Macroeconomic volatility is considered an important determinant of a wide variety of economic outcomes. Numerous studies identify its effects on long-run growth (Ramey and Ramey 1995), welfare (Pallage and Robe 2003, Barlevy 2004), as well as inequality and poverty (Gavin and Hausmann 1998, Laursen and Mahajan 2005). The question of what are the main determinants of macroeconomic volatility has thus attracted a great deal of attention in the literature. In particular, it has been argued that trade openness plays a role (Rodrik 1997, ILO 2004). As world trade has experienced exponential growth in recent decades, understanding the relationship between trade and volatility has become increasingly important. Figure 1 shows a scatterplot of trade openness and the volatility of GDP growth in the 1990s for a large sample of countries, after controlling for per capita income. Differences in volatility are pronounced: countries in the 75th percentile of the output volatility distribution exhibit a standard deviation of growth some three times higher than those in the 25th percentile. At the same time, it appears that the correlation between openness and volatility is positive in the data.2
Figure 1.Volatility and Openness in the 1990s
Notes: This figure reports the partial correlation between trade openness and macroeconomic volatility, after controlling for average per capita income. The estimated equation is reported at the bottom of the plot. Volatility is calculated using annual growth rates over 1990–99 for per-capita GDP, and trade openness is the average of imports plus exports divided by GDP over the same period. Source: Penn World Tables.
There is currently no consensus, either empirically or theoretically, on the nature of the relationship between trade openness and macroeconomic volatility. In part, this is because the mechanisms behind it are not well understood. For instance, does trade affect volatility primarily by exposing industries to external shocks? Or because it changes the comovement properties of the trading sectors with the rest of the economy? Or does trade affect volatility through its impact on the diversification of production across sectors?3 The main purpose of this paper is to answer these questions by examining the relationship between trade openness and volatility using an industry-level panel dataset on production and trade. The use of industry-level data allows us to look into the individual channels through which trade can be related to aggregate volatility.
We begin by testing three hypotheses. The first is that trade openness is associated with changes in the volatility of individual sectors. For instance, it has been suggested that in an economy open to international trade, an industry is more vulnerable to world supply and demand shocks (Newbery and Stiglitz 1984). The second hypothesis is that greater trade openness comes with changes in comovement between sectors within the economy. For example, when a sector is very open, it may depend more on global shocks to the industry, and less on the domestic cycle (Kraay and Ventura 2006). This channel has not, to our knowledge, been investigated empirically in the literature. The third hypothesis is that trade is accompanied by changes in the pattern of specialization. For instance, if trade leads to a less diversified production structure, aggregate volatility will increase, and vice versa.
The main results can be summarized as follows. First, sectors more open to international trade are more volatile. Second, more trade in a sector is accompanied by a lower correlation between growth in that sector and aggregate growth, an effect that leads to a reduction in aggregate volatility, all else equal. Third, countries that are more open exhibit greater specialization, which works as a channel for creating increased volatility. The results are remarkably robust for all three channels, over different sized panels, and to the inclusion of a plethora of fixed effects, additional controls, and the use of instrumental variables.
Having estimated the three effects individually, we would like to establish whether these have an appreciable impact on aggregate volatility. It could be, for instance, that a rise in sector-specific volatility related to trade has a completely negligible impact on aggregate volatility, because on average countries are well diversified across sectors. Thus, we use the point estimates to calculate how important the three effects are quantitatively when it comes to their impact on aggregate volatility. It turns out that an increase in sector-level volatility associated with moving from the 25th to the 75th percentile in the distribution of trade openness — equivalent to a movement in the trade-to-output ratio of about 60 percentage points — raises aggregate volatility by about 10.2% of the average aggregate variance observed in the data, all else held equal. The reduction in comovement that comes with increased trade leads to a fall in aggregate volatility roughly equivalent to 6.3% of its average. Increased specialization in turn implies an increase in aggregate variance of 13.5%. Adding up the three effects, these estimates imply that moving from the 25th to the 75th percentile in trade openness is associated with an increase in aggregate volatility of about 17.3% of the average aggregate variance observed in the data.
The impact of openness on volatility varies a great deal depending on country characteristics, however. For instance, we estimate that an identical change in trade openness is accompanied by an increase in aggregate volatility that is five times higher in the average developing country compared to the average developed country. Lastly, we estimate how the impact of trade changes across decades. It turns out that all three channels, as well as the overall effect, increase in importance over time: the impact of the same trade opening on aggregate volatility in the 1990s is double what it was in the 1970s. While our approach is silent on how or whether the nature of the underlying shocks has changed over this period, it is clear that trade has become an increasingly important conduit for their transmission through the world economy.4
To summarize, all three channels — sector-level volatility, comovement, and specialization — have a sizeable impact on aggregate volatility. It appears, however, that the comovement effect, which acts to reduce volatility, is considerably less important in magnitude than the other two. Thus, trade is associated with increased aggregate volatility, through its positive relationship to both sector-level volatility and specialization.
This paper uses data on production, quantity indices, employment, and prices for the manufacturing sector from the United Nations Industrial Development Organization (2006), and combines them with the World Trade Database (Feenstra et al. 2005) for the period 1970–99. The resulting dataset is a three-dimensional unbalanced panel of 61 countries, 28 manufacturing sectors, and 30 years.5 Our approach has several advantages over the more traditional country-level analysis. First and foremost, the use of industry-level data makes it possible to estimate the individual channels for the relationship between trade and volatility, something that has not been done before in the literature. Second, the three-dimensional panel makes it possible to include a much richer array of fixed effects in order to control for many possible unobservables and resolve most of the omitted variables and simultaneity concerns in estimation. In addition to country, sector, and time effects, we can control for time-varying sector or country characteristics, or characteristics of individual country-sector pairs. Third, besides looking at the volatility of GDP per capita (the standard measure used in previous studies), we can also look at other outcome variables, such as quantity, price, number of firms, output per firm, and employment at the industry level to further check robustness.
This paper is part of a growing literature that studies the determinants of volatility, and its subcomponents, using industry-level data. Most papers, however, focus on the determinants of one of the mechanisms we consider. For instance, Imbs and Wacziarg (2003) and Kalemli-Ozcan, Sørensen and Yosha (2003) explore the patterns of specialization, while Raddatz (2006) and Imbs (2006) study sector-level volatility. Krebs, Krishna and Mahoney (2005) use Mexican data at the individual level and examine the impact of trade liberalization on wage volatility and its welfare consequences. Buch, Döpke and Strotmann (2006) examine the link between export openness and volatility at the firm level using German data. Koren and Tenreyro (2007) use industry-level data to provide a decomposition of aggregate volatility into several subcomponents, and describe how they vary over the development process. The purpose of our paper is to analyze the relationship between trade and volatility, rather than to decompose volatility per se. In addition, we control for a country’s level of development in various ways. To summarize, our paper is unique in its emphasis on trade and its use of trade data along with production. Thus, its contribution is in the comprehensive empirical exploration of multiple channels of the trade-volatility link.
The rest of the paper is organized as follows. Section II describes the empirical strategy and the data. Section III presents the regression results, while section IV discusses what these imply about the impact of the three channels on aggregate volatility. Section V concludes.
II. Empirical Strategy and Data
A. Empirical Strategy
In an economy comprised of I sectors, the volatility of aggregate output growth
where ai is the share of sector i in total output,
In particular, using the sector-level panel dataset on production and trade, it is straightforward to estimate the relationship between trade in a sector and the volatility of output in that sector,
where i denotes sector, c denotes country, and t denotes time. The left-hand side, Volatilityict, is the log variance of the annual growth rate of output per worker.6 In the cross-sectional specifications, the variance is computed over the entire sample period, 1970–99. In panel specifications, the volatility is computed over non-overlapping ten year periods: 1970–79, 1980–89, 1990–99. Tradeict is imports plus exports divided by output within a sector. The openness measure is the average for the same time periods over which the left-hand side variables are computed and is always in logs. The log of the beginning-of-period output per worker, Outputict, controls for sector-specific, time-varying productivity. We experiment with various configurations of fixed effects u. The cross-sectional specifications include both country and sector fixed effects. The panel specifications include country × sector fixed effects, country×time fixed effects, and sector × time fixed effects in alternative specifications.
To analyze the second effect, rewrite equation (1) as:
where the subscript A − i is used to denote the sum of all the sectors in the economy except i. Thus, ρi, A−i is the correlation coefficient of sector i with the rest of the economy, and σA−i is the standard deviation of the aggregate output growth excluding sector i. This way, rather than writing the aggregate variance as a double sum of all the covariances of individual sector pairs, equation (3) rewrites it as the sum of covariances of each sector i with the rest of the economy. Note that aggregate variance can be expressed this way without any loss of generality.
The relationship between trade openness and the correlation between an individual sector and the rest of the economy, ρi, A−i, is the subject of the second empirical exercise. We call this the Comovement Effect.7 Just like
The right-hand side variables are the same as in the volatility specifications (see above). The left-hand side variable is the correlation of output per worker growth in sector i with the overall manufacturing excluding that sector, ρi, A−i. In the cross-sectional specifications, these correlations are computed over thirty years. In the panel, we compute correlations over non-overlapping ten-year periods.8 In contrast to the volatility estimation in the previous section, the left-hand side is in levels rather than in logs because correlation coefficients can be negative. Note also that we use correlation rather than covariance. This is because the correlation coefficient is a pure measure of comovement, whereas changes in the covariance are influenced by changes in the sector-level variance. These are themselves affected by trade, as shown by the estimated impact of trade on sector-level volatility.
We next analyze whether trade is associated with increased specialization in a small number of sectors. Going back to equation (1), it is clear that aside from its effect on
where h is the Herfindahl index of production shares in the economy.9 A higher value of h represents a more specialized (less diversified) economy, and thus, at a given level of σ2, leads to a higher aggregate volatility. We call this the Specialization Effect. We use industry-level production data to compute indices of specialization directly at the country level, and relate them to trade openness in the following empirical specification:
Here, c indexes countries, and the left-hand side variable is the log of the Herfindahl index of production shares of sectors in total manufacturing output, h, averaged over the sample period.10 Tradec is the log of total manufacturing trade divided by total manufacturing output. Xc are controls such as per capita GDP.
Note that the Specialization Effect estimates in this paper are reported for the cross-section of countries, rather than a panel with fixed effects. This is because in this sample of countries and years there is insufficient time series variation: the cross-sectional dispersion soaks up some 90% of the variation in these data.11 Thus, there is very little variation left to work with, especially in a cross-country setting with so few observations. For these reasons, the estimates in the paper rely on the cross-sectional sample to estimate the Specialization Effect.
B. Additional Methodological Issues
As mentioned above, we estimate the Sector Volatility and Comovement Effects in both cross-sectional and ten-year panel specifications. The advantage of the cross-sectional specifications is that the left-hand side variables — variances and correlations — are calculated over a long time series, reducing measurement error. The advantage of the panel specifications is that they make it possible to control for a much richer array of fixed effects.
In this context, it is worth discussing the issue of endogeneity. In our view, the main concern in this analysis is that there are factors affecting both openness in a sector and the volatility or comovement simultaneously. The major strength of our approach is the use of a variety of fixed effects to sweep out the vast majority of these concerns. In the cross section, country effects would control for any country characteristic that has not changed over the sample period, for instance any geographical or population features such as natural resources, climate, remoteness, colonial history, human capital, institutional quality, the legal system, the political system, and many others. Sector fixed effects would control for any inherent technological feature of industries, including, but not limited to, overall volatility, tradability, capital, skilled and unskilled labor intensity, R&D intensity, tangibility, reliance on external finance, liquidity needs, or institutional intensity.
In the panel, the use of interacted fixed effects enables us to control for a much wider array of omitted variables. For example, country×time effects would absorb not just inherent country characteristics mentioned above, but also the average effect of time-varying country characteristics, such as overall level of development, growth, macroeconomic volatility, financial liberalization, any other reforms, episodes of political instability, monetary and fiscal policy changes, political regime changes, exchange rate regime changes, accession to WTO, any other trade blocks, currency unions, balance of payments/currency/banking crises, natural disasters, wars, and many others. Sector×time fixed effects will capture changes in sector characteristics over time across all countries, such as global growth opportunities and world demand and supply shocks. Finally, country×sector effects will capture the peculiar characteristics of each sector within each country that have not changed over the sample period 1970–99, such as the particular technological characteristics or sector-specific factor endowments varying at the country×sector level, or the importance of certain country×sectors, such as petroleum in Saudi Arabia or copper in Chile, for the national and global economy. Note that when country×sector fixed effects are included in the regressions, we are estimating how changes in trade openness over time relate to changes in volatility or comovement of that sector. That is, though we have a three-dimensional panel of countries and sectors, in that specification the identification comes purely from the time variation in the variables of interest within each sector in each country.
Including a plethora of fixed effects may still not resolve simultaneity problems at the country×sector×time level, however. We therefore reestimate the core specification adding a variety of controls and interaction terms. The list of variables includes terms-of-trade (TOT) volatility interacted with sector-level openness, the volatility of trade at the sector level, and a measure of financial development interacted with the Raddatz (2006) sector-level measure of liquidity needs. Another omitted variables concern has to do with the growth-volatility nexus. The macroeconomics literature finds a negative relationship between growth and volatility (Ramey and Ramey 1995), though recent work shows that at the sector level the opposite is true (Imbs 2006). In addition, faster growing sectors may also be more open to trade. Therefore, besides including initial output per worker as a proxy for growth potential in the baseline estimations, we also control for average levels and growth rates of output per worker as a further robustness check. Another concern is the role of sector size. For instance, it has been observed that larger sectors are less volatile. We control for this by including the size of the sector as an additional regressor. Finally, while in the main specifications the dependent variables are variances and correlations of output per worker growth, we also use a quantity index and a constructed sector-level price index to check robustness of the results.
Note that the most common approach in the literature has been to analyze the relationship between openness and volatility in a cross-country framework. The use of the sector-level data is in our view a step forward not only because it lets us investigate the individual channels as we do, but also because it allows us to overcome a vastly larger set of potential simultaneity problems.
There still remains the possibility that openness and volatility or comovement are jointly determined in a two-way causal relationship. Our estimates could then be thought of as tracing out the equilibrium relationship between the variables. Even under such an interpretation, the findings in this paper are still informative and far from trivial. After all, any omitted variable or reverse causality mechanism could instead generate correlations between the variables of interest exactly opposite from what we find. Claims of endogeneity are difficult to evaluate in this case precisely because currently we do not have a good theoretical or empirical understanding of the nature of the causal interrelationships between these variables. This literature is in its infancy partly because even the basic features of the data have until now been largely unknown. This paper fills this gap.
However, in the meantime we would also like to make progress on the issue of causality. To do so requires an instrument for trade openness at the sector level. We follow the approach of Do and Levchenko (2007), which extends the methodology of Frankel and Romer (1999) to sector-level data. Frankel and Romer (1999) use the gravity model to predict bilateral trade volumes between each pair of countries based on a set of geographical variables such as bilateral distance, common border, area, and population. Summing up across trading partners then yields, for each country, its “natural openness”: the overall trade to GDP as predicted by its geography.
Because we need an instrument for trade at sector level rather than total trade volumes, our point of departure is to estimate the Frankel and Romer gravity regressions for each industry. Following their methodology, we then obtain “sector-level natural openness”: predicted trade volume as a share of output not just in each country, but also in each sector within each country. Appendix I lays out the details of this approach. Though the gravity right-hand side variables are all at country level and do not differ across sectors, the procedure generates variation in predicted openness across sectors within a country. The key is that the gravity coefficients differ across sectors. The approach exploits the fact that trade volumes respond differentially to geographical characteristics in different sectors — a common finding in the gravity literature.12 Note that this instrument is not available in a panel, because the gravity coefficients do not exhibit sufficient time variation. Thus, it can only be used in the cross-sectional specifications. Finally, to examine the Specialization Effect, we must rely on cross-country regressions because h is measured at the country level. We therefore use original the Frankel and Romer (1999) measure of aggregate natural openness to instrument for trade, and also consider numerous controls previously suggested in the literature.
A recent paper by Koren and Tenreyro (2007) (henceforth KT) uses sector-level data to decompose aggregate volatility into several components, and analyze how these components change with the level of development. Our paper investigates a different question, examining the relationship between trade openness and volatility instead.13 It is also important to emphasize that our results cannot be explained by KT’s. To summarize briefly, KT find that poorer countries tend to specialize in fewer and more volatile sectors, and that poorer countries experience more severe macroeconomic (aggregate) shocks. KT’s conclusions therefore suggest that we must control for the overall level of development in our regressions, as different aspects of macroeconomic volatility decline with per capita income. In the Sector Volatility and Comovement Effects estimates, this is accomplished by country and country×time effects. In the Specialization regressions, we control for the level of income, as well as the level of income squared, to pick up the potential U-shape between income and diversification.
Thus, it is clear that the results in this paper are not driven by the facts that KT uncover. On the flip side, do our results imply any of KT’s results? There does not seem to be a clear relationship. Since the level of development is absorbed in our regressions, it appears that the impacts of trade and the overall level of development on macroeconomic volatility are each important independently. In other words, this paper and KT describe conceptually and empirically distinct relationships between different sets of variables, and neither is a subset of the other. At a more impressionistic level, it is also clear that the implications of the two papers are not that similar. We find that trade is on average accompanied by increased macroeconomic volatility. At the same time, KT find that as countries develop, volatility decreases. The two would seem to imply the opposite impacts on the evolution of macroeconomic volatility, if we believe that both incomes and trade openness went up on average in the past few decades.
C. Data and Summary Statistics
Data on industry-level production, quantity indices, employment, number of firms, and prices come from the 2006 UNIDO Industrial Statistics Database. We use the version that reports data according to the 3-digit ISIC Revision 2 classification for the period 1963–2003 in the best cases. There are 28 manufacturing sectors, plus the information on total manufacturing. We use data reported in current U.S. dollars, and convert them into constant international dollars using the Penn World Tables (Heston, Summers and Aten 2002).14 We also correct inconsistencies between the UNIDO data reported in U.S. dollars and domestic currency. We dropped observations that did not conform to the standard 3-digit ISIC classification, or took on implausible values, such as a growth rate of more than 100% year to year.15 The resulting dataset is an unbalanced panel of 61 countries. We insure that for each country-year we have a minimum of 10 sectors, and that for each country, there are at least 10 years of data.
We combine information on sectoral production with international trade flows from the World Trade Database (Feenstra et al. 2005). This database contains bilateral trade flows between some 150 countries, accounting for 98% of world trade. Trade flows are reported using the 4-digit SITC Revision 2 classification. We convert the trade flows from SITC to ISIC classification and merge them with production data. The final sample is for the period 1970–99, or three full decades.
Appendix Table A1 reports the list of countries in the sample, along with some basic descriptive statistics on the average growth rate of output per worker in the manufacturing sector, its standard deviation, its import penetration, and the share of output that is exported. The median growth rate of total manufacturing output per worker in this sample is 2.8%, and the median standard deviation is 7%. There is some dispersion in the average growth rates of the manufacturing output per worker, with Honduras at the bottom with a mean growth rate of −5.2% per year over this period, and Pakistan at the top with 6.2% per year. There are also differences in volatility, with the United States having the least volatile manufacturing sector, and Malawi the most. Import penetration and the share of total manufacturing production that gets exported vary a great deal across countries. Appendix Table A2 lists the sectors used in the analysis, along with similar descriptive statistics. Average growth rates of output per worker across sectors range from roughly 2% per year for leather products to 6% for petroleum refineries. Individual sectors have much higher volatility than manufacturing as a whole, and differ among themselves as well. The least volatile sector, wearing apparel, has an average standard deviation of 11%. The most volatile sector is petroleum refineries, with a standard deviation of 26%.
Using these data, we can calculate the variance of the growth rate of total manufacturing output per worker, and compare it with the variance of per capita GDP growth from Penn World Tables. The scatterplot of that comparison, in logs, is presented in Figure 2, along with a linear regression line. There is a close relationship between the two, with the correlation coefficient of around 0.7. The volatility of manufacturing output growth from the UNIDO dataset is considerably higher than the volatility of per capita GDP growth from Penn World Tables. This is sensible, because manufacturing output is a subset of GDP. Figure 3 reports a scatterplot of trade openness and volatility of the manufacturing sector for the countries in the sample, along with a regression line. There does seem to be a positive relationship between trade openness and volatility in the sample. We now move on to an in depth analysis of this relationship at the sector level.
Figure 2.Comparison of Manufacturing and Aggregate Volatility
Notes: This figure reports the scatterplot of the volatility of per capita GDP from the Penn World Tables against the volatility of total manufacturing output per worker from UNIDO. Volatility is calculated using annual growth rates over 1970–99.
Figure 3.Manufacturing Output Volatility and Openness
Notes: This figure reports the scatterplot of the volatility of total manufacturing output per worker against manufacturing trade as a share of output. Manufacturing output volatility is calculated using annual growth rates over 1970–99, and the manufacturing trade-to-output ratio is an average over 1970–99.
The results can be summarized as follows. Trade openness is associated with (i) higher sector-level volatility; (ii) lower comovement of a sector with the rest of the manufacturing sector; and (iii) higher specialization. These results are robust across both cross-sectional and panel estimations, to the battery of fixed effects and controls that we use to deal with omitted variables and simultaneity issues, and an instrumental variables approach.
A. Trade and Volatility within a Sector
We first analyze the relationship between trade and the volatility of output within a sector,
|Output per worker||0.007|
The last two columns present the two-stage least squares estimates using the gravity-based instrument for trade at the sector level described in Section B and Appendix I. As detailed in the Appendix, we use two variations on the instrument: (i) based on the in-sample prediction; and (ii) based on the pseudo-maximum likelihood estimates suggested by Santos Silva and Tenreyro (2006). Columns (5) and (6) report the results. The point estimates do not differ greatly compared to the OLS, though they are less significant. The first stage is highly significant, with the partial R2’s between 0.08 and 0.1, and the F -statistics for the instrument between 50 and 100, indicating that the instrument is not weak (Stock and Yogo 2005).
Table 2 reports estimation results for the ten-year panel regressions. All panel estimation results in this paper are reported with standard errors clustered at the country × sector level, to correct for possible serial correlation in the error term. We include specifications with no fixed effects, country, sector, time effects separately and together, and then interacted with each other. The most stringent possible specification, in terms of degrees of freedom, includes country×sector, sector × time, and country×time fixed effects. The coefficients on trade openness are actually quite stable across specifications, and always statistically significant. Overall, the cross-sectional and panel results yield remarkably similar conclusions.
|Output per worker||-0.055|
The link between trade and volatility, while highly significant, is not implausibly large quantitatively. In particular, a one standard deviation increase in the right-hand side trade variable, the log of exports plus imports to output, is associated with an increase in the log variance of output per worker growth of between 0.15 and 0.25 standard deviations, depending on the coefficient estimate used.
Appendix Tables A3 and A4 present a slew of robustness checks using a variety of different controls and interaction terms. The coefficient of interest remains positive and significant at the 1% level across all specifications, and the point estimates do not vary dramatically relative to the baseline estimates in Tables 1 and 2. First, turning to columns (1) and (2) in Table A3, using either average productivity or average growth rates instead of initial output per worker does not alter the results. As discussed above, both of these variables are positively related to volatility at the sector level, as reported in Imbs (2006). Column (3) instead controls for sector size by including the share of the sector in total output as an additional control. The results are robust. Column (4) drops country effects, and uses the volatility of a country’s terms of trade (TOT) instead. Terms-of-trade data are obtained from the Penn World Tables. TOT volatility is indeed positively related to volatility of production, but trade openness itself remains significant. The TOT volatility on its own was controlled for in the baseline regressions by country and country×time effects. However, it could be that TOT volatility affects more open sectors disproportionately, and this effect is driving the results. Column (5) interacts the country-level TOT volatility with total trade in a sector while including country fixed effects, which is a more general specification than including TOT volatility on its own. The main result is not affected; in fact, the coefficient on this interaction is insignificant. It could also be that what really matters is not the average trade openness in a sector, but the volatility of trade in that sector. To see if this is the case, Column (6) controls for the sector-level volatility of trade. It turns out that the coefficient on the volatility of trade is not significant, providing further confidence that simultaneity is not a major issue.16 Interacting the level of trade with its volatility in Column (7) also leaves the main result unchanged. Column (8) uses another country-level variable, the share of manufacturing trade to total trade, instead of country effects. This share is negatively related to the volatility of production, which may simply reflect that the share is greater for industrial countries, which experience less volatility on average.17Raddatz (2006) studies volatility at the sector level using a version of the UNIDO database, and finds that financial development matters more in industries with higher liquidity needs. Column (9) includes the interaction of the Raddatz liquidity needs measure with a country’s financial development, where the latter is proxied by private credit as a share of GDP coming from the Beck, Demirgüç-Kunt and Levine (2000) database. The coefficient on trade openness remains significant at the 1% level. The negative coefficient on the interaction term in column (9) corresponds to Raddatz (2006).18 Appendix Table A4 repeats these robustness checks in the panel specifications, and reaches the same conclusion.
Sector-Level Volatility in Price and Quantity per Worker
In addition to total output and employment, the UNIDO database also reports sector-level quantity indices. It is therefore possible to construct annual growth rates of the quantity of output per worker for each sector, and calculate the same volatility measure as we did for output per worker.19 Furthermore, given that output per worker equals price times quantity per worker, it follows that we can back out the growth rate of the sector-specific price index by subtracting the growth rate of quantity per worker from the growth rate of output per worker.20 We then calculate the volatility measures for the sector-specific price index.
This rough separation of the growth rates of output per worker into the growth rate of quantity and of price does not help identify the channels through which trade openness affects volatility. Indeed, no matter what the shock, one would expect both the price and the quantity to move. Nonetheless, examining the effect of trade on quantities and prices serves as a further robustness check on the results, by showing that trade affects the volatility of both. Table 3 presents the baseline volatility regressions for quantity per worker and price. The openness coefficient is positive and significant for both left-hand side variables across all specifications.21
|I. Quantity per Worker|
|Output per worker||-0.254**|
|Output per worker||-0.103*|
Sector-Level Volatility in Number of Firms and Output per Firm
The UNIDO database also reports the number of firms in each sector. This variable makes it possible to get a glimpse at two possible channels underlying the trade-volatility link. In particular, trade openness could be positively related to volatility through higher entry and exit of firms (i.e., the extensive margin), through volatility in the output of existing firms (i.e. the intensive margin), or both. Therefore, we compute two measures. The first is the volatility of the annual growth rate in number of firms, and the second is the volatility in the growth rate of output per firm. The former is meant to shed light on the extensive margin, that is, entry and exit of firm, and the latter on the intensive margin, the output volatility of a typical firm.22Table 4 reports the results for the volatility in the number of firms and output per firm. The openness coefficient is positive and significant for both left-hand side variables across all specifications except for three of the IV regressions.23 Thus, the data are broadly consistent with both the extensive and the intensive margin hypotheses.
|I. Number of Firms|
|Output per worker||-0.065|
|Output per worker||-0.027|
B. Trade and Sector Comovement
We next estimate equation (4), the relationship between trade and the correlation of a sector’s output growth with the rest of the manufacturing sector (ρi,A−i). Table 5 presents the cross-sectional results. Intriguingly, more trade in a sector comes with a reduced correlation of that sector with the rest of the economy. This negative relationship is robust across specifications, although the significance level is typically not as high as in the volatility regressions, and the magnitude of coefficients not as stable. It is clear that increased exposure to the world cycle for a sector decouples it from the domestic economy. This comovement effect acts to reduce the overall variance in the economy, ceteris paribus. The last two columns of Table 5 report the IV results, which are weaker than the OLS results. While the coefficient of interest is negative, it is only significant for one of the two versions of the instrument.
|Output per worker||0.012|
Table 6 presents results for the ten-year panel estimation. The results are broadly in line with those of the cross section, and robust to almost the entire battery of fixed effects. The only exception is the most stringent possible set of fixed effects, which includes the country×sector, country×time, and sector×time effects simultaneously. The coefficient of interest is still negative, but no longer significant. Overall, the relationship between trade and comovement is economically significant, and plausible in magnitude. A one standard deviation increase in the overall trade is associated with a decrease in correlation of between 0.07 and 0.17 standard deviations, depending on the coefficient estimate used.
|Output per worker||-0.012|
Table 7 presents the baseline correlation specifications on the price and quantity per worker variables separately.24 The OLS coefficients are all negative and significant. Note that the IV results are more robust for the price and quantity variables than for the output per worker volatility. Though the comovement effect is less robust to the IV strategy, one could argue that reverse causality arguments are more difficult to make in the case of the comovement effect. There are currently no models of the causal effect of comovement with aggregate growth on trade openness.
|I. Quantity per Worker|
|Output per worker||-0.022*|
|Output per worker||0.014|
Appendix Tables A5 and A6 present numerous robustness checks using a variety of different controls and interaction terms. The openness coefficient remains negative and significant across all specifications, and the point estimates do not vary dramatically relative to the baseline estimates in Tables 5 and 6. All of the panel specifications include country×sector and time effects, and thus identify the relationship purely from the time series variation within each sector in each country. The properties of sector-level correlation with the aggregate growth have not been previously studied in the literature. Therefore, it is much less clear than in the case of sector-level volatility which additional controls it is important to include alongside the fixed effects. The approach here is to use the same battery of robustness checks as those employed in the sector volatility regressions. We control for average level and growth rate of output, sector size, TOT volatility (both as main effect and interacted with sector-level trade), sector-level volatility of trade, share of manufacturing trade in total trade, and Raddatz’s interaction of liquidity needs and financial development. Since these were used above, we do not discuss them in detail. The coefficient of interest is robust to all of the alternative specifications.
C. Trade and Specialization
Finally, we estimate the relationship between trade and specialization (h), equation (6). Table 8 reports the results. Column (1) is the bivariate OLS regression of trade openness on the Herfindahl index, while column (2) controls for log per capita PPP-adjusted GDP from Penn World Tables. The coefficient on trade is significant at the 1% level. Since trade openness is likely endogenous to diversification, columns (3) and (4) repeat the exercise instrumenting for trade using natural openness from Frankel and Romer (1999). Results are unchanged, and the magnitude of the coefficient is not affected dramatically. In order to probe further into this finding, columns (5) and (6) control directly for how the export patterns are related to industrial specialization. We construct the Herfindahl index of export shares in a manner identical to our index of production concentration. The coefficient on trade openness decreases, but remains significant at the 1% level. The coefficient on the Herfindahl of export shares is highly significant as well.
|GDP per capita||-0.081|
|Herfindahl of exports||0.561**|
Figure 4 illustrates these results. It presents partial correlations between trade openness and the Herfindahl index of sector shares for the available countries, once per capita income has been netted out. It is clear that there is a positive relationship between trade and specialization. The effect of trade openness and export concentration on the specialization of production is sizeable. A one standard deviation change in log trade openness is associated with a change in the log Herfindahl of production equivalent to about 0.54 of a standard deviation. A one standard deviation change in export specialization is associated with a change in the log Herfindahl of production of roughly 0.68 standard deviations.
Figure 4.Trade and Specialization
Notes: This figure reports the partial correlations between the Herfindahl of production shares and manufacturing trade as a share of output, after controlling for per capita GDP. The Herfindahl of production shares and the manufacturing trade-to-output measures ratio are averages for 1970-99.
Appendix Table A7 presents further robustness checks. All of the specifications in that table include per capita income and the Herfindahl of exports as controls, and are estimated using IV unless otherwise indicated.25 Column (1) checks whether the results are driven by outliers. Dropping outliers improves the fit of the regression, and the results remain significant. Columns (2) and (3) check that the results are robust to an alternative measure of trade openness. We use total trade openness as a share of GDP from the Penn World Tables instead of total manufacturing trade as a share of manufacturing output from our data. It is clear that the main result is not driven by our particular measure of trade openness: both OLS and IV coefficients are robustly significant. We next control for other potential geographic determinants of specialization. Column (4) includes distance to equator and shares of agriculture and mining in GDP. Column (5) adds more geographic controls, such as a percentage of land area in the tropics, mean temperature, and the average number of days of frost.26 Those coefficients are not significant and are not reported to conserve space. Column (6) adds region dummies.27 Finally, the specification in column (7) is based on the work of Kalemli-Ozcan et al. (2003), and includes a wide variety of additional controls, such as income risk sharing, population density, population, and distantness.28 In addition, we follow Imbs and Wacziarg (2003) and include GDP per capita and its square to capture the U-shaped pattern of diversification over the development process. The results are robust to this specification.
IV. The Impact on Aggregate Volatility
The preceding section estimated the relationship between trade and the variance of individual sectors
We do this in a number of ways. The first exercise calculates the effect of moving from the 25th to the 75th percentile in the distribution of trade openness observed in the sample. It is meant to capture mainly the consequences of cross-sectional variation in trade across countries. The second exercise considers the average increase in trade openness in the sample over time, from the 1970s to the 1990s, and uses it to calculate the expected impact of this trade expansion on aggregate volatility, through each channel as well as combined. Third, we calculate how the estimated impact of trade openness on aggregate volatility differs across countries based on observed characteristics of these countries. The final exercise examines how the nature of the relationship between trade and volatility has changed over time. To do so, we reestimate the three sets of equations from the previous section by decade, and use the decade-specific coefficients to calculate the impact of trade on aggregate volatility for each decade.
These exercises are straightforward extensions of a common one performed in most empirical studies, which asks “what is the effect of a one standard deviation change in the right-hand side variable of interest on the left-hand side variable?” This calculation was carried out after each set of regressions separately, but in this case it is also important to compare the relative magnitudes of these three effects, and estimate the average impact of each channel on aggregate volatility. We do this using a Taylor expansion to relate sector-level changes to aggregate ones and separate the effects of each channel on aggregate volatility. This requires some simplifying assumptions, discussed below. It turns out that these assumptions do not appreciably affect the main conclusion about the average impact of the three channels on aggregate volatility in this sample of countries.
A. The Relationship between Each Channel and the Aggregate Volatility
The aggregate variance,
In order to evaluate the estimated effect of trade-induced changes in
Using a Taylor approximation, the effect of changes in the three variables (∆σ2, ∆ ρ, and ∆h) on the aggregate volatility is:
We can compute the partial derivatives using equation (8):
Each term represents the partial effect of the three channels on the aggregate volatility, and their sum is the combined impact.
The values of ∆ σ2, ∆ρ, and ∆h as a function of changes in openness come from the estimated equations:
It is important to emphasize that this paper does not provide a decomposition of the effects of trade on volatility for each individual country. This would not be feasible in a regression-based approach. Instead, the estimates in this section come from a counterfactual thought experiment in which trade openness increases by a given amount holding other country and sector characteristics constant. Thus, these estimates are intended to reflect the average impact of trade through these three channels across countries in the sample.
In this context, how restrictive is the assumption of symmetry in σ, ρ, and σA− across sectors, used to simplify equation (7) to equation (8)? Appendix II offers a detailed treatment of this question. The main result is that while (8) may not be a good approximation for the actual aggregate variance in every country, on average in this sample it is a good approximation for
Finally, we must mention an additional point regarding aggregation. Our exercise considers the impact of an overall increase in trade openness in a country, across all industries. Meanwhile, the empirical specifications estimated in this paper, (2) and (4), assume that volatility and comovement in a sector are affected by the trade openness only in that sector.
As such, the aggregation exercise could be missing the total impact of an increase in overall trade openness if there is an independent effect of trade openness in some sectors on volatility or comovement of other sectors. To ascertain whether or not this is the case, we carried out supplementary estimation allowing trade in the rest of the economy except sector i, TradeA−i, ct, to affect volatility and comovement in sector i. The results show that there is no robust independent effect of aggregate trade outside of sector i on volatility or comovement in sector i. In addition, the estimated coefficients on the within-sector openness are virtually unchanged relative to our baseline results. However, the coefficient on TradeA−i, ct is highly unstable across specifications, an indication that the omitted variables problem looms large for this variable.32 Thus, while the evidence suggests that the aggregation procedure described above is indeed informative, it must be kept in mind that it is based on a model in which volatility and comovement in a sector are affected only by trade within the sector.
B. The Impact Across Countries and Over Time
The first two exercises use the average values of σ2, ρ, and h found in the sample. These are reported in the first row of Table T1. The average Herfindahl index in our sample is h = 0.12. The average comovement of a sector with the aggregate is ρ = 0.34, while the average variance of a sector is σ2 = 0.038. For the variance of the entire economy minus one sector,
The dispersion in the overall manufacturing trade as a share of output in the sample implies that moving from the 25th to the 75th percentile in overall trade openness is equivalent to an increase in total trade to manufacturing output of about 60 percentage points (or moving from the manufacturing trade openness of the United Kingdom to that of Indonesia). This change in overall trade is associated with a change in sector-level variance of ∆σ2 = 0.0046. From equation (10), it follows that this increase in sector-level volatility raises aggregate volatility by 0.0009, which is of course considerably smaller than the sector-level increase, due to diversification among sectors. This change is sizeable, however, relative to the observed magnitudes of aggregate volatility. In particular, it is equivalent to about 10.2% of the average aggregate variance found in our data.
Moving on to the Comovement Effect, the regression estimates indicate that the same increase in trade comes with a reduction of correlation between the sector and the aggregate equal to ∆ρ = −0.034. Plugging this into equation (10) and evaluating the partial derivative, the reduction in the aggregate variance due to decreased comovement is equal to 0.0005. This amounts to a reduction equivalent to 6.3% of the mean aggregate variance observed in the data. Finally, according to the estimates, the change in overall trade openness equivalent to moving from the 25th to the 75th percentile is associated with a change in the Herfindahl index of ∆h = 0.036. The resulting change in aggregate volatility from this increased specialization is
These calculations, summarized in the first two rows of Table 10, imply changes in aggregate volatility related to trade that are relatively modest and plausible in magnitude. Two of the effects imply increased volatility, while the other leads to a reduction. Adding up the three effects, the overall change in aggregate volatility as implied by equation (10) is
The previous exercise was informative of the kind of differences in aggregate volatility one can expect from the dispersion of trade openness found in the cross section. That is, we computed the expected differences in volatility as a function of differences in trade openness across countries. Alternatively, we can ask how the increase in trade over time within the sample period is expected to affect aggregate volatility. To learn this, we calculate the mean difference in the total trade to manufacturing output between the 1970s and the 1990s in the sample. It turns out that trade openness increased by about 30 percentage points over the period, going from below 60 percent in the 1970s to almost 90 percent in the 1990s. The change in trade openness of this magnitude implies an estimated increase in aggregate volatility of roughly 0.0007. Since this calculation uses the same mean values of σ2, ρ, h, σA−, and the same
How sizeable is this effect? Relative to what is observed in the cross section, this implied change in volatility is equivalent to 8 percent of the average aggregate variance in the sample. Alternatively, it can also be compared to the changes in aggregate volatility that occurred between the 1970s and the 1990s. It turns out that on average, aggregate volatility has decreased by 0.0037 over this period. By this metric, the implied increase in volatility of 0.0007 associated with growing trade is equivalent to almost one fifth of the observed decrease in aggregate volatility. Trade has therefore counteracted the general tendency of the smoothing out of business cycles over time.34
C. Country Characteristics and the Impact on Aggregate Volatility
The two calculations above imply that the trade-related change in aggregate volatility acting through the three channels is appreciable but modest. However, these are based on sample averages of σ2, ρ, h, and σA−, and clearly the estimated impact of trade will differ depending on these country characteristics. For instance, the sectoral volatility effect would be significantly less important in a highly diversified economy (low h), while the comovement effect will be magnified in a country with a high volatility (σ2 and σA−). Thus, it is important to get a sense of how the magnitudes change as these country characteristics vary.
We do this in two ways. First, we calculate the averages of σ2, ρ, h, and σA− for the developed and developing country subsamples, and use them to calculate the impact of trade on these two groups of countries.35 The subsample averages of σ2, ρ, h, and σA− are summarized in Table T1. Developing countries are considerably more volatile, somewhat less diversified, and have lower average comovement of sectors. Table 10 presents the comparison of the impact of trade in the developed and developing countries. These calculations keep the magnitude of the trade opening and the β’s the same for both.36 The differences between the two groups are pronounced. It turns out that the same change in openness is associated with a rise in aggregate volatility of 0.0004 in the average developed country, and of 0.0022, or five times as much, in the average developing country. In developed countries, the effect is also weaker when measured as a share of the average aggregate volatility. The increase in volatility corresponds to 14.6% of the average aggregate volatility found in the developed subsample, compared to 19.2% in the developing subsample. The relative importance of the three individual effects does not differ greatly between the two samples, as evident from Table 10. Perhaps surprisingly, the sector-level volatility and comovement effects are relatively less important in the developing country sample. The specialization effect, while still the largest quantitatively, is less important in the developed country sample.
The developed and developing countries differ significantly along every variable that goes into calculating the magnitudes. However, one might also like to know how changes in an individual variable affect these magnitudes. To do this, we go back to the full sample baseline calculation of the previous subsection, and vary σ2, ρ, and h individually. Table 11 reports the results. In this table, rather than evaluating the three effects using the sample means of σ2, ρ, and h as we had done above, we evaluate them using each of these at the 25th and the 75th percentile of its distribution, one by one. Thus, this table demonstrates how the sizes of the Sector Volatility Effect, the Comovement Effect, and the Specialization Effect differ between countries at the 25th and the 75th percentile in the distribution of σ2, for example.
It turns out that moving from the 25th to the 75th percentile in the distribution of sector-level volatility increases the overall effect of trade opening by a factor of almost 5. What is interesting here is that the strongest effect of changing σ2 is not on the Sector Volatility Effect itself, but on the Specialization Effect: while the magnitude of the former almost triples, the latter increases by a factor of 4.4. The increase in σ2 also doubles the magnitude of the comovement effect. By contrast, moving from the 25th to the 75th percentile in the distribution of ρ hardly changes anything. The net effect is positive, but the increase in overall volatility due to trade is only 5% higher for the more correlated country. Differences in h change the impact of trade appreciably, but much less than differences in σ2: moving from the 25th to the 75th percentile in the distribution of h increases the overall impact of trade by a factor of 1.8.
To summarize, the implied association between trade opening and aggregate volatility varies a great deal depending on country characteristics. For instance, the impact of the same trade opening is likely to be five times higher in absolute terms for a typical developing country compared to a typical developed country. Furthermore, the country characteristic that is by far most responsible for the differences in estimated impact of trade is sector-level volatility. The impact of trade on aggregate volatility is highest for countries whose sectors are already most volatile on average. Its magnitude is such that it cannot be ignored when considering the effects of trade opening in developing countries. Note that this estimated role of trade is obtained controlling for a wide variety of country characteristics, such as institutions, macroeconomic policies, or the overall level of development.
D. Changes in the Impact on Aggregate Volatility Across Decades
The final exercise estimates how the association between trade and aggregate volatility changes over time. For this calculation, we reestimate the three baseline specifications in the previous section by decade, in order to obtain potentially different coefficients for
The results are summarized in Table 10. Not surprisingly, the rising β’s in the regressions over time imply that the estimated role of trade openness increases substantially. In the 1970s and 1980s, increasing trade openness from the 25th to the 75th percentile comes with a rise in aggregate volatility of 0.001. In the 1990s, the same increase in trade openness is associated with an increase in aggregate volatility of 0.002, double the absolute impact. As a share of aggregate volatility, the effect goes from less than 10% of the average in the 1970s to 31% in the 1990s.
Also worth noting is how the relative importance of the three effects changes over time. In the cross-sectional exercise using 30-year averages, we found that the Specialization and the Sector Volatility Effects are the two most important ones, while the Comovement Effect is small in magnitude. It turns out that this pattern varies somewhat across decades, even as all three effects become larger in magnitude over time. In the 1970s, the Sector Volatility Effect is substantially greater than the other two, while the Specialization Effect is much weaker than in the full sample. Furthermore, relative to the full sample, the Comovement Effect is more important in the 1970s as well. Intriguingly, in the 1980s all three effects are more or less equal in absolute value, and only in the 1990s do we see the Comovement Effect falling substantially behind the other two.
The result that the impact of trade has become stronger over time is distinct from the simple observation that trade has increased over the period. The increase in trade itself need not imply that the relationship between trade and volatility would have strengthened. Perhaps more interestingly, this finding is not at all inconsistent with the fall in overall macroeconomic volatility over this period. What seems to be happening is that while aggregate volatility has decreased, differences between the volatilities of country-sectors are better explained by the variation in trade openness. These quantitative results are valuable in their own right as they reveal the changing nature of trade’s impact on the macroeconomy over time. Furthermore, they provide a rich set of facts to build upon in future empirical and theoretical work aiming to better understand the nature of the global business cycle. For example, in the macroeconomics literature sector-level dynamics underlying aggregate business cycles have been explored in a closed economy,38 and recent work has moved to the firm level.39 Our results can help provide a foundation for future work in the open economy setting.
Whether increased trade openness has contributed to rising uncertainty and exposed countries to external shocks remains a much debated topic. This paper uses industry-level data to document several aspects of the relationship between openness and volatility. The main conclusions can be summarized as follows. First, higher trade in a sector is associated with higher volatility in that sector. Second, more trade also implies that the sector is less correlated with the rest of the economy. Third, higher overall trade openness comes with increased specialization in the economy. The sum of these effects implies that moving from the 25th to the 75th percentile in the distribution of trade openness is associated with an increase in aggregate volatility of about 17.3% of the average aggregate variance observed in our sample. The estimated impact differs a great deal between countries and over time, however. The same change in trade openness is accompanied by an estimated rise in aggregate volatility that is roughly five times higher in a typical developing country than in a typical developed country. Over time, the association between trade and volatility acting through all three channels has become stronger.
While the results in this paper are informative, our understanding of the trade-volatility relationship can be improved along many dimensions. For instance, the exercise in this paper imposes symmetry between sectors, and thus does not allow us to investigate whether some countries tend to specialize systematically in more or less risky sectors, something that could be another channel for the relationship between trade and volatility. We address this question in di Giovanni and Levchenko (2007), which can thus serve to complement the analysis carried out here. The change over time in the impact of trade on volatility also deserves much more careful study. In particular, the increasing impact of trade, together with growing trade itself, needs to be analyzed jointly with the well-documented fact that business cycle volatility has actually decreased over the same period. Finally, this paper remains silent on the relationship between trade and growth. This relationship must also be considered if we wish to make any claims on the welfare consequences of opening to trade. We consider these to be promising avenues for future research.
I. Sector-Level Gravity-Based Instrument
This appendix gives a detailed description of the sector-level instrument for trade openness used in estimation. The material here draws heavily on the treatment in Do and Levchenko (2007), which can be used for more detailed reference. The strategy applies the methodology of Frankel and Romer (1999) at sector level. For each industry i, we run the Frankel and Romer regression:
where LogTicd is the log of bilateral trade as a share of sectoral output in industry i, from country c to country d. The right-hand side consists of the geographical variables. In particular, ldistcd is the log of the distance between the two countries, defined as distance between the major cities in the two countries, lpopc is the log of the population of country c, lareac is the log of land area, landlockedcd takes the value of zero, one, or two depending on whether none, one, or both of the trading countries are landlocked, and bordercd is the dummy variable for a common border. The right-hand side of the specification is identical to the one Frankel and Romer (1999) use.
Having estimated equation (A.1) for each industry, we then obtain the predicted logarithm of industry i bilateral trade to output from country c to each of its trading partners indexed by d,
That is, predicted total trade as a share of sectoral output for each industry and country is the sum of the predicted bilateral trade to output over all trading partners.
We require an instrument for trade openness at sector level. How can the strategy described above yield this type of instrument even though the variation in the gravity variables in equation (A.1) is by country? The key is that we estimate an individual gravity equation for each sector. Thus, crucially for the identification strategy, if the vector of estimated gravity coefficients ηi differs across sectors, so will the predicted total exports
The intuition is easiest to explain in terms of the coefficient on distance. Suppose that some industries are more sensitive to distance than others. Then, countries that are more remote — farther from the potential trading partners — will have relatively higher predicted trade in sectors that are less distance-sensitive. Going beyond the distance coefficient, the empirical strategy relies on variation in all of the regression coefficients in equation (A.1), along with the entire battery of exporting and destination country characteristics.
It is therefore crucial for this procedure that the gravity coefficients (hopefully all 13 of them) vary appreciably across sectors. When we discuss the actual estimation results for the gravity regressions, we demonstrate that this is indeed the case. But before describing the gravity results, it is worth mentioning briefly the theoretical rationales and existing empirical evidence on the variation in sector-level gravity coefficients.
Existing research has focused on the effect of trade barriers on trade volumes. Thus, it is most informative about the variation in the coefficients on distance and common border variables, that are often used as proxies for bilateral trade barriers. Anderson and van Wincoop (2003, 2004) show that the estimated coefficients on distance and common border in the gravity model are a function of (i) trade costs and (ii) the elasticity of substitution between product varieties within the sector. Available direct estimates of freight costs do indeed show large variation across sectors. According to Hummels (2001), freight costs in the U.S. in 1994 ranged between 1% and 27% across sectors. In addition to the direct shipping costs, goods may differ in the cost of acquiring information about them. Rauch (1999) and Rauch and Trindade (2002) find that the volume of trade reacts differently to informational barriers in differentiated goods sectors compared to homogeneous ones. Thus, empirically it does seem to be the case that trade costs — both simple and informational — vary significantly across industries. When it comes to the estimated elasticity of substitution across sectors, a large number of studies utilizing various approaches reach quantitatively similar conclusions. Anderson and van Wincoop (2004) summarize existing evidence, which produces a range of estimated elasticities from 3 to 10across industries. In addition to trade costs and elasticities of substitution, Chaney (2006) demonstrates that the degree of firm heterogeneity, which varies across sectors, also has a significant effect on the sector-specific distance coefficient in the gravity regression.
To summarize, there are strong reasons to expect the coefficients in equation (A.1) to vary across sectors. But is this the case in practice? Estimating the gravity model using sector-level data is becoming increasingly common (Rauch 1999, Rauch and Trindade 2002, Hummels 2001, Evans 2003, Feenstra, Markusen and Rose 2001, Lai and Trefler 2001, Chaney 2006). Though studies differ in the level of sectoral disaggregation and specifications, it is indeed typical to find significant variation in the gravity coefficients across sectors. For instance, Hummels (2001) finds that the distance coefficients vary from 0 to −1.07 in his sample of sectors, while the coefficients on the common border variable range from positive and significant (as high as 1.22) to negative and significant (as low as 1.23). Chaney (2006) reports that it is common to find sector-specific distance coefficients−ranging from −0.5 to −1.5. When we present the results of our own estimation, we will compare them to these studies.
We now discuss another potentially important issue, namely, the treatment of zero trade observations. In our sample, only about two-thirds of the possible exporter-importer pairs record positive exports, in any sector. At the level of individual industry, on average only a third of possible country-pairs have strictly positive exports, in spite of the coarse level of aggregation (28 sectors).40 How does our estimation procedure deal with zero observations? As a preliminary point, because we develop an instrument for trade patterns rather than trade volumes, we can safely disregard country pairs in which no trade is observed in any sector. Following the large majority of gravity studies, we take logs of trade values, and thus our baseline gravity estimation procedure ignores zeros. Hence, we generate predicted values of trade only when the actual value is positive. One interpretation of our procedure is that it “predicts” zero trade when it observes zero trade. This strategy may contaminate the instrument if the estimated gravity coefficients would instead predict large trade values for some countries and sectors in which actual trade is zero.
We deal with this potential problem by instead estimating the gravity regression in levels using the Poisson pseudo-maximum likelihood estimator suggested by Santos Silva and Tenreyro (2006). The advantage of this procedure is that it actually includes zero observations in the estimation, and can predict both zero and nonzero trade values in-sample from the same estimated equation. Its disadvantage is that it assumes a particular likelihood function, and is not (yet) a standard way of estimating gravity equations found in the literature.41
In order to build the instrument, our procedure estimates equation (A.1) for each industry. In order to do so, we retain information on bilateral trade flows from the World Trade Database, deflating them by output from UNIDO. We merge bilateral trade data with geography variables taken from Centre d’Etudes Prospectives et d’Informations Internationales (CEPII). The CEPII database contains information on bilateral distance between the major cities for each pair of countries, whether two countries share a border, as well as information on land area and whether a country is landlocked.42 Population data are taken from World Bank’s World Development Indicators for the period 1970 to 1999. The left-hand side variable is averaged over the period 1970 to 1999, allowing us to increase the sample size as trade observations are sometimes missing in individual years. In the set of the sector-level regressions, the smallest number of observations is 4200, and the largest is 8257, with a mean of 6270. The R2’s range from 0.20 to 0.43, with a mean of 0.36.
Because the right-hand side variables are the same in all regressions, the empirical strategy in this paper would only work if the gravity coefficients differ significantly across sectors. Thus, the first important question is whether or not there is much variation in the estimated coefficients. Figure A1 presents, for each coefficient, the range of estimates across sectors. Below the plot for each coefficient, we report the minimum, median, and maximum values that the estimates take across all industries. It is apparent that the coefficient estimates differ a great deal between sectors. For instance, the distance coefficient pictured in the first plot ranges from −0.83 to −1.6. This is very close to what is reported in Chaney (2006). Note that several of the coefficients, such as the one on the common border dummy, actually range from positive to negative, a finding similar to Hummels (2001). The variation in the Poisson coefficients, which we do not picture here to conserve space, exhibit a similar degree of variation.
We formally tested for equality of the gravity coefficients by pooling observations across sectors but letting the each coefficient vary by sector. The data overwhelmingly reject the null hypothesis that all of the coefficients are the same across sectors. Furthermore, we tested the hypothesis of equality of each individual coefficient across sectors. Out of 13 coefficients, the null that they are the same across sectors is rejected in 9 cases.
II. The Symmetry Assumption
This appendix gives the detailed derivations showing that the assumption of symmetry across sectors of the
The derivation proceeds in two steps. The first step starts with the fully general identity for the aggregate variance, and rewrites it as a sum of the symmetric term in equation (8), and some additional terms. The second step shows that these additional terms are small on average as a fraction of the level of variance in our sample of countries, and do not significantly affect the computation of the Sector Volatility and Comovement Effects.
For each country, the identity for the aggregate variance,
Where, following the notation in the main text, σ2 is the average variance across sectors, while
To begin considering how equation (B.3) differs from (8), note that (B.3) uses the average covariance of a sector with the rest of the manufacturing sector,
We conclude that it is a good approximation to write,
The first two terms are identical to the approximate formula for the variance used in the paper to set up our decomposition, equation (8). The third term reflects whether a country on average specializes in risky or safe sectors. It equals zero if all sectors have the same variance
As a preliminary point, we can ascertain how important these terms are in the data. The median value across countries of the symmetric component of the variance, hσ2 + (1 - h)ρσσA - in our sample of countries is about 0.006. The median of
How do the third and fourth terms affect the calculations of the impact of trade in equation (10)? We now use equation (B.4) to evaluate whether the third and fourth terms affect appreciably the calculations for the Sector Volatility and Comovement Effects. Write the Sector Volatility Effect as a Taylor approximation of the change in
Note that this formula is completely general, and does not rely on any symmetry assumptions at this stage. Using equation (B.4) and the fact that
The key symmetry assumption is that ΔLog(Openness) is the same across sectors. That is, the thought experiment in the paper is that of an identical increase in trade openness across all sectors. This assumption follows most naturally from the regression-based approach of this paper, which estimates the average effect of the level of trade openness across countries and sectors. Since the sector volatility regressions are estimated in logs, this leads to the same proportional increase in
The first term is the Sector Volatility Effect analyzed in the paper. The second term follows from the fact that proportional changes in volatility will increase the aggregate variance by more in countries that have systematically higher production shares in sectors more volatile than the average. This term will be zero in countries that are perfectly diversified
Similarly, it is possible to write out the general expression for the Comovement Effect that does not rely on any symmetry assumptions:
Proceeding in similar steps, we use equation (B.4) to compute each derivative
Once again, the first term in brackets is the Comovement Effect analyzed in the paper. The second comes from the asymmetry of sectors with respect to σi. This term exists because changes in the correlation coefficient will affect the covariances conditional on the standard deviation of the sector. The relative importance of the second term turns out to be quite minor as well. The value of (1 − h) σσA−, which is used to calculate the Comovement Effect in the paper is 0.0112. By contrast, across countries the median for the second term is −0.0007, more than 10 times lower.
We conclude from these exercises that as long as ΔLog(Openness) is the same across sectors — as follows naturally from the regression-based approach — imposing symmetry on the levels of σ2 and ρ across sectors does not appreciably affect the calculations of the Sector Volatility and Comovement Effects. Finally, it is evident from equation (B.3) that we cannot perform a similar exercise for the Specialization Effect. This is because we cannot take the derivative of the third and fourth terms in equation (B.3) with respect to h. As discussed above, these terms could be large and positive in countries that specialize systematically in sectors with higher volatility and higher correlation with the aggregate economy. Analyzing the effect of these terms requires focusing on the variation in patterns of export specialization. A companion paper (di Giovanni and Levchenko 2007) is entirely devoted to that topic. However, these terms are also very small in magnitude on average. Because this paper estimates the average effects of the three channels on aggregate volatility, the full treatment of the country-specific information contained in these extra terms is beyond the scope of the analysis presented here.
|Country||Avg.||St. Dev.||Output||Output||Country||Avg.||St. Dev.||Output||Output|
|China,P.R.: Hong Kong||0.050||0.081||2.160||0.973||Netherlands*||0.026||0.073||0.539||0.647|
|China,P.R.: Macao||0.032||0.062||0.494||1.171||New Zealand*||0.013||0.055||0.314||0.299|
|Hungary||0.036||0.064||0.271||0.250||Syrian Arab Republic||0.037||0.175||0.633||0.127|
|Indonesia||0.050||0.068||0.714||0.379||Trinidad and Tobago||0.049||0.135||0.563||0.716|
|ISIC||Sector Name||Avg.||St. Dev.||Output||Output|
|322||Wearing apparel, except footwear||0.025||0.114||0.797||1.047|
|324||Footwear, except rubber or plastic||0.030||0.156||1.997||0.374|
|331||Wood products, except furniture||0.031||0.166||1.013||0.302|
|332||Furniture, except metal||0.034||0.155||0.315||0.249|
|341||Paper and products||0.034||0.149||0.729||0.184|
|342||Printing and publishing||0.039||0.131||0.173||0.065|
|354||Misc. petroleum and coal products||0.049||0.251||1.433||0.489|
|361||Pottery, china, earthenware||0.038||0.168||1.740||0.435|
|362||Glass and products||0.047||0.150||2.273||0.562|
|369||Other non-metallic mineral products||0.044||0.141||0.446||0.304|
|371||Iron and steel||0.034||0.182||1.258||0.282|
|381||Fabricated metal products||0.028||0.142||0.577||0.183|
|382||Machinery, except electrical||0.037||0.154||12.188||3.878|
|385||Professional & scienti_c equipment||0.034||0.179||13.210||1.642|
|390||Other manufactured products||0.030||0.174||1.299||1.251|
|Output per worker||0.015|
|Avg. output per worker||0.150*|
|Growth of output per worker||7.299**|
|Share in Total Output||-1.286**|
|Share of manuf. Trade||-1.700**|
|Liq. needs×Private credit/GDP||-2.322+|
|Output per worker||-0.138|
|Avg. output per worker||0.158|
|Growth of output per worker||5.398**|
|Share in Total Output||0.289|
|Share of manuf. Trade||-1.315**|
|Liq. needs×Private credit/GDP||-0.868|
|µi × µt||No||no||no||no||yes||no||no||no|
|µc × µt||no||no||no||no||no||no||no||no|
|Output per worker||-0.051**|
|Avg. output per worker||-0.091**|
|Growth of output per worker||0.057|
|Share in Total Output||0.209|
|Share of manuf. trade||0.276**|
|Liq. needs×Private credit/GDP||-1.560**|
|Output per worker||-0.020|
|Avg. output per worker||-0.037|
|Growth of output per worker||-0.007|
|Share in Total Output||0.341|
|Share of manuf. trade||0.442**|
|Liq. needs×Private credit/GDP||0.650+|
|GDP per capita||0.029|
|(GDP per capita)2||-0.088*|
|Herfindahl of exports||0.424**|
|Distance to Equator||0.121**|
|Mining GDP share||0.433|
|Agr. GDP share||0.027*|
|Income Risk Sharing||0.010**|
|Additional Geographic Controls||yes|
|Notes||IV; no outliers||OLS||IV||IV||IV||IV||IV|Figure A1.Sector-Level Gravity Coefficients
Notes: This figure reports the sector-level gravity coefficients from estimating equation (A.1). Each subplot is a coefficient, while each bar within the subplot represents a sector.
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