The finding that Japanese foreign exchange intervention has affected the yen/dollar exchange rate so clearly after 1999 is very robust and begs the question as to possible explanations.
After 1999 we couldn’t observe any fundamental change in the strategy of Japanese foreign exchange intervention with respect to intervention volume, number of events or volume per event (Figure 1 and Table 2).

Given the high degree of capital mobility between Japan and the US, the probability for a portfolio balance effect is low.
Further, as interest rates declined to zero in early 1999, there is little evidence that foreign exchange intervention announced a fundamental change in interest rate policy.
Further, as Japanese foreign exchange intervention after 1999 was purely unilateral, the argument for enhanced effectiveness of co-ordinated intervention does not hold.

Given the caveat that the period since 1999 is too short to conclude that Japan’s foreign exchange intervention will be also effective in the future, the following explanations for effective Japanese foreign exchange intervention (after 1999) might apply.

First, there is the portfolio equilibration function of Japanese foreign exchange intervention as outlined by Goyal and McKinnon (2003).
Based on a sustained saving surplus, Japan has generated high current account surpluses for more than two decades.

The respective net capital exports have produced a huge stock of Japanese net international foreign assets, which constitute an inherent and sustained appreciation pressure on the Japanese currency.

Given Japan’s net external foreign asset position, successful foreign exchange intervention can be explained with a simple market clearing condition, assuming that current account (CA), net capital flows (KA) and changes in official foreign reserves (∆RES) add up to zero:

Capital flows are assumed exogenous.
If Japanese private investors decide to repatriate parts of their foreign assets, they sell US dollar treasuries and convert the earnings into yen (buying yen). The yen comes under appreciation pressure.

Two possible adjustment channels then apply.
If the government decides to tolerate the appreciation (∆RESt = 0), the decline in the net capital exports will be matched by an equal decline in the current account surplus, which is achieved via appreciation.

If the government wants to sustain the current account at the present level (CAt = const.), the changes in net capital inflows have to be matched by a respective change of foreign reserves, which corresponds to foreign exchange intervention.

If all additional net capital inflows are absorbed by official currency purchases, the exchange rate and the current account remain constant.

The original foreign investment position is restored.
Only the structure of Japanese foreign assets has changed. Public foreign assets are substituted by private foreign assets. Foreign exchange intervention is successful.

While the portfolio equilibration approach provides a possible rationale for successful Japanese foreign exchange intervention, it does not explain why the success started in 1999.
To this end De Grauwe and Grimaldi (2003) provide an alternative explanation approach.

Based on a framework where chartists and fundamentalists interact they argue that sterilized foreign exchange intervention can affect the exchange rate by reducing speculative noise.

As exchange rates tend to take systematic deviations from their fundamentals, intervention could be effective by reducing the share of chartists in the market, thereby re-directing the exchange rate towards fundamentals.

De Grauwe and Grimaldi (2003) admit that occasional intervention is unlikely to be effective, as it has very unpredictable effects on the exchange rate.

Instead they suggest that successful intervention should be systematic following a clear pattern.
Following this line of argument, Japanese foreign exchange intervention could be successful because—as outlined in section 4—Japanese monetary authorities were (are) successful in establishing informal exchange rate targets or target zones which enhance(d) the credibility of intervention.