sticky prices, sticky information or rational inattention ... prices, sticky information or rational...

Sticky Prices, Sticky Informationor Rational Inattention?

Evaluating Microfoundations.

Jorge Diego Solorzano∗

University of Warwick.

September 2017

Abstract

This paper evaluates competing sets of microfoundations on firms’ price-setting behaviour widely

used in monetary economics. The contribution of this project is twofold. The first contribution is

to use as inflation driver a relevant measure of marginal cost from wage microdata. To that end,

I calculate the User Cost of Labor as in Basu and House (2016) for the first time in a different

dataset, and confirm their findings. The second contribution is the micro-evidence on the three

leading price-setting theories used in macro models. I show compelling evidence that Calvo’s (1983)

sticky price model fits well for good prices; service prices favour Mankiw and Reis’ (2002) sticky

information model; and that there is little empirical support for Mackowiak and Wiederholt’s (2009)

rational inattention model. These results suggest that models with a single price-setting decision

process may be insufficient to adequately capture the monetary transmission mechanism.

∗I would like to thank Huw Dixon for his useful comments. This paper has greatly benefited fromcomments received at the International-Macro Workshop at Warwick. Errors are all mine. Department ofEconomics, University of Warwick, Coventry CV4 7AL, UK. E-mail: [email protected]

1 Introduction

Microfoundations are key elements in nowadays mainstream macroeconomic models.

Micro-founded frictions are found crucial for the degree of monetary non-neutrality, inflation

persistence and optimal monetary policy rule in DSGE modelling.

Perhaps the most important difference between microfoundations is how firms set prices

and process information. Three widely known models are: sticky prices, as proposed by

Calvo (1983); sticky information, as developed by Mankiw and Reis (2002); and rational

inattention, as introduced by Mackowiak and Wiederholt (2009).

Yet, there is only a handful of papers on the empirical credibility of these three models.

In this paper we use three large price and wage micro-datasets to shed light on the validity

of these frameworks. The contribution of this paper is twofold. First, we calculate the User

Cost of Labor (UCL) as in Basu and House (2016) and Kudlyak (2014) using a different

dataset. The UCL provides the cost of expanding labor input with an unchanged composi-

tion of worker type, which is one of the main criticisms faced by other measures of labor cost

over the business cycle. Our data confirms results from Basu and House (2016) and Kudlyak

(2014) that UCL is cyclical. In addition, we show that the UCL does not vary substantially

between formal and informal workers, though it does vary by industry.

Second, we evaluate the three competing frameworks in price formation. Since marginal

cost is potentially an endogenous variable, we use Generalised Methods of Moments (GMM)

with the UCL, as well as lag values, instrumenting for marginal cots. Carlsson and Skans

(2012) follow the same econometric strategy. It is worth noticing that our analysis relies

on actual cost proxies driving price-setting, as instead of most aggregate data studies using

output as an indirect marginal cost measure.

Our results can be summarised as follow. Firstly, regarding the sticky price framework,

we find that current and future marginal costs explain firms’ price-setting practices, as sug-

gested in the Calvo model. However, the original model predicts that the role of future

marginal cost monotonically decays depending how far ahead its forecasted. We do not find

supporting evidence of this prediction for the full dataset. For prices in the service sector,

current and future marginal cost have similar effects on pricing decisions. In contrast, in line

with the Calvo framework, the role of future marginal costs diminish for goods prices.

Secondly, with respect to the sticky information model, our estimates show that firms do

1

not fully react to changes in marginal cost that could have been forecasted by their infor-

mation set. Recall that in this model information is sticky, not prices. Hence, this result is

at odds with the benchmark model proposed by Mankiw and Reis (2002). Our calculations

are obtained by using instruments lagged back sufficiently far to ensure that firms have up-

dated their information set and in order to deal with expectations. However, if one allows

for strategic complementarities in the model, firms would not fully pass-through their pro-

jected marginal cost.1 Yet, our estimates with the complete dataset are significantly lower

than what we would expect and therefore reject the sticky information model. Neverthe-

less, service prices display support to Mankiw and Reis (2002) model allowing for strategic

complementarities passing nearly one-third of changes in forecasted marginal cost; whereas

goods prices reject the model.

Thirdly, we find little evidence in favour of the rational inattention model. Mackowiak

and Wiederholt (2009) propose that firms react strongly to and immediately to idiosyncratic

shocks. Instead, we find a price-cost elasticity of about one-fifth. This incomplete adjust-

ment forcefully reject the rational inattention model, regardless of focusing on services or

goods prices.

Closest to this paper is research by Carlsson and Skans (2012). We deviate from this study

in three main directions. First, Carlsson and Skans (2012) use annual data, while our micro-

data sets report monthly price and wage records. Annual data is not optimal for analysing in-

termittent price adjustments as these price-setting theories suggest. Second, their study cen-

tres its attention on goods’ prices, while our research provide evidence on goods and services.

Third, we use a different instrument in our econometric strategy. We use the UCL, as first

proposed by Kudlyak (2014), as the main price inflation driver over the business cycle. Carls-

son and Skans (2012) find evidence supporting the Calvo (1983) framework and the Mankiw

and Reis (2002) model. The latter only after allowing for strategic complementarities (real

rigidities). Their findings speak against the Mackowiak and Wiederholt (2009) framework.

Our analysis is based on three main sources reporting 5.5 million earnings and 150 million

wage observations, as well as 4 million price quotas. These micro-datasets are merged by

(4-digit) industry codes. Our first microdata comes from the largest labor survey in Mexico,

Encuesta Nacional de Ocupacion y Empleo (ENOE). It contains self-reported earnings from

1Carlsson and Skans (2012) uses simulations for Swedish data in order to determine what estimates areto be expected and finds a coefficient of 0.49.

2

individual workers. All in all, the data consists of over 5.5 million earnings observations.

Importantly for the calculation of UCL, we observe the starting date of the worker’s current

position, among other job and demographic characteristics. The second dataset comes from

administrative wage records from the Mexican Institute of Social Security (IMSS). These ad-

ministrative records constitute a census of all formal workers employed in the private sector.

Our data is a panel of employee clusters reporting the wage bill and number of workers in the

cluster on a monthly basis.2 We combine our wage dataset with disaggregated measures of

output at industry level (4-digit) in order to construct a measure of unit labor cost (consistent

with the vast majority of DSGE models in the literature). Finally, the third microdata, re-

ports monthly price dynamics of individual goods and services collected for CPI calculations.

This paper is organised as follows. Section 2 outlines the three models we consider:

sticky prices, sticky information and rational inattention. Section 3 describes our empirical

strategy and presents preliminary results. Section 4 concludes.

2 Models

If in sector k at time t firms have market power, the optimal frictionless price Pk,t is set

as a markup µk,t over marginal cost MCk,t. That is,

lnPk,t = µk,tMCk,t

From the cost minimisation problem, the cost associated with each possible margin of

adjustment should be the same at the optimum. Hence, it is sufficient to look at one of

them, in this case we focus on labour-input margin.

MCk,t =∂Costk,t∂Lk,t

∂Lk,tYf,t

If we have a production function of the form

Yk,t = (Lk,t)α g(Othersk,t)

The marginal cost is equal to

MCk,t =1

α

WageBillk,tYk,t

2Clusters are defined by state, district, county, firm’s size, age, gender, industry and income level. Giventhe granular characteristics defining each cluster, nearly 80% of clusters have only one or two workers.

3

Thus, the frictionless model implies that

lnPk,t = β0 + lnMCk,t

2.0.1 Rational inattention

Mackowiak and Wiederholt (2009) propose that prices adjust freely, however, firms face

constraints on the amount of information to be processed each period. In their original

calibration based on micro-evidence, firms allocate 96% of their attention to idiosyncratic

conditions. Hence, firms react strongly and quickly to idiosyncratic conditions, whereas

reaction is dampened and delayed to aggregate conditions.

lnPk,t = β0 + βMW lnMCk,t

H0 : βMW ' 1 (1)

2.0.2 Sticky information

Mankiw and Reis (2002) suggest firms update their information set with a fixed proba-

bility. After updating their information set, firms decide upon a price path that will remain

in place until the firm is drawn to update the next time. The firm’s optimal price is period

t+ s is given by

lnPk,t+s = β0 + βMREt−rlnMCk,t+s

where t+ s denotes the firm’s price plan, t− r is the time period when the information set

was last updated. Thus, our hyphotesis is

H0 : βMR < 1 (2)

2.0.3 Sticky prices

Calvo (1983) propose that only a fraction of firms can reset their prices every period.

Thus, the optimal price under Calvo-style nominal rigidities is characterised as the discounted

value of current and expected future marginal cost. Therefore, we have

lnPk,t = β0 + (1− θβ)Et

∞∑s=0

(θβ)s lnMCk,t+s

lnPk,t = β0 +∞∑s=0

βC,t+slnMCk,t+s

4

H0 : 1 > βC,t > βC,t+1 > ... > 0 (3)

H0 :∑s

βC,t+s <∞ (4)

3 Econometric framework

We use Arellano-Bond estimator for a number of reasons. First, our panel is small-T

with large-N. We observe around 100,000 individual price quotas on a quarterly basis for 10

years. Second, our independent variable (marginal cost) is not strictly exogenous, meaning it

is correlated with past and possible current realisations of the error term. Third, individual

fixed effects are likely to be present. Forth, hetoroskedasticity and autocorrelation within

individual prices quotas but not across them.

Our instruments must identify causal effects of marginal cost changes on price-setting

behaviour. Similarly, in order to handle expectations when taking the Mankiw and Reis and

the Calvo models to the data, we also rely on instruments.

3.1 Instrumentation

Instruments must be correlated with the items’ marginal costs, but independent to the

pricing decision. Beside lagged marginal cost, we construct an external instrument. We fol-

low Basu and House (2016) to construct the User Cost of Labor (UCL) which is our external

instrument.3

The User Cost of Labor is defined as the (expected) difference between the present dis-

counted value of wages paid to a worker hired in the current quarter and that paid to a

worker hired in the next quarter. Kudlyak (2014) shows that the UCL is the relevant price

for a firm considering to add a worker.

Moreover, the microdata application of the “marginal cost” concept in macro theory is

the cost of expanding labor input without changing the composition of worker types. There-

fore, the UCL, as cost associated with expanding the number-of-employees margin while

controlling for variations in the labor force composition, is an automatic guess as a relevant

instrument.

3See Kudlyak (2014) and Haefke et al. (2013) for more.

5

We start our calculation of the UCL by fitting one linear model

lnwi,kτ,t = c+ γt+ ΨX i,k +T∑

do=1

T∑d=do

χdo,dDi,kdo,d + εi,kt (5)

Here wi,kτ,t is the real wage at time t of individual i employed in industry k hired at time-τ

at her current position. Covariates in matrix X i are expedience (and experience squared),

tenure (and tenure squared), schooling years, sex, industry (4-digit) and regional fixed ef-

fects.4 The dummy variables Di,kdo,d take the value 1 if do = τ and d = t and 0 otherwise.

At time t, all workers who began their current job at date-τ get an additional adjustment

to their predicted wage given by the coefficient χτ,t. These adjustments imply that individ-

uals who started working at date-τ experience an expected strip of (log) wage realisations

given by {χτ,τ , χτ,τ+1, χτ,τ+2...}. Notice that χτ,τ indicates the wage of a newly hired worker,

controlling for differences in human capital over the business cycle.

We construct the projected wage payments as

ln wkτ,t = c+ γt+ ΨXk + χτ,t (6)

The forecast of the present value of wage payments for workers hired at time-τ and still

employed (with probability ψ) is calculated as

PDV kt=τ =

∑j=0

(βψ)j exp{ lnwkτ,τ+j} (7)

Hence, UCL is uncovered by Kudlyak (2014) as

UCLkt = PDV kt − βψPDV k

t+1 (8)

4Future analysis will include covariates of job position and type of job.

6

Figure 1: User Cost of Labor

2005q1 2007q3 2010q1 2012q3 2015q1date

UCL New hires Unemployment

3.2 Taking models to the data

3.2.1 Calvo (1983)

The Calvo model only defines the optimal reset price. Hence, only prices which actually

change can be used in our analysis.

A further complication with this model is the infinite sum of current and future marginal

cost. Using a quarterly estimation of θ = 38.59% and assuming β = 0.99, we expect the

elasticity for Et lnMCt+4 is 0.0535.5 Since the terms in the sum fades fairly rapidly towards

zero, we truncate the sum to 5 terms in our empirical application.

In other to handle expectations we define ZCalvo,t−n as a set of variables observed in time

t-n. We need to use instruments lagged sufficiently far backwards.

We rely on a GMM estimator with a dynamic instrument matrix, which allows us to use

lags as they become available. Thus, our moment conditions are

Et

{(lnPi,t − β0 −

4∑k=0

βklnMCi,t+k

)ZCalvo,t−2

}

3.2.2 Mankiw and Reis (2002)

Mankiw and Reis (2002) suggest that firms update their information set with a fixed

probability. After updating, firms decide upon a price path that will remain in place until

5Defined as (1− α(1− θ))(α(1− θ)) where 1− θ is the prob of not changing.

7

the firm is drawn to update the next time. The firm’s optimal price is period t+k is given

by

lnPk,t+k = γk + Et−rlnMCf,t+k (9)

where t+ k denotes the firm’s price plan, t− r is the time period when the information set

was last updated.

3.2.3 Mackowiak and Wiederholt (2009)

Prices can be changed freely in any period, but the firm faces a constraint on the amount

of information that can be processed at each period. They calibrate their model to match

micro-evidence on price. Firms allocate 96% of their attention to idiosyncratic conditions.

Hence, firms reacting as strongly and quickly to idiosyncratic conditions whereas reaction is

dampened and delayed to aggregate conditions.

8

Table 1: Calvo ModelGMM GMM GMM

Sample All Goods Services

ln MCt -0.173*** 0.0861*** 0.234(0.0336) (0.0234) (0.216)

Et ln MCt+1 0.452*** 0.0860* 0.695***(0.0406) (0.0445) (0.220)

Et ln MCt+2 0.0773*** 0.0682* 0.533***(0.0228) (0.0405) (0.156)

Et ln MCt+3 0.327*** 0.0172 0.621***(0.0275) (0.0250) (0.138)

Et ln MCt+4 0.422*** -0.0495 0.605***(0.0468) (0.0348) (0.184)

Et ln MCt+5 -0.372*** -0.000797 -0.0363(0.0461) (0.0368) (0.147)

Sum 0.733*** 0.207* 2.652***(0.087) (0.125) (0.563)

Observations 599,527 153,273 18,676Number of id 118,886 28,808 7,610IV MC Lags 7...13 7...13 7...13IV UCL Lags 7...13 7...13 7...13Hansen J 0.000 0.000 0.000

Robust standard errors in parentheses*** p<0.01, ** p<0.05, * p<0.1

Table 2: Mankiw and Reis modelGMM GMM GMM


ln MCt 0.0522*** 0.0578*** 0.280***(0.016) (0.022) (0.092)

Observations 697,017 180,069 21,535Number of id 125,499 29,841 8,082IV MC Lags 6...12 6...12 6...12IV UCL Lags 6...12 6...12 6...12Hansen J 0.000 0.000 0.000


9

Table 3: Mackowiak and Wiederholt modelGMM GMM GMM


ln MCt 0.153*** 0.0681*** 0.0297(0.00655) (0.0154) (0.0307)

Observations 585,873 153,142 19,252R-squared 0.004 0.002 0.002Number of id 99,515 25,055 5,543IV MC Lags 1...4 1...4 1...4IV UCL Lags 0...4 0...4 0...4Hansen J 0.000 0.000 0.280


4 Conclusions

In this paper we use three large price and wage micro-datasets to shed light on the validity

of three widely known price-setting models: sticky prices, sticky information, and rational

inattention.

We evaluate these three competing frameworks in price formation by using Generalised

Methods of Moments (GMM) with the UCL, as well as lag values, instrumenting for marginal

cots. It is worth noticing that our analysis relies on actual cost proxies driving price-setting,

as instead of most aggregate data studies using output as an indirect marginal cost measure.

Our results are summarised as follows. Firstly, regarding the sticky price framework, we

find that current and future marginal costs explain firms’ price-setting practices, as suggested

in the Calvo model. However, the original model predicts that the role of future marginal

cost monotonically decays depending how far ahead its forecasted. We find that for service

prices current and future marginal cost have similar effects on pricing decisions. In contrast,

in line with the Calvo framework, the role of future marginal costs diminish for goods prices.

Secondly, with respect to the sticky information model, our estimates show that firms do

not fully react to changes in marginal cost that could have been forecasted by their infor-

mation set. Hence, this result is at odds with the benchmark model proposed by Mankiw

and Reis (2002). However, if one allows for strategic complementarities in the model, firms

10

would not fully pass-through their projected marginal cost. Yet, our estimates with the

complete dataset are significantly lower than what we would expect and therefore reject the

sticky information model. Nevertheless, if one allows for strategic complementarities, then

service prices, by passing nearly one-third of changes in forecasted marginal cost, support

the Mankiw and Reis (2002) model.

Thirdly, we find little evidence in favour of the rational inattention model. Mackowiak

and Wiederholt (2009) propose that firms react strongly to and immediately to idiosyn-

cratic shocks. Instead, we find a price-cost elasticity of about one-fifth. This incomplete

adjustment forcefully reject the rational inattention model for both service or good sectors.

These results indicate that models with a single price-setting decision process may be

insufficient to adequately capture the monetary transmission mechanism.

11

5 Appendix

Table 4: Calvo model - All broad sectorsGMM GMM GMM GMM GMM

Sample All Fresh Food Goods Services Other Servs

ln MCt+1 -0.173*** -0.367*** 0.0861*** 0.234 -0.211(0.0336) (0.0387) (0.0234) (0.216) (0.293)

Et ln MCt+1 0.452*** 0.305*** 0.0860* 0.695*** -0.0339(0.0406) (0.0413) (0.0445) (0.220) (0.251)

Et ln MCt+2 0.0773*** 0.0663*** 0.0682* 0.533*** -0.266(0.0228) (0.0256) (0.0405) (0.156) (0.463)

Et ln MCt+3 0.327*** 0.324*** 0.0172 0.621*** 0.678**(0.0275) (0.0440) (0.0250) (0.138) (0.330)

Et ln MCt+4 0.422*** 0.490*** -0.0495 0.605*** 1.109***(0.0468) (0.0425) (0.0348) (0.184) (0.327)

Et ln MCt+5 -0.372*** -0.358*** -0.000797 -0.0363 0.179(0.0461) (0.0485) (0.0368) (0.147) (0.239)

Sum 0.733*** 0.46*** 0.207* 2.652*** 1.456***(0.087) (0.078) (0.125) (0.563) (1.2401)

Observations 599,527 406,864 153,273 18,676 8,616Number of id 118,886 75,298 28,808 7,610 4,620IV MC Lags 7...13 7...13 7...13 7...13 7...13IV UCL Lags 7...13 7...13 7...13 7...13 7...13Hansen J 0.000 0.000 0.000 0.000 0.000


12

Table 5: Calvo model - IV composition

GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMMSample All All All Fresh Food Fresh Food Fresh Food Fresh Food Fresh Food Fresh Food Services Services Services Other Servs Other Servs Other Servs

Et ln MCt -0.173*** -0.0460 -0.399*** -0.367*** 0.128** -0.603*** 0.0861*** 0.200*** -0.00625 0.234 0.588 0.599 -0.211 1.165 -0.159(0.0336) (0.131) (0.0656) (0.0387) (0.0556) (0.0731) (0.0234) (0.0458) (0.0514) (0.216) (1.532) (1.060) (0.293) (0.850) (0.791)

Et ln MCt+1 0.452*** 1.961*** 0.413*** 0.305*** -0.0544 0.174** 0.0860* 0.245** 0.189* 0.695*** 4.392* 0.827 -0.0339 1.580*** 0.474(0.0406) (0.433) (0.0526) (0.0413) (0.116) (0.0777) (0.0445) (0.0961) (0.103) (0.220) (2.357) (0.857) (0.251) (0.550) (0.414)

Et ln MCt+2 0.0773*** -0.392*** 0.0846*** 0.0663*** -0.0150 0.170*** 0.0682* 0.192 0.235** 0.533*** 2.464 0.271 -0.266 0.685 -0.0565(0.0228) (0.0854) (0.0284) (0.0256) (0.0583) (0.0387) (0.0405) (0.125) (0.110) (0.156) (1.539) (0.251) (0.463) (0.596) (1.589)

Et ln MCt+3 0.327*** 1.388*** 0.273*** 0.324*** -0.160 0.241*** 0.0172 0.148 0.0468 0.621*** 3.507* 0.383 0.678** 0.926** 1.124(0.0275) (0.300) (0.0365) (0.0440) (0.137) (0.0814) (0.0250) (0.0951) (0.0476) (0.138) (1.811) (0.243) (0.330) (0.369) (0.918)

Et ln MCt+4 0.422*** 0.600** 0.617*** 0.490*** -0.0919 0.631*** -0.0495 -0.0103 -0.0294 0.605*** 3.419* 0.0938 1.109*** -0.251 0.554(0.0468) (0.263) (0.0763) (0.0425) (0.0785) (0.0559) (0.0348) (0.0826) (0.141) (0.184) (1.881) (0.973) (0.327) (0.972) (1.501)

Et ln MCt+5 -0.372*** -2.239*** -0.479*** -0.358*** 0.194* -0.440*** -0.000797 -0.0421 0.0673 -0.0363 -0.265 -0.128 0.179 -1.601* -0.294(0.0461) (0.526) (0.0772) (0.0485) (0.101) (0.0815) (0.0368) (0.0905) (0.156) (0.147) (1.060) (0.718) (0.239) (0.879) (0.859)

Sum 0.733*** 1.271*** 0.509*** 0.46*** 0.001 0.174 0.207* 0.732 0.503** 2.652*** 14.106* 2.046** 1.456 2.504 1.641(0.083) (0.326) (0.112) (0.078) (0.109) (0.138) (0.125) (0.448) (0.248) (0.563) (7.5) (0.897) (1.24) (1.582) (4.093)

Observations 599,527 599,527 599,527 406,864 406,864 406,864 153,273 153,273 153,273 18,676 18,676 18,676 8,616 8,616 8,616Number of id 118,886 118,886 118,886 75,298 75,298 75,298 28,808 28,808 28,808 7,610 7,610 7,610 4,620 4,620 4,620IV MC Lags 7...13 7...13 - 7...13 7...13 - 7...13 7...13 - 7...13 7...13 - 7...13 7...13 -IV UCL Lags 7...13 - 7...13 7...13 - 7...13 7...13 - 7...13 7...13 - 7...13 7...13 - 7...13Hansen J 0 0 . 0 0 . 0 0 . 0 0 . 0 0 .


13

Table 6: Calvo model - More lags

GMM GMM GMM GMM GMMSample All Fresh Food Goods Services Other Servs

ln MCt 0.238*** 0.334*** 0.0802*** -0.0402 -1.050***(0.0191) (0.0266) (0.0175) (0.181) (0.301)

Et ln MCt+1 -0.130*** -0.313*** 0.0674*** 0.587*** -0.677***(0.0188) (0.0231) (0.0239) (0.195) (0.230)

Et ln MCt+2 -0.197*** -0.234*** -0.0488 0.584*** 1.631***(0.0187) (0.0196) (0.0348) (0.156) (0.601)

Et ln MCt+3 0.0195 -0.188*** -0.00374 0.533*** 1.506***(0.0175) (0.0245) (0.0232) (0.128) (0.393)

Et ln MCt+4 -0.370*** -0.336*** -0.132*** 0.615*** 2.250***(0.0229) (0.0304) (0.0228) (0.175) (0.513)

Et ln MCt+5 0.0414 0.347*** -0.0801*** 0.00867 0.808***(0.0303) (0.0364) (0.0230) (0.133) (0.308)

Sum -0.398*** -0.389*** -0.117 2.288*** 4.469***(0.062) (0.059) (0.101) (0.542) (1.610)

Observations 599,527 406,864 153,273 18,676 8,616Number of id 118,886 75,298 28,808 7,610 4,620IV MC Lags 7...15 7...15 7...15 7...15 7...15IV UCL Lags 7...15 7...15 7...15 7...15 7...15Hansen J 0.000 0.000 0.000 0.000 0.000


14

Table 7: Mankiw and Reis model - Broad sectorsGMM GMM GMM GMM GMM

Sample All Fresh Food Goods Services Other Servs

ln mc 0.0522*** -0.0315 0.0578*** 0.280*** 0.199(0.016) (0.020) (0.022) (0.092) (0.131)

Observations 697,017 471,210 180,069 21,535 9,948Number of id 125,499 79,715 29,841 8,082 4,932IV MC Lags 6...12 6...12 6...12 6...12 6...12IV UCL Lags 6...12 6...12 6...12 6...12 6...12Hansen J 0 0 0 0 0


15

Table 8: Mankiw and Reis model - IV composition

GMM GMM GMM GMM GMM GMM GMM GMM GMM GMMSample All All Fresh Food Fresh Food Goods Goods Services Services Soc Serv Other Services

ln mc 0.0229 0.0522*** -0.0975*** -0.0315 0.175*** 0.0578*** 0.0829 0.280*** 0.458*** 0.199(0.026) (0.016) (0.031) (0.012) (0.036) (0.022) (0.115) (0.092) (0.132) (0.131)

Observations 697,017 697,017 471,210 471,210 180,069 180,069 21,535 21,535 9,948 9,948Number of id 125,499 125,499 79,715 79,715 29,841 29,841 8,082 8,082 4,932 4,932IV MC Lags 4...10 6...12 4...10 6...12 4...10 6...12 4...10 6...12 4...10 6...12IV UCL Lags 4...10 6...12 4...10 6...12 4...10 6...12 4...10 6...12 4...10 6...12Hansen J 0 0 0 0 0 0 0 0 0 0


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Table 9: Mackowiak and Wiederholt - Broad sectorsGMM GMM GMM GMM GMM

Sample All Fresh Food Goods Services Other Services

ln MCt 0.153*** 0.201*** 0.0681*** 0.0297 -0.567***(0.007) (0.006) (0.015) (0.031) (0.096)

Observations 585,873 391,461 153,142 19,252 8,898R-squared 0.004 0.007 0.002 0.002 -0.007Number of id 99,515 63,485 25,055 5,543 3,109IV MC Lags 1...4 1...4 1...4 1...4 1...4IV UCL Lags 0...4 0...4 0...4 0...4 0...4Hansen J 0 0 0 .28 0


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Table 10: Mackowiak and Wiederholt model - IV composition

GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMM GMMSample All All All Fresh Food Fresh Food Fresh Food Goods Goods Goods Services Services Services Soc Serv Soc Serv Soc Serv

ln MCt 0.153*** 0.132*** -0.225*** 0.201*** 0.186*** -0.257*** 0.0681*** 0.0173* -0.0279 0.0297 0.0784*** 0.249 -0.567*** -0.467*** 0.987**(0.007) (0.005) (0.030) (0.007) (0.005) (0.028) (0.015) (0.010) (0.074) (0.031) (0.024) (0.182) (0.096) (0.072) (0.449)

Observations 585,873 705,055 585,873 391,461 472,450 391,461 153,142 183,544 153,142 19,252 22,962 19,252 8,898 10,828 8,898R-squared 0.004 0.004 -0.030 0.007 0.009 -0.037 0.002 0.001 -0.002 0.002 0.004 -0.009 -0.007 -0.006 -0.021Number of id 99,515 106,043 99,515 63,485 66,899 63,485 25,055 26,681 25,055 5,543 6,266 5,543 3,109 3,679 3,109IV MC Lags 1...4 1...4 - 1...4 1...4 - 1...4 1...4 - 1...4 1...4 - 1...4 1...4 -IV UCL Lags 0...4 - 0...4 0...4 - 0...4 0...4 - 0...4 0...4 - 0...4 0...4 - 0...4Hansen J 0 0 0 0 0 0 0 0 .14 .28 .066 .642 0 0 .175


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sticky prices, sticky information or rational inattention ... prices, sticky information or rational...

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