Theresa May says Brexit means difficult times ahead – these are the economic signs that will prove if she's right

There may be difficult times ahead, warns the Prime Minister, speaking from the G20 summit meeting in Hangzhou. Indeed, and not just for us. But how are we to gauge how serious these might be? What should we look for to help us guess (it can be little more) whether the world is heading for a serious downturn, or whether things will be business as usual? Start with the UK.

The immediate question is whether the economy has taken a serious hit from the Brexit vote. In the early days after, it seemed it would. Markets reacted badly, especially the foreign exchanges, and the forward-looking indicators suggested there might well be a recession next year. But now that looks too pessimistic. Share markets have recovered and moved ahead, the pound has recovered a bit, and the purchasing manager indices (the PMIs), which measure the mood of the business community, seem to be recovering too.

This week the key thing to look for will be the PMI for services, which comes out on Monday. We have had those for manufacturing, which were strongly up, and for construction, which were much better than before but still showing a slight contraction. But the biggest part of the economy by far is services. If the services industry expects decent growth, then the economy is likely to grow decently, at least until the end of this year. The PMIs don’t tell us much about the outlook beyond 2016, but growth through the next few months will provide a better backdrop to the next big fiscal event, the Autumn Statement, in late November or early December. We have been promised there will be a “reset” of policy, but the better the performance of the economy, the less of a reset there will need to be.

Second among the other UK data expected this week is the August house prices from the Halifax. House prices are a lagging indicator, in that they reflect decisions made a couple of months earlier, but a massively important one. If they start to fall month on month that will bring heart to home buyers but also cut consumer confidence. They were flat in July, suggesting concern over Brexit, but since then there has been a cut in interest rates. Don’t set too much store by one month, and August is an atypical month for home sales anyway, but any commentary associated with the numbers will be interesting.

There will be other UK data coming this week, such as trade figures, but this will be backward-looking, so the third thing I will want to see concerns Europe. One of the reasons why European leaders are upset with Britain is that Brexit may be damaging their economies more than ours, partly because of the hit to European exports as a result of the fall in the pound against the euro. On Thursday the European Central Bank has its policy meeting and press conference. The issue will be whether it is sufficiently concerned about the flagging eurozone economy that it will try yet more measures to boost growth and inflation. Expect something, but perhaps more important is what Mario Draghi, its president, will say about the European economy.

Fourth, look at the US. This is a short working week for Americans, for Labor Day on Monday is the public holiday that informally marks the end of the holiday season. The immediate issue facing the US is how quickly to press on with interest rate increases, and on Wednesday the Federal Reserve publishes the so-called Beige Book, which outlines the Fed’s view of what is happening to the US economy. It won’t tell us what the Fed governors will do at their next meeting, on 20 and 21 September, but it will give the background to their discussions.

Finally, the world – for that G20 meeting should remind us there is a world economy beyond the UK and Europe, and beyond the US. About half the additional demand in the world economy next year will come from the emerging nations, not the developed ones. Most emerging economies have benefited greatly from cheaper energy, and this year one measure of that will be whether India has moved from balance of payments current account deficit to a surplus. The Japanese securities group Nomura thinks this may have happened in the second quarter, and if this is right it will be the first such surplus for nine years. If you are Russia, cheap oil is a disaster, but for China and India (and many other emerging countries) it has been a key driver of higher living standards. For all our quite reasonable concerns about our own living standards, which at best are rising only slowly, in human terms what surely matters more is what has been the success story in the emerging world.