NEW YORK (Reuters) -Monthly U.S. inflation data is under increased scrutiny after President Donald Trump removed the head of the U.S. Bureau of Labor Statistics, a move that could undermine confidence in the $2.1-trillion market for Treasury debt designed to protect against inflation. 

The Consumer Price Index, which will be released on Tuesday, will test investors' trust in the integrity of U.S. economic data after Trump fired the BLS head this month, accusing her of manipulating jobs numbers. 

It is unclear who will replace former BLS Commissioner Erika McEntarfer. Still, any signs that lead investors to suspect data is being politicized could exacerbate concerns about CPI data collection. 

In that case, investors are likely to demand higher compensation to hold TIPS, or Treasury Inflation-Protected Securities, whose value is linked to the CPI, and raise the federal government's cost of funding itself, analysts said. Rises in TIPS yields could be exacerbated by poorer liquidity compared to the much larger market for nominal Treasuries.

"This isn't just an academic discussion about getting the right numbers - these numbers matter for TIPS," said Michael Feroli, chief U.S. economist at JPMorgan Chase. "There's real money on the line here."

A White House official told Reuters, "historically abnormal revisions in BLS data over the past few years since COVID have called into question the BLS's accuracy, reliability, and confidence," and that Trump plans to restore trust in the BLS. The bureau did not immediately respond to a request for comment.

Trump ordered McEntarfer's removal on August 1 after data showed a surprise weakening in the U.S. labor market last month. The BLS employment report revealed meaningful revisions to job figures for the prior two months that raised investor worries that the Federal Reserve may need to play catch-up with interest rate cuts.

The BLS is also responsible for the CPI report - a key data point for the Fed and investors to assess inflation dynamics that influence monetary policy decisions.

"That's a problem if you're a policymaker, (and) if you're an investor - TIPS are indexed to changes in the CPI. The Fed needs to know what inflation is," said Michael Gapen, chief U.S. economist at Morgan Stanley.

"It could be a situation where the signal is less credible, which could affect term premiums in the markets, but it may also worsen your ability to conduct not only good policy, but good policy in a timely fashion," he said.

The BLS compiles the CPI by tracking monthly price changes in a basket of goods and services, drawing thousands of quotes nationwide from stores, service providers, rental units, and online sellers.

HIGHER MARGIN OF ERROR

With trust in U.S. data on the line, investors will likely increasingly look for alternative ways to form a picture of the U.S. economy, for instance, by relying more on private sector data providers, such as research from banks.

They may also reduce their reaction to single-data releases and wait for longer time periods to draw conclusions. 

"Maybe the margin of error around some of these estimates, both for inflation as well as labor markets, is a little bit wider, and that's why you need to take a step back from just the month-to-month prints," said Garrett Melson, portfolio strategist at Natixis Investment Managers Solutions.

When it comes to TIPS, however, investors will still have to rely on CPI, as the bonds are linked to that index.

So far, TIPS have not moved meaningfully since McEntarfer's firing. Yields on 10-year TIPS were last at 1.864%, slightly higher than on August 1. 

But the TIPS market would get "nervous" if the next BLS head is perceived as biased, TD Securities said in a note. The White House did not comment on potential moves in TIPS yields.

"In a scenario where TIPS are unable to provide a hedge against inflation because of the uncertainty around the CPI index published by BLS, its overall demand might start decreasing," Morgan Stanley analysts said in an August 6 note.

Lower demand would push TIPS prices lower, reducing the difference between nominal Treasury yields and TIPS yields - a measure used by policymakers and investors to gauge the path of inflation. Yields move inversely to prices.

The byproduct of that scenario would be data indicating lower inflation expectations, supporting rate cuts, Melson at Natixis said. 

"That could actually have some feedback into policy decision-making by the Federal Reserve," he added.