Abstract. We examine convergence of prices among 35 Pakistani cities and also explore how location of cities affects the convergence. We have found that there is bilateral price-level convergence for only food group and speed of convergence is around 3 months. On the other hand, prices of non-food commodities have very low speed of adjustment with 20 months. As a result, the overall CPI basket (food and non-food combined) has a moderate speed of convergence â€“ 8 months. Moreover, relative prices have been found sensitive to locality as well as distance among them.

Keywords: Inflation, Price convergence, Law of one price, Relative price variability

JEL classification: E31, F49

I. INTRODUCTION

According to the law of one price (LOP), the efficient market arbitrage and trade will keep the prices of identical commodities same in two or more markets. However, the transport and transaction costs may prevent the LOP to hold. A number of studies have shown that the distance between the two markets has positive relationship with deviation from LOP (see for example Crucini and Shintani (2006)). Earlier, Engel and Rogers (1996) in their pioneer work on CPI data of US and Canadian cities, found both distance and borders matter for relative price variability and thus the law of one price. In case of Pakistan, however, the behaviour of relative prices across cities has not been studied yet except some similar work by two papers; one by Mohsin and Gilbert (2010) which estimates relative city price convergence in overall CPI during July 2001 to June 2008, and second by Akmal (2012) which explores the relationship between relative price variability and overall inflation in Pakistan using commodity groups.

This study undertakes a comprehensive examination of city-wise and commodity-wise data of consumer prices in order to explore the price convergence in Pakistani cities.

Mohsin and Gilbert (2010) estimated relative price convergence using CPI data of 35 Pakistani cities from July 2001 to June 2008. They considered Lahore and Karachi as numeraire cities and found speed of convergence, as measured by half-life, less than 5 months but it varies from 1.3 to 68 months in the case of individual cities. They used two techniques for estimating half- life: spatial GLS and OLS, and found that spatial GLS estimates are lower than OLS which shows importance of spatial correlations for the estimation of half-life. Their result also showed that average half-life of price shock in Lahore is less than that of Karachi.

Akmal (2012) explored the nature of relationship between relative price variability and inflation using monthly data of CPI (seasonally adjusted) on commodity groups from July 1986 to June 2011. He found a U-shape relationship between the two. He also found that threshold level of inflation in terms of RPV varies with general inflationary phases, i.e., in period of high inflation, the threshold inflation is also high and vice versa.

Parslay and Wei (1996), using quarterly price data of goods and services in 48 US cities, found much faster convergence of prices to purchasing power parity in case of US than typically found in cross-country data. They also found that tradable goods converge very fast to price parity with around 4 to 5 quarters half-life of the price gap compared with 15 quarters for services. Additionally, they also present evidence of non-linearities in the rate of convergence.

Cecchetti et al. (2002) studied the behaviour of price indices in major US cities by using panel econometric methods. They found relative price levels among cities mean revert at an exceptionally slow rate â€“ with a half- life of convergence about 9 years. Transportation costs, varying speeds of adjustments to large and small shocks, and presence of non-traded goods prices in the overall price index are given as explanation of slow rate of convergence.

The behaviour of prices in a cross-country set up has also been studied by Crucini and Shintani (2006). They examine the dynamics of commodity- wise real exchange rates using a panel of 270 prices taken from major cities of 63 countries and 258 prices taken from 13 US cities. They found an average commodity had a similar pattern of convergence in OECD, LDC and within US with about 1 year of half-life of deviations from the law of one price. The average non-traded good has a half-life higher than traded goods for the OECD, with lesser differences elsewhere.

In these studies, price level convergence across regions is tested jointly by using panel unit root tests, and most of the studies use benchmark or numeraire for calculating relative prices. However, Crucini and Shintani (2006) and Pesaran (2007) used a different technique which does not use arbitrary benchmark. In this study, we use Pesaran (2007) methodology.

The rest of the paper is organized as follows. Section II describes the data and methodology; section III presents the empirical result; and section IV concludes the paper.

II. DATA AND METHODOLOGY

We use item-wise and city-wise data of consumer price index (CPI) collected and disseminated by Pakistan Bureau of Statistics (PBS). PBS publishes two series of CPI: item-wise and city-wise price data of 374 individual commodities; and 92 indices of composite items at base year of 2000-01.1

The data set used in this study includes CPI indices of 92 composite commodities for 35 cities for period from July 2001 to June 2011. The list of cities is given in Table 1.

We undertake the analysis not only for a full sample of 92 commodities but also for its two sub-groups, viz., food group (including 40 items and having weight of 40.34 percent) and non-food group (including the remaining 52 items and weight of 59.66 percent).

We have used pair-wise approach developed by Pesaran (2007) to study the convergence analysis of relative prices across cities. Convergence requires prices to be co-integrated with a vector of the form (1, â€“1), i.e. the

difference between them,

â€¦ â€¦, N, should be stationary for all N (Nâ€“1)/2 possible relative prices in 35 cities. We have applied this test on 595 relative price pairs.

TABLE 1: List of Cities in CPI Basket (2000-01 Base) 01 Lahore 19 Karachi 02 Faisalabad 20 Hyderabad 03 Rawalpindi 21 Sukkur 04 Multan 22 Larkana 05 Gujranwala 23 Mirpur Khas...