Advanced counterfactual evaluation methods : guidance document.
Date: 2019-10-29
Institutions: Directorate-General for Employment, Social Affairs and Inclusion
Subjects: EU employment policy, European Social Fund, business policy, labour market, user guide

Advanced counterfactual 
evaluation methods 

  Guidance document

Social 
Europe

 
 
Advanced counterfactual 
evaluation methods

Guidance document

European Commission 
Directorate-General for Employment Social Affairs and Inclusion 
Directorate G

This guidance material has been produced based on the work by the following experts: 
Claudio Deiana, Andrea Geraci and Elena Claudia Meroni (European Commission, Joint 
Research Centre, Centre for Research on Impact Evaluation)

LEGAL NOTICE 

Manuscript completed in October 2019

Neither the European Commission nor any person acting on behalf of the European Commission is 
responsible for the use that might be made of the following information. More information on the European 
Union is available on the Internet (http://www.europa.eu). 

Luxembourg: Publications Office of the European Union, 2019 

PDF   ISBN 978-92-76-11881-7

doi:10.2767/464242

KE-04-19-627-EN-N

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Purpose of the guidance document ................................................................................................................................................................. 3 

1.  Introduction ............................................................................................................................................................................................................ 4 

2.  SEQUENCE ANALYSIS ........................................................................................................................................................................................ 5 

2.1.  Background ................................................................................................................................................................................................. 5 

2.2.  Method and data requirements ....................................................................................................................................................... 5 

2.3.  How it works in practice: An example from the academic literature .......................................................................... 8 

2.4.  References ................................................................................................................................................................................................ 10 

3.  DYNAMIC MATCHING ...................................................................................................................................................................................... 11 

3.1.  Background .............................................................................................................................................................................................. 11 

3.2.  Method and data requirements .................................................................................................................................................... 12 

3.3.  How it works in practice: An example from the academic literature ....................................................................... 13 

3.4.  References ................................................................................................................................................................................................ 16 

4.  SYNTHETIC CONTROL METHOD ................................................................................................................................................................ 17 

4.1.  Background .............................................................................................................................................................................................. 17 

4.2.  Method and Data Requirements .................................................................................................................................................. 17 

4.3.  How it works in practice: An Example from the academic literature....................................................................... 20 

4.4.  References ................................................................................................................................................................................................ 22 

5.  Conclusions .......................................................................................................................................................................................................... 23 

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Purpose of the guidance document 

The aim of this guidance material is to provide an accessible introduction to advanced counterfactual impact 
evaluation  (CIE)  methods.  The  guidance  material  is  mainly  intended  for  the  managing  authorities  of  the 
European  Social  Fund (ESF) and European Social Fund Plus (ESF+). It can  also  be used  by  other  institutions 
involved in implementing and evaluating operations funded by the ESF and ESF+ and by the wider evaluation 
community.  

Focusing on results is one of the main principles of EU investments, and quality evaluations are essential in 
providing credible evidence about the performance of EU-funded interventions. CIE methods help to answer the 
fundamental  question  of  whether  or  not  the  intervention  actually  worked.  The  European  Commission 
encourages Member States to carry out CIEs in order to have more credible evidence about the impacts of the 
ESF and ESF+ funded operations. Carrying out a high quality CIE is not easy, and the current guidance material 
is one element of the broader support the Commission gives to the Member States in conducting high-quality 
CIEs. 

This guidance material builds on the previous publication by the European Commission, Directorate-General for 
Employment, Social Affairs entitled ‘Design and commissioning of counterfactual impact evaluations’1, which 
introduced the principled and use of CIEs and explained the most common CIE methods. It also complements 
the support for CIEs provided by the European Commission, Centre for Research on Impact Evaluation2, at Joint 
Research Centre which includes video-tutorials, guidance notes, examples of CIEs and other materials. 

1https://publications.europa.eu/en/publication-detail/-/publication/f879a9c1-4e50-4a7b-954c-

9a88d1be369c/language-en  

2 https://crie.jrc.ec.europa.eu/  

3 

 
 
 
                                          
1. 

Introduction 

The guidance note describes some recent developments of counterfactual impact evaluation methods. The three 
methodologies proposed are sequence analysis, dynamic matching and synthetic controls.  

Sequence  analysis  can  be  used  in  combination  with  other  matching  techniques,  such  as  propensity  score 
matching, when there is information on some sequences of an event happening before the treatment. In the 
case of active labour market policies, knowing the sequence of events and employment statuses  that occur 
before the policy starts can be relevant information to be used in combination with matching on other relevant 
observable characteristics. 

Dynamic  matching  is also useful  when  evaluating  active  labour  market  policies,  in particular  in  the  case  of 
ongoing  programmes,  i.e.  programmes  which  can  start  at  any  point  in  time  and  where  eventually  all  the 
individuals can be treated at one point. 

Synthetic control is an extension of difference-in-difference, and can be used to evaluate a policy which affects 
a whole single region or country, using a pool of non-treated regions or countries as a comparison group. 

Details of these three methods are reported in the three sections below. 

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2.  SEQUENCE ANALYSIS 

2.1.  Background 

Sequence  analysis  can  be  described  as  a  set  of  statistical  techniques  applied  within  the  stream  of  the 

sociological literature dealing with life-course studies. In this context, sequence analysis has been developed as 

a  method  of  empirically  describing  and  investigating  properties,  outcomes,  and  determinants  of 

individual trajectories. The method was introduced in the sociological literature by Andrew Abbott in the mid-

1980s, and has been applied since then in studies dealing with different topics, including family formation, 

health trajectories and career trajectories. 

While a more detailed methodological definition of a sequence (trajectory) is given in the next section, it can be 

broadly described as the representation of a longitudinal process by a series of states in successive time periods 

(e.g., the succession of states of employment, unemployment, training, and inactivity of an individual in the last 

2 years).  

In  the  context  of  life-course  studies,  the  sequence  per  se  is  the  object  of  primary  interest.  A  number  of 

techniques originally developed in non-sociological fields (mainly computer science) have been applied to study 

the  features  of  longitudinal  sequences  for  the  purpose  of  uncovering  patterns  of  social  change,  i.e.,  how 

trajectories change across different cohorts and countries3. 

An obvious question is why and how these tools, aimed at a quite different exploratory task, can be of help in 

estimating the impact of policies.  

The  core  idea  is  that  the  past  matters,  and  sequence  analysis  provides  some  useful  tools  to  condense  the 

information about the past contained in the individual trajectories. If two individuals are observed at a specific 

point  in  time,  some  of  their  observable  characteristics  can  be  measured.  Looking  at  this  snapshot,  the  two 

individuals  might  seem  alike  in  terms  of  some  (or  all)  of  these  observable  characteristics,  and  standard 

matching techniques could be applied. However, their respective past might be substantially different. In other 

words, if we were to observe the sequence of events that led to the instant in time when the snapshot was 

taken, then it could be possible that these trajectories were very different. Individuals with similar trajectories 

might be more alike, and this might play a crucial role in matching performance. For instance, in the field of 

labour economics,  work  histories  could  be  used  as  a  proxy  for  individual  ability  and  help  mitigate  selection 

issues. 

The  key  contribution  made  by  the  tools  of  sequence  analysis  is  to  provide  an  operational  definition  of  the 

similarity between two different sequences based on the properties and the ordering of the elements that they 

are composed of. The advantage for policy evaluation is that these similarity measures can then be used in a 

matching approach to identify more appropriate controls for units subject to intervention. 

2.2.  Method and data requirements 

The first step of any analysis of sequences is to define what the sequence is. A sequence can be broadly seen 

as a way of summarising the information contained in longitudinal data. The latter needs to contain enough 

3 Aisenbrey and Fasang (2010) 

5 

 
                                          
detail to be able to re-construct the entire sequence of events that took place before the treatment under study. 

Consequently, data from administrative registers are likely to play a major role in this context.  

From a methodological point of view, a sequence can be described as a string containing a finite number of 

characters, each representing a state where the individual has been in the time-span between the beginning 

(hereafter t0) and the end of the observational period (hereafter T). This time span is related to the study and 

has to be decided beforehand. In the case of applications dealing with policy impacts, this observational period 

is generally the pre-treatment period, and its end-point corresponds with the beginning of the intervention. For 

example, consider the simple case of yearly observations with the pre-treatment period of 3 years, where each 

individual can be only in one state in each year. The states in this example are represented by the letters A, B, 

C, or D. Alternative sequences could be represented by: 

ABA 

AAB 

AAA 

ABC 

BBD 

Each letter in the above sequences stands for a different state of the world in a given period of time (in this 

case a year). As an example, in the context of career trajectories A, B, C, D could represent different labour 

market states such as: employment, unemployment, maternity leave and training.  

It can be noticed that one of the fundamental characteristics of the sequence is the list of alternative possible 

states. This is referred to as the ‘state-space’. It is a full list of states of the world mutually exclusive in time, 

in this case A, B, C, D. Identifying this list of possible states depends on the particular situation.  

When dealing with register data, observations are rarely available at yearly intervals, as would be the case in 

standard longitudinal surveys. In these cases the data can be organised in order to be spaced monthly, and 

monthly records made use of. The ABA sequence above could then become the following sequence (defining 

12 states each year, and observing the transition between A and B in January of the second year): 

AAAAAAAAAAAA BBBBBBBBAAAA AAAAAAAAAAAA 

Once the state-space has been defined and the data coded accordingly, the result is a string for each individual 

containing the full sequence of events occurring between t0 and T. The next step is to adopt a method to compare 

sequences across individuals in order to identify those that are ‘more similar’.  

The most common method used in sequence analysis to compare sequences was applied in sociology by Andrew 

Abbott (1995) and is called ‘optimal matching’. The core idea of optimal matching is to construct a measure of 

similarity between two sequences, ‘i’ and ‘j’, based on the edit operations required to transform one sequence 

into  the  other.  There  are  two  types  of  operations  available:  substitution  and  insertion/deletion  (‘indel’:  in-

insertion, del-deletion).  

As  an  example,  consider  the  instance  of  the  sequence  AABC  and  the  sequence  ABBD.  The  first  can  be 

transformed  into  the  latter  by  deleting  the  first  element  A  (deletion),  adding  an  extra  B  (insertion),  and 

substituting the final C with a D. Another possibility would be to substitute the second A with a B, and the last 

C with a D, which is to say that there are a number of possible ways to ‘align’ two sequences.  

The choice between alternative alignments depends on the ‘cost’ of each operation. The core idea is that each 

edit operation comes at  the cost  of altering the  original sequence.  The  issue of the link between costs and 

6 

 
operations is widely discussed in the methodological literature. The most common method used in the social 

sciences  is  to  apply  a  data-driven  approach  to  set  substitution  costs,  and  to  avoid  using  indel  operations 

especially in the analysis of equal-length sequences.  

As described by Lesnard (2010), ‘When an event is inserted or deleted, it is also time that is either added or 

removed. On the other hand, substituting an event by another preserves the timing of the sequences, but at the 

cost of approximating an event by another.’ In the example above, after the first deletion of A, the remaining 

bit of the sequence, ABC, ‘slides backward’ to match the other one. This implicitly amounts to assuming that 

the same events (AB) occurring at different times are perfectly identical (zero cost of transformation).  

As for the computation of substitution costs, the data-driven approach mentioned above suggests that these 

costs should be set using the inverse of the transition frequencies between two different states. For example, 

if  the  transition  between  A  and  B  at  time  t  in  the  data  at  hand  happens  to  have  a  probability  of  0.1,  then 

substituting A for B would “cost” 1/01=104. It should be noted that what is important is not the cost per se, but 

its relative value. Intuitively, it is desirable that transitions that occur more frequently are associated with lower 

costs of substitution.  

When sequences are of unequal length, for example, due to the existence of gaps, indel operations are indeed 

necessary. In these cases the rule of thumb identified in the literature is to set the cost of indel operations 

equal to half the maximum substitution cost. 

Finally, the distance between two sequences, — ‘i’ and ‘j’ - is computed as the sum of the costs implied by the 

transformation of ‘i’ into ‘j’. 

The final question to be answered is how this procedure helps in identifying an appropriate control group for 

units subject to an intervention. The key principle is that low transformation costs between sequences mean a 

short distance between them, which translates into similarity between individuals.  

Imagine having a list of units in the treatment and control groups, and sequences representing the succession 

of states in the pre-intervention period. The distance between the sequence of each unit in the treatment group 

and  each  of  the  sequences  of  units  in  the  control  group  can  be  computed.  Once  the  distances  have  been 

computed using optimal matching, the closest control unit(s) represent the most similar individuals, and so can 

be chosen as a match for the treated unit. 

As in the simpler case of propensity score matching or exact matching, the average treatment effect on the 

treated is ultimately obtained as the difference between the average value of the outcome for the treated units 

and that of the matched control units. The assumptions that allow this causal effect to be identified are the 

same as those needed in the case of propensity score  matching and exact matching. Significantly, only  the 

selection of observable characteristics can be accounted for, so any selection bias arising from differences in 

unobservable  characteristics  between  treated  and  control  units  may  affect  estimates  of  the  causal  effect. 

However, this method enriches the information set available by exploiting the longitudinal dimension of the 

4 The transition probability is computed as the fraction of individuals transiting from state A to state B at time t 
out  of  the  total  number  of  individual  in  state  A  at  time  t.  The  full  set  of  all  possible  transitions  can  be 
summarised in a transition matrix, and can be computed separately for each time period (e.g., each month). 

7 

 
                                          
data. Adding the full trajectory observed before treatment in order to match treated and control units should 

help to mitigate any concerns about the selection bias, as this makes it possible to better control for the role of 

unobservable characteristics. For example, when interventions targeting unemployed individuals are evaluated, 

observing a worker’s past employment history can add a lot of precious information that can be used in the 

matching. By considering the sequences of events occurring before a given intervention, it is possible to match 

treated  individuals  with  non-treated  individuals  similar  not  only  in  terms  of  the  usual  observable  variables 

normally available (gender, level of education, age, etc. ) but also in terms of their labour market history, which, 

as  shown  by  Caliendo  et  al.  (2017),  is  as  good  as  controlling  for  personality  traits  (which  are  normally  not 

available for the evaluators in the set of observable characteristics). 

Longitudinal data from administrative registers are the best candidate for applying the method described when 

evaluating policy. This type of data typically enables tracking individuals through time, and contains enough 

information to re-construct pre-treatment trajectories after the state-space has been carefully defined. 

2.3.  How it works in practice: An example from the academic literature 

Causal  Effects  of  the  Timing  of  Life-course  Events:  Age  at  Retirement  and  Subsequent 

Health. (Barban,  N.,  De  Luna,  X.,  Lundholm,  E.,  Svensson,  I.,  &  Billari,  F.  C.  2017)).  Sociological  Methods  & 

Research 

The  work  by  Barban  et  al.  (2017)  is  a  perfect  example  of  how  sequence  analysis  techniques,  and  optimal 

matching specifically, can be applied to causal inference. The authors wanted to evaluate the effects of the 

timing of retirement on subsequent health. Retirement is the treatment individuals are exposed to: individuals 

self-select into treatment, and this may cause selection bias. More specifically, individuals retiring earlier on a 

voluntary basis are likely to have worse health conditions as well as worse health future outcomes compared 

to those retiring later. The authors wanted to identify an appropriate control group able to represent what would 

have happened to early retirees had they stayed at work, in order to estimate the causal effect of voluntary 

early retirement.  

The authors applied a standard matching based on propensity scores, using pre-treatment characteristics. The 

chosen  variables  used  to  calculate  the  propensity  score  were:  education,  income,  marital  status,  partner’s 

retirement, unemployment status and health status.  

The authors highlight that the full observable health trajectory of an individual is also likely to play a key role 

in shaping retirement decisions while also being a potential factor influencing post-retirement health. In order 

to exploit the information contained in the pre-retirement health history, the authors use sequence analysis 

techniques.  

The authors use yearly data from linked longitudinal administrative records from different sources. Since the 

interest is in matching pre-treatment health trajectories, the state-space is defined by 8 potential states ranging 

from ‘No hospitalization or any health related benefits in year t’ to ‘Spent more than 3 days in hospital during 

year t’, and encompasses other potential states comprising a mixture of hospitalisation and/or benefits in year 

t.  

8 

 
 
Having defined the state-space, the authors match treatment units (early retiree) with their nearest neighbour 

in  the  control  group  by  applying  the  optimal  matching  algorithm  on  the  individual  pre-retirement  health 

trajectories.  

The  final  step  also  combines  propensity  score  matching  based  on  pre-treatment  covariates  with  optimal 

matching based on the full health trajectories. It should also be noted that, given the large sample dimension 

typical of register data, the authors use a combination of propensity score and  optimal matching on health 

trajectories: the authors first match treated and control units on year of birth and educational level at time of 

retirement, and then they combine the other two matching techniques within each cell.  

The graphs in Figure 1 are taken from Barban et al. (2017) and show the evolution of the outcome of interest 

and the number of hospitalisations before and after early retirement for men. The cut-off for early retirement 

for  men  (i.e.  the  treatment)  is  set  at  the  age  of  61.  The  comparison  between  treated  and  control  units  is 

presented  separately  for  each  of  the  matching  procedures  described  above,  i.e.  propensity  score,  optimal 

matching on health trajectories, and a combination of these two.  

Figure  1  –  Source:  Barban  et  al.  (2017).  The  outcome  of  interest  is  the  number  of 

hospitalisations before and after retirement for men. The threshold for early retirement is 

set at the age of 61. 

9 

 
 
 
 
 
One  crucial  finding  in  their  study  is  that  the  pre-retirement  health 

trajectory  is  a  major  confounding  factor.  While  it  is  true  that  early 

retirees  exhibit  faster  deterioration  of  their  health,  the  decision  to 

retire early is also influenced by the full preceding health trajectory. 

Once the latter is accounted for, the magnitude of the negative effect 

of  retirement  on  subsequent  health  (measured  as  the  number  of 

hospitalisations) shrinks substantially. 

2.4.  References 

Abbott,  A.  (1995).  Sequence  analysis:  new  methods  for  old 
ideas. Annual review of sociology, 21(1), 93-113. 

Aisenbrey,  S.,  &  Fasang,  A.  E.  (2010).  New  life  for  old  ideas:  The 

‘second wave’ of sequence analysis bringing the ‘course’ back into the 

life course. Sociological Methods & Research, 38(3), 420-462. 

Barban,  N.,  De  Luna,  X.,  Lundholm,  E.,  Svensson,  I.,  &  Billari,  F.  C. 

(2017).  Causal  Effects  of  the  Timing  of  Life-course  Events:  Age  at 

Retirement and Subsequent Health. Sociological Methods & Research 

Caliendo, M., Mahlstedt, R. and Mitnik, O. (2017): Unobservable, but 

Sequence 
analysis 
PROS AND CONS    

 

It is a useful tool for 

condensing the information 

about the individual’s past 

trajectories. 

 

It can be used in combination 

with standard matching 

techniques to add information 

to the usual observable 

characteristics used when 

performing matching, which 

should help to mitigate 

concerns about the selection 

Unimportant? The Relevance of Usually Unobserved Variables for the 

bias.  

Evaluation of Labor Market Policies, Labour Economics, 46, 14-25. 

Lesnard,  L.  (2010).  Setting  cost  in  optimal  matching  to  uncover 

- 

It is data demanding, as the 

contemporaneous  socio-temporal  patterns. Sociological  Methods  & 

Research, 38(3), 389-419. 

data used should contain 

enough information to be able 

to re-construct pre-treatment 

trajectories. 

10 

 
 
 
 
 
3.  DYNAMIC MATCHING 

3.1.  Background 

Dynamic  matching  is  an  extension  of  the  widely  used  matching  technique  called  static  matching.  Static 

matching is usually applied when a group of individuals receive a treatment (e.g. participation in a programme), 

and this group is matched to a group of individuals not receiving the treatment according to a set of observable 

characteristics. The impact of the treatment is recovered by simply comparing the outcome in the treated group 

with  that  in  the  selected  similar  control  group.  There  are  various  techniques  that  can  be  used  to  match 

individuals,  the  most  common  being  propensity  score  matching.  The  main  assumption  for  the  estimate  to 

represent the true causal effect of the treatment is that the matching is based on all characteristics that affect 

selection  into  the  treatment  and  future  outcome,  and  that  there  are  no  unobservable  characteristics  which 

influence selection into the treatment5.  

An example when static matching can be used is a programme administered at a fixed point in time, where 

unemployed individuals are either treated (that is, participate in the programme) or not treated (that is, do not 

participate).  Among  the  pool  of  non-treated  individuals,  a  group  resembling  the  treated  one  in  terms  of 

observable  characteristics  has  to  be  selected.  The  matching  approach  assumes  that  participation  in  the 

programme  and  future  labour  market  status  only  depends  on  observable  characteristics  and  there  are  no 

unobserved differences in motivation or unobserved ability between treatment and control groups. The effect 

of  the  treatment  is  estimated  by  comparing  the  labour  market  outcome  (i.e.  whether  the  individuals  are 

employed or not) of the treated with that of the controls, a reasonable amount of time after the programme 

has ended.  

On the other hand, dynamic matching is useful in the case of ongoing programmes where any eligible individual 

can potentially become a participant sooner or later as long as they are still eligible, because the programme 

is offered constantly. Using static matching in this setting can have limitations: if one wishes to evaluate the 

impact  of  the  programme  by  comparing  participants  to  similar  non-participants  by  using  static  matching 

techniques, a predetermined point in time would need to be set in order to identify those who have actually 

been treated by that time, and those who still had not been treated. For example, when evaluating a programme 

for the unemployed,  the fixed point could either be an exact date (all those starting the programme by April 

20xx are considered to have been treated, while those not starting by that date are placed in the potential 

control group); alternatively a fixed number of months after registration into unemployment (all those starting 

the programme within 6 months after the registration are considered to have been treated, while those not 

starting  at  all  or  starting  later  are  placed  in  the  potential  control  group).  However,  this  approach  would  be 

incomplete because the choice of participating in the programme is not made once and for all, as individuals 

can choose to join it at any time. Therefore, as a comparison to the treated group, a group of individuals who 

were never treated simply cannot be chosen because they may represent a very different group of individuals. 

Similarly, it is not appropriate to set a fixed time threshold since the choice that an individual is facing at any 

5 This assumption is called ‘conditional independent assumption’.  

11 

 
                                          
given moment  for an ongoing programme is not whether to start a programme or not at all, but whether to 

start it now or not to start it now. 

3.2.  Method and data requirements 

In dynamic matching the evaluator compares individuals who are similar up to a given point in time, but at that 

point  some  receive  the  treatment  and  others  do  not  receive  it  (yet).  The  treatment  is  therefore  starting  a 

programme  (in  a  given  month).  What  is  estimated  is  the  impact  of  joining  a  programme  at  a  given  time 

compared to not joining at least up to then. Therefore, the estimated effect is different from the impact of 

participating  in  a  programme  rather  than  not  participating  at  all,  or  from  the  effect  of  participating  in  a 

programme from time t1 rather than from time t2. The comparison group is composed of eligible individuals 

who have not participated in a programme yet, including individuals who may participate in the future.  

The  dynamic  matching  method  is  a  propensity  score  matching  generalisation  used  to  estimate  a  specific 

matching estimator for each time interval. This methodology iterates the propensity score matching estimator 

(or other matching estimators) over different time spans while dynamically (re)defining the control group. This 

approach requires individuals to be observed through a set of points in time, possibly close to each other, e.g. 

months, which makes it more data demanding than the standard static framework. In practice, the propensity 

score is estimated a given number of times corresponding to the number of months (or group of months) of 

interest. In each period there will be a new group of treated, i.e. those starting the programme in month u, and 

a  new  group  of  non-treated,  i.e.  those  still  not  participating  in  month  u.  In  this  process,  the  treatment  is 

continuously updated vs. the control-group definition over the time span involved. At the beginning of each time 

window the eligible population comprises individuals who were still not participating in the programme at the 

end  of  the  preceding  period.  Individuals  starting  the  programme  in  month  u  are  matched  with  those  never 

treated or starting the programme at month u+1 or later. Therefore, the comparison group at u is composed of 

all those still not engaged in the programme at u, irrespective of what happens after u. Some of them may go 

into a programme later whereas others may never participate. For both controls and treated at  u, whatever 

happens after u is viewed as an outcome of joining a programme vs not joining at u. 

The evaluators can then compare these estimates and find an answer to questions like ‘When is it better to 

start a specific programme for the eligible population?’ and ‘Is a programme starting at a given point in time 

still effective for the eligible population?’. In addition, the average of the effects through time can be computed 

in order to obtain a general answer about the effectiveness of the programme overall. 

The  causal  effect  of  interest  is  identified  under  two  main  conditions.  First,  just  as  in  the  standard  static 

framework, dynamic matching is based on all characteristics that affect selection into the treatment and future 

outcome, and on there being no unobservable characteristics which influence selection into the treatment (the 

conditional  independence  assumption),  which  must  hold  sequentially.  Just  as  for  the  static  matching,  this 

assumption requires detailed knowledge of the factors that drive participation as well as availability of data 

suitable for capturing those participation determinants that are also likely to affect outcomes. In addition, in 

the dynamic setting, the evaluator needs to observe monthly or quarterly information about the treated and 

non-treated population, and the sample size should be large enough to perform reasonable matching in each 

of these months/quarters. Consequently, administrative data containing rich observable variables capturing the 

12 

 
background of individuals are the most appropriate data for applying this methodology. Secondly, identification 

requires that, conditional on observed covariates, the exact timing of current and future treatment statuses and 

future outcomes cannot be anticipated by individuals (no anticipation assumption). Examples of when violation 

of this condition would happen are: 1) if an individual refuses to participate in a programme because he knows 

that he will be offered an opportunity to participate in another programme in the next few months – anticipation 

of future treatment status; 2) if an individual refuses to participate in a programme because he has already 

received a job offer which will start in the near future (e.g. seasonal workers, who know that they will be called 

back from their employer) – anticipation of future outcome status.  

According to the details of the data and the sample size available, different time windows can be chosen: if the 

data is very detailed and the sample size large enough, individuals can be compared on a monthly basis. In 

contrast, if sample size is limited or information is only collected quarterly, several months can be grouped 

together. 

The effect of interest can be defined for each time window (whether it is a single month or a group of months) 

given that the treatment is received within that time window.  

In addition to the evaluation of single programmes, dynamic matching can also be used to evaluate systems 

of active labour market policies, composed by different actions taking place continuously. (See Sianesi, 2004 

summarized in the following  section).  Finally,  dynamic matching can be  extended to the multiple treatment 

framework and allows comparisons of the effectiveness of many different programmes. In this case, rather 

than comparing the individuals participating in a programme to the ones still in open unemployment, one has 

to  compare  them  to  the  ones  participating  in  another  programme.  By  doing  this,  the  effectiveness  of  one 

programme can be directly assessed against the effectiveness of another. (See Sianesi, 2008) 

3.3.  How it works in practice: An example from the academic literature 

An evaluation of the Swedish system of active labour market programmes in the 1990s. (Sianesi, B., 

2004. Rev. Econ. Stat. 86 (1), 133–155.) 

The subject of the evaluation is a system with a wide array of different ongoing programmes which are held 

continuously through time and are open to all registered job-seekers. Sweden’s active labour market policy is 

considered  in  its  totality:  all  of  the  various  programmes  are  aggregated  into  one  ‘programme’  so  that  the 

treatment is any programme that a first-time unemployed person can join. The treatment is therefore starting 

a programme (in a given month). The effect estimated is the impact of joining a programme at a given time in 

unemployment  compared  to  not  joining  it  at  least  up  to  that  time.  This  is  different  from  the  effect  of 

participating in a programme rather than not participating, and from the effect of joining a programme at time 

t1 rather than at time t2. 

The  data  was  obtained  from  two  main  sources,  which  reflect  the  programme  component  and  the  benefit 

component  of  the  labour  market  policy.  The  first  source  is  the  unemployment  register,  which  contains 

information on all unemployed individuals registered at the public employment office. It is available from 1991 

13 

 
 
onward and provides each individual’s labour market status information over time (unemployed, on a given 

programme,  temporarily  employed,  or  similar),  together  with  important  personal  characteristics  of  the  job-

seeker and of the occupation sought. The second source, available from 1994, is the unemployment insurance 

funds and provides additional information for those unemployed individuals who are entitled to unemployment 

benefits and assistance, in particular information on the amount and type of compensation paid out, previous 

wage and working hours.  

The whole data set thus contains information about the duration of being in a labour market state, a set of 

demographic information (age, gender, citizenship), occupation being sought and human capital characteristics 

(specific  and  general  education  and  occupation-specific  experience),  and,  for  entitled  individuals,  additional 

information  on  type  of  entitlement,  unemployment  benefits  and  previous  working  conditions.  There  is  also 

information from an overall evaluation by the caseworker on the situation, character and needs of service of 

the job-seeker. This assessment relates to the job-seeker’s degree of job readiness (judged to be able to take 

a job immediately, to be in need of guidance, or to be difficult to place) and to the job-seeker’s preferences, 

inclinations, and sense of urgency (whether willing to move to another locality, looking for a part-time job or 

already having a part-time job). 

Dynamic  matching  is  applied  in  the  following  way:  each  individual  enters  the  pool  of  those  eligible  for  the 

treatment  in  the  month  that  the  individual  registers  as  unemployed.  Each  month  after  the  registration, 

individuals can be observed in three main states: still unemployed, participating in the programme or out of 

unemployment (including several options: finding a job, going back to full time education, inactive, etc..). The 

main comparison of interest is between individuals starting the programme and those who are unemployed 

until that time and do not participate in a programme yet. 

Unemployment  duration  is  set  at  a  maximum  of  18  months,  since  this  captures  94%  of  all  programme 

participants. A series of 18 regressions is estimated, corresponding to the maximum number of months after 

registration  into  unemployment  when  an  individual  can  start  a  programme.  Each  regression  models  the 

probability of joining a programme in month u, conditional on the observed characteristics and on having been 

unemployed for u months. The propensity score is estimated through these regressions just as in the static 

case, and it is used to perform nearest neighbour matching, imposing common support. 

The main outcome considered is labour market status up to 5 years after the first registration as unemployed. 

Labour market status is divided into two main categories: registered and deregistered from the employment 

office. Individuals registered can either be in open unemployment (receiving or not receiving unemployment 

benefits)  or  participating in  a  programme. Deregistered individuals  can either  be  in employment or  in other 

states (in education, inactive, or no longer in the system). 

14 

 
 
 
The paper answers two main questions:  

1) How do unemployed individuals who join a programme perform on average compared to a situation where 

they would have searched further in open unemployment? This is found by calculating averages of the monthly 

effects to obtain a general idea of the effects.  

2) What are the treatment effects by month of placement? This is found by looking separately at the time series 

of the various treatment effects for different subgroups of the treated that is based on the time they have 

spent in unemployment. 

The main results of the analysis can be summarized as follow:  

Average effects: 

1)  Treated  individuals  are  more  likely  to  be  on  programme  participation  and  to  be  on  unemployment 

benefits for 4 years after joining that programme. No effects are found for the probability of being in 

open unemployment. 

2)  After the lock-in effect, which is typical of individuals participating in programmes for the unemployed, 

over the 5 years since the programme started, the treated have a 6% higher ‘average’ probability of 

being in employment. 

3)  A detailed analysis of the mechanism carried out to explain the apparent contradiction of points 1) and 

2) shows that the positive effects on employment, mentioned in point 2), are due to the fact that the 

programme reduced the probability of being unemployed outside the official unemployment system. 

Consequently, participants experience higher employment rates (point 2), but when they do become 

unemployed, they are significantly more likely to be entitled to benefits (point 1). 

4)  No effect is found on the probability of being in education while a small negative effect is found on 

the probability of being inactive. 

Effects by month of placement 

1)  Looking  at  the  effects  by  month  of  placement  also  helps  to  explain  the  apparent  contradiction 

mentioned above. 

2)  Starting the programme within the first 6 months of being unemployed is found to have positive effects 

on employment, while starting the programme after 15 months of being unemployed is found to have 

no effect on employment.  

3)  On the other hand, starting the programme after 15 months has a larger effect on being compensated 

in the form of benefits, while starting earlier on has much smaller effects. This is visible evidence of 

the  disincentive  to  work  that  is  embedded  in  the  institutional  setup  of  the  programmes:  joining  a 

programme greatly increases the probability of being in benefit-compensated unemployment through 

time, of participating in further programmes with the passing of time and more generally of remaining 

within the unemployment system. This is due to individuals who join the programme relatively late 

15 

 
(after 15 months from registering as unemployed) and who 

probably  only  joined  the  programme  to  continue  to  be 

eligible for unemployment benefits. 

3.4.  References 

Sianesi,  B.,  2004.  An  evaluation  of  the  Swedish  system  of  active 

labour market programs in the 1990s. Rev. Econ. Stat. 86 (1), 133–

155.  

Sianesi,  B.,  2008.  Differential  effects  of  active  labour  market 

programmes for the unemployed. Labour Econ. 15 (3), 370–399 

Fredriksson, P., Johansson, P. , 2008. Dynamic treatment assignment: 

the  consequences  for  evaluations  using  observational  data.  J.  Bus. 

Econ. Stat. 26 (4), 435–445. 

16 

Dynamic 
matching 
PROS AND CONS 

  Dynamic matching can be 

used to estimate the 

impact of joining a 

programme at a given time 

compared to not joining it 

at that point in time. It is 

useful in the case of an 

ongoing programme. This 

means that it could also be 

used in settings where all 

individuals potentially 

receive the treatment at 

some point. 

 

It is data demanding:  in 

addition to the 

requirements of the static 

matching (availability of 

characteristics determining 

programme participation), 

the evaluator should be 

able to observe monthly or 

quarterly information 

about the treated and non-

treated populations, and 

the sample size should be 

large enough to perform 

reasonable matching in 

each of these time 

windows. 

 
 
 
 
4.  SYNTHETIC CONTROL METHOD 

4.1.  Background 

The synthetic control method (SCM) is useful in evaluating the effects of policies or programmes that take place 

at aggregate level. For example, it can be used when a whole country is affected by a policy. The typical setting 

where  this  method  is  applied  is  when  there  is  one  treated  unit  and  a  few  control  units,  and  the  aggregate 

outcome of interest is repeatedly observed through time, before the policy under investigation is implemented. 

This method shares some similarities with difference-in-difference. While difference-in-difference is used when 

the number of observations (in the treated and control group) is large but the outcome is only observed at a 

few points in time, the SCM is used with aggregate values of the treated and of the control group when the  

number of observations is small but the outcome is observed many times. 

This method was first developed by Abadie and Gardeazabal (2003) and many applications have since followed. 

In brief, the SCM is a statistical tool that has been increasingly used to evaluate the effect of an intervention 

on  different  aggregate  outcomes (e.g.  school  dropout  rate,  educational  attainment,  economic  growth, 

employment rate, average income) where a single unit is subjected to a particular policy intervention. This unit 

is compared to a synthetic control unit, which is created artificially to resemble the characteristics of the treated 

unit as much as possible, and it is constructed as a weighted average of different untreated units. Untreated 

units contribute with a larger or smaller weight (or do not contribute at all) in the construction of the synthetic 

control depending on certain observable characteristics which are relevant for the outcome of interest.  

This  method  has  recently  been  adopted  to  evaluate  the  effect  of  a  policy  change/introduction  targeting 

aggregate entities such as geographic or administrative areas (countries, regions at NUTS2, or NUTS3 level). 

The opportunity of estimating policy impacts in cases where one unit (or a few) is treated is what makes SCM 

an important tool in the overall evaluation of interventions. 

4.2.  Method and data requirements 

SCM is usually applied when there are J+1 units (regions or countries) among which only one unit is exposed to 

the intervention of interest, and the remaining J units are therefore potential controls.  

As in the usual counterfactual framework, the effect of the intervention is simply defined as the difference 

between  the  observed  outcome  of  the  treated  unit  after  the  policy  implementation  and  what  would  have 

happened in the same unit had the policy not been implemented. As this latter outcome cannot be observed, 

one has to find something which closely resembles what would have happened if the policy had not been put 

in place. The method proposes building a fake (synthetic) control unit by combining all of the available potential 

control units, which are defined as ‘donor pool’. 

In the absence of the treatment, the outcome for the treated is a function of observable (and non-observable) 

characteristics. The SCM is used to find a combination of weights of control units so that the weighted average 

of the characteristics of the control units closely resembles the characteristics observed for the treated unit in 

the pre-intervention period. This is done by minimising differences in the observable characteristics which are 

17 

 
 
relevant  to  the  outcomes.  As  a  result,  the  pre-intervention  outcome  of  the  synthetic  control  also  closely 

resembles the pre-intervention outcome of the treated unit.  

The impact of the treatment is quantified by a simple difference of the treated unit against its synthetic cohort 

after the treatment. One of the great advantages of SCM is a very intuitive graphical analysis that shows the 

impact of a policy for the treatment and what would have happened to the same unit in the absence of the 

treatment (as represented by the synthetic cohort). 

For  example,  a  policy  or  a  reform  aimed  at  tackling early  dropout  from  schools  in  a  given  country  is  to  be 

evaluated. As the policy affects the whole country, all secondary schools are treated. Therefore to estimate the 

causal impact of the policy on the country’s average dropout rate, a control group has to be found somewhere 

else outside the country. Simply comparing the dropout rate in the affected country to the same rates in other 

countries  does  not,  of  course,  provide  the  causal  effects  of  the  policy:  countries  may  be  different  in  the 

outcomes  for  many  other  reasons.  In  addition,  it  is  usually  very  difficult  to  find  a  single  country  with 

approximately the same characteristics of the affected country. The idea is that a combination of units should 

provide a better comparison for the treated unit than any individual unit on its own. 

Figure 2 below provides a useful representation. The x-axis shows the timeline and y-axis the dropout rate in 

secondary schools of the country implementing the policy. The evolution of the dropout rate for the treated unit 

through time, i.e., country A, is displayed as a blue line while the red dashed line illustrates the counterfactual 

of country A. This latter is constructed as a weighted average of units from the donor pool, i.e., countries not 

affected by the policy. To form the closest match for the treated unit in the time period prior to treatment, 

similar potential control units are selected and assigned a positive weight. Observable characteristics considered 

to be those contributing to the dropout rate could for example be: expenditure in education as a function of 

GDP, presence of early tracking in the country, employment disadvantage for individuals with low educational 

achievement compared to individuals with a higher education, and lagged dropout rates. SCM builds a synthetic 

country, assigning different weights to the non-treated countries in a way that the four characteristics of the 

fake country are similar to those of the treated country. It is possible that many potential control units are not 

selected in the computation of the synthetic group due to non-trivial differences compared to the treated unit 

in  the  pre-treatment  period.  These  units  will  be  given  a  weight  of  zero  in  the  construction  of  the  synthetic 

control.  

18 

 
 
Figure 2: Synthetic cohort, graphical example 

Figure 2 shows that the synthetic of country A closely resembles the evolution of the dropout rate in country A 

through time before the policy was implemented. Country A and its counterfactual follow a similar pattern at 

times 1, 2, and 3 (the pre-treatment period). Once the policy is introduced (at time 4), the treatment unit (country 

A) shows a sharp decrease in the percentage of pupils dropping out of school. The comparison between the two 

lines (red vs. blue) provides an initial hint of what would have happened without the change in the policy setup 

for country A. 

Furthermore,  the  SCM  allows  a  list  of  standard  placebo  tests  to  be  carried  out  that  help  validate  the 

intervention’s causal effect. The placebos provide the probability of obtaining an estimate at least as large as 

that obtained for the unit representing the case of interest when the intervention is randomly reassigned in the 

data set (Abadie, Diamond, and Hainmueller, 2015). In this respect, it demonstrates what would have happened 

if the policy had been assigned at random to a given unit. The placebo effect should be close to zero. If, on the 

other side, the placebo policy shows a significant change in the outcome, larger than the effect estimated with 

the true model, this provides some indirect insights into the validity of the estimated model, meaning that the 

model is not valid and the estimated effect cannot be trusted.  

Valid implementation of the SCM requires that the synthetic control closely matches the treated outcome during 

pre-treatment.  If  so,  the  comparison  after  the  treatment  provides  a  reliable  estimation  of  the  treatment’s 

(policy) effect.  

Additional requirements are:  

-  Data must be available for several periods before the intervention of the policy in 

the treated unit and the pool of potential donor units.  

1.  Only the treated unit is affected by the policy intervention without any externalities to other units. In 

the  example  of  the  policy  aimed  at  reducing  dropout  from  secondary  schools,  this  means  that 

untreated countries are not affected by the treatment. The evaluator needs to check whether or not 

19 

Country ASynthetic of Country A12345% of drop out at secondary schoolTime 
 
countries used to build the synthetic control did not implement similar policies during the time period 

considered. 

2.  The policy intervention must not have any effect before it is enacted, which means that the outcomes 

(e.g. dropout rate in country A) do not vary due to the policy before the policy is implemented because 

of anticipation effects.  

4.3.  How it works in practice: An example from the academic literature 

The impact of ‘free choice’: Family reforms in France and Belgium, a synthetic control analysis by 

Federico Podestà (2017). 

This paper analyses the introduction of long-leave schemes and different actions to support childcare at home 

in  France  and  Belgium  between  1980  and  1990.  This  policy  was  characterised  by  women  voluntarily 

participating  in  the  programme.  The  author  exploits  the  SCM  to  evaluate  the  impact  of  the  reforms  on  the 

female labour participation rate (FLPR) at country level. His idea was to compare the treated countries (France 

and  Belgium)  with  the  synthetic  units  constructed  using  the  following  pool  of  countries:  Australia,  Austria, 

Canada, Denmark, Finland, Germany, Greece, Ireland, Japan, Luxembourg, Norway, Portugal, Spain, Sweden, the 

UK and the USA. The research question is to understand how the FLPR would have evolved had there not been 

these family programmes.  

Figure 3 - Source Podestà (2017), page 8 

20 

 
 
 
 
 
The first step is to assign weights to each untreated country in order to build the two synthetic units that best 

mimic France and Belgium6. Using the routine available for many statistical software packages (STATA, R), the 

weights are optimised by selecting untreated countries similar to the treated ones and assigning a weight to 

them in the construction of the synthetic index. Indeed, the Belgium synthetic is constructed using a weighted 

average of Australia (11.4%), Canada (22.5%), Ireland (47.7%), Norway (7.1%) and the UK (11.4%), taking into 

consideration the following list of pre-intervention characteristics: percentage of workers in service, level  of 

higher education attained by women, total fertility rate, number of weeks of maternity leave and unemployment 

rate. In addition, four lagged values of FLPR were included in the set of predictors (FLFP measured in 1984, 

1978, 1974 and 1970). All of this data is available for the period 1970–2008, which makes the use of SCM 

appropriate.  Similarly,  this  was  carried  out  for  France  where  it  is  important  to  underline  the  fact  that  the 

construction of the synthetic control unit for France was based on a different sample of donors (Ireland 15.9%, 

Japan 29.3%, Norway 8.3% and the UK 46.5%).  

Figure 3 displays the trends in the Belgian and French FLPR compared to the synthetic unit and population-

weighted  average  calculated  on  all  units  in  the  donor  pool.  Note  that  the  distance  between  treated  and 

population-weighted  averages  using  all  the  donor  countries  is  drastically  larger  than  the  distance  between 

treated and synthetic controls, providing a graphical representation of the goodness of the counterfactual event. 

In other words, the synthetic units reasonably approximate the FLPR that would have been experienced by these 

countries through the pre-intervention period. 

Figure 4 - Right panel Belgium; Left panel France; Source: Podestà (2017), 3 page 9 

Figures 4 show that if both France and Belgium were not exposed to the reforms, their FLPR rates would have 

been higher than those actually observed. This is actually expected since the aim of the reform in both countries 

was to move both countries towards a more familistic model. It is worth noting that France (right figure) shows 

a slightly divergent path one year before the intervention (i.e. in 1984), which invalidates the identification of 

the  causal  path.  However,  the  author  finds  that  after  also  including  Germany  in  the  donor  pool,  the  bias 

disappears due to the fact that Germany has a relevant weight that improves the fit.  

6  In  this  example  there  are  two  countries  that  are  treated,  but  in  the  analysis  they  are  considered  to  be  two 

separate cases, and two separate estimates are computed. 

21 

 
 
 
                                          
PROS AND 
CONS 
 

It can be used to evaluate 

policies affecting single units 

(one country, one region, ...) 

- 

To create a synthetic control, 

data must be available for a 

very long period before the 

intervention in the treated 

unit and the pool of potential 

donor units. The time series 

used in most academic 

papers is as long as 20 years. 

Figure 5 –Placebo exercise. Source: Podestà (2017), Figure 7 page 9 

The authors also provide the placebo test. In the case of this paper, 

Figure  5  demonstrates  that  the  gaps  in  the  FLPR  for  Belgium  and 

France (solid lines) are larger than the six placebos under a random 

year of reform implementation. The SCM exercise concludes that, if 

France  and  Belgium  had  not  implemented  this  reform,  women’s 

participation in the labour market would actually have been higher. 

4.4.  References 

Abadie,  Alberto,  Alexis  Diamond,  and  Jens  Hainmueller.  "Comparative  politics  and  the  synthetic  control 

method." American Journal of Political Science 59.2 (2015): 495-510. 

Abadie,  Alberto,  and  Javier  Gardeazabal.  "The  economic  costs  of  conflict:  A  case  study  of  the  Basque 

Country." American economic review 93.1 (2003): 113-132. 

Athey, Susan, and Guido W. Imbens. "The state of applied econometrics: Causality and policy evaluation." Journal 

of Economic Perspectives 31.2 (2017): 3-32. 

Podestà,  Federico.  "The  impact  of  ‘free  choice’:  Family  reforms  of  France  and  Belgium,  a  synthetic  control 

analysis." International Journal of Social Welfare 26.4 (2017): 340-352. 

22 

 
 
 
 
 
 
 
5.  Conclusions 

This document presents three methodologies that can be of help when carrying out a counterfactual impact 

evaluation. 

The first two, sequence analysis and dynamic matching, rely on matching, where the evaluator seeks to find a 

control  group  of  individuals  as  similar  as  possible  to  the  treated  group.  Sequence  analysis  can  be  used  in 

combination  with  standard  matching  techniques,  when  the  data  available  goes  back  in  time  and  allows 

recovering  past  history  about 

relevant 

information  on 

the  population.  Examples  are  past 

employment/unemployment history, when evaluating the effect of an active labour market programme; past 

hospitalisation history when evaluating the effect of a medical treatment, and so on. The past history is collected 

in the form of a sequence of events, and this is used to assess how similar a treated individual and a potential 

control  individual  are.  While  this  can  be  of  help,  especially  when  the  remaining  observable  characteristics 

available to the evaluators to perform the matching are not so informative or are very few, the amount of data 

required  by  this  technique  is  substantial.  One  should  be  able  to  observe  the  status  of  each  individual  on  a 

monthly/yearly basis for a reasonable amount of time before the intervention starts. 

Dynamic matching can be used for ongoing programmes where at any time eligible individuals can start the 

treatment.    In  the  academic  literature,  this  method  has  been  used  especially  to  evaluate  active  labour 

programmes, which did not have a pre-set starting date and that were offered constantly to eligible unemployed 

individuals. With this method it is possible to estimate the effect of starting an intervention after u months of 

unemployment, rather than not starting it yet. Note that the comparison group includes individuals who will 

start the treatment later and those who will never start it. It is useful to assess if the effects of the treatment 

vary according to the starting month of the intervention. Similarly to static matching, dynamic matching requires 

that  the  evaluator  is able  to observe  all the variables affecting selection into  the  treatment  and outcomes, 

including also potential time varying variables. In order to be applied, a sufficient sample size in each of the 

months (or periods) of interest should be observed. If this is the case, then dynamic matching can really improve 

the estimation compared to static matching in the case of ongoing programmes, where potentially all individuals 

will receive the treatment at one point. 

Finally,  the  synthetic  control  method  was  discussed.  This  method  can  be  considered  an  extension  of  the 

difference-in-difference,  where  only  one  unit  is  treated.  This  can  be  the  case  of  policies  affecting  a  whole 

country or a single region. The method proposes to find a synthetic control unit, based on a weighted average 

of all the non-treated units (countries or regions). Then, by comparing the outcome of the treated unit to the 

one  of  the  synthetic  unit,  it  is  possible  to  identify  the  causal  effect  of  interest.  To  apply  this  method,  the 

evaluator should be able to observe a long history of outcomes and control variables measured before the 

intervention. This is needed to identify the right set of control units to build the synthetic control. Additionally, 

it requires that the non-treated units are not affected by similar policies in the period after the intervention. 

Therefore, if similar policies are implemented in all the countries to be used as potential control, this method 

cannot be used to find a proper synthetic control unit.  

23 

 
 
 
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