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I. INTRODUCTION

Unit Root Properties (URP) have implications for how applied researchers and policymakers interpret and use data. URP assists in understanding the form of data. There are two forms data can take, either stationary or non-stationary. In simple terms, stationary time-series data have mean, variance, and co-variance that do not change over time. By comparison, a non-stationary series is best characterized as one whose mean, variance, and co-variance change over time. Precise knowledge of the form of the time-series data is important, because when its form is stationary, this implies that shocks will have short-term (or temporary) effects. On the other hand, a non-stationary series implies that shocks have long-term or permanent effects on the variable. This knowledge has policy implications because policymakers need to understand the form of variables to deduce how they will react to policy changes and/or shocks.

The second advantage from understanding the form of variables has roots in econometric modeling. Applied researchers are constrained by theory in modeling data. Theory also tends to dictate the form in which variables need to be modeled. There are many examples of this. Two are offered here for demonstration. First, consider the Purchasing Power Parity (PPP) hypothesis, which holds that prices equalize across countries, meaning that any price differences on a good/service in any two like countries should be stationary for PPP to hold; see Narayan (2006a). Second, the popular efficient market hypothesis argues that asset prices (such as stock prices) should be stationary (see Narayan and Smyth, 2007).

So great has been the influence of unit roots pioneered by Nelson and Plosser (1982)—considering the need to understand the shock reaction of variables and the form in which they enter econometric modeling, as discussed above—that there is a separate literature on new tests for unit roots; see also Perron (1989), which marks the starting point for research based on structural break(s). In other words, researchers have focused attention on developing more robust unit root tests that can offer greater precision when testing for the precise form of the data. Two avenues for improvement noted recently are important to highlight. Endogenous structural break treatment has a notable history in unit root testing. However, while the tests became available following Lee and Strazicich (2003), subsequent work (see, for instance, Narayan and Popp, 2010) took issue with the precision in estimating the break dates themselves, because accurate identification of breaks has implications for precise understanding of the form of the data (Narayan and Popp, 2010). More recent work (Narayan and Liu, 2015; Narayan, Liu and Westerlund, 2016) takes issue with the fact that when modeling for unit roots, it is not only structural breaks that are important, but also the role of a time trend and data heteroskedasticity can be equally important in delivering an unbiased understanding of the data.

Macroeconomic data are also important for Indonesia. Several studies analyze Indonesian macroeconomic data via testing different relations. For instance, Amir, Asafu-Adjaye, and Ducpham (2013) examine the impact of Indonesia’s income tax reforms on various macroeconomic variables, namely real Gross Domestic Product (GDP), real private consumption, real investment, real government consumption, real exports, real imports, consumer price index,

GDP price index, and average real wage. Dutu (2016) examines economic growth slowdowns in Indonesia. Hsing (2012) examines the impact of macroeconomic forces and external shocks on Indonesia’s real output. Chowdhury, Uddin, and Anderson (2018) examine the influence of monetary and fiscal policy variables on the market and firm-level liquidity of eight emerging stock markets in Asia. Tanuwidjaja and Choy (2006) examine the role of Indonesian central bank credibility in achieving an inflation target. Hadiwibowo and Komatsu (2011) examine the macroeconomic trilemma and international capital flows under several financial structures in Indonesia. Djuranovik (2014) develops a model of the term structure of interest rates in Indonesia to create a link between the yield curve and macroeconomic fundamentals, namely real activity, inflation, and interest rate. Sowmya and Prasanna (2018) examine interaction between the yield curve and macroeconomic factors of Asian economies. Such studies and future research would benefit from greater understanding of the importance of unit root tests.

Returning to the idea of understanding the form of the variable, what started off as instrumental knowledge in using macroeconomic data spread quickly to other fields of research where shocks were relevant in understanding how variables respond to them. The unit root idea, for instance, was popularized in Narayan and Smyth (2007) in a time-series setting and extended to a panel data setting in Narayan, Narayan, and Smyth (2008). In tourism economics, the idea was introduced by Narayan (2005a,b) and in health economics by Narayan (2006b). The main message of these studies is that unit root evidence is important to understanding the nature and impact of shocks not only with macroeconomic data (see Section II), but also with other time-series data where shocks are relevant, such as in energy, tourism, and health.

This paper proceeds as follows. Section II reviews the literature on the presence of unit root in macroeconomic data. Section III discusses our data and results. Finally, Section IV sets forth concluding remarks.

II. THE LITERATURE

This section provides a feel for the importance of understanding the unit root behavior of macroeconomic data. We choose selected studies from this literature that we believe best offers a snapshot of the work done on unit roots devoted to macroeconomic data.

Table 1 summarizes selected literature on unit roots. We believe that these studies provide a reasonable representation of the literature and the features that characterize this literature. Let us identify these features more precisely. First, note from Column 2 that unit root tests of macroeconomic data are conducted at different data frequencies (annually, weekly, quarterly, and monthly), although most work seems to use annual data followed by monthly data. The dominance of annual data is expected given that, for most countries, macroeconomic data (over time) is available only annually. One issue arising from this concerns robustness. The question arises of whether the evidence on unit root data is frequency-dependent. We address this by undertaking a unit root test on both annual and monthly data. A caveat here is that one ends up with different start dates when using

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higher frequency data. The implication is that a strict comparison of the unit root hypothesis across data frequencies is impossible. However, the advantage is that we have some results that we can consider, depending on policy objectives.

The second feature of the literature, which can be read from Column 3, is that a wide range of macroeconomic data are utilized in unit root tests. The most popular data series seem to be GDP, inflation, and exchange rate; the highest number of variables used is around 14. Our study presents an extensive unit root analysis focusing on Indonesia—our sample includes 33 annual time-series data and 31 monthly time-series data. This represents a first comprehensive analysis of unit root testing of macroeconomic data.

The third feature concerns the econometric approach taken to test the unit root hypothesis. There are several points to note here. First, early studies seem to use tests without structural breaks. These studies are complemented by papers that address the unit root issue with structural breaks. Second, recent studies employ panel data models. Thus, the literature has progressed from time-series– based methods to panel data–based methods for testing the unit root hypothesis. We position our study within the popular structural break unit root testing methodology.

The final feature concerns the evidence on unit root. At best, the evidence appears mixed. Two trends are notable, however. First, panel data models offer greater evidence of stationarity. One reason for this is the gain in power to reject the unit root null that results from an increase in sample size when data is pooled across cross-sections and over time. Second, time-series models that accommodate structural break(s) offer greater evidence of stationarity (evidence against the unit root null hypothesis). These factors have implications for how one should approach unit root testing in macroeconomic data. We employ structural break unit roots tests within a time-series setting.

III. DATA AND RESULTS

Time-series data are used for unit root testing. A total of 31 monthly and 33 annual time-series macroeconomic variables for Indonesia are employed in this study. A complete list of variables is provided in Tables 2 (monthly series) and 3 (annual series). In summary, our dataset has three bond yield variables (separated by maturity), four interbank interest rate variables (separated by maturity), nine financial variables (business confidence index, capital value added, cash return index, dividend yield, Dow Jones stock index, market capitalization to GDP, Jakarta stock exchange Islamic index, price-to-earnings ratio, stock return index), and 17 monetary/trade-related variables (CPI, deposit rate, industrial production, composite index, exchange rate, export goods, export index, import goods, import index, industrial production, lending rate, M1, M2, producer price index, foreign exchange reserves, unemployment, and wholesale price index). All data are obtained from the Global Financial Database.

Table 2.

Descriptive Statistics of Monthly Data

This table presents descriptive statistics for monthly data. Thirty-one data series are considered, and Column 3 contains the sample period for each series followed by the number of observations (Obs.) in the sample. The mean, Standard Deviation (SD), skewness, Jarque–Bera (JB) test coefficient and its respective p-values are presented in Columns 5 to 9, respectively. The JB test examines the

null hypothesis of a normal distribution.

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Table 2.

Descriptive Statistics of Monthly Data (Continued)

Table 3.

Descriptive Statistics of Yearly Data

This table presents descriptive statistics for yearly data. Thirty-three data series are considered, and Column 3 contains the sample period for each series followed by the number of observations (Obs.) in the sample. The mean, Standard Deviation (SD), skewness, Jarque–Bera (JB) test coefficient and its respective p-values are presented in Columns 5 to 9, respectively. The JB test examines the

null hypothesis of a normal distribution.

Table 3.

Descriptive Statistics of Yearly Data (Continued)

A plot of the annual time-series data is available in Figure 1. Tables 2 and 3 show descriptive statistics based on monthly and annual time-series data, respectively. Given the time-series nature of the data, we note from both these tables the start data. Not all series have lengthy data. For example, some series, like exchange rate, have data going as far back as 1876. Inflation and deposit rate data are available from the 1960s and 1970s, respectively, while for other series much smaller data samples are available. Details are found in Columns 2 and 3 of these tables. Thus, data series have different start dates. This is dictated entirely by data availability.

Figure 1. A Plot of Annual Time-Series Data

This figure plots annual time-series data for 33 variables. Full variable description is given in Appendix Table A1. The time-span of each variable is dependent on data availability and is explicitly noted in Tables 2-3.

Cash Return Index

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Figure 1. A Plot of Annual Time-Series Data (Continued)

Figure 1. A Plot of Annual Time-Series Data (Continued)

Dow Jones Indonesia

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Figure 1. A Plot of Annual Time-Series Data (Continued)

Dividend Yield

Market Capitalization

Figure 1. A Plot of Annual Time-Series Data (Continued)

1-month JIBOR

3-month JIBOR

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Figure 1. A Plot of Annual Time-Series Data (Continued)

Price to Earning Ratio

Lending Rate

12-month JIBOR

Figure 1. A Plot of Annual Time-Series Data (Continued)

Foreign Reserves

Real GDP

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Figure 1. A Plot of Annual Time-Series Data (Continued)

Stock Index

Producer Price Index

10

0

Figure 1. A Plot of Annual Time-Series Data (Continued)

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Figure 1. A Plot of Annual Time-Series Data (Continued)

Import Index

Figure 1. A Plot of Annual Time-Series Data (Continued)

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Figure 1. A Plot of Annual Time-Series Data (Continued)

The Narayan and Popp (2010) test results for monthly data are reported in Table 4. We document that regardless of the type of model specification (i.e., Model 1 or Model 2), the unit root null hypothesis with monthly data is rejected for business confidence index, capital value traded, cash return index, consumer confidence index, exchange rate, 1- and 3-month interbank interest rate, industrial production (volume), lending rate, M1, price-earnings ratio, and foreign reserves. In total, therefore, we discover that the unit root hypothesis can be rejected in 13/31 monthly series, equivalent to 42% of the time-series data on hand.

Table 4.

Unit Root Results for Monthly Data

This table shows Narayan and Popp (2010) unit root results for monthly data. Columns 3 and 4 show the sample period and the corresponding number of observations (T). We refer to Table 3 of Narayan and Popp (2010) for critical values for unknown break dates. Models 1 and 2 are two models for testing unit root. Model 1 (see Column 5) allows for two breaks in level and the Model 2 allows for two breaks in level as well as slope (see Column 6). The true break dates are denoted by TB1 and TB2; k represents the optimal lag length; and ***, **, and * indicate that the unit root null hypothesis is rejected at the 1%, 5%, and 10% levels of

significance, respectively.