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Erschienen in: Empirical Economics 1/2023

29.04.2022

Sales and promotions and the great recession deflation

verfasst von: Demetris Koursaros, Nektarios Michail, Niki Papadopoulou, Christos Savva

Erschienen in: Empirical Economics | Ausgabe 1/2023

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Abstract

This paper investigates the effect of sales and promotions on the pricing decisions of firms by providing a novel theoretical model where firms face price adjustment costs and offer items on sale to attract bargain hunters. It is demonstrated that in a recession, the frequency of items on sale increases as well as the effort of consumers to locate such offers. Since the decrease in the cost of living following a recession comes both from price decreases and the combination of more frequent sales and more active bargain hunting by consumers, a price index that simply focuses on prices and neglects high-frequency sales and their weight in the consumer’s basket appears to be less responsive to shocks. This can explain the low response of inflation in the post-crisis period and thus the breakdown of the Phillips curve as sales items is under-represented in common price indexes. This study also shows that a price index created by placing more weight on sale items in the UK CPI correlates better with the output gap, confirming the model’s predictions. Additionally, if agents form inflation expectations using indices that neglect sales and promotions, recessions are exacerbated.

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Fußnoten
1
The phenomenon has been attributed to various sources: Gilchrist et al. (2017) attribute it to financial frictions; Christiano et al. (2015) to the fall in total factor productivity as well as to the rising cost of working capital; Millard and O’Grady (2012) to the rising share of firms with sticky prices.
 
2
Such promotions include more high-frequency sales, the “buy one get the other half price,” bundling items together, loyalty cards, promotional coupons and many others.
 
3
This index is derived by multiplying the weight of the sales items by 1.2 and thus decreasing the weight on non-sale items, respectively.
 
4
The proxy for the output gap is calculated using gross domestic product and an HP filter. All data were downloaded from the Bank of England.
 
5
The only instrument that was excluded from the estimation of Galı and Gertler (1999) is the output gap, as we are using it for the Phillips curve relation instead of the marginal cost.
 
6
The number of lags is determined using all LR, FPE, AIC, SC and HQ criteria.
 
7
Endogenizing N requires imposing a free entry within product categories up to a zero profit equilibrium that pins down \(N_{t}\) each period making it time varying.
 
8
If there was free entry and thus N time varying, \({\bar{s}}_{t}\) would be the sale fraction consistent with zero profit.
 
9
By equating the profits under different sales fractions, the adjustment costs for the price cancel out.
 
10
For a store to be cheapest from the rest must receive a sales draw \(s_{t}\) lower than the competition which occurs with probability \(\left( 1-F\left( s_{t}\right) \right) ^{N-1}\) which is the probability for all the rest \(N-1\) competitors to pick a less generous sales offer.
 
11
The problem should not be confused with a Bertrand competition model as setting price equal to marginal cost is not a Nash equilibrium because setting a slightly higher price attracts the non-searchers resulting in a nonzero profit.
 
12
If any \(\Xi \left( s_{t}\right) \) implies a higher profit than the rest of the choices then the equilibrium would be a pure strategy one.
 
13
The probability to be the cheapest and get all the bargain hunters makes the firms ex post different.
 
14
That is \(I_{V}=\int \nolimits _{{\bar{s}}_{t}}^{1}\left( 1-F\left( s_{jt}\right) \right) ^{N-1}f\left( s_{jt}\right) \mathrm{d}s_{jt}\).
 
15
Calvo pricing makes the model very hard to track without additional assumptions.
 
16
In later sections, the dynamics of the model are investigated under the assumption that households and/or policymakers form expectations using inflation measures such as (18) instead of \(\pi _{t}\).
 
17
The comparison of the distributions of \(\frac{\left( 1-F\left( s_{it}\right) \right) ^{N-1}f\left( s_{it}\right) }{I_{V}}\) and \(f\left( s_{it}\right) \) are depicted in Fig. 4.
 
18
For the first-order condition in (33) to reach a zero value in steady state, a sufficient condition is for \(\left[ \left( 1-\theta \right) s_{t}\Omega _{t}+\theta mc_{t}\right] \) to change sign. Since this function is monotone and increasing, for the lowest possible value of the sales fraction \(s_{t}={\bar{s}}_{t}\), \(\left( \theta -1\right) {\bar{s}}_{t}\Omega _{t}<\theta mc_{t}\) and when \(s_{t}=1\), \(\left( \theta -1\right) \Omega _{t}>\theta mc_{t}\). For the sales distribution it is necessary that \(\frac{ \theta -1}{\theta }\frac{p_{t}}{P_{t}}\le m_{t}\le {\bar{s}}_{t}\frac{p_{t}}{ P_{t}}\) implying that another condition it is needed for the foc to be zero.
 
19
Every firm sets the price equal to the marginal cost.
 
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Metadaten
Titel
Sales and promotions and the great recession deflation
verfasst von
Demetris Koursaros
Nektarios Michail
Niki Papadopoulou
Christos Savva
Publikationsdatum
29.04.2022
Verlag
Springer Berlin Heidelberg
Erschienen in
Empirical Economics / Ausgabe 1/2023
Print ISSN: 0377-7332
Elektronische ISSN: 1435-8921
DOI
https://doi.org/10.1007/s00181-022-02243-3

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