Testing for Structural Breaks in Small Samples

Abstract

This Working Paper should not be reported as representing the views of the IMF.The views expressed in this Working Paper are those of the author(s) and do not necessarily represent those of the IMF or IMF policy. Working Papers describe research in progress by the author(s) and are published to elicit comments and to further debate.In a recent paper, Bai and Perron (2006) demonstrate that their approach for testing for multiple structural breaks in time series works well in large samples, but they found substantial deviations in both the size and power of their tests in smaller samples. We propose modifying their methodology to deal with small samples by using Monte Carlo simulations to determine sample-specific critical values under the null each time the test is run. We draw on the results of our simulations to offer practical suggestions on handling serial correlation, model misspecification, and the use of alternative test statistics for sequential testing. We show that, for most types of data generating processes in samples with as low as 50 observations, our proposed modifications perform substantially better.

What Makes Growth Sustained?

“…At the ten percent significance level and h = 5, our algorithm identifies a total of 290 breaks-139 "upbreaks" and 151 "downbreaks", that is, a little more than one upbreak and one downbreak per country on average. This is dramatically higher than the total number of breaks (74) that the standard Bai-Perron algorithm identifies using the same data, p-value and interstitiary period, and is consistent with the findings reported in Antoshin, Berg, and Souto (2008). Upbreaks tend to be most common in the 1950s and 60s, driven by Europe and Latin America, and in the 1990s, driven by Africa (see figure and Table 1).…”

“…Our approach differs from the Bai-Perron approach in that it uses sample-specific critical values that take into account heteroskedasticity and small sample size as opposed to asymptotic critical values; and in that it extends Bai-Perron's algorithm for sequential testing of structural breaks, as described below. Antoshin, Berg, and Souto (2008) describes these extensions in more detail and shows that they improve both the power and size properties of the test in applications such as ours.…”

Growth Breaks and Growth Spells in Sub-Saharan Africa

“…We begin by identifying structural breaks in the growth of per capita GDP (growth turning points). 1 We follow Antoshin, Berg, and Souto (2008), who develop a variant of the Bai and Perron (1998) procedure to test for multiple structural breaks in time series when both the total number and the location of breaks are unknown. 2 The procedure requires setting in advance two parameters for the determination of structural breaks: the minimum possible number of years between potential breaks (h) and the statistical significance to test for the existence of structural breaks (p).…”

Which Reforms Work and Under What Institutional Environment: Evidence from a New Dataset on Structural Reforms

“…Figures 4 and 5 plot the average level of the residuals, obtained through a panel regression of each index on country and year fixed effects, for a period starting five years before 12 Antoshin, Berg, and Souto (2008) provide a detailed description of these extensions and document how they improve both the power and the size properties of the test in applications with a small number of observations. a structural break in growth (denoted as 0 on the horizontal axis) and ending five years after it.…”