A new approach to the relative convergence test

ABSTRACT

This article proposes a new approach to the relative convergence test. The original relative convergence test proposed by Phillips and Sul (2007) recommends discarding the first 1/3 of the time-series data to achieve the best performance in terms of the size and power of the test. My new approach to the relative convergence test does not require discarding any time-series data by assuming the unobservable data are already discarded. In this article, I compare the new approach to the Phillips and Sul (2007)’s test and determine, through a Monte-Carlo simulation, at what fraction the new approach achieves the best performance in terms of size and power of the test. I confirm that the new approach performs better than the original approach when the fraction is set 1/10 of a penalty function. To compare my new method to the Phillips and Sul (2007) method, I provide an empirical example using the U.S. Per Capita Personal Income data and how the new approach affects the convergence club classification.

KEYWORDS:

• Relative convergence
• convergence
• common factor
• log t regression
• panel data

JEL CLASSIFICATION:

• Number: C33 2

Disclosure statement

No potential conflict of interest was reported by the author.

Notes

¹ There exists three different types of the convergence: $\beta -$convergence, $\sigma -$convergence, and relative convergence. See Sul (2019) for more detailed discussion.

² The data is collected from Bureau of Economic Analysis (BEA).

³ See PS(2007) for the detailed clustering algorithm. In step 3 of the clustering algorithm, they recommend setting $c=0$ but I set $c=1$ to increase discriminatory power of $logt$ test.