What color is the rainbow? On average, white. What is the current level of inflation in the UK? The average was 5.4%. Both answers are correct. Both are missing something important.

The Consumer Price Index or CPI aims to measure the average price paid by UK consumers.But when the latest CPI figures came out, the food writer and poverty activist Jack Monroe Tweeting some examples from her local supermarket: 500g of cheap pasta went from 29p to 70p; 1kg of rice went from 45p to £2; baked beans went from 22p to 32p. As the examples piled up, Monroe concluded that poor households faced inflation well above the 5.4% CPI.

“The system we use to measure the impact of inflation is fundamentally flawed,” she added – a post that has been read by millions. I agree, for different reasons. Monroe worries about soaring prices for the poorest households. I worry that our current inflation measurement process simply cannot tell us whether she is right or wrong.

Instead, we must rely on clues. One clue comes from the reweighted CPI. Chris Giles of the Financial Times did just that. He noted that while energy prices are rising rapidly, so are the prices of snacks such as restaurant meals.Reweighted CPI to reflect spending by poorer households (more food and heating) or wealthier households (more dining out and flying), inflation rate everyone is the same.

Another clue comes from industry watchers. Retail analyst Steve Dresser noted that Jack Monroe’s data came from Asda, but “Asda has been cutting value tier products . . . that’s not representative of the broader market.”

A third clue comes from a recent large survey of consumer spending by academic economists in the United States. They concluded that “low income, low education and black households” had higher inflation in late 2020. However, the difference is only half a percentage point or less.

But we shouldn’t rely on clues. Reweighting the CPI doesn’t tell us what’s going on with the ultra-cheap food that’s so important to people on a tight budget. In fact, NBS inflation director Mike Hardy told me that NBS data collectors target the most popular products based on shelf space. Are these products the cheapest staples? “We haven’t done the analysis to know,” Hardy admitted.

I have some sympathy. It makes sense to calculate inflation by looking at the same items month by month. But savvy budget shoppers may head to the “reduce to clear” section first. Then they might buy some cheap carbs. Rice one week and pasta the next – whatever the special deal. What is the inflation rate for such a shopper? Even in theory, the answer is elusive.

However, the answer is important. It may not matter to the Bank of England, as it tries to ensure price stability across the economy, but it should matter to the government, which sets benefit levels and state pensions. It’s certainly important for desperate parents at the checkout trying to figure out if they can afford a jar of peanut butter or if the toast is going to dry out this week.

Jack Monroe told me her “primary interests are math and cheap pasta” — she’s now volunteering to work together to compile a price index of cheap staples and other basics like menstrual supplies, toothpaste and shampoo.

But this is not comparable to the resource that the National Bureau of Statistics uses to compile the CPI, which collects 6,000 quotes every day across the country. ONS has just announced plans to augment this work with scanner data from supermarkets.

Is this statistical fire target correct? Yes, if the goal is to measure inflation across the economy. No, if we want to know what happens to the poorest households.

Collecting really good data is expensive and priceless. But often shockingly, some issues have slipped through the cracks. In 2007, we were shocked to realize how little we knew about risk in banking. In 2019, Caroline Criado Perez’s invisible woman A compelling case is made that data related to women is often overlooked. In 2020, the Office for National Statistics quickly established infection surveys to represent the population, but such surveys may have been established a few years earlier. Now Jack Monroe points to another gap.

There are nerds and bean counters all over the place – people like me – who need to work hard to fill these gaps in our knowledge rather than stumble across them. There are white rainbows everywhere, and it’s not always easy to tell the colors apart. But we have to try.

Tim Harford’s new book is “How to make the world add up“

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