J curve

The term J curve refers to a variety of non-linear mathematics in which a number sequence, when graphed, exhibits initial numbers that track or rise relatively horizontally along the x-axis of a graph, but whose values at some point begin to skyrocket explosively upward along the y-axis of the graph (image pending).

While such graphs can occur in many different fields, an initial appreciation is readily suggested by two of the most famous J-curves in all of human history, both of which took place at the close of World War II in the geometric or exponential J-curve fission progressions that produced the atomic detonations that destroyed the cities of Hiroshima and Nagasaki, Japan. (The most destructive and devastating moments of each of the above progressions took place in the closing moments of the progressions as the numbers suddenly skyrocketed upward along the y-axis) (and thereby demonstrating a decided capacity to wreak virtually inescapable calamity during the rocketing y-axis phases of the progressions).

The two dramatic J-curves from atomic physics (above) introduced humankind to the need to both recognize and closely monitor any numbers behaving in such a pattern. And in addition, another J-curve - this time from population biology - appears to be unfolding along the y-axis of humankind's worldwide graph. It turns out that an un-manipulated graph of worldwide human population growth over the 10,000 years of civilization to the present day and to the close of this century (image pending) appears to exhibit a pronounced J-curve. And in this latter case, humankind's currently-unfolding worldwide numbers appear to occupy the skyrocketing y-axis phase of our graph - with implications worth discussing below and elsewhere in Wikipedia.

The first two sections of this article (pending) will address the two World War II physics progressions already cited, plus the population/sustainability-science implications of humankind's current worldwide population J-curve. The above natural science examples will then be followed by the occurrence of J-curves in several other fields such as economics and the social sciences.

Balance of trade model(economics)

It is common theory that the trade balance increases when the real exchange rate rises. However, there is strong evidence that refutes this claim as is evident in Figure 7-4(see cited book for details), which shows the "U.S trade balance(as a share of GDP) in recent years compared with the U.S. real exchange rate with the rest of the world".^[1] For example, in the mid-1980s there is particularly a gap between a real depreciation and a rise in the trade balance which attributes to the main idea of the 'J curve' that "Import and export flows may react only slowly or weakly to changes in the real exchange rate, so the trade balances can react in unexpected ways."^[1] This evidence sets forth the framework that in the presence of sticky prices there may not be the correlation between a real deprecation and a rise in trade balance that is generally accepted and taught.

In economics, the 'J curve' refers to the trend of a country’s trade balance following a devaluation or depreciation under a certain set of assumptions. A devalued currency means imports are more expensive, and on the assumption that the volume of imports and exports change little immediately, this causes a depreciation of the current account (a bigger deficit or smaller surplus). After some time, though, the volume of exports may start to rise because of their lower more competitive prices to foreign buyers, and domestic consumers may buy fewer of the costlier imports. Eventually, if this happens, the trade balance should improve on what it was before the devaluation.^[1] Likewise, if there is a currency revaluation or appreciation the same reasoning may be applied and will lead to an inverted J-curve.

Immediately following the depreciation or devaluation of the currency, the total value of imports will increase and exports may remain largely unchanged due in part to pre-existing trade contracts that have to be honored. This is because in the short run, prices of imports rise due to the depreciation and also in the short run there is a lag in changing consumption of imports, therefor there is an immediate jump followed by a lag until the long run prevails and consumers stop importing as many expensive goods and along with the rise in exports cause the current account to increase(a smaller defect or a bigger surplus).^[1] Moreover, in the short run, demand for the more expensive imports (and demand for exports, which are cheaper to foreign buyers using foreign currencies) remain price inelastic. This is due to time lags in the consumer's search for acceptable, cheaper alternatives (which might not exist).

Over the longer term a depreciation in the exchange rate can have the desired effect of improving the current account balance. Domestic consumers might switch their expenditure to domestic products and away from expensive imported goods and services, assuming equivalent domestic alternatives exist. Equally, many foreign consumers may switch to purchasing the products being exported into their country, which are now cheaper in the foreign currency, instead of their own domestically produced goods and services.

Empirical investigations of the J-curve have sometimes focused on the effect of exchange rate changes on the trade ratio, i.e. exports divided by imports, rather than the trade balance, exports minus imports. Unlike the trade balance, the trade ratio can be logged regardless of whether a trade deficit or trade surplus exists.^[2]

The shape of the J curve can conclude as, first, the trade balance falls due to the price effects mentioned above,gradually after a lag quants gradually adjust and effectively the trade balance rises and hence creates the shape of a J-curve.^[1] The following components behave as follow, The exchange rate immediately rises and remains flat, exports remain flat and then gradually increase, imports at first rise then stay flat until they begin to gradually fall, and these components make up the shape of the J-Curve. The duration of expenditure switching generally will take at most 1 year.This duration will generally depend on the length of long term contracts as well as how long it takes for consumers to switch goods.

Private equity

An illustration of the J curve in Private Equity

In private equity, the J curve is used to illustrate the historical tendency of private equity funds to deliver negative returns in early years and investment gains in the outlying years as the portfolios of companies mature.^[3][4]

In the early years of the fund, a number of factors contribute to negative returns including management fees, investment costs and under-performing investments that are identified early and written down. Over time the fund will begin to experience unrealized gains followed eventually by events in which gains are realized (e.g., IPOs, mergers and acquisitions, leveraged recapitalizations).^[5]

Historically, the J-Curve effect has been more pronounced in the US, where private equity firms tend to carry their investments at the lower of market value or investment cost and have been more aggressive in writing down investments than in writing up investments. As a result, the carrying value of any investment that is underperforming will be written down but the carrying value of investments that are performing well tend to be recognized only when there is some kind of event that forces the private equity firm to mark up the investment.^[6]

The steeper the positive part of the J curve, the quicker cash is returned to investors. A private equity firm that can make quick returns to investors provides investors with the opportunity to reinvest that cash elsewhere. Of course, with a tightening of credit markets, private equity firms have found it harder to sell businesses they previously invested in. Proceeds to investors have reduced. J curves have flattened dramatically. This leaves investors with less cash flow to invest elsewhere, such as in other private equity firms. The implications for private equity could well be severe. Being unable to sell businesses to generate proceeds and fees means some in the industry have predicted consolidation amongst private equity firms.

Country status model

Another 'J-Curve' refers to the correlation between stability and openness. This theory was suggested initially by the author Ian Bremmer, in his book The J Curve: A New Way to Understand Why Nations Rise and Fall.

The x-axis of the political J-Curve graph measures the 'openness' of the economy in question and the y-axis measures the stability of that same state. It suggests that those states that are 'closed'/undemocratic/unfree (such as the Communist dictatorships of North Korea and Cuba) are very stable; however, as one progresses right, along the x-axis, it is evident that stability (for relatively short period of time in the lengthy life of nations) decreases, creating a dip in the graph, until beginning to pick up again as the 'openness' of a state increases; at the other end of the graph to closed states are the open states of the West, such as the United States of America or the United Kingdom. Thus, a J-shaped curve is formed.

States can travel both forward (right) and backwards (left) along this J-curve, and so stability and openness are never secure. The J is steeper on the left hand side, as it is easier for a leader in a failed state to create stability by closing the country than to build a civil society and establish accountable institutions; the curve is higher on the far right than left because states that prevail in opening their societies (Eastern Europe, for example) ultimately become more stable than authoritarian regimes.

Bremmer's entire curve can shift up or down depending on economic resources available to the government in question. So Saudi Arabia's relative stability at every point along the curve rises or falls depending on the price of oil; China's curve analogously depends on the country's economic growth.

Medicine

In medicine, the 'J-curve' refers to a graph in which the x-axis measures either of two treatable symptoms (blood pressure or blood cholesterol level) while the y-axis measures the chance that a patient will develop cardiovascular disease (CVD). It is well known that high blood pressure or high cholesterol levels increase a patient's risk. What is less well known is that plots of large populations against CVD mortality often takes the shape of a J curve which indicates that patients with very low blood pressure and/or low cholesterol levels are also at increased risk.^[7]

Political science (Model of revolutions)

In political science, the 'J-curve' is part of a model developed by James Chowning Davies to explain political revolutions. Davies asserts that revolutions are a subjective response to a sudden reversal in fortunes after a long period of economic growth, which is known as relative deprivation. Relative deprivation theory claims that frustrated expectations help overcome the collective action problem, which in this case may breed revolt. Frustrated expectations could result from several factors, including growing levels of inequality within a country, which may mean those who are increasingly poor relative to the rich are getting less than they expected, or a period of sustained economic development, lifting general expectations, followed by a crisis.

This model is often applied to explain social unrest and efforts by governments to contain this unrest. This is referred to as the Davies' J-Curve, because economic development followed by a depression would be modeled as an upside down and slightly skewed J.

References

1. Feenstra and Taylor, Robert and Alan (2014). International Macroeconomics. New York,NY 10010: Worth Publishers. pp. 261–264. ISBN 978-1-4292-7843-0.
2. Hacker, RS and Hatemi-J, A. (2004) [url=https://ideas.repec.org/a/bla/etrans/v12y2004i4p777-799.html The effect of exchange rate changes on trade balances in the short and long run: Evidence from German trade with transitional Central European Economies. Economics of Transition. 12(4) 777-799.]
3. Grabenwarter, Ulrich. Exposed to the J-Curve: Understanding and Managing Private Equity Fund Investments, 2005
4. A discussion on the J-Curve in private equity. AltAssets, 2006
5. Understanding Private Equity Performance: The J-CURVE Effect: Earning Acceptable Returns Takes Time. California Public Employees' Retirement System
6. J-Curve Effect
7. J-Curve Phenomenon