By Franklin D. Berger
Federal Reserve Bank of Dallas

Two years ago, we reported on these pages about difficulty in correctly interpreting Mexico's GDP reports.1 The complication involves Easter's habit of moving around in the Gregorian calendar. Sometimes this religious holiday occurs in the first quarter and sometimes in the second. Because economic activity is reduced in the quarter in which Easter falls, when Easter switches quarters from one year to the next, the situation is ripe for the confusion we pointed out earlier.

Easter fell in the second quarter in both 2003 and 2004, so last year the issue was moot. This year, Easter fell in the first quarter, leading to possible confusion.

In the opening sentence of its statistical release on Mexico's second quarter 2005 gross domestic product, the Instituto Nacional de Estadística, Geografía e Informática (INEGI, Mexico's census bureau) reports that GDP was 3.1 percent greater than in the second quarter of 2004. This statistic is calculated from data that have not been seasonally adjusted and, in particular, have not been adjusted for Easter's wayward effects. The report further notes that GDP declined 0.42 percent in second quarter 2005 relative to first quarter 2005.

The year-over-year statistic is what the Mexican report has historically headlined-and with good reason. Until fairly recently, INEGI did not calculate, or at least did not report, seasonally adjusted statistics. When analyzing data that are not seasonally adjusted but are subject to seasonality, it is standard operating procedure to look at year-over-year changes. When seasonal effects are irregular with respect to the calendar, such as Easter's, the year-over-year calculation is not valid when Easter falls in different quarters in successive years. In other words, INEGI's lead statistic sometimes suffers from statistical bias.

INEGI's seasonal adjustment procedure is sophisticated, taking full account of the Easter effect. The seasonally adjusted data have been purged of the potentially distorting effect of Easter moving around in the calendar. This makes it possible to report meaningful quarter-over-quarter statistics, which INEGI does-but does not emphasize. Although the main reason for emphasizing year-over-year changes has been eliminated with INEGI's now more sophisticated approach to seasonal adjustment, it may still be useful to calculate such changes. But to be meaningful, these changes must be calculated from the seasonally adjusted data. According to INEGI's own seasonally adjusted data, Mexico's GDP grew 1.9 percent from second quarter 2004 to second quarter 2005. INEGI's reported figure of 3.1 percent is biased upward because Easter's occurrence in second quarter 2004 depressed that period's output.

In spite of the stumbling block placed before them, analysts are often able to make sense of the situation. However, their reportage is often awkward and confusing. In one example of many, DismalScientist reports, "The Mexican economy showed a rebound in the second quarter, positively influenced by the Easter holiday."2 Note that the terminology "in the second quarter" is confusing. One might think DismalScientist is referring to growth between the first and second quarters, but that is not the case. It is referring to INEGI's reported growth of 2.4 percent from first quarter 2004 to first quarter 2005, compared with 3.1 percent from second quarter 2004 to second quarter 2005. Such reportage is typical of articles about Mexican GDP. In other contexts, reporters often use the expression "in the quarter" to mean "during the quarter," a more appropriate usage.

According to INEGI's seasonally adjusted (and Easter-corrected) data, GDP declined by 0.42 percent from first to second quarter 2005. What sort of "rebound" is this? Even the year-overyear data show no rebound when corrected for Easter. The year-over-year figures above for first- and second-quarter growth (2.4 and 3.1 percent, respectively)become 3.7 and 1.9 percent, respectively. In other words, year-overyear growth declined, primarily due to severe slowing in the first quarter (0.18 percent) and an actual decline of 0.42 percent in the second quarter.

How much clearer to report, simply, "After averaging growth of about 1 percent per quarter in 2004, GDP growth fell to 0.18 percent in the first quarter of 2005 and GDP declined 0.42 percent in the second quarter. There is no need to mention Easter at all.

-Franklin D. Berger
Berger is director of technical support and data analysis in the Research Department of the Federal Reserve Bank of Dallas.

Notes:
1. "(Mis)reporting Mexico's Gross Domestic Product,' by Franklin D. Berger, Federal Reserve Bank of Dallas Southwest Economy, Issue 5, September/October 2003.

2. "Mexico: GDP," by Alfred Coutino, in DismalScientist, August 16, 2005,
www.economy.com/dismal/pro/blog.asp?cid=16827.