The first approach consists of examining the co‐movement of prices for homogeneous products (both the co‐movement among spatially separated markets within India, and between Indian markets and international markets), purging the price series from their irregular components. Thus, this analysis focuses on co‐movements of substantial price changes. Since the raw series for prices are highly volatile, a smoother is applied that preserves cycles but reduces the noise in the series. For each city‐ commodity, the Christiano and Fitzgerald (2003) filter is applied to isolate cycle‐components. This filter has the property of approximating the optimal linear smoother, which can only be applied to an infinite time series. The filter minimizes the mean squared error between the filtered series and the series filtered by an ideal band‐pass filter. We select periodicities between 12 and 36 months.<sup>7</sup> The choice of these periodicities was driven by visual inspection of the peak‐to‐peak analysis of price data.

This approach allows visualizing the extent of transmission of substantial price changes, as well as other patterns, such as the symmetry of transmissions from peak‐to‐peak and from bust‐to‐bust.

The second approach directly tests the relative version of the LOP. Relative LOP establishes that the growth rate of domestic prices reflects the growth rate of international prices and of the nominal exchange rate. The absolute LOP postulates that in the long‐run there are no arbitrage opportunities, because the price of a homogenous good in spatially separated markets needs to be equal. Given the price in market i, Pi , the price in market j, Pj, the absolute LOP postulates that:

# Pi�Pj

In growth rates (denoting log differences in minuscule), the relative PPP can be defined as: Empirically, to assess the extent of spatial integration we analyze how the prices in i and j co‐move.

A natural way of testing the relationship for India is to estimate a vector error correction model for all goods in all states. Following Pesaran 2000, the VEC model for panel data is specified as follows: Where _p_ict_ is the domestic price in city _i_ of commodity _c_ at month _t_ . The first term between parentheses is the equation for the long‐run relationship of interest. The gamma coefficient provides an indicator of the pass through from price shocks in _j_ to prices in _i_ . If the gamma coefficient equals 1, the LOP holds in the long‐run. That is, market _i_ is found to be integrated with market _j_ for commodity _c_ . The coefficient φ provides an indicator of the speed at which domestic prices in _i_ adjust after shocks in _j_ bring the long‐run relationship of prices between the two prices away from long‐run equilibrium (the speed of adjustment). Pesaran’s approach allows one to estimate different short‐run coefficients for each state commodity and control for unobserved city‐commodity fixed effects. In addition, the speed of adjustment parameter is allowed to vary through city and commodity.

To analyze patterns of transmission with world prices, _pj_ is substituted with _p*_ , the international price, and an exchange rate variable is added into the regression to compare international and domestic prices measured in the same currency.

> 7 The Christiano and Fitzgerald filter is a band‐pass filter. It keeps periodicities within the chosen band‐pass and attenuates the ones outside the band.

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