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Federal Reserve Bank of Chicago
Fast Micro and Slow Macro:
Can Aggregation Explain the
Persistence of Inflation?
Filippo Altissimo, Benoît Mojon, and
Paolo Zaffaroni
WP 2007-02
Fast Micro and Slow Macro: Can Aggregation
Explain the Persistence of Inflation?
Filippo Altissimo (Brevan Howard, London; …lippo.altissimo@brevanhoward.com)
Benoît Mojon (Federal Reserve Bank of Chicago; bmojon@frbchi.org)
Paolo Za¤aroni (Imperial College, London; p.za¤aroni@imperial.ac.uk)
First draft: November 2004. This draft: September 2006
Abstract
An aggregation exercise is proposed that aims at investigating whether the fast average
adjustment of the disaggregate in‡ation series of the euro area CPI translates into the slow
adjustment of euro area aggregate in‡ation. We …rst estimate a dynamic factor model for
404 in‡ation sub-indices of the euro area CPI. This allows to decompose the dynamics of
in‡ation sub-indices in two parts: one due to a common "macroeconomic" shock and one
due to sector speci…c "idiosyncratic" shocks. Although "idiosyncratic" shocks dominate the
variance of sectoral prices, one common factor, which accounts for 30 per cent of the overall
variance of the 404 disaggregate in‡ation series, is the main driver of aggregate dynamics. In
addition, the heterogenous propagation of this common shock across sectoral in‡ation rates,
and in particular its slow propagation to in‡ation rates of services, generates the persistence
of aggregate in‡ation. We conclude that the aggregation process explains a fair amount of
aggregate in‡ation persistence.
JEL CLassi…cation: E31, E32.
Key words: aggregation and persistence; in‡ation dynamics.
This paper was written while Filippo Altissimo and Benoit Mojon were working at the ECB. We are grateful
to Laurent Baudry, Laurent Bilke, Herve Le Bihan and Sylvie Tarrieu (Banque de France), Johannes Ho¤mann
(Bundesbank) and Roberto Sabbatini and Giovanni Veronese (Banca d’Italia) for sharing their data with us.
We also would like to thank Anna-Maria Agresti and Martin Eiglsperger (ECB) for their assistance in the reconstruction of historical time series of the German CPI sub-indices. Finally, we thanks Gonzalo Camba-Méndez,
Steven Cecchetti, M. Hashem Pesaran, Jim Stock and participants to the Eurosystem In‡ation Persistence Network
for helpful comments on previous presentations of this research. The opinions expressed here are those of the authors
and do not necessarily re‡ect views of the European Central Bank or of the Federal Reserve Bank of Chicago. Any
remaining errors are of course the sole responsability of the authors.
1
1
Introduction
Understanding the source and degree of in‡ation persistence is key both to improve our ability
to forecast in‡ation and to discriminate among di¤erent structural models of the economy. Successful out-of-sample forecasting of in‡ation requires in …rst instance to decide the appropriate
degree of persistence and, eventually, of non-stationarity of the data generating process. The
long adjustment of the aggregate in‡ation appears to be well approximated by a long memory
stationary process, whose autocorrelation function decays very slowly ("hyperbolically") toward
zero as the lag increases. Such a slow rate of decay has, in the case of in‡ation, led many empirical
studies to assume a unit root behavior for aggregate in‡ation 1 .
Turning to models of the business cycle, price stickiness is seen by many as the key ingredient
that allows micro founded DSGE models to deliver the in‡ation and output persistence that we
see in macroeconomic data (see Sbordone, 2003, Galì and Gertler, 1999, Christiano et al., 2005,
Smets and Wouters, 2003, among others.). Critics of sticky price models have stressed that the
degree of price stickiness usually assumed are far too large to make economic sense (Chari, Kehoe
and Mac Grattan, 2000)2 and inconsistent with the much faster average frequency of adjustments
that can be observed in the micro data (Bils and Klenow, 2004 and Dhyne et al., 2005, Horváth
and Coricelli, 2006).
However, the theory of cross-sectional aggregation of dynamic processes (see Robinson, 1978,
Granger, 1980, Forni and Lippi, 1997, and Za¤aroni, 2004) show that slow macroeconomic adjustments may very well be consistent with much faster average speed of adjustments at the micro
level. This paper uses sectoral prices of the euro area to test whether these explicit models of
the aggregation process can solve the apparent dilemma between the ‡exibility of sectoral prices
and the persistence of macroeconomic in‡ation.
To start with, aggregation is a necessary step in the construction of macroeconomic price
indices from survey prices on individual goods and services. For instance, in the US the Bureau
of Labor Statistics collects prices for approximately 80,000 goods and services each month, which
are divided into 350 categories called entry level items; those data are aggregated up to the overall
CPI. The link between the monthly micro price quotes for each entry level item, whose relative
frequencies of changes has been analyzed by Bils and Klenow (2004) and Dhyne et al. (2005),
and the aggregate CPI implies at least two layers of aggregation: the …rst one goes from the
individual price records to the price index of the relevant subcategory. The second one relates
the subcategories to the aggregate CPI. This paper focuses on this second layer.
We estimate a linear dynamic factor model for 404 sub-indices of the euro area CPI between
1985 and 2003. In the model, each in‡ation series depends on a macroeconomic shock, the
common factor, and a subcategory (or "sectoral" thereafter) speci…c idiosyncratic factor. We
then aggregate back the 404 models of micro level in‡ation and decompose the dynamics of this
1
2
See for instance O’Reilly and Whelan (2005) and references therein.
See also Golosov and Lucas (2006) and Mackowiak and Wiederhot (2005).
2
aggregate into the e¤ects of the common and the idiosyncratic shocks.
Our main …ndings can be summarized as follows. First, we …nd that one common factor
accounts for 30 per cent of the overall variance of the 404 series. This share is twice as large
if one focuses on low frequencies, i.e. on the persistent components of the series. Second, the
propagation mechanism of shocks is highly heterogenous across sectors. This heterogeneity is
the prerequisite ingredient for the aggregation mechanism to be maximally e¤ective. Third, the
implied persistence from the aggregation exercise mimics remarkably well the persistence observed
in the aggregate in‡ation. In particular, the cross-sectional distribution of the micro parameters
implies an autocorrelation function of the aggregate CPI in‡ation which decays hyperbolically
toward zero and displays long memory. Altogether, the high volatility and low persistence,
observed on average at the level of sectoral in‡ation, is consistent with the aggregate smoothness
and high persistence.
This work is related to a recent stream of literature that stresses the importance of understanding micro heterogeneity and the aggregation process in order to explain the dynamic properties of aggregate variables. Imbs, Mumtaz, Ravn and Rey (2005) show that the persistence of
aggregate real exchange rates is substantially magni…ed because the dynamics of disaggregated
relative prices is heterogenous. Carvalho (2006) derives a generalized new Keynesian Phillips
curve that accounts for heterogeneity in price stickiness across sectors and shows that the process
of adjustment to nominal shocks tends to be more sluggish than in comparable identical …rms
economies. Altissimo and Za¤aroni (2004) show that the properties of aggregate income for the
US can be reconciled with the dynamic properties of a cross section of individual level income
extracted from the PSID panel.3
The paper is organized as follows. The following section presents the elements of cross-section
aggregation relevant to our analysis. Section 3 presents the data used in the empirical analysis
and addresses the presence of common factors across the price sub-indices. Section 4 introduces
the micro model and the estimation methodology. It then discusses the estimation results and
their implications for the aggregate persistence. Section 7 concludes.
2
Aggregation of heterogeneous AR(1) models
In this section we revisit, by means of examples, the relevant results on contemporaneous aggregation of heterogeneous ARMA models, when the number of units gets arbitrarily large (see
3
On a related issue, Caballero and Engel (2005) have shown that if the adjustment process is lumpy or step-wise
then estimating the speed of adjustment by linear method tend to over-estimate the speed of adjustment and that
this e¤ect washes out in the case of cross sectional aggregation but at a very low speed. Their result can be
regarded as a criticism to the common practice of using linear method to measure persistence.
Clark (2003) and Boivin et al.(2006) also stress the importance of the decomposition of sectoral price dynamics
into common aggregate shocks and sectoral idiosyncratic ones. They however do not model the aggregation process
and its impact on in‡ation persistence.
3
Robinson, 1978, Granger, 1980, and Za¤aroni, 2004). For sake of simplicity, let the ith sub-index
be described by an AR(1) model
yit = i yit 1 + it ;
(1)
where both the coe¢ cients and the random shocks vary across units. When considering an
arbitrarily large number of units, a convenient way to impose heterogeneity is to assume that
the coe¢ cients i are i:i:d: random drawn from some underlying distribution with probability
density function f ( ). Stationarity of each of the yit then requires j i j< 1 a:s: or, alternatively,
that f ( ) has support ( 1; 1). The random shock is the sum of a common and of an idiosyncratic
component
(2)
it = ut + it ;
with the ut being an i:i:d: sequence (0; 2u ) and it being an i:i:d: sequence (0; 2;i ). The i;t are
also assumed independent across ith. The aggregate variable is simply the sample average of the
individual units.
It is well known that summing a …nite number of ARMA processes yields again an ARMA
process. For example, the sum of n distinct AR(1) models, with di¤erent auto-regressive parameters, yields an ARMA(n; n 1). However, when n goes to in…nity, it turns out that under mild
conditions on f ( ), the limit of the aggregate as n ! 1 will not belong to the class of ARMA
processes, in contrast to the individual yit . We explore such a case.
In view of (2), by stationarity and linearity of the individual models it follows that
n
Yn;t
n
ut
1X
1X
+
=
n
1
n
1
iL
i=1
it
iL
i=1
= Un;t + En;t ;
(3)
meaning that the aggregate could be decomposed into a common and idiosyncratic component.
Although the statistical properties of each unit are well-de…ned, conditioning on i , knowledge of
the entire history of each individual yit , or at most for a …nite number n of them, is uninformative
with respect to the distribution, f ( ). However, when looking at an arbitrarily large number of
units, the distribution f ( ) will then entirely determine the properties of the limit aggregate,
which we de…ne as the limit (in mean-square) of the Yn;t for n ! 1.
To this end, let us focus on the common component. This can be written as
Un;t = ut + ^ 1 ut
1
+ ^ 2 ut
2
+ ::: + :::;
(4)
P
setting ^ k = n1 ni=1 ki for every k. When n gets large, by the strong law of large numbers, each
R k
^ k will converge a:s: to the population moments of the i , i.e. k =
f ( )d : The dynamic
pattern of the k represents the impulse response of the common shocks ut on the aggregate.
The dynamic pattern of the k uniquely depends on the shape of the density f ( ) and in
particular on its behavior around the unit root. In particular, Za¤aroni (2004) shows that for any
distribution whose behavior around unit root can be represented, up to a scaling coe¢ cient, as
(1
)q 1 ; q > 0, then it follows k ck q as k ! 1, where denotes asymptotic equivalence.
4
Thus, an exponential rate of decay of the impulse response of the micro units ( ki ) corresponds
to an hyperbolic rate of decay for the aggregate (k q ), that depends on f ( ) through q. The
smaller is q, the denser is f ( ) distribution around the unit root (i.e. more micro units are very
persistent), the longer it takes for k to converge towards zero (recall that q > 0 for f ( ) to be
integrable and thus be a proper probability density function).
To further illustrate this result, let us consider the following parametrization of f ( )
(
B 1 (p; q) p 1 (1
)q 1 ; 0
< 1;
f( ) =
0;
otherwise;
corresponding to the Beta(p; q) distribution, with parameters p; q > 0. Table 1 reports the dynamic pattern of k for various values of q with the mean of Beta(p; q) set equal to 0:8 ( 1 = 0:8).4
The results are contrasted with the case of homogeneous AR(1), with impulse response given by
k (auto-regressive coe¢ cient equal to
1 ). This example illustrates the e¤ect of aggregation
1
taking, as a benchmark, the case where all sub-indices are similar AR(1) processes with autoregressive coe¢ cient equal to 1 = 0:8, i.e are quite persistent.
Table 1: Impulse response functions of limit aggregate Ut
k
q=
1
2
5
10
50
200
0:2
0:8
0:72
0:61
0:54
0:39
0:36
k
1
f( )
0:7
0:8
0:67
0:48
0:33
0:12
0:09
1
0:8
0:66
0:44
0:28
0:07
0:05
3
0:8
0:65
0:37
0:17
0:01
0:01
0:8
0:64
0:33
0:11
1:4 10
4:1 10
5
20
The e¤ects of heterogeneity and aggregation are substantial: the impulse response function
of the aggregate process (common component) decays towards zero with a much slower decay
than the homogeneous coe¢ cient case. Note that the smaller q is, the larger is the mass of the
distribution around the unit root and the slower will the e¤ect of random shocks fade away. In
other words, the average impulse response is markedly di¤erent from the impulse response of the
average.
The characterization of the impulse response implies a neat representation of the autocovariance function (acf) and spectral density of the limit aggregate Ut . In particular, when
q > 1=2, the autocovariance function of the limit aggregate process satis…es
var(Ut ) < 1; cov(Ut ; Ut+k )
ck 1
2q
as k ! 1;
(5)
with c being an arbitrary scaling constant. One can easily see that cov(Ut ; Ut+k ) decays toward
zero albeit at an hyperbolically rate. When q > 1, the density f ( ) will have little mass around
4
1
In order to consider Beta(p; q) distributions with di¤erent q but same mean
q.
5
= 0:8; one needs to set p =
the unit root (f ( ) # 0 as approaches 1) and the cov(Ut ; Ut+k ) is summable, meaning that
it decays to zero su¢ ciently fast. This is known as a case of short memory. Instead, when
1=2 < q < 1, large mass of the f ( ) will be around the unit root (f ( ) " 1 for approaching
1). For this case, the cov(Ut ; Ut+k ) still decays toward zero but too slowly to ensure summability,
resembling the classical de…nition of long memory. In particular, we say that Ut is a stationary
process displaying long memory with memory parameter 0 < d < 1=2 whenever
cov(Ut ; Ut+k )
ck 2d
1
;
as k ! 1:
(6)
The previous Beta distribution example yields a particular case of (6) setting d = 1 q. Hence,
the smaller is q, the larger is the frequency of units whose i is close to unity, and the more
persistent is the limit aggregate. Finally in the extreme case when 0 < q < 1=2; the aggregate
process will be non stationary; this is evident since the autocovariance function does not even
decay to zero as k increases.
Two …nal remarks are warranted. First, the idiosyncratic component can be neglected as long
as the aggregate is stationary, because their e¤ect should vanish through aggregation. However,
in the case of non-stationary aggregate, namely 0 < q < 1=2, the idiosyncratic components of the
very persistent micro processes can still show up in the aggregate. Second, the above results can
be extended within a general ARMA framework where the implication for aggregation depend
on the shape of the distribution of the largest autoregressive root of the ARMA process. See
Za¤aroni (2004) for more details.
3
The data
The data consist of 404 seasonally adjusted quarter over quarter (q-o-q) in‡ation rates of CPI
sub-indices from France, Germany and Italy. In this section, we …rst discuss our choice of data
and sample period. Second, we present descriptive statistics on sectoral and aggregate in‡ation
and their persistence. Finally, we propose some evidence on the presence of a common driver
among the 404 in‡ation subindices.
3.1
Choice of data and sample period
We use CPI data rather than HICP because the latter are available only since 1995. However,
because earlier data are not readily available in all the countries of the euro area, we limited our
data to France, Germany and Italy. These countries together account for roughly 70 per cent of
the euro area population and consumption. The three CPI original databases together comprise
470 sub-indices. 66 of these were not suitable for estimation of an ARMA either because they
have too few observations (e.g. some sub-indices are available only since 2000), or because they
correspond to items which prices are set at discrete intervals (e.g. Tobacco or Postal services).
6
We are left with 404 "well-behaved" series that are proper to be modeled.5
We focus on the post 1985 data for two reasons. First, the German data are not available
beforehand. Second, many studies have showed that the mid-eighties marked a signi…cant break
in average in‡ation in most OECD countries. Corvoisier and Mojon (2005) suggests that Italian,
French and German time series of in‡ation all admit a break in the mid-eighties. Bilke (2005)
obtains that most of the 148 French sectoral in‡ation rates (exactly our data as far as France
in concerned) admit a break in their mean around 1985 and very infrequently at any other time
of the 1972-2003 sample period. Bilke argues that this coincidence of changes in the dynamics
of sectoral in‡ation rates may actually re‡ect a major shift in French monetary policy regime
in the mid-1980’s. According to Gressani, Guiso and Visco (1988), such a regime shift is also
very likely to happen at about the same time in Italy. As regards Germany, where the monetary
policy regime was more stable, the breaks in average in‡ation of its two largest trade partners is
a major event in itself.
For all these reasons, we deem the post-1985 sample as appropriate to study the persistence of
in‡ation in the euro area. This choice of sample leaves us up to 77 observations of q-o-q in‡ation
rates for each of the 404 sub-indices.
3.2
Sectoral in‡ation series: descriptive statistics
We now turn to the properties of the sub-sector in‡ation rates. Table 2 reports descriptive
statistics of aggregate in‡ation and of the distribution of the 404 sectoral in‡ation rates. First,
the in‡ation sectoral means are quite disperse with …fty per cent of their distribution ranging
from 1:8 to 4:2 percent. The mean of aggregate in‡ation is 2:6 percent. Second, sectoral in‡ation
is noticeably more volatile than aggregate in‡ation. On average, the standard deviation of the
in‡ation sub-indices is equal to 3:5 percent, i.e. nearly three times as large the standard deviation
of the aggregate. This much higher volatility is a common feature of the in‡ation rates of sectoral
prices as shown in Bilke (2005) and Clark (2003). Third, the persistence of sectoral in‡ation rates
is also clearly smaller than the one of the aggregate in‡ation series. The largest root of the ARMA
…tted to the aggregate in‡ation amounts to 0:93.6 This roughly equals to the 75th percentile of
the sector’s persistence.
If the sectoral data would already display long memory, so that (6) holds for the large majority
of the sub-indices in‡ation rates, then the aggregation exercise would be trivial. The last column
of the table, which reports the statistics relative to the distribution of estimated long memory
parameters, based on the the parametric Whittle estimator (see Brockwell and Davis, 1991),
con…rms that only very few sectoral in‡ation rates exhibit fractional integration. d is not di¤erent
from or close to 0:5 for a vast majority of the cross-section. However, as shown below, our
5
See the Appendix for the source of the data and the data treatment.
The largest root is the one associated to the best ARMA(p; q) as selected by the Akaike (AIC) criteria with
0
p; q
4, estimated on the q-o-q in‡ation time series for the 1985q2-2004q2 sample, using the ARMAX
procedure of MatLab.
6
7
estimate of d for the aggregate in‡ation rate is 0:18, well above the 75th percentile of the sectoral
d parameters ( 0:18). Fourth, we observe sharper di¤erences in persistence across the main
sectoral groupings of the CPI (processed food, unprocessed food, energy, non-energy industrial
goods-NEIG- and services) than across countries. The gap between the ARMA largest root of
the in‡ation process of unprocessed food prices (0.52) and one of the energy (0.78) is wider than
between the root associated to the ARMA processes …tted on the in‡ation of German, French
and Italian prices. Comparing the main groupings of CPI sub-indices across countries, we also
…nd that the sectoral hierarchy at the euro area level applies within each country.
To conclude, we …nd clear evidence that the in‡ation rates of the individual sub-indices are
way more volatile and much less persistent than the in‡ation rate of the aggregate CPI index.
Moreover, volatility and persistence are more sector than country dependent.
Table 2: Descriptive statistics of the 404 sectoral in‡ation rates
(…rst two columns annualized q-o-q in‡ation rates)
Aggregate of 404
Mean
Stand. dev.
Larg. ARMA root
Long mem. d
2.6
1.1
0.93
0.18
Cross section characteristics
Weighted mean
2.6
3.6
0.78
-0.33
Unweighted mean
2.4
3.5
0.72
-0.36
Minimum
-11.3
0.7
-0.81
-0.50
25th percentile
1.8
1.7
0.71
-0.50
Median
2.6
2.5
0.83
-0.43
75th percentile
4.2
4.0
0.90
-0.18
Maximum
8.1
25.4
1.02
0.32
Mean for selected sub-sets
3.3
France
1.8
3.0
0.72
-0.34
Germany
1.5
3.2
0.71
-0.34
Italy
3.6
4.3
0.73
-0.36
Processed food
2.6
3.1
0.68
-0.20
Unprocessed food
2.3
3.9
0.52
-0.33
NE Indus. goods
2.0
2.2
0.77
-0.38
Energy
1.9
8.4
0.78
-0.37
Services
3.3
3.0
0.74
-0.33
Behind the aggregation mechanism: common shock and heterogeneous
parameters
This section assesses the two elements that play a crucial role in shaping the e¤ect of crosssection aggregation of time series: the presence of common shocks and the heterogeneity in the
propagation mechanism of those shocks. This means that, using the notation of Section 2, there
8
is a common shock ut and that the i are di¤erent across i. We start by investigating the
presence of common shocks in the cross-section of the in‡ation sub-indices before enquiring on
the heterogeneity in the propagation of this common shock across sectors.
Following the recent literature on factor model in large cross-sections7 we estimate the …rst
ten dynamic principal components of the autocovariance structure of the sectoral in‡ation series.
The dynamic principal component analysis provides indications on the number of common shocks
explaining the correlation structure in the data (see Forni et al., 2000).
Figure 1 presents the spectrum of the …rst ten dynamic principal components8 of the 404
in‡ation time series.
0.3
Spectrum
0.25
0.2
0.15
0.1
0.05
0
0
0.5
1
1.5
2
2.5
3
Frequencies
Figure 1: First ten principal components.
The variance of sectoral in‡ation is strikingly dominated by one common factor. Figure 1 also
shows that this …rst common factor is the only one of which the spectrum is concentrated on
7
See Forni et al. (2000), Stock and Watson (2002) and the application by Clark (2003) to US disaggregate
consumption de‡ators.
8
Dynamic principal components are calculated as the eigenvalue decomposition of the multivariate spectra of
the data at each frequency (see Forni et al. (2000) for details). The autocovariance function up to eight lags has
been used in the construction of the multivariate spectral matrix. The data has been standardized to have unit
variance before estimating the multivariate spectra.
9
low frequencies. Hence this factor is the driver of persistence observed in sectoral in‡ation.9 The
other factors account for a much smaller share of the variance than the …rst one. They are also
more equally relevant at all frequencies, as indicated by their relatively ‡at patterns in Figure
1.10
On the basis of these results, we opt for a factor model of the sectoral in‡ation series that
admits a single common shock. We then model the sectoral in‡ation time series as:
yit =
0i
+
i (L)ut
+
it ;
i = 1; :::; N
(7)
where ut is the common shock, it is a stationary idiosyncratic component, orthogonal to the
common one and 0i is the constant term. i (L) is a unit speci…c lag polynomial which represents
the propagation of the common shock through the yit process.
We now look at whether the propagation mechanism of the common shock in the crosssection of price sub-indices is homogenous across items. Still resorting to spectral analysis, we
estimate the coherence of the …rst principal component and each one of the 404 series, in order
to obtain "correlation" at di¤erent frequencies. Figure 2 reports the cross-section distribution of
the squared coherence values at three frequencies: 0, =6 (three years periodicity) and =2 (one
9
The height of the spectrum at frequency zero is a well-known non parametric measure of the persistence of a
time series.
10
These …ndings are in line with Clark (2003)’s results. He also shows that the common factor of the disaggregate
US in‡ation rates is more persistent than the idiosyncratic components.
10
year periodicity) respectively.
Rel. Freq.
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sq. Coherence at zero frequency
Rel. Freq.
40
30
20
10
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Sq. Coherence at π/6 frequency
Rel. Freq.
40
30
20
10
0
0
Sq. Coherence at π/2 frequency
Figure 2: Distribution of the squared coherence.
The di¤erences in the mode and the shape of the histograms across the three frequencies is a
…rst, yet strong, indication of the presumption that the common shock transmission to sectoral
in‡ation is heterogenous. The following section models this heterogeneity.
4
4.1
Model: speci…cation and estimation
The model
The quarterly rate of change of each sectoral price sub-index is assumed to behave according to
(7):
yit =
=
with ut
i:i:d: (0; 1) and
operator satisfy i (z) 6= 0;
it
+ it
(L)
i (L)
i
ut +
0i +
Ai (L)
Ai (L)
0i
+
i (L)ut
(8)
it ;
i:i:d: (0; 2i ); i = 1; :::; N . The above polynomials in the lag
1. Each yit behaves as a stationary
i (z) 6= 0; Ai (z) 6= 0 jzj
11
ARM A(pi ; qi ) with a possibly non zero mean, where 1
pi ; q i
2, in the estimation part,
and the order qi ; pi of the models are estimated based on the Akaike criteria. Note that we
are imposing that the common part, involving the ut , and the idiosyncratic part, involving the
i;t , have the same autoregressive structure but they are not constrained in the moving average
part. Moreover, for the sake of simplicity, we are also assuming that both the common and
the idiosyncratic component have an MA component at most of order qi in both cases. These
assumptions simplify greatly the estimation procedure and, at the same time, allow a su¢ ciently
rich dynamics. Note that the sectoral coe¢ cients are estimated freely so that, for example, the
parameters in i (L) and i (L) are sector speci…c.
4.2
The estimation strategy
The estimation of model (8) is non standard. First, the large dimensionality (large N ) rules
out the recourse to the conventional Kalman …lter approach. Second, the recent techniques for
estimation of dynamic factor models, all based on the principal component approach such as
Stock and Watson (2002) and Forni et al. (2005), would be inappropriate in our model due to
the presence of sector speci…c autoregressive components, Ai (L). This is why we estimate the
parameters of the model (8) by means of a multi-stage procedure:
(i) For each unit i, we estimate an ARMA(pi ; qi ) with non-zero mean but without distinguishing between the common and the idiosyncratic component. In fact the sum of two moving
average components of …nite order,
i (L)ut
+
i (L) it
Bi (L)zit ;
turns out to be an M A of the same order with polynomial Bi (L) and an innovation sequence zi;t
(we are not interested in extracting the zi;t although it is technically possible). Moreover, we do
not need to specify the coe¢ cients of Bi (L) as a function of the coe¢ cients i (L); i (L), in order
to obtain consistent estimate of the constant term, 0i ; and of the coe¢ cients of autoregressive
part, Ai (L);
(N )
^i (L)^
(ii) we average the estimated MA component B
zi;t across i. This yields an estimate x
bt
P
of N 1 N
i=1 i (L) ut , where the approximation improves as N grows since the idiosyncratic
P
component N 1 N
i=1 i (L) i;t vanishes in mean-square as N ! 1. Thus we …t a …nite order
(N )
M A to the estimated x
bt and obtain an estimate of the common innovation u
^t ;
(iii) using the u
^t as an (arti…cial) regressor, we …t a ARM AX(pi ; qi ; qi ) process (an ARMA
process with exogenous regressors) to each yit , in order to obtain also consistent estimate of the
coe¢ cients of i (L) and i (L).
The steps (ii) and (iii) of the procedure can be iterated in order to improve the estimate of the
common shock as well as of the autoregressive parameters. Such procedure does not require any
distributional assumption. Implicitly it requires that both N; T to diverge to in…nity. Estimation
of each of the ARMA and MA processes is carried out using the ARMAX procedure of MatLab.
12
Details of the algorithm can be found in Altissimo and Za¤aroni (2004). The described
iterative procedure is similar to a recent modi…cation of the EM algorithm for the estimation
of factor models in the presence idiosyncratic autoregressive components recently proposed by
Stock and Watson (2005).
4.3
4.3.1
Results
Results for sectorial in‡ation rates
This section brie‡y describes the estimates of over three thousand parameters (8 parameters for
each of the 404 time series) of the model. First, the estimated common shock ut turns out to
be white, with a non-signi…cant autocorrelation, corroborating the i:i:d: hypothesis. Second, we
compare (in Figure 3) the distribution of the absolute value of the …rst loading of the common
shock, which is a measure of the size of the e¤ect of the common shock in the individual time series,
with the cross-sectional distribution of the standard deviation of the idiosyncratic components.
The idiosyncratic volatility i is substantially larger than the common shock volatility, in fact six
times larger. The median of the distribution of the absolute value of the estimated …rst loading
is 0:06; whereas we obtain 0:38 for the standard deviation of the idiosyncratic component. This
strikingly con…rms that most of the variance of sectoral prices is indeed due to sector speci…c
13
shocks.
7
6
Rel. freq.
5
4
3
2
1
0
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
Abs first loading u
t
2
Rel. freq.
1.5
1
0.5
0
0
0.5
1
1.5
2
2.5
Std idios yncratic shock
Figure 3: Distributions of
0i
and
i:
Third, we turn to Ai (L), which dominates the dynamic e¤ects of the common shock on sectoral
in‡ation. In Figure 4 we report the distribution of the signed modulus of the maximal autoregressive root of such polynomia.11 This distribution is dense near unity with a median of 0.82, a
11
We did sign such modulus so that we could distinguish between the e¤ect of a negative root from a positive
one and also consider the e¤ect of complex roots.
14
mode at 0.93 and a long tail to the left.
3.5
3
Density
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Max. auto. root
Figure 4: Max autoregressive roots.
Fourth, we compare the dynamics of sectoral in‡ation rates and main CPI groupings in Table
3. The table reports the number and the relative frequency of series having roots above given
thresholds in speci…c sub-category as well as the total weight of such series in the overall CPI.
15
Table 3: Summary statistics of estimated parameters for sectorial in‡ation rates
#
CPI weight
Largest root >0.875
Largest root >0.925
#
freq
CPI weight
#
freq
CPI weight
EA3
404
1
142
0.35
0.48
54
0.27
0.26
Germany
87
0.42
31
0.34
0.23
11
0.12
0.14
France
147
0.30
55
0.38
0.15
23
0.17
0.06
Italy
170
0.28
56
0.35
0.11
20
0.12
0.06
Processed food
65
0.14
9
0.14
0.03
2
0.03
0.01
Unprocessed food
42
0.07
7
0.17
0.01
3
0.07
0.00
Non-energy ind. goods
167
0.33
68
0.42
0.14
25
0.15
0.08
Energy goods
18
0.07
8
0.50
0.05
5
0.31
0.03
Services
114
0.39
50
0.44
0.25
19
0.17
0.14
Looking at the cross country pattern, highly persistent sub-sectors in Germany account for a
much larger share of the overall euro area CPI; this e¤ect is mainly due the high persistence (autoregressive root of 0.96) of German housing expenditure in‡ation12 , which accounts for around
10 per cent of the overall CPI. Furthermore, while Energy and Service has the highest frequency
of persistent series, Services and, to some degree, Non-energy industrial goods sub-sectors turn
out to be more relevant for the dynamics of aggregate in‡ation because they have a higher weight
in the consumption basket.
4.3.2
Results for aggregate in‡ation rate
Given the estimates of the micro parameters, we are now in a position to infer the dynamic
properties of the aggregate induced by the behavior of the micro time series. We consider three
di¤erent types of aggregation schemes. First, we reconstruct the aggregate as an exact weighted
average of the individual micro time series and in this way we exactly recover the contribution of
the common shocks to the aggregate in‡ation and to aggregate persistence. Second, we exploit
the theoretical link between the distribution of the largest autoregressive root of sectoral in‡ation
rates and the autocovariance structure of the aggregate, as presented in section 2, to infer the
dynamic properties of the latter. Third, we consider a so-called naive aggregation scheme based on
the (wrong) presumption that the aggregate model has the same functional form as the individual
models, in our case an ARMA.
12
The subindex is apartment rent (incl. the value of rent in case of owner-occupied houses), which account for
around 20 per cent of the German CPI, while it is only 3 per cent of the Italian and French.
16
Exact aggregation
The aggregate in‡ation data is de…ned as the weighted average of the sectoral in‡ation rates.13
Therefore using the estimates of the model in (8) it follows:
Yn;t =
n
X
wi yit
i=1
wib0i + ut
i=1
=
n
X
n
X
wi
i=1
b0 + b (L)ut + b
t
b i (L)
bi (L)
A
+
n
X
i=1
wi
b i (L)
bi (L)
A
it
where the wi are the euro area CPI weights. So the aggregate in‡ation is decomposed into two
components, one associated with the common shocks, ut ; and its propagation mechanism, b (L);
and a second associated with the micro idiosyncratic process, t : Figure 5 shows the reconstructed
aggregate, Yn;t ; versus its common component, b (L) ut : There is a high correlation between
the two components, around 0.76, but the former is clearly more volatile pointing to the fact that
the idiosyncratic component t is still relevant in the aggregate. Given that the idiosyncratic
component has little persistence, b (L) ut can be interpreted as a measure of core in‡ation,
13
Statistical o¢ ces do not aggregate in‡ation rates but …rst they aggregate price indices and then compute the
aggregate in‡ation rate. Here we ignore the possible e¤ect induced by such non-linear transformation. In fact it
can be shown that this is not relevant for the dynamic properties of the aggregate.
17
possibly relevant for monitoring and forecasting in‡ation.
4.5
4
3.5
Q-o-Q Inflation
3
2.5
2
1.5
1
0.5
0
1988
1990
1992
1994
1996
1998
2000
2002
2004
Tim e
Figure 5: Aggregate in‡ation (solid line) and common component.
The aggregate propagation mechanism, b (L); is a weighted average of the propagation at micro
level, b i (L) and its estimates can be used to recover the autocovariance structure of the component of the aggregate in‡ation that is driven by the common shock, i.e.: b (L) ut : The upper
panel in Figure 6 shows the autocovariances of aggregate in‡ation, Yn;t ; (solid line) versus the
one of b (L) ut (dotted line), while the lower panel reports the average autocovariance of micro
18
process.14
0.07
0.06
Autocovariance
0.05
0.04
0.03
0.02
0.01
0
-0.01
0
5
10
15
20
25
Lag
Figure 6a:Autocovariances aggregate (solid) and common
component.
1.4
1.2
Average Autocovariance
1
0.8
0.6
0.4
0.2
0
-0.2
0
5
10
15
Lag
Figure 6b: Average autocovariance.
14
Two graphs were needed given the di¤erent scale of the results.
19
20
25
The autocovariance of the reconstructed common components tracks well the covariance structure
of the aggregate data, in particular in term of its decay. The variance of the aggregate in‡ation
remains slightly larger than the one of the common component, i.e. the component associated
with micro idiosyncratic noise is still relevant in the aggregate data, even if it seems to have
little or no dynamic structure. The contrast between the results across the two panels of Figure
6 is even more striking. The cross-sectional average variance of the micro data is an order of
magnitude larger than the one of the aggregate data or of the common component in the aggregate
data but it decays to zero very quickly. Finally, Figure 7 compares the autocorrelation of the
aggregate and the one of the common component. The same conclusion emerges. The common
component is the main driver of the dependence of the aggregate data and it properly captures
the slow decay of autocorrelation of the data.
1.2
1
Autocovariance
0.8
0.6
0.4
0.2
0
-0.2
0
5
10
15
20
25
Lag
Figure 7: Autocorrelation of aggregate in‡ation (solid line)
and of the common component.
Asymptotic aggregation
The above discussion has been based on the analysis of the exact autocovariance structure of
the common component. Similar conclusion can also be derived by analyzing the cross-sectional
distribution of the largest root of the autoregressive part (Figure 4) using the analytic apparatus
presented in Section 2.
However we …rst need to take into account that sectors have di¤erent weights in the aggregate.
Therefore the distribution in Figure 4 which represents the distribution of the 404 maximal roots
20
is not directly relevant because the weighting scheme in the aggregation can change the relative
importance of the sectors for the dynamics of the aggregate. To overcome this problem, we
implement a relative re-weighting of the 404 maximal autoregressive roots in function of the
relative weights of the respective sectors. Precisely, we bootstrap a sample of 10,000 data out
of the 404 roots with relative frequency equal to the weighting scheme; hence roots associated
to sectors will a larger weight will be re-sampled more often. The density function associated to
this simulated sample is compared to the equal weight one in Figure 8.
5
4.5
4
3.5
Density
3
2.5
2
1.5
1
0.5
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
Max. auto. root norm alized
Figure 8: Renormalized distribution of max autoregressive root (solid) and
original one.
The implication for aggregation are associated to the behavior near unity of such new distribution.
In particular, the above distribution can be approximated near unity as
f^( )
c(1
)
0:13
as
!1 ;
implying that our estimate of the q as in Section 2 is equal to 0:87: Following (5) in Section 2
and the results in Za¤aroni (2004), it is possible to show that the acf of the common component
of the aggregate, b (L) ut ; satis…es:
cov( b (L)
ut ; b (L)
ut+k )
21
ck
0:74
as k ! 1:
According to de…nition in Section 2, the process has long memory with parameter d = 0:13.
Therefore, the common component of the aggregate in‡ation appears to be a stationary but long
memory process. Therefore, the acf decays toward zero with an hyperbolic decay, and thus is
markedly di¤erent from the behavior of the sectoral in‡ation processes.
We then estimate the memory parameter for the aggregate data using the Whittle parameteric
estimator (see Brockwell and Davis, 1991). The direct estimate of the memory parameter on
aggregate data turns out to be equal to 0:18, with standard error of the estimate equals to 0:24;
which, given the distribution reported in the last column of Table 2, is reasonably close to 0:13;
as recovered from the micro structure. Therefore, the aggregate data presents a long memory
behavior that is not present in the micro time series; such a long memory behavior appears to
be fully accounted for by aggregation.
Naive aggregation
The above results are framed in term of autocovariance function and they show why the di¤erence
in persistence between the micro dynamic and macro one are not necessarily inconsistent. Another
way to highlight the e¤ects of aggregation on persistence is to consider the following naive exercise.
We construct an hypothetical ARMA process, whose roots are the mean of the individual roots
of the 404 estimated ARMAs. We then contrast the impulse response function to a common shock
of such a hypothetical ARMA with the one of the common component, b (L) ut : The idea of
the exercise is to see the aggregate response to shock in case the propagation mechanism is equal
across agents versus the case of di¤erent propagation mechanisms, i.e., to quantify the e¤ect of
heterogeneity and aggregation15 . Figures 9 compares the impulse response for the ARMA and
15
See also the presentation of similar exercises in the context of micro-founded models, though on hypothetical
distributions by Carvalho (2006).
22
the one implied by b (L):
1
0.9
0.8
Impulse Response
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0
5
10
15
20
25
Lag
Figure 9: Impulse response of the common component and of the
naive ARMA.
The exercise is quite instructive. In the case of a homogeneity of the micro propagation mechanism, after four years (16 periods on the x axis in Figure 9) a shock ut would be completely
absorbed, while in reality, due to the presence of heterogeneity and of some very persistent micro
units, around 20 per cent of the original shock has not been absorbed.
Summarizing, we can claim that the analysis of the micro determinants of the aggregate
in‡ation supports the view that aggregate in‡ation in our sample period can be well described
by a stationary but long memory process. We have shown that starting from very simple ARMA
process at micro level we have been able to properly reconstruct the dynamic properties of the
aggregate. We have also shown that the micro volatility and low persistence can be squared with
the aggregate smoothness and persistence.
5
Conclusion
In this paper, exploiting the heterogeneity in the in‡ation dynamics across CPI sub-indices,
we investigate the role played by cross-sectional aggregation in explaining some of the di¤erence
observed between micro and macro evidence regarding in‡ation dynamics. We focus in particular
on the link between CPI sub-indices and the aggregate CPI.
23
We estimated time series models for 404 sub-indices of “items/sectors” of euro area CPI
between 1985 and 2003. We …tted ARMA processes at micro level distinguishing the propagation
mechanism of the common and idiosyncratic shocks. Our …rst result is that the propagation
mechanism of shocks at the micro level is heterogenous across sectors. This heterogeneity implies
a non trivial link between sectoral and aggregate persistence. We perform an aggregation exercise
and compute the aggregate persistence as a function of the 404 sectors persistence. Our model
is able to square the high volatility and low persistence observed, on average, at the level of
sectoral in‡ation with the smoothness and persistence of the aggregate. The persistence that
we obtain through this aggregation exercise mimics remarkably well the persistence observed
in the aggregate in‡ation. In particular, aggregate in‡ation turns out to be a stationary but
long-memory process and the persistence of the aggregate in‡ation is mainly due to the high
persistence of some sub-indices mainly concentrated in the service sector, such as housing rents
in Germany.
Altogether, this paper demonstrated the importance of heterogeneity and aggregation for
understanding the persistence of in‡ation at the macroeconomic level. We leave the design and
estimation of stylized models of the business cycle that can be consistent with both heterogeneity
at the micro level and the implied persistence at the macro level for future research.
24
Data appendix
The French CPI sub-indices
The French data consist of 161 monthly sub-indices. They are available since 1972 and they
have been back-dated the INSEE CPI (1998 base year). The later is publicly available since 1990
for 148 sub-indices while the prices of 13 items enter the CPI basket only after this date.
The German CPI sub-indices
The German data consist of 100 prices of the 3 Digits classi…cation of HICP sub-indices.
These prices are available monthly from early 90s to 2004.
To back date the HICP, we used about 150 3-digits sub-indices of the 1990 base year CPI
data, which are available between 1985 and 1995.
The Italian CPI sub-indices
The Italian data consist of 167 monthly indices underlying the Italian CPI constructed by
ISTAT. The data, kindly provided by the Bank of Italy Research Department, start in 1980 and
were rebased to 1995 equal to 100. The full list, and corresponding description, of the sectors is
available upon request from the authors.
Seasonal adjustment
The data were seasonally adjusted with TRAMO-SEATS. The main advantage of this routine
is that it is used regularly for the o¢ cial HICP statistics, and that it allows for integrated seasonal
components. This latter aspect is particularly important for our data because EUROSTAT has
required that, from the mid-1990’s on, the biannual sales campaigns are re‡ected in the HICP
sub-indices of interest. This may a¤ect in particular our French and our German data. As a
matter of facts, the Banca d’Italia keeps track of the prices both with the new method and
consistently with the historical data. And we used the historically consistent series.
In the seasonal adjustment procedure, we utilized the longest available monthly series, i.e.
1972-2004 for France, 1981-2004Q2 for Italy and 1985-2004 for Germany.
The monthly price level has been transformed into quarterly average and the analysis has
been performed on quarter on quarter in‡ation rates. We use this frequency both to limit the
noise of the monthly series and to compare directly our results with the business cycle literature
and available studies of sectoral in‡ation in the euro area (e.g. Lünnemann and Mathä, 2004)
and elsewhere Cecchetti and Debelle (2004).
Data cleaning
We further clean our data according to the following steps. First, we eliminate all the series
that start only in the mid 1990’s. This is because these series do not have enough degrees of
freedom to carry out the estimation of ARMA models. We exclude from our sample 8 French
and 9 German sub-indices that are available only after 1995, 1998 or 2000.
Second, we eliminate all the series which are adjusted at rare discrete steps. The typical such
series include the price of Tobacco or mailing services. We exclude 6 German, 4 French and 12
Italian sub-indices of this type.
25
Altogether we keep 404 sub-indices out of the 444 available in the initial dataset, 377 of which
are available from 1985 Q1 to 2004Q2. A last step before, the estimation is to corrections of
outliers in the in‡ation series. We …lter out these outliers by replacing observations that are
more than 3 standard deviations away from the time series mean of each in‡ation series by a
local median observation. This outlier correction mainly eliminates discrete shifts in the levels of
the price indices.
Figure A1 plots the time series of the aggregates that we can reconstruct from the wellbehaved in‡ation series at the national level and for the aggregate of the three countries (using
1995 PPP-GDP weights of 0.422, 0.296 and 0.282 for Germany, France and Italy, respectively)
together with the o¢ cial CPI in‡ation rate. We take from the picture that our sub-set of wellbehaved sectoral in‡ation series o¤ers, when aggregated, a reasonable approximation of the o¢ cial
aggregate index.
26
Euro area
8
6
4
2
0
Germany
8
6
4
2
0
France
8
6
4
2
0
Italy
Figures
8
6
4
2
0
"Official" series
Reconstructed series
1987
1990
1992
1995
1997
2000
2002
1987
1990
1992
1995
1997
2000
2002
1987
1990
1992
1995
1997
2000
2002
1987
1990
1992
1995
1997
2000
2002
Figure A1: Aggregate q-o-q "o¢ cial" and reconstructed in‡ation rates
27
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30
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Policy Externalities: How US Antidumping Affects Japanese Exports to the EU
Chad P. Bown and Meredith A. Crowley
WP-04-12
Sibling Similarities, Differences and Economic Inequality
Bhashkar Mazumder
WP-04-13
Determinants of Business Cycle Comovement: A Robust Analysis
Marianne Baxter and Michael A. Kouparitsas
WP-04-14
The Occupational Assimilation of Hispanics in the U.S.: Evidence from Panel Data
Maude Toussaint-Comeau
WP-04-15
1
Working Paper Series (continued)
Reading, Writing, and Raisinets1: Are School Finances Contributing to Children’s Obesity?
Patricia M. Anderson and Kristin F. Butcher
WP-04-16
Learning by Observing: Information Spillovers in the Execution and Valuation
of Commercial Bank M&As
Gayle DeLong and Robert DeYoung
WP-04-17
Prospects for Immigrant-Native Wealth Assimilation:
Evidence from Financial Market Participation
Una Okonkwo Osili and Anna Paulson
WP-04-18
Individuals and Institutions: Evidence from International Migrants in the U.S.
Una Okonkwo Osili and Anna Paulson
WP-04-19
Are Technology Improvements Contractionary?
Susanto Basu, John Fernald and Miles Kimball
WP-04-20
The Minimum Wage, Restaurant Prices and Labor Market Structure
Daniel Aaronson, Eric French and James MacDonald
WP-04-21
Betcha can’t acquire just one: merger programs and compensation
Richard J. Rosen
WP-04-22
Not Working: Demographic Changes, Policy Changes,
and the Distribution of Weeks (Not) Worked
Lisa Barrow and Kristin F. Butcher
WP-04-23
The Role of Collateralized Household Debt in Macroeconomic Stabilization
Jeffrey R. Campbell and Zvi Hercowitz
WP-04-24
Advertising and Pricing at Multiple-Output Firms: Evidence from U.S. Thrift Institutions
Robert DeYoung and Evren Örs
WP-04-25
Monetary Policy with State Contingent Interest Rates
Bernardino Adão, Isabel Correia and Pedro Teles
WP-04-26
Comparing location decisions of domestic and foreign auto supplier plants
Thomas Klier, Paul Ma and Daniel P. McMillen
WP-04-27
China’s export growth and US trade policy
Chad P. Bown and Meredith A. Crowley
WP-04-28
Where do manufacturing firms locate their Headquarters?
J. Vernon Henderson and Yukako Ono
WP-04-29
Monetary Policy with Single Instrument Feedback Rules
Bernardino Adão, Isabel Correia and Pedro Teles
WP-04-30
2
Working Paper Series (continued)
Firm-Specific Capital, Nominal Rigidities and the Business Cycle
David Altig, Lawrence J. Christiano, Martin Eichenbaum and Jesper Linde
WP-05-01
Do Returns to Schooling Differ by Race and Ethnicity?
Lisa Barrow and Cecilia Elena Rouse
WP-05-02
Derivatives and Systemic Risk: Netting, Collateral, and Closeout
Robert R. Bliss and George G. Kaufman
WP-05-03
Risk Overhang and Loan Portfolio Decisions
Robert DeYoung, Anne Gron and Andrew Winton
WP-05-04
Characterizations in a random record model with a non-identically distributed initial record
Gadi Barlevy and H. N. Nagaraja
WP-05-05
Price discovery in a market under stress: the U.S. Treasury market in fall 1998
Craig H. Furfine and Eli M. Remolona
WP-05-06
Politics and Efficiency of Separating Capital and Ordinary Government Budgets
Marco Bassetto with Thomas J. Sargent
WP-05-07
Rigid Prices: Evidence from U.S. Scanner Data
Jeffrey R. Campbell and Benjamin Eden
WP-05-08
Entrepreneurship, Frictions, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-05-09
Wealth inequality: data and models
Marco Cagetti and Mariacristina De Nardi
WP-05-10
What Determines Bilateral Trade Flows?
Marianne Baxter and Michael A. Kouparitsas
WP-05-11
Intergenerational Economic Mobility in the U.S., 1940 to 2000
Daniel Aaronson and Bhashkar Mazumder
WP-05-12
Differential Mortality, Uncertain Medical Expenses, and the Saving of Elderly Singles
Mariacristina De Nardi, Eric French, and John Bailey Jones
WP-05-13
Fixed Term Employment Contracts in an Equilibrium Search Model
Fernando Alvarez and Marcelo Veracierto
WP-05-14
Causality, Causality, Causality: The View of Education Inputs and Outputs from Economics
Lisa Barrow and Cecilia Elena Rouse
WP-05-15
3
Working Paper Series (continued)
Competition in Large Markets
Jeffrey R. Campbell
WP-05-16
Why Do Firms Go Public? Evidence from the Banking Industry
Richard J. Rosen, Scott B. Smart and Chad J. Zutter
WP-05-17
Clustering of Auto Supplier Plants in the U.S.: GMM Spatial Logit for Large Samples
Thomas Klier and Daniel P. McMillen
WP-05-18
Why are Immigrants’ Incarceration Rates So Low?
Evidence on Selective Immigration, Deterrence, and Deportation
Kristin F. Butcher and Anne Morrison Piehl
WP-05-19
Constructing the Chicago Fed Income Based Economic Index – Consumer Price Index:
Inflation Experiences by Demographic Group: 1983-2005
Leslie McGranahan and Anna Paulson
WP-05-20
Universal Access, Cost Recovery, and Payment Services
Sujit Chakravorti, Jeffery W. Gunther, and Robert R. Moore
WP-05-21
Supplier Switching and Outsourcing
Yukako Ono and Victor Stango
WP-05-22
Do Enclaves Matter in Immigrants’ Self-Employment Decision?
Maude Toussaint-Comeau
WP-05-23
The Changing Pattern of Wage Growth for Low Skilled Workers
Eric French, Bhashkar Mazumder and Christopher Taber
WP-05-24
U.S. Corporate and Bank Insolvency Regimes: An Economic Comparison and Evaluation
Robert R. Bliss and George G. Kaufman
WP-06-01
Redistribution, Taxes, and the Median Voter
Marco Bassetto and Jess Benhabib
WP-06-02
Identification of Search Models with Initial Condition Problems
Gadi Barlevy and H. N. Nagaraja
WP-06-03
Tax Riots
Marco Bassetto and Christopher Phelan
WP-06-04
The Tradeoff between Mortgage Prepayments and Tax-Deferred Retirement Savings
Gene Amromin, Jennifer Huang,and Clemens Sialm
WP-06-05
Why are safeguards needed in a trade agreement?
Meredith A. Crowley
WP-06-06
4
Working Paper Series (continued)
Taxation, Entrepreneurship, and Wealth
Marco Cagetti and Mariacristina De Nardi
WP-06-07
A New Social Compact: How University Engagement Can Fuel Innovation
Laura Melle, Larry Isaak, and Richard Mattoon
WP-06-08
Mergers and Risk
Craig H. Furfine and Richard J. Rosen
WP-06-09
Two Flaws in Business Cycle Accounting
Lawrence J. Christiano and Joshua M. Davis
WP-06-10
Do Consumers Choose the Right Credit Contracts?
Sumit Agarwal, Souphala Chomsisengphet, Chunlin Liu, and Nicholas S. Souleles
WP-06-11
Chronicles of a Deflation Unforetold
François R. Velde
WP-06-12
Female Offenders Use of Social Welfare Programs Before and After Jail and Prison:
Does Prison Cause Welfare Dependency?
Kristin F. Butcher and Robert J. LaLonde
Eat or Be Eaten: A Theory of Mergers and Firm Size
Gary Gorton, Matthias Kahl, and Richard Rosen
Do Bonds Span Volatility Risk in the U.S. Treasury Market?
A Specification Test for Affine Term Structure Models
Torben G. Andersen and Luca Benzoni
WP-06-13
WP-06-14
WP-06-15
Transforming Payment Choices by Doubling Fees on the Illinois Tollway
Gene Amromin, Carrie Jankowski, and Richard D. Porter
WP-06-16
How Did the 2003 Dividend Tax Cut Affect Stock Prices?
Gene Amromin, Paul Harrison, and Steven Sharpe
WP-06-17
Will Writing and Bequest Motives: Early 20th Century Irish Evidence
Leslie McGranahan
WP-06-18
How Professional Forecasters View Shocks to GDP
Spencer D. Krane
WP-06-19
Evolving Agglomeration in the U.S. auto supplier industry
Thomas Klier and Daniel P. McMillen
WP-06-20
Mortality, Mass-Layoffs, and Career Outcomes: An Analysis using Administrative Data
Daniel Sullivan and Till von Wachter
WP-06-21
5
Working Paper Series (continued)
The Agreement on Subsidies and Countervailing Measures:
Tying One’s Hand through the WTO.
Meredith A. Crowley
WP-06-22
How Did Schooling Laws Improve Long-Term Health and Lower Mortality?
Bhashkar Mazumder
WP-06-23
Manufacturing Plants’ Use of Temporary Workers: An Analysis Using Census Micro Data
Yukako Ono and Daniel Sullivan
WP-06-24
What Can We Learn about Financial Access from U.S. Immigrants?
Una Okonkwo Osili and Anna Paulson
WP-06-25
Bank Imputed Interest Rates: Unbiased Estimates of Offered Rates?
Evren Ors and Tara Rice
WP-06-26
Welfare Implications of the Transition to High Household Debt
Jeffrey R. Campbell and Zvi Hercowitz
WP-06-27
Last-In First-Out Oligopoly Dynamics
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-28
Oligopoly Dynamics with Barriers to Entry
Jaap H. Abbring and Jeffrey R. Campbell
WP-06-29
Risk Taking and the Quality of Informal Insurance: Gambling and Remittances in Thailand
Douglas L. Miller and Anna L. Paulson
WP-07-01
Fast Micro and Slow Macro: Can Aggregation Explain the Persistence of Inflation?
Filippo Altissimo, Benoît Mojon, and Paolo Zaffaroni
WP-07-02
6
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