Dame Susan Rice, chairwoman of the Scottish Fiscal Commission, said there had been an unexpectedly large number of claims for the Pregnancy and Baby Payment after it was opened for applications in December last year.
The payment replaces the UK Government's Sure Start Maternity Grant, with eligible families provided with £600 on the birth of their first child and £300 on the birth of any subsequent children.
It is one of a number of new benefits being rolled out as part of a new Scottish social security system following the devolution of powers in 2016.
Speaking at Holyrood's Finance Committee on Wednesday, Dame Susan said: "We underestimated spending on the new pregnancy and baby grant by £2.5 million, or 59%, because of an unexpectedly large number of claims in the first few days after launch.
"While forecasting new and reformed benefits will always be difficult, as the benefits become established and we have new data sources we'd expect our forecast errors to reduce over time.
"But during the next few years, we should expect some volatility in fairly large forecast errors for social security as more benefits are devolved and the Scottish Government introduces reforms to them."
Dame Susan also referred to the "significant error" made in the Scottish Government's income tax forecasts for 2017-2018, in which revenues were overestimated by £941 million.
She said the errors in forecasts made in February 2017 could be attributed to the use of imperfect survey data.
Dame Susan said the forecast had been deemed as "reasonable" by the commission and was signed off at the time.
"We did that for this forecast and we judged it reasonable at the time. We now know that this forecast overestimated revenue by £941 million, or 8.6%.
"That's a significant error and 2.8 percentage points higher than the OBR's average two-year-ahead forecast error which is the benchmark we use."
She added: "We estimate that £820 million of that total £941 million - so £820 million of that error - was due to what we've labelled the '2016-17 baseline error', which was the result of having to use an imperfect survey data source that was three years old to estimate 2016-17 income tax revenues as the starting point of the 2017-18 forecasts, so that was our baseline.
"Taking that amount away, it leaves £121 million of the £941 million to be explained.
"Our report shows that, roughly, £90 million of this error was because of the Government's economic forecasts - total earnings growth was overestimated by 0.2 percentage points. We describe this as quite a small forecast error.
"The remaining £30 million is explained by a combination of modelling issues, HMRC incorporation estimates and changes in the cost of UK policies."