Spatial dynamics of consumer price in Indonesia: convergence clubs and conditioning factors

Abstract

This paper aims to identify convergence clubs in regional price across 34 provinces in Indonesia and investigate conditioning factors of club formation. We analyze regional monthly consumer price data from January 2012 to December 2019 with a novel club convergence test developed by Phillips and Sul (Econometerica 756:1771–1855, 2007), and show that regional consumer price does not converge into a single universal equilibrium. Instead, there are four convergence clubs identified. Further investigation shows that labor productivity, inflation expectation, consumption growth, and spatial externalities influence the convergence club formation. From a policy perspective, our findings of multiple convergence clubs and their influencing factors alert policy makers to rethink the possibility of augmenting uniform monetary policy with region-specific inflation management measures.

Appendix

1.1 Appendix 1: Club-clustering algorithm

Although the null hypothesis of overall convergence ($H_{0} )$ tested using log t regression is rejected, it does not necessarily mean that the convergence in the sub-sample of the panel is not present. To identify the presence these convergence clubs, Phillips and Sul (2007) developed a club-clustering algorithm. In brief, the implementation of the club-clustering algorithm within the scope of our study involves the following four steps (a detailed description of the procedure in club clustering is given in Phillips and Sul (2007)):

• Step 1: Cross-section ordering.

Sample units (provinces) are arranged in a decreasing order according to their value (CPI) in the last period (December 2019).

• Step 2: Constructing the core group.

A core group of sample units (provinces) is identified by conducting the log t test for the first k = 2 provinces. If the null hypothesis of convergence ($H_{0} )$ is not rejected, that is $t_{{\hat{b}}}$ (k = 2) > $-$ 1.65, both provinces assemble the core group $G_{k} .$ This procedure is implemented sequentially for $G_{k}$ + the next province as long as $t_{{\hat{b}}}$ (k) > $t_{{\hat{b}}}$ (k $-$ 1). Thus, if $t_{{\hat{b}}}$ (k = 3) > $t_{{\hat{b}}}$ (k = 2), the last province is added to the core group $G_{k}$.

• Step 3: Deciding club membership.

After the core group $G_{k}$ is constructed, log t test is implemented on $G_{k}$ with each subsequent unit (province) according to the decreasing order established in Step 1. Sample units (provinces) not belonging to the core group $G_{k}$ are re-evaluated one at a time with log t regression in Eq. (8). If the test strongly supports the convergence hypothesis (log t $\ge$ 0), all those units (provinces) are added to the core group $G_{k}$, forming the first convergence club in the panel.

• Step 4: Iteration and stopping rule.

Step 1–3 are applied for the remaining sample units (provinces), if any, to determine the next convergence club. If the process shows the rejection of null hypothesis of convergence ($H_{0} )$, the procedure is terminated. In this case, the remaining sample units (provinces) are labeled as divergent if no core group is found, and the algorithm stops.

Table 5 Summary statistics of CPI in 34 Indonesian provinces

Table 6 Summary statistics of ordered logit variables

1.2 Appendix 2: Test for clubs merging

To evaluate whether the clubs identified according to the clustering algorithm described in Sect. 3.2 and “Appendix 1” can be merged, in this study, we use a “club merging algorithm” by Phillips and Sul (2009). By testing for merging between adjacent clubs, the procedure works as follows: first, apply log t test on the first two initial groups identified in the clustering mechanism. If the t-statistic > − 1.65, these two groups together form a new convergence club. Second, repeat the first step by adding the next club. Continue this process until the condition of t-statistic > − 1.65 is achieved. Third, if convergence hypothesis is rejected, that is when t-statistic > − 1.65 does not hold, we assume that all previous groups converge, except the last added one. Hence, we restart the merging algorithm from the club for which the hypothesis of convergence does not hold.

1.3 Appendix 3: Data imputation for missing values on number of employed people for North Kalimantan province, 2012–2014

As defined in Table 3, we computed labor productivity by dividing Gross Regional Domestic Product (constant price 2010)/number of people employed in each province. Indonesian Central Bureau of Statistics publishes data of number of people employed based on National Labour Force Survey (Sakernas). The survey is specifically designed to collect information on labor force statistics.

As a new proliferated province in 2013 from the main province of East Kalimantan, series of number of people employed in North Kalimantan province is available only from the year of 2015. Before that year, the series for North Kalimantan province is combined the series for East Kalimantan province. Thus, we faced the problem of missing values of number of people employed series for North Kalimantan province for three observations; 2012, 2013 and 2014. We implemented two following steps to solve this missing values problem. First, we conducted imputation by using linear regression method with the reference province and year as regressors. East Kalimantan province (the origin province) is chosen as reference for imputation, implying the assumption of co-movements between these two provinces. Second, we subtracted the values of original data for East Kalimantan province in the year of 2012, 2013 and 2014 with the imputed values for North Kalimantan province and used these subtracted values as final series for East Kalimantan province. Figure 5 compares number of people employed series in East Kalimantan and North Kalimantan province before and after imputation process.

Fig. 5

Comparison between original series and imputed series