Chapter 4
The Terms of Trade
Abstract
Let’s generalize the results to a disturbance that improves the US terms of trade or real exchange rate. If the after-tax cash flows to US-based companies increase, what would we expect to see happening to the foreign exchange value of the dollar and the market value of US-based assets? It would not be too difficult to argue that the asset values should rise. Will the adjustment be instantaneous? We would argue that it would not. One key reason is that the adjustment is costly. We would argue that the real exchange rate cycles associated with local disturbances are best described as an inverted V. This is also an important fact that leads to some interesting economic and investment insights.
Investors who, as a result of a positive disturbance, see the potential of realizing a higher after-tax cash flow would bid up the value of these cash flows. But that is not all. Foreigners see the higher after-tax cash flows too, and they would like to take advantage of them. Their investment will generate a capital inflow into the United States. In order to buy the US assets, they need to acquire US dollars. The demand for dollars will rise relative to other currencies. As we have a floating exchange rate system, the balance of payments is always zero. That means the capital inflows will be the mirror image of the trade deficit. As capital flows in, the differential rate of returns between the US assets and the rest of the world will diminish. The adjustment costs will prevent the instantaneous adjustment. However, over time, capital flows will completely eliminate the excess returns and purchasing power parity (PPP) will be reestablished. In other words, the deviation from PPP will be temporary and mean reverting. The PPP deviation will look like an inverted V for the country with the real exchange rate appreciation.
Our framework suggests that an improved terms of trade leads to higher asset values, higher levels of economic activity, a trade deficit, and positive capital inflows. For the investors, the important point is that the terms of trade improvement leads to higher asset values and equity returns, while the real exchange rate appreciation means that the United States will outperform the rest of the world. The investment implication is straightforward: increase exposure to equities, in particular, US equities. Empirically, the data shows that the closeness of the relationship varies across the different economies, but the nature and direction of the relationship is undeniable. A rising terms of trade is associated with an improvement in the relative economic performance. This empirical regularity is very important in several ways and illustrates the value of the terms of trade as both a policy and investment indicator.
Keywords
terms of trade
purchasing power parity
PPP
the Big Mac index
real exchange rate
In a frictionless world where factors and products are free to move, we would expect to find that the price of each commodity would be arbitraged across localities. That is, the law of one price or purchasing power parity (PPP) will hold at the individual level. Under these conditions, if the tastes are the same across different localities, one can then show that the consumer basket will be the same across the world. In such a case, the CPI in local currency converted into a common currency will also be the same across the world. The law of one price or PPP can be extended to the broad consumer basket.
Relaxing some of these assumptions or allowing for different tastes, some of the immobile factors and/or differences in technology will insure that the consumer baskets will not be the same across localities, even though PPP holds at the individual commodity level. The terms of trade measure how much of a consumer basket in one country, say the United States, will buy of another country consumer basket, say Germany. On a practical level, these are not foreign concepts. Recall a few years back when The Economist reported in the back of its issues the price of a Big Mac in local currency converted back into US dollars and compared it to the US price of a Big Mac. The Economist was giving the reader a quick and dirty way to determine whether PPP held across the world economies. And if PPP did not hold, the Big Mac prices gave people an idea of how large was the deviation from PPP across the various economies, that is, the terms of trade.
A Broader Estimate
The Big Mac is just a single commodity, and as it may be representative of an economy, a more precise estimation of the deviations from PPP is needed. Fortunately, the IMF estimates the member countries’ GDP based on current prices, current dollars, and a PPP-adjusted basis. In our case, we take a more US-centric view of the world by taking a weighted average of the terms of trade of major trading partners of the United States to construct a broader and more ready measure of the terms of trade or real exchange rate index. Fortunately, the Federal Reserve Bank of Saint Louis’ economic database, FRED, publishes a series consisting of the trade-weighted foreign exchange value of the dollar. In order to convert the series into the US terms of trade, we have to account by the changes in each of the countries domestic price levels. Fig. 4.1A shows our estimate of the US terms of trade. The data presented in Fig. 4.1A identifies three major exchange-rate cycles—both the first two complete cycles denote an inverted V. We can also see that troughs in the index return to a value along a flat line. So, the data clearly does not show a secular long-term trend. The real exchange rate cycles measure identifies major changes in the US terms of trade during the 1980s, the 1990s, and more recently in the aftermath of the financial crisis.
Figure 4.1 The US terms of trade.
(A) The real exchange rate, Federal Reserve Bank of Saint Louis’ economic database (FRED) data. (B) Organisation for Economic Co-operation and Development (OECD) versus FRED data.
(A) The real exchange rate, Federal Reserve Bank of Saint Louis’ economic database (FRED) data. (B) Organisation for Economic Co-operation and Development (OECD) versus FRED data.
The FRED-based data is not the only estimate we use for the terms of trade, the OECD also does that job for us. It publishes a dollar-based PPP adjusted GDP, which is divided by the country’s GDP in dollars yields the real exchange rate or terms of trade relative to the United States, unfortunately the data is only available for a smaller sample period (Fig. 4.1B). Comparing the two series, both identify the same inflection points; the one major difference between the two is the magnitude of the upswing in the US terms of trade since the financial crisis. The most important differences between the two series is that the FRED data is based on the trade weighted index among the United States major trading partners while the OECD data is based on a GDP weighted index that includes all nations. These differences in weighting schemes that can in principle provide us with potential explanations for the differences in the index.
Policy Links
Fig. 4.1A shows three major real exchange rate cycles. One begins in 1980, peaks in 1985, and troughs somewhere around 1988. The second cycle begins in 1995, peaks around 2001, and troughs in 2008. The third cycle begins around 2008. In between the first two cycles the real exchange rate moves sideways, although one could argue that there is a slight downward trend.
The timing of the cycles may be coincidence, yet they are highly correlated to major policy changes. During the 1980s, the United States adopted a very different policy mix than the one that had prevailed during the previous decade. Recall that Paul Volcker changed the Fed operating procedures and, according to our interpretation of the data, the Fed moved to a domestic price rule. This was important for a number of reasons, not the least being that under a domestic price rule with the inflation within a target range; fluctuations in the nominal exchange rate would solely reflect fluctuations in the real exchange rate. But more on this in a later Part IV, Chapter 3. On the fiscal side, President Reagan enacted a tax rate cut that lowered the top personal income tax rate of the US taxpayers to 50% from 70%. Recall that the tax rate cut was phased in over 3 years.
During President Bush the elder, the top tax rate was raised to 31% and then President Clinton raised it some more to 39.6%; and, as shown in Fig. 4.1A, the dollar drifted downward. It was not until 1995 that the dollar surged. What happened then? Three things occurred. The first one was the Contract With America, when the Republicans took over Congress and that led to gridlock. The Gingrich victory meant a slowdown or derailing of the Clinton’s healthcare agenda and other programs. Second, whether it was luck, we had the productivity surge, which we believe was the result of previous policies. More importantly, President Clinton changed strategies. He adopted his famous triangulation policy and enacted some interesting reforms and even lowered the capital gains tax rate. Finally, some critics also argued that the period’s easy credit fueled a couple of bubbles (the tech bubble and ultimately the real estate bubble). Perhaps it is a coincidence, but the top of the real exchange rate occurred right around Y2K, when the Maestro flooded the market with cash and after nothing happened, he quickly withdrew it. It is possible that the rapid expansion and withdrawal of cash may have had an impact on the real exchange rate. If the Maestro made a monetary mistake, as we claim, his mistake may have marked the end of the cycle and accelerated the reversal.
Needless to say, the United States was not alone in the world. We have highlighted the US policy actions, however, it is clear that the rest of the world was also reacting to our policy changes. During the 1980s, the developed world and much of the emerging markets lowered their tax rates too and adopted price rule-like monetary policies. These policy changes partially reversed or offset the impact of the US policies on the real exchange rate. However, these are not the only reasons for the round trip on the real exchange rate. The markets equilibrating process has something to do with it.
The Adjustment Process: Investment Implications
In the absence of adjustment costs, the adjustment to a new equilibrium would be instantaneous. In turn, the presence of adjustment costs will slow the economy’s speed of adjustment to a new equilibrium. This is an important feature for portfolio managers; the costly adjustment gives rise to differential return cycles that an astute investor may take advantage to deliver an above average performance. One striking feature of Fig. 4.1 is that the exchange rate cycles are fairly long. The dollar appreciation cycles and corresponding depreciation cycles each lasts several years. One justification for the duration of the cycles is that adjustment is costly.
The presence of adjustment costs leads to a simple conclusion: if disturbances take several years to dissipate before the economy reaches a new long-run equilibrium, trends will develop. Simple momentum-based investment models will be able to exploit these trends. No knowledge of the causes or consequences is needed for the momentum investor during this trend period. However, if the evidence in Fig. 4.1A–B is correct, the momentum models invariably fail around the turning point until a new trend is established. However, our framework offers the possibility of not only taking advantage of the trend, but it may also allow us to anticipate the turning points in the real exchange rate and relative rates of returns. Let’s consider an example based on the Reagan tax rate cuts.
The Disturbance: When President Reagan got elected, the top personal income tax rate was lowered from 70% to 50%. Let’s look at the impact of the tax rate reduction in the after-tax cash flows of US-based entities. Before President Reagan, a $100 worth of pretax income, after paying the 70% tax rate, would yield only $30 worth of after-tax income. Immediately after the Regan tax rate cuts were passed, the same $100 worth of pretax income would now be subject to only a 50% tax rate, thereby delivering an after-tax income of $50. Put another way, the Reagan tax rate cuts would increase the after tax cash flow by 66%, that is, $50/$30.
The Economy and Market Adjustments: Let’s generalize the results to US-based activities. If their after-tax cash flows increased by 66%, what would we expect to see happening to the foreign exchange value of the dollar and the market value of US-based assets? It would not be too difficult to argue that the asset values should rise by 66%. Will the adjustment be instantaneous? We would argue that it would not for two different reasons that we have already alluded to. One reason is that the adjustment is costly. The second reason is that the tax rate cut was phased in over 3 years. Looking at Fig. 4.1A, we can see that the real exchange rate cycles associated with lower tax rates are best described as an inverted V. This is also an important fact that leads to some interesting economic and investment insights. As we have already mentioned, the Reagan tax rates resulted in a 66% increase in the keep rate. By the simple stroke of a pen, President Reagan increased the after-tax cash flows of US-based economic activity by 66%. Investors who see the potential of realizing a higher after-tax cash flow would bid up the value of these cash flows. How much? We would argue that a 66% increase in a valuation would not be out of the question. But that is not all. Foreigners see the higher after-tax cash flows too, and they would like to take advantage of them. Their investment will generate a capital inflow into the United States. In order to buy the US assets, they need to acquire US dollars. The demand for dollars will rise relative to other currencies. How much? Again the 66% appreciation is a pretty good number. As we have a floating exchange rate system, the balance of payments is always zero. That means that the capital inflows will be the mirror image of the trade deficit. As capital flows in, the differential rate of returns between the US assets and the rest of the world will diminish. The adjustment costs will prevent the instantaneous adjustment. However, over time capital flows will completely eliminate the excess returns and PPP will be reestablished. In other words, the deviation from PPP will be temporary and mean reverting. The PPP deviation will look like an inverted V for the country with the real exchange rate appreciation.
Putting it all together, our framework suggests that lower tax rates would lead to higher asset values, higher levels of economic activity, a trade deficit, and positive capital inflows. For the investors, the important point is that the tax rate cuts would lead to higher asset values and equity returns, while the real exchange rate appreciation means that the United States will outperform the rest of the world. The investment implication is straightforward: increase exposure to equities, in particular, US equities.
Does Our Theory Hold Water?
When we look at Fig. 4.1A–B, we find support for the adjustment cost theory. The peak in the US dollar was in 1985, 2 years after the tax rate cuts were fully enacted. However, looking at the peak, we find that the real exchange rate only appreciated about 35%. Why? Our answer is simple. As the rest of the world saw the US success, the rest of the world began to adopt similar policies and, as a result, lowered their top income tax rate. The rest of the world tax rate reductions eroded some of the US relative returns advantages. However, we should not be too upset with this. The competition from the rest of the world increased the after tax returns of their assets. We could argue that the Reagan policies fueled a global bull market.
The data also shows that, as expected, the real exchange rate reflected a temporary deviation from PPP and in due course PPP was restored (the inverted V). This also means that during the time between the Reagan and Contract With America cycles, the United States was around the PPP trend line.
So far, so good. Now we need to focus on the relationship between the real exchange rate and relative stock returns. The latter is calculated as the ratio of the United States and the World ex-US MSCI stock indices. As shown in Fig. 4.2A–B, the relative stock returns follow a path similar to that of the real exchange rate. The relationship also holds when applied to the share of US GDP relative to the world economy’s GDP (Fig. 4.3A–B). The rising terms of trade increases the relative price of US goods. That is a unit of the US consumer basket buys more of the foreign goods consumer basket. The higher relative price increases not only the profitability, but also the incentives to work and produce in the US. The positive correlation between the terms of trade and the relative stock market valuation, as well as the relative share of GDP are quite robust as shown in Fig. 4.2A–B, as well as Fig. 4.3A–B.
Figure 4.2 (A) The US terms of trade, FRED data, versus the ratio of the United States to the MSCI Ex-US World Stock Index. (B) The US terms of trade, World Bank data, versus the ratio of the United States to the MSCI Ex-US World Stock Index.
Figure 4.3 (A) The US terms of trade versus the ratio of the United States to the World Ex-US GDP. (B) The US terms of trade, OECD data, versus the ratio of the United States to the World EX-US GDP.
According to our interpretation of the data, and the information presented in Fig. 4.1A we have identified two distinct full cycle real exchange rate episodes: the Reagan cycle (1980–88) and the beginning of Contract with America (1994). In between, we observe the real exchange rate drifting slightly lower, but, in the big scheme of things, we characterize that period as one of approximate PPP. The figures show that the FRED and OECD base terms of trade produce a good fit for the relative stock market performance and the relative GDP performance (Fig. 4.1A–B). The data suggests that either of the two terms of trade measures have a pretty good explanatory power. Therefore, although we lean to the Fred-based terms of trade series, either of the two series is acceptable for the analysis at hand.
Does the Relationship Hold for Other Countries?
The IMF database contains information on the stock market and real exchange rate for 189 countries in the world. As already mentioned the real exchange rate or terms of trade is a bilateral relationship that measures how much of one country’s goods, say Australia’s consumer basket, buys of another country’s goods, that is, the other country’s consumer basket. As there are 189 countries, it follows that there will be 188 terms of trade or relative prices. One versus each of the other 188 countries. This hold true for all countries. However, as we move to the next country, say Afghanistan, we do not need to calculate 188 terms of trade. The terms of trade between Afghanistan and Australia are the inverse of Australia–Afghanistan terms of trade. Hence, we only need to calculate 187 relationships. The next round means that we only have to calculate 186 independent relationships. The sequence can be expressed in algebraic form as:
Obviously, 17766 is a large number of time series requiring significant amount of space and difficult to present in a succinct way. For that reason we have chosen to illustrate the process using a small subsample, thus focusing on a handful of countries. The way we envision using the framework and the relationships developed here is taking a narrow focus, on the countries that interest us for the particular issue at hand. In the process, we illustrate how easily it would be to extend the analysis to any other individual and or group of countries.
Let’s assume that for some reason we are focused on five individual countries—the United States, Australia, Germany, the United Kingdom, and Mexico. The previous formula suggests that we will have 4, 3, 2, and 1 for a total of 10 independent relationships describing all the interactions among the 5 economies. The first step in the process is to calculate the ratio of the MSCI Stock Indices of each country relative to the US Index, as well as calculating the terms of trade for each country in terms of the US goods. The process yields four different graphs, one for each country relative to the United States (Fig. 4.4A–D). However, this is only a start. It does not provide us with the complete set of relationships among the different countries.
Figure 4.4 (A) Australia Terms of Trade in terms of the United States versus the ratio of Australia to the US MSCI Index. (B) EMU Terms of Trade in terms of the United States versus the ratio of EMU to the US MSCI Index. (C) Mexico Terms of Trade in terms of the United States versus the ratio of Mexico to the US MSCI Index. (D) UK terms of trade in terms of the United States versus the ratio of United Kingdom to the US MSCI Index.
Next we calculate the same information with respect to the Australian economy. We have already noted that the Australia terms of trade with respect to the US economy is the inverse of the US terms of trade with respect to the Australian good and services; however, we can skip this calculation. That leaves us three different relationships to calculate. The terms of trade and stock market ratio between EMU, Mexico, the United Kingdom, and Australia (Fig. 4.5A–C). Next as we continue the process, we focus on the EMU and we now only have to estimate two independent relationships between the German economy and those of the United Kingdom (Fig. 4.6B) and Mexico (Fig. 4.6A). Finally the last round leaves us to calculate the relationship between the United Kingdom and Mexico (Fig. 4.7).
Figure 4.5 (A) EMU terms of trade in terms of Australia versus the ratio of EMU to the Australia MSCI Index. (B) Mexico terms of trade in terms of Australia versus the ratio of Mexico to the Australia MSCI Index. (C) UK terms of trade in terms of Australia versus the ratio of United Kingdom to the US MSCI Index.
Figure 4.6 (A) Mexico terms of trade in terms of the EMU versus the ratio of Mexico to the Australia MSCI Index. (B) UK terms of trade in terms of the EMU versus the ratio of the United Kingdom to the EMU MSCI Index.
Figure 4.7 Mexico terms of trade in terms of the United Kingdom versus the ratio of Mexico to the UK MSCI Index.
Once the 10 graphs are calculated we have identified all the possible relationships between the 5 economies in question. As one looks at the 10 graphs, it is clear that a relationship exists between the terms of trade and the ratio of the GDP between the 2 countries in question. The closeness of the relationship varies across the different economies, but the nature and direction of the relationship is undeniable. A rising terms of trade is associated with an improvement in the relative performance. This empirical regularity is very important in a number of ways and illustrates the value of the terms of trade as both a policy and investment indicator.
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