Category Archives: Measures, Statistics & Technicalities

Melitz and Redding on heterogeneous firms and gains from trade

In a recent VoxEU column, Marc Melitz and Stephen Redding describe the logic of Melitz (Ecma, 2003) and Arkolakis, Costinot, and Rodriguez-Clare (AER, 2012). Those should be familiar to Trade Diversion readers (e.g. ACR 2010 wp, Ossa 2012 wp). They then explain their new paper:

In Melitz and Redding (2013b), we show that firm-level responses to trade that generate higher productivity do in fact represent a new source of gains from trade.

  • We start with a model with heterogeneous firms, then compare it to a variant where we eliminate firm differences in productivity while keeping overall industry productivity constant.

We also keep all other model parameters (such as those governing trade costs and demand conditions) constant.

  • This ‘straw man’ model has no reallocations across firms as a result of trade and hence features no productivity response to trade.

Yet it is constructed so as to deliver the same welfare prior to trade liberalisation. We then show that, for any given reduction in trade costs, the model with firm heterogeneity generates higher aggregate welfare gains from trade because it features an additional adjustment margin (the productivity response to trade via reallocations). We also show that these differences are quantitatively substantial, representing up to a few percentage points of GDP. We thus conclude that firm-level responses to trade and the associated productivity changes have important consequences for the aggregate welfare gains from trade.

How can these findings be reconciled with the results obtained by Arkolakis, Costinot, and Rodriguez-Clare (2012)? Their approach compares models that are calibrated to deliver the same domestic trade share and trade elasticity (the sensitivity of aggregate trade to changes in trade costs). In so doing, this approach implicitly makes different assumptions about demand and trade costs conditions across the models that are under comparison (Simonovska and Waugh 2012). By assuming different levels of product differentiation across the models, and assuming different levels of trade costs, it is possible to have the different models predict the same gains from trade – even though they feature different firm-level responses. In contrast, our approach keeps all these ‘structural’ demand and cost conditions constant, and changes only the degree of firm heterogeneity (Melitz and Redding 2013b). This leads to different predictions for the welfare gains from trade.

One potential criticism of our approach is that one can estimate the trade elasticity (the sensitivity of aggregate trade to changes in trade costs) using aggregate trade data only – without requiring any specific assumptions about the firm-level responses to trade. Whatever assumptions are made about those firm-level responses (and the demand and trade-cost conditions), they should then be constructed so as to match that estimated aggregate elasticity. However, recent empirical work has shown that those underlying assumptions radically affect the measurement of the aggregate trade elasticity, and that this trade elasticity varies widely across sectors, countries, and the nature of the change in trade costs (see for example Helpman et al. 2008, Ossa 2012, and Simonovska and Waugh 2012). There is thus no single empirical trade-elasticity parameter that can be held constant across those different models.

Given the lack of a touchstone set of elasticities, we favour our approach to measuring the gains from trade arising from different models; one that maintains the same assumptions about demand and trade costs conditions across those models.

“Large cities” in the EU and US, redux

The Economist is six months late to the party, but the latest print edition has a piece on that McKinsey comparison of American and Europe cities. I have some quibbles, again.

I don’t understand the piece’s opening, though it has little to do with what follows. It begins:

AMERICA is full of vast, empty spaces. Europe, by contrast, seems chock-a-block with humanity, its history shaped by a lack of continental elbowroom. Ironically, Europe’s congestion partly reflects the fact that its large cities suck up relatively few people.

Moving people across cities wouldn’t change the (unweighted) average population density of the US or EU, so what does this comparison mean? Europe is going to be full of humanity because the land area of the EU is roughly half that of the continguous US (1.7m vs 3.1m square miles). Since larger cities are generally denser, the population-weighted density of Europe would rise if its large cities had higher population shares.

Never mind the elbowroom. The Economist continues:

Although America and the euro zone have similar total populations, America’s 50 largest metropolitan areas are home to 164m people, compared with just 102m in the euro area. This striking disparity has big consequences.

Differences in metropolitan populations may help explain gaps in productivity and incomes. Western Europe’s per-person GDP is 72% of America’s, on a purchasing-power-parity basis. A recent study by the McKinsey Global Institute, the consultancy’s research arm, reckons that some three-quarters of this gap can be chalked up to Europe’s relatively diminutive cities. More Americans than Europeans live in big cities: there is a particular divergence in the size of each region’s “middleweight” cities, those that teem just a little less than the likes of New York and Paris (see chart). And the premium earned by Americans in large cities relative to those in the countryside is larger than that earned by urban Europeans.

As I explained back in April, the MGI report does not say Europeans would reach American prosperity levels if the population shares of their large cities reached American levels:

The gap in per capita GDP between the US and Europe is about 35%, according to the MGI figures in Exhibit 2. The “large city” premia in the United States and Europe of 34% and 30% are virtually the same. That means that the difference in per capita income attributable to the difference in “large city” population shares is the large city premium (~30pp) times the difference in large city population shares (22pp). The six to seven percentage points explained by this difference in population shares is at best one-fifth of the 35% gap between US and EU incomes. You can confirm this quick calculation by studying the decomposition in MGI’s Exhibit 2. Moving more people into large cities wouldn’t meaningfully reduce the US-EU per capita income gap.

Look at Exhibit 2 for yourself:

The Economist mentions the big-city population share and big-city premium components. They neglect that 53 of those 74 percentage points are strictly attributable to the difference in average income. Differences in metropolitan populations are not at the heart of the story.

After citing all the advantages of cities, the Economist considers two reasons why European cities aren’t as large as US cities: regulatory barriers and incomplete integration. While the former might matter, I put a lot of stock in the latter. As I explained in my prior post, Zipf’s law holds at the country level. Since no European state has a population close to 300 million, we should not expect any European city to approach the size of NYC or LA. Until intra-European mobility looks anything like intra-US mobility, I think we should expect Zipf’s law to hold at the country level. And since MGI used a common cutoff of population > 150,000 for defining a “large city”, it’s not at all surprising that a larger share of the US population lives in its large cities. I wrote before:

Given the UK population, increasing the fraction of UK residents who live in “large cities” with populations greater than 150,000 would require the emptying out of smaller metropolitan areas. While such migration is entirely possible, it would violate the expected city size distribution… If you know the populations of New York and London and are familiar with Zipf’s law, then it’s not at all surprising that a greater fraction of the US population is found in metropolitan areas above some common population threshold. I don’t think that tells us much about the economic mechanisms determining the role of US cities in the global economy.

Update: Related to my comparison of US and UK city-size distributions, see Henry Overman on the details of Zipf’s law for UK cities.

Atkin & Donaldson – Who’s Getting Globalized? The Size and Nature of Intranational Trade Costs

David Atkin and Dave Donaldson are presenting this paper tomorrow afternoon at the NBER summer institute:

This paper uses a newly collected dataset on the prices of narrowly defined goods  across many dispersed locations within multiple developing countries to address the  question, How large are the costs that separate households in developing countries from the  global economy? Guided by a flexible model of oligopolistic intermediation with variable mark-ups, our analysis proceeds in four steps. first, we measure total intranational trade costs (ie marginal costs of trading plus mark-ups on trading) using price gaps over space within countries—but we do so only among pairs of locations that  are actually trading a good by drawing on unique data on the location of production  of each good. Second, we estimate, separately by location and commodity, the passthrough rate between the price at the location of production and the prices paid by inland consumers of the good. Our estimates imply that incomplete pass-through—and therefore, intermediaries’ market power—is a commonplace, and that pass-through is especially low in remote locations. Third, we argue that our estimates of total trade costs (Step 1) and pass-through rates (Step 2) are sufficient to infer the primitive effect  of distance on the marginal costs of trading; after correcting for the fact that mark-ups  vary systematically across space we find that marginal costs are affected by distance  more strongly than typically estimated. finally, we show that, in our model, the estimated pass-through rate (Step 2) is a sufficient statistic to identify the shares of social  surplus (ie the gains from trade) accruing to inland consumers, oligopolistic intermediaries, and deadweight loss; applying this result we find that intermediaries in  remote locations capture a considerable share of the surplus created by intranational  trade.

You can listen to a podcast of Donaldson presenting a much earlier version of this work from the International Growth Centre. He does a really nice job of summarizing the issues involved in inferring trade costs from price data.

How big are the gains from trade?

One of the most-mentioned trade papers of the last couple years is “New Trade Models, Same Old Gains?” by Arkolakis, Costinot & Rodriguez-Clare, now published in the AER. Their theoretical work shows that, for a broad class of theoretical models that includes the Armington, Eaton and Kortum (2002), and Melitz-Chaney approaches, the gains from trade are characterized by a formula involving only two numbers – the domestic expenditure share and the trade elasticity. The former can be straightforwardly obtained from the data. The latter needs to be estimated, which is more involved but feasible. ACR shows that their formula says that US welfare is about 1% higher than it would be under autarky.

In the words of Ralph Ossa, “either the gains from trade are small for most countries or the workhorse models of trade fail to adequately capture those gains.” Different people come down on different sides of that choice. Ed Prescott, for example, is clearly in the latter camp.

Ossa has a new paper, “Why Trade Matters After All“, aimed at reconciling this divide:

I show that accounting for cross-industry variation in trade elasticities greatly magnifies the estimated gains from trade. The main idea is as simple as it is general: While imports in the average industry do not matter too much, imports in some industries are critical to the functioning of the economy, so that a complete shutdown of international trade is very costly overall…

I develop a multi-industry Armington (1969) model of international trade featuring nontraded goods and intermediate goods and show what it implies for the measurement of the gains from trade…

Loosely speaking, the exponent of the aggregate formula is therefore the inverse of the average of the trade elasticities whereas the exponent of the industry-level formula is the average of the inverse of the trade elasticities which is different as long as the elasticities vary across industries.

allowing for cross-industry heterogeneity in the trade elasticities substantially increases the estimated gains from trade for all countries in the sample. For example, the estimated gains from trade of the US increase from 6.4 percent to 42.0 percent if I do not adjust for nontraded goods and intermediate goods and from 3.8 percent to 23.5 percent if I do…

the 10 percent most important industries account for more than 80 percent of the log gains from trade on average.

Thinking about the firm-size distribution

[Note: This post isn’t about international economics. I’ll use an example from trade to comment on a feature of the US real-estate market.]

In a letter to the Economist, the president of the National Association of Realtors writes:

[I]t is not true that large brokers dominate the industry. In fact, the real-estate industry consists mostly of independent contractors and small firms. Eight out of ten realtors work as independent contractors for their firms.

The second sentence appears to be a non-sequitur, unless one thinks that existence is informative about dominance. It’s not. In their first glance, antitrust authorities would look at concentration ratios or Herfindahl–Hirschman indices, because dominance is about economic outcomes, such as market shares, not mere existence.

According to Bernard, Jensen, Redding, and Schott’s JEP survey, four percent of the 5.5 million US firms export. That makes 220,000 exporters. The top ten percent, just 22,000 exporters, are responsible for 96% of US exports. Would we say that “larger exporters do not dominate exporting because the exporting set of firms consists mostly of small exporters”? Of course not.

When thinking about the sales distribution, we care about the exponent of the power law characterizing it, not merely the fact that its support includes small sizes.

US abandons zeroing (for now?)

I’m seeing a lot of news about the US federal government dropping its practice of zeroing in calculating antidumping duties. The WTO news item is uninformative. I don’t have time this week to follow the latest developments, so I’ll just drop links:


The US has reached deals with the European Union and Japan to drop a contentious practice in its anti-dumping calculations known as “zeroing”, ending a longstanding international trade dispute in order to prevent retaliation against American products. The agreements, signed in Geneva, will close the books on a fight that began in 2003 when the EU first filed a case against the US at the World Trade Organisation.

USTR press release:

After the WTO found that the United States had not brought its antidumping methodologies into compliance, the EU and Japan requested authorization to impose hundreds of millions of dollars of trade retaliation. Had these agreements not been reached today, substantial volumes of U.S. exports could have been closed out of markets in the EU and Japan, resulting in job loss for U.S. workers and financial loss for U.S. farms and businesses…

Under the agreements signed today, the United States will complete the process – which began in December 2010 – of ending the zeroing practices found in these disputes to be inconsistent with WTO rules. In return, the EU and Japan will drop their claims for trade retaliation.

Politics-oriented coverage from The Hill includes this detail: “the Obama administration said it will try to negotiate a future deal at the WTO to permit the practice.” Here’s Scott Lincicome on the news.

What we don’t learn from looking at exports/GDP

I’m afraid that I found “The Quiet Driver of Economic Growth: Exports“, a NYT Economix post by Binyamin Appelbaum, to be more confusing than illuminating. In this post, I’ll try to explain why one must be careful in interpreting a number of economic statistics.

Appelbaum writes:

The estimates of the nation’s economic performance last year, released Friday, highlight a striking trend: Exports have never been more important.

Foreign buyers purchased more than $2 trillion in goods and services, the first time exports have topped that threshold. And those exports accounted for almost 14 percent of gross domestic product, the largest share since at least 1929.

We usually talk about exports alongside its opposite number, imports, and since the United States buys much more than it sells – our “trade deficit” — the general impression is that foreign trade is a drag on the economy. But that tends to obscure the importance of exports, which have accounted for about 10 percent of G.D.P. over the last two decades and, since the recession, considerably more…

Much of the rise in exports is a consequence of domestic problems… This is a good thing on the whole. The ability of American companies to make money in foreign markets is helping to offset the pain of those domestic problems.

I found this confusing in three senses:

  1. In purely accounting terms, GDP depends on net exports, not gross exports.
  2. In compositional terms, the export-GDP ratio doesn’t tell you if international commerce is offsetting domestic problems.
  3. The key phrase “exports accounted for X% percent of GDP” is meaningless at best and misleading at worst.

National accounts

To the extent that gross domestic product is our measure of economic performance, should we think about net exports or gross exports? Recall the expenditure definition of GDP:

Y = C + I + G + X – M

If you want to talk about — in accounting terms, not causal terms — what’s happening to US GDP, then net exports are informative. They appear on the right-hand side. When you talk about gross exports while holding gross imports constant, you are losing information. If X and M both increased by the same amount, then GDP would not increase, but X/GDP would rise.

Suppose that I were describing a firm’s economic performance to you. If we had an accounting definition of our performance that said

corporate profits = revenues – costs,

would the following claim seem reasonable? “We usually talk about revenues alongside their opposite numbers, costs, and since the company buys much more than it sells — our ‘negative profits’ — the general impression is that doing business is a drag on the firm. But that tends to obscure the importance of revenues, which have accounted for 110 percent of (the absolute value of) net profits…”

If you care about the international component of GDP, you are losing information when you switch from looking at net exports to solely considering exports. If you look at the BEA press release, you learn that real exports grew 4.7% and real imports grew 4.4%. But recall that we run a trade deficit, so real imports are growing from a larger base. If we go to table 3 of the full BEA announcement (pdf), my reading is that net exports moved from -$562b in the third quarter to -$582b in the fourth quarter. If I’m reading the table correctly, then net exports actually fell. That means that the way we usually talk about trade, which looks at net exports, tells you something different than what is implied by looking at gross exports (implicitly holding imports constant).

Are exports offsetting domestic problems?

Exports as a share of GDP is a ratio. If exports stay the same while GDP shrinks, the exports-to-GDP ratio will rise. Is that a sign of exports offsetting domestic problems? I suppose that it is if the counterfactual is that exports would shrink at the same rate of GDP. But if net exports actually fell, then the increase in the trade deficit “reduced” US GDP (in accounting, not causal, terms), so exports/GDP seems like the wrong statistic to study.

What do exports “account for”?

Applebaum writes that “exports accounted for almost 14 percent of gross domestic product” and that we’ve negleted “the importance of exports, which have accounted for about 10 percent of G.D.P. over the last two decades.” I do not know what the phrase “accounts for” means in these statements.

It’s true that Y = C + I + G + X – M, so exports are a component of GDP. But when I read “accounts for”, I imagine a decomposition of GDP into pieces that sum to 100%. That’s not true when you talk about gross exports. We’re back to the distinction between gross values and value-added measures that I have repeatedly emphasized. What would it mean to say that “exports account for 223% of Hong Kong’s GDP“?

I would suggest that exports/GDP is meaningless as a measure of how international commerce has benefited the US economy during the last quarter. At worst, the “accounts for” language might cause readers to interpret the measure as representing a decomposition of GDP’s components.


Be careful with economic statistics! There are important differences between gross exports and net exports and between gross value and value added.

I’ve tried to be careful here, but I may have read Applebaum’s post or written my post too quickly, so if I’ve made an error in handling statistical definitions or the BEA data, please point it out in the comments. Thanks!


I’ve tried to write carefully, but there’s a danger that readers might think I’m treating “net exports” as a scorecard for US economic performance. I am certainly not saying that exports are good and imports are bad. Remember that the current account deficit is the amount by which domestic investment exceeds domestic savings. These outcomes are jointly determined in general equilibrium. My story about “net profits” was an accounting analogy, not an economic analogy.

Addendum (28 Jan, 12pm): Here’s my Twitter exchange with Appelbaum. It doesn’t change anything I said above.

Cross-country wage comparisons

On Saturday, I listened to Orley Ashenfelter’s AEA presidential address about cross-country wage comparisons. For a few years, Ashenfelter has been collecting data on “McWages“, so as to “to measure wages for virtually identical jobs, producing identical products in firms with identical technology.” In making these comparisons, he deflates the McDonald’s wage by the price of a Big Mac, thereby calculating the real producer wage.

Yesterday, the Atlantic’s Richard Florida had a post titled “Which Countries Pay Blue Collar Workers the Most?” It featured this BLS table:

Country Pay for Time Worked Total Hourly Compensation
1. Norway NA $57.53
2. Switzerland $34.29 $53.20
3. Belgium $24.01 $50.70
4. Denmark $34.78 $45.48
5. Sweden $25.05 $43.81
6. Germany $25.80 $43.76
7. Finland $22.35 $42.30
8. Austria $21.67 $41.07
9. Netherlands $23.49 $40.92
10. Australia $28.55 $40.60
11. France $21.06 $40.55
12. Ireland $26.29 $36.30
13. Canada $24.23 $35.67
14. United States $23.22 $34.74
15. Italy $18.96 $33.41
16. Japan $18.32 $31.99
17. United Kingdom $21.16 $29.44
18. Spain $14.53 $26.60
19. Greece $13.01 $22.19
20. New Zealand $17.29 $20.57

What does this table mean? Florida writes:

A quick look at the table above suggests that the level of compensation provided to manufacturing workers reflects a nation’s overall level of economic, social, and human development. And that is indeed the case, according to a simple statistical analysis by my colleague Charlotta Mellander.

Manufacturing compensation is closely related to productivity (measured as economic output per capita), global economic competitiveness and overall human development as well as my own Global Creativity Index. This is all in line with basic economics. And manufacturing compensation and wages are higher in nations with higher levels of education and where greater shares of the workforce are employed in knowledge, professional and creative jobs. In other words, manufacturing compensation and wages rise as nations become more post-industrial. Higher manufacturing compensation is also related to lower levels of inequality and higher levels of happiness.

Manufacturing workers are paid the best in the most advanced nations, places that boast advanced safety nets, generous benefit systems and high productivity. Post-industrial economies might not have the most manufacturing jobs, but their workers are the best paid. Instead of adopting a low-road strategy of trying to reduce manufacturing costs and wages in order to compete with China or other emerging economies, the U.S. would be better off with a high-road one, promoting policies that improve innovation, skills and productivity.

I think that we learn a lot about cross-country wage comparisons by thinking about what this table does not mean.

Does this table rank countries by the welfare of their blue-collar workers? No. Welfare depends on real consumer wages, not nominal wages, so a welfare comparison would necessitate deflating these nominal wages by local prices. For example, Switzerland is a notoriously expensive place to live; its price level is about 1.5 times that of the US. Those interpreting the table as saying that a US-to-Switzerland migration would raise their wages by 50% would be disappointed when they discovered the accompanying 50% price increase. So this table isn’t about workers’ welfare.

Does this table rank countries by their manufacturing TFP? No, for many (potential) reasons. For example, worker quality may differ considerably across countries. Suppose that all these countries are producing the same goods using the same technology, but different countries’ workers embody different numbers of efficiency units of labor. You’ll then observe substantial wage variation even if the unit cost of labor and manufacturing TFP are identical across countries.

Does this table rank countries by their labor productivity in manufacturing? It would if you believe we’re in a world of factor price equalization so that differences in wage rates must reflect differences in workers’ labor productivity. But are these workers making the same product using the same technology? Are enough factors of production sufficiently mobile to put us in the FPE set? Can large trade costs support differences in unit costs? And so forth.

[By the way, manufacturing employees aren’t all “blue-collar workers”. There is cross-country variation in the white-collar-blue-collar ratio of manufacturing, which will move the average hourly compensation measure.]

The BLS measure “hourly compensation costs in manufacturing” is a straightforward number, but cross-country wage comparisons are not a straightforward economic concept. Richard Florida suggests that we understand something about it by looking at its correlates. I would suggest that teaching students what this table does not mean may convey even more economic lessons.

When trade raises welfare and lowers measured GDP

This nifty note by Bajona, Gibson, Kehoe, and Ruhl points out that there may be little connection between real GDP and welfare; in fact, welfare-improving trade liberalization may lower measured real GDP. Here’s a simple example in the Heckscher-Ohlin setting:

The intuition behind the decrease in measured real GDP for the autarky to free trade scenario is simple: given factor endowments, the base-year production pattern in country i is the optimal production pattern for country i at the base year prices among all feasible production plans… Any deviation from that production pattern will lower the value of production at those prices.

The global trade surplus

The Economist on Exports to Mars: “The world exported $331 billion more than it imported in 2010, according to the IMF’s World Economic Outlook… Either the current-account deficits of countries such as America are being understated or the surpluses of countries like China are being overstated, and by a rising amount… Indeed, the global “surplus” now exceeds China’s.”