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Breakpoint model application to Turkish population growth

2. Data and Methods
Within our research study, a multivariate regression model of the Turkish POPG rate was applied. Data are provided
consisting of 57 annual observations for the period 1965 – 2021 on the POPG rate, CMR, TFR, and net rate of migration
(NMR) from the Macrotrends database (https:///www.macrotrends.net/countries/topic-overview), (Macrotrends, 2022).
It is worth noting that data sources on key demographic indicators for Türkiye within this Macrotrends web platform are
available from the United Nations – World Population Prospects.
There is increasing attention in statistical and econometric research studies devoted to detecting structural breaks in
long time series datasets and then to specify the effect from major breaks (Zarei, Ariff, Hook, et al., 2015). Structural
changes happen if at least one parameter in the model has changed at some period, that is, date (Czech, 2016). This change
could include a change in mean or a change in other parameters in the procedure that generates the series. By identifying
when the structure of time series changes, the researchers are provided with understanding into the analyzed problem.
Furthermore, to determine when and whether there is a significant change in data, structural break tests can be applied.
The researchers in demography have obviously paid little attention to this aspect, so this research on POPG is based on
this method of identifying and then explaining the periods of the POPG as a result of the impact of the main demographic
events embedded in the dataset used. As shown in this research study, this method uses a rigorous pre-analysis filter
procedure which will be applied to POPG and other demographic time series. Furthermore, testing for structural change
has always been an important matter in econometrics because a multitude of political and economic factors could cause
the relationships among studied variables to change over time (Önel, 2005).
The breakpoints may be known a priori, that is, from theory or to be estimated using different approaches. For instance,
the maximum breaks and maximum levels setting restricts the number of breakpoints permitted through global testing as well
as in sequential or mixed versus l+1 testing and the user-specified method permits to determine break dates by the user (IHS
Global Inc., 2017). Therefore, the breakpoint estimation methods can be in general considered into two categories: Global
maximizers for the breakpoints and sequentially determined breakpoints (IHS Global Inc., 2017). In Bai and Perron from
1998, the global optimization techniques are described in order identifying the multiple breaks and connected coefficients
which minimize the sums-of-squared residuals of the regression model (IHS Global Inc., 2017). If the preferred number of
breakpoints is known, the global break optimizers represent the set of breakpoints and the appropriate coefficient estimates
that minimize the sum-of-squares for that regression model. If the preferred number of breakpoints is not known, there may be
specification of the maximum number of breakpoints and to apply testing to determine the “optimal” number of breakpoints.
A large number of test approaches are available. In Bai from 1997, an intuitional approach for obtaining estimates for more
than 1 break has been described (IHS Global Inc., 2017). The procedure includes sequential application of breakpoint tests.
If the number of breakpoints is pre-determined, then the estimation of the specified number of breakpoints is used simply
with the one-at-a-time method. The sequential evaluation method selects the last significant number of breaks, determined
sequentially. In other words, the procedure is employed sequentially, starting with a single break until the null is not rejected.
The Quandt-Andrews framework, as it was known earlier, was extended later by Bai (1997) and also by Bai and
Perron in 1998, 2003 to obtain multiple unknown breakpoints. The latest tests developed by Bai and Perron in 1998; 2003
comprise an efficient algorithm that is based on dynamic programming method (Zarei, Ariff, Hook, et al., 2015). This
method allows global minimizers of the sum of squared residuals in a simple regression test model in a very common
framework that permits for pure as well as partial structural changes. With this general structure, the tests can control for
different serial correlations, distributions of data, and the errors across divided parts. In 1998, Bai and Perron evaluated
the estimation of multiple structural changes in a linear model estimated by least squares. Thus, they proposed a test for
structural shift in case without trend regressors and a procedure based on a sequence of tests to estimate consistently the
number of break points (Önel, 2005). The adequacy of these methods was assessed through simulation. The size and
power of tests for structural change, the coverage rates of the confidence intervals for the break periods, as well as the
advantages and disadvantages of model selection procedures were studied by Bai and Perron (2003). Hence, Bai and Perron
developed a methodology for finding multiple structural breaks in time series and testing their statistical significance
(Antoshin, Berg, and Souto, 2008). In the opinion of Antoshin, Berg, and Souto (2008), the simulation analysis handled
in Bai and Perron shows that the size and power of their tests may be significantly distorted by several factors, such as
small sample sizes, small break size, breaks clustering and apply of heteroskedasticity, and autocorrelation corrections.
The sequential Bai-Perron test is considered a more advanced and compounded way to detect structural breaks. The worth
of this test could be seen in identifying more than 1 breakpoint. There are some presumptions that should be made before
conducting the sequential Bai-Perron test, like: The maximum number of breaks is 5, trimming percentage to be 15, and
the significance level for sequential testing is 0.05 (Czech, 2016). The Trimming percentage, e = 100(h/T) without reserve

28 International Journal of Population Studies | 2021, Volume 7, Issue 1