieties and the extensive margin increases over time after a decline in trade costs. Figure 20 in the Appendix is a chloropleth map of per capita income by county, which can be compared to the distribution of import-competing manufacturing in Figure 21. It is immediately obvious that both are highly correlated with access to sea-navigable waterways -and that the US north was still much richer than the south in 1979. I posit that this owes more to the past history of trade costs than it does to low shipping costs on Lake Erie today.

RER Levels vs. Log Changes: Does the Latter Imply Hysteresis?
In the paper, I assert that when we interact the level of the log of the RER and regress it on log changes in employment, this implies "hysteresis". Does it? To see, let us first consider the familiar solution to a simple CES demand system: (7.14) Where x kjt is exports from country k to j at time t. Y jt is output in country j, p kt is the price level of a good produced in country k, τ kjt are the iceberg trade costs from country k to j, σ is the elasticity of substitution, and P jt is the CES price index in country j. Now, let's make a few simplifying assumptions. First, let's assume that sectoral output is proportional to sectoral labor demand. Second, let's sum up the total labor demand across all geographic destinations for each sector i, and get rid of the k and j indices, and let's use our RER index instead of prices, as we'll also consider sectors that are relatively open to trade. Taking log changes from one year to the next, we have: In this case, a log change in the RER (or, basically, prices) should result in a change in the level of manufacturing employment for an open industry. The puzzle, as we've discussed, is that this equation does not seem to work very well.
However, we also know that New Trade Theory implies the potential for hysteresis, or at least for persistence. Let us now assume that not just the price level today matters for the level of output/labor employment in a tradable sector, but also the past history of the RER, with annual decay rate ρ, potentially less than one. Thus, we'd have: Now, let's subtract the same equation for the previous year multiplied by ρ, and simplify to: In the case when there is perfect hysteresis (no decay, or a ρ of 1), we would thus 42 have it that: Thus, in this case, the level of the RER impacts the log change in sectoral manufacturing employment.

Additional Notes on RER Indices (Online Appendix, Cont.)
The main measure of the real exchange rate used in this paper is the Weighted Average Relative Unit Labor Cost (WARULC) index designed by  to address the shortcomings of the IMF's Relative Unit Labor Cost (RULC) index. The four key problems with the IMF's index are that it (1) is computed as an index-of-indices, and thus does not reflect compositional changes in trade toward countries that have lower unit labor costs, (2) does not include China, (3) uses fixed trade weights, which have become outdated (Japan still held a 20% weight in the 2000s while China was excluded), and (4) uses country-specific deflators, which can become biased over time without the benefit of multiple benchmarks. (This last point is the same problem that afflicted older versions of the Penn World Tables predating version 8.0).
Note that most real exchange rate indices, such as those produces by the Federal Reserve, the OECD, the BIS, and many other central banks, also use time-varying trade weights, and that time-varying trade weight indices are often used in studies on the impact of RER movements on manufacturing, such as in Klein et al. (2003).  introduced WARULC, a simple weighted-average of RULCs which includes China, uses time-varying trade-weights, and also uses multiple-benchmarking of country-specific productivity series using PWT v8.0 methodology. This last point will be subtle for general readers, and so I would refer interested parties to Campbell 2016.
The WARULC index is computed as where and where Ω i,t are time-varying trade weights (a weighted average of import, export, and third-country competition weights, the same as used by the BIS and very similar to the Fed's weights), and where w i,t are manufacturing wages of country i at time t, e i,t is the local currency price of a dollar, and Y i,t is manufacturing production, converted to dollars at PPP (equal to one for the US). One of the key differences with the IMF's index is that for this index the ULCs are actual unit labor costs rather than indices of unit labor costs. Manufacturing PPP data were computed using ICP data for benchmark years, and then interpolated in between using manufacturing deflators from the OECD, or country-specific sources in the case of China.  Figure 13 vs. the IMF's RULC index. The IMF's index suggests a steady depreciation of US relative unit labor costs over the period, implying that US manufacturing has become steadily more competitive since the 1970s. WARULC, by contrast, implies that US manufacturing became less competitive in the early 2000s.
It turns out that all four of the adjustments from the IMF's RULC to WARULC are important. For example, changing the indexing method while using fixed trade-weights would yield an index almost identical to the IMF's index, even if China is included. Without the multiple benchmarking, WARULC would still have a more negative slope. I refer readers interested in the differences in these indices when some of these adjustments are left out to 2016.
I also consider alternative measures of relative prices. Figure 14 compares several state-of-the-art measures of relative prices which use PWT v8.0 data and methodology to more commonly used measures provided by the Federal Reserve Board and IMF. Indexing the IMF's RULC series to begin at the same level as the WARULC index in 1975, the IMF's index implies that US ULCs were nearly 40% lower than trading partners by the 2000s, which is implausible. I have also plotted an updated version of .   (2016). The Federal Reserve's CPI-based Broad Trade-Weighted Real Exchange Index, plotted in yellow, also implies that the dollar tended to depreciate over the period. The three "Weighted Average Relative" (WAR) indices all yield broadly similar results, although there are certainly differences in the details and in the implied degree of overvaluation. One of the differences is that the other WAR measures show a slower dollar depreciation in the mid-2000s, which is consistent with the finding that relatively open manufacturing sectors continued to fair poorly in this period ( Figure 16). Another difference is the slightly more negative overall slope of WARULC, which is due to the declining share of labor income in manufacturing in the US relative to many other developed countries, which appears to be a broad-based phenomenon in manufacturing not caused by outsized changes in a small number of sectors.

Additional Cross Sectional Results
In the exercises in Figures 3 and 8, I used fixed categories of openness. What is the appropriate functional form for how openness impacts employment growth by sector in periods when the RER is elevated? Figure 15(a) demonstrates a correlation, between initial sectoral openness in 1979 and subsequent employment declines from 1979 to 1986, a period which is conveniently arranged from one business-cycle peak to the next. The R-squared is .05, and the coefficient on lagged openness is -.74 vs. robust standard errors of .21. The fit gets better when additional controls are added in. However, in the next low RER period, from 1986 to 1996, also measured at similar points in the business cycle, there is no correlation between openness and employment changes by sector (panel b). The more open sectors which had experienced sizeable employment declines in the mid-1980s did not experience disproportionate gains in the period when the dollar returned to fundamentals (panel c). Similarly, in the 1970s, when US relative prices were near unity, there was no correlation between openness and employment declines, but in the period of dollar appreciation from 1997 to 2005, there was, once again, a fairly strong negative correlation (d). These dates were chosen to coincide with the sharpest movements in relative prices and to be at similar points in the business cycle, but are robust to changes in the cutoff dates.
This exercise implies a relatively straightforward linear functional form for the relationship between openness and employment declines in periods when the RER is overvalued. However, what is the impact by year, and does this relationship hold up once we include more control variables? One of the most fundamental variables to control for is a measure of sectoral demand. When the economy is doing poorly, consumer durables, which are also highly traded, tend to do relatively worse. Some sectors may experience increasing demand for any number of reasons. However, if we control for demand directly, a measure of domestic consumption (defined as: demand = shipments+imports−exports), one might worry that this would be an endogenous control given that it contains shipments. Thus, I create a sector-specific instrument for demand based on changes in US real GDP and sector-specific elasticities. First, for each sector h, I regress: (8.1) Then I use the predictions of demand growth (D) from this equation, ∆ln(D ht ), as the main measure of sectoral demand to be used as a control variable, but I also try using actual demand, omitting this control altogether as is standard in this literature, or excluding recession years as well (Appendix Table 31).
Next, we plot the correlation between openness and employment growth by year, running the following regression on repeated annual cross-sections of the data: ∆ln(L ht ) = α t + β 0 Openness h,t−1 + β 2 ∆ln(D ht ) + β 2 ∆ln(P rod. ht )+ (8.2) 1973, ..., 2009. This is a regression of log changes in sectoral employment, L ht , on lagged openness, controlling for a measure of productivity (such as shipments per production worker), an IV for sectoral demand growth,D ht , and two other China-related controls, following Pierce and Schott (2016). The first is the interaction between China's accession to permanent normal trade relations (PNTR) interacted with a control for the NTR gap by sector. The second is a measure of exposure to the expiration of Chinese textile quotas. As many authors, including Brambilla et al. (2010) and Khandelwal et al. (2013) have highlighted, the end of Chinese textile quotas associated with the end of the Agreement on Textile and Clothing (ATC) (the successor to the Multifiber Arrangement, MFA), had a large impact on the sectors in which the quotas were binding. Thus, I have also included a control for the weighted average of the fill rate -the imports divided by the allowable quotas -just before the quotas were lifted (also following Pierce and Schott (2016)). 22 Lastly, openness is defined as a weighted average of import penetration and the export share of shipments: where S it are shipments in sector i at time t, M it are imports, X it are exports. One could also use trade divided by shipments, and still get similar results, but this specification has the advantage that employment losses should be a linear function of openness, while trade over shipments would likely need to be transformed, particularly in cases in which imports are greater than shipments. This specification also indeed fits the data better (see the Additional Appendix for a comparison). The annual coefficient on openness is plotted in Figure 16 in blue, along with two standard deviation error bounds. I have also plotted a measure of the RER, weighted average relative unit labor costs (WARULC), and the real interest rate, defined here as the interest rate on 30-year mortgages minus the core CPI (both from FRED). Coeff. on Openness 2 s.e. Error Bound Real Interest Rate*2 WARULC

Figure 16: Correlation between Openness and Employment Growth by Year
Notes: Real interest rate data are computed as the 30-year conventional mortgage rate less the Core CPI, from FRED and the BLS (via FRED), WARULC is a measure of the RER from Campbell (2016), and the coefficients came from annual regressions of log changes in employment on changes in demand (using an IV), productivity, the China Post-PNTR*NTR Gap and MFA Exposure (explained in the text), with standard errors conservatively clustered at the 2-digit SIC level. Figures 3, 8, 15 and 16 suggest a functional form for the relationship between relative unit labor costs and the evolution of sectoral manufacturing employment. When unit labor costs are high in the US relative to trading partners, more open sectors lose employment relative to less open sectors. When the level of WARULC is close to unity, there does not appear to be a differential change in jobs for more open sectors. This makes intuitive sense, as when unit labor costs are roughly the same at home and abroad, increased from -.2 to 0. Using the Core PCE deflator instead of the Core CPI to calculate the RIR instead would give even more anomalous results, as the RIR measured using the PCE deflator spiked in 1980, a year in which more open sectors did slightly better than non-open sectors.
there is no large advantage for foreign firms over domestic firms, nor would there be a reason for domestic firms to incur the costs of moving production abroad, and so we should not expect differential employment changes in more open sectors. These findings imply that a temporary overvaluation will have a persistent effect.

Impact on Output, TFP, and Other Variables
Movements in relative prices impact manufacturing employment, but if they were to only affect manufacturing employment and not other variables such as output and productivity, this might suggest that the apparent impact on employment may be spurious, or perhaps even beneficial. In addition, if appreciations in the dollar also happened to be correlated with movements in other variables in more open sectors which should not theoretically be affected, such as the price of energy inputs, then this could imply that the estimation method used in this paper is prone to yielding spurious results. 24 In this section, I test the impact of relative price movements on several other variables, and provide several falsification tests.
First, for exchange rate movements to impact manufacturing employment, a necessary condition is that exchange rates affect trade. Figure 9 shows that when the dollar fell from 1972 to 1979, the entire distribution of log changes in US exports disaggregated by both sector and destination country is centered around a higher percentage change than the distribution of changes in imports. When the dollar spiked in the mid-1980s, the distribution of log changes in imports then shifted far to the right of the distribution of exports, with the median log change in imports close to one vs. slightly greater than zero for exports, corresponding to a 72% increase in imports relative to exports. The same pattern holds up over the period of dollar weakness from 1986 to 1996, and dollar strength from 1996 to 2005.
In Table 5, I find a modest decline in production worker hourly wages in more open sectors when relative prices are elevated, although a caveat is that lagged openness itself has the opposite sign, making an interpretation of this result less than straightforward. Nevertheless, this result is new, as Ebenstein et al. (2014) did not find an effect of globalization on industry wages using the Current Population Survey (although, they did find an impact on the occupations most exposed). In a subsequent follow-up to this paper, Campbell and Lusher (2016) did not find an impact generally of RER shocks on wages using CPS data, although some sub-groups, such as those without college education, did experience a reduction. I separately found no significant impact on nonproduction worker wages, but that value-added, TFP, and production worker hours all declined. Note that while the theoretical impact on TFP may be ambiguous, one intuitive reason why you might have a negative sign here is that if sectors have substantial overhead costs, then a decline in sales will lead to a decline in measured productivity. There was no significant impact on the log change in prices or on inventory. Since theory does not necessarily provide a strong rationale why inventory should be affected by movements in real exchange rates, this is arguably a falsification exercise. Predicting the changes in the sectoral deflators for investment, materials, and energy are perhaps even stronger candidates for falsification exercises, since any finding that real exchange rate movements lead to disproportionate changes in the costs of more open sectors would likely be spurious, raising doubts as to whether the estimation method in this paper has a tendency to find false positives. However, I find that the interaction term on WARULC and relative openness does not significantly predict the growth of any of these deflators, even for various leads and lags. 25 In addition, multi-year leads and lags of the RER interacted with openness are not significant predictors of differential changes in any of the dependent variables. Two-way clustered standard errors in parentheses, clustered by year and industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions weighted by initial sectoral value-added, and include 4-digit SIC industry and year fixed effects over the period 1973-2009. The dependent variables are 1) log changes in production worker hourly wages, 2) value-added, 3) 5-Factor TFP (from NBER-CES), 4) Hourse worked, 5) production worker hours, and 6) prices of shipments. Other significant controls from Table  1 are suppressed for space.
In addition, I find an impact of exchange rate movements on job creation, job destruction, and shipments. 26 When unit labor costs in the US rise relative to trading partners, there is suppressed job creation, but the impact on job destruction is much larger. Since job creation varies much less than job destruction overall, this asymmetry is an indication of persistence.

Manufacturing Employment
The existence of a unit root for sectoral manufacturing employment, i.e., if one regressess log employment on a lag of itself, whether the coefficient is one, is evidence consistent even with hysteresis/path dependence. This would also justify a simple functional form for a panel regression, of the log difference in employment on the left-hand side, and it would also be an indication that temporary shocks to employment in general tend to have a long-lasting impact.
In Table 6, I present several different commonly-used panel unit root tests. The first is a test developed by Levin et al. (2002). It assumes that all panels share a common autoregressive parameter, and works best with N larger than T, which is the case we have. The null hypothesis is that the panel contains a unit root. The p-value on the test of one indicates that we cannot reject the null at any level of confidence. Next we perform a related series of tests by Im et al. (2003), which appealingly allows the autoregressive parameter to differ by sector. These tests have the null hypothesis that all panels contain unit roots. In Column (2), using the Im-Pesarin-Shin (IPS) test, we again can not reject the null hypothesis that all sectors contain a unit root. In column (3), we now add in lags, using the Akaike information criterion (AIC) to choose the appropriate number of lags for each panel (up to 4). In column (4), we choose the appropriate number of lags for each panel using the Bayesian information criterion (BIC) is used instead. In Column (5), we allow for each panel to have its own mean, in column (6) we allow for time trends, and in column (7), we allow for lags, means, and trends. In no case can we reject the null hypothesis even at 10%, although in column (6) there is some uncertainty. However, in practice, it is also worth noting that, for practical purposes, a lagged dependent variable close to one, implying that a temporary shock would take a long time to fade out, would not be much different in terms of economic significance.

Are our RER indices Stationary?
First, when we run a simple regression of log WARULC on a lag of itself, we get a coefficient of .79, roughly two standard errors from one. Of course, in the presence of serial correlation, this can be biased, so we also perform a variety of panel unit root tests. First, we implement an augmented Dickey-Fuller regression, which has the null hypothesis that there is a unit root, and we cannot reject, with a p-value of .18. Next we try alternatives allowing for drift or lags, and we find that we can reject with 95% The first column runs the Levin-Lin-Chu (LLC) test, the others run different versions of the Im-Pesaran-Shin (IPS) test. The Null hypothesis of the LLC test is that the panels contain unit roots. For the IPS tests, the null is that all panels contain unit roots. A P-value near zero indicates that one can reject the null. In none of these cases can the null hypothesis of a unit root be rejected at 10%.
confidence, as the p-values shrink to .015 and .019. Next we run a Phillips-Perron test instead, and can only reject with 90% confidence. As the WARULC index is a weighted average of bilateral RULCs, we try instead to test whether the panel of US bilateral RULCs have unit roots. Using the Levin-Lin-Chu test with the null hypothesis that all panels contain unit roots, we can reject with a 99% level of confidence. An alternative is the Hadri test, with the null that all panels are trend stationary: we can also reject. While these results suggest that the WARULC RER index does not contain a unit root, it is also true that they don't provide unambiguous evidence. However, even in the case where we cannot reject a unit root, it doesn't mean that there is one. In addition, two other types of considerations also point in the direction of no unit root. First, from a theoretical perspective, if WARULC had a unit root, this implies that it would vary without trend. A RER which is even very overvalued would have no tendency to depreciate if the WARULC had a unit root. However, a very overvalued RER is likely to depreciate for several reasons: (1) this implies that it will be losing jobs in tradable sectors, lowering the equilibrium level of the nominal exchange rate -and part of this is mechanical, as importers exchange the local currency for foreign currency to buy imports, (2) this loss in jobs will typically induce it's central bank to lower interest rates, also putting downward pressure on the RER, and (3) the loss in jobs will also cause wage growth to fall, reducing labor costs (and thus the WARULC).
The second consideration is that WARULC is a real exchange rate, and thus we can appeal to a wide literature testing bilateral RERs for unit root, some of which uses very long-run data, and generally finds that RERs do not have a unit root (see Taylor and Taylor (2004) for an overview). The first column merely regresses the log of WARULC on a lag. Column (2) runs an augmented Dicky-Fuller test, where the null hypothesis is that there is a unit root (it cannot be rejected). Column (3) runs an augmented DF test with drift, and rejects a unit root. Column (4) runs a DF test with an extra lag term, and similarly rejects the null of a unit root. Column (5) runs a Phillips-Perron test, and only rejects the null of a unit root at a 10% level of confidence. Column (6) is a panel unit root test of bilateral using Levin-Lin-Chu (LLC), where the null hypothesis is that the panels contain unit roots. Column (7) runs the Hadri panel unit root, where the null hypothesis is that all panels are stationary. A P-value near zero indicates that one can reject the null.

Error Correction Model (and other Dynamic Models)
Of course, our key dependent variable is not just WARULC, but WARULC interacted with sectoral openness. A unit root for this variable also tends to be rejected in panel unit root tests (an Im-Pesaran-Shin panel unit root test has a p-value of 0.0, vs. .027 for just WARULC alone). Below in Table 8, we compare unit root tests for employment and openness interacted with WARULC, and then also test for cointegration. We find that we cannot reject a unit root for employment, but that we can for the interaction. Lastly, we find that these variables are cointegrated. The first two columns run variations of the Im-Pesaran-Shin (IPS) test on employment (column two demeans the panels and includes trends). Unit roots cannot be rejected. Columns (3) and (4) include the interaction term, the 3-6 year average of lagged openness interacted with WARULC, in which case we can decisively reject a unit root for all panels. Lastly, in columns (5) and (6) we implement cointegration tests, and reject the null of no cointegration.
Even though our RER indices do not appear to have a unit root, it's also true they do exhibit a high level of persistence, and a formal cointegration test would reveal that manufacturing employment and WARULC interacted with openness are cointegrated. In addition, while the results in the main paper are suggestive of strict hysteresis, it's natural to suspect that there is not perfect, or strict hysteresis, but rather that RER movements have very persistant impacts on manufacturing employment (this can be described as a main point of the paper). Thus here we proceed with several error correction models and then examine several alternative autoregressive distributed lag models.
I postulate the following error correction formulation: Here, L ht is labor employed in sector h at time t, O h,t−3,6 is weighted average openness lagged from three to six years, ∆ln(RER t−1 ) is the log change in the RER lagged one period, X k are various other controls, and α h and ν t are sector and year FEs. Here it is assumed that movements in the RER (lagged one period), cause movements in manufacturing employment, but also that even if the RER were fixed, there would be movements in manufacturing employment as it adjusts to the long-run level, which is assumed to be a function of the level of the RER. (The long run relationship hypothesizes that there is an equilibrium level of manufacturing employment for each level of the RER.) As this relationship between manufacturing employment and the RER is only hypothesized for more open sectors, we include the interaction term, which makes this somewhat of an unorthodox error correction model. Also, since we include sectoral FEs, and yet have a lagged dependent variable, there will of course be Nickel-type biases, but with T= 39, these will be fairly small (the standard Nickel Bias would be on the order of 2%). The "long run" semi-elasticity of employment with respect to RER (interacted with openness) innovations is thus −β 3 /θ. Next, we try alternative simple dynamic models, including a version of a simple autoregressive distributed lag model. First, we continue with our benchmark regression using the interaction between the RER (WARULC) the period before and lagged openness, but we also control for lags in log changes in sectoral employment, and also the lagged level of manufacturing employment. ∆ln(L ht ) = ρ∆ln(L ht−1 ) + θln(L h,t−1 ) + β 0 O h,t−3,6 + β 1 ln(RER t−1 ) * O h,t−3,6 (8.5) Here, the "long-run" effect of a "permanent" RER change will also be −β 3 /θ. However, this formulation, while similar to the previous models, is a bit overly complicated, as it includes the lag of labor three times (including in the two log change terms). A simplified version would be the following (a 2nd LDV could be added if necessary): In this case, the long-run elasticity will be 1 1−ρ β 1 , whereas the short-run will merely be β 1 .  Two-way clustered standard errors in parentheses, clustered by year and industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions weighted by initial sectoral value-added, and include 4-digit SIC industry and year fixed effects over the period 1973-2009. The first two regressions are error correction models, and the last two columns run alternative dynamic regression models.

Japan
Just as China has become the center of focus for those wishing to explain the decline of US manufacturing today, similarly, in the 1980s many Americans blamed manufacturing job losses on Japan's rise. During this period it was widely thought that Japan's dominance owed to superior Japanese business practices such as Kaizen costing and Kanban scheduling, support from MITI, and innate features of Japanese culture. While these and other factors may have been important, it turns out that relative prices alone can largely explain Japan's ascent and then stagnation in the US market. Japan is a particularly good case study since the yen was heavily managed and then appreciated substantially shortly after the full liberalization of Japanese capital markets. The yen was fixed after World War II until the early 1970s, when President Nixon, worried about what were very small trade deficits by recent standards, imposed a 10% tariff to force other countries, namely Japan and Germany, to revalue their currencies (Irwin (2013)). In the 1970s, the yen continued to be managed in a dirty float, with most controls on capital lifted in 1980. At that point the dollar began its appreciation for reasons unrelated to Japan. In 1984 Japan, under intense pressure from the US Treasury, added substantial additional liberalization measures in the Yen-Dollar Agreement Frankel (1990). As the dollar continued to soar in 1985, the Reagan Administration responded with the Plaza Accord, an agreement among major nations to reduce fiscal imbalances and intervene in the currency markets to weaken the dollar, and the 1985 Gramm-Rudman-Hollings Deficit Control Act. Figure 17, panel (a) and (b) demonstrate that the combination of the end of capital controls, the move toward fiscal balance in the US in late 1985, and the Plaza Accord had a major impact on relative prices between the US and Japan. US manufacturing workers went from enjoying hourly wages twice that of their Japanese counterparts in 1985 to earning wages that were close to parity three years later. US unit labor costs relative to Japan fell 47% and the real exchange rate using PPP from the Penn World Tables, v8.1, implies an appreciation of Japanese relative prices of 37%. Thus the case of Japan yields a relatively clean quasi-natural experiment for the impact of currency undervaluation and large exchange rate adjustments.
The result of this real appreciation was that as wages in the Japanese manufacturing sector suddenly increased relative to their American counterparts, the meteoric Japanese export growth from 1946 to 1986 suddenly ground to a halt (Figure 17(c)). However, Japan kept the gains in market share it had made even though it did not make further inroads-another indication of persistence. Japan's gains through 1986 were also not purely due to domestic factors in Japan, such as government encouragement to increase market share in export markets, since the same trends are not evident in other markets.
In the UK case, Japanese exports grew very quickly in the early 1980s, when the yen was weak relative to the pound, but Japanese import penetration into the UK market did not grow at all from 1983 to 1985, when Japanese unit labor costs were higher than UK unit labor costs. Hence, on balance Krugman (1986) appears to have been correct in guessing that the yen's appreciation in that year meant that "the Japan problem was over." The first column of Table 10 regresses the log change in Japanese import penetration (imports divided by domestic demand) in the US on the lagged log of bilateral relative unit labor costs for the manufacturing sector between the US and Japan, while controlling for changes in overall US import penetration. The coefficient indicates that when ULCs were relatively higher in the US, Japanese sectors gained market share in the US, and when US ULCs were relatively lower, the growth in Japanese import penetration decreased (in fact it became stagnant). In column (2), I include a dummy variable for the period after the Plaza Accord -after the end of capital controls and the strong dollar -and find that after 1985, Japanese import penetration fell relative to the period when the Yen was weaker. In column (3), I use UK data, and find that when unit labor costs in the UK are high relative to Japan, Japanese industries increased their market share in the UK. In column (4), I rerun the regression in column (1), and control for Japanese changes in import penetration in the UK. In column (5), I stack data for each of the G6 countries, and find a similar elasticity as to the US initially.
Thus, the example of Japan would appear to provide another confirmation that relative prices matter and that persistence is a quantitatively important aspect of the economic landscape, using quasi-experimental evidence which is effectively out-of-sample.  The dependent variable is the log change in sectoral Japanese import penetration. Errors clustered for 29 ISIC industries in parentheses. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions include 3-digit ISIC Rev.2 industry fixed effects over the period 1978-2003. Columns (1), (2), and (4) use US data, column (3) uses UK data, and column (5) includes stacked observations from the US, the UK, Canada, Germany, Japan, France, and Italy. The data come from Comtrade, UNIDOs, and Campbell (2016).

Additional Robustness Exercises
The results are robust to using various measures of openness. For example, the results do not change significantly using a geometric rather than an arithmetic average of export share and import penetration as a measure of openness, when one uses a simple average of import penetration and the export share of shipments, or if one uses trade/shipments instead. Earlier versions of this paper used "relative openness" instead of openness, which yielded very similar results. One could also use openness lagged one period instead, or, in fact, simply use openness in 1972, the first year we have data for, and the results are still robust. The results are also robust to using various measures of RERs. One could also use the Fed's RER index (and control for Chinese penetration separately), or various other Weighted Average Relative RERs such as WARP introduced by Thomas et al. (2008) or the Penn-Adjusted version introduced by Campbell (2016). One could also use a WARP index computed not using trade shares, but computed with GDP. This shows that endogeneity in the trade weights are not somehow driving the results. One can also use a sectoral version of WARULC, although sectoral RULC data is not available for US trading partners and thus the only thing sector-specific about it is the trade weights. It turns out that sectors that experienced larger than average depreciations also lost more employment and output. Lastly, one could proxy the US RER using changes in the defense share of GDP, defense spending over shipments, or changes in the US structural budget. In each case, these measures will also predict employment declines.
One could also separate import penetration and the export share of shipments, and interact these with import and export-weighted versions of WARULC (iWARULC and eWARULC). The coefficient on both happens to be roughly the same for the full period, although the interaction between eWARULC and the export share of shipments is not significant in the early 2000s. Changes in import penetration and export share are also generally highly correlated with changes in employment-a necessary condition for the lagged relative openness interaction with the real exchange rate to predict innovations in employment.
The results are also unchanged when including controls for tariffs or the cost of insurance and freight, for which I did not have complete coverage for all years and so omitted from the main regressions. US tariffs and freight costs did not exhibit sharp changes during this period, and perhaps as a result neither variable was significant in any specification or with alternative dependent variables. Tariffs faced by US industries abroad, tariffs faced by US industries exporting to China, and tariffs faced by US industries interacted with the share of shipments bound for China all do not predict changes in employment. Even as of 2008, on average industries only sent 1.4% of shipments to China, so it is not surprising to find no effect of Chinese tariff policy on employment or output.
I also tested whether the decline in the 2000s was more pronounced in unionized sectors, and whether RER movements have a bigger impact on unionized sectors, but found no relationship (as expected). Unionization has been steadily declining in the manufacturing sector over this period, and had already declined from 38.9% in 1973 to 16.3% in 1997. There is a positive raw correlation between unionization in the 1990s and job growth in the early 2000s, but this correlation does not survive the inclusion of controls and is unlikely to be causal.   Standard errors clustered by sector in parenthesis. *p < 0.1, ** p < 0.05, *** p < 0.01. The first five columns include year and 3-digit ISIC industry fixed effects using data from 1979 to 2003 for 29 sectors (West German data here is only through 1990). Columns (6) and (7) are stacked regressions with data from all 7 countries (including the US and Canada), with country*ISIC interactive FEs. Column (7) is a quantile regression.    Table 1 omitted for space. "Imported Inputs" is for 1997. "L.avg.MPInputs" is the average of imported inputs lagged 3, 4, 5, and 6 years. "L.avg.NarrowMPinputs" is an average of lagged intermediate inputs within the same 2 digit sectoral classification. "L.avg.NotNarrowMPInputs" is the average of lagged intermediate inputs which are not within the same 2-digit SIC classification. Two-way Clustered standard errors in parenthesis, clustered by year and 4-digit SIC sectors. *p < 0.1, **p < 0.05, ***p < 0.01. Each cell is a separate regression, with 28 regressions total, and with other controls from the benchmark regression suppressed. In addition, each regression controls for relative openess at the same number of leads and lags as the reported interaction term. The dependent variable in the first column is the log change in sectoral manufacturing employment. These results demonstrate that this estimation strategy is not generally prone to yielding spurious results.  Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period 1973-2009. The dependent variable is the log change in sectoral manufacturing employment. In Panel A the first two columns add lagged dependent variables. Note that given T=37, Nickell Bias will be relatively small. The third column includes sector trends, which control for second-derivative trends in employment. The fourth column uses openess interacted with ln(WARULC) instead of relative openness as the regressor of interest, and the fifth column uses WARULC-1 in place of ln(WARULC), and the last column includes controls for the cost of insurance and freight. In Panel B, the key regressor is the lagged log of WARULC interacted with longer and longer lags of relative openness (RO). The last column interacts the lag of log WARULC Value-Added in 1972. The other controls from the baseline regression in Table I      *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period . The dependent variable is log sectoral employment, and includes a lagged dependent variable. Note that in a 35 year panel, the resulting Nickell Bias will be small, and should also shrink the coefficient on the lagged dependent variable itself. Without FEs, it will be closer to one. The last column is a quantile regression minimizing the sum of absolute deviations, the other regressions are OLS. Sectoral changes in the cost of investment, energy, and materials are omitted for space. L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years as elsewhere.  and 1975-2009 for the third. The dependent variables are job creation, job destruction, and the log change in shipments. Job creation and destruction data are from Davis et al. (1998). L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years as elsewhere.  1973-1989 1990-2009 1973-2009 1973-2009 1990-2009 1990-2009 Two-way clustered standard errors in parenthesis, clustered by year and 4-digit SIC sectors. *p < 0.1, **p < 0.05, ***p < 0.01. There are five sets of six regressions, for 30 regressions total, with the same controls as in column (5) of Table I, the baseline regression in the paper, with the other controls suppressed for space. Panel A varies the fixed effects (SIC industry effects, and year effects) and whether or not the full list of controls are included. L.Avg. Openness is again defined as the average of openness lagged 3, 4, 5, and 6 years. Panel B uses the interaction between ln(WARULC) and openness lagged just one year as the key variable of interest, and also includes a control for the weighted average of lagged opennnes. Panel C varies the weighting scheme used in the paper, between using initial Value-Added (VA), vs. no weights, initial employment or shipments, average VA or VA lagged one period. Panel D adds and subtracts industries which are either unbalanced, or for which there are logical reasons why they should be excluded. In the first three columns of panel E, the key variables are now the import-Weighted Average RULC index interacted with import penetration, and export-WARULC interacted with the export share of shipments. In the last three columns, I interact the Fed's RER index with the Import Penetration ex-China versus Chinese Import Penetration interacted with bilateral Sino-American RULCs. Note: This figure reports the coefficient on Import Penetration excluding China from the following regression: ln∆L ht = α t + β 0 M P P en.exChina h,t−1 + β 1 ChineseM P P en. h,t−1 + β 2 ln∆D h,t + β 3 ln∆T F P h,t + β 4 P ostP N T R * N T RGap h + β 5 M F AExposure ht + ht , for 359 sectors. Note that the Fed's Index is calculated using an index-of-indices approach that doesn't reflect the role of rising trade integration with China. Standard errors conservatively clustered at the 3-digit SIC level. D is an IV for sectoral demand as is used elsewhere in the paper.    Table 1 for two sectors. One sector has average openness and the other is one of the most open sectors in the economy (with an average openness of 50% in the early 1980s. The y-axis is thus the log change in sectoral employment. I thank a referee for the suggestion.

Proxies and Alternative Measures of RER Indices
Large US fiscal deficits were a likely cause of the dollar's strength during the early 1980s. Fiscal deficits can affect the tradable sector in at least four ways. First, even in a closed economy setting, higher government spending could induce more resource allocation away from manufacturing via rising wages or real interest rates. Secondly, government purchases of defense equipment could impact those sectors directly (part of the motivation for controlling for domestic demand growth, and for dropping defense-related sectors). Thirdly, in an open economy, higher real interest rates can cause currency appreciation due to international interest rate parity. Additionally, a larger supply of US Treasuries may induce foreign purchases of dollars given that there is a globally limited supply of safe, highly liquid, positive-yielding assets whose value appreciates during periods of financial turmoil. Empirically, Guajardo et al. (2014) examine the impact of fiscal changes on RERs in OECD countries, finding that fiscal consolidation leads to RER depreciation precisely as textbook theory predicts. Hence, in this section, I estimate reduced-form regressions using changes in defense spending and the budget deficit ex-automatic stabilizers to predict differential changes in employment in more tradable sectors. The benefit of this research design is that the changes in defense spending and budget posture were the result of longstanding campaign  Figure 24: Employment Growth vs. Openness: 1996Openness: to 2005Openness: vs. 2004Openness: , 2006Openness: , & 2007 Notes: At the request of a referee, we compare the correlation between openness in 1996 with other ending dates beside 2005. The correlation holds up if we consider 2004, 2005, 2006, or 2007. Note that the y-axis does change as the job losses become more severe.
promises that came to fruition after the outcomes of close presidential elections. Thus, I would argue that these elections were exogenous from the perspective of the subsequent evolution of manufacturing employment in more open sectors. Figure 29(a) shows that defense spending as a share of GDP increased dramatically after the US election of 1980, and then increased again after the election in 2000. Changes in the US budget deficit appear to be related to changes in WARULC (Figure 29(b)), although the correlation with other measures of the real exchange rate, such as WARP or the Fed's index, is even more pronounced. In Table 20 column (1), I regress lagged relative openness interacted with log changes in defense spending over GDP (divided by ten to normalize the coefficient). Once again, I get a negative, statistically significant coefficient, which implies that in 1985, when defense spending as a share of GDP increased by 10%, a sector with a relative openness of twice the average would have experienced a decline in employment by two percent relative to a closed sector. This effect is not driven by GDP as the denominator, since if we deflate defense spending with total manufacturing shipments instead, as in column (2), the results only get stronger. In column (3), I use the interaction of relative openness with changes in the budget deficit ex-automatic stabilizers and find that increases in the budget balance are also good for relatively more tradable sectors.
Next I consider alternative measures of relative prices, including several versions of Weighted Average Relative Price (WARP) indices, and sector-specific WARULC indices (discussed more in Appendix Section 7.4). As argued in , unit labor cost-based relative price measures are not necessarily a priori better measures of compet-itiveness than Penn-Adjusted Weighted Average Relative Price (PWARP) indices. This is because manufacturing requires many more inputs, including nontraded inputs, than just labor, as labor costs fell to just 23% of total costs by 2007 (or 32% of value-added). Thus broader measures of prices may be just as appropriate to gauge competitiveness as ULC indices.
In Table 20, I show that the results hold for the other WAR exchange rate indices. In column (4), I use the lagged log of a GDP-Weighted Average Relative Price (G-WARP) index. This is an important robustness check for those who may be concerned that the trade-weights themselves are endogenous and may be driving the result. The GDPweighted version of WARP is plotted in Figure 26. In column (5) I use the log of the PWARP index (the Penn or Balassa-Samuelson adjusted version of WARP). In each case, the results are little changed.  weights (following Revenga (1992) and Gourinchas (1999)) in addition to controlling for the sector-wide WARULC. The only change with sectoral WARULC is that the trade weights are computed as imports plus exports at the sectoral level, as opposed to using economy-wide trade data. Unfortunately, complete unit labor cost data, including for manufacturing PPP, is not available internationally at a disaggregated level. Sectoral real exchange rates may a priori seem like a vast improvement over using real exchange rates for the manufacturing sector as a whole, and, indeed, they do add significant explanatory power as the "between" R-squared nearly doubles, while the overall Rsquared also increases modestly, providing further evidence that relative prices affect manufacturing employment. However, in earlier versions of this paper which simply used single lags in openness and relative openness, I had also found that this result was sometimes sensitive the exact specification and controls, which is why I chose to use the economy-wide rate in the main regression tables.    **p < 0.05, *** p < 0.01. Standard errors in parenthesis. Intercept omitted. The dependent variable is the coefficient on openness of an annual regression of employment growth on openness, and thus represents the correlation between openness and employment growth for each year. Columns (1) and (3) use data from 1975 (when the IMF's index begins) through 1990. I then predict the coefficient on openness for all years, and report the mean absolute error in the last row. Note: This graph plots WARULC, the same index only using a divisia method (very similar to the IMF RULC index), and then the difference between the two, which essentially captures the impact of shifting trade toward low ULC countries.

Using Alternative Measures of Openness
An alternative measure of openness is simply to take total trade and divide this by total shipments. I compare this second measure of openness in Figure 33 below. In  Figure 31, I compare the employment declines in both periods of appreciation using each measure of openness, to gauge the fit. In fact, the fit looks good for both, which isn't surprising given that the measures are highly correlated. One difference though is that most observations of Trade/Shipments are less than 1, so that it's hard to see how good the fit is for the majority of the sectors.
Thus, in Tables 23 and 26, we test the R-squareds for how openness predicts employment declines for the two periods when the dollar was overvalued. We do this for the full sample in Table 23, and for a restricted sample in Table 26, where we eliminated sectors with (1) negative raw values for import penetration, (2)   One is total trade/Shipments (special thanks to an anonymous referee for suggesting). The second is a weighted average of import penetration and the export share of shipments: openness = m*(imports/(imports+shipments-exports) + (1m)*(exports/shipments), where m = imports/(imports+exports).  1979-1986 1979-1986 1996-2005 1996-2005   Note: This figure compares t-scores from 100 synthetic "noise" regressions where I began with the benchmark regression (column 5, Table 1) and replaced actual openness for each sector with another sector within the same 2-digit sector. The t-scores here are for the key interaction term: sectoral openness interacted with the log of WARULC. The actual t-score is in red. Note: This figure compares t-scores from 1,000 synthetic "noise" regressions where I (column 5, Table  1) and replaced the actual WARULC series with artificial RER indices created by randomly scrambling the initial level and year-to-year changes of the actual WARULC index. The t-scores here are for the key interaction term: sectoral openness interacted with the log of WARULC. The actual t-score is in red.

Falsification Exercises: Noise Simulations
(3) (4) 1979-1986 1979-1986 1996-2005 1996-2005 (2), the lags of Pay per worker, the ratio of Skilled to non-skilled workers (proxied by the non-production to production worker ratio) are added as controls, and a three year moving average of these variables is added in column (5). The three year moving average is an average of the variable lagged 1, 2, and 3 years. *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. This Table repeats the regression in Column (4) of Table 1, only adding in various countrols for foreign demand. Column (2) includes a control for a average of foreign demand, weighted by exports at the 4-digit SIC level. Column (3) multiplies this amount by the domestic demand elasticity for each 4-digit domestic sector (creating a quasi-IV). Column (4) interacts a weighted average of the export share and the foreign demand IV.  *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period . The dependent variable is the log change in sectoral manufacturing employment in the first five columns, and the 5 year log change in the last column. Sectoral changes in the cost of investment, energy, and materials are omitted for space. L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years, and is interacted with the logged lag of WARULC, a measure of the RER. The variable "3-6yr.Avg.MPInp/Ship." is the moving average of imported inputs divided by shipments lagged 3, 4, 5, and 6 years.   *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period 1975-2009. The dependent variable is the log change in sectoral manufacturing employment in the first five columns, and the 5 year log change in the last column. Sectoral changes in the cost of investment, energy, and materials are omitted for space. L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years, and is interacted with the logged lag of WARULC, a measure of the RER. The variable "3-6yr.Avg.MPInp/Ship." is the moving average of imported inputs divided by shipments lagged 3, 4, 5, and 6 years. I thank Bryan Kovak for the suggestion to do this.  Standard errors clustered by sector in parentheses. *p < 0.1, ** p < 0.05, *** p < 0.01. Each column is a quantile regression including year and 3-digit ISIC industry fixed effects. Data for the first four regressions span from 1977 to 1995 and 1998-2003 for 31 sectors, and the last two regressions span 1991-2010 for 104 sectors. The dependent variables in the first two columns are the log change in sectoral manufacturing employment and output. In the 3rd and 4th columns, the dependent variables are the log change in manufacturing employment (and output) relative to the average log change in employment (and output) in the same sectors in other major economies. Data in the last two columns are for Canada. In the 5th column, I normalized WARULC by adding .15. In the last column, oil prices are used as a proxy for Canada's RER.

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To normalize oil prices, I took the log and of the price of a barrel of crude oil and subtracted three.  Standard errors clustered by sector in parentheses. *p < 0.1, ** p < 0.05, *** p < 0.01. Each column is an OLS regression including year and 3-digit ISIC industry fixed effects. Data for the first four regressions span from 1977 to 1995 and 1998-2003 for 31 sectors, and the last two regressions span 1991-2010 for 104 sectors. The dependent variables in the first two columns are the log change in sectoral manufacturing employment and output. In the 3rd and 4th columns, the dependent variables are the log change in manufacturing employment (and output) relative to the average log change in employment (and output) in the same sectors in other major economies. Data in the last two columns are for Canada. In the 5th column, I normalized WARULC by adding .15. In the last column, oil prices are used as a proxy for Canada's RER. To normalize oil prices, I took the log and of the price of a barrel of crude oil and subtracted three.   Errors clustered by year and 4-digit SIC sectors. *p < 0.1, **p < 0.05, ***p < 0.01. There are five sets of six regressions, with the same controls as in column (5) of Table I, the baseline regression, with other controls suppressed for space. Panel A varies the fixed effects (SIC industry effects, and year effects) and the inclusion of other controls. L.3-6yr. Openness is again defined as the average of openness lagged 3, 4, 5, and 6 years. Column (6) includes 2-digit SIC*year interactive fixed effects or 20*37= 740 FEs, in addition to SIC FEs. Panel B repeats Panel A using quantile regressions. Panel C varies the weighting scheme used in the paper, between using initial Value-Added (VA), vs. no weights, log initial value-added, initial employment or shipments, or VA lagged one period. Panel D adds and subtracts industries which are either unbalanced, or for which there are logical reasons why they should be excluded. In Panel E, I interact openness with dummy variables for WARULC in different bins. I thank a referee from JEEA for the suggestions    (5), and bootstrapped errors are in columns (2), (4), and (6). *p < 0.1, ** p < 0.05, *** p < 0.01. Two-way clustered standard errors in parentheses, clustered by year and by 4-digit SIC industry. *p < 0.1, ** p < 0.05, *** p < 0.01. All regressions are weighted by initial sectoral value-added, and include 359 SIC industry and year fixed effects over the period 1975-2009. The dependent variable is the log change in sectoral manufacturing employment in the first five columns, and the 5 year log change in the last column. Sectoral changes in the cost of investment, energy, and materials are omitted for space. L.3-6yr.Openness equals average openness lagged 3, 4, 5, and 6 years, and is interacted with the logged lag of WARULC, a measure of the RER. The variable "3-6yr.Avg.MPInp/Ship." is the moving average of imported inputs divided by shipments lagged 3, 4, 5, and 6 years.