If you wanted to be optimistic about UK inflation and interest rates, then at first sight looking at the US might help. Here is inflation in both countries since the start of 2022.US inflation peaked in June last year at 9.1%, and at first its fall from this peak was slow. By February 2023, eight months after the peak, it had fallen by only just over 3% to 6.0%. In the UK inflation peaked four months later than the US, at 11.1% in October 2022. Eight months later, in June 2023, it had also fallen gradually by around 3% to 7.9%. However in recent months US inflation has been falling quite rapidly, and in June it was only 3%. Might UK inflation also begin to fall rapidly? Are we following the US with a lag of around 4 months?
The way the central bank has behaved in both countries tells a similar story, with the UK lagging behind the US in raising rates.Although inflation was pretty high at the beginning of 2022, central banks had kept interest rates low because they expected the increase in inflation to be temporary and they wanted to protect the recovery from the pandemic. But from mid-2022 the US Fed increased rates faster than the Bank of England, and that has helped ensure US inflation is now falling rapidly. (Quite how much it has helped is another question.)
UK inflation is indeed expected to fall quite quickly in the UK in the next few months. The Bank of England’s latest forecast is for inflation to be below 5% by the last quarter of this year. However if that suggests to you that interest rates will soon start to come down, you will be disappointed. Once again a look at the US is instructive. Despite inflation falling to 3%, the Fed raised interest rates at their last meeting. The Bank too has said that rates will stay high for some time. If the inflation outlook is improving, why are rates staying high?
The answer lies in the labour market, which in both countries still looks tight. In both countries wage inflation is still well above what would normally be regarded as consistent with a 2% inflation target. Here is a comparison of wage inflation in the UK and US. (For the UK I have shown a three month rate rather than the usual year on year rate to better pick up possible turning points, and I have used the Atlanta Fed Wage Growth tracker for the US. Official US data on wages shows a similar picture.)In the US wage inflation reached a peak in the middle of last year, but falls since then have been modest. In the UK we cannot be sure that wage inflation has peaked. In both cases, but particularly in the UK, this rate of growth in earnings is well above what would be consistent with 2% inflation. (Something between 3% and 4% would be consistent with 2% inflation over time.)
As I noted in a recent post, you can tell two very different stories about what is currently happening. In the first story, wage inflation is high because price inflation has been high, and so once price inflation starts falling so will wage inflation. In this story, the inflation problem will be largely self-correcting, and what we are seeing now is the ‘second round’ effects of a very large but temporary inflation hike.  The second story acknowledges the temporary inflation hike, but says there is a second problem arising from the pandemic recovery that requires a policy reaction. This second problem is a tight labour market.
Until the beginning of last year, central banks believed in the first story. But since then in both countries the data has suggested a persistently tight labour market, and it is this that is the main reason why interest rates have increased. As ever with macroeconomic data, there is a lot of debate about how reliable any particular labour market indicator might be (see this for the US, for example), but the key question is how tight the market is, rather than is it tight at all.
Where the two countries differ greatly, however, is in the principle reason why the labour market is tight, and therefore why wage inflation is high. In the US it is a story of economic success, with a very strong recovery from the pandemic. (See the final chart in this post.) In part this is because fiscal policy supported the recovery, rather than (in most of Europe) just supporting the economy during the recession. In contrast the UK has had a terrible recovery from the pandemic, with GDP per capita still below pre-pandemic levels. The tight labour market in the UK is the result of a contraction in labour supply rather than an increase in labour demand, where causal factors include health problems createdby NHS underfunding and labour shortages as a result of Brexit in some sectors.
Over the next few months, therefore, interest rate decisions will focus on what is happening to wage inflation much more than what is happening to price inflation. As in the US, in the UK we may find that although price inflation starts coming down quickly, nominal interest rates will not start coming down and may even rise. As I emphasised here, what makes interest setting hard is trying to judge whether you have done enough when there are considerable lags before higher interest rates have their full impact on activity, and therefore the labour market and wage inflation. 
Perhaps the most important factor behind the Bank of England’s decision to raise interest rates last week was this chart, shown at the MPC press conference.
The solid white area represents the output of various models of year on year wage growth, and the white line is the actual data plus the Bank’s forecast for year on year wage inflation. The models (based on inflation expectations and various measures of labour market pressure) are suggesting wage inflation should have started falling this year, but the actual data hasn’t. The Bank’s/MPC’s reaction is to assume that wage inflation will continue to be above the models' predictions, and as a result to tighten policy. 
What is clear is that the UK is entering a new phase of this inflationary period (which the US has been in for several months), where the focus shifts from energy and food prices and large cuts in real incomes to the labour market and positive real wage growth.  In the UK average private sector wage inflation has almost caught up with price inflation. The key issue now becomes whether, as price inflation falls, wage inflation will also do so, allowing interest rates to stop increasing and start falling.
 You could call this a price-wage spiral, but I wouldn’t. ‘Spiral’ is one of those words often used in the 1970s that implies an explosive process, whereas today is a very different world. The idea behind the first story about current inflation is for periods where either price or wage inflation lead the other, but both naturally decrease over time.
 A lot of popular discussion about inflation on the left focuses on profits rather than wages. As I have argued before, there was a case for stronger windfall profits on energy producers, and there remains a very strong case for windfall profits on banks to offset the gains they are making on holding reserves. However, none of this can avoid the fact that wage inflation running at current levels in most of the private sector is inconsistent with achieving the inflation target, which is why interest rates have increased so much over the past year and a half.
 There are a whole host of reasons why wage inflation in the UK might be higher than most models would predict, including data errors or backward rather than forward looking inflation expectations.
 Food inflation is still high however, and this will particularly impact those with lower incomes, some of whom may experience further falls in their real incomes.
 Because US growth is much healthier than in the UK, as well as other reasons, real wages have been rising for a year in the US.