Forecasting aggregate productivity using informationfrom …rm-level data
Eric J. Bartelsmana , Zoltán Wolfb;1;2aVrije Universiteit Amsterdam, Tinbergen Institute and IZA Bonnb

Vrije Universiteit Amsterdam and Tinbergen Institute
April 2009

1 Address for correspondence: Free University Amsterdam, Department of Economics, Room

2E-71, De Boelelaan 1105, 1081 HV Amsterdam, The Netherlands. Tel: +31 20 598 6030. Fax+31 20 598 9870. E-mail : zwolf@feweb.vu.nl.
2 We acknowledge the remote access facilities provided by Statistics Netherlands. We thankDave Reifschneider of the Federal Reserve Board, Jerome Henry of the ECB and Joris de Windof the DNB for providing information on current central bank productivity forecasting practices.
Further thanks for comments from seminar participants at the Tinbergen Institute.

Abstract
This paper contributes to the productivity literature by using results from …rm-level productivity studies to improve forecasts of macro-level productivity growth. The paper
employs current research methods on estimating …rm-level productivity to build timesseries components that capture the joint dynamics of the …rm-level productivity and size
distributions. The main question of the paper is to assess whether the micro-aggregatedcomponents of productivity— the so-called productivity decompositions— add useful information to improve the performance of macro-level productivity forecasts.
The theoretical links between …rm-level decisions and the interactions between …rms
and customers in a market have not been well modelled, and the sources of …rm-level
heterogeneity and the triggers of resource reallocation have not yet been explored in acomprehensive manner. Some early work attempts to provide explanations of how …rmlevel productivity interacts with resource allocation to determine aggregate growth. Thismodelling does not yet provide a framework for using the full information in …rm-level
data for macro-level forecasting. Nevertheless, they provide the intuition for using microaggregated representations of the underlying relationships among size, productivity, …rms’
decisions, market selection and such to aid in macro forecasting.
The literature on decomposing aggregate productivity growth has grown extensively
over the past few years and indicates that there are many ways to de…ne or modify thedecompositions. Our primary objective is to improve forecasts of aggregate productivity
growth using disaggregated information and not to favor one method of decomposition
over another. To this end, we work with two standard decompositions.
Our …rm-level dataset, provided by Statistics Netherlands, consists of a large yearlypanel of Dutch manufacturing …rms over 1978-2004. Our aggregate datasource is the
EUKLEMS database. There have been two EUKLEMS releases so far. We used theone that was published in March 2008. The …les contain 62 variables, including basic
data and growth accounting variables. The data…les are structured to follow an industry
classi…cation list which corresponds with the NACE list.

Forecasting productivity using micro data

The paper explores various speci…cations of decompositions and various forecasting
experiments. The result from these horse-races is that micro-aggregated components
improve simple aggregate total factor productivity forecasts. While the results are mixed
for richer forecasting speci…cations, the paper shows, using Bayesian model averaging
techniques (BMA), that the forecasts using micro-level information were always better
than the macro alternative
JEL classi…cation: C11, C14, C32, C33, D24, O12, O47
Keywords: economic growth, production function, total factor productivity, aggregation, panel data, Bayesian analysis, forecasting2

1

Introduction

1

Introduction

This paper contributes to the productivity literature by using results from …rm-levelproductivity studies to improve forecasts of macro-level productivity growth. The paper employs current research methods on estimating …rm-level productivity to build
times-series components that capture the joint dynamics of the …rm-level productivity
and size distributions. The main question of the paper is to assess whether the microaggregated components of productivity— the so-called productivity decompositions— add
useful information to improve the performance of macro-level productivity forecasts. To
our knowledge, our study is a novel attempt to connect micro and macro level analysis
whereby micro-level productivity estimates and decompositions of aggregate productivity
provide additional information to be used in making macro forecasts.
Much of the recent research e¤ort in the …eld of productivity, both at the micro andmacro level, has been aimed at measurement. This research has achieved some notable
results regarding several important issues - accounting for adjustment costs, variable factor utilization, intangible investments, etc. (e.g. Oliner et al. (2007), Basu and Kimball(1997), Kátay and Wolf (2008)); and issues connected to aggregation (e.g. Petrin andLevinsohn (2008)). Research into the practical matter of forecasting aggregate productivity has made much less progress. Forecasting total factor productivity (TFP) can bequite complicated, much more so than for well-understood primary economic measures.
TFP essentially is computed as the ratio of output to inputs and measurement errors
in either the numerator or the denominator do not cancel but exacerbate each other. A
common …nding of the productivity literature is that the yearly growth rates of TFP areoften unstable or erratic, which makes forecasting exceedingly di¢ cult.1
Forecasting is further complicated by the fact that our theoretical understanding of
aggregate productivity movements is less advanced than our understanding of, say, thelabor market. Theory is not unambiguous to the level of analysis at which exogenous
factors cause TFP movement to take place. Are explicit actions at the …rm level thesource and does aggregate TFP change owing to within-…rm changes in productivity
1

For this reason, most studies report annual percent changes calculated over several years dependingon the dataset (for example: Corrado et al. (2006) and Oliner et al. (2007)).

3

Forecasting productivity using micro data

and between-…rm movements in market share, or are representative …rms merely able topluck the fruits of movements in some exogenous productivity frontier (as is assumed in
the RBC literature)? Macro-level productivity forecasting uses historical timeseries ofaggregate productivity to uncover an underlying macro-level statistical process of TFP
movements, essentially assuming the latter. However, evidence clearly points to the importance of …rm-level decisions within an evolving market as the source of productivity
growth (Bartelsman and Doms (2000), Bartelsman et al. (2005)). The issue of understanding and forecasting aggregate productivity movements thus requires good …rm-levelmeasures and proper theory on …rm-level actions and market selection. The main contributions on …rm-level TFP measurement are Olley and Pakes (1996), Levinsohn andPetrin (2003), and a more recent study by Petrin and Levinsohn (2008). The classicalpapers on aggregation of TFP are Domar (1961) and Hulten (1978). However, the aggregation papers either assume that the …rms operate in a frictionless world or assume thatall …rms are essentially identical ’representative …rms’.
Unfortunately, the theoretical links between …rm-level decisions and the interactions
between …rms and customers in a market have not been well modelled, and the sourcesof …rm-level heterogeneity and the triggers of resource reallocation have not yet been
explored in a comprehensive manner. Some early work attempts to provide explanationsof how …rm-level productivity interacts with resource allocation to determine aggregate
growth. One example is Bartelsman et al. (2008a), who model the joint distribution ofsize and productivity. Another is Lentz and Mortensen (2005), who structurally estimatea model of creative destruction. This modelling does not yet provide a framework forusing the full information in …rm-level data for macro-level forecasting. Nevertheless,they provide the intuition for using micro-aggregated representations of the underlying
relationships among size, productivity, …rms’decisions, market selection and such to aid
in macro forecasting.
The micro-aggregated components of aggregate productivity growth may help explaining the aggregate for several reasons. First, the ’within’component or productivity
growth among individual …rms, is a simple weighted average of individual growth rates.
It is the sole factor behind aggregate productivity dynamics in a neoclassical world. In
our view, the within component can be expected to have forecasting power because it4

1

Introduction

captures common behavior over the business cycle (such as factor hoarding), and steadyfactors at lower frequencies (such as technology di¤usion). Second, the’between’ component is assumed to represent the underlying forces of reallocation of resources across…rms. It captures market selection mechanisms whereby more productive …rms gain andless productive …rms lose market share. Based on the …ndings of earlier work by Bailyet al. (2001), Basu and Kimball (1997), and Basu et al. (1998) we may expect it toexplain behave quite di¤erently over the cycle than the within component, while overtime it may re‡ect changes in demand conditions or policy environment. Third, the net
entry component captures the entry and exit at the fringe, as well as the rejuvenation ofindustries through high-growth startup. If, for instance, the net entry term is large, it
implies that entrants’productivity is larger than that of exiters, possibly indicating newopportunities arising through technological breakthroughs.
In our work, we do not attempt to put such structure or meaning on the contribution of the …rm-level productivity decompositions to the macro forecasts. The literature
on decomposing aggregate productivity growth has grown extensively over the past few
years and indicates that there are many ways to de…ne or modify the decompositions.
Our primary objective is to improve forecasts of aggregate productivity growth using
disaggregated information and not to favor one method of decomposition over another.
To this end, we work with two standard decompositions (Olley and Pakes (1996), Bailyet al. (2001)). We also introduce and estimate simple auxiliary equations, based on theoretical notions from the literature, for both individual productivity changes and evolutionof …rm-level market shares. The objective of the auxiliary models is to extract further
information from the joint distribution of productivity and market share.
Our …rm-level dataset, provided by Statistics Netherlands (CBS)2 consists of a large
yearly panel of Dutch manufacturing …rms over 1978-2004. More details can be found in
Appendix 5.1.
The paper is organized as follows. Section 2 lays down the outline of the method
we use to estimate TFP at the …rm-level and describes the productivity decompositions
2

The CBS ’Centrum voor Beleidsstatistiek’provides remote access facilties to the con…dential data,
under strict rules for disclosure.

5Forecasting productivity using micro data

used to generate the micro-aggregated productivity components used in the forecasting
exercises. Section 3 discusses the various forecasting experiments and the metric used
to evaluate their performance. The results of the various exercises are presented andthe Bayesian Model Average outcomes show how the …rm-level information improves theability to forecast aggregate productivity. Section 4 concludes.

2

Firm-level TFP measures and productivity decompositions

In this paper, the empirical work is separated into measurement and aggregation procedures using micro-level panel data, and forecasting exercises using aggregated timeseries. This section describes the work conducted in a secure computing environment
using con…dential …rm-level information. The output of this section will be a collectionof micro-aggregated time-series components of productivity that are analyzed outside of
the secure environment, together with other macro-level timeseries, in order to forecast
aggregate productivity. The forecasting analysis is described in section 3.
In this section, we provide a brief description of the methods used to construct …rmlevel TFP measures, as well as the methods by which the …rm-level information is aggregated into micro-aggregated productivity components. To generate estimates of TFP
at the …rm-level we applied a standard procedure introduced by Olley and Pakes (1996)(OP) and modi…ed by Levinsohn and Petrin (2003) (LP henceforth). The decompositionsof aggregate productivity— i.e. micro-aggregates of …rm-level productivity— are based on
methods available in the literature, Olley and Pakes (1996) and Baily et al. (2001), andextended to allow a di¤erent dynamic interpretation.

2.1

Firm-level TFP measures

In estimating …rm-level productivity measures, a main issue is controlling for endogeneityof the primary inputs into production. Consider a Cobb-Douglas production function
6

2

Firm-level TFP measures and productivity decompositions(indices i and t were dropped for simpli…cation)
y=

0+

ll +

kk +

+"

(1)

where y is log value-added, k is log capital, l is log labour, is log productivity and " isassumed to be an iid disturbance. is unobservable by the econometrician but known3
to the …rm. Since is in the information set on which the …rm conditions its optimal
choices of inputs, there will always be a nonnegative correlation between input factors
and . This dependence renders simple OLS parameter estimates to be biased.
One of the key assumptions in the procedure to control for the endogeneity bias,
is that capital is pre-determined, i.e. its level is chosen before production takes place.
Hence, the orthogonality of k to the innovation in can be used to identify k . To solve
the endogeneity problem with respect to freely variable labor, the method makes use of aproxy. The key assumption is that the proxy is monotonic in because then the proxy canbe used to invert out the unobserved productivity shock. The main di¤erence between
OP and LP is that the former uses investment, the latter uses intermediate material use
as a proxy.
There are, of course, caveats to both procedures, i.e. which proxy one should use.
Ackerberg et al. (2005) lists several arguments and suggests further modi…cations tobetter measure the parameters of the production function. Yet, we chose LP because (i)our forecasting exercises do not concern parameter-measurement in the …rst place, (ii) it
is easily tractable and has strong intuitive arguments for identi…cation, (iii) the data do
not have direct estimates of investment needed to produce …rm-level capital measures.
We did not want to introduce more measurement error by applying another proxy forinvestment.
2.1.1

Production function parameter estimates

Production function parameter estimates are presented for two concepts of production,
namely value added (table 3) and gross output (table 4). Column 1 shows the industry
codes— table 1 provides the legend— columns 2-4 contain the point estimates for K; L and3

7at least up to its expected valueForecasting productivity using micro data

M , column 5 lists the value of a 2 test statistic for constant returns to scale, columns 5-6
show standard errors for bk and bl , and the last column shows the number of …rm-year
observations. The parameter estimates and their variation across industries seem in linewith …ndings in the literature. The bk are found non-signi…cant more frequently for thegross output production function, which was against our expectations. Since the output
speci…cation requires a more complex IV-technique together with a grid-search algorithm,
it is less clear whether the di¤erence between the two production concepts is explainedby the estimation method or measurement issues. While we generated micro-aggregated
TFP components for use in the forecast exercises for both the value added and gross
output concepts, in the remainder of the paper we focus on results for value added.

2.2

Productivity Decompositions

Starting with the …rm-level measures of productivity, accounting identities provide thelink with aggregate productivity. In general, productivity (growth) at the aggregate levelcan be computed as a weighted average of …rm-level productivity growth, with the weights
related to …rm size.4 The accounting identities can then be parsed into components that
add up to aggregate productivity and that re‡ect movements in the …rm-level productivity
and reallocation processes. We start by looking at a simple decomposition Baily et al.
(2001), and continue by building on a decomposition given by Olley and Pakes (1996).
Both of these are augmented with a further re…nement that models the ’push and pull’process by which market shares evolve depending on a …rm’s position in the …rm-levelproductivity distribution.
The outputs of this part of the empirical exercise are sets of speci…cations that are
to be used in the forecasting exercise. These speci…cations are based on binary choices
4

If one wants measures of aggregate productivity growth that are derived in a welfare theoretic setting,many assumptions need to be made that likely do not hold for …rms or industries (see e.g. Hulten (1978),
Petrin and Levinsohn (2008))). Aggregated productivity computed following an accounting identity may
therefore not re‡ect how aggregate welfare changes if …rm-level productivity changes and and all resources
are reallocated instantaneuosly to their optimal use. Of course, frictions prevent such instantaneous
reallocation and provide the reason that …rm-level information may provide information about aggregate
movements.

8

2

Firm-level TFP measures and productivity decompositions

along four dimensions. We start with components based on value added or gross output
measures of …rm-level TFP as described above.5 Next, the accounting identities requirea measure of market share or …rm size. These may be constructed using the …rm’s shareof industry output (either value added or gross output), or the …rm’s share of industry
inputs (aggregating the factor inputs using the estimated output elasticities as weights).
Next, the productivity components are computed using either of the two decomposition
methods described below in equations 2 and 6. Finally, auxiliary models (equations 7
and 8 below) are estimated to capture productivity ’push and pull’e¤ects. The models
generate …tted values for individual …rms’market shares and productivity growth. The
productivity components are then based on either the actual or …tted values of these…rm-level indicators.
2.2.1

Accounting Identities

The …rst dynamic decomposition, laid out by Baily et al. (2001), is the following:
X
X
X
X
e
e);
(
e
)
(e
e
)
+
+
it
i
it
t =
it 1 ( it 1
it
i
i
i2C

i2C

i2E

(2)

i2X

where it is the TFP-level of …rm i in period t, it is the market share of …rm i in periodt, e = t +2 t 1 ,is the di¤erence operator, C is the set of continuers, E is the set of
entrants and X is the set of exiters in time t. The terms in the previous equation areoften called within-, between-, entry-, and exit-terms, respectively.
In the second decomposition, we combine a static decomposition with equation 2. The
static equation was introduced by Olley and Pakes (1996). The static decomposition is
X
( it
(3)
t = t+t );t )( itNt

P
P
where t = N1t Nt it , and Nt ( itt ) is a covariance measuring thet )( itassociation between productivity and size. This decomposition informs us about characteristics of ’s cross-section distribution. When the covariance-term is high, the weighted
5However, we present results based on value-added productivity for reasons outlined at the end of
Section 2.1.1.

9

Forecasting productivity using micro data

average is higher than the unweighted average. It also implies that the change in aggregate productivity is the sum of the change in the unweighted average productivity andchange in the covariance-term. Di¤erencing 3 yields:
t+

t =

X

( it

t )( it

X

t)

Nt

Nt

( it 1t 1 )( it 1t 1 );(4)

1

i.e. aggregate productivity change is sum of the change in the unweighted average
productivity and change in the covariance term. Entry and exit are implicitly accounted
for here as the cross section sums run from i = 1:::Nt and i = 1:::Nt 1 respectively.
P
P
Hence, the weights are such that Nt it = 1 and Nt 1 it 1 . Now express e using 3:
t+

e =

t 1

=

t+

t 1

2
2
f
= [ t ] + cov(f ; ):+

covt ( ; ) + covt 1 ( ; )2(5)We expect cov(f ; ) to reveal information about the cross section characteristics of the
distribution. We base our analysis on 2, but we also want to introduce information about
the size and productivity distributions. To this end, we plug 5 into the between term of
2 to get
X

e) =

i (ei

C

=

X
C

X
C

so 2 looks like6
t

=

X
C

+

e

X
E

6

i

it +

X
C

it ( it

e)

i ei

i ei

i (ei

X
X

X
C

X
C

[ft ])ieif ; ) ;[ft ] + cov(X

it 1 ( it 1

C

e):

f
i cov(; )(6)

This manipulation does not a¤ect the validity of the decomposition. Had we rewritten all the terms
in 2, we would have got

10

2

Firm-level TFP measures and productivity decompositionsPP
The it weights were de…ned at the beginning such that Nt it = 1, and hence CiP
is not necessarily zero (it would be zero had we de…ned C it = 1). Therefore thePcovariance term is not killed by C
i . However, the between-term is now di¤erent: itsums up the share-changes weighted by deviations from the time-average of the simple
cross-section average. The covariance-term is shown separately.
Push and pull e¤ects Equations 2 and 6 show the two main decompositions weused in the forecasting exercises. Both are identities separating aggregate productivity
growth into dynamic components. In the case of 2 we have three components (’within’,’between’and a combined ’net-entry’contribution), and in the case of 6 we have a di¤erent
between component and an additional ’cross-term’. We denote these components as
4 it ; i 2 fdc1; dc2g in the two di¤erent decompositions. Both of these approaches takethe underlying …rm-level market share indicator and productivity growth rate as given.
In order to put more structure on the evolution of these variables we model two e¤ects:

t

=

X
C

+

e

it +

i

X

cov(
f ; ))

=

=

=

cov(
f ; )

cov(
f ; )

cov(
f ; )

X

X

"

"

X

X

it

i

( it

X

cov(
f ; ))
it 1 ) +

"

X

it

E

X

it

+

X

it

E

it

it

1

it 1

3

X

it 1

X

it 1

X

it 1

5=0

i

C

X

C

X

Nt

X

X

[g
t ])

#

E

C

2
X
cov(
f ; )4

it 1

X

C

cov(
f ; )

it 1 ( it 1

X

E

C

Nt

11

"

X

[g
t ])

it ( it

[g
t ])

i (ei

C

E

where

X

X
X

#

#

it 1

#

Forecasting productivity using micro dataa "pull" and a "push" e¤ect. The speci…cation is derived form the literature on frontier
productivity, both theoretical (Acemoglu et al. (2002)) and empirical (Bartelsman et al.
(2008b)). The approach essentially pins down a …rm’s position relative to the frontier.
The pull-equation says that individual productivity growth depends positively on the
distance from the frontier, in other words, …rms further away are pulled more strongly
towards it as technology spreads out:
it =

( Ft

it ) +

it ;(7)

where Ft is frontier productivity and it is an autonomous or noise component. A
case can be made for both < 0 and > 0. In the …rst case …rms closer to the frontier
can be thought to have greater absorption capacity7 (greater human capital, which isunmeasured, and hence it shows up as higher productivity), so they can take on newtechnologies and grow faster. In the > 0 case - investigated by the studies above - lessproductive …rms tend to grow faster. For instance, these …rms can be though as being
new entrants with relatively high growth potential.8
Frontier productivity ( Ft ) for each industry was calculated as the average of the
top decile from a truncated distribution. We got rid of the top and bottom 1% of theobservations to kill the possibly erratic e¤ects on aggregates.9 We took a moving average
it + it 1of m
to further guard against extreme observations. The resulting truncatedit =2
distribution was then used to calculate the average of the top decile.
The push equation is assumed to encapsulate the market selection mechanism whereby
less e¢ cient …rms are crowded out of the market. Assume the following speci…cation:
it =

0+

1 ( itt ) + "it :(8)This equation reads: higher-than-average productivity …rms end up gaining market
share ( 1 > 0), and lower-than-average productivity …rms lose market share.
7

cf. with the "second face" of research as called in the R&D literature
The literature calls the > 0 case - when less productive …rms grow faster - as -convergence. The
concept was introduced by Robert Barro and Xavier Sala-i-Martin in their 1991 paper.
9
I ignored the top and bottom 1% of the productivity distribution because it turned out that frontier
time-series exhibited unplausibly large time-variation if these observations were included.
8

12

2

Firm-level TFP measures and productivity decompositions

The use of equations 7 and 8 is that once we estimated parameters ; 0 and 1 , the…tted values dt and cit from these simple models inform about the underlying10 catchup components and shares. If they have explanatory power in our dataset then dt
and cit should add to the forecasting power of the set of components that are computed
using these …tted values rather than the actual data on …rm-level productivity growthand market share.

Estimation of the auxiliary models The distance variables in both 7 and 8 areendogenous. For 7, the endogeneity problem is immediate. As for 8, a case can be madethat a …rm gains market share exactly because its productivity increased in the wake ofa positive productivity shock. One way to get around it is to apply an IV estimator. The
sample moment condition for b is
E[zi

i

b ( F
IV
t

it )

] = 0;and the simple Anderson-Hsiao-type IV estimator is given by
N X
TX

i=1 t=2
b =
IV
N
T
XX

zit

zit ( Ftitwith zit = ( Ft 2

it 2 ).

it )i=1 t=2

The instruments can also be zit but that results in the loss of more observations. As
for the push-equation (8), rewriting it = x 0 + "it where = [ 0 ; 1 ] and x = [1; it
].
10

13

in the sense of the simple econometric models 7 and 8.

Forecasting productivity using micro data

The conventional IV-estimator again is

bIV

=

N
X

zi0 i

i=1

N
X

= (Z 0 X)

Z0

with

zi0 xii=1

zi = [( i1i1= [ i2 ; :::;

1 ); :::; ( iT 10
T 1 )] ;0
iT ] and0 0];
Z = [z10 :::zN= [ 01 ::: 0N ]0 :The IV-results of equations 7 and 8 were in line with our expectations. appeared signi…cantly positive at conventional levels in all twelve industries when a value-added-based
production function was used11 . Results were very similar in the case of gross output, except that did not appear signi…cant in the textiles industry.12 The ’s were signi…cantly
positive for value-added-based productivity measures. The output-based speci…cations
showed more ambiguous associations: 0 were negative in Nonmetallic mineral products
and Electrical and optical equipment. Estimates were invariant to whether we measured…rm size by input- or output-side indicators of …rms.13

3

Forecasting

The previous section described the estimation and computation of a set of micro-aggregatedproductivity components that are to be used in conjunction with macro timeseries in order to forecast aggregate productivity. The basic idea in this section is to assess whether
adding the timeseries components built up from the …rm-level data improves the traditional forecasts that are made using only published aggregate timeseries. In this section
we describe the experiments used in the assessment. First we argue that the proper metric
11

The mean and standard deviation of across the twelve industries was :039 and :014.
The mean and standard deviation of across the twelve industries was :032 and :016.
13
That is, using input shares or value added/gross output shares did not a¤ect point estimates at
4-digit precision.
12

14

3

Forecasting

is not to compare forecasts to actual annual TFP growth, but to the annual average trend
growth rate. Next, we describe the ’horse races’comparing forecast performance of themacro timeseries to the forecast performance when a set of productivity components isused as well. The …rst horse race attempts to shed light on whether we can improve on theaccuracy of aggregate productivity forecasts by forecasting microcomponents separately.
The second investigates whether microcomponents better predict aggregate productivity
in a multivariate framework. The third experiment uses the same multivariate framework
but the target is the published aggregate.

3.1

Methodology

Yearly growth rates of total factor productivity are often found to be volatile. A common
way to cope with the large variation is to analyze changes over a longer period. As an
illustration, …gure 1 shows yearly TFP-changes and table 5 shows average yearly changes
for …ve-year periods for several countries.
Figure 2 depicts our micro-based and ‘published’TFP measures for aggregate Dutch
manufacturing. Micro-based aggregates are built using …rm-level productivity estimates,‘published’ aggregates, built from national accounts data, come from the EUKLEMS
database (O’Mahony et al. (2007b)). We will refer to our …rm-based TFP aggregatesas micro-aggregated TFP hereafter. Although the two datasources characterize the same
set of …rms, the published and micro-aggregated TFP measures di¤er for a variety ofreasons related to statistical practice. To trace these di¤erences to underlying measuresof inputs and outputs, …gures 3 and 4 graph year-on-year growth rates for value added
and labor.
Several stylized facts emerge from these graphs. First, aggregate yearly growth rates
exhibit large variation in all countries (…gure 1). Second, micro-aggregated measuresgenerally vary more than published aggregates (…gures 3, 4). Third, micro-aggregateddynamics are similar on the input and output side of the …rm suggesting that yearly TFP
growth numbers actually make sense despite their variation.14 Finally, micro-aggregated
14

The same conclusion emerges from industry-by-industry analysis, not shown here. Micro-macro
discrepancies are all the more obvious looking at level charts.

15

Forecasting productivity using micro data

TFP-growth series - although more volatile - captures the dynamics of the publishedaggregate reasonably well (…gure 2).
The most prominent of all the above observations is that yearly aggregate productivity
growth exhibits large variation. Instead of focusing on yearly forecasts, we evaluate ourestimates in 3-year forecast windows. We do not calculate MSE-type values but simply
compare average growth rates implied by extrapolated yearly values. The relatively longtime-span of the sample allowed us to evaluate results in four rolling forecast windows:
1998-2000, 1999-2001, 2000-2001, 2001-2003. These forecast windows are useful for atleast two reasons. First, they allow us to investigate the e¤ect of adding more data to
our models. Second, they give insight about the predictive content of components 4 itover di¤erent phases of the business cycle15 .
We make use of the two decompositions developed in 2.2, to reveal components thatfacilitate interpreting the dynamics of aggregate productivity. Both decompositions consist of three or four building blocks that aggregate to overall productivity growth. First,
the within component shows the e¤ects of …rm-level productivity change. Second, thebetween component shows how the reallocation of resources among …rms contributes toaggregate productivity growth. The third component encapsulates the e¤ects of …rm
entry and exit. In decomposition 6 a cross-term component also is included.
The idea of the ’horse races’ was to compare forecast performance of the aggregate
timeseries to the forecast performance when a set of productivity components was used aswell. The performance metric we chose was the average growth of the Hodrick-Prescotttrend16 of the aggregate, thus, for any two competing speci…cations we calculated thefollowing:

15

c Ag
4
t+s

HP
c Mi
4 t+s vs 4t+s

HP

4 t+s ;

(9)

Dutch manufacturing exhibited fast growth over the …rst forecast window (1998-2000). These werethe last years of a high-growth-period, which started in the …rst half of the nineties. The second forecasting window (1999-2001) contains the turning point in the cycle with negative growth in 2001 but
still strong activity over the entire three-year horizon. The remaining two windows were periods ofdownturns. See …gure 3 for an illustration of these periods.
16
Figure 5 shows the actual and HP-trend series of EUKLEMS aggregate productivity.

16

3

Forecastingc Ag denotes the forecast of the aggregate, 4c M i denotes the forecast of microwhere 4
t+s
t+s
HP
components, and 4 t+s denotes the average growth of the Hodrick-Prescott-trend of theaggregate, and s denotes the particular forecast window in which the forecast is evaluated.
We now describe the forecasting experiments. Experiment 1 was designed to investigate whether disaggregate information help forecast the aggregate, to be more speci…c,whether separate forecasts of disaggregates could improve on forecasting of the aggregate.
Disaggregate information was encapsulated by the dynamic microcomponents implied by(2) and (6), which - in shorthand notation - specify aggregate productivity growth as
b
ne
4 Ag
= 4 w
t
t +4 t +4 t =

4

Ag
t

= 4

w
b1
t +4 t

4

X
dc1

4 it

b2
ne
t +4 t =

(dc1)
X
dc2

4 it .

(dc2)

(10)

In technical terms, we …rst estimated separate univariate autoregressive speci…cations
17
Then wefor all the microcomponents 4 it ; i 2 fdc1; dc2g and the aggregate 4 Agt .
c i suchcomputed the microcomponents forecasts from the disaggregate speci…cations 4
t+s
thatc Mi =
4t+s

X

c i ; i 2 fdc1; dc2g.
4
t+s

(11)

c Ag was computed from its own autoregressive model. Finally,
The aggregate forecast 4
t+s
c Ag and 4
c M i using the metric in (9).
we compared the performance of 4
t+s

t+s

c i perform relative to otherA related question is how the dynamic components 4
t+s
disaggregate information. We investigated this issue in experiment 10 , which amounted
to rerunning experiment 1 but using conventional statistical industry components as disaggregates. We formed four groups within manufacturing following EUKLEMS-practice.
These are consumer goods, intermediate goods, electrical machinery and other investment
17

We selected the order of all the AR(p) models based on the BIC rather than the AIC because
BIC more heavily penalizes the loss of degrees of freedom. The BIC suggested that for our yearlyobservations the AR(1) speci…cations - relative to AR(2) - were rich enough to capture the dynamics
of 4 it and 4 Ag
t . We did not estimate models with p > 2 because we wanted to preserve degrees of
freedom.

17

Forecasting productivity using micro data

goods industries.18 Then, just like above, we forecasted aggregate productivity using disaggregate information, which was encapsulated by these four industry components. In
c M i is now implied byshort, our 4t+sc Mi =
4
t+s

X
i2I

ci ;
4
t+s

(12)

c i are all generated by separate univariate
where I = fcons, inter, inv, elecg and the 4t+s
autoregressive speci…cations.

The set of speci…cations in the experiments above is spanned by three dimensions.
First, we have two decompositions shown in equations 2 and 6. Second, the values forthe shares it were calculated using output- or input19 -side measures of …rms. Third, ourauxiliary models in section 2.2.1 allowed us to use either measured and …tted values oftand it in the decompositions. Overall, the three dimensions yielded eight speci…cations
for the microcomponents and the aggregate forecasts. The industry components forecasts
were evaluated for four speci…cations as there we had only one decomposition.
Experiment 2 was intended to investigate whether microcomponents could improve
aggregate forecasts in a multivariate framework. This experiment attempts to shed lighton two issues. First, it is of interest to see how results are a¤ected in a multivariate forecast
model, which is common in macro-practice. Second, it is also important to know how
results are a¤ected by combining micro-aggregated information with published aggregate
information. To this end, we estimated vector autoregressions where the regressand is avector of logarithmic di¤erences of value added, capital, labor and microaggregated TFP:
20
yt = (4vat ; 4kt ; 4lt ; 4 Ag
Regressors included some of yt ’s own lags together witht ).
lagged microcomponents. We denote the latter as 4 it q ; ; i 2 fdc1; dc2g. Data for 4vat ;4kt ; 4lt came from the published EUKLEMS database, while 4 Ag
and 4 it q weretconstructed from …rm-level data using equations 2 and 6. In short, and using the genericnotation V AR(p; q) for a VAR with p endogenous lags and q lags of microcomponents 4 it ,18

See Table 1 for classi…cation details.
These are the …tted values from production function estimation: the weighted average of primary
inputs where the weights are the production function parameters.
20
The components of yt are suggested by the production function.
19

18

3

Forecasting

we estimated V AR(1; 2); V AR(2; 1) and V AR(1; 1) using least squares. Correspondingly,
the set of speci…cations described under the experiment 1 were extended by the order ofthe VARs.
We asked a similar question in experiment 3. The di¤erence with experiment 2 isthat we are now interested in whether microcomponents improve published aggregate
EU KLEM S
forecasts in a multivariate framework. This amounted to replacing 4 Ag
t by 4 t
in yt above. This experiment simulates a more realistic forecasting environment because,
at time t, microaggregated information 4 Ag
is generally not available to the researchert
EU KLEM S
is. The purpose here was to investigate the relationship between thewhereas 4 t
KLEM Sand the lagged microcomponents 4 it and see whether
published aggregate 4 EUt(lagged) microcomponents have marginal forecasting power over the lagged publishedaggregate.

3.2

Forecast results

Our evaluation method amounts to comparing the performance of the microcomponents
speci…cations and their aggregate alternatives by calculating the deviations from our
Hodrick-Prescott benchmark given by 9.
In experiment 1, forecasts are speci…ed by equations 11 (and 12 for experiment 10 ).
Tables 6 and 7 show forecast performance in the …rst and the last forecast window forvalue-added-based productivity.21 The …rst column of each table identi…es whether direct
measures or …tted values were used forit and it in the speci…cations. This column
also shows whether the shares it were calculated using output- or input-side measuresof …rms Columns 2 and 3 contain the microcomponents forecasts speci…ed in (11) for
the two decompositions speci…ed in (10). Column 4 shows the forecasts for industryc Ag forcomponents speci…ed in (12). Columns 5 and 6 show the aggregate forecasts 4
t+s
total manufacturing. The …rst entry in column 2 of table 6 says that the microcomponents
forecast (using observed productivity and observed output-shares) is 2.4 percentage points
lower than the HP-trend over 1998-2000. All the other entries are to read analogously.
21

We do not present results for all the windows to save on space. Detailed results for the other forecast
windows are available upon request.

19

Forecasting productivity using micro data

The corresponding aggregate forecast, the …rst entry in column 5, is 3:2%. These two
numbers imply that the aggregate alternative to microcomponents is 0.8 percentage point
farther away from the observed HP-trend. If we compare numbers in the previous manner
we can conclude that aggregate forecasts would have missed to detect the productivity
acceleration of the late nineties whereas several of our speci…cations would have not. It isalso clear that all microcomponents forecasts beat the aggregate forecasts. This conclusion
carried over to all remaining forecast windows, Table 7 shows it for the 2001-2003 window.
As for industry components (column 4 in tables 6 and 7), we found that their forecasts
were closer to aggregate ones. More importantly, industry components could not beat
the micro-aggregated components forecasts in any of the four forecast windows. Thisis an interesting result and suggests that the decompositions of aggregate productivity
among incumbents and entrants, and among within and between contributions are more
informative about aggregate productivity dynamics than the productivity dynamics ofindustry subgoups.
These results are remarkable for several reasons. First, they suggest that microcomponents’predictive power is strong not only in particular periods but over all phases of thebusiness cycle (see footnote 15 in Section 3.1 for details). This is in contrast with Hendry
and Hubrich (2006), who found that disaggregate forecasts based on subaggregates of theconsumer price index performed worse than aggregate forecasts.22 We also found that
decomposition 6 produced more precise forecasts than decomposition 2, suggesting that
introducing information about the cross section distribution proved to be useful.
Experiment 2 was designed to reveal the predictive power of microcomponents over agc Ag was generated from VARs where
gregate productivity growth in a VAR-framework. 4
t+s
c Mi
no lagged microcomponents were present in the set of explanatory variables and 4t+s

was generated from VARs with microcomponents. We note the main conclusions here
without presenting detailed results.23 First, the superiority of microcomponent-VARs
were not obvious. They performed better in some speci…cations and forecast windows,
22

Upon re‡ection, this was to be expected. Micro-level pricing behavior depends in an important wayon (expected) aggregate prices and the individual di¤erences may cancel. Feedback from the aggregate
to individual productivity behavior likely is small.
23
Numbers are available upon request.

20

3

Forecasting

while in others they did not. Second, the issue of model selection proved to be critical.
An obvious criterion to choose from a set of VARs is the Bayesian Information Criterion(BIC). We found that using BIC to choose between a microcomponent-VAR and an aggregate VAR may lead to serious errors. For instance, choosing a microcomponent-VAR
based on BIC could lead to errors up to 1 2 absolute percentage points as measured byour metric in equation 9. On the other hand, not choosing a microcomponent-VAR basedon BIC could lead to errors up to 1 absolute percentage points by our metric. Furthermore, we always found a microcomponent-VAR in our speci…cation-set, which performed
better24 than the aggregate-VAR. The overall message of experiment 2 is that (i) we canalways …nd a microcomponent-VAR performing better than the aggregate-VAR, even in
our restricted speci…cation set; (ii) model selection is critical but ambiguous; (iii) selecting
a particular VAR based on BIC may lead to large errors.
To explore the practical question whether microcomponents can better predict the
KLEM Spublished aggregate we replaced 4 Ag
by 4 EUin experiment 3. As above, wett
only note the main conclusions here. Results resemble those in experiment 2 in that BIC
and our performance measure did not yield the same rank in our speci…cation-set. For
instance, BIC favored a VAR featuring input shares in the …rst forecast window witha 1:2 percentage deviation, however, measured shares led to only :08 percentage point
deviation (not shown here). We also found that we could always do better than theaggregate-VAR with at least one microcomponent-VAR speci…cation. However, just likein experiment 2, we did not …nd clear superiority of microcomponents.

3.3

Bayesian analysis

This section outlines the Bayesian forecasting approach to experiment 3. It has at least
three advantages over the Frequentist exercise. First, it is easy to compare and testdi¤erent speci…cations even if they are not nested. This is an important advantage because
we saw that model selection is a critical issue when microcomponents are combinedwith macro-information in a multivariate framework. Second, combining forecasts is
simple and intuitive in a Bayesian framework. Third, the Frequentist analysis does not
24

21

in terms of our performance measure in 9

Forecasting productivity using micro data

fully account for uncertainty. We could calculate con…dence bands around the forecasts
but those would only re‡ect forecast uncertainty. A Bayesian extension re‡ects bothparameter uncertainty and the inherent randomness of forecasting.
This section outlines the Bayesian approach assuming we retrieved a posterior distribution for the coe¢ cients and error covariance matrix of a VAR. Denote them by andV , respectively. A technical description of the estimation and forecasting can be foundin Appendix 5.2.
The main object of interest is the predictive density
Z 1Z 1p(yT +1 jyT ; M ) =p(yT +1 jV; ; M )p(V; jyT ; M )d dV;
0

(13)

1

where ys is observed data up to time s, V is the covariance matrix of shocks andis the parameter matrix in the VAR, and M denotes the model we are using. The predictive density coherently integrates (i) the uncertainty about , V and (ii) the intrinsic
uncertainty about the future yT +1 , conditional on the history yT of observed data andmodel M . p(V; jyT ; M ) and p(yT +1 jV; ; M ) are retrieved from a customized Gibbssampler (MCMC posterior simulator see, e.g. Koop (2003)). An illustrative exampleof the descriptives of p(yT +s jV; ; M ); s = 1; 2; 3 in our case is shown by …gure 6 andtables 8 and 9. These performance measures for value added/output, capital, labor andproductivity are similar in nature to the ones in experiments 2 and 3. In the sequel wereport performance measures only for TFP. Deviations from average HP-trend growth
were computed using the means of the distributions of individual growth trajectories, notthe means of the yearly distributions.
We estimated and forecasted several VARs with various lag-order in the four forecast
windows. As an example, we present detailed results for the …rst window (1998-2000) in
Table 10. All numbers are to read as explained in Section 3.2. For instance, the …rst entry
of column 2 of Table 10 says that measured output-side shares in a V AR(1; 2) yielded :3
percentage point higher productivity growth forecasts than the average HP-trend.
What is di¤erent is that Table 10 gives a Bayesian Model Average (BMA) forecast.
The average is taken over decompositions and structures and is weighted by the model’s
Predictive Bayes Factor (PBF). The logic of averaging is the following. The predictive22

3

Forecasting

likelihood p(yT +s jyT ; Mi ) can be calculated in time T + s; s = 1. It is a real number
given by evaluating p( jyT ; Mi ) at the observed yT +s (Geweke and Amisano (2008), van
Dijk et al. (2007)). The idea is to calculate the probabilities that the observed yt+s
was generated by model i. We evaluated them using the posterior simulator deployed toP(r)estimate and V . That is, we computed the real number R 1 R),
r=1 p(yT +s jyT ; M;
(r)
(r)
(r)
where
=(
; V ) and r = 1:::R are the indices of the elements of the chain afterconvergence. Given these values, we constructed model weights using PBFs. We assumed
the same model-priors, so the weights were given by the predictive likelihoods25 .
The …rst four rows of Table 10 already show that some of the microcomponents give
more accurate forecasts than the aggregate alternative, and some do not. However, theirPBF-weighted average is more accurate. It is remarkable that, in every forecast windowand every V AR speci…cation - not shown here -, the PBF-weighted (over decompositions
and structures) average forecast always proved to be more accurate than the aggregate
alternative even if some speci…cations performed worse.
We extended this way of model averaging over the entire set of speci…cations we haveinvestigated so far. That is, the two decompositions and four structures and the threelag-order speci…cations (V AR(2; 1), V AR(1; 2), V AR(1; 1)) yielded 24 microcomponentVARs and three aggregate-VARs in each forecast window.
Table 11 summarizes the result of model-averaging over the entire set of speci…cations.
Several interesting conclusions emerge from these results. First, individual performancemeasures of VARs showed that forecasts were much more similar than in the Frequentist
exercise26 . Second, BMA-forecasts using micro components were always better than themacro-alternative, whether averaging over only structures and decompositions or overthe entire set of speci…cations. It holds true even if individual speci…cations performed
less well. This is an interesting result and may be explained by the BMA-logic: every
model is as good as its forecasts. Since we weighted forecasts by their predictive likeli25

after appropriate transformation.
This has probably to do with our strong prior on the variance of the shocks. We speci…ed a restrictedvariance shock-distribution for reasons explained in Appendix 5.2. As a result, the estimated means ofsimulated distributions di¤er less than in the frequentist exercise. Di¤erences, or improvements shouldbe evaluated in light of this.
26

23

Forecasting productivity using micro data

hoods, speci…cations with less explanatory power were assigned smaller weights whereas
speci…cations with more explanatory power were assigned larger weights.

4Conclusions and Extensions

The aim of this paper is to build aggregate productivity forecasts using information on…rm-level productivity and market share evolution. Our work builds upon the literature
on measuring and analyzing …rm-level productivity, but our question was not how to measure productivity at the …rm level but rather how to apply these estimates in forecasting.
To our knowledge, our study is a novel attempt to connect micro and macro level analysis
whereby micro-level productivity estimates are used to build aggregates and forecasts.
We carried out several forecasting experiments for di¤erent speci…cations and models.
The result from these horse-races is that micro-aggregated components improve simple
aggregate total factor productivity forecasts. While the results are mixed for richer
forecasting speci…cations, the paper shows, using Bayesian model averaging techniques(BMA), that the forecasts using micro-level information were always better than themacro alternative.
The paper does not address the important question of choosing the optimal forecasting tool. One natural extension in this direction is to investigate the performance of
microcomponents in structural timeseries forecasting models. These signal extraction
techniques are relevant because they impose explicit structure on the dynamic behaviorof trends, cycles and irregular terms. As a consequence of the richer structure, we may expect them to capture observed dynamics better than simple autoregressive speci…cations.
Another area for future work is choosing the optimal benchmark. The Hodrick-Prescott…lter is known to perform poorly at the sample endpoints, leading to the developmentof other real-time …ltering techniques in recent years. Some alternatives are based on
univariate approaches (see Wildi (1998), for an early example) others are based on multivariate approaches (see Stock and Watson (2002) for a dynamic factor modelling example). Although these issues are important and relevant aspects of our forecast evaluation
exercises, they are beyond the scope of the paper and left for future research.
24

References

References
Acemoglu, D., P. Aghion and F. Zilibotti (2002), “Distance to Frontier, Selection and Economic Growth”, Discussion Paper 3467, Center for Economic Policy
Research.
Ackerberg, D. A., K. Caves and G. Frazer (2005), “Structural Indenti…cationof Production functions”, .
Baily, M. N., E. J. Bartelsman and J. Haltiwanger (2001), “Labor Productivity: Structural Change and Cyclical Dynamics”, The Review of Economics
and Statistics, vol. 83, no. 3, pp. 420–433.
Bartelsman, E. J. and M. Doms (2000), “Understanding productivity: lessons
from longitudinal microdata”, Journal of Economic Literature, vol. 38, no. 3, pp.
569–594.
Bartelsman, E. J., J. Haltiwanger and S. Scarpetta (2005), “Measuring
and analyzing coss-country di¤erences in …rm dynamics”, draft, NBER/CRIW
conference, Washington DC., March 2005.
Bartelsman, E. J., J. Haltiwanger and S. Scarpetta (2008a), “Cross Country Di¤erences in Productivity: The Role of Allocative E¢ ciency”, mimeo.
Bartelsman, E. J., J. Haskel and R. Martin (2008b), “Distance To Which
Frontier? Evidence on Productivity Convergence from International Firm-Level
Data”, Discussion Paper 7032, Centre for Economic Policy Research.
Basu, S., J. Fernald and M. Kimball (1998), “Are Technology Improvements
Contractionary?”, Discussion Papers 625, International Finance.
Basu, S. and M. S. Kimball (1997), “Cyclical Productivity with Unobserved Input
Variation”, Working Paper 5915, National Bureau of Economic Research.
Corrado, C., J. Beaulieu, E. J. Bartelsman and P. Lengermann (2006),“Modeling Aggregate Labor Productivity and a Disaggregate Level: New Resultsfor US sectors and industries”, mimeo.
25

Forecasting productivity using micro data

van Dijk, H. R., F. Ravazzolo and M. Verbeek (2007), “Predictive gains fromforecast combinations using time varying model weights”, Econometric institutereport, Econometric Institute, Erasmus University Rotterdam.
Domar, E. D. (1961), “On the Measurement of Technological Change”, The Economic Journal, vol. 71, no. 284, pp. 709–729.
Geweke, J. and G. Amisano (2008), “Comparing and evaluating Bayesian predictive distributions asset returns”, Working Paper 969, European Central Bank.
Hendry, D. F. and K. Hubrich (2006), “Forecasting Economic Aggregates by
Disaggregates”, Working Paper 589, European Central Bank.
Hulten, C. R. (1978), “Growth Accounting with Intermediate Inputs”, The Review
of Economic Studies, vol. 45, no. 3, pp. 511–518.
Kátay, G. and Z. Wolf (2008), “Driving Factors of Growth in Hungary - a Decomposition Exercise”, Working Paper 6, Magyar Nemzeti Bank.
Koop, G. (2003), Bayesian Econometrics, Wiley and Sons.
Lentz, R. and D. T. Mortensen (2005), “An Empirical Model of Growth throughProduct Innovation”, Working Paper 11546, National Bureau of Economic Research.
Levinsohn, J. and A. Petrin (2003), “Estimating Production Functions Using
Inputs to Control for Unobservables”, Review of Economic Studies, vol. 70, no. 2,
pp. 317–341.
Oliner, S. D., D. E. Sichel and K. J. Stiroh (2007), “Explaining a Productive
Decade”, Finance and Economics Discussion Series 63, Board of Governors of
the Federal Reserve System.
Olley, G. S. and A. Pakes (1996), “The Dynamics of Productivity in the Telecommunications Equipment Industry”, Econometrica, vol. 64, no. 6, pp. 1263–1297.
O’Mahony, M., B. V. Ark and G. Ypma (2007a), “The EUKLEMS Productivity
Report”, mimeo, 2007 march.
26

5

Appendix

O’Mahony, M., M. P. Timmer and B. V. Ark (2007b), “EUKLEMS Growthand Productivity Accounts: Overview November 2007 Release”, mimeo.
Petrin, A. and J. Levinsohn (2008), “Measuring Aggregate Productivity Growth
Using Plant-level Data”, mimeo.
Stock, J. H. and M. W. Watson (2002), “Forecasting Using Principal Components from a Large Number of Predictors”, Journal of the American Statistical
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Wildi, M. (1998), “Detection of Compatible Turning-Points and Signal-Extraction
for Non-Stationary Timeseries”, Operations Research Proceedings 1998, pp. 298–
199.

5

Appendix

5.1

The data

5.1.1

CBS data

General description The microlevel database consists of a large panel of Dutch manufacturing …rms. The database is under close surveillance by the Centrum voor Beleidsstatistiek27 . The time dimension of the panel spans between 1978 and 2004.
To compile our working data, we …rst established longitudinal links in the databasebecause the CvB changed …rm identi…ers as of 1993. We used correspondences between…rm identi…ers included in the underlying data…les. There was no documentation aboutsuch aspects of …rm dynamics as mergers, acquisitions and split-ups so we could notcontrol for these transformations.
The industry classi…cation system also changed in 1993. Since both the 1974-based(’old’) and the 1993-based (’new’) industry codes were available in 1990-1992, we generated a correspondence between the two industry classi…cations. We could then use this27

27

Dutch Statistics O¢ ce

Forecasting productivity using micro data

correspondence to generate de‡ators that originated from the EUKLEMS dataset, which
in turn is based on the new industry classi…cation.
Table 1 explains names of industry codes. In order not to lose observations andmaintain a reasonable size, we merged industries 23 and 24.
Table 2 describes how many …rms were used in the decompositions, the last columnsof tables 3 and 4 show the how many observations were used in TFP-estimation. The
last columns in tables 3 and 4 show …rm-year observations whereas table 2 treats each…rm as a single observation.
Variables The dataset did not have observed capital so we used depreciation as a proxy
for the capital stock. We de‡ated nominal depreciation using an industry-speci…c implicit
capital de‡ator that was calculated from EUKLEMS data. The other …rm-speci…c microvariables were: number of employees, output, value added, input materials, energy andpayroll.
Outliers We …ltered outliers using the interquartile-range method. This method is astandard way of dealing with skewed distributions. For TFP-estimation, we considered
an observation to be outlier if either of the following was true:xo < q25

1:5 IQR

xo > q75 + 1:5 IQR;
where xo fK=Y ; M=Y ; W EXP=Lg and K denotes capital, M denotes input materialpurchases, W EXP denotes wage expenditures, Y denotes either value added or output
depending on which model we used. q25 and q75 stand for the lower and upper quartilesof the distribution of the variables in the set xo , and IQR q75 q25:
For aggregation, we used slightly di¤erent …ltering. Since depreciation is not observedin the …rst six years of the panel, we had to backcast individual productivity growth
rates in 1978-1983. The backcasting procedure was based on the (geometric) averageof non-outlier value-added/revenue labor-productivity growth. Using these "imputed"
productivity numbers we carried out a secondary outlier …ltering in order to get rid of28

5

Appendix

implausibly large or small productivity-observations. The logic of this secondary …ltering
was the same as above with the exception that we deployed energy instead of depreciation.

5.1.2

The EUKLEMS data

History and general description The EUKLEMS "... project aims to create a database on measures of economic growth, productivity, employment creation, capital formation and technological change at the industry level for all European Union member statesfrom 1970 onwards. This work will provide an important input to policy evaluation, inparticular for the assessment of the goals concerning competitiveness and economic growthpotential as established by the Lisbon and Barcelona summit goals. The database should
facilitate the sustainable production of high quality statistics using the methodologies ofnational accounts and input-output analysis. The input measures will include various
categories of capital, labour, energy, material and service inputs. Productivity measures
will be developed, in particular with growth accounting techniques. Several measures onknowledge creation will also be constructed. Substantial methodological and data researchon these measures will be carried out to improve international comparability. There willbe ample attention for the development of a ‡exible database structure, and for the progressive implementation of the database in o¢ cial statistics over the course of the project.
The database will be used for analytical and policy-related purposes, in particular by studying the relationship between skill formation, technological progress and innovation on the
one hand, and productivity, on the other. To facilitate this type of analysis a link will also
be sought with existing micro (…rm level) databases. The balance in academic, statisticaland policy input in this project is realized by the participation of 15 organizations fromacross the EU, representing a mix of academic institutions and national economic policy
research institutes and with the support from various statistical o¢ ces and the OECD."28

Structure There have been two EUKLEMS releases so far. We used the one that was
published in March 2008. The …les contain 62 variables, including basic data and growth28

29

http://www.euklems.net

Forecasting productivity using micro dataaccounting variables. The data…les are structured to follow an industry classi…cation list
which corresponds with the NACE29 list.

Variables For a detailed description of the variables, see O’Mahony et al. (2007b) andO’Mahony et al. (2007a). This project used growth accounting variables in forecasting
exercises and de‡ators in the nonparametric identi…cation procedure. To be more speci…c,the following variables were used in forecasting experiments.
GO_QI:
Gross output, volume indices, 1995 = 100,
VA_QI:
Gross value added, volume indices, 1995 = 100,
LAB_QI: Labour services, volume indices, 1995 = 100,
CAP_QI: Capital services, volume indices, 1995 = 100,
TFPva_I: TFP (value added based), 1995=100,
TFPgo_I: TFP (gross output based) growth, 1995=100,
GO:
Gross output at current basic prices (in millions of local currency),
VA:
Gross value added at current basic prices (in millions of local currency).
The following were used for …rm-level calculations at the …rst stage of the project:
GO_P:
Gross output, price indices, 1995 = 100,
VA_P:
Gross value added, price indices, 1995 = 100,
II_P:
Intermediate inputs, price indices, 1995 = 100,
CAP:
Capital services (in millions of local currency),
CAP_QI: Capital services, volume indices, 1995 = 100,
the last two were used to calculate implicit capital de‡ators for every industry.

29

NACE –Classi…cation of Economic Activities in the European Community.

30

5

Appendix

5.2

Bayesian analysis

5.2.1

Notation

Consider the following unrestricted VAR (1) speci…cation
y1t =
y2t =
..
.

11 y1t 1 +ynt =n1 y1t 1 +21 y1t 1 +

..
.

..
.

+ 1p ynt p +"1t
+ 2p ynt p +"2t
..
..
.
.
+ np ynt p +"nt

in a matrix representation as
y t = y t 1 + "twhere yt is an n 1 vector containing the variables of the VAR, is a n p matrixre‡ecting the dynamic structure of the VAR and "t is an iid mean-zero normal random
vector with covariance matrix V . This last assumption says there is no autocorrelation
left in the error term but the errors of di¤erent equations at time t can be correlated.
A more convenient representation of the above VAR is the following. Let yt =(y1t :::ynt )0 be the t-th observation vector of dimension (n 1) in the sample, xt =(y1t 1 :::ynt p )0 be the n p-vector containing the p lags of the n variables. Collect thecoe¢ cients equation-by-equation in the (n p)-vectors 1 ; :::; n :The error vector stays
the same "t = ("1t :::"nt )0 . Then the above system can be written as
yt = Xt + "t

Xt = In
0

0

xt
B
B 0
xt = B
B ..
@ .
1

0
xt
..
.

0

B .1 C. C= B@ . A ; 8t = 1:::T

1
0
C
0 C
C
..
. 0 C
A
xt

n

This implies that yt 2 Rn 1 ;
31

2

2 R(n

p) 1

2

, Xt 2 Rnpand "t 2 Rn 1 .

Forecasting productivity using micro data

5.2.2

Bayesian representation

The …nal objective of the forecasting exercise is to describe our beliefs about the joint
evolution of future observations and parameters based on our sample up to time T . In
other words, we want to characterize the posterior predictive density. We can write thisasp(yT +1 :::yT +H ; V; jyT );(14)i.e. the joint posterior density of future observations and parameters conditional on
observed data. Using standard laws and the direct consequence of Bayes’ theorem wedeconvolve (14) asp(yT +1 :::yT +H ; V; jyT ) = p(yT +1 :::yT +H jV; ; yT ) p(V; jyT ):(15)

The …rst term of the right hand side represents the beliefs about the future realizationsof the VAR, the second term is the posterior density of the parameters. Rewriting 15
gives an operational representation of y T +1 ’s posterior predictive density:
Z 1Z 1p(yT +1 jyT ) =p(yT +1 jV; )p(V; jyT )d dV
(16)
0

1

such that we integrate out the VAR-parametersvector "t .
5.2.3

and the covariance matrix of the error

Prior elicitation

To understand we …rst characterize the posterior p( ; V jyT ) in 16. In the usual manner,
this posterior can be written asp( ; V jyT ) / p(yT j ; V )p( ; V ):(17)

The …rst term on the right hand side of 17 is the Gaussian likelihood. The second termis the joint prior. We choose a natural conjugate joint prior speci…cation because - whencombined with a Gaussian likelihood - it yields full conditional posterior distributions
32

5

Appendixof the same family30 . The most obvious natural conjugate prior for V is the Inverse
Wishart (IW ) distribution. In short, this prior elicitation is a matrix-generalization of
the Gamma-prior in the univariate case. Similarly, choosing a normal prior for results
in a normal full conditional posterior. To sum up the priors, we write
V(18)

IW V ; df
N ( ; Q)

where the positive de…nite V matrix plays the role of the scaling parameter and df isdegrees of freedom. The probability density function of the IW -distributed n n matrix
V looks like this:jV jdf =2 jV j (df +n+1)=2 e trace(V V
p(V ) =
2df n=2 n (df =2)
where

1 )=2

n (df =2) is the multivariate gamma function.

Using 18, we can write out the joint prior asp( ; V ) / N ( ; Q)IW V ; df ;(19)

and the joint posterior in 17 asp(yT j ; V )N ( ; Q)IW V ; df :(20)

Prior parameters ; Q; V and df A frequently used prior for macro VARs is the socalled Litterman-Minnesota prior. Our priors are similar to but slightly di¤erent fromthis well-known prior. In the Litterman-Minnesota case a VAR is written in levels andthe prior on the coe¢ cient matrix is such that the …rst lag has a prior mean of 1, theother lags have prior mean zero. This prior assumes that there are n random walks inthe system.
30

33

See, for instance, Koop (2003).

Forecasting productivity using micro data

Our endogenous variables value added/output, capital, labor and productivity are
implied by the production function speci…cations. Our decompositions characterize aggregate productivity growth that we think can be described by the …rst di¤erence of a
= 0 2 Rn 1 for the
random walk. Correspondingly, we take zero prior means, i.e.
individual coe¢ cients. We also assume that individual parameters are independent sothat Q is diagonal.
Our data approximate yearly growth rates by log-di¤erences. A 0.3 log point changearound zero is approximately equivalent to a growth rate of 0.26, a -0.3 log point change
corresponds to a growth rate of -0.36. Moreover, if we move further away from zero along
the real line, the log di¤erences are even poorer approximations of the real growth rates.
In terms of aggregate productivity and the other endogenous variables, these relatively
small log-changes imply already so large shifts on the original scale of the variables that
we expect it to happen very rarely. So it seemed reasonable to restrict prior variances ofthe shocks and the coe¢ cients.
Therefore, the diagonal elements of the error variance-covariance matrix V were set to
10 2 . The non-diagonal elements of V were set to zero because we did not have a strong
prior on the contemporary covariance structure of the errors. In terms of a scalar zeromean normal distribution, this corresponds with 99% of the probability mass falling into
the interval [ 0:258; +0:258]. On the one hand, this is the range where there is a small
chance of atypical shocks. On the other, with this prior variance setting, the majority ofthe support corresponds to the interval [ 0:2; +0:2], where the log approximation works
reasonably well and where we would expect the principal part of the typical aggregate
growth rates. The same argument holds for parameter variances Q. Roughly speaking,nontypical -draws would blow up/shrink already implausible values for yt in the next
period, which may result in forecasts of log-shifts changes that would imply implausibly
large changes in our endogenous variables.
df was also set to zero as this corresponds to the non-informative prior on the degreesof-freedom parameter.
34

5Appendix

5.2.4

Posterior distributions, estimation and forecasting

Using the joint posterior we can develop a Gibbs-sampler based on the full conditional
posterior distributions of and V (see Koop (2003) for more details).
Full conditional distributions: p( jV; yT ) and p(V j ; yT ) The full conditional distribution of the parameter vector is proportional to a multivariate normal distribution.
It is so because if V and yT are nonrandom, the only thing that is random in the joint
posterior (20) is . p( jV; yT ) can be written as
jV; yTN ( ; Q)
= Q Q

1

+

T
X

Xt0 V

t=1

Q 1+

Q =

T
X

Xt0 V

1

Xt

t=1

1

yt

!

! 1

.

The full conditional distribution of the error covariance matrix is proportional to the
product of the Gaussian likelihood and the IW (V ; df ) prior about V .31 We use thefact that this product is also proportional to an IW V 1 1 ; df1 -density with a new scale
matrix 1 1 and degrees of freedom parameter df1 :V j ; yTIW V ; df ,where the updated scale and the degrees-of-freedom parameters V and df are calculated as
V

=

V

1

+

T
X
t=1

df = T + df .

(ytXt ) (yt

Xt )0

! 1

The Gibbs-sampler amounts to iterating the following algorithm until convergence:
31

35

Again, based on the joint posterior distribution given by (20).

Forecasting productivity using micro data

1. Give starting values to

0 = (

(0)

; V (0) ):2. Simulate (m+1) from p( jV (m) ; yT ) and thensimulate V (m+1) from p(V j (m+1) ; yT ).
3. Set m = m + 1 and go to step 2.
Forecasting After the Markov-Chain has converged we can consider the elements ofthe chain (after discarding the burn-in observations and thinning the chain) as sample
from the joint posterior. Now we turn to the …rst term of the right hand side of (15):p(yT +1 :::yT +H ; V; jyT ). Conditional on y = (y1 ; :::; yT ); and V , " is distributed normallyalong the future path of the VAR, i.e., yT +k is also conditionally normally distributed.
So in order to obtain draws from the forecast distribution of yt we have to the simulate
future paths of yt+i i = 1:::k. To this end, we take each element, indexed by (m), of theMarkov-chain after the burn-in value (m = R) and thinning. A trajectory at time T canbe constructed at the (m)-th element of the Markov-chain as:
(m)

(m)

(m)

1. Draw the random vectors "t+1 ; "t+2 ; :::; "t+kN (0; V (m) )2. Calculate(m)(m)
yt+1 = (m) yt + "t+1
(m)
(m)
(m)
yt+2 = (m) yt+1 + "t+2
..
.
(m)

yt+k =(m)(m) (m)yt+k 1 + "t+k3. Go to the (m + 1)-th element of the Markov-chain.
(m)

4. Calculate the appropriate moments of the forecast distribution from yt+i i = 1:::k,m = R:In this manner, we have a simulated trajectory for each element of the Markovchain so we can calculate moments of the forecast distribution. The forecast distribution
approximated this way fully re‡ects parameter uncertainty.32
32

If we forecast the system at the mean or median of the posterior error covariance matrix V (parameter
vector ), the forecast distributions miss the uncertainty in the coe¢ cient vector (error covariances
V ).

36

Tables and …gures

Tables and …gures

Figure 1: Tfp-growth in overall manufacturing in di¤erent countries.
0.1

0.08

0.06

0.04

0.02

0

-0.02

-0.04

-0.06

USA

37

UK

GER

FRA

IRL

NED

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

1977

-0.08

Forecasting productivity using micro data

Figure 2: Tfp growth by micro-based and EUKLEMS-based aggregate; overall manufacturing.
0.2

0.15

0.1

0.05

0

-0.05

-0.1

micro-based

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

-0.15

Euklems-based

Figure 3: Value added growth by micro-based and EUKLEMS-based aggregates; overall
manufacturing (solid line: micro-based aggregate; dashed line: EUKLEMS aggregate).
0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

-0.05

-0.1

micro-based

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

1977

1976

1975

1974

1973

1972

1971

1970

-0.15

euklems38

Tables and …gures

Figure 4: Labor input growth by micro-based and EUKLEMS-based aggregates; overall
manufacturing (solid line: micro-based aggregate; dashed line: EUKLEMS aggregate).
0.25

0.2

0.15

0.1

0.05

0

-0.05

-0.1

micro-based

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

1977

1976

1975

1974

1973

1972

1971

1970

-0.15

euklems

Figure 5: EUKLEMS aggregate tfp index (1995=100) and its HP-trend
120

110

100

90

80

70

actual39HP-trend

2005

2004

2003

2002

2001

2000

1999

1998

1997

1996

1995

1994

1993

1992

1991

1990

1989

1988

1987

1986

1985

1984

1983

1982

1981

1980

1979

1978

60

Forecasting productivity using micro data

Figure 6: Forecast distributions of yearly tfp growth rates on a three-year horizon (19982000).

t+1

tfp fcast distributions: G=10000; burn-in:5000; thin-value:10; MC-elements:500; p=2
10

5

0
-0.4

-0.3

-0.2

-0.1

0

-0.2

0

0.1

0.2

0.3

t+2

4

2

0
-1

-0.8

-0.6

-3

-2

-0.4

0.2

0.4

0.6

0.8

2

3

4

3
t+3

2
1
0
-4

-1

0

1

40

Tables and …gures

Table 1: Key to industry codes
Manufacturing classificationindustry code
Consumer manufacturing
15t16
Food products, beverages and tobacco
17t19
Textiles, textile products, leather and footwear
36t37
Manufacturing nec; recycling
Intermediate manufacturing
20
Wood and products of wood and cork
21t22
Pulp, paper, paper products, printing and publishing
23
Coke, refined petroleum products and nuclear fuel24
Chemicals and chemical products
25
Rubber and plastics products
26
Other non-metallic mineral products
27t28
Basic metals and fabricated metal products
Investment goods, excluding hightech
29
Machinery, nec
34t35
Transport equipment
Electrical machinery and communication services
30t33
Electrical and optical equipment

Source: Table 4 in O’Mahony et al. (2007a).

Table 2: Number of …rms in the analysis
industry code
15t16
17t19
20
21t22
24
25
26
27t28
29
30t33
34t35
36t37
overallmanufacturing

41

original
5994
3823
1321
5908
1585
1713
2076
7617
4804
3296
2291
3743

va model
4284
2503
1040
4064
1088
1307
1395
5117
3358
2140
1504
2205

output model
4421
2429
1038
4224
1132
1321
1472
5246
3367
2197
1534
2265

44171

30005

30646

Forecasting productivity using micro data

Table 3: Estimation results - Value added modelindustry code
15t16
17t19
20
21t22
24
25
26
27t28
29
30t33
34t35
36t37

L
0.52
0.54
0.58
0.60
0.44
0.53
0.52
0.65
0.62
0.65
0.72
0.59

K
0.22
0.23
0.12
0.13
0.23
0.24
0.21
0.12
0.12
0.16
0.06
0.13

M
.
.
.
.
.
.
.
.
.
.
.
.

ctrs
581.607390.991431.116660.952
101.387
84.735191.860
1056.116
458.341211.017183.449
322.399

seL
0.007
0.008
0.017
0.009
0.016
0.019
0.013
0.008
0.012
0.013
0.014
0.013

seK
0.014
0.011
0.015
0.006
0.023
0.015
0.016
0.008
0.010
0.010
0.010
0.012

nobs
19745
9457
4624
20196
6390
6800
7094
24428
18231
8008
6861
9033

Table 4: Estimation results - Output modelindustry code
15t16
17t19
20
21t22
24
25
26
27t28
29
30t33
34t35
36t37

L
0.25
0.40
0.31
0.36
0.23
0.33
0.34
0.45
0.42
0.47
0.44
0.38

K
0.12
0.16
0.01
0.07
0.13
0.02
0.02
0.01
0.06
0.05
0.01
0.1

M
0.65
0.42
0.66
0.56
0.59
0.59
0.69
0.54
0.53
0.63
0.55
0.37

ctrs
2.64392.98650.0296
0.06572.09371.8747
0.03680.00020.42902.89800.01946.7575

seL
0.013
0.019
0.012
0.008
0.017
0.011
0.010
0.008
0.007
0.013
0.015
0.013

seK
0.019
0.022
0.007
0.033
0.153
0.047
0.152
0.003
0.018
0.036
0.000
0.020

nobs
19745
9457
4624
20196
6390
6800
7094
24428
18231
8008
6861
9033

Table 5: Average tfp-growth in overall manufacturing in di¤erent countries, source: EUKLEMS database (average percent per annum rates over period indicated in …rst column)
USA

UK

GER

FRA

IRL

NED

1981-1985

0.024

0.039

0.018 0.012

#N/A

0.024

1986-1990

0.015

0.034

0.010 0.008

#N/A

0.012

1991-1995

0.022

0.019

0.014 0.022

#N/A

0.018

1996-2000

0.026-0.0040.020 0.028

0.046

0.021

2001-2005

0.035

0.026

0.015 0.015 -0.006 0.016

42

Tables and …gures

Table 6: Out-of-sample forecast performance, percentage point deviation from HP-trendof aggregate manufacturing productivity growth, estimation sample: 1978-1997, forecast
period: 1998-2000
structureobserved VA-shares

microcomp.
dc1

dc2

-2.4

-2.2

aggregate

industry comp.
-3.5

dc1

dc2

-3.2

-3.3

observed input shares

-0.9

-0.9

-2.8

-3.1

-3.1

fitted VA shares & tau

-1.7

-1.4

-4.7

-4.6

-4.7

fitted input shares & tau

-1.2

-0.9

-3.3

-3.3

-3.4

dc1: equation 2; dc2: equation 6; microcomp. forecast is impliedby equation 11; industry comp. is implied by equation 12; theaggregate forecast was computed from its own autoregressivemodel.

Table 7: Out-of-sample forecast performance, percentage point deviation from HP-trendof aggregate manufacturing productivity growth, estimation sample: 1978-2000, forecast
period: 2001-2003
structure

microcomp.
dc1

industry comp.

dc2

aggregatedc1

dc2

observed VA-shares

-2.9

-1.7

-2.9

-3.2

-3.6

observed input shares

-2.1

-2.6

-3.0

-3.0

-3.0

fitted VA shares & tau

-5.0

-5.6

-8.5

-8.8

-8.9

fitted input shares & tau

-3.3

-3.9

-5.5

-5.7

-5.7

dc1: equation 2; dc2: equation 6; microcomp. forecast is impliedby equation 11; industry comp. is implied by equation 12; theaggregate forecast was computed from its own autoregressivemodel..

43

Forecasting productivity using micro data

Table 8: Predictive distribution statistics over forecast horizon 1998-2000, macro VAR
on growth rates
Variable

Mean

Stdev

NSE

Medianva/q-0.00880.08030.0025-0.0093cap-0.0050.06550.0021-0.0048lab-0.00080.05270.00170.0003tfp

0.00370.06510.0021

0.006

va/q

0.02080.17740.00560.0137cap

0.02140.13020.00410.0136lab-0.00210.119

0.0038-0.0047

tfp

0.00720.14080.00450.0011va/q-0.05310.44080.0139-0.006cap-0.0604

0.34860.011-0.0105

t+1

t+2

t+3

lab

0.00540.25

0.00790.0011

tfp-0.0353

0.35680.0113-0.0061va/q-0.01370.23280.0074-0.0005cap-0.01470.18140.0057-0.0006lab

0.00080.14060.0044-0.0011tfp-0.00810.18760.00590.0004

Average

Gibbs-iterations:10000; burn-in:5000; thin-value:10; MC-elements:500.
Growth rates are approximated by logarithmic di¤erences44

Tables and …gures

Table 9: Descriptives of overall trajectory distributions over forecast horizon 1998-2000,
macro-VAR on growth rates
Variable

Mean Stdev

NSE Medianva/q -0.0071
0.11 0.0035-0.0012cap -0.0091
0.101 0.0032-0.0039lab 0.0036 0.0751 0.0024-0.002
tfp -0.0031 0.0969 0.0031-0.0017
G=10000; burn=5000; thin=10; MC-elements:500.
Table 10: Bayesian forecast results: average value added tfp-growth rates for overall EUKLEMS manufacturing (percentage point deviation from HP-trend, estimation sample:
1978-1997, forecast period: 1998-2000)
VAR(1,2)*

structure

VAR(2,1)**

dc1

dc2

dc1

dc2

va/q shares

0.3

1.5

1.0

6.0

input shares

-0.9

2.3

-1.2

0.4

fitted va/q shares & tau

0.4

-1.5

-0.9

2.4

fitted input shares & tau

0.6

0.0

-0.1

VAR - micro & macro

4.7

PBF-weighted average of fcasts:

0.3

0.3

VAR - macro

-2.3

-2.3

* VAR(1,2): 1st lag of endogenous variables (growth rates of aggregate capital services, labor sevices, tfp, value added), 1st and2nd lags of exogenous variables. Exogenous variables are lagged values of components in the micro-based decompositions (ie.

**VAR(2,1): 1st and 2nd lags of endogenous variables (growth rates of aggregate capital services, labor sevices, tfp, value
added), 1st lag of exogenous variables. Exogenous variables are lagged values of components in the decompositions (ie. X(t-1)).

Table 11: Bayesian Model Averages of forecast results: value added tfp-growth rates
for overall manufacturing, percentage point deviations from HP-trend. Averages arecalculated using all models used in a forecast window
VARForecast horizon microcomponents

45

VARaggregate

1998-2000

-0.7

-1.8

1999-2001

-1.1

-1.9

2000-2002

-1.4

-1.9

2001-2003-1.5-2.1