Inflation and Its Uncertainty: Evidence from Indonesia and the Philippines

Abstract

This article investigates the relationship between inflation and its uncertainty under the inflation-targeting regime in Indonesia and the Philippines over 2005(7)–2021(12). The Kernel density function and entropy index applications reveal that the price level in both countries is heterogeneous. The non-linear quantile regression estimation shows that inflation affects inflation uncertainty positively. Inflation more likely induces its uncertainty in higher quantiles. The effect exhibits an inconsistent linearity property. While the symmetric behavior holds in the Philippines, inflation in the case of Indonesia affects the inflation uncertainty differently, not only inter-quantiles but also intra-quantiles. Given that Indonesia and the Philippines have low inflation rates relative to other emerging markets, our findings suggest that announcing higher inflation targets may be costly to provoke higher inflation uncertainty. Accordingly, controlling inflation uncertainty in the inflation-targeting regime can be achieved if monetary policy is credible and independent.

JEL Classification

C14, C21, D08, E31, O23

Keywords

Inflation inflation uncertainty Kernel distribution entropy index quantile regression

Introduction

Since the first implementation in New Zealand, Canada, the United Kingdom, Sweden, and Australia in the early 1990s, inflation targeting has been a reference for Central Banks in many countries (Kuncoro, 2015). The inflation-targeting adoption becomes much more powerful by discarding capital flow restrictions, removing interest rate limitations, substituting fixed exchange rates with flexible exchange rates, and deregulating almost the entire financial system (Rojas, 2019). Therefore, the monetary policy framework emphasizes transparency, credibility, independence, and accountability and is believed to be more effective in controlling the inflation rate (Phiri, 2016).

Along with its popularity, however, there is conceptual disagreement and empirical evidence of controversy in adopting the inflation-targeting regime. The main challenge is that a Central Bank has the advanced analytical capacity and technical infrastructure to forecast future inflation (Batini et al., 2006). This claim could be eroded when actual inflation steadily diverges from the target level (Hartmann et al., 2020). Despite the evaluation of inflation targeting has received much attention in the recent literature (Ardakani et al., 2018; Brito & Bystedt, 2010; Thornton, 2016), the issue of how inflation uncertainty appears in inflation targeting and inflation deviates from the targeted level have not been well understood yet.

The knowledge of the inflation-inflation uncertainty nexus is divergent so far. On the one hand, an inflation target helps to reduce uncertainty about future inflation. Even inflation targeting lowers inflation and inflation uncertainty (Broto, 2011). On the other hand, the focus of monetary policy on price stability has been the leading cause of disinflation (Greenspan, 2004). Hence, it is not surprising that the impact of inflation targeting is insufficient in declining inflation variability, resulting in high uncertainty (Ardakani et al., 2018; Karahan, 2012). The high inflation rate relative to the target level could accentuate the uncertainty about future inflation.

Recognizing the exact link between inflation and its uncertainty is essential. Therefore, from the researcher’s point of view, the relationship between inflation and its uncertainty is a critical test for the validity of Friedman’s (1977) and Ball’s (1992) hypotheses. They argue for causality running from inflation to its uncertainty; that is, higher inflation leads to higher inflation uncertainty. In contrast, Pourgerami and Maskus (1987) and Ungar and Zilberfarb (1993) believe that higher inflation reduces inflation uncertainty. Other studies introduced different points of view like Cukierman and Meltzer (1986) propose the opposite causal relationship that higher inflation uncertainty causes higher inflation. Moreover, Holland (1995) also postulates that higher inflation uncertainty can dampen inflation levels.

The conceptual contradiction also occurs in the empirical realm. A growing body of empirical studies in developed countries (Barnett et al., 2020; Hossain, 2014; Kontonikas, 2004) and developing countries (Nene et al., 2022; Rojas, 2019; Thornton, 2007) shows diverging results. The mixed findings could be due to differences in the samples of countries examined, the econometric technique chosen, and the time periods covered. In addition, there are substantial differences in socio-economic and country-specific factors. Governments may have economic issues and macroeconomic policies which differ from others. Hence, the link between inflation and uncertainty is only partially comparable across the countries (Sharaf, 2015).

Regarding policy-makers, incomplete information on the relationship structure between the two variables means that some high inflation and inflation uncertainty will exist in any policy regime. High inflation is generally believed to be costly. Uncertainty about future inflation levels will distort saving and investment decisions which may have an unfavorable impact on the efficiency of resource allocation (Friedman, 1977). The inflation uncertainty also makes the decision-making for businesses and consumers more difficult and reduces the level of real activity (Golob, 1994). The high inflation uncertainty also hurts the poor (Son, 2008). Moreover, inflation uncertainty often arises from the supply side, which is generally considered beyond monetary policy control.

Indonesia and the Philippines cannot be separated from those problems. The two emerging markets in South East Asia suffered adverse impacts from external turbulence during the Asian monetary crisis in 1997/1998. Experiencing a high inflation rate, deep economic contraction, and sharp currency depreciation has urged both economies to institute economic recovery and stabilization programs. During the 2007/2008 global financial crisis, the Central Bank of both countries carried out various monetary action measures to save domestic economic activity. In the COVID-19 pandemic era, the two countries released various fiscal stimulus packages to restore the diminishing purchasing power trends.

From the monetary strand, both countries implemented an inflation-targeting regime in the early 2000s, resulting in solid economic growth, low inflation rates, and stable exchange rates. However, the question is whether the low inflation rates in both countries are irreversible or transitory in nature. As a small open country, their individual economic performances have little repercussions from the standpoint of the global economy. In addition, implementing a floating exchange rate regime makes both countries’ currencies sensitive to inflation disparity against the US. Meanwhile, their interest rate policies (as the main instrument to float inflation expectations) are also responsive to interest rate differences and imported inflation.

The answer to the above question returns to the discussion on inflation uncertainty. This article enriches the empirical literature on inflation–inflation uncertainty in the two countries. This study uses nonparametric tools to assess inflation uncertainty. Kernel distribution function and entropy index permit the outlier observations which often emerge in developing countries. We also designed a nonlinear quantile regression approach to identify the asymmetric change of inflation position in the entire inflation uncertainty distribution. The structure of this study is as follows: the section below briefly highlights a review of the existing literature on the link between inflation and its uncertainty. The next section presents the estimation procedures and data used in the estimation process. The results of the estimation and discussion of the empirical findings follow this. The subsequent section draws out the conclusions and presents the relevant policy implications.

Literature Review

The relation between inflation and inflation uncertainty can be traced back to Okun (1971). He argues that economies with high inflation rates will also suffer high inflation volatility, and under this condition, the future of monetary policy becomes unpredictable. However, the conceptual framework underlying this idea was formally introduced by Friedman (1977). He explained how an increase in the average inflation rate stimulates larger uncertainty regarding the future inflation rate. The monetary policy in inflationary episodes is typically unsustained and, therefore, unforeseeable.

Ball (1992) further extends the Friedman hypothesis. He constructed a game theory under asymmetric information between policymakers and the public. When low inflation levels are present, policymakers will exert to preserve low inflation. Nevertheless, with high inflation levels observed in the economy, only the anti-inflationary policymakers consider the economic costs of disinflation. Hence, the limited information about the type of policy maker (anti-inflationary or not) creates uncertainty. In his model, episodes of high inflation amplify greater uncertainty since the public is unsure about the future policy.

In contrast to the above hypothesis, Cukierman and Meltzer (1986) state that high inflation uncertainty leads to a high inflation level. Over the episodes of high inflation uncertainty, policymakers conduct discretionary monetary policy to stimulate output growth. The discretionary monetary policy in the form of monetary expansions fuels higher inflation. The lack of policymakers’ commitment is the primary source of uncertainty. In these circumstances, higher inflation uncertainty generates greater inflation and is known in the literature as an opportunist or myopic Central Bank.

As opposed to the Friedman–Ball hypothesis, other theories posit a negative relationship between the inflation level and its uncertainty. According to Pourgerami and Maskus (1987), and Ungar and Zilberfarb (1993), during periods of high inflation, the public keeps themselves safe from its adverse effects. By investing their resources, the public can better anticipate the future inflation rate. Under the same environment, Holland (1995) argues that the policymaker attempts to lower the welfare costs of inflation by disinflationary strategies. Such a “stabilizing hypothesis” postulates a negative impact of inflation uncertainty on the inflation level.

Multi-Country Evidence

Based on the four competing theories above, a number of empirical studies have been conducted to investigate the causal relationship between inflation and its uncertainty. In the last two decades, there have been a growing number of studies covering a wider range of countries using more advanced econometric techniques over more extended periods. For example, in a cross-country study of 12 emerging market economies, Thornton (2007) finds strong evidence of the Friedman–Ball hypothesis in the entire economies they observed. However, the impact of inflation uncertainty on inflation is unconvincing. Kim and Lin (2012), using a simultaneous equation system for a panel study of 105 countries, obtained a two-way positive interaction, which confirms both the Friedman–Ball and the Cukierman–Meltzer hypotheses.

In the case of multiple countries, Viorica et al. (2014) observed that the dominant behavior for the Baltic economies indicates high inflation having a positive link to inflation uncertainty. The group of economies with early economic reforms is characterized by uncertainty about inflation that has had a direct effect on inflation. Rojas (2019) found that most Latin American economies supported the Friedman–Ball hypothesis. The adoption of inflation targets in some countries reduces inflation volatility. In the case of African countries, Nene et al. (2022) found that inflation targeting policy was ineffective in lowering inflation uncertainty.

Similarly, Zivkov et al. (2014) examined the relationship between inflation and inflation uncertainty in 11 Eastern European countries. Using the GARCH (generalized autoregressive conditional heteroskedasticity) type model along with quantile regression, they found inconclusive evidence on the causal direction. They supported Friedman–Ball and Cukierman–Meltzer’s hypotheses for countries adopting a flexible exchange rate regime. On the contrary, there was no evidence to support the two hypotheses for countries implementing fixed exchange rate systems.

Conducting a systematic econometric study (frequency approach, wavelet, semi-parametric approach, and stochastic volatility), Barnett et al. (2020) analyzed inflation and inflation uncertainty in the US, UK, and Euro area as developed countries; and China and South Africa as two emerging countries. They obtained a significant relationship between inflation and its uncertainty. However, the inflation–inflation uncertainty nexus was ambiguous. Given that the relationship is time- and frequency-varying, they concluded that the link seems positive in the short- and medium-terms during stable periods, supporting the Friedman–Ball hypothesis. The relationship is negative during the crisis, thus confirming the Holland theory.

Single Country Evidence

While cross-country studies dominate the literature, several works have examined the relationship between inflation and its uncertainty in the scope of individual countries. By employing data for the UK over the period 1972–2002 and using various GARCH-in-mean models, Kontonikas (2004) found a positive link between past inflation and future inflation uncertainty, which is in line with the Friedman–Ball causal relationship. The other interesting result is that implementing the inflation-targeting regime in the UK since 1992 has reduced inflation persistence and eliminated long-run uncertainty.

Hossain (2014) found a one-way relationship between inflation and its uncertainty from 1949 to 2013 in Australia. He concluded that inflation shock asymmetrically affects inflation uncertainty. Karahan (2012) deployed a two-step procedure to examine the relationship between inflation and uncertainty in Turkey from 2002 to 2011. He observed that inflationary periods yield high inflation uncertainty. His evidence supported the Friedman–Ball hypothesis, as seen in the study of Heidari and Bashiri (2010) in Iran, and Nasr et al. (2015) in South Africa. In contrast, Chowdhury (2014) obtained a two-way causal link between the two variables, confirming both the Friedman–Ball and Cukierman–Meltzer hypotheses. A similar result was found by Sharaf (2015) in the case of Egypt.

In another avenue, Gülsen and Kara (2019) assessed the Central Bank of Turkey survey data. Inflation uncertainty was measured by standard deviation, entropy, and disagreement among forecasters. They found that the presence of higher inflation promotes inflation uncertainty. Gao et al. (2021) showed one-way causality from inflation-to-inflation uncertainty in China. It works asymmetrically and time-varying, indicating that inflation causes inflation uncertainty in higher quantiles. They concluded that the linear model based on conditional mean might overestimate in a lower quantile interval.

In line with the rapid economic growth in South East Asian countries, inflation volatility has also been a focus of attention. For empirical works focused on South East Asian economies, Buth et al. (2015) studied the relationship between inflation and its uncertainty in Cambodia, Lao PDR, and Vietnam. Based on the conditional variance in a family of GARCH models, they found that inflation boosts inflation uncertainty in these countries, except Lao PDR. Payne (2009) found strong support for Holland’s stabilization hypothesis in Thailand that higher inflation induces greater inflation uncertainty and higher inflation uncertainty suppresses inflation. He asserts that inflation-targeting adoption in Thailand reduces inflation uncertainty concerning inflationary shocks.

In the case of the Philippines, Ozdemir and Fisunoglu (2008) obtained the Friedman–Ball hypothesis, and there is weak evidence to support the Cukierman–Meltzer hypothesis. This finding was confirmed by Mohd et al. (2013) that inflation uncertainty increases more in response to positive inflation surprises than to negative surprises in South East Asian countries, including Indonesia and the Philippines. The high inflation uncertainty in this region is due to a weakening transmission mechanism (Tuaño-Amador, 2013) and a strong spillover effect (Pratikto & Ikhsan, 2016). More recently, Jiranyakul (2020) showed that inflation was positively affected by inflation uncertainty in selected Asian economies, regardless of whether they are inflation-targeting countries or not. However, Kuncoro et al. (2021) argue that the relatively low inflation rate is related to the Central Bank’s commitment to safeguarding the inflation rate target.

Research Method

The results of panel data, cross-country, and individual-country studies on the causal relationship between inflation and its uncertainty seem inconclusive. Econometric studies generally use a family of GARCH models to measure inflation uncertainty. The GARCH-type models focus mainly on estimating the conditional mean function. The mean effects are gained through the conditional mean regression. The characteristics of distributional impact still need to be fully identified, and therefore the impact of covariates would be biased. Only some works have used different approaches but with ambiguous results. Given the lack of econometric properties, this article applies nonparametric approaches that do not require a certain distribution shape.

In terms of statistics, uncertainty can be understood as unpredictable variability in the values of a data set. The greater variability in the distribution of the observation means higher uncertainty. To demonstrate the shape of the distribution, we used univariate density functions. A density function is a smooth curve that highlights the probability distribution of a continuous random variable. The density function is estimated non-parametrically by the Kernel method. The estimated Kernel distribution function is drawn from a set of observations—in this case, relative positions of the price level (for details, see Silverman, 1998).

In formal terms, the Kernel density estimate of a series X at a point x is mathematically given by the following expression:

f (x) = \frac{1}{n h} \sum_{i = 1}^{n} K (\frac{x - X_{i}}{h})

(1)

where n is the sample size, K is the Kernel function, h is the smoothing parameter, X_i is the value of the regressor, and x is the value of the regressor for which one seeks an estimate. This method normally incorporates selecting a narrow interval (smoothing parameter or bandwidth) around the point x and estimating f(x) by the number of observations X_i belonging to the interval. Thus, the Kernel density is a weighting function given the weights of the nearby data points in making this estimate.

The unconditional probability was estimated with which each of these values could have occurred. The probability of each point was computed as the weighted average of the distance of that point from the given value, with the weights taken from a normal or Gaussian distribution concentrated at that point. Weights derived from an Epanechnikov distribution, which is also often used as a weighting method, do not significantly alter the shape of the estimated Kernels. The relative frequencies of these points were filtered for noise. The filtered relative frequencies establish the Kernel of the relative ranking in the entire observation period. The area of the distribution is standardized to unity or 100%.

Furthermore, to quantitatively measure a distribution’s dispersion, we used the entropy index as done by Gülsen and Kara (2019) to analyze the data survey. The entropy index is a good alternative indicator to measure uncertainty because it identifies the degree of concentration of a probability distribution without any direct dependence. Hence, it offers robust estimators relative to the standard deviation metric, primarily when each data is not normally distributed. The entropy index (E_i) takes the following form:

E i = \frac{1}{n} \sum_{i = 1}^{n} \frac{x_{i}}{\bar{X}} \log (\frac{x_{i}}{\bar{X}})

(2)

where n is the number of cases, x_i is the income for case i, and $\bar{X}$ is the mean value.

The entropy index offers extra information relative to variance-based measures. Given a certain standard deviation, the entropy index moves with the shape of the distribution. The entropy index describes whether the probability is centered on a few points or scattered over many points, which may reduce the assigned weight of tail concentrations relative to variance-based measures. Therefore, the idea of the entropy index fits to allow bi-modal distributions due to structural breaks and may emerge during episodes of enhanced uncertainty (Gülsen & Kara, 2019).

While the Kernel estimators provide a fruitful graphical representation of the distribution, the entropy index tells us how likely it is quantitatively dispersed. It measures a certain price level, on average, as a particular fraction of the average price level in the whole observation. The Kernel density distribution and entropy index are also useful to identify the shape of the price level distribution or even how it evolves over the periods if the distribution is divided into several sub-periods. In our case, the applications of Kernel estimators and entropy index on Indonesia’s and the Philippines’ price level data gave a fair comparison of how they change over time.

Unfortunately, the two measures cannot serve as each transition probability of the distribution converges toward each steady state. For this reason, the transition probability was examined by quantile regressions as used by Yeh et al. (2009) and Jiranyakul (2020). The quantile regression, first developed by Koenker and Bassett (1978), has the interesting feature that it can estimate a family of conditional quantile functions with a more detailed picture of covariate effects. The quantile regression method is based on the sum of absolute error minimization instead of minimizing the sum of the squared errors. It fits medians to a linear function of covariates and produces an approximation to the mean function of the conditional distribution of the dependent variable.

As an alternative indicator of the central tendency of a distribution, the application of quantile regressions on the inflation–inflation uncertainty nexus offers some advantages (Yeh et al., 2009). The quantile regression produces a robust estimator even if the set data on the dependent variable contains some outlier observations. Baillie et al. (1996) point out that most unconditional inflation uncertainty distribution is typically right-skewed. Accordingly, quantile regression provides an important insight. The quantile regression could give a unique estimator for each quantile. Therefore, the position on the inflation uncertainty distribution can be specifically evaluated along with the most effective available policy options.

Quantile regression is suitable when the set data observation suffers highly heterogeneous conditions. The right-skewed inflation and inflation uncertainty distributions suggest that the coefficient of the inflation uncertainty increases with the quantiles. It implies further that the impact of inflation on the inflation uncertainty is greater for the upper quantiles. Hence, dramatic changes in the quantile estimates are not merely due to data differences but also differences across the distribution.

According to Koenker and Bassett (1978), the unconditional quantile regression model can be adopted to examine the relationship between inflation and inflation uncertainty.

{v i}_{t} = a + b π_{t} + ε_{t}

(3)

where π is the monthly inflation rate defined as the relative change in the price level (P):

π_{t} = \frac{(P_{t} - P_{t - 1})}{P_{t - 1}} \approx \log (P_{t}) - l o g (P_{t - 1})

(4)

vi is inflation uncertainty which is measured by the moving average of unconditional standard deviation over consecutive 12 months

{v i}_{t} = \sqrt{\frac{\sum_{i}^{12} {(X_{i} - \bar{X})}^{2}}{n - 1}}

(5)

and ε is a disturbance term.

Coefficients a and b are the unknown parameters to be estimated for various quantile values. The sign of b is expected to be positive. By setting the quantile value from 0 to 1, we can detect the entire distribution of the explained variable conditional on the explanatory variables.

The monthly relative change in price level depicts inflation or deflation rates. The latter are rarely captured in the year-on-year inflation rates. In our view, inflation and deflation may produce higher uncertainty compared to inflation instability only. Unlike other research, this article estimates the unconditional inflation uncertainty by splitting up the monthly relative change in price level into inflation and deflation states:

d_{1} = \begin{matrix} 1 - i f π_{t} > 0 \\ 0 - i f π_{t} \leq 0 \end{matrix} a n d d_{2} = \begin{matrix} 1 - i f π_{t} < 0 \\ 0 - i f π_{t} \geq 0 \end{matrix}

(6)

where d is a dummy variable. Substituting Equation (6) into (3), we have:

{v i}_{t} = a + b_{1} [d_{1} \times π_{t}] + b_{2} [d_{2} \times π_{t}] + ε_{t}

(7)

The symmetric impact of inflation or deflation states on the inflation uncertainty can be examined by testing the hypothesis H₀: b₁ = b₂. The Wald test was carried out to test against the alternative hypothesis, H_a: b₁ ≠ b₂. Therefore, Equation (7) could also solve the asymmetric and non-linearity problems which often arise in the financial markets (see, for example, Law, 2019) and be comparable to the GARCH method.

Equation (7) was applied to Indonesia and the Philippines. Since we focus on the degree of uncertainty, we require long-span and reliable time series data on inflation rates which are derived from the price levels. The price levels deal with the CPI (consumer price index, 2012 = 100). The sample periods extend from 2005(M7) to 2021(M12), capturing the inflation-targeting regime adoption in both countries. The total observation is 198 sample points. Most of the monthly data come from the central bank of Indonesia (BI) and the Philippines (Bangko Sentral ng Pilipinas).

Results and Discussion

Table 1 provides descriptive statistics on the price level, inflation, and uncertainty for Indonesia and the Philippines. The mean value of the price level is not far from the base year (2012 = 100) respectively. The mean value is also close to the median value, suggesting that the price level in both countries is normally distributed. However, the non-normal distribution of the data is apparent from the negative values of its skewness. The shape of the data distribution is slightly left-skewed.

Table 1.

Descriptive Statistics.

	Indonesia			The Philippines
	P	π	vi	P	π	vi
Mean	109.96	0.0019	0.0024	103.42	0.0013	0.0013
Median	111.51	0.0012	0.0017	104.82	0.0011	0.0011
Maximum	147.09	0.0362	0.0100	132.66	0.0070	0.0033
Minimum	61.46	−0.0020	0.0006	74.21	−0.0026	0.0006
Std. Dev.	25.31	0.0033	0.0021	15.88	0.0015	0.0006
Skewness	−0.14	6.3814	2.7346	−0.10	0.9383	1.4085
Kurtosis	1.70	63.9115	10.0890	2.05	4.7059	4.7735
Entropy index	0.0118	–	–	0.0052	–	–
pre-GFC	0.0008	–	–	0.0001	–	–
post-GFC	0.0071	–	–	0.0030	–	–
Correlation	–	0.2532		–	0.0908

The Kernel distribution function supports the non-normal distribution of the price level data. As shown in Figure 1, Indonesia’s price level data distribution departs largely from the “bell-shaped” distribution. The probability density is right-skewed and performs bi-modal; the first peak is at around 90, and the second at 135. In particular, some back-of-the-envelope computations show that a large proportion of the price level occupies more than half of the total observation. On the contrary, the data distribution for the Philippines has a unimodal shape, peaking at 110.

Figure 1.

The Kernel Distribution of Price Level.

Regarding the data dispersion, the price level distribution for Indonesia is wider compared to the Philippines, confirmed by the distances between maximum and minimum values and the standard deviation. The Kernel distribution function also supports higher dispersion for Indonesia. The range of the Kernel distribution function is higher in Indonesia relative to the Philippines. The entropy index indicates that the price level distribution in Indonesia (0.012) shows higher variability (0.005). Observation pre- and post-global financial crisis in 2008 does not change the conclusion. Accordingly, the notion of entropy justifies bi-modal distributions as found by the Kernel density function to cover structural breaks and culminated uncertainty (Gülsen & Kara, 2019).

Figure 2 presents inflation and its uncertainty. Indonesia’s high inflation rate at the beginning of observation was associated with the government policy to increase domestic oil prices (Insukindro & Sahadewo, 2010). Given the low correlation (0.25 and 0.09), it is notable that the higher price level (in the case of Indonesia) tends to have a lower inflation rate and uncertainty. On the contrary, the lower price level (in the case of the Philippines) tends to have a higher inflation rate and uncertainty. Price convergence seems to be currently evolving in the South East Asia region. However, our concern is not about price convergence but whether inflation leads to inflation uncertainty or inflation uncertainty provokes inflation.

Figure 2.

Inflation and Its Uncertainty.

To ascertain the causal relationship, the Granger causality test (Table 2) confirms a unidirectional causality. Using six lags (based on the LR [Log-likelihood ratio], FPE [Final prediction error], and AIC [Akaike information criterion] optimum criteria) for the case in two countries, the causal relationship moves from inflation to inflation uncertainty, which supports the Friedman–Ball hypothesis. It does not hold in the opposite direction. The inflation uncertainty does not Granger cause inflation. In other words, inflation is the cause, and otherwise, inflation uncertainty is the effect. This conclusion holds for Indonesia and the Philippines. Considering the causal relationship, our question then is how large is the influence of inflation on the inflation uncertainty.

Table 2.

Granger Causality Test.

Null Hypothesis:	Lag	F-stat	Prob.
Indonesia
vi does not Granger cause π	6	1.5077	0.1780
π does not Granger cause vi	6	2.4971	0.0241
The Philippines
vi does not Granger cause π	6	0.1035	0.9959
π does not Granger cause vi	6	2.6509	0.0173

Before solving the above question, it is essential to check the stationarity of the data series. The stationary data requires that the series data has a unit root. The unit root of the data ensures a non-spurious regression with time-invariant estimates. Accordingly, prior to any estimation, two unit root tests were used; the Augmented Dickey–Fuller (ADF) test and the Phillips–Perron (PP) test. The ADF unit root test could give wrong information regarding unit root data series in level, especially if they are trend-stationary with a structural break. The PP test is better for examining the validity of series data toward the existence of unknown multiple structural breaks.

Each test was applied on the data level and the first difference. The results of the ADF and PP tests are presented in Table 3. The results indicate that both tests reject the null hypothesis of a unit root in the price level at a 5% significance level. After first differencing, the data series has a unit root. This means that the price level series data for Indonesia and the Philippines are integrated into order one I(1). In other words, the inflation series data are integrated into order zero I(0). A similar result is found in the inflation uncertainty series data. It implies that the impact of any shock will disappear over time and the two series data will evolve to its long-run mean. Eventually, the two variables tend to move towards the long-run equilibrium relationship as expected by theory.

Table 3.

Unit Root Tests.

	ADF		PP		Conclusion
	Level	First-diff.	Level	First-diff.	Conclusion
Indonesia
P	−2.4337	−10.5828***	−2.4550	−10.0531***	I (1)
Vi	−5.1264***	–	−2.9635**	–	I (0)
The Philippines
P	−0.1758	−9.0958***	−0.1929	−8.8897***	I (1)
Vi	−3.9722***	–	−2.7212*	–	I (0)

Notes: *, **, and *** denote significance at 10%, 5%, and 1% levels, respectively.

Table 4 provides the estimation results of Equation (3) from the OLS (ordinary least squares) parametric mean and quantile regressions. In the most basic form, the conditional mean results for Indonesia in the first column indicate that the OLS estimate of 0.16 is significant at a 1% significance level. It has the expected sign and therefore serves as a preliminary endorsement of the Friedman–Ball hypothesis, as many researchers in the literature review section found. Similar results are also obtained for quantiles of 0.05, 0.25, 0.50, 0.75, and 0.90 in the conditional median.

Table 4.

Estimation Results of Quantile Regression.

	OLS	Quantile
	OLS	0.05	0.25	0.50	0.75	0.90
Indonesia
C	0.00***	0.00***	0.00***	0.00***	0.00***	0.00***
π	0.16***	0.19***	0.15***	0.12***	0.13**	0.17***
Pseudo R²	0.06	0.10	0.08	0.04	0.02	0.04
Adj R²	0.06	0.10	0.08	0.04	0.02	0.03
S.E.R	0.00	0.00	0.00	0.00	0.00	0.00
The Philippines
C	0.00***	0.00***	0.00***	0.00***	0.00***	0.00***
π	0.03	0.06*	0.02	0.04	0.06*	0.02
Pseudo R²	0.01	0.04	0.00	0.01	0.02	0.00
Adj R²	0.00	0.03	0.00	0.00	0.01	0.00
S.E.R	0.00	0.00	0.00	0.00	0.00	0.00

Notes: *, **, and *** denote significance at 10%, 5%, and 1% levels, respectively.

For those significant coefficients at a 1% significance level in a particular equation, the size of the coefficients does not vary across the quantiles. The quantile process estimate for inflation fails to exhibit an upward linear trend. For quantiles in the bottom 5% of the conditional inflation uncertainty distribution, the estimated coefficient on inflation is 0.19; it decreases to 0.15 for quantiles 0.25 and decreases again to 0.17 in the top 10% of the distribution.

The application of the same method for the Philippines data does not offer a better result. Values of coefficient b, are found to be significant for quantiles 0.05 and 0.75, respectively. The alternative hypothesis is that b ≠ 0 for both quantiles can be accepted at a 10% significance level. However, the numerical results in both countries are in line with the study of Jiranyakul (2020). At this point, dividing the change in price level into inflation and deflation states potentially opens a clearer explanation.

Partitioning the inflation rate component with respect to the two classifications as specified in Equation (7), there is an interesting result. For the case of Indonesia, the magnitude of the coefficients is substantially different across the quantiles. The quantile process estimates for the inflation state exhibit a linear increasing trend, ranging only from 0.19 to 0.22. In the deflation state, in contrast, the quantile process estimates are quite larger, ranging from −0.42 to −1.26.

In the case of the Philippines, a linear increasing trend holds only in the deflation state. The quantile process estimates are slower compared to Indonesia, ranging from −0.07 to −0.92. Accordingly, the symmetric test infers that there is no different impact on inflation uncertainty between inflation and deflation states both in the lower quantile and the upper quantile. On the contrary, for Indonesia, there is a significantly different impact of inflation on the inflation uncertainty between inflation and deflation states both in the lower quantile and the upper quantile.

Those results confirm that the impact of inflation (or deflation) has a greater effect on the upper quantile of the inflation uncertainty distribution. These findings are useful to gain the potential information related to the estimation of the whole conditional inflation uncertainty distribution when confronted with the conditional mean. In addition, OLS estimates of the conditional mean function are more sensitive to the tails of the data distribution compared to estimates of the conditional median function.

Furthermore, it is necessary to test whether the estimation results of the simple model (Table 4) are statistically equal to the estimation results of the extended model (Table 5). Table 6 presents the results of the Wald test for equality of slope coefficients across the quantiles for the explanatory variables. For the Philippines, there are no different slope coefficients across the quantiles, suggesting that all coefficients in each quantile are equivalent. In contrast, for Indonesia, the test results reveal that the slope coefficients are quite different from each other. The slope coefficients substantially vary between 0.05th–0.75th, 0.25th–0.75th, and 0.75th–0.90th pairwise quantiles.

Table 5.

Estimation Results of the Extended Quantile Regression.

	OLS	Quantile
	OLS	0.05	0.25	0.50	0.75	0.90
Indonesia
C	0.00***	0.00***	0.00***	0.00***	0.00***	0.01***
π+	0.18***	0.19***	0.16***	0.17***	0.22***	0.17***
π−	−0.37	−0.42**	−0.44*	−0.66	−1.26***	0.18
Pseudo R²	0.07	0.13	0.10	0.07	0.05	0.04
Adj R²	0.06	0.13	0.09	0.06	0.04	0.03
S.E.R	0.00	0.00	0.00	0.00	0.00	0.00
Symmetric test
t-stat	1.10	2.90***	2.30**	1.94*	5.32***	0.04
F-stat	1.21	8.39***	5.30**	3.76*	28.31***	0.00
χ2-stat	1.21	8.39***	5.30**	3.76*	28.31***	0.00
Conclusion	Yes	No	No	No	No	Yes
The Philippines
C	0.00***	0.00***	0.00***	0.00***	0.00***	0.00***
π+	0.10***	0.07**	0.09***	0.11***	0.10***	0.07**
π−	−0.57***	−0.07	−0.49***	−0.42***	−0.76	−0.92**
Pseudo R²	0.11	0.05	0.04	0.06	0.07	0.09
Adj R²	0.11	0.04	0.03	0.05	0.06	0.08
S.E.R	0.00	0.00	0.00	0.00	0.00	0.00
Symmetric test
t-stat	4.84***	0.43	4.91***	3.89***	1.14	2.09**
F-stat	23.40***	0.18	24.08***	15.14***	1.31	4.37**
χ2-stat	23.40***	0.18	24.08***	15.14***	1.31	4.37**
Conclusion	No	Yes	No	No	Yes	No

Notes: *, **, and *** denote significance at 10%, 5%, and 1% levels, respectively.

Table 6.

Wald Test for Slope Equality Across Quantiles.

Quantile	0.05	0.25	0.50	0.75	0.90
0.05	Indonesia	2.3158	1.7712	1.2110	2.6615
0.25	0.8579	–	1.4976	0.2198	1.1811
0.50	0.9893	0.4076	–	0.3429	2.8788
0.75	6.8576**	7.7394**	3.9283	–	0.9360
0.90	2.4529	3.0367	3.5687	26.5046***	The Philippines

Notes: ** and *** denote significance at 5% and 1% levels, respectively.

Those test results confirm the graphical analysis using the Kernel distribution function. The “twin peaks” of price level distribution, as presented in Figure 1, means that inflation tends to be also polarized into “twin peaks” at a different rate. Consequently, the size impact of inflation on the inflation uncertainty will be different following the variability of the data as indicated by the entropy index. Overall, these findings support the claim that the link between inflation and its uncertainty and inflation affects inflation uncertainty holds in varied ways, not only inter-quantiles but also intra-quantile.

The high inflation volatility in both countries is due to food inflation (Son, 2008). However, monetary policy in the Philippines does not influence food inflation; hence, there is a weakening transmission mechanism to the inflation uncertainty (Tuaño-Amador, 2013). Meanwhile, there is a strong spillover effect of food inflation on aggregate inflation, resulting in the monetary policy in Indonesia effectively affecting the inflation volatility (Pratikto & Ikhsan, 2016).

Furthermore, the higher inflation volatility in Indonesia is accompanied by the increase in administered price. The inflation rate in late 2005, for example, reached 8.7% on a quarterly basis since Indonesia was faced with increasing gasoline prices that affected production costs. The oil crisis at the beginning of 2008 also fueled inflation to a rather high average of 5.45% per quarter (Insukindro & Sahadewo, 2010). However, the high inflation volatility in both countries eventually decreased subsequent to the global slowdown set off by the financial crisis. During the COVID-19 outbreak period, the inflation volatility in the two countries was relatively flattening as the weakening aggregate demand and gradual economic recovery.

Overall, since Indonesia and the Philippines are still considered developing countries, the numerous institutional deficiencies and policy distortions in the economies will be an internal source of inflation instability. Those findings imply that the monetary authority in both countries should concern with inflation expectations in the medium term as one of the important policy-driven objectives to maintain price stability in the long run. The lack of controlling inflation expectation suggests that the overall inflationary impact of changes in food prices has been persistent, and the inflation uncertainty will be persistently high.

Conclusion and Policy Implication

This article aims to analyze the linkage effect between inflation and uncertainty in the case of Indonesia and the Philippines. We used nonparametric tests, comprising Kernel density function, entropy index, and parametric test, which is a quantile regression method. The first two procedures may capture the price level heterogeneity and characterize the full distribution of price level and hence inflation uncertainty. The results of quantile regression estimation indicate that inflation drives inflation uncertainty in favor of the Friedman–Ball hypothesis. The relation between average inflation and inflation uncertainty is positive and statistically significant.

We also found that the inflation coefficient has an upward linear pattern. The regression quantile process estimate is larger in the higher quantiles compared to the lower quantiles. The corresponding slope coefficient can be understood as an increasing effect of inflation on the inflation uncertainty, in relation to a particular inflation’s position on the inflation uncertainty distribution. Given the parameter heterogeneity, the quantile regression model is an interesting way to portray the change in inflation uncertainty. In such a case, the quantile regression model significantly contributes to the empirical evidence of the increasing effect of inflation on the higher inflation uncertainty along with the greater costs to be covered.

Finally, inflation affects inflation uncertainty differently across the types of inflation. For Indonesia, the quantile process estimates for the deflation state are significantly higher than for the inflation state. In the case of the Philippines, a linear increasing trend holds only in the deflation state. The quantile process estimates in the deflation state are slower compared to Indonesia. At this point, we conclude that deflation may produce higher uncertainty compared to inflation instability solely. Their effect on uncertainty may operate in non-linear and asymmetric manners. In other words, the different impact of inflation in the inflation uncertainty holds not only between quantiles but also within quantiles.

Overall, the adoption of an inflation-targeting policy both in Indonesia and the Philippines have already successfully managed the inflation rates. But the inflation-targeting policy in Indonesia, not in the Philippines, has not succeeded yet in controlling inflation uncertainty. Since Indonesia and the Philippines have low inflation rates relative to other emerging markets, our findings suggest that announcing higher inflation targets may be costly in terms of provoking higher inflation uncertainty. Those findings imply that controlling inflation uncertainty in both countries can be achieved if monetary policy is credible and independent in the frame of the inflation-targeting regime.

Footnotes

Declaration of Conflicting Interests

The author declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Haryo Kuncoro

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