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.

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Notes

  1. 1.

    The paper studies convergence in three efficiency measures: overall efficiency, pure efficiency, and scale efficiency. Although the paper finds regional convergence in efficiency according to the classical convergence framework results, the paper also reports the existence of two local convergence clusters in overall and pure efficiency distributions based on the results from the distributional convergence approach. Finally, the paper emphasizes that two clusters of pure efficiency are the main drivers of Indonesia’s overall regional efficiency dynamics. This is also consistent with the standard consensus in the context of growth literature, where the distribution of income per capita across economies exhibits clustering patterns rather than a common growth path. For a comprehensive survey of the convergence literature, see Islam (2003).

  2. 2.

    Testing convergence using Consumer Price Index (CPI) may lead to misleading results due to the base year problem in CPI construction that affects the first observation. To overcome this problem, we followed the suggestion of Phillips and Sul (2007) and applied \(r\) = 0.33. This means that the first 33% of our observation is discarded and thus the log t regression model focuses attention on the latter part of the sample data.

  3. 3.

    Please refer to Appendix B of Phillips and Sul (2007) for detail demonstration of deriving the log t regression shown in Eq. (8).

  4. 4.

    We conducted club convergence test in Stata using commands developed by Du (2017) and in R using convergence club package by Sichera and Pizzuto (2019). Both systems show identical results.

  5. 5.

    The detailed procedure of club merging test is provided in Appendix 2.

  6. 6.

    While π is the average annual inflation (%, yoy) of all provinces in each club from 2013 to 2019, \(\hat{\alpha }\) is the convergence rate defined from Eq. (8) as \(\hat{b}\) /2.

  7. 7.

    As described by Samuelson (1994), the Penn effect emphasizes the positive relationship between productivity and the price levels, while the Balassa–Samuelson effect points to the differences in productivity between tradable and non-tradable sectors that describe inflation differential between countries/regions.

  8. 8.

    We imputed missing values for the data of the number of employed people in North Kalimantan province to compute labor productivity as defined in Table 3. Details on this imputation process are provided in Appendix 3.

  9. 9.

    All explanatory variables used in the ordered logit model are measured as the mean values during the 2012-2019 period. We performed ordered logit regression using the command ologit in Stata.

  10. 10.

    Note that since the sum of probabilities for all four clubs must equal one, the partial derivatives across the clubs are equal to zero.

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Appendix

Appendix

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

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.

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
figure5

Comparison between original series and imputed series

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Aginta, H. Spatial dynamics of consumer price in Indonesia: convergence clubs and conditioning factors. Asia-Pac J Reg Sci (2020). https://doi.org/10.1007/s41685-020-00178-0

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Keywords

  • Regional inflation
  • Monetary policy
  • Convergence clubs
  • Indonesia

JEL classification

  • C23
  • E31
  • R10