Price convergence across regions in India

Empirical Economics (2008) 34:299–313DOI 10.1007/s00181-007-0123-8

O R I G I NA L PA P E R

Price convergence across regions in India

Samarjit Das · Kaushik Bhattacharya

Received: 15 February 2006 / Accepted: 15 September 2006 / Published online: 16 February 2007© Springer-Verlag 2007

Abstract The paper attempts to examine whether there is price convergenceacross various regions in India. Using panel unit root tests that are robust tocross-sectional dependence, it is found that relative price levels among variousregions in India are mean-reverting. Further, we decompose each series intoa set of common factors and idiosyncratic components. The decompositionenables us to test stationarity and estimate half-lives of the common factorsand the idiosyncratic components separately. Both these components are foundto be stationary. Idiosyncratic price shocks, however, are found to be morepersistent as compared to the common factor. Results also indicate that trans-portation cost proxied by distance can explain a part of the variation in pricesbetween two locations in India.

Keywords Cross co-integration · Cross-sectional dependence ·Panel unit root tests · Common factor · Price convergence

JEL Classification C23 · E31

The authors would like to thank Dibyendu Bhaumik for arranging the data for this study. Viewsexpresed in the paper are personal and do not reflect the views of the organizations.

S. Das (B)Economic Research Unit, Indian Statistical Institute,203 B.T. Road, Kolkata 700108, Indiae-mail: [email protected]

K. BhattacharyaReserve Bank of India, Mumbai, India

300 S. Das, K. Bhattacharya

1 Introduction

The issue of price convergence across regions within a single economy has recei-ved increasing attention in recent literature. A high dispersion value of inflationacross regions and its persistence over time may have serious implications onregional wage rates and standard of living. It also poses concern regarding allo-cation of resources. The existence of large systematic price divergence despitea common currency and no implicit or explicit restrictions on factor mobilitymay, therefore, indicate market segmentation, and its eradication is, therefore,a challenge to policymakers.

The studies on regional price convergence provide a benchmark by testingthe law of one price under more controlled conditions, as problems due tofluctuations in exchange rate or factor market rigidities are eliminated. Priceconvergence in these studies could be examined by testing the existence of unitroot in the regional price relatives. Insofar as earlier attempts towards univariatetests are concerned, it is well known that for series with short span and nearunit root situations, these tests suffer from power deficiency. Increasing the timeseries length may, in fact, compound the problem as chances of structural breakincrease, leading to further loss of power. Recent literature, therefore, suggeststesting stationarity jointly by conducting panel unit root tests on the regionalprice relatives. Some such applications are due to Parsley and Wei (1996) andCecchetti et al. (1998, 2002) for the US, Ceglowski (2003) for Canada, Engeland Rogers (1996) for both the US and Canada, Menna (2001) for Italy andFan and Wei (2003) for China.

In this study, we examine price convergence across regions in India. Commonsense suggests that due to a single currency, near-free factor movements andpolicies adopted by the central authority, prices in different regions in Indiawould be contemporaneously correlated. At the same time, it is also plausiblethat due to its large size, different agro-climatic and economic conditions andfederal structure of governance, prices would also be affected by local shocks.We stress that a recognition of this dichotomy has important implications onpanel unit root testing and hence, on the existing findings on regional priceconvergence. Recent studies by O’Connell (1998) and Breitung and Das (2005)have highlighted that, in the presence of contemporaneous correlation, standardpanel unit root tests like those proposed by Maddala and Wu (1999), Levin et al.(2002) and Im et al. (2003) may suffer from oversize problem. Another problemwith these tests is the possibility of the presence of cross cointegration, i.e., thesituation where individual series are non-stationary but have a common trend.In these cases, Banerjee et al. (2004) have shown that these tests are oversized.

A major implication of incorporating contemporaneous cross-sectionaldependence in a panel framework is that any series in that framework maybe decomposed into a number of common factors, besides the series specificidiosyncratic term. Econometrically, this decomposition serves three purposes.First, it provides a framework to test for non-stationarity separately for commonfactors and idiosyncratic components. Separate tests for them are meaningfulbecause the common factors and idiosyncratic components may have different

Price convergence across regions in India 301

orders of integration, and it is well known that if a series is the sum of a non-stationary and a stationary series, it is difficult to establish the presence ofunit root in the summed one (Pantula 1991; Bai and Ng 2004). In such situa-tions, it is desirable to test unit root hypothesis separately (Bai and Ng 2004).Non-stationarities in the common factors, in fact, provide a parsimonious wayof identifying common trends in the series without specifying a cointegratingVAR model. If, in addition, the idiosyncratic terms are found to be stationary,the series are then interpreted as being cross cointegrated (Bai and Ng 2004).Second, factor models capture the extent of dependence across cross-sectionalunits and one should use tests that are robust to such dependence. Third, thedecomposition also enables one to examine the speeds of convergence of thecommon factors and the series specific local shocks separately. This is impor-tant for policy as well because if the idiosyncratic shocks are dominant, primaryresponsibility of control of inflation rests with the local governments, ofteninvolving the management of local supplies alone. In contrast, predominanceof common shocks reflects that inflation should be a concern for the centralauthority.

To the best of our knowledge, no empirical work on regional price conver-gence so far has focussed on the decomposition of data into factors and idio-syncratic components, exploited the strength of separate unit root tests, andfinally conducted tests on convergence hypothesis. Existing studies have alsonot taken into account the possibilities of cross cointegration and its econome-tric implications. In this paper, we attempt to examine to what extent pricesin different places in India are affected due to common or local shocks, usingpanel unit root tests under both ‘weak’ and ‘strong’ cross-sectional dependence,as formalised in Breitung and Das (2006). We also attempt to analyse to whatextent transportation costs (proxied by distance or its monotonic functions)could explain deviations in inflation across regions in India.

The plan of the paper is as follows: Sect. 2 presents a brief discussion onthe methodology. Section 3 describes the data and the results of a preliminaryanalysis. The empirical results on decomposition of prices into factors andidiosyncratic components are presented in the next section. Section 5 attemptsto find out the impact of distance on price deviations among pairs of regions.Finally, Sect. 6 summarizes the findings with some concluding observations.

2 Econometric methodology

To test cross-sectional dependence, we use Lagrange multiplier (LM) type testsas proposed by Breusch and Pagan (1980). A simple modified Lagrange multi-plier (MLM) test as suggested by Pesaran (2004) is also considered as it is moreappropriate in our context.

Cross-sectional dependence may be ‘weak’ or ‘strong’ depending upon thenature of the eigenvalues of the error variance covariance matrix. As discussedin Breitung and Das (2006), ‘weak’ dependence means all the eigenvalues ofthe error covariance matrix are bounded (‘weak’) even for large N (N being the


number of cross sectional units), whereas ‘strong’ dependence implies and isimplied by the presence of unbounded eigenvalues. Under strong dependence,each series may be decomposed into two components, viz. (i) a few commonfactors and (ii) the idiosyncratic term (Forni et al. 2000).

Under weak cross-sectional dependence, our discusions are confined to fourstatistics discussed in Chang (2002, 2004), and Breitung and Das (2005). Consi-der the data generating process

�yit = µi + φyi,t−1 +pi∑

j=1

νij�yi,t−j + εit (1)

where the starting values yi0 · · · yi,−pi are set equal to zero. To take care ofautocorrelations, Eq. (1) includes the term

∑pij=1 νij�yi,t−j. Individual specific

intercepts µi have also been included because series means are generally notzeroes. The error vector εt = [ε1t, . . . , εNt]′ is i.i.d. with E(εt) = 0 and E(εtε

′t) =

�, where � may not necessarily be a diagonal matrix.The null hypothesis is

H0 : φ = 0 ,

that is, all time series are random walks. Under the alternative, it is assumedthat all the time series are stationary with φ < 0.1 Testing the hypothesis ofprice convergence typically involves conducting unit root tests for the log-ratio of regional prices to that of a common numeraire. If the unit root nullhypothesis is rejected, then this ratio is mean reverting and any deviations fromthe numeraire should diminish over time suggesting deviation from ‘one price’is temporary and hence one may conclude that ‘law of one price’ holds. Incontrast, if the unit root tests fail to reject the null hypothesis, then the evidencesuggests that these ratios follow random paths and hence the deviation fromthe numeraire becomes permanent rejecting ’law of one price’ theory.2

Chang (2002) proposed a nonlinear instrumental variable (IV) approach andshowed that the usual individual OLS t statistics are asymptotically independenteven in the presence of cross sectional dependence. Thus, the actual test sta-tistic is simply defined as a standardized sum of individual IV t ratios and itasymptotically follows N(0, 1) under H0.

Another method developed by Chang (2004) is the bootstrap method whichtakes care of the oversize problem involved in the standard OLS or GLS tstatistics. In this method, one estimates Eq. (1), resamples the residual vectorsand uses them to generate pseudo observations. The OLS or GLS t statisticsare calculated based on this pseudo observations. Collection of these t statisticsform the bootstrap distribution under H0.

1 Some tests are applicable with hetergeneous and more general alternatives.2 As we have allowed the possibility of non-zero intercepts in Eq. 1, the convergence may beconsidered as conditional one as opposed to absolute convergence (see Evans and Karras 1996).


The third method that also works even when N is greater than T, the totalnumber of time series observations, is the one proposed by Breitung and Das(2005). As the OLS standard error is biased under cross-sectional dependence,Breitung and Das (2005) have used modified standard error that is robust tocross-sectional dependence and showed that under H0 the test statistic trobfollows N(0, 1). We call these four statistics as IV (tiv), OLS based bootstrap t(t∗ols), GLS based bootstrap t (t∗gls) and the robust test statistic (trob), respectively.

However, as shown by Breitung and Das (2006), the above tests may not beappropriate in the presence of strong dependence. The first problem in factormodels is to determine the number of factors (k). Factors are estimated usingprincipal components. In this paper, we follow the procedures developed byBai and Ng (2002), e.g., we use three PCp criteria and three ICp criteria. Afterestimating factors, one can apply standard univariate unit root test to each ofthe factors to gauge stationarity/non-stationarity of factors or do a joint test assuggested by Bai and Ng (2004). Each factor, as estimated by principal com-ponent follows standard Dickey–Fuller test under the null hypothesis of unitroot (Bai and Ng 2004). Similarly, we can test for stationarity of idiosyncraticerrors using panel approach. Moon and Perron (2004) have developed panelunit root test based on idiosyncratic errors after removing the factors from thedata. Further, Breitung and Das (2006) have shown that the robust test followsthe standard Dickey–Fuller test under the null hypothesis of unit root whencross-sectional dependence is strong, i.e., when there is a factor.

Here it is emphasised that common factors (i.e., common trends) are thebinding force for the series to move together. Hence, under factor models,convergence may take place in two ways. First, when both factors and idiosyn-cratic errors are stationary, and the other when there is cross cointegration.

3 Data and descriptive analysis

Our empirical study on the Indian economy has been carried out with thedata on monthly consumer price indices for industrial workers (CPIIW). Thetime frame considered in this study is from January 1995 to June 2004, i.e.,the span of 114 months. Choice of this period is somewhat conscious to limit thepossibilities of structural breaks in the series. The data on CPIIW are collectedby the Indian Labour Bureau (ILB) from 76 different cities/towns or regions,which appear to be more or less uniformly distributed across 24 states or unionterritories (UTs) in India. The large number of centres available enables one toobserve the spatial distribution of the prices clearly. As the distances betweenpairs of centres vary over a wide range- from about 10 km between Kolkataand Howrah to more than 2,000 km between Ahmedabad and Guwahati, thepairwise distance has been used to explain variations in regional price relatives.The details on coverages, weighting scheme of CPIIW and locations of centrealong with their respective latitudes and longitudes are available in Das andBhattacharya (2005).


-2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.50.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

Fig. 1 Kernel density of the annual average deviation of regional inflation rates from the all-Indiaaverage (between January 1995 and June 2004)

The long-run cross-sectional variation in regional inflation in India could beseen in Fig. 1. In Fig. 1, we plot the estimated kernel density (Epanechnikovkernel, bandwidth = 0.40) of the annual average deviations of the regional in-flation rates from the All-India average between January 1995 and June 2004.Figure 1 reveals a range of about 3.0 percentage points in the rates of inflationexperienced by different regions in India, compared to a range of about 1.13percentage point in case of US.3

The descriptive statistics relating to annual inflation rates for different yearsare presented in Table 1. Table 1 reveals a fall in inflation rates from the year2000 due to improvements in the general macroeconomic environment in India.However, it also reveals that the range over which regional inflation rates varycould be as high as about 20.0 percentage points in a single year, as in 1998.Moments of higher order in Table 1 reveal that the skewness changes signfrequently. Further, the distributions tend to be slightly leptokurtic for most ofthe years.

The observed kurtosis could be due to two possibilities, viz., large local priceshocks in a few places or measurement errors. Table 2 examines this aspectfurther. In Table 2, we identify five lowest and five highest centres in eachyear with respect to inflation rate. There are three numbers correspondingto each centre in Table 2. The first is the rate of inflation in that particularcentre for the corresponding year. The second number is the rate of inflationin its ‘neighbourhood. The ‘neighbourhood’ is defined in this study as the 10th percentile of the distribution of the distances for the 2,850 pairs of centres

3 In case of US, earlier periods reveal a range of about 1.55 percentage points (Cecchetti et al.1998).


Table 1 Descriptive statistics relating to annual rates of inflation across centres

1996 1997 1998 1999 2000 2001 2002 2003 2004

Mean 9.2 6.7 13.4 5.1 3.4 3.5 3.9 3.7 3.3Median 9.0 6.8 13.4 5.0 3.6 3.6 3.7 3.8 3.5SD 2.2 2.2 3.7 2.4 2.4 2.4 2.1 1.6 2.1Skewness 1.6 −0.1 −0.3 0.8 −0.2 0.4 0.6 0.1 −1.0Kurtosis 6.5 2.0 0.8 1.4 −0.5 0.4 0.1 −0.6 2.0Minimum 5.3 −1.4 0.9 0.6 −2.9 −1.7 −0.4 0.7 −4.4Maximum 19.9 12.4 21.7 13.9 7.9 10.6 9.3 7.3 7.9

For the year 2004, rate of inflation is computed based on average CPI’s from January to June ofthat year

Table 2 Centres that experienced lowest or highest inflation

Year Centres with lowest inflation Centres with highest inflation

1996 Saharanpur (5.3,7.6,9), Ludhiana (5.7,7.5,8),Srinagar (5.7,7.3,1), Delhi (5.9,7.9,9),Tripura (6.6,9.0,5)

Pondichery (12.5,9.0,8), Gudur (12.7,9.1,6),Mundakayam (12.9,9.8,9), Jamshedpur(14.4,9.4,13), Rajkot (19.9,7.3,4)

1997 Rajkot (−1.4,4.9,4), Tinsukia (3.4,4.8,3),Indore (3.5,5.3,8), Barbil (3.6,6.5,12),Solapur (4.0,8.4,7)

Pondichery (10.6,7.4,8), Mercara(10.6,7.4,7), Tiruchirapally (11.3,7.5,11),Goa (11.5,6.7,4), Rourkela (12.4,6.0,9)

1998 Quilon (0.9,8.4,8), Tiruchirapally(7.2,8.0,11), Coonor (7.2,8.1,11), Bangalore(8.2,9.6,10), Salem (8.3,8.8,12)

Faridabad (18.9,15.1,9), Srinagar(19.3,16.2,1), Howrah (20.8,14.6,11), Vara-nasi (21.4,14.5,6), Jalpaiguri (21.7,15.6,6)

1999 Jaipur (0.6,5.4,6), Pondichery (0.6,4.7,8),Kethgudem (1.1,4.9,4), Noamundi(1.6,5.3,14), Rourkela (1.6,4.2,9)

Thiruvanthapuram (8.9,5.4,7), Monghyr(9.4,4.3,12), Howrah (9.7,4.3,11), Chandi-garh (11.3,4.7,8), Srinagar (13.9,3.7,1)

2000 Kodarma (−2.9,2.0,12), Varanasi(−1.3,0.2,6), Lalbac-Silchar (−1.1,1.4,8),Tezpur (−0.9,2.0,4), Darjeeling (−0.3,0.8,3)

Delhi (7.1,3.3,9), Coimbatore (7.6,4.1,11),Nasik (7.6,5.0,8), Goa (7.8,3.4,4), Mumbai(7.9,4.9,5)

2001 Mariani-Jorhat (−1.7,1.3,3), D.D.Tinsukia (−1.2,1.1,3), Mundakayam(−0.4,1.8,9), Mercara (−0.4,2.5,7),Monghyr (−0.1,3.2,12)

Durgapur (7.8,3.6,14), Bhopal (8.2,4.4,5),Srinagar (8.4,3.9,1), Kolkata (9.2,4.3,11),Haldia (9.3,4.7,9)

2002 Tezpur (−0.4,2.1,4), Noamundi (0.2,4.2,14),Mariani-Jorhat (0.2,1.7,3), Mercara(0.4,4.8,7), Lalbac-Silchar (0.8,2.1,8)

Kolkata (7.8,4.0,11), Guntur (7.9,5.3,6),Durgapur (8.8,3.9,14), Tiruchirapally(6.6,5.2,11), Quillon (7.3,4.5,8)

2003 Tripura (0.7,2.3,5), Vadodara (0.7,2.9,7),Jalpaiguri (0.9,3.8,6), Surat (1.0,3.3,8),Ranchi-Hatia (1.2,3.6,14)

Bhilai (6.2,3.2,4), Pondichery (6.5,4.8,8),Guntur (6.6,4.4,6), Tiruchirapally(6.6,4.8,11), Quillon (7.3,4.5,8)

2004 Tiruchirapally (−4.4,2.2,11), Surat(−2.1,2.2,8), Kethgudem (−1.5,1.7,4),Warangal (−0.9,0.9,3), Rajkot (−0.1,1.0,4)

Jharia (6.3,4.7,13), Faridabad (6.4,3.8,9),Raniganj (6.7,4.4,12), Solapur (6.7,3.7,7),Lalbac-Silchar (7.9,4.7,8)

For the year 2004, rate of inflation is computed based on average CPI’s from January to June

in our data. The second number is the simple arithmetic mean of the rates ofinflation of the centres in the neighbourhood. The third, an integer, refers tothe number of such centres in the ‘neighbourhood’.

It is expected that if the price rise (fall) is due to genuine economic factors,the rate of inflation in the neighbouring centres would reflect similar patterns.


Thus, the closeness of the first two numbers corresponding to each centre eachyear could be viewed as a cross-validation of the existence of local price shocks.In Table 2, there are several such clusters. In a few cases (e.g., Rajkot in theyear, Quilon in the year 1998 , etc.), however, the regional inflation rates appearto be outliers, implying that the possibility of measurement errors in data cannot be completely ruled out.

4 Empirical results

As contemporaneous cross-sectional dependence is a major problem with panelunit root tests, we first apply LM and MLM tests that could indicate its presenceor otherwise in the data. In this paper, we have worked with the log-ratio ofregional prices to that of all India averages. However, to check robustness ofthe numeraire, we have also considered Nagpur prices as numeraire.4 It maybe noted that specifying a numeraire causes cross sectional dependence byconstruction.5 However, despite this limitations, using log-ratio is a commonpractice because the measure has the important interpretation of regional pricerelatives. The rejection of the unit root null hypothesis has the natural inter-pretation of mean reverting of the log ratio and hence any deviations fromthe numeraire should be temporary in nature implying price convergence withrespect to the numeraire. Similar agrument is not conceivable for level series.Furthermore, policy makers would be more interested whether these pricerelatives converge or not rather than levels.

For empirical analysis, the data for different centres have also been pre-whitened to remove traces of serial correlation present in it. To do that, anAR(12) filter has been applied to all the series after some preliminary analysisand appears to be reasonable, given that we have monthly data.

Results on both the LM and MLM tests in Table 3 clearly establish thepresence of contemporaneous cross-sectional dependence. This conclusion doesnot change whether we consider centres as units or aggregate the centres tohave state specific CPIIWs or separately apply the tests to states that have atleast 4 centres. In fact, the results remain same when (i) Nagpur is specifiedas the numeraire or (ii) the tests are applied to smaller group of panels (withN = 5, 10, 15, 20) where the units are randomly chosen. This finding suggestsuse of panel unit root tests which are robust to cross-sectional dependence.Therefore, in this study, we have not considered tests that are based on cross-sectional independence, like those proposed by Maddala and Wu (1999), Levinet al. (2002) and Im et al. (2003).

Table 3 also summarizes the results of panel unit roots tests undercross-sectional dependence. These tests implicitly assume that cross-sectional

4 Nagpur is chosen as a numeraire because it is located near the centre of India.5 We are grateful to one of the anonymous referees for this observation. We have checked crosssectional dependence for the level variables as well. We found even stronger cross sectional depen-dence in most of the cases.


Table 3 Panel unit root tests and cross-sectional dependence tests

Region t∗ols t∗gls trob tiv LM MLM Estim-atedhalf-life

Andhra Pradesh (N = 6) −4.44 −3.56 −4.13 −4.21 67.33 9.55 11.00(−1.80) (−1.93) (−1.65) (−1.65) (7.26) (1.96)

Assam (N = 5) −2.38 −2.70 −1.98 −2.72 179.30 37.85 43.80(−2.08) (−1.60) (−1.65) (−1.65) (3.94) (1.96)

Gujarat (N = 5) −2.88 −4.01 −2.48 −4.19 76.40 14.84 12.46(−1.93) (−1.90) (−1.65) (−1.65) (3.94) (1.96)

Jharkhand (N = 5) −3.32 −3.51 −2.89 −3.09 54.21 9.88 14.21(−1.77) (−1.91) (−1.65) (−1.65) (3.94) (1.96)

Karnataka (N = 4) −3.04 −2.35 −2.97 −2.25 69.33 18.21 17.56(−1.97) (−1.84) (−1.65) (−1.65) (1.63) (1.96)

Kerala (N = 4) −4.50 −4.73 −3.95 −4.79 90.53 24.40 06.77(−1.91) (−1.75) (−1.65) (−1.65) (1.63) (1.96)

Madhya Pradesh (N = 5) −1.64 −1.81 −1.85 −0.98 47.81 5.99 –(−1.78) (−1.89) (−1.65) (−1.65) (3.94) (1.96)

Maharashtra (N = 5) −4.68 −4.30 −4.25 − 4.30 35.22 5.64 8.90(−2.00) (−1.90) (−1.65) (−1.65) (3.94) (1.96)

Tamil Nadu (N = 6) −2.83 −3.38 −2.07 −3.87 243.78 41.78 18.90(−1.80) (−1.93) (−1.65) (−1.65) (7.26) (1.96)

Uttar Pradesh (N = 5) −2.57 −2.59 −2.57 −2.67 247.25 53.05 25.80(−2.11) (−1.90) (−1.65) (−1.65) (3.94) (1.96)

West Bengal (N = 8) −2.67 −3.30 −2.01 −2.58 340.12 41.72 26.94(−2.10) (−1.97) (−1.65) (−1.65) (16.92) (1.96)

All states (N = 24) −5.23 −4.24 −4.12 −6.11 1402.07 47.92 18.85(−2.08) (−1.81) (−1.65) (−1.65) (238.52) (1.96)

All centres (N = 76) −10.22 −6.26 −6.18 −11.32 9561.09 91.09 19.83(−2.64) (−1.29) (−1.65) (−1.65) (1152.74) (1.96)

t∗ols, trob, t∗gls and tiv Denote the t statistics corresponding to bootstrap-OLS, robust-OLS, bootstrap-

GLS and Chang’s (2002) instrumental variable method, respectively. The LM and MLM statisticsare presented for testing cross sectional dependence; 5% critical values are given in parenthesisbelow the test statistic values. Half-lives are presented in months. Tests corresponding to MadhyaPradesh (MP) suggest possible presence of unit root. Hence, we have not reported half life estimatefor MP

dependence is of arbitrary form and ‘weak’ in nature. For all these tests, in-dividual specific intercepts are incorporated. For robust test, first observationhas been subtracted from all observations to take into account individual spe-cific intercepts (Breitung and Das 2005). For bootstrap based tests, we haveconsidered 5,000 bootstrap replication.

For centre wise data, Table 3 suggests that unit root null hypothesis is rejectedby all tests. In other words, all tests suggest that the regional prices (relative toa common numeraire) are jointly stationary, implying that shocks to regionalrelative prices do not drive them away from the average All India prices. Inother words, all tests strongly support price convergence. This finding does notchange when centre-specific CPIIW’s are aggregated to state level, (i.e., whenstates are considered as cross-sectional units with N = 24, instead of regionswith N = 76).


Table 4 Selection criteria for the number of factors for centres (N = 76)

R PCp1 PCp2 PCp3 ICp1 ICp2 ICp3

1 16434.4 16606.9 16023.2 9.7 9.7 9.72 28058.3 28604.5 26756.3 10.3 10.3 10.23 70501.7 72420.7 65927.7 11.2 11.2 11.14 97887.8 101214.6 89958.4 11.5 11.6 11.45 89871.0 93460.7 81314.9 11.5 11.5 11.36 111952.6 117016.0 99883.8 11.7 11.8 11.67 101667.5 106745.7 89563.4 11.7 11.7 11.58 98313.3 103641.1 85614.3 11.7 11.7 11.49 87067.2 92119.3 75025.4 11.6 11.7 11.3

10 110570.3 117371.0 94360.6 11.8 12.0 11.6

R denotes the possible number of factors. PCpi’s and ICpi’s are the selection criteria as suggestedby Bai and Ng (2002)

When we carry out similar tests for states that have at least four centres toexamine price convergence within a state, all states except Madhya Pradeshindicate price convergence unambiguously. The evidence in case of MadhyaPradesh is mixed. Though the precise reason of non-rejection of unit rootby some tests for Madhya Pradesh is difficult to identify, it may be noted thatMadhya Pradesh is one of the largest and backward states in India. It is plausiblethat the large size of this state coupled with poor management of local shockshave led to market segmentation within the state. Panel unit root tests actuallytest joint stationarity. Therefore, it is not surprising that in a large panel, erraticprice behaviour of a few centres do not change results of panel unit root testssignificantly. Our results thus highlight that further examinations at micro-levelare perhaps necessary to identify erratic price movements within specific areasin India. Interestingly, panel unit root tests like those by Levin et al. (2002)and Im et al. (2003) which ignore cross-sectional dependence, suggest priceconvergence in Madhya Pradesh, as probability of rejection of a unit root ishigh in these tests.6

The possible presence of common factors may provide a different conclu-sion. Therefore, we need to decompose the data into factors and idiosyncraticcomponents. We have considered all six criteria of Bai and Ng (2002) to selectoptimal number of factors, searching for over 10 possible factors. The valuesof the criteria corresponding to centres (N = 76)are presented in Table 4.7

Interestingly all six criteria uniformly suggest presence of only one factor, irres-pective of whether the tests are applied to centres (N = 76) or aggregated tostates (N = 24). As the number of factors is only one and the number of idio-syncratic error terms is relatively quite large, it is likely that idiosyncratic errorswill dominate the test performance. Therefore, separate tests for the commonfactor as well as idiosyncratic errors are quite appropriate here. To that end, we

6 The value of the test statistic for Levin et al. (2002) is −1.79 and for Im et al. (2003), −2.08.7 Results corresponding to states are similar and are not presented here.


Table 5 Results of various panel unit root tests under common factor

Region DDF trob MP Half-life of common factor Half-life of localshock

Centre (N = 76) −2.54 −6.18 −10.08 8.14 22.89State (N = 24) −2.16 −4.12 −6.48 9.20 16.85Critical value −1.945 −1.945 −1.645 — —

DDF, trob and MP denote the t statistics corresponding to direct Dickey–Fuller tests based onestimated principal component, Robust-OLS and Moon-Perron (2002) methods, respectively. Forall three tests, the nominal size is 0.05, Half-lives are presented in months

present Moon-Perron (2003) (MP) test and direct Dickey–Fuller (DDF) teston the estimated factor and the robust test as developed by Breitung and Das(2006) on the series as a whole.

Table 5 summarizes panel unit roots tests under common factor structure.All three tests uniformly suggest price convergence across regions/states whenthe series are bifurcated into common factors and idiosyncratic components.

The extent of persistence of shocks may be observed from the estimated half-lives in Tables 3 and 5.8 Table 3 reveals that estimated half lives for differentStates vary over a wide range. One plausible explanation for this phenomenon ismarket segmentation. However, in our case, the price series in different regionsalso contain non-tradables in differential proportions. Studies have found thatestimated half-lives of convergence in non-tradables tend to be more thanthat of tradables. For example, in the case of US economy, Parsley and Wei(1996) have found that the median rates of convergence for perishables, non-perishables and services are four, five and fifteen quarters, respectively. Similarfindings have also been obtained by Menna (2001) for Italy. It is plausible thatin case of India the differential impact of non-tradables have led to the variedrange of estimated half-lives pertaining to the states.

In Table 5, while half lives of shocks to the common factor is estimated as 8.14and 9.20 months for regional and state-specific data, respectively, the corres-ponding figures are 22.89 and 16.85 months for the idiosyncratic components.One possible reason for such differences of estimated half-lives between thecommon factor and the idiosyncratic components may be due to the presence ofnon-tradables in aggregate CPIIW, which are expected to have more impact onidiosyncratic errors.9 Another possibility is persistence in wage at the regionallevel and its implicit or explicit indexation to regional prices. The difference inspeeds of convergence between the common factor and the idiosyncratic errorscould also be explained in policy terms as well. A rise in the common factorleads to an all-around increase in prices in India and immediately raises policyconcerns. In contrast, reaction times to local shocks might not be as fast due

8 All half-lives in this paper are adjusted for ‘Nickell Bias’ of first order assuming an AR(1) process.9 Lack of availability of detailed commoditywise regional data on prices constrained us to examinethis in further detail.


to lack of sufficient media attention and in case of India, may as well indicatemarket segmentation at the micro-level.

It may be noted that we have not presented any result on half-lives of commonfactors and idiosyncratic components within specific states. This is because thenumber of cross-sectional units that are required to estimate factors is quitelarge and given that the maximum number of centres within a state is onlyeight (for West Bengal) in our case, such applications are not possible. Wehave, however, repeated the exercise with Nagpur as the common numeraireinstead of all India average, and the overall results (not reported here) remainunchanged.

5 The impact of distance on price deviations

Prices in two different regions could be different due to transportation costs. Inthe literature, Engel (1993), Engel and Rogers (1996), Parsley and Wei (1996),Cecchetti et al. (1998) and Menna (2001) have all used regression framework fortheir analysis in which a measure of regional price differential is explained bysome measure of “distance” between the regions. These regressions are oftencarried out with respect to a specific city or region that acts as a numeraire(Cecchetti et al. 1998; Menna 2001) Thus, data on N cities typically lead to(N − 1) observations in a cross-sectional regression. The impact of distance onthe prices of a city pair (i, j) is ignored, unless one of them is the numeraire city.

In this study, we have considered an alternative approach. For any specificmeasure, we find its values for all possible pairs of regions and regress it on mea-sures relating to distance between the pair. This approach lead to an increasein the number of observations in our case dramatically to 76C2, i.e., 2,850.

Insofar as the dependent variable is concerned, we consider two measures inthis study. The first, INFCORR, attempts to measure the correlations of monthlyrate of inflations between two cities. The second, INFGAP, is the deviationbetween the average annual rate of inflation between two cities during thesampled period. Thus, the first and the second variable, respectively, attemptsto measure short and long-run variations in prices. As explanatory variables,we consider four standard alternatives in the literature, viz., distance, square ofdistance, log of distance and double log of distance (Engel and Rogers 1996;Cecchetti et al. 1998). Approximations of distance between pairs of cities havebeen obtained from the latitudes and the longitudes (Das and Bhattacharya2005).

Results reporting different regressions are presented in Table 6. Table 6reveals that the short-run movements in prices are more similar in nearby areas.In all regressions in which INFCORR is a dependent variable, the explanatoryvariables are significant, with a negative sign. Among different regressions, theone with DISTANCE as an explanatory variable performs the best in terms ofR2. The impact of distance on long-run price deviations, however, appears to besmall. In all regressions involving INFGAP, though explanatory variables aresignificant and have the expected sign, the fit in terms of R2 is not good. Taken


Table 6 Regression results of impact of distance on regional price deviations

Dependent Intercept Distance Square of distance Log of Double-log R2

variable distance of distance

INFCORR 0.4550 −0.0101 0.1138(71.0) (−19.1)

INFCORR 0.4070 −0.0004 0.1070(92.0) (−18.5)

INFCORR 0.4963 −0.0687 0.0888(52.3) (−16.7)

INFCORR 0.4065 −0.0850 0.0624(75.3) (−13.7)

INFGAP 0.6912 0.0075 0.0049(29.3) (3.88)

INFGAP 0.7204 0.0004 0.0061(44.4) (4.31)

INFGAP 0.6507 0.0557 0.0045(18.9) (3.72)

INFGAP 0.7372 0.0524 0.0016(38.0) (2.35)

The numbers in parenthesis are t ratios

together, the results indicate that transportation costs can explain only a smallpart of the variation in prices between two locations.

6 Conclusion

The paper has made an attempt to examine whether there is price convergenceacross various regions in India. The results indicate significant presence ofcontemporaneous cross-sectional dependence in prices in India, rendering someof the earlier and more traditional panel unit root tests inapplicable. Usingvarious panel unit root tests that are robust to cross-sectional dependence,evidences in favour of mean reversion of regional relative price levels havebeen obtained. The evidence appear to be similar when tests are restricted tospecific parts of India, as well as when the number of cross-sectional units areaggregated to reflect state specific measures. A decomposition of each seriesinto a set of common factors and idiosyncratic component has revealed theexistence of only one common factor in case of India. The decomposition hasalso enabled us to test stationarity and estimate half lives of the common factorand the idiosyncratic component separately. Both these components in caseof India have been found to be stationary. Local price shocks have, however,been found to be more persistent as compared to the common factor. Furtheranalysis indicates that proportional transportation cost could perhaps explaina part of the variation in prices between two locations, limiting thereby thepossibilities of unexploited arbitrage opportunities.

The paper ends with two comments. First, both the central and stategovernment’s influence on wage movements in India is substantial. Given the


dominance of the public sector in the organized segment of the Indian economy,wage movements in the private sector are naturally influenced by those in thepublic sector. So far as prices are concerned, indexation of wages for large sec-tions of public sector employees could indeed be a reason behind persistenceof local shocks.10 Unfortunately, reliable panel data on wages are not easilyavailable in India so that the wage-price causality and other related problemscould be tested rigorously. Second, in this paper we have worked with the ag-gregate CPIIW series that also contains non-tradables. As it is well known thatprices of non-tradables tend to be more dispersed across regions, it is likely thata restriction to tradable commodities alone would yield stronger evidence infavour of price convergence. An interesting future research work would be toexamine these problems in further detail.

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