The Terms of Trade of Brazil


An article in the New York Times by Paul Krugman talked about a current economic downturn in Brazil. What happened:

First, the global environment deteriorated sharply, with plunging prices for the commodity exports still crucial to the Brazilian economy. Second, domestic private spending also plunged, maybe because of an excessive buildup of debt. Third, policy, instead of fighting the slump, exacerbated it, with fiscal austerity and monetary tightening even as the economy was headed down.

What didn’t happen:

Maybe the first thing to say about Brazil’s crisis is what it wasn’t. Over the past few decades those who follow international macroeconomics have grown more or less accustomed to “sudden stop” crises in which investors abruptly turn on a country they’ve loved not wisely but too well. That was the story of the Mexican crisis of 1994-5, the Asian crises of 1997-9, and, in important ways, the crisis of southern Europe after 2009. It’s also what we seem to be seeing in Turkey and Argentina now.

We know how this story goes: the afflicted country sees its currency depreciate (or, in the case of the euro countries, its interest rates soar). Ordinarily currency depreciation boosts an economy, by making its products more competitive on world markets. But sudden-stop countries have large debts in foreign currency, so the currency depreciation savages balance sheets, causing a severe drop in domestic demand. And policymakers have few good options: raising interest rates to prop up the currency would just hit demand from another direction.

But while you might have assumed that Brazil was a similar case — its 9 percent decline in real G.D.P. per capita is comparable to that of sudden-stop crises of the past — it turns out that it isn’t. Brazil does not, it turns out, have a lot of debt in foreign currency, and currency effects on balance sheets don’t seem to be an important part of the story. What happened instead?

Slowly going over the three points that Krugman made in the beginning:

1. Commodity prices went down and Brazil exports a lot of commodities.

Brazil’s exports in 2016:


At a glance, we have among commodities: vegetable products, mineral products (5% crude petroleum, 10% iron and copper ore), foodstuffs, animal products, metals, and precious metals. Though picking out these may be over or underestimating the true percentage of commodity exports among all of Brazil’s exports, let’s use these for our approximation. The total percentage of these products is about 60%, where around 36% are agricultural commodities, around 27% are metal commodities (metals + iron and copper ore), around 5% is crude petroleum, and around 2% are precious metals. These categorizations that I did are improvisational and not following any definitions – they are simplifications.

Looking at the S&P GSCI Agricultural & LiveStock Index Spot (SPGSAL):


we definitely do see a downtrend in the last several years in agricultural commodities.

Looking at the S&P GSCI Industrial Metals Index Spot (GYX):


there was a decline from 2011 but a rise from 2016.

Looking at the S&P GSCI Precious Metals Index Spot (SPGSPM):


it’s been flat since around 2013.

Looking at S&P GSCI Crude Oil Index Spot (G39):


it has been low after a decline in 2014 with volatility in 2017-2018.

But instead of eyeballing this phenomenon with a bunch of different charts, there’s a way that can mathematically eyeball this in one chart, called the terms of trade.

Investopedia’s definition of terms of trade:

What are ‘Terms of Trade – TOT’?

Terms of trade represent the ratio between a country’s export prices and its import prices. The ratio is calculated by dividing the price of the exports by the price of the imports and multiplying the result by 100. When a country’s TOT is less than 100%, more capital is leaving the country than is entering the country. When the TOT is greater than 100%, the country is accumulating more capital from exports than it is spending on imports.

But how exactly do you calculate the “price of exports and imports” of a country like, say Brazil, that has USD 190B exports a year and surely thousands if not more different products, and what to do about the changing quantities of each of those products every year? How do we understand the terms of trade in a way that doesn’t vaguely seem like the current account balance? (which is the total value of exports minus imports, or net value of exports: \( EX – IM = \sum_{i}^{}{p_i \cdot q_i} – \sum_{i}^{}{p’_i \cdot q’_i} \) where \( p_i\), \( q_i \) is the price and quantity of export product \(i\) and \( p’_i\), \( q’_i \) is the price and quantity of import product \(i\).

The answer is by deciding on a base year to compare the year in question. For example, for the prices of products in the year in question, we sum the values of exports for each product in that year, i.e. \( \sum_{i} {p_{i,n} \cdot q_{i,n}} \) where \(i\) is the index for each different product and \(n\) is the year in question. For the prices of products in the base year \(0\), we take the price of each product \(i\) in that base year multiplied by the quantity of that product \(i\) in the year in question \(n\). In other words, we fix the quantity of each product \(q_i\) to the quantity of each product in the year in question \(q_{i,n}\) so that we are strictly comparing prices between year \(n\) and \(0\) and not letting changes in quantity \(q\) get in the way. This is the Paasche index.

Another way we can do this is: for the prices of products in the year in question \(n\), we sum the prices of each product in that year \( p_{i,n} \) multiplied by the quantity of each product from the base year \( q_{i,0} \), and for the prices in the base year \(0\), we take the price of each product \(i\) in that base year multiplied by the quantity of that product \(i\) also in the base year \(0\). So this time, instead of fixing the quantity of each product in the year in question \(n\), we fix the quantity of each product to the base year \(0\). This is the Laspeyre index.

Paasche index:

$$ P_{\textrm{Paasche}} = \frac{\sum_{i}{p_{i,n} \cdot q_{i,n}}}{\sum_{i}{p_{i,0} \cdot q_{i,n}}} $$

Laspeyre index:

$$ P_{\textrm{Laspeyre}} = \frac{\sum_{i}{p_{i,n} \cdot q_{i,0}}}{\sum_{i}{p_{i,0} \cdot q_{i,0}}} $$


Thus, by using such a price index calculation we “cancel out” the effect of changing export or import quantities so that we are only looking at the change of price of exports or imports between two time periods. With a base year \(0\), we can calculate the price index for exports in year \(n\), the price index for imports in year \(n\), and then divide the former by the latter to achieve the terms of trade for year \(n\):

$$ \textrm{Terms of Trade} \ = \frac{P_{\textrm{Paasche, exports}}}{P_{\textrm{Paasche, imports}}} \ \textrm{or} \ \frac{P_{\textrm{Laspeyre, exports}}}{P_{\textrm{Laspeyre, imports}}} $$


A terms of trade chart quantitatively summarizes all the above eyeballing we did with the visualization of Brazil’s exports and the charts of commodities indices as well as the eyeballing we didn’t do with Brazil’s imports. And we see what we expect in the above graph, which is a drop in Brazil’s terms of trade in the last several years.

What is the conceptual difference between the

\( \textrm{Terms of Trade} \ = \frac{P_{\textrm{Paasche, exports}}}{P_{\textrm{Paasche, imports}}} \ \textrm{and} \)

\( \textrm{Current Account} \ = \sum_{i}{p_{i,n,exp} \cdot q_{i,n,exp}} – \sum_{j}{p_{j,n,imp} \cdot q_{j,n,imp}} \ \textrm{?} \)

2. Brazil’s consumer spending declined due to rising household debt (the red graph):


3. Brazil implemented fiscal austerity to try to deal with “long-term solvency problems” and raised interest rates to try to deal with inflation, which was caused by depreciation in the currency. The currency depreciated due to lower commodity prices, which of course is also reflected in the terms of trade graph above.

Depreciating currency (blue) and inflation (change in or first derivative of red):


Interest rates raised to combat inflation:


We can see that interest rates rise in late 2015 as a response to rising inflation. Inflation drops as a response in the next couple of years, but this rise in interest rates contributed to the slow down in Brazil’s economy.


So we have a drop in the terms of trade (due to a drop in commodity prices), a drop in consumer spending (due to a rise in household debt in preceding years), and then fiscal austerity and monetary contraction as government policy responses, causing a recession in Brazil.

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