If firms operated in perfectly competitive markets where each firm was a price taker and charged the industry price (i.e, _pit_ = _pIt_ ), (25) and (28) would be equivalent to each other. However, when we deviate from the assumption of perfect competition (i.e, _pit_ = _pIt_ ), two problems arise.

The first is the omitted price bias. In the absence of firm prices, if industry prices are used to measure output as _q_ � _it_ instead of _qit_ , the estimates of the coefficients of the production function will be biased. As long as _E_ [( _pit − pIt_ ) _zit_ ] = 0, where _zit_ refers to the vector of inputs, the use of industry level price deflators to deflate revenues to proxy for output will yield incorrect estimates of the coefficients of the production function. See Klette and Griliches (1996) for a detailed exposition of the omitted price bias.<sup>12</sup> The second problem is specific to the export-productivity question when we try to estimate within-firm changes to total productivity from export entry (see Garcia-Marin and Voigtlnder (2013)). If firms face downward sloping demand curves and pass on some of the benefits of gains in productivity to consumers by lowering prices, _pit_ falls as _ωit_ rises. In this case, using estimates of productivity from (28) will underestimate gains to firms post export market entry.<sup>13</sup> There is a wide variation in price changes across firms in a given industry in any year. I discuss concerns with using industry level price deflators to deflate firm revenues and use that to proxy for quantities by using the example of the transport equipment industry. Table 2 shows the yearly price change (over the previous year) for the transport equipment industry. The last column (6) gives the yearly price change as given by the Output Deflator of the transport equipment industry at the aggregate industry level as calculated by the Central Statistical Organization, Government of India. The average growth rates from the industry level indices are positive for every year in the period. Column (5) gives the standard deviation of firm price changes for each year as observed in the data set.

Columns (1) and (2) the percentage of firms that experienced decline in prices over the previous year and the mean reduction in prices over the previous year (for firms with negative growth) while columns (3) and (4) give the percentage of firms that experienced a positive growth in prices over the previous year and the average increase in prices (for the firms with positive growth). For example, in the year 2000, 37 % of firms saw on average, a 9 percent fall in their prices from 1999 while 63 % of the firms experienced a 10 percent increase in prices on average. Price changes of firms varied widely as can be seen by the standard deviation. The use of the industry-level deflator would assume that every firm experienced a 3 percent increase in prices over the previous year. Deflating revenues by the industry deflator would underestimate the quantity changes for firms

> 12Everything else being equal, firms charging higher prices would have lower market shares. They would sell fewer units of output and employ fewer inputs i.e., price and inputs would be negatively correlated. However, more productive firms also need fewer inputs to produce the same output. So the relationship may not be so clear-cut.

> 13Theoretical models of trade such as Melitz (2003) model firms as operating in monopolistically competitive markets. In equilibrium, firms charge a price in domestic and export markets which is a constant mark up over marginal cost. The mark-ups are given by the inverse of the elasticity of demand in the two markets. If firms improve productivity and reduce marginal costs, these models predict a complete pass-through of these gains to consumers in the form of lower prices.

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