ECON 626: Applied Microeconomics Lecture 5: Regression - - PowerPoint PPT Presentation

ECON 626: Applied Microeconomics Lecture 5: Regression Discontinuity

Professors: Pamela Jakiela and Owen Ozier

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

• Academic test scores: scholarships or prizes, higher education

admission, certificates of merit

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

• Academic test scores: scholarships or prizes, higher education

admission, certificates of merit

• Poverty scores: (proxy-)means-tested anti-poverty programs

(generally: any program targeting that features rounding or cutoffs)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

• Academic test scores: scholarships or prizes, higher education

admission, certificates of merit

• Poverty scores: (proxy-)means-tested anti-poverty programs

(generally: any program targeting that features rounding or cutoffs)

• Land area: fertilizer program or debt relief initiative for owners of

plots below a certain area

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

• Academic test scores: scholarships or prizes, higher education

admission, certificates of merit

• Poverty scores: (proxy-)means-tested anti-poverty programs

(generally: any program targeting that features rounding or cutoffs)

• Land area: fertilizer program or debt relief initiative for owners of

plots below a certain area

• Date: age cutoffs for pensions; dates of birth for starting school with

different cohorts; date of loan to determine eligibility for debt relief

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea

A precise rule based on a continuous characteristic determines participation in a program. When do we see such rules? Five example categories, but surely more:

• Academic test scores: scholarships or prizes, higher education

admission, certificates of merit

• Poverty scores: (proxy-)means-tested anti-poverty programs

(generally: any program targeting that features rounding or cutoffs)

• Land area: fertilizer program or debt relief initiative for owners of

plots below a certain area

• Date: age cutoffs for pensions; dates of birth for starting school with

different cohorts; date of loan to determine eligibility for debt relief

• Elections: fraction that voted for a candidate of a particular party

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 2

Regression discontinuity - basic idea (“sharp”)

Not eligible Eligible

Source: Gertler, P. J.; Martinez, S., Premand, P., Rawlings, L. B. and Christel M. J. Vermeersch, 2010, Impact Evaluation in Practice: Ancillary Material, The World Bank, Washington DC (www.worldbank.org/ieinpractice)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 3

Regression discontinuity - basic idea (“sharp”)

IMPACT

Source: Gertler, P. J.; Martinez, S., Premand, P., Rawlings, L. B. and Christel M. J. Vermeersch, 2010, Impact Evaluation in Practice: Ancillary Material, The World Bank, Washington DC (www.worldbank.org/ieinpractice)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 3

Regression discontinuity - basic idea (“sharp”)

IMPACT

Source: Gertler, P. J.; Martinez, S., Premand, P., Rawlings, L. B. and Christel M. J. Vermeersch, 2010, Impact Evaluation in Practice: Ancillary Material, The World Bank, Washington DC (www.worldbank.org/ieinpractice)

Note: Local Average Treatment Effect

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 3

Regression discontinuity - basic idea (“sharp”)

.2 .4 .6 .8 1 Probability

• 1
• .5

.5 1 Running variable D=program participation = T=treatment assignment

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 4

Regression discontinuity - outcome

5.9 6 6.1 6.2 6.3 6.4

• 1
• .5

.5 1

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 5

Regression discontinuity - basic idea (“fuzzy”)

.2 .4 .6 .8 1 Probability

• 1
• .5

.5 1 Running variable D=program participation

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 6

Regression discontinuity - basic idea (“fuzzy”)

.2 .4 .6 .8 1 Probability

• 1
• .5

.5 1 Running variable D=program participation T=treatment assignment

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 6

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

• Rubin (1977; statistics) first wrote about it as part of a larger

discussion of treatment assignment based on the covariate;

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

• Rubin (1977; statistics) first wrote about it as part of a larger

discussion of treatment assignment based on the covariate;

• Finkelstein et al (1996; biostatistics) called it the risk-allocation

design;

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

• Rubin (1977; statistics) first wrote about it as part of a larger

discussion of treatment assignment based on the covariate;

• Finkelstein et al (1996; biostatistics) called it the risk-allocation

design;

• and Trochim (1980; statistics) finished up calling it the

cutoff-based design.”

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

• Rubin (1977; statistics) first wrote about it as part of a larger

discussion of treatment assignment based on the covariate;

• Finkelstein et al (1996; biostatistics) called it the risk-allocation

design;

• and Trochim (1980; statistics) finished up calling it the

cutoff-based design.” Boom since 1990s in economics: applications and methodology.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

History of the RD design - Cook (2008)

“Several themes stand out in the half century of RDD’s history. One is its repeated independent discovery. ...

• Campbell (1960; psychology / education) first named the design

regression-discontinuity;

• Goldberger (1972; economics) referred to it as deterministic

selection on the covariate;

• Sacks and Spiegelman (1977,78,80; statistics) studiously avoided

naming it;

• Rubin (1977; statistics) first wrote about it as part of a larger

discussion of treatment assignment based on the covariate;

• Finkelstein et al (1996; biostatistics) called it the risk-allocation

design;

• and Trochim (1980; statistics) finished up calling it the

cutoff-based design.” Boom since 1990s in economics: applications and methodology. See Journal of Econometrics, 2008 Vol.142 (2) - special issue on RD.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 7

Thistlethwaite and Campbell (1960)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 8

Thistlethwaite and Campbell (1960)

Observation: scholarship winners have different attitudes.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 9

Thistlethwaite and Campbell (1960)

Observation: scholarship winners have different attitudes. Are attitudes changed by the scholarship? (Is it a causal link?)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 9

Thistlethwaite and Campbell (1960)

Observation: scholarship winners have different attitudes. Are attitudes changed by the scholarship? (Is it a causal link?)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 9

Thistlethwaite and Campbell (1960)

Observation: scholarship winners have different attitudes. Are attitudes changed by the scholarship? (Is it a causal link?) Outcome: scholarships

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 9

Thistlethwaite and Campbell (1960)

Observation: scholarship winners have different attitudes. Are attitudes changed by the scholarship? (Is it a causal link?) Outcome: scholarships Outcome: attitudes

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 9

Thistlethwaite and Campbell (1960)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 10

RD, a little more formally

We can (locally) approximate any smooth function:

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 11

RD, a little more formally

We can (locally) approximate any smooth function: Yi = f (xi) + ρDi + ηi (1) Substitute: f (xi) ≈ α + β1xi + β2x2

i + ... + βpxp i

(2)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 11

RD, a little more formally

We can (locally) approximate any smooth function: Yi = f (xi) + ρDi + ηi (1) Substitute: f (xi) ≈ α + β1xi + β2x2

i + ... + βpxp i

(2) And thus: Yi = α + β1xi + β2x2

i + ... + βpxp i + ρDi + ηi

(3)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 11

RD, a little more formally

We can (locally) approximate any smooth function: Yi = f (xi) + ρDi + ηi (1) Substitute: f (xi) ≈ α + β1xi + β2x2

i + ... + βpxp i

(2) And thus: Yi = α + β1xi + β2x2

i + ... + βpxp i + ρDi + ηi

(3) But because the smooth function may behave differently on either side of the cutoff, we will expand on this. First, transform xi notationally (and for ease of regression). Let ˜ xi = xi − x0 (4)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 11

RD, a little more formally

We can (locally) approximate any smooth function: Yi = f (xi) + ρDi + ηi (1) Substitute: f (xi) ≈ α + β1xi + β2x2

i + ... + βpxp i

(2) And thus: Yi = α + β1xi + β2x2

i + ... + βpxp i + ρDi + ηi

(3) But because the smooth function may behave differently on either side of the cutoff, we will expand on this. First, transform xi notationally (and for ease of regression). Let ˜ xi = xi − x0 (4)

Angrist and Pishke, Chapter 6, pp. 251-267

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 11

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

Then, allowing different trends (and indeed, completely different polynomials) on either side of the cutoff (with and without the program), we can write the conditional expectation functions: E[Y0i] = f0(xi) = α + β01˜ xi + β02˜ x2

i + ... + β0p˜

xp

i

(5) E[Y1i] = f1(xi) = α + ρ + β11˜ xi + β12˜ x2

i + ... + β1p˜

xp

i

(6)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 12

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

Then, allowing different trends (and indeed, completely different polynomials) on either side of the cutoff (with and without the program), we can write the conditional expectation functions: E[Y0i] = f0(xi) = α + β01˜ xi + β02˜ x2

i + ... + β0p˜

xp

i

(5) E[Y1i] = f1(xi) = α + ρ + β11˜ xi + β12˜ x2

i + ... + β1p˜

xp

i

(6) And because Di is a deterministic function of xi (this is important for writing the conditional expectation): E[Yi|Xi] = E[Y0i] + (E[Y1i] − E[Y0i])Di (7)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 12

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

Then, allowing different trends (and indeed, completely different polynomials) on either side of the cutoff (with and without the program), we can write the conditional expectation functions: E[Y0i] = f0(xi) = α + β01˜ xi + β02˜ x2

i + ... + β0p˜

xp

i

(5) E[Y1i] = f1(xi) = α + ρ + β11˜ xi + β12˜ x2

i + ... + β1p˜

xp

i

(6) And because Di is a deterministic function of xi (this is important for writing the conditional expectation): E[Yi|Xi] = E[Y0i] + (E[Y1i] − E[Y0i])Di (7) So, substituting in for the regression equation, we can define β∗

j = β1j − β0j for any j, and write:

Yi =α + β01˜ xi + β02˜ x2

i + ... + β0p˜

xp

i +

(8) ρDi + β∗

1Di ˜

xi + β∗

2Di ˜

x2

i + ... + β∗ p ˜

xp

i + ηi

(9)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 12

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

But this can all really be simplified in many practical cases. For small values of ∆:

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 13

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

But this can all really be simplified in many practical cases. For small values of ∆: E[Yi|x0 − ∆ < xi < x0] ≈ E[Y0i|xi = x0] (10) E[Yi|x0 ≤ xi < x0 + ∆] ≈ E[Y1i|xi = x0] (11)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 13

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

But this can all really be simplified in many practical cases. For small values of ∆: E[Yi|x0 − ∆ < xi < x0] ≈ E[Y0i|xi = x0] (10) E[Yi|x0 ≤ xi < x0 + ∆] ≈ E[Y1i|xi = x0] (11) and then, in the most extreme case, we can take the limit:

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 13

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

But this can all really be simplified in many practical cases. For small values of ∆: E[Yi|x0 − ∆ < xi < x0] ≈ E[Y0i|xi = x0] (10) E[Yi|x0 ≤ xi < x0 + ∆] ≈ E[Y1i|xi = x0] (11) and then, in the most extreme case, we can take the limit: lim

∆→0 E[Yi|x0 ≤ xi < x0 + ∆] − E[Yi|x0 − ∆ < xi < x0] = E[Y1i − Y0i|xi = x0]

(12) So the difference in means in an extremely (vanishingly!) narrow band on each side of the cutoff might be enough to estimate the effect of the program, ρ. In practice, usually include linear terms and use a narrow region around the cutoff.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 13

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0).

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0). Now, following the equations in the text, we arrive at two (piecewise) polynomial approximations: Yi = µ + κ1xi + κ2x2

i + ... + κpxp i + πρTi + ζ2i

(14)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0). Now, following the equations in the text, we arrive at two (piecewise) polynomial approximations: Yi = µ + κ1xi + κ2x2

i + ... + κpxp i + πρTi + ζ2i

(14) Di = γ0 + γ1xi + γ2x2

i + ... + γpxp i + πTi + ζ1i

(15)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0). Now, following the equations in the text, we arrive at two (piecewise) polynomial approximations: Yi = µ + κ1xi + κ2x2

i + ... + κpxp i + πρTi + ζ2i

(14) Di = γ0 + γ1xi + γ2x2

i + ... + γpxp i + πTi + ζ1i

(15) So to estimate ρ, we use instrumental variables, and in essence divide the coefficient estimate on Ti in the “first stage” regression (variations on Equation 15) by the coefficient estimage on Ti in the “reduced form” regression (variations on Equation 14).

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0). Now, following the equations in the text, we arrive at two (piecewise) polynomial approximations: Yi = µ + κ1xi + κ2x2

i + ... + κpxp i + πρTi + ζ2i

(14) Di = γ0 + γ1xi + γ2x2

i + ... + γpxp i + πTi + ζ1i

(15) So to estimate ρ, we use instrumental variables, and in essence divide the coefficient estimate on Ti in the “first stage” regression (variations on Equation 15) by the coefficient estimage on Ti in the “reduced form” regression (variations on Equation 14). Again, as in IV: Exclusion restriction, standard errors

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

RD, a little more formally

Angrist and Pishke, Chapter 6, pp. 251-267

What if the assignment rule is discontinuous, but does not completely determine treatment status? Prob(Di = 1|xi) = g1(xi) if xi ≥ x0 g0(xi) if xi < x0 , where g1(x0) = g0(x0) (13) We need a different notation for being on the left or the right of the cutoff, now that Di doesn’t jump from zero to one. Let Ti = I(xi ≥ x0). Now, following the equations in the text, we arrive at two (piecewise) polynomial approximations: Yi = µ + κ1xi + κ2x2

i + ... + κpxp i + πρTi + ζ2i

(14) Di = γ0 + γ1xi + γ2x2

i + ... + γpxp i + πTi + ζ1i

(15) So to estimate ρ, we use instrumental variables, and in essence divide the coefficient estimate on Ti in the “first stage” regression (variations on Equation 15) by the coefficient estimage on Ti in the “reduced form” regression (variations on Equation 14). Again, as in IV: Exclusion restriction, standard errors

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 14

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth
• Standard errors (confidence interval)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth
• Standard errors (confidence interval)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth
• Standard errors (confidence interval)

Methodological updates and extensions:

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth
• Standard errors (confidence interval)

Methodological updates and extensions:

• Cattaneo, Calonico, and Titiunik series (SE’s, visualization)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Practical considerations

Five basic issues are highlighted by Guido Imbens and Thomas Lemieux in their paper, Regression discontinuity designs: A guide to practice:

• Specification tests: density, covariates, other jumps
• Density: analogy to attrition. This is conceptually important.
• Visualization
• Specification: polynomial order (linear in many cases), “kernel”
• Bandwidth
• Standard errors (confidence interval)

Methodological updates and extensions:

• Cattaneo, Calonico, and Titiunik series (SE’s, visualization)
• Card, Lee, Pei, and Weber (Kink design)

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 15

Visualization: Dube, Giuliano, Leonard example

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 16

Visualization: Dube, Giuliano, Leonard example

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 17

Visualization: Dube, Giuliano, Leonard example

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 17

Manipulation of the running variable

What if the population of potential program participants is able to precisely influence the running variable, and knows the program assignment rule?

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 18

Manipulation of the running variable

What if the population of potential program participants is able to precisely influence the running variable, and knows the program assignment rule? Example from Camacho and Conover (2011) in Colombia: program rule became known in 1997; watch what happens.

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 18

Poverty score distribution - Camacho and Conover (2011) in Colombia

Percent 1994

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

1995 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

1996 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

1997 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

1998 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

1999 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

2000 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

2001 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

2002 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

Poverty score distribution - Camacho and Conover (2011) in Colombia

2003 Percent

6 5 4 3 2 1

7 14 21 28 35 42 49 56 63 70 77 84 91 98

Poverty index score

UMD Economics 626: Applied Microeconomics Lecture 4: Regression Discontinuity, Slide 19

An example.