Lecture 1: Introduction to RegressionDiscontinuity Designs in Economics

Thomas Lemieux, UBCSpring Course in Labor EconometricsUniversity of Coimbra, March 18 2011

Plan of the three lectures onregression discontinuity designs! Lecture 1:

" Introduction to regression discontinuity (RD) designs" RD designs as local randomized experiments and the

manipulation problem

! Lecture 2:" RD designs: A User Guide

! Lecture 3:" Recent Advances and Applications

! The main reference for the lectures is D.S. Lee and T.Lemieux “Regression Discontinuity Designs inEconomics” Journal of Economic Literature, June 2010

Introduction to RD Designs

! Before introducing any formalities and telling you exactly what a “RDdesign” means, I will work through a motivating example.

! RD Designs were first introduced by Thistlethwaite and Campbellfifty years ago (“RD Analysis: An Alternative to Ex Post FactExperiments,” Journal of Education Psychology, 1960)." The application they consider is merit awards given in recognition of good

academic performance (university grades above a certain cutoff GPS)" They use the RD design to see whether these merit awards have an

(psychological) impact on future academic achievement, e.g. on the decision togo to graduate school.

! I will work through a related example from a recent paper by MarkHoekstra (“The Effect of Attending the Flagship State University onEarnings: A Discontinuity-Based Approach,” Review of Economicsand Statistics, November 2009, pp. 717-724)

Selection problem in schooling! A large number of studies have shown that graduates from more

selective programs or schools earn more than others" Medecine, science, economics?" MBAs from HBS earn more than others

! Lead to sometimes extreme competition in some countries" Grandes écoles in France" University of Tokyo in Japan

! But it is difficult to know whether the positive earnings premium isdue to" a true “causal” impact of human capital acquired in the academic program, or" a spurious correlation linked to the fact that good students selected in these

programs would have earned more no matter what

! The latter point can either reflect a “signalling” effect, or a straight“selection” effect:" Famous Harvard dropouts (Bill Gates and Mark Zuckerberg): consistent with

selection but not necessarily with signalling

RD: solution to the selection problem! Untangling the causal and selection effects is a difficult challenge! Lots have been written about this in econometrics and labour

economics, but in many cases suggested methods (e.g. IV) are notapplicable or not very convincing

! A great way to answer that question would be to run an experiment:" Take BC students applying both to UBC (Vancouver) and UBCO (Kelowna)" Instead of admitting them the regular way, just flip a coin to decide whether they

get into UBC or UBCO" Follow them up 10 years later to see whether those admitted to UBC earn more

than those admitted to UBCO.

! Great idea, but nobody will let me run that experiment…! But say that the entry cutoff is a high school GPA of 88 percent at

UBC." They would perhaps let me flip a coin for those with GPAs of 87 or 88 percent" RD strategy: but since the 87s and 88s are essentially identical, I can do “as

well” as in a randomized experiment by tracking down the long term outcomes forthe 88s (admitted to UBC) and the 87s (admitted at UBCO) :

Hoekstra paper

! “Where there is a cutoff there is a RD”! Fortunately, it is typical for selective schools and programs to use

fairly strict grade cutoffs for admission! In the United States, most schools used SAT (or ACT) scores in

their admission process! For example, the flagship state university considered here uses a

strict cutoff based on SAT score and high school GPA! For the sake of simplicity, let’s just focus on the SAT score (adjusted

depending on GPA)! Hoekstra is then able to match (using social security numbers)

students applying to the flagship university in 1986-89 to theiradministrative earnings data for 1998 to 2005

! As in any good RD study, pictures tell it all, so let’s just focus onthose

Enrollment data

A few comments! The graphs show what we mean by a RD design:

" The smooth relationship between earnings and SAT score likely reflects the factthat more able students are also more productive workers

" But it is hard to think of any reason for the discontinuity besides the cutoff rule inadmission

" So the discontinuity is what enables us to estimate the causal effect

! This is a example of what is called a “fuzzy: RD design:" Sharp RD design: Nobody below the cutoff gets the “treatment”, everybody above

the cutoff gets it" Fuzzy RD design: The probability of getting the treatment jumps discontinuously

at the cutoff, but it needs not jump from 0 to 1

! To get the causal effect in a fuzzy RD design, we need to adjust theeffect on earnings (0.095) by the fraction of people induced to go theflagship university (0.388). Implies a very large effect of 0.245(0.095/0.388) or about 28 percent.

! SAT score is what we will later call the “assignment” variable(sometimes called “forcing” or “running” variable)

RD designs: a brief history of thought

! What do we mean by a “design”?! Internal vs. external validity! Formal modelling:

" The “intuitive” regression approach" Hahn, Todd and van der Klaauw (HTV, Econometrica

2001): the potential outcomes approach" Lee (Journal of Econometrics, 2008): RD designs as a

localised randomized experiment! Threat to validity:

" The manipulation problem

RD as a research design

! According to Wikipedia “Research designs are concerned withturning the research question into a testing project”

! Not a traditional way of thinking about research in economics, butvery common in medical science, for example (randomizedcontrolled trials, etc.)

! Provides a useful way of thinking about the broader “identificationstrategy” and the narrower “estimation methods” as two separatethings" Research design/identification strategy: RD, randomized experiments, natural

experiments, non-experimental methods" Estimation methods: IV, difference-in-differences, matching, local linear

regressions (in RD designs), etc.

! If you have a “RD research design” for the problem at hand, you canthen implement it using a variety of tools we will talk about in thenext lecture

Internal vs. external validity

! Internal validity:" According to Brewer (Research Design and Issues of Validity, 2000) “Inferences

are said to possess internal validity if a causal relation between two variables isproperly demonstrated”

" We think that RD design have typically a high level of internal validity becausethey provide a convincing way of estimating a causal effect

! External validity:" Brewer: “Inferences about cause-effect relationships based on a specific scientific

study are said to possess external validity if they may be generalized from theunique and idiosyncratic settings, procedures and participants to otherpopulations and conditions”

" Problematic for randomized experiment (Heckman, Deaton, etc.)" Even more problematic for RD design as we only identify a causal effect for

agents right at the cutoff point

Thistlethwaite and Campbell: simpleregression approachRegression:

Yi = Di! + Xi" + #i

Xi : assignment variableDi : treatment variable, Di =1[Xi !c]

General problem in such a regression:#i and Di are potentially correlated

RD solution:Di only depends on Xi (Di =1[Xi !c]), so #i and Dicannot be correlated once we have controlled for Xi(in a smooth way)

Figure 1: Simple Linear RD Setup

0

1

2

3

4

Assignment variable (X)

Out

com

e va

riabl

e (Y

)

C

!

HTV: The potential outcomes approach

« Potential Outcomes »Y = Y(1) when D =1Y = Y(0) when D =0E[Y(1) - Y(0)] (the average treatment effect or ATE)

Hahn, Todd et van der Klauuw (2001):The TE at X=c

! = E(Y(1)-Y(0)|X=c)is identified under the assumption that the functions E(Y(1)|X) etE(Y(0)|X) are continuous.

HTV suggest estimating ! using local linear regressions (LLR)

Figure 2: Potential outcomes approach

0.00

0.50

1.00

1.50

2.00

2.50

3.00

3.50

4.00

0 0.5 1 1.5 2 2.5 3 3.5 4

Assignment variable (X)

Out

com

e va

riabl

e (Y

)

Xd

B

AE[Y(1)|X]

E[Y(0)|X]

Observed

Observed

Lee (2008): local randomization

! Randomization: experimental approach (in laboratory or fieldsetting) => comparison of means

! While RD is a non-experimental design, we have localrandomization provides that the following assumption holds (Lee,2008):

! Assumption: agents have imperfect control over X. For instance, youcan study harder to do well in a test, but there is always somerandomness left in the result" Intuition: the randomness guarantees that the potential outcome curves are

smooth (e.g continuous) around the cutoff point! It is then possible to test whether this assumption holds as in the

case of a randomized experiment:" Should not be any difference between predetermined covariates on each side of

the cutoff point (« balanced covariates »)" The density of X should be continuous at the cutoff point c (McCrary 2008)

Figure 3: Randomized Experiment as a RD Design

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

0 0.5 1 1.5 2 2.5 3 3.5 4

Assignment variable (random number, X)

Out

com

e va

riabl

e (Y

)

E[Y(1)|X]

E[Y(0)|X]

Observed (treatment)

Observed (control)

Threat to (internal) validity:manipulation problem! Key assumption in Lee (2008) is that agents have imperfect control

over the assignment variable! A test score is a good example of such a variable, but potential

problems can arise if we have" Cheating (to get just right above the cutoff)" Instructor “moves up” student a few points below the passing grade to exactly the

passing grade" Students who fail are allowed to retake the test

! In all cases, the result is that people just to the left and just to theright of the cutoff are no longer comparable

! The manipulation problem is potentially more severe in cases whereagents have more direct control over the assignment variable" Example: numbers of weeks/hours to qualify for UI.

Testing for manipulation

! Important advantage of RD over many other approaches (includingIV) is that the key identifying assumption (no manipulation) istestable

! Balanced covariates:" We only need to include the treatment variable (D) and the assignment variable

(X) in the regression model. Gives us the “freedom” to see whether othercovariates (e.g. family background) evolve smoothly around the cutoff point

" Similar to randomized experiments in this regard

! Continuous density:" If instructor moves up students with a 48 or 49 percent grade to 50 percent, we

will see in the data an abnormal concentration of students at 50 percent

Lecture 2: A User Guide to RD

Thomas Lemieux, UBCSpring Course in Labor EconometricsUniversity of Coimbra, March 18 2011

Step-by-step approach using Lee’svoting application as an example! Graphing the raw data

" Treatment and outcome graphs" Density of the assignment variable

! Estimating the regression" Polynomial models" Local linear regressions and choice of bandwidth

! Testing the validity of the RD design" Discontinuity in the density" Testing whether covariates are balanced

! Should we include covariates?! Checklist

Voting example

! Voting and election rules a fertile ground for using RD designs! Lee (2008) uses data from elections at the US House of

Representatives to look at incumbency effects! Most (80-90 percent) representatives get re-elected two years later.

Could either reflect heterogeneity (good politicians get re-elected) ora causal effect of incumbency (fund raising, etc.)

! Can sort this out by looking at close elections: probability that ademocrat gets elected depending on whether he/she narrowly wonor narrowly lost the election two years ago

! RD design… (“first stage” or treatment graph is trivial)

Treatment and outcome graph! These are the two core graphs in a RD study

" Treatment (D) graph indicates the cutoff rule “binds” in practice (sometimes trivial)" Outcome (Y) graph is the most convincing evidence for whether or not there is a

treatment effect

! Suggestion is to show both the raw data (typically mean of D or Y ina small bin) and smoothed data (e.g. cubic or quartic function in X)

! Bin means (k=1,..K) are computed as follows:

! Choice of binwidth (h=bk+1 - bk) is an issue:" Too narrow we get very noisy data and don’t see much" Too wide we can oversmooth the raw data and fail to see what happens “right at

the cutoff”" In addition to the “eyeball estimator” we suggest more formal procedures such as

cross-validation in the JEL paper

Density of the assignment variable

! Consider the number of observations in each bin k

! An abnormal concentration of observations right at the cutoff pointsuggests there may be a manipulation problem

! A usual way of visually looking at this is to either show the" Histogram: plot Nk/N" Density: plot Nk/(Nh), where h=bk+1 - bk

! As we will later see, one can formally test for manipulation bylooking at whether there is discontinuity in the density at the cutoff" Run regression of Nk/(Nh) on X on each side of the cutoff and test whether there

is a significant jump at the cutoff

Estimating the regressions

! This is the key part of the empirical analysis" Provides regression estimates of the treatment effect

! Two most popular methods consists of either fitting" flexible polynomial regressions over a relatively wide range of data (“parametric

estimates”)" Local linear regressions (LLR) in a narrow range around the cutoff

(“nonparametric approach”)

! Both approaches are defendable though LLRs are closer in spirit tothe RD concept where we should focus on what happens “right atthe cutoff”

! In practice, varying the range of the estimation (the bandwidth) andthe order of the polynomial is a good way of assessing therobustness of the results

! The two approaches are, thus, complementary

Estimating the regressions

! Highly advisable to run separate regressions (different slopes) oneach side of the cutoff

! Otherwise we are constraining the treatment effect to be a constantfunction of X (see potential outcomes graph)

! The most convenient way of implementing this in practice is to run apooled regression with interactions between D and X as it providesa direct estimate of the treatment effect (estimated effect of D) andits standard error

! For a linear specification the regression is:

! Where we first subtract c from X so that ! gives us the effect of Dwhen X=c (X-c=0), ie the treatment effect at the cutoff

Polynomial regressions

! We simply increase the order of the polynomial in X starting with thelinear regression

! For example, for a third order polynomial just estimate:

! Procedure such as AIC can then be used to more formally select theorder of the polynomial. Nothing special about RD here relative toother searches for adequate specification in regression analysis.

Local linear regressions (LLR)

! Estimate linear regression in the neighbour hood of the cutoff" Estimate the model for c-h ! X ! c+h, where h is the bandwidth

! The approach is non-parametric because “we promise” that we willchoose a smaller and smaller value of h as the number ofobservations increases" This is a good idea as we ideally like to use data as close as possible to the cutoff" But having h→0 as N→" is a bit of an empty promise, as we only have one data

set with a fixed N…" So even though this is a non-parametric approach, from a practical point of view

this just amounts to running standard regressions…

! A more important question from a practical point of view is how tochoose h in our one data set with a given N?" Rule 1: try different values to see how robust the results are" Rule 2: try formal procedures such as rule-of-thumb or cross-validation

Bandwidth choice: cross validation

! Well known tradeoff in the choice of h:" We lose efficiency (precision) when h gets smaller" But the bias (if the underlying regression is not linear) increases when h gets

larger

! Optimal bandwidth is the one that minimizes the mean square error(variance plus bias squared)

! Problem in practice is that we don’t know what the true functional(and thus the bias) is.

! Cross validation procedure:" For observations i on the left (X<c), run a linear regression with observations

within a window h to the left of Xi, and compute the predicted value of Y using thisregression.

" Do the opposite for observations on the right hand side of c" The mean square error is the average of the square of the prediction errors

Cross validation

! Formally, the cross validation criterion is defined as

! We just pick the value of h that minimizes the cross validationcriterion by doing a grid search

! Econometricians have suggested other procedures for choosing thebandwidth. See, e.g. Imbens and Kalyanaraman (2009)

! For the voting example, the optimal bandwidth (CV) is 0.282 for theshare of vote, and 0.172 for the probability of winning the nextelection. Pretty wide bandwidths...

Regression results

! Table 2a: Share of votes! Table 2b: Probability of winning! Figure B1: A graphical illustration of the

robustness of the results

Testing for manipulation

! Important advantage of RD over many other approaches (includingIV) is that the key identifying assumption (no manipulation) istestable

! Balanced covariates:" Use covariates W instead of the outcome variable Y on the left hand side of the

regressions. If the RD design is valid, we should not find a discontinuity in Wsince agents just to the left and just to the right of the cutoff should be very similar

" Similar to randomized experiments where we first test whether baselinecovariates are the same for the treatment and control groups. Systematicdifferences suggest that randomization failed

! Continuous density:" One we have computed the density in each bin, we can once again run the

regressions using the density (as opposed to Y) as the left hand side variable andsee whether there is a significant jump at the cutoff

Should we include covariates?

! When the RD design is valid, other covariates (e.g. familybackground in Hoekstra) should be similar on both sides of thecutoff

! Orthogonal to the treatment dummy D conditional on X! No bias linked to the exclusion of covariates! But including the covariates (W) may reduce the estimation noise Yi = Di! + Xi" + Wi# + $i

! When W is not included in the regression, the error is Wi# + $iinstead of $i which results in a higher residual variance and lessprecise estimates of the treatment effect

! Same argument as with randomized experiments! But if your results change a lot when you include the covariates you

should be worried. Likely reflects an imbalance in the covariates.

Lee and Lemieux’s “checklist”

1. To assess the possibility of manipulation of theassignment variable, show its distribution

2. Present the main RD graph using binned localaverages

3. Graph a benchmark polynomial specification4. Explore the sensitivity of the results to a range of

bandwidths, and a range of orders to the polynomial5. Conduct a parallel RD analysis on the baseline

covariates6. Explore the sensitivity of the results to the inclusion of

baseline covariates

Implementation in Stata: Lee data set

! The data set used in Lee and Lemieux (2010) is available athttp://faculty.arts.ubc.ca/tlemieux/leedata.dta

! Key variables are" margin: margin of victory, the “assignment variable”" treat: dummy variable for where a Democrat got elected (margin>0). This is the

treatment variable" share: first outcome variable, the winning share in the next election." win: second outcome variable, dummy for whether a Democrat got elected in the

next election

! One can the running simple regression. For instance, to estimate alocal linear regression for share with a bandwidth of 0.1, just do:

use leedata.dtagen tmargin=treat*marginreg share treat margin tmargin if margin>=-.1 & margin<.1

Output on the next slide

. use leedata.dta

. gen tmargin=treat*margin

. reg share treat margin tmargin if margin>=-.1 & margin<.1

Source | SS df MS Number of obs = 1209-------------+------------------------------ F( 3, 1205) = 139.31 Model | 5.14618423 3 1.71539474 Prob > F = 0.0000 Residual | 14.8374209 1205 .012313212 R-squared = 0.2575-------------+------------------------------ Adj R-squared = 0.2557 Total | 19.9836052 1208 .01654272 Root MSE = .11096

------------------------------------------------------------------------------ share | Coef. Std. Err. t P>|t| [95% Conf. Interval]-------------+---------------------------------------------------------------- treat | .0605677 .012993 4.66 0.000 .0350763 .0860592 margin | .6444595 .1631107 3.95 0.000 .324447 .9644719 tmargin | .0043078 .2257596 0.02 0.985 -.4386177 .4472333 _cons | .4640352 .0093888 49.42 0.000 .4456149 .4824555------------------------------------------------------------------------------

Guido Imbens’ stata software

! Available athttp://www.economics.harvard.edu/faculty/imbens/software_imbensalong with an artificial data set for practice

! Description of the software at:http://www.economics.harvard.edu/faculty/imbens/files/rd_software_09aug4.pdf

! Provides an automatic way of selecting the optimal bandwidth forlocal linear regressions for both the sharp and fuzzy RD design

! Main stata command is “rdod.ado”! Example of program (rd_log_09aug4.do) on the next slide

/* example of fuzzy regression discontinuity design *//* read in data */infile y w x z1 z2 z3 using art_fuzzy_rd.txt, clear

/* display summary statistics */summ

/* estimate rd effect *//* y is outcome *//* x is forcing variable *//* z1, z2, z3 are additional covariates *//* w is treatment indicator *//* c(0.5) implies that threshold is 0.5 */

rdob y x z1 z2 z3, c(0.5) fuzzy(w)

/* if details on estimation are required */

rdob y x z1 z2 z3, c(0.5) fuzzy(w) detail

Lecture 3: Miscellaneous topicsin RD designs

Thomas Lemieux, UBCSpring Course in Labor EconometricsUniversity of Coimbra, March 18 2011

Plan for the lecture

! Fuzzy RD design" Connection with TSLS" Fuzzy RD, LATE, and general interpretation issues

! Discrete assignment variable! An incomplete survey of recent applications

" Lots of them…" Fields of application" Types of cutoffs

! Two examples from labour…! Questions and discussion

Fuzzy RD design

! Here there is a discontinuity in the probability of treatment at thecutoff, but unlike the case of the sharp RD it does not go up from 0to 1

! It is useful to introduce a new dummy variable Ti =1[Xi !c], whichsimply indicates whether the assignment variable has crossed thecutoff point

! In the sharp RD design we have D=T, but not here! One can think of T as an instrumental variable for D in a regression

model for Y on X and D! The influential Angrist and Lavy paper on Maimonides rule (QJE

1999) was actually a fuzzy RD study (cutoff at 40 pupils for schoolclasses) but they presented it as an IV study

Fuzzy RD: Basic setup

! Two equations model (f(.) and g(.) are flexible functions)

! We can also write the reduced form:

! The parameter !r="! can be interpreted as an “intent totreat” (ITT) effect

! Very similar to a standard IV setup

Fuzzy RD: Estimation

! One could either:" Estimate the two reduced forms in X and T and compute the treatment effect ! as

the ratio of !r over "" Run TSLS using T as an instrument for D

! Advisable to use the same specification for f(.) and g(.)." Polynomial model: use the same order of polynomial" LLR: use the same bandwidth. The one for the Y equation is the most natural one

to use (we expect the bandwidth for D to be quite wide)

! An advantage of TSLS is that it provides a simple way of obtainingthe standard errors

! Exactly identified model (by design, one instrument T for oneendogenous regressor D)

! But weak first stage problem may occur if the jump in the probabilityof D=1 at c is small.

Fuzzy RD: interpretation! In the model we wrote we implicitly assume that we have a constant

treatment effect !! But if the treatment effect is heterogenous we have a similar

interpretation problem as in an IV setting:" Under the assumption of monotonicity (Imbens and Angrist, 1994) we can identify

a local average treatment effect (LATE) among those induced to treatment(compliers)

! Even narrower here since we only get the LATE for people at X=c! But things are not as bad as they seem since agents at the cutoff

come with various values of observable (W) and unobservable (u)characteristics." It can be shown in the sharp RD case (bit more complicated in fuzzy RD) that the

estimated treatment effect is the following weighted average

Discrete assignment variable

! When the assignment variable is discrete we can no longer go “asclose as possible” to the cutoff.

! The role of the regression is now (in part) to extrapolate to the cutoff! Not as “clean” as in the case with a continuous X, but unless X is

very coarse not much problems arise in most empirical applications! Since we now have a grouping structure, it is important to correct

standard errors by clustering on X.! Natural goodness-of-fit test of the regression model based on the

square deviation between the regression line and the average valueof Y for each (discrete) value of X

Applications! RD not used much in economics until the late 1990s.! But hundreds of studies since then, starting with Van der Klaauw

(IER, 2002)! We provide a partial survey in the JEL piece that would have been

many times larger had we included working papers! Few people (in my opinion) could have predicted only 10 years ago

the sheer volume of recent research based on RD designs! Two possible explanations:

" Cutoff rules are very wide spread…" Much more data available now, especially administrative data sets

! An important advantage of RD designs is that they are well suited tolarge administrative data sets with" Few covariates" Lots of observations and all the relevant information about cutoffs and assignment

variables since those have to be used in the administration of programs

Main fields of applications

! In Table 4 of the JEL paper, we summarize 77 recent RD studies.The distribution across fields is as follows:" Education: 26" Labour markets: 18" Political economy: 8" Health: 7" Crime: 5" Environment 4:" Others: 11

! Example of cutoffs include" Age: 21 for drinking, 65 for US medicare, 18 for young offenders, 25 for the British

“New Deal’ (employment programs), 30 for welfare in Quebec, etc." Pollution levels (non-attainment cutoff)" Weeks or years of work (UI, pension eligibility, etc.)" Geographical (school boundaries, UI regions)

Examples of recent applications inlabour…! Lemieux and Milligan (2008): Age 30 cutoff

for social assistance in Quebec until the late1980s

! Lalive (2008): UI in Austria. Lots of cutoffs,both geographical and age based.

Lemieux and Milligan, 2008

! Social assistance (SA) in Québec! During the 1980s, SA benefits were much

lower for adults with no dependent childrenunder the age of 30 than for those age 30and above.

! Data from the Canadian Census! Focus on male high school dropouts

Figure 1: Social Assistance Benefits, Single Employable Individual (benefits in constant 1986 dollars)

0

50

100

150

200

250

300

350

400

450

500

1980 1981 1982 1983 1984 1985 1986 1987 1988 1989 1990 1991 1992

Mon

thly

ben

efits

(198

6 $)

Under 30 30 and over

0.50

0.52

0.54

0.56

0.58

0.60

0.62

0.64

0.66

0.68

0.70

24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40Age (census day)

Em

ploy

men

t ra

te

Employment rate in 1986 (reference week)

Empl. rate Empl. Rate Difference WeeklySpecification for age last year at census in empl. rate hours

Mean of the dependent variable

0.562 0.618 0.056 24.39

Regression discontinuity estimatesLinear -0.045 *** -0.041 *** -0.029 ** -1.45 **

(0.012) (0.012) (0.011) (0.54)

Quadratic -0.048 *** -0.051 *** -0.031 ** -1.75 **(0.013) (0.012) (0.012) (0.61)

Cubic -0.043 ** -0.048 *** -0.030 ** -1.47 *(0.018) (0.014) (0.013) (0.70)

Linear spline -0.047 *** -0.049 *** -0.032 ** -1.72 ***(0.013) (0.011) (0.013) (0.55)

Quadratic spline -0.038 -0.056 ** -0.035 * -1.66(0.024) (0.018) (0.016) (0.94)

Goodness of fit statistic (p-value)Linear 0.48 0.52 0.91 0.48

Linear spline 0.47 0.72 0.85 0.00

Regression results

Employment rate for the whole population of men (1/5 in the long form census)

0.70

0.75

0.80

0.85

0.90

0.95

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39Age

Em

ploy

men

t rat

e (c

ensu

s w

eek)

Quebec 86 Quebec 91 ROC 86 ROC91

Lalive, Journal of Econometrics 2008

! Incentive effect of the maximum duration ofunemployment insurance in Austria

! In June 1988, maximum duration went upfrom 30 to 209 weeks for individuals age 50and above living in certain regions of thecountry

! Linked to the collapse of the steel industry,which was concentrated in some regions ofthe country