#### By Michael J. Mahony

The aim of our new ESCoE paper “Measuring Flexible Prices, Flexible Output and Marginal Costs using Survey Data” is to exploit survey microdata so as to provide new measures of flexible prices, flexible output and marginal costs for the UK. The methods we provide in this paper can straightforwardly be applied to other countries, given the right data. We are grateful to the Confederation of British Industry (CBI) who kindly provided their survey microdata for the Industrial Trends Survey (ITS), Service Sector Survey (SSS) and Distributive Trades Survey (DTS). These surveys cover the manufacturing, services and distributive trades industrial sectors – which constitute more than 90% of UK private sector activity.

For our purposes, the key strength of these surveys is that they directly ask firms if their selling price, level of output or average costs have changed over the previous quarter. In terms of prices, from the survey microdata we are able to observe the proportion of firms which change their selling price each quarter (and the corresponding proportion of firms that don’t). This measure is a key variable in the workhorse of modern monetary economics, the New Keynesian Model, and is often assumed fixed (i.e. doesn’t change from quarter to quarter). Our work shows this assumption is not justified – in fact there is substantial variation from quarter to quarter across the three industrial sectors we examine (as well as the disaggregate primary and secondary manufacturing). As an example see Figure 1, which graphs the proportion of firms in the manufacturing sector that changed their prices in the previous quarter (denoted λ* ^{p}_{t}*) alongside the standard assumed fixed value of 0.25 (denoted λ

*). In each sector examined in the paper, the proportion of firms adjusting their price each quarter typically exceeds 0.25. This is noticeably true in the distributive trades sector.*

^{p}While this insight is informative in its own right, its main significance is in allowing an accurate construction of a flexible price level for each industrial sector. In the paper, we derive our measure of flexible prices via a straightforward decomposition (using first principles) of the aggregate price level. Given sticky prices, in any period the aggregate price level is a weighted average of the flexible price (chosen by firms changing their prices) and the previous period’s price level (for those firms which do not change prices) – where the weights are determined by the proportion of firms adjusting and not adjusting their price each period (respectively). Given that we can directly and accurately measure the proportion of firms changing and not changing their prices, we can thus compute the flexible price index for each industrial sector. It is also worth noting that our straightforward decomposition is consistent with the microfoundations of price-setting firms in a monopolistically competitive market. In each industrial sector our derived flexible prices indices are more volatile than the corresponding actual price index. In fact, the flexible price index amplifies the underlying volatility in the price level. This can be seen in Figure 2, which for the manufacturing sector graphs the flexible price index (denoted *q*_{t}) and the actual price level (denoted *p _{t}*). In the paper we also present and discuss some alternative flexible price iterations – such as allowing firms to index prices in the straightforward decomposition, using the Atlanta Fed methodology and assuming a fixed proportion (25%) of firms adjust prices each period.

The decomposition methodology applied to prices is also applied to output in the paper. Again, the ability to directly measure the proportion of firms which change their output each quarter is used to derive a flexible output index. Once more, the flexible output index amplifies the volatility of the output series. However, there is an additional benefit to being able to directly measure the proportion of firms changing their output – given data on changes in average costs (which the CBI dataset has), we can construct a direct measure of marginal costs. Making no assumption regarding functional form average costs equal the sum of fixed costs and variable costs divided by output. We show that focusing on firms where output remains unchanged, the change in average costs is proportionate to changes in variable costs – which given output remains unchanged represent marginal costs. Intuitively, if firms are facing higher (lower) average cost without changing their output quantities, then they must be facing increased (decreased) marginal costs. These new direct measures of marginal cost closely track inflation with strong positive correlations being observed. As an example, see Figure 3 which (for the manufacturing sector) depicts marginal costs (denoted φ_{t} ) and inflation (denoted π_{t}).

Ultimately the key contribution of this paper is that important economic variables which have typically gone unmeasured have now been provided for a large section of the UK economy.

Read the full ESCoE discussion paper here.

*ESCoE blogs are published to further debate. Any views expressed are solely those of the author(s) and so cannot be taken to represent those of the ESCoE, its partner institutions or the Office for National Statistics.*