In general, looting and a general breakdown of order was a lot less common during World War II than many military planners had originally expected, particularly by military planners in the decades prior to World War II.

The three main fears of the civilian population that had to endure extensive and prolonged air campaigns were mental breakdown, panic movement, and mass demoralization.

These three threats or potential problems formed much of the various countries' domestic strategies on how to deal with air raids.

For example, in the UK, military planners were afraid that if they opened deep air raid shelters to the public, it would produce a 'shelter mentality' that would be detrimental to overall morale as well as hinder war time productivity.

They feared that the lack of equal and egalitarian access for all to deep shelters, which were the only assured safe place from bombs, would engender a negative attitude that risk was not equally shared by all, leading to a decrease in overall morale and resentment toward leadership.

The other fear was that as extensive air campaigns went on longer and longer, workers would be unwilling to emerge from the safety of shelters, greatly affecting the productivity of essential war time industries.

But in general, various postwar research showed that most civilian populations were much more resilient to air campaigns than previously thought. The average civilian's threshold for destruction of urban areas and casualties was much higher than prewar estimates.

For example, in I.L. Janis' psychological research Air war and Emotional Stress: Psychological studies of bombing and civilian defense, even after the Japanese populations of Hiroshima and Nagasaki endured the atomic bombings, there were no appreciably higher rates of chronic psychological disorders, nor was there a mass breakdown of order or a panicked rush of civilians.

Similarly, in the research of Edgar Jones, R. Woolven, B. Durodie, et al in Civilian Morale During the Second World War: Response to air raids re-examined, even after extensive bombings in China, Chinese civilian populations, such as in Nanking, showered 'good discipline and control' and were described by British military observers as 'apathetic' despite the extensive and indiscriminate nature of the bombings.

Reading the various wartime diaries of Japanese people show a distinct lack of crime or disorder following bombings, which would probably feature a great deal considering how much the diaries go into the aftermaths of the bombings of cities. What does feature prominently in the diaries, as time goes on, is the growing war weariness as well as feelings of futility and helplessness as the air campaigns grew in intensity. The growing

Throughout the years of various natural disasters as well as wartime disasters, the Japanese population's reaction usually has extremely low rates of looting or disorder.

During World War 2 specifically though, it's a bit difficult to compare rates of looting but in general as I have not seen hard numbers extensively researched in any comparative sense.

War time Japan specifically did not have to deal with looting or any rise in crime following most air raids as far as I have seen in research and study. If there are any other experts who can chime in it would be helpful!