* Output gap data puzzles policymakers, investors
* Central bank uses gap as key tool to decide on rates
* Problems measuring gap could trigger policy mishaps
By Ana Nicolaci da Costa and Guillermo Parra-Bernal
BRASILIA, Dec 11 (Reuters) - Brazilian factories are ramping up output and shoppers are back at stores, but disappointing third-quarter economic growth data suggests that a recovery still remains frail enough for policymakers to keep borrowing costs on hold for awhile yet.
Growth last quarter surprised economists on the downside, with many concerned that their tools to measure the slack present in the economy, known as the output gap, are outdated or, even worse, can lead to false assumptions.
While evidence that consumer prices are broadly contained holds up, questions remain over whether the output gap is shrinking slowly enough to keep inflation at bay and avert a cycle of interest-rate increases early in 2010.
"Do the math, run a model and you will see how hard it is for us to measure it," said Luciano Rostagno, an economist with CM Capital Markets. "Data has changed a lot since the crisis, making the central bank extra cautious in its decisions."
The bank raises interest rates if the output gap closes too fast during economic expansions. Policymakers, led by bank chief Henrique Meirelles, have recently voiced worries that a quick reduction in the gap could stoke future inflation.
But some economists doubt that the central bank's own output gap estimates reflect reality after violent swings in data series from car sales to factory usage in the past year.
Policymakers on Dec. 9 kept the benchmark Selic lending rate at a record-low 8.75 percent but again highlighted in an accompanying statement the importance of monitoring actual and potential growth when deciding rates. Similar references were made in its September and October statements.
A slight change in the bank's policy statement gave what some economists saw as the first signal authorities were laying the groundwork for an eventual tightening of monetary policy.
The bank's monetary policy committee, called the Copom, said that "at this moment" rates are consistent with a benign price scenario given the "remaining gap in factory capacity."
This change "probably led market players to believe that the statement is suggesting the Copom might increase the Selic rate at upcoming meetings," Nilson Teixeira, chief Brazil economist at Credit Suisse, said in a note.
Yet, the unfavorable growth data may force the bank to stand pat on rates through the second quarter, he noted.
MIND THE GAP
Ilan Goldfajn, a former central banker who is now chief economist for Itau Unibanco, warns that growth has come in quite brisk since the economy emerged from recession in June.
Some data supports his view. Even as the inflation rate still remains below the bank's 4.5 percent target for 2009, buoyant consumer demand is fanning price pressures.
Industry, which suffered most after the collapse of global credit markets, expanded for a tenth month straight in October. Unemployment fell to its lowest this year and wages have significantly won purchasing power.
Economists use complex econometric models, such as the Hodrick-Prescott filter -- one of its creators, Edward C. Prescott, was a Nobel Prize-winning economist -- to measure the gap.
CM's Rostagno said that such a filter suggests the central bank is faced with another challenge: while industry is quickly recovering, it is still operating below potential. Yet services, the largest component of Brazil's economy, are expanding above trend.
"It's an uneven process of growth, which makes policy decisions tougher," he added.
Investment jumped in the third quarter, but its level is about 13 percent below last year's. Sluggish investment was seen for years as the culprit behind Brazil's frequent boom-and-bust cycles and inflationary woes.
Officials have urged a fast resumption of investment, which is key to avert a quick narrowing of the output gap.
Services sector data are the main figures to watch for insight on how fast the economy is growing free of inflationary pressures. The sector, for which there is no known measure of utilization capacity, has not only braved the crisis but is roaring on.
"If we had a measure of capacity utilization in services... it probably would be much tighter than you'd think," said Marcelo Carvalho, chief Brazil economist at Morgan Stanley.
"My warning would be that if you just look at industry you may be underestimating how fast the output gap is shrinking." (Editing by Theodore d'Afflisio)