A recent NHK World report indicates that Japan's Ministry of Defense is considering shooting down unmanned aerial vehicles (UAVs) that invade its airspace. Considering the recent test flight of China's UAV above the Diaoyu Islands, such a report advocates confrontation and reminds international audiences about the lasting tension between the two countries.

In the debate about the causes of worsening Sino-Japanese relations, in-depth studies on the comparison of bilateral strength are needed.

Taking a look at the speed curve of China narrowing GDP gap against Japan and the curve of bilateral relations based on quantitative measurement, one can find that structural imbalance between the two countries plays a vital role.

A basic pattern of bilateral relation trend is that the faster China narrows its GDP gap against Japan, the more aggressive Japan's China policy becomes, and hence the worse bilateral relations we have.

Such aggression can be explained by the frustration Japan receives from the comparison of bilateral strength.

From 2001 to now, China's GDP rose from a quarter of that of Japan to being equal, then higher. During the process, the accumulation of such frustration generates aggressive reaction from the Japanese government, and therefore more and worse clashes occur in bilateral relations.

During the 1970s and 1980s, China was a big power only in terms of population and political influence, the latter of which was barely supported by its veto power in the UN Security Council.

In economic terms, China's GDP was just a tenth of Japan, and GDP per capital even as low as an eightieth. When China renounced its demand for war reparation from Japan and Japan kept expanding its Official Development Assistance to support China's economic and social development, a better foundation of improving relations was secured.

However, there are two pivotal points in the curve that caused turbulence in bilateral relations.

The first was in 2001, when China's GDP at purchasing power parity surpassed Japan. China's nominal GDP exceeded a third of Japan's in the following year and was rapidly catching up with Japan, marking a significant change in bilateral strength.

Then Japanese prime minister Junichiro Koizumi adopted revisionist policies on Japanese history textbooks on WWII and supported official visits to the controversial Yasukuni Shrine, generating a huge wave of protests among Asian victims of Japanese invasion and pressing Sino-Japanese relations to record lows.

The second point was in 2010, when China's nominal GDP surpassed Japan's. Compared to China's increasing political influence and international image as driving engine of world economy, Japan was suffering from setbacks on issues including its pursuit of "normal country status" and a seat as permanent member of the UN Security Council, plus decades of stagnating economic growth.

These help the rise of the right-wing in Japan. Outstanding disputes on historical cognition and territorial possessions as well as the alleged security threats further drove mutual misconceptions to historic highs.

Bilateral relations became even worse after 2010, as China's GDP further grew. In the fall of 2012, the Japanese government agreed to purchase Diaoyu Islands, an aggressive move making China's status quo policy of shelving disputes lose its efficacy. The bilateral curve shows worse bilateral relations than Koizumi's time and a historical low since 1972.

If the frustration-aggression scenario is valid, that Japanese aggression may hit an inverted U shape. That is to say, when China's countermeasures reach a certain intensity, Japanese projection about the risk will be transformed, and when it realizes that aggression will do more harm than good and such harm is unaffordable, it will tune down its assertive stance.

If this logic applies, the turning point will come when China's GDP is triple that of Japan. If we set China's annual GDP growth at 7.5 percent and Japan 2 percent, and start the calculation from 2011, the first year after China's GDP surpasses Japan, this point can come in 15 years. Depending on the way we make the calculations, this could be even sooner. But by 2025, relations are likely to be very different.

The author is a PhD candidate at the Institute of Modern International Relations, Tsinghua University. opinion@globaltimes.com.cn