state‐level value chains, which increases the competitiveness (reduces the price) of the final good. A more recent study using detailed GPS data for Indian trucks before and after the implementation of the GST shows that internal borders in India reduce the driving speed of trucks by around 3km per hour. The implementation of the GST is shown to have increased driving speed at the border by 1% (Krishna and Van Leemput, 2018a).

## Dispersion over time

Spatial price dispersion has fallen over time in wholesale markets, but not in retail markets. Coefficients of variation for retail prices across spatially separated locations have _not_ been decreasing over time, for the period analyzed.<sup>5</sup> On the contrary, when pooling all commodities, price dispersion has increased at a low rate of half a percent from 2006 to 2014. The coefficient of variation varies by commodity. Increases in dispersion are significant for bananas, coconut oil, split and whole grams and rice. It is only for mustard oil where price dispersion has fallen. For the rest, the trend is not significant (see Appendix, Figure 26).

At the wholesale level, price dispersion has been decreasing at a rate of a third of a percentage point per year. Dispersion in potato and wheat wholesale prices has been on the rise, while for all other products, dispersion has fallen – in the case of onions and paddy, dispersion has fallen at a rate of 1 percent per year (see Appendix, Figure 27).<sup>6</sup> To what extent are these patterns of price dispersion associated with the way price shocks are transmitted across Indian districts or cities? To what extent are they associated with the way international price shocks are transmitted? The following subsection focuses on these questions.

# Patterns of price transmission and market integration

Price differences across spatially separated locations are in part related to different patterns of price transmission. To examine patterns of price transmission we focus on three characteristics: the completeness of transmission of shocks in the long run, measured by the pass‐through; the speed with which shocks transmit, measured by the speed of adjustment parameter; and the extent to which transmission is symmetric when comparing shocks that imply price increases and those that imply price reductions. For the analyzed products, transmission of price shocks is found to be incomplete (the law of one price is generally rejected), heterogeneous by region and product both in terms of speed and in terms of completeness, although symmetric upwards and downwards, with strong co‐ movement of prices both within India and between India and international markets.

## Methodology

The first requirement to assess market integration is to have an operative definition of integration. In this paper, spatially separated markets are considered to be integrated when they are connected by trade in such a way that the forces of arbitrage make the long‐run price differences that remain among them reflect transport costs. This means that shocks arising in one region are transmitted to another region (Fackler and Goodwin, 2001). Thus, the underlying framework is that of the law of one price (LOP), and the tests of integration to be performed are tests of the relative version of this law.

To quantify patterns of price co‐movements, we use two complementary approaches. The first one focuses on transmission of large price shocks and relies on a non‐parametric framework. The second one focuses on transmission of shocks along the whole distribution and relies on a parametric framework.

> 5 The coefficient of variation is an indicator of dispersion of prices. It measures, at every point in time and for each commodity, the standard deviation of prices relative to their mean.

> 6 For mustard, the reduction in dispersion of prices is only significant at 10 percent.

10