Regression Discontinuity Designs in Economics

• p. 4 Footnote 2

  two recent overview papers by Van der Klaauw (2008b)

• p. 89 Reference list, Van der Klaauw entries

  Approach,” Labour, June

Judge's note: Checked reference list p.89 (printed p.87). Both Van der Klaauw entries are dated only "February 2008" and "June 2008", with no suffix. Footnote 2 (p.4) cites 2008b, and Table 4 and Section 6 cite 2008a. The mapping can be inferred from context but is not stated.

Second check: another model agreed

• p. 21 Section 3.2.3, after Eq. (4)

  We return to how to implement this in practice in Section 4.4.

• p. 55 Section 4.5 heading

  Incorporating Covariates in Estimation

Judge's note: Checked p.21 and the text of Sections 4.4 and 4.5. Section 4.4 is titled "Implementing Empirical Tests of RD Validity and Using Covariates", and its intro says it covers incorporating covariates, but its subsections only cover validity tests. Section 4.5 contains the implementation and refers back to equation (4), and later pointers cite Section 4.5. The pointer is partly defensible, so this is minor.

Second check: another model agreed

• p. 69 Table 4, Health

  Card et al. (2009a)

• p. 84 Reference list, Card entries

  American Economic Review, forthcoming 2009.

• p. 83 Reference list, Black et al. entries

  Working Paper, University of Michigan 2007.

• p. 89 Reference list, Van der Klaauw 2008 entries

  Labour, June 2008, 22 (2), 219–245.

Judge's note: Reference list images on pp.83, 84 and 89 show the Card-Dobkin-Maestas 2009 AER and QJE entries, the Black et al. 2007 WP and AER entries, and the Van der Klaauw 2008 J. Econometrics and Labour entries, all without suffixes. The text uses suffixes (main.txt lines 118, 1595, 2348, 2368, 2540, 2545, 2826). The reader can mostly infer the mapping from context (e.g. Table 4 'utilization' = AER), so this is minor. The Jacob and Lefgren point in reviewer note 1 is not a defect: the list has '2004' and '2004a', matching the text's 2004/2004a.

Second check: another model agreed

• p. 3 Introduction, para 2

  exploited the presence of discontinuities at the geographical level (school district boundaries)

• p. 76 Section 6.3.2

  Black (1999) and Bayer et al. (2007) examine housing prices on either side of school attendance boundaries

• p. 65 Table 4, Black (1999) row

  Inclusion in school attendance region

Judge's note: Checked p.3: the intro reads "(school district boundaries)". Section 6.3.2 on p.76 says "school attendance boundaries". The Table 4 row for Black (1999) on p.65 says "Inclusion in school attendance region". The quotation on pp.74-75 refers to "attendance district boundary". Probably loose wording, but the intro is inconsistent with the rest of the paper.

Second check: another model agreed

• p. 3 Introduction, para 2

  the effects of Medicaid on health outcomes

• p. 69 Table 4, Health section, Card and Shore-Sheppard (2004)

  Overall insurance coverage

Only the authors can say what is right here.

Judge's note: Checked p.3 and the Health section of Table 4 on p.69. Card and Shore-Sheppard (2004): Medicaid, outcome "Overall insurance coverage". Card et al. (2009a/b): Medicare, outcomes utilization and mortality. Nothing in the paper supports Medicaid effects on health outcomes. The authors may mean Medicare, or studies they do not list, so this is a query for them.

Second check: another model agreed

• p. 11 Section 2.2, overlap paragraph

  it is not possible to observe units with either D = 0 or D = 1 for a given value of the assignment variable X

Judge's note: Checked p.11. The next sentence ("we cannot observe treatment and non-treatment for the same value of X") gives the intended meaning. The sentence as written says something different, though the meaning is clear from context.

Second check: another model agreed

• p. 30 Section 3.5.2, Heckit equations and Eq. (8)

  E [U|W = w,V ≥−wδ2]

• p. 28 Section 3.5.1 equation

  E [U|W = w,V ≥c−wδ2]

Judge's note: Model (2) on printed p.~11 defines D = 1[X ≥ c] with X = Wδ2 + V, so D = 1 iff V ≥ c − Wδ2. Section 3.5.1 (PDF p.28) writes c − wδ2. The Heckit equations and Eq. (8) on PDF p.30 write −wδ2. I found no statement that normalises c to 0 in this section (the normalisation on p.36 concerns the voting example). It is a notational inconsistency; the identification argument is unaffected once c is restored.

Second check: another model agreed

• p. 46 Section 4.3.1, paragraph on Table 3

  the suggested bandwidth ranges from 0.14 to 0.28

• p. 93 Table 3, Panel A, Right, Win next election

  0.130

Judge's note: Table 3 image: the values are 0.162, 0.208, 0.180, 0.164, 0.130, 0.141, 0.192, 0.282, 0.282, 0.247, 0.141 and 0.172; the minimum is 0.130. The 'Both' rows (0.141 to 0.282) fit the stated range, but the text does not restrict the claim to them.

Second check: another model agreed

• p. 72 Section 6.2.1

  Urquiola (2006), and Urquiola and Verhoogen (2007)

• p. 78 Section 7, Sorting bullet

  A recent analysis that illustrates this standard is that of Urquiola and Verhoogen (2007)

• p. 66 Table 4, Education

  Urquiola and Verhoogen (2009)

• p. 78 Section 7, Sorting and Manipulation bullet

  Urquiola and Verhoogen (2007)

Judge's note: Both the July 2007 working paper and the 2009 AER article are in the reference list, so neither citation is broken. The point is that one study is cited inconsistently across text and table. Verified on page images p.66, p.72 and p.78.

Second check: another model agreed

• p. 6 Footnote 5

  where it is argued that is is more helpful

• p. 6 Footnote 5

  can simultaneously viewed as solutions

• p. 6 Footnote 5

  where it is argued that is is more helpful to view

Judge's note: The duplication "is is" is visible in footnote 5 on the page image (p.6). The missing "be" that one reviewer also raised is handled separately as C007.

Second check: none (judge only)

• p. 6 Footnote 5, last sentence

  the same least squares estimator can simultaneously viewed as solutions to

• p. 6 footnote 5

  can simultaneously viewed as solutions

Judge's note: Visible in footnote 5 on the page image (p.6).

Second check: none (judge only)

• p. 88 Reference list

  “Estimation of Semiparametric,”

• p. 88 Reference list, Powell entry

  Powell, James L., “Estimation of Semiparametric,”

• p. 6 Footnote 5

  See Section 1.2 of Powell (1994)

Judge's note: The page 88 image shows the title as typeset, ending at the adjective 'Semiparametric' with no noun, so this is not an extraction artefact. The likely full title, 'Estimation of Semiparametric Models', comes from outside knowledge, but the truncation is plain from the page itself. Footnote 5 cites this entry.

Second check: none (judge only)

• p. 12 Section 2.3, first paragraph

  As we disucss throughout the paper

• p. 12

  As we disucss throughout the paper, however, we do not

Judge's note: The misspelling is visible on the page image (p.12).

Second check: none (judge only)

• p. 20 Section 3.2.2, first line

  Perfroming this kind of test

• p. 20 Section 3.2.2, third paragraph

  values of the observalbe characteristics

• p. 20

  Perfroming this kind of test is arguably more important

Judge's note: Visible on the page image (p.20). The "observalbe" misspelling also listed here is handled in C012.

Second check: none (judge only)

• p. 20 Sec. 3.2.2, last paragraph

  observalbe characteristics

• p. 20

  observalbe characteristics, some discontinuities in the density of X

Judge's note: Visible on the page image (p.20).

Second check: none (judge only)

• p. 26 Text after Eq. (7)

  discontinuity in the relation between y and X

• p. 25 Section 3.4.1

  has no impact on y except by influencing D

Judge's note: Both are visible in italic lower-case y on the page images. Elsewhere in the same passages the outcome is Y.

Second check: none (judge only)

• p. 29 Footnote 22

  nonpaparmetric regression

• p. 29

  nonpaparmetric regression.

Judge's note: Misspelling visible in the page image crop of footnote 22.

Second check: none (judge only)

• p. 29 Section 3.5.1, first line

  work, however,when W has continuous elements

Judge's note: The page image shows 'however,when' with no space.

Second check: none (judge only)

• p. 35 Section 4.1

  choosing how to the plot

• p. 35 Section 4.1

  a range a bandwidths often yield similar values

• p. 35 Sec. 4.1

  Furthermore, a range a bandwidths often yield

• p. 35 Sec. 4.1

  choosing how to the plot the data

Judge's note: Both errors are visible in the page image.

Second check: none (judge only)

• p. 36 Section 4.1

  We suggests two such tests.

• p. 36 Section 4.1

  degrees of freedom can used

• p. 36 Section 4.1

  that the the mean value of Y

• p. 36

  a standard F-test with K′ degrees of freedom can used

Judge's note: All three slips are visible on the page 36 image.

Second check: none (judge only)

• p. 37 Section 4.1

  for the entire date range

• p. 37 Section 4.1

  the bin and regression tests suggests than

• p. 37 first paragraph

  for the entire date range on both the left and right

Judge's note: Both slips are visible on the page 37 image. The same page later says 'entire data range'.

Second check: none (judge only)

• p. 40 Footnote 28

  of magnitude lower that at the cutoff

• p. 40

  the bias is of an order of magnitude lower that at the cutoff

Judge's note: Visible in the page image crop.

Second check: none (judge only)

• p. 43 Sec. 4.3.1

  One the one hand, using a larger bandwidth

Judge's note: Visible in the page image crop ('One the / one hand').

Second check: none (judge only)

• p. 54 Sec. 4.4.2, SUR paragraph

  discontinuity gaps in all questions being zero

Judge's note: Page 54 image shows 'all questions being zero' in a sentence about a SUR system where each equation represents a covariate; the following text refers to 'the K equations'. This is a word slip.

Second check: none (judge only)

• p. 56 Footnote 43

  which will hold when, for example, when ε is orthogonal

Judge's note: The duplicated 'when' is visible in the crop of footnote 43 on PDF p.56.

Second check: none (judge only)

• p. 57 Footnote 44

  preceeding footnotes

• p. 57 Checklist item 1

  The bin widths should as small as possible

Judge's note: Both slips are visible on the page image crops of p.57.

Second check: none (judge only)

• p. 78 Section 7, Sorting bullet

  schools receive a fixed payment per student from the government .

Judge's note: The space before the period is visible in the p.78 crop.

Second check: none (judge only)

• p. 79 Section 7, Locally Randomized Experiments bullet

  of testing of the RD design include, Matsudaira (2008)

Judge's note: The comma is visible in the p.79 crop.

Second check: none (judge only)

• p. 80 Section 7, Graphical Analysis bullet

  a rough sense of the range of the both the assignment variable

Judge's note: Visible in the p.80 crop.

Second check: none (judge only)

• p. 81 Section 7.1, para 1

  but instead possesses and a slightly noisy measure of the variable

• p. 81

  possesses and a slightly noisy measure of the variable

Judge's note: Visible in the p.81 crops.

Second check: none (judge only)

• p. 84 Reference list

  February 2006, 41(2) (11113), 294–318.

Judge's note: The stray parenthetical number is visible in the p.84 crop; it looks like a leftover working-paper number. The rest of the entry is not questioned.

Second check: none (judge only)

• p. 88 Pettersson-Lidbom (2006)

  Evidence from Two Nautral Experi-

• p. 89 White (1980)

  A Heteroskedasticty-Consistent Covariance Matrix

• p. 85 Ding and Lehrer (2007)

  Review of Economic and Statistics

• p. 85 Ferreira and Gyourko (2009)

  2009, 124(1) (1), 399–422.

Judge's note: I confirmed all four in the page images. Page 88 has 'Nautral'. Page 89 has 'Heteroskedasticty' (while 'Heteroskedasticity' is spelled correctly in the same title). Page 85 has 'Review of Economic and Statistics'. Page 85 also has '124(1) (1)', which prints the issue number twice.

Second check: none (judge only)

• p. 88 Porter (2003) reference

  University ofWisconsin

Judge's note: The page 88 image shows 'ofWisconsin' run together in italics as typeset.

Second check: none (judge only)

• p. 110 Figure A4

  Figure A4: Cross-validation Function for Local Linear Regression: Winning the Next Election

• p. 110 Figure A4

  Figure A4: Cross-validation Function for Local Linear Regression:

Judge's note: The upright page 110 image shows only tick values (428–435; 0.00–0.45) with no x or y axis title. The upright page 109 image (Figure A3) shows both axis titles. This is a cosmetic omission; the meaning can be recovered from the caption.

Second check: none (judge only)