Qualifications in comparing macro estimates and microdata, and implications for the Phillips curve

A key result is that South Africa’s microdata shows prices to be more flexible, or less sticky, than the pricing parameters estimated in the open economy DSGE model, with the implication that there is less inflation persistence, and that interest rate responses to a variety of shocks may need to be sharper, but less persistent, than those predicted by the baseline open economy DSGE model. It is, nonetheless, important to frame this finding within the general qualification that there is an identified tendency for microdata to reveal shorter average price durations (or greater price flexibility) than those implied by estimated Calvo parameters in New Keynesian models.

In this regard, Dennis (2006) reports that Calvo-shares estimated with the New Keynesian Phillips curve find a level of price rigidity that is greater than that measured using microdata on the frequency of price adjustment. For example, Sbordone (2002) estimates the

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θ to be around 0,8 for the United States, that is, about 20 percent of firms reset prices each quarter, implying an average price duration of about 5 quarters, or 15 months, as

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(1− 0,8)−1_{= 5 quarters or 15 months. But, using the US Bureau of Labour Statistics} microdata on price change, Bils and Klenow (2004) report that the average duration between price changes is about 4,3 months. Similarly, as has been noted, in the South African case, the open economy DSGE model’s estimations for both θh and θf imply

price durations that are significantly longer than the price durations revealed by the microdata study.

Dennis (2006) argues that “care must be taken when comparing macro-models to microdata” (p.2). He suggests the following key reason for the tendency for macro models to estimate a higher degree of price stickiness than that which is revealed by the microdata. The Calvo-share describes the proportion of firms that make an optimal price change, whereas microdata reveal whether a price has changed at all, whether the change is optimal or not. In fact, some price changes may be suboptimal and it may be optimal not to change prices on occasions.44 A particular problem is that an analysis of the microdata is unable to distinguish between optimal and non-optimal price changes, whereas certain macro models “require a price change and an optimal price change to be the same thing” (Dennis (2006), p.2). This is a problem which the decomposition method utilised in the previous section goes some way to addressing.

Another approach which addresses this problem is a model developed by Gali and Gertler (1999), as “it has a structure that can be compared more readily to microdata than the Calvo model” (Dennis (2006), p.3). In the Gali-Gertler model certain firms change prices optimally, certain firms change their prices by a ‘rule of thumb’ (indexing price changes to the previous period’s inflation) and certain firms do not change their prices at all.45 Such a model incorporates a role for menu costs and for information-gathering costs. 







44 _{Dennis (2006) discusses two further reasons for the disjuncture between macro estimates and microdata,}

which are not taken further here:

- the Calvo model assumes that firms change prices once per period at most, whereas in practice price may change more frequently; and

- the Calvo model ignores the possibility that there may be heterogeneity in the frequency of price adjustment across firms

45 _{This insight is confirmed by South Africa’s CPI and PPI microdata that in a given period some prices do}

not change and other prices do change (where either the changing price is optimised or it is fully or partially indexed to the prevailing rate of inflation). Using the price change frequencies for the CPI monthly data as the basis for the calculation and assuming that price changes are limited to one change per quarter, on average from 2001m12 to 2007m12, each quarter 49,42% of prices do not change, 45,24% of prices are re-optimised and 5,34% of prices are indexed to prevailing inflation (based on the decomposition method discussed in the previous section with

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δ=0,25). For the import component of the PPI monthly data, on average from 2001m12 to 2007m12, each quarter 30,55% of prices do not change, 60,75% of prices are re-optimised and 8,41% of prices are indexed to prevailing inflation (based on the decomposition method discussed in the previous section with δ=0,25).

When menu costs are high, a larger share of firms will not change their prices. When information-gathering costs are high then a larger share of firms will resort to ‘rule of thumb’ pricing.

Formally expressed, the Gali-Gertler model allows that in each period a proportion of firms

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θ do not change their prices, a proportion of firms

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ω(1− θ) change their prices by ‘rule of thumb’ and a proportion of firms

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(1− ω)(1− θ) set their firms prices optimally to maximize profits, where

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(1− ω),ω[0,1) is the proportion of firms that change prices optimally. Firms fall randomly into one of the three categories each period, independently of their history of price changes. Menu costs are associated with

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θ as these costs are incurred by firms whenever they change prices whether or not the price change is optimal. Information costs are associated with

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ω as the costs with information gathering are associated with the efforts involved in establishing the optimal price.

The Gali-Gertler-Dennis Phillips curve is expressed as follows46:

€ ˙ π t = ω(1− θ) θ + ω(1− θ)(1+ β)π ˙ t−1+ β[θ + ω(1− θ)] θ + ω(1− θ)(1+ β)Etπ ˙ t +1+ (1− ω)(1− θ)(1− βµ) θ + ω(1− θ)(1+ β) mct

The properties of modified Gali-Gertler-Dennis Phillips curve are such that: - when € ω = 0 and € θ €

≠ 0, no firms index prices and backward dynamics are

eliminated so that the equation collapses into the Calvo Phillips curve, as follows

€ ˙ π t =βEtπ ˙ t +1+ (1−θ)(1−βθ) θ mct - when € θ = 0 and € ω €

≠ 0, all firms change prices in each period so that the equation

is simplified into the full-indexation Phillips curve (as per Christiano et al (2005)), as follows: € ˙ π t = 1 1+ βπt−1+ β 1+ β Etπt +1+ (1− ω)(1− βω) (1+ β)ω mct 







What remains is the partial indexation Phillips curve of Smets and Wouters (2003), which assumes that firms that do not optimise their prices index their price change magnitudes to a proportion of the previous period’s inflation rate. This is expressed as follows:

€ ˙ π _t = η 1+ ηβπ ˙ t−1+ β 1+ ηβ Etπ ˙ t +1+ (1− βξ) (1+ ηβ)ξmct When €

η = 0 this equation is equivalent to the Calvo Phillips curve and when

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η = 1 it is equivalent to the full-indexation Phillips curve.

The implication of the partial indexation model is that it is costless to change prices, but costly to optimise prices. As a consequence, all prices are assumed to change every period, either optimally or through indexation. Such an assumption of continuous price changing is clearly at odds with the microdata. The open economy DSGE model suffers from the same disjuncture with the pricing microdata. This is because the model makes use of a partial indexation Phillips-curve – where, each period, prices change as they are either re-optimised or re-set as a proportion (

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δ) of the previous period’s rate of inflation.

In conclusion, a key problem is that the form of Phillips curve relation generally used in open economy DSGE models, such as that developed by Steinbach et al (2009) is not supported by the non-continuous pricing conduct revealed in studies of the price microdata. A Gali-Gertler-Dennis style Phillips curve may be preferable as in each period it allows for a situation where certain prices are re-optimised, where certain prices are partially indexed to the prevailing inflation rate, and where certain prices do not change.

5.5
 Conclusion:
Summary
of
findings


There are two important implications of the analysis outlined in this Chapter, the first being at the policy level and the second at the level of methodology.

Firstly, when Calvo parameters aligned to the microdata findings for average price durations are used, then it is found that due to the higher degree of price flexibility

implied by the data, the conduct of interest rate policy should generally, in response to a range of positive and negative shocks, be more aggressive, but less persistent than that response-path implied by a standard open economy DSGE model such as that of Steinbach et al (2009).

This suggests, for example, that the correct interest rate response to the recent economic recession of 2008 and 2009 would have been a sharper, but somewhat less persistent, cut in the policy interest rate (Repo rate) and real interest rates than that implied by the open economy DSGE model. The higher degree of price flexibility for domestic and importing price-setters, respectively, means sharper but less persistent Repo rate and real interest rate cuts in response to the kind of negative demand shock characteristic of the recent global recession. On the other hand, a rising inflation rate due to a cost shock would require a comparatively sharp increase in the policy interest rate (Repo rate) over a somewhat shorter period.

Secondly, Robert King has recently highlighted that the modeling practice of allowing firms “to costlessly index frequently to the past inflation rate, but not to make frequent fully optimal adjustments… is dramatically inconsistent with the micro price data” (in King (2009) p.348). This comment pinpoints a key methodological issue, raised in this Chapter, that the form of Phillips curve relation used in open economy DSGE models is not supported by the non-continuous pricing conduct revealed in studies of the price microdata.

More specifically, it is argued that a Gali-Gertler-Dennis style Phillips curve may be preferable, in that it allows in each period for certain prices to be re-optimised, certain prices to be partially indexed to the prevailing inflation rate, and for certain prices that do not change. Furthermore, based on the evidence of the pricing microdata, there may be further refinements required to enable models to deal better with heterogeneity in pricing conduct, state dependency (particularly in the form of synchronisation), seasonality and cost channel effects in response to interest rate changes.