To describe the events as a currency war may seem logical because another type of "war" between the U.S. and China, namely the trade war, has been on everybody’s mind for the past year and a half. Moreover, the Trump administration itself has continued this game by classifying China as a "manipulator" of its currency immediately after this latest devaluation.
In the same way as the U.S. Treasury is not following its own script when classifying China as a currency manipulator, neither should we think of the yuan mini-devaluation as China initiating a currency war with the U.S. The reason is simple: the yuan–which is not convertible–cannot afford a war with the dollar, nor can the U.S. Federal Reserve control its currency so as to use it as a weapon against China. In other words, neither of the two rivals have the instruments to successfully engage in a currency war against each other.
Starting with the dollar, there is no doubt that its value is determined by the market, as it could not be otherwise being the reserve currency of a world still governed by flexible exchange regimes for major currencies. The Fed can influence the dollar with expansive or restrictive monetary policies, but there are many other factors that it and the Treasury simply cannot control. One important factor is risk aversion: the more the Trump administration tightens the screws on China and, thereby increases the risk of recession globally, the more the dollar appreciates, contrary to what Trump wants.
Moving to the yuan, the PBOC is much closer to determining its value than the Fed can for the dollar, as it retains control on capital flows and does not need to intervene in a highly liquid forex market like that of the dollar. Nevertheless, the reality is that capital is ubiquitous, so capital controls will never be completely effective. In other words, the value of the yuan is not exempt from the forces of demand and supply, nor is its value in the medium term, no matter what the PBOC may opt to do on a specific date or period.
Considering the yuan's mini-devaluation, the beginning of a currency war is a mistake for one more very important reason. The PBOC has accommodated market pressure by devaluing while central banks tend to move against the market during currency wars. It's true, though, that the timing of the devaluation could mislead us towards the idea of a China-initiated currency war because it happened right after the U.S. announcement of additional import tariffs on Chinese products. More than a war, we should see this reaction as a tantrum of Chinese policy makers facing additional pressure from the U.S. Besides, as happens for every tantrum, its consequences may not be the desired ones as such mini-devaluation will only prompt more capital outflows from China, undoing part of the monetary stimulus that the Chinese central bank has been carrying out for more than a year to sustain economic growth. In other words, it will not help China to grow, but rather the opposite.
Thus, it is important to distinguish between a war and a tantrum. In the former you control your weapons, in the latter you do not.