Propensity Score-Matching Methods for

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES Rajeev H. Dehejia and Sadek Wahba* Abstract—This paper considers causal inference and sample selection bias in nonexperimental settings in which (i) few units in the nonexperimental comparison group are comparable to the treatment units, and (ii) selecting a subset of comparison units similar to the treatment units is difficult because units must be compared across a high-dimensional set of pretreatment characteristics. We discuss the use of propensity score-matching methods, and implement them using data from the National Supported Work experiment. Following LaLonde (1986), we pair the experimental treated units with nonexperimental comparison units from the CPS and PSID, and compare the estimates of the treatment effect obtained using our methods to the benchmark results from the experiment. For both comparison groups, we show that the methods succeed in focusing attention on the small subset of the comparison units comparable to the treated units and, hence, in alleviating the bias due to systematic differences between the treated and comparison units.

I.

Introduction

A

n important problem of causal inference is how to estimate treatment effects in observational studies, situations (like an experiment) in which a group of units is exposed to a well-defined treatment, but (unlike an experiment) no systematic methods of experimental design are used to maintain a control group. It is well recognized that the estimate of a causal effect obtained by comparing a treatment group with a nonexperimental comparison group could be biased because of problems such as self-selection or some systematic judgment by the researcher in selecting units to be assigned to the treatment. This paper discusses the use of propensity score-matching methods to correct for sample selection bias due to observable differences between the treatment and comparison groups. Matching involves pairing treatment and comparison units that are similar in terms of their observable characteristics. When the relevant differences between any two units are captured in the observable (pretreatment) covariates, which occurs when outcomes are independent of assignment to treatment conditional on pretreatment covariates, matching methods can yield an unbiased estimate of the

Received for publication February 12, 1998. Revision accepted for publication January 24, 2001. * Columbia University and Morgan Stanley, respectively. Previous versions of this paper were circulated under the title “An Oversampling Algorithm for Nonexperimental Causal Studies with Incomplete Matching and Missing Outcome Variables” (1995) and as National Bureau of Economic Research working paper no. 6829. We thank Robert Moffitt and two referees for detailed comments and suggestions that have improved the paper. We are grateful to Gary Chamberlain, Guido Imbens, and Donald Rubin for their support and encouragement, and greatly appreciate comments from Joshua Angrist, George Cave, and Jeff Smith. Special thanks are due to Robert LaLonde for providing, and helping to reconstruct, the data from his 1986 study. Valuable comments were received from seminar participants at Harvard, MIT, and the Manpower Demonstration Research Corporation. Any remaining errors are the authors’ responsibility.

treatment impact.1 The first generation of matching methods paired observations based on either a single variable or weighting several variables. (See, inter alia, Bassi (1984), Cave and Bos (1995), Czajka et al. (1992), Cochran and Rubin (1973), Raynor (1983), Rosenbaum (1995), Rubin (1973, 1979), Westat (1981), and studies cited by Barnow (1987).) The motivation for focusing on propensity scorematching methods is that, in many applications of interest, the dimensionality of the observable characteristics is high. With a small number of characteristics (for example, two binary variables), matching is straightforward (one would group units in four cells). However, when there are many variables, it is difficult to determine along which dimensions to match units or which weighting scheme to adopt. Propensity score-matching methods, as we demonstrate, are especially useful under such circumstances because they provide a natural weighting scheme that yields unbiased estimates of the treatment impact. The key contribution of this paper is to discuss and apply propensity score-matching methods, which are new to the economics literature. (Previous papers include Dehejia and Wahba (1999), Heckman et al. (1996, 1998), Heckman, Ichimura, and Todd (1997, 1998). See Friedlander, Greenberg, and Robins (1997) for a review.) This paper differs from Dehejia and Wahba (1999) by focusing on matching methods in detail, and it complements the Heckman et al. papers by discussing a different array of matching estimators in the context of a different data set. An important feature of our method is that, after units are matched, the unmatched comparison units are discarded and are not directly used in estimating the treatment impact. Our approach has two motivations. First, in some settings of interest, data on the outcome variable for the comparison group are costly to obtain. For example, in economics, some data sets provide outcome information for only one year; if the outcome of interest takes place in a later period, possibly thousands of comparison units have to be linked across data sets or resurveyed. In such settings, the ability to obtain the needed data for a subset of relevant comparison units, discarding the irrelevant potential comparison units, is extremely valuable. Second, even if information on the outcome is available for all comparison units (as it is in our data), the process of searching for the best subset from the comparison group reveals the extent of overlap between the treatment and comparison groups in terms of pretreatment characteristics. Because methods that use the full set of 1 More precisely, to estimate the treatment impact on the treated, the outcome in the untreated state must be independent of the treatment assignment.

The Review of Economics and Statistics, February 2002, 84(1): 151–161 © 2002 by the President and Fellows of Harvard College and the Massachusetts Institute of Technology

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comparison units extrapolate or smooth across the treatment and comparison groups, it is extremely useful to know how many of the comparison units are in fact comparable and hence how much smoothing one’s estimator is expected to perform. The data we use, obtained from LaLonde (1986), are from the National Supported Work (NSW) Demonstration, a labor market experiment in which participants were randomized between treatment (on-the-job training lasting between nine months and a year) and control groups. Following LaLonde, we use the experimental controls to obtain a benchmark estimate for the treatment impact and then set them aside, wedding the treated units from the experiment to comparison units from the Population Survey of Income Dynamics (PSID) and the Current Population Survey (CPS).2 We compare estimates obtained using our nonexperimental methods to the experimental benchmark. We show that most of the nonexperimental comparison units are not good matches for the treated group. We succeed in selecting the comparison units that are most comparable to the treated units and in replicating the benchmark treatment impact. The paper is organized as follows. In section II, we discuss the theory behind our estimation strategy. In section III, we discuss propensity score-matching methods. In section IV, we describe the NSW data, which we then use in section V to implement our matching procedures. Section VI tests the matching assumption and examines the sensitivity of our estimates to the specification of the propensity score. Section VII concludes the paper. II.

Matching Methods

A. The Role of Randomization

A cause is viewed as a manipulation or treatment that brings about a change in the variable of interest, compared to some baseline, called the control (Cox, 1992; Holland, 1986). The basic problem in identifying a causal effect is that the variable of interest is observed under either the treatment or control regimes, but never both. Formally, let i index the population under consideration. Y i1 is the value of the variable of interest when unit i is subject to treatment (1), and Y i0 is the value of the same variable when the unit is exposed to the control (0). The treatment effect for a single unit, ␶ i , is defined as ␶ i ⫽ Y i1 ⫺ Y i0 . The primary treatment effect of interest in nonexperimental settings is the expected treatment effect for the treated population; hence ␶兩 T⫽1 ⫽ E共␶ i 兩T i ⫽ 1兲 ⫽ E共Y i1 兩T i ⫽ 1兲 ⫺ E共Y i0 兩T i ⫽ 1兲, 2 Fraker and Maynard (1987) also conduct an evaluation of nonexperimental methods using the NSW data. Their findings were similar to LaLonde’s.

where T i ⫽ 1 (⫽ 0) if the ith unit was assigned to treatment (control).3 The problem of unobservability is summarized by the fact that we can estimate E(Y i1 兩T i ⫽ 1), but not E(Y i0 兩T i ⫽ 1). The difference, ␶ e ⫽ E(Y i1 兩T i ⫽ 1) ⫺ E(Y i0 兩T i ⫽ 0), can be estimated, but it is potentially a biased estimator of ␶. Intuitively, if Y i0 for the treated and comparison units systematically differs, then in observing only Y i0 for the comparison group we do not correctly estimate Y i0 for the treated group. Such bias is of paramount concern in nonexperimental studies. The role of randomization is to prevent this: Yi1, Yi 0 储Ti f E共Yi0兩Ti ⫽ 0兲 ⫽ E共Yi0兩Ti ⫽ 1兲 ⫽ E共Yi兩Ti ⫽ 0兲, where Y i ⫽ T i Y i1 ⫹ (1 ⫺ T i )Y i0 (the observed value of the outcome) and 储 is the symbol for independence. The treated and control groups do not systematically differ from each other, making the conditioning on T i in the expectation unnecessary (ignorable treatment assignment, in the terminology of Rubin (1977)), and yielding ␶兩 T⫽1 ⫽ ␶ e . 4 B. Exact Matching on Covariates

To substitute for the absence of experimental control units, we assume that data can be obtained for a set of potential comparison units, which are not necessarily drawn from the same population as the treated units but for whom we observe the same set of pretreatment covariates, X i . The following proposition extends the framework of the previous section to nonexperimental settings: Proposition 1 (Rubin, 1977). If for each unit we observe a vector of covariates X i and Y i0 储 T i 兩X i , @i, then the population treatment effect for the treated, ␶兩 T⫽1 , is identified: it is equal to the treatment effect conditional on covariates and on assignment to treatment, ␶兩 T⫽1,X , averaged over the distribution X兩T i ⫽ 1 5. 3 In a nonexperimental setting, the treatment and comparison samples are either drawn from distinct groups or are nonrandom samples from a common population. In the former case, typically the interest is the treatment impact for the group from which the treatment sample is drawn. In the latter case, the interest could be in knowing the treatment effect for the subpopulation from which the treatment sample is drawn or the treatment effect for the full population from which both treatment and comparison samples were drawn. In contrast, in a randomized experiment, the treatment and control samples are randomly drawn from the same population, and thus the treatment effect for the treated group is identical to the treatment effect for the untreated group. 4 We are also implicitly making what is sometimes called the stableunit-treatment-value assumption (Rubin, 1980, 1986). This amounts to the assumption that Y i1 (Y i0 ) does not depend upon which units other than i were assigned to the treatment group; that is, there are no within-group spillovers or general equilibrium effects. 5 Randomization implies Y , Y 储 T , but Y 储 T 兩X is all that is required i1 i0 i i0 i i to estimate the treatment effect on the treated. The stronger assumption, Y i1 , Y i0 储 T i 兩X i , would be needed to identify the treatment effect on the comparison group or the overall average. Note that we are estimating the treatment effect for the treatment group as it exists at the time of analysis. We are not estimating any program entry or exit effects that might arise if

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES

Intuitively, this assumes that, conditioning on observable covariates, we can take assignment to treatment to have been random and that, in particular, unobservables play no role in the treatment assignment; comparing two individuals with the same observable characteristics, one of whom was treated and one of whom was not, is by proposition 1 like comparing those two individuals in a randomized experiment. Under this assumption, the conditional treatment effect, ␶兩T⫽1, is estimated by first estimating ␶兩T⫽1,X and then averaging over the distribution of X conditional on T ⫽ 1. One way to estimate this equation would be by matching units on their vector of covariates, X i . In principle, we could stratify the data into subgroups (or bins), each defined by a particular value of X; within each bin, this amounts to conditioning on X. The limitation of this method is that it relies on a sufficiently rich comparison group so that no bin containing a treated unit is without a comparison unit. For example, if all n variables are dichotomous, the number of possible values for the vector X will be 2 n . Clearly, as the number of variables increases, the number of cells increases exponentially, increasing the difficulty of finding exact matches for each of the treated units. C. Propensity Score and Dimensionality Reduction

Rosenbaum and Rubin (1983, 1985a, b) suggest the use of the propensity score—the probability of receiving treatment conditional on covariates—to reduce the dimensionality of the matching problem discussed in the previous section. Proposition 2 (Rosenbaum and Rubin, 1983). Let p(Xi) be the probability of a unit i having been assigned to treatment, defined as p(Xi) ⬅ Pr(Ti ⫽ 1兩Xi) ⫽ E(Ti兩Xi). Then, 共Y i1 , Y i0 兲 储 T i 兩X i f 共Y i1 , Y i0 兲 储 T i 兩p共X i 兲. Proposition 3. ␶兩 T⫽1 ⫽ E p(X) [(␶兩 T⫽1,p(X) )兩T i ⫽ 1]. Thus, the conditional independence result extends to the use of the propensity score, as does by immediate implication our result on the computation of the conditional treatment effect, now ␶兩 T⫽1,p(X) . The point of using the propensity score is that it substantially reduces the dimensionality of the problem, allowing us to condition on a scalar variable rather than in a general n-space. III.

Propensity Score-Matching Algorithms

In the discussion that follows, we assume that the propensity score is known, which of course it is not. The appendix discusses a straightforward method for estimating it.6 the treatment were made more widely available. Estimation of such effects would require additional data as described by Moffitt (1992). 6 Standard errors should adjust for the estimation error in the propensity score and the variation that it induces in the matching process. In the application, we use bootstrap standard errors. Heckman, Ichimura, and Todd (1998) provide asymptotic standard errors for propensity score

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Matching on the propensity score is essentially a weighting scheme, which determines what weights are placed on comparison units when computing the estimated treatment effect: ␶ˆ 兩 T⫽1 ⫽

1 兩N兩

冘 冉 Y ⫺ 兩J1 兩 冘 Y 冊 , i

i僆N

j

i j僆J i

where N is the treatment group, 兩N兩 the number of units in the treatment group, J i is the set of comparison units matched to treatment unit i (see Heckman, Ichimura, and Todd (1998), who discuss more general weighting schemes), and 兩J i 兩 is the number of comparison units in J i . This estimator follows from proposition 3. Expectations are replaced by sample means, and we condition on p(X i ) by matching each treatment unit i to a set of comparison units, J i , with a similar propensity score. Taken literally, conditioning on p(X i ) implies exact matching on p(X i ). This is difficult in practice, so the objective becomes to match treated units to comparison units whose propensity scores are sufficiently close to consider the conditioning on p(X i ) in proposition 3 to be approximately valid. Three issues arise in implementing matching: whether or not to match with replacement, how many comparison units to match to each treated unit, and finally which matching method to choose. We consider each in turn. Matching with replacement minimizes the propensityscore distance between the matched comparison units and the treatment unit: each treatment unit can be matched to the nearest comparison unit, even if a comparison unit is matched more than once. This is beneficial in terms of bias reduction. In contrast, by matching without replacement, when there are few comparison units similar to the treated units, we may be forced to match treated units to comparison units that are quite different in terms of the estimated propensity score. This increases bias, but it could improve the precision of the estimates. An additional complication of matching without replacement is that the results are potentially sensitive to the order in which the treatment units are matched (Rosenbaum, 1995). The question of how many comparison units to match with each treatment unit is closely related. By using a single comparison unit for each treatment unit, we ensure the smallest propensity-score distance between the treatment and comparison units. By using more comparison units, one increases the precision of the estimates, but at the cost of increased bias. One method of selecting a set of comparison units is the nearest-neighbor method, which selects the m comparison units whose propensity scores are closest to the treated unit in question. Another method is caliper matching, which uses all of the comparison units within a predefined propensity score radius (or “caliper”). A benefit of estimators, but in their application paper, Heckman, Ichimura, and Todd (1997) also use bootstrap standard errors.

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caliper matching is that it uses only as many comparison units as are available within the calipers, allowing for the use of extra (fewer) units when good matches are (not) available. In the application that follows, we consider a range of simple estimators. For matching without replacement, we consider low-to-high, high-to-low, and random matching. In these methods, the treated units are ranked (from lowest to highest or highest to lowest propensity score, or randomly). The highest-ranked unit is matched first, and the matched comparison unit is removed from further matching. For matching with replacement, we consider single-nearestneighbor matching and caliper matching for a range of calipers. In addition to using a weighted difference in means to estimate the treatment effect, we also consider a weighted regression using the treatment and matched comparison units, with the comparison units weighted by the number of times that they are matched to a treated unit. A regression can potentially improve the precision of the estimates. The question that remains is which method to select in practice. In general, this depends on the data in question, and in particular on the degree of overlap between the treatment and comparison groups in terms of the propensity score. When there is substantial overlap in the distribution of the propensity score between the comparison and treatment groups, most of the matching algorithms will yield similar results. When the treatment and comparison units are very different, finding a satisfactory match by matching without replacement can be very problematic. In particular, if there are only a handful of comparison units comparable to the treated units, then once these comparison units have been matched, the remaining treated units will have to be matched to comparison units that are very different. In such settings, matching with replacement is the natural choice. If there are no comparison units for a range of propensity scores, then for that range the treatment effect could not be estimated. The application that follows will further clarify the choices that the researcher faces in practice. IV.

The Data

A. The National Supported Work Program

The NSW was a U.S. federally and privately funded program that aimed to provide work experience for individuals who had faced economic and social problems prior to enrollment in the program (Hollister, Kemper, and Maynard, 1984; Manpower Demonstration Research Corporation, 1983).7 Candidates for the experiment were selected on the basis of eligibility criteria, and then were either randomly assigned to, or excluded from, the training program. 7 Four groups were targeted: Women on Aid to Families with Dependent Children (AFDC), former addicts, former offenders, and young school dropouts. Several reports extensively document the NSW program. For a general summary of the findings, see Manpower Demonstration Research Corporation (1983).

TABLE 1.—SAMPLE MEANS AND STANDARD ERRORS FOR MALE NSW PARTICIPANTS

OF

COVARIATES

National Supported Work Sample (Treatment and Control) Dehejia-Wahba Sample Variable

Treatment

Control

Age Years of schooling Proportion of school dropouts Proportion of blacks Proportion of Hispanic Proportion married Number of children No-show variable Month of assignment (Jan. 1978 ⫽ 0) Real earnings 12 months before training Real earnings 24 months before training Hours worked 1 year before training Hours worked 2 years before training Sample size

25.81 (0.52) 10.35 (0.15) 0.71 (0.03) 0.84 (0.03) 0.06 (0.017) 0.19 (0.03) 0.41 (0.07) 0 (0) 18.49 (0.36) 1,689 (235) 2,096 (359) 294 (36) 306 (46) 185

25.05 (0.45) 10.09 (0.1) 0.83 (0.02) 0.83 (0.02) 0.10 (0.019) 0.15 (0.02) 0.37 (0.06) n/a 17.86 (0.35) 1,425 (182) 2,107 (353) 243 (27) 267 (37) 260

Table 1 provides the characteristics of the sample we use, LaLonde’s male sample (185 treated and 260 control observations).8 The table highlights the role of randomization: the distribution of the covariates for the treatment and control groups are not significantly different. We use the two nonexperimental comparison groups constructed by LaLonde (1986), drawn from the CPS and PSID.9 B. Distribution of the Treatment and Comparison Samples

Tables 2 and 3 (rows 1 and 2) present the sample characteristics of the two comparison groups and the treatment group. The differences are striking: the PSID and CPS sample units are eight to nine years older than those in the NSW group, their ethnic composition is different, and they have on average completed high school degrees, whereas NSW participants were by and large high school dropouts, and, most dramatically, pretreatment earnings are much higher for the comparison units than for the treated units, by more than $10,000. A more synoptic way to view these differences is to use the estimated propensity score as a summary statistic. Using the method outlined in the appendix, we estimate the propensity score for the two composite samples (NSW-CPS and NSW-PSID), incorporating the covariates linearly and with some higher-order terms. 8 The data we use are a subsample of the data used in LaLonde (1986). The analysis in LaLonde is based on one year of pretreatment earnings. But, as Ashenfelter (1978) and Ashenfelter and Card (1985) suggest, the use of more than one year of pretreatment earnings is key in accurately estimating the treatment effect, because many people who volunteer for training programs experience a drop in their earnings just prior to entering the training program. Using the LaLonde sample of 297 treated and 425 control units, we exclude the observations for which earnings in 1974 could not be obtained, thus arriving at a reduced sample of 185 treated observations and 260 control observations. Because we obtain this subset by looking at pretreatment covariates, we do not disturb the balance in observed and unobserved characteristics between the experimental treated and control groups. See Dehejia and Wahba (1999) for a comparison of the two samples. 9 These are the CPS-1 and PSID-1 comparison groups from LaLonde’s paper.

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES TABLE 2.—SAMPLE CHARACTERISTICS

Control Sample

Mean No. of Propensity Observations ScoreA

NSW

185

0.37

Full CPS

15992

0.01 (0.02)D

Without replacement: Random

185

Low to high

185

High to low

185

With replacement: Nearest neighbor

119

Caliper, ␦ ⫽ 0.00001

325

Caliper, ␦ ⫽ 0.00005

1043

Caliper, ␦ ⫽ 0.0001

1731

ESTIMATED IMPACTS

AND

FROM THE

NSW

AND

CPS SAMPLES

Age

No School Black Hispanic Degree Married RE74 RE75

U74

U75

25.82

10.35

0.29

0.40

2095

1532

Treatment Effect Regression (Diff. in Treatment Means) Effect 1794B (633) ⫺8498 (583)E

1672C (638) 1066 (554)

0.37 0.51 (0.05) (0.05) 0.37 0.51 (0.05) (0.05) 0.37 0.51 (0.05) (0.05)

1559 (733) 1605 (730) 1559 (733)

1651 (709) 1681 (704) 1651 (709)

0.35 (0.07) 0.36 (0.06) 0.35 (0.06) 0.34 (0.06)

1360 (913) 1119 (875) 1158 (852) 1122 (850)

1375 (907) 1142 (874) 1139 (851) 1119 (843)

0.84

0.06

0.71

33.23 12.03 (0.53) (0.15)

0.07 (0.03)

0.07 (0.02)

0.30 (0.03)

0.71 14017 13651 0.88 0.89 (0.03) (367) (248) (0.03) (0.04)

0.32 (0.03) 0.32 (0.03) 0.32 (0.03)

25.26 10.30 (0.79) (0.23) 25.23 10.28 (0.79) (0.23) 25.26 10.30 (0.79) (0.23)

0.84 (0.04) 0.84 (0.04) 0.84 (0.04)

0.06 (0.03) 0.06 (0.03) 0.06 (0.03)

0.65 (0.05) 0.66 (0.05) 0.65 (0.05)

0.22 (0.04) 0.22 (0.04) 0.22 (0.04)

2305 (495) 2286 (495) 2305 (495)

1687 (341) 1687 (341) 1687 (341)

0.37 (0.03) 0.37 (0.03) 0.37 (0.02) 0.37 (0.02)

25.36 (1.04) 25.26 (1.03) 25.29 (1.03) 25.19 (1.03)

0.84 (0.06) 0.84 (0.06) 0.84 (0.05) 0.84 (0.05)

0.06 (0.04) 0.07 (0.04) 0.07 (0.04) 0.07 (0.04)

0.69 (0.07) 0.69 (0.07) 0.69 (0.06) 0.69 (0.06)

0.17 (0.06) 0.17 (0.06) 0.17 (0.06) 0.17 (0.06)

2407 (727) 2424 (845) 2305 (877) 2213 (890)

1516 (506) 1509 (647) 1523 (675) 1545 (701)

10.31 (0.31) 10.31 (0.30) 10.28 (0.32) 10.36 (0.31)

0.19

155

0.49 (0.07) 0.50 (0.06) 0.49 (0.60) 0.50 (0.06)

Variables: Age, age of participant; School, number of school years; Black, 1 if black, 0 otherwise; Hisp, 1 if Hispanic, 0 otherwise; No degree, 1 if participant had no school degrees, 0 otherwise; Married, 1 if married, 0 otherwise; RE74, real earnings (1982US$) in 1974; RE75, real earnings (1982US$) in 1975; U74, 1 if unemployed in 1974, 0 otherwise; U75, 1 if unemployed in 1975, 0 otherwise; and RE78, real earnings (1982US$) in 1978. (A) The propensity score is estimated using a logit of treatment status on: Age, Age2, Age3, School, School2, Married, No degree, Black, Hisp, RE74, RE75, U74, U75, School 䡠 RE74. (B) The treatment effect for the NSW sample is estimated using the experimental control group. (C) The regression treatment effect controls for all covariates linearly. For matching with replacement, weighted least squares is used, where treatment units are weighted at 1 and the weight for a control is the number of times it is matched to a treatment unit. (D) The standard error applies to the difference in means between the matched and the NSW sample, except in the last two columns, where the standard error applies to the treatment effect. (E) Standard errors for the treatment effect and regression treatment effect are computed using a bootstrap with 500 replications.

Figures 1 and 2 provide a simple diagnostic on the data examined, plotting the histograms of the estimated propensity scores for the NSW-CPS and NSW-PSID samTABLE 3.—SAMPLE CHARACTERISTICS

Control Sample

Mean No. of Propensity Observations ScoreA

NSW

185

0.37

Full PSID

2490

0.02 (0.02)D

Without replacement: Random

185

Low to high

185

High to low

185

With replacement: Nearest Neighbor

56

Caliper, ␦ ⫽ 0.00001

85

Caliper, ␦ ⫽ 0.00005

193

Caliper, ␦ ⫽ 0.0001

337

Caliper, ␦ ⫽ 0.001

2021

AND

ples. Note that the histograms do not include the comparison units (11,168 units for the CPS and 1,254 units for the PSID) whose estimated propensity score is less

ESTIMATED IMPACTS

FROM THE

NSW

Age

No RE74 School Black Hispanic Degree Married US$

25.82

10.35

0.84

PSID SAMPLES

RE75 US$

U74

U75

Treatment Effect Regression (Diff. in Treatment Means) Effect

2095

1532

0.87 (0.03)

1794B (633) 19429 19063 0.10 0.09 ⫺15205 (449) (361) (0.04) (0.03) (657)E

0.60 (0.05) 0.60 (0.05) 0.60 (0.05)

0.52 (0.05) 0.52 (0.05) 0.52 (0.05)

4659 (554) 4659 (554) 4659 (554)

3263 0.40 0.40 (361) (0.05) (0.05) 3263 0.40 0.40 (361) (0.05) (0.05) 3263 0.40 0.40 (361) (0.05) (0.05)

⫺916 (1035) ⫺916 (1135) ⫺916 (1135)

77 (983) 77 (983) 77 (983)

0.53 (0.12) 0.53 (0.12) 0.53 (0.11) 0.53 (0.11) 0.53 (0.10)

0.14 (0.11) 0.13 (0.12) 0.14 (0.10) 0.14 (0.09) 0.13 (0.07)

2206 (1248) 2216 (1859) 2247 (1983) 2228 (1965) 2398 (2950)

1801 (963) 1819 (1896) 1778 (1869) 1763 (1777) 1882 (2943)

1890 (1202) 1893 (1198) 1928 (1196) 1973 (1191) 1824 (1187)

2315 (1131) 2327 (1129) 2349 (1121) 2411 (1122) 2333 (1101)

0.06

0.71

0.19

34.85 12.12 0.25 (0.57) (0.16) (0.03)

0.03 (0.02)

0.31 (0.03)

0.25 (0.03) 0.25 (0.03) 0.25 (0.03)

29.17 (0.90) 29.17 (0.90) 29.17 (0.90)

10.30 0.68 (0.25) (0.04) 10.30 0.68 (0.25) (0.04) 10.30 0.68 (0.25) (0.04)

0.07 (0.03) 0.07 (0.03) 0.07 (0.03)

0.70 (0.07) 0.70 (0.08) 0.70 (0.06) 0.70 (0.05) 0.70 (0.03)

24.81 (1.78) 24.85 (1.80) 24.83 (2.17) 24.92 (2.30) 24.98 (2.37)

10.72 (0.54) 10.72 (0.56) 10.72 (0.60) 10.73 (0.67) 10.74 (0.70)

0.09 (0.05) 0.09 (0.05) 0.09 (0.04) 0.09 (0.04) 0.09 (0.04)

0.78 (0.11) 0.78 (0.12) 0.78 (0.11) 0.78 (0.11) 0.79 (0.09)

AND

0.29

0.54 (0.11) 0.54 (0.10) 0.54 (0.09) 0.54 (0.07) 0.53 (0.06)

0.40

0.69 (0.11) 0.69 (0.11) 0.69 (0.09) 0.70 (0.08) 0.69 (0.06)

1672C (638) 4 (1014)

(A) The propensity score is estimated using a logit of treatment status on: Age, Age2, School, School2, Married, No degree, Black, Hisp, RE74, RE742, RE75, RE752, U74, U75, U74 䡠 Hisp. (B) The treatment effect for the NSW sample is estimated using the experimental control group. (C) The regression treatment effect controls for all covariates linearly. For matching with replacement, weighted least squares is used, where treatment units are weighted at 1 and the weight for a control is the number of times it is matched to a treatment unit. (D) The standard error applies to the difference in means between the matched and the NSW sample, except in the last two columns, where the standard error applies to the treatment effect. (E) Standard errors for the treatment effect and regression treatment effect are computed using a bootstrap with 500 replications.

156

THE REVIEW OF ECONOMICS AND STATISTICS FIGURE 1.—HISTOGRAM OF ESTIMATED PROPENSITY SCORE, NSW AND CPS

FIGURE 3.—PROPENSITY SCORE FOR TREATED AND MATCHED COMPARISON UNITS, RANDOM WITHOUT REPLACEMENT

than the minimum estimated propensity score for the treated units. As well, the first bins of both diagrams contain most of the remaining comparison units (4,398 for the CPS and 1,007 for the PSID). Hence, it is clear that very few of the comparison units are comparable to the treated units. In fact, one of the strengths of the propensity score method is that it dramatically highlights this fact. In comparing the other bins, we note that the number of comparison units in each bin is approximately equal to the number of treated units in the NSW-CPS sample, but, in the NSW-PSID sample, many of the upper bins have far more treated units than comparison units. This last observation will be important in interpreting the results of the next section.

Figures 3 to 6 provide a snapshot of the matching methods described in section III and applied to the NSW-CPS sample, where the horizontal axis displays treated units (indexed from lowest to highest estimated propensity score) and the vertical axis depicts the propensity scores of the treated units and their matched comparison counterparts. (The corresponding figures for the NSW-PSID sample look very similar.) Figures 3 to 5, which consider matching without replacement, share the common feature that the first 100 or so treated units are well matched to their comparison group counterparts: the solid and the dashed lines virtually overlap. But the

FIGURE 2.—HISTOGRAM OF ESTIMATED PROPENSITY SCORE, NSW AND PSID

FIGURE 4.—PROPENSITY SCORE FOR TREATED AND MATCHED COMPARISON UNITS, LOWEST TO HIGHEST

V.

Matching Results

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES FIGURE 5.—PROPENSITY SCORE FOR TREATED AND MATCHED COMPARISON UNITS, HIGHEST TO LOWEST

treated units with estimated propensity scores of 0.4 or higher are not well matched. In figure 3, units that are randomly selected to be matched earlier find better matches, but those matched later are poorly matched because the few comparison units comparable to the treated units have already been used. Likewise, in figure 4, where units are matched from lowest to highest, treated units in the 140th to 170th positions are forced to use comparison units with ever-higher propensity scores. Finally, for the remaining units (from approximately the 170th position on), the comparison units with high propensity scores are exhausted and matches are found among comparison units with much lower estimated propensity scores. Similarly, when we match from highest to lowest, the quality of matches begins to decline after the first few treated units, until we reach treated units whose propensity score is (approximately) 0.4. Figure 6 depicts the matching achieved by the nearestmatch method.10 We note immediately that by matching with replacement we are able to avoid the deterioration in the quality of matches noted in figures 3 to 5; the solid and the dashed lines largely coincide. Looking at the line depicting comparison units more carefully, we note that it has flat sections that correspond to ranges in which a single comparison unit is being matched to more than one treated unit. Thus, even though there is a smaller sample size, we are better able to match the distribution of the propensity scores of the treated units. In table 2, we explore the matched samples and the estimated treatment impacts for the CPS. From rows 1 and 10 Note that, in implementing this method, if the set of comparison units within a given caliper is empty for a treated unit, we match it to the nearest comparison unit. The alternative is to drop unmatched treated units, but then one would no longer be estimating the treatment effect for the entire treated group.

157

FIGURE 6.—PROPENSITY SCORE FOR TREATED AND MATCHED COMPARISON UNITS, NEAREST MATCH

2, we already noted that the CPS sample is very different from the NSW. The aim of matching is to choose subsamples whose characteristics more closely resemble the NSW. Rows 3 to 5 of table 2 depict the matched samples that emerge from matching without replacement. Note that the characteristics of these samples are essentially identical, suggesting that these three methods yield the same comparison groups. (Figures 3 to 5 obscure this fact because they compare the order in which units are matched, not the resulting comparison groups.) The matched samples are much closer to the NSW sample than the full CPS comparison group. The matched CPS group has an age of 25.3 (compared with 25.8 and 33.2 for the NSW and full CPS samples), its ethnic composition is the same as the NSW sample (note especially the difference in the full CPS in terms of the variable Black), no degree and marital status align, and, perhaps most significantly, the pretreatment earnings are similar for both 1974 and 1975.11 None of the differences between the matched groups and the NSW sample are statistically significant.12 Looking at the nearestmatch and caliper methods, little significant improvement can be discerned, although most of the variables are marginally better matched. This suggests that the observation made regarding figure 1 (that the CPS, in fact, has a 11 The matched earnings, like the NSW sample, exhibit the Ashenfelter (1978) “dip” in earnings in the year prior to program participation. 12 Note that both LaLonde (1986) and Fraker and Maynard (1987) attempt to use “first-generation” matching methods to reduce differences between the treatment and comparison groups. LaLonde creates subsets of CPS-1 and PSID-1 by matching single characteristics (employment status and income). Dehejia and Wahba (1999) demonstrates that significant differences remain between the reduced comparison groups and the treatment group. Fraker and Maynard match on predicted earnings. Their matching method also fails to balance pretreatment characteristics (especially earnings) between the treatment and comparison group. (See Fraker and Maynard (1987, p. 205).)

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THE REVIEW OF ECONOMICS AND STATISTICS

sufficient number of comparison units overlapping with the NSW) is borne out in terms of the matched sample. Turning to the estimates of the treatment impact, in row 1 we see that the benchmark estimate of the treatment impact from the randomized experiment is $1,794. For the full CPS comparison group, the estimate is ⫺$8,498 using a difference in means and $1,066 using regression adjustment. The raw estimate is very misleading when compared with the benchmark, although the regression-adjusted estimate is better. The matching estimates are closer. For the without-replacement estimators, the estimate ranges from $1,559 to $1,605 for the difference in means and from $1,651 to $1,681 for the regression-adjusted estimator. The nearest-neighbor with-replacement estimates are $1,360 and $1,375. Essentially, these methods succeed by picking out the subset of the CPS that is the best comparison for the NSW. Based on these estimates, one might conclude that matching without replacement is the best strategy. The reason why all the methods perform well is that there is reasonable overlap between the treatment and CPS comparison samples. As we will see, for the PSID comparison group the estimates are very different. When using caliper matching, a larger comparison group is selected: 325 for a caliper of 0.00001, 1,043 for a caliper of 0.0001, and 1,731 for a caliper of 0.0001. In terms of the characteristics of the sample, few significant differences are observed, although we know that the quality of the matches in terms of the propensity score is poorer. This is reflected in the estimated treatment impact which ranges from $1,122 to $1,149. Using the PSID sample (table 3), somewhat different conclusions are reached. Like the CPS, the PSID sample is very different from the NSW sample. Unlike the CPS, the matched-without-replacement samples are not fully comparable to the NSW. They are reasonably comparable in terms of age, schooling, and ethnicity, but, in terms of pretreatment earnings, we observe a large (and statistically significant) difference. As a result, it is not surprising that the estimates of the treatment impact, both by a difference in means and through regression adjustment, are far from the experimental benchmark (ranging from $⫺916 to $77). In contrast, the matched-with-replacement samples use even fewer (56) comparison units, but they are able to match the pretreatment earnings of the NSW sample and the other variables as well. This corresponds to our observation regarding figure 2, namely that there are very few comparison units in the PSID that are similar to units in the NSW; when this is the case, we expect more sensitivity to the method used to match observations, and we expect matching with replacement to perform better. The treatment impact as estimated by the nearest-neighbor method through a difference in means ($1,890) is very similar to the experimental benchmark, but differs by $425 when estimated through regression adjustment (although it is still closer than the estimates in rows 1 to 4). The difference in the two esti-

mates is less surprising when we consider the sample size involved: we are using only 56 of the 2,490 potential comparison units from the PSID. For the PSID, caliper matching also performs well. The estimates range from $1,824 to $2,411. Slightly lower standard errors are achieved than nearest-neighbor matching. In conclusion, propensity score-matching methods are able to yield reasonably accurate estimates of the treatment impact, especially when contrasted with the range of estimates that emerged in LaLonde’s paper. By selecting an appropriate subset from the comparison group, a simple difference in means yields an estimate of the treatment effect close to the experimental benchmark. The choice among matching methods becomes important when there is minimal overlap between the treatment and comparison groups. When there is minimal overlap, matching with replacement emerges as a better choice. In principle, caliper matching can also improve standard errors relative to nearest-neighbor matching, although at the cost of greater bias. At least in our application, the benefits of caliper matching were limited. When there is greater overlap, the withoutreplacement estimators perform as well as the nearestneighbor method, and their standard errors are somewhat lower than the nearest-neighbor method, so, when many comparison units overlap with the treatment group, matching without replacement is probably a better choice. VI.

Testing

A. Testing the Matching Assumption

The special structure of the data we use allows us to test the assumption that underlies propensity score matching. Because we have both an experimental control group (which we use to estimate the experimental benchmark estimate in row 1 of tables 2 and 3) and two nonexperimental comparison groups, we can test the assumption that, conditional on the propensity score, earnings in the nontreated state are independent of assignment to treatment (Heckman et al., 1998; Heckman, Ichimura, and Todd, 1997). In practice, this amounts to comparing earnings for the experimental control group with earnings for the two comparison groups using the propensity score. We apply the propensity score specifications from section V to the composite sample of NSW control units and CPS (or PSID) comparison units. Following Heckman et al. (1998), we compute the bias within strata defined on the propensity score. The bias estimates—earnings for the experimental control group less earnings for the nonexperimental comparison group conditional on the estimated propensity score—are presented graphically in figures 7 and 8. For both the CPS and PSID, we see a range of bias estimates that are particularly large for low values of the estimated propensity score. This group represents those who are least likely to have been in the treatment group, and, based on tables 2 and 3, this group has much higher earnings than those in the NSW. But none of the bias estimates are statistically significant.

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES FIGURE 7.—BIAS ESTIMATES, CPS

Of course, in practice a researcher will not be able to perform such tests, but it is a useful exercise when possible. It confirms that matching succeeds because the nontreated earnings of the comparison and control groups are not statistically significantly different, conditional on the estimated propensity score. B. Testing Sensitivity to the Specification of the Propensity Score

One potential limitation of propensity score methods is the need to estimate the propensity score. In LaLonde’s (1986) paper, one of the cautionary findings was the sensitivity of the nonexperimental estimators to the specification adopted. The appendix suggests a simple method to choose a specification for the propensity score. In table 4, we consider sensitivity of the estimates to the choice of specification. In table 4, we consider dropping in succession the interactions and cubes, the indicators for unemployment, and finally squares of covariates in the specification. The final specification for both samples contains the covariates linearly. For the CPS, the estimate bounces from $1,037 to $1,874, and for the PSID from $1,004 to $1,845. The estimates are not particularly sensitive, especially compared to the variability of estimators in LaLonde’s original paper. Furthermore, a researcher who did not have the benefit of the experimental benchmark estimate would choose the full-specification estimates because (as explained in the appendix) these specifications succeed in balancing all the observed covariates, conditional on the estimated propensity score. VII.

Conclusion

This paper has presented a propensity score-matching method that is able to yield accurate estimates of the

159

treatment effect in nonexperimental settings in which the treated group differs substantially from the pool of potential comparison units. The method is able to pare the large comparison group down to the relevant comparisons without using information on outcomes, thereby, if necessary, allowing outcome data to be collected only for the relevant subset of comparison units. Of course, the quality of the estimate that emerges from the resulting comparison is limited by the overall quality of the comparison group that is used. Using LaLonde’s (1986) data set, we demonstrate the ability of this technique to work in practice. Even though in a typical application the researcher would not have the benefit of checking his or her estimate against the experimental-benchmark estimate, the conclusion of our analysis is that it is extremely valuable to check the comparability of the treatment and comparison units in terms of pretreatment characteristics, which the researcher can check in most applications. In particular, the propensity score method dramatically highlights the fact that most of the comparison units are very different from the treated units. In addition to this, when there are very few comparison units remaining after having discarded the irrelevant comparison units, the choice of matching algorithm becomes important. We demonstrate that, when there are a sufficient number of relevant comparison units (in our application, when using the CPS), the nearest-match method does no worse than the matchingwithout-replacement methods that would typically be applied, and, in situations in which there are very few relevant comparison units (in our application, when using the PSID), matching with replacement fares better than the alternatives. Extensions of matching with replacement (caliper matching), although interesting in principal, were of little value in our application.

FIGURE 8.—ESTIMATED BIAS, PSID

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THE REVIEW OF ECONOMICS AND STATISTICS TABLE 4.—SENSITIVITY

OF

MATCHING

Specification CPS Full specification Dropping interactions and cubes Dropping indicators: Dropping squares PSID Full specification Dropping interactions and cubes Dropping indicators: Dropping squares

WITH

REPLACEMENT

TO THE

SPECIFICATION

OF THE

ESTIMATED PROPENSITY SCORE

Number of Observations

Difference-in-Means Treatment Effect (Standard Error)B

Regression Treatment EffectA (Standard Error)B

119 124 142 134

1360 (633) 1037 (1005) 1874 (911) 1637 (944)

1375 (638) 1109 (966) 1529 (928) 1705 (965)

56 61 65 69

1890 (1202) 1004 (2412) 1845 (1720) 1428 (1126)

2315 (1131) 1729 (3621) 1592 (1624) 1400 (1157)

For all specifications other than the full specifications, some covariates are not balanced across the treatment and comparison groups. (A) The regression treatment effect controls for all covariates linearly. Weighted least squares is used where treatment units are weighted at 1 and the weight for a control is the number of times it is matched to a treatment unit. (B) Standard errors for the treatment effect and regression treatment effect are computed using a bootstrap with 500 replications.

It is something of an irony that the data that we use were originally employed by LaLonde (1986) to demonstrate the failure of standard nonexperimental methods in accurately estimating the treatment effect. Using matching methods on both of his samples, we are able to replicate the experimental benchmark, but beyond this we focus attention on the value of flexibly adjusting for observable differences between the treatment and comparison groups. The process of trying to find a subset of the PSID group comparable to the NSW units demonstrated that the PSID is a poor comparison group, especially when compared to the CPS. Given the success of propensity score methods in this application, how might a researcher choose which method to use in other settings? An important issue is whether the assumption of selection on observable covariates is valid, or whether the selection process depends on variables that are unobserved (Heckman and Robb, 1985). Only when the researcher is comfortable with the former assumption do propensity score methods come into play. Even then, the researcher still can use standard regression techniques with suitably flexible functional forms (Cain, 1975; Barnow, Cain, and Goldberger, 1980). The methods that we discuss in this paper should be viewed as a complement to the standard techniques in the researcher’s arsenal. By starting with a propensity score analysis, the researcher will have a better sense of the extent to which the treatment and comparison groups overlap and consequently of how sensitive estimates will be to the choice of functional form. REFERENCES Ashenfelter, Orley, “Estimating the Effects of Training Programs on Earnings,” this REVIEW 60:1 (February 1978), 47–57. Ashenfelter, Orley, and D. Card, “Using the Longitudinal Structure of Earnings to Estimate the Effect of Training Programs,” this REVIEW 67:4 (November 1985), 648–660. Barnow, Burt, “The Impact of CETA Programs on Earnings: A Review of the Literature,” Journal of Human Resources 22:2 (Spring 1987), 157–193. Barnow, Burt, Glen Cain, and Arthur Goldberger, “Issues in the Analysis of Selectivity Bias,” (pp. 42–59), in Ernst W. Stromsdorfer and George Farkas (Eds.), Evaluation Studies Review Annual, 5 (Beverly Hills: Sage Publications, 1980).

Bassi, Laurie, “Estimating the Effects of Training Programs with Nonrandom Selection,” this REVIEW 66:1 (February 1984), 36–43. Cain, Glen, “Regression and Selection Models to Improve Nonexperimental Comparisons” (pp. 297–317), in C. A. Bennett and A. A. Lumsdaine (Eds.), Evaluation and Experiments: Some Critical Issues in Assessing Social Programs (New York: Academic Press, 1975). Cave, George, and Hans Bos, “The Value of a GED in a Choice-Based Experimental Sample,” (New York: Manpower Demonstration Research Corporation, 1995). Cochran, W. G., and D. B. Rubin, “Controlling Bias in Observational Studies: A Review,” Sankhya, ser. A, 35:4 (December 1973), 417–446. Cox, D. R., “Causality: Some Statistical Aspects,” Journal of the Royal Statistical Society, series A, 155, part 2 (1992), 291–301. Czajka, John, Sharon M. Hirabayashi, Roderick J. A. Little, and Donald B. Rubin, “Projecting from Advance Data Using Propensity Modeling: An Application to Income and Tax Statistics,” Journal of Business and Economic Statistics 10:2 (April 1992), 117–131. Dehejia, Rajeev, and Sadek Wahba, “An Oversampling Algorithm for Non-experimental Causal Studies with Incomplete Matching and Missing Outcome Variables,” Harvard University mimeograph (1995). , “Causal Effects in Non-Experimental Studies: Re-Evaluating the Evaluation of Training Programs,” Journal of the American Statistical Association 94:448 (December 1999), 1053–1062. Fraker, T., and R. Maynard, “Evaluating Comparison Group Designs with Employment-Related Programs,” Journal of Human Resources 22 (1987), 194–227. Friedlander, Daniel, David Greenberg, and Philip Robins, “Evaluating Government Training Programs for the Economically Disadvantaged,” Journal of Economic Literature 35:4 (December 1997), 1809–1855. Heckman, James, Hidehiko Ichimura, Jeffrey Smith, and Petra Todd, “Sources of Selection Bias in Evaluating Social Programs: An Interpretation of Conventional Measures and Evidence on the Effectiveness of Matching as a Program Evaluation Method,” Proceedings of the National Academy of Sciences 93:23 (November 1996), 13416–13420. , “Characterizing Selection Bias Using Experimental Data,” Econometrica 66:5 (September 1998), 1017–1098. Heckman, James, Hidehiko Ichimura, and Petra Todd, “Matching as an Econometric Evaluation Estimator: Evidence from Evaluating a Job Training Programme,” Review of Economic Studies 64:4 (October 1997), 605–654. , “Matching as an Econometric Evaluation Estimator,” Review of Economic Studies 65:2 (April 1998), 261–294. Heckman, James, and Richard Robb, “Alternative Methods for Evaluating the Impact of Interventions” (pp. 63–113), in J. Heckman and B. Singer (Eds.), Longitudinal Analysis of Labor Market Data, Econometric Society Monograph, No. 10 (Cambridge, UK: Cambridge University Press, 1985).

PROPENSITY SCORE-MATCHING METHODS FOR NONEXPERIMENTAL CAUSAL STUDIES Holland, Paul W., “Statistics and Causal Inference,” Journal of the American Statistical Association 81:396 (December 1986), 945– 960. Hollister, Robinson, Peter Kemper, and Rebecca Maynard, The National Supported Work Demonstration (Madison, WI: University of Wisconsin Press, 1984). LaLonde, Robert, “Evaluating the Econometric Evaluations of Training Programs,” American Economic Review 76:4 (September 1986), 604–620. Manpower Demonstration Research Corporation, Summary and Findings of the National Supported Work Demonstration (Cambridge, MA: Ballinger, 1983). Moffitt, Robert, “Evaluation Methods for Program Entry Effects” (pp. 231–252), in Charles Manski and Irwin Garfinkel (Eds.), Evaluating Welfare and Training Programs (Cambridge, MA: Harvard University Press, 1992). Raynor, W. J., “Caliper Pair-Matching on a Continuous Variable in Case Control Studies,” Communications in Statistics: Theory and Methods 12:13 (June 1983), 1499–1509. Rosenbaum, Paul, Observational Studies (New York: Springer Verlag, 1995). Rosenbaum, P., and D. Rubin, “The Central Role of the Propensity Score in Observational Studies for Causal Effects,” Biometrika 70:1 (April 1983), 41–55. , “Constructing a Control Group Using Multivariate Matched Sampling Methods that Incorporate the Propensity,” American Statistician 39:1 (February 1985a), 33–38. , “The Bias Due to Incomplete Matching,” Biometrics 41 (March 1985b), 103–116. Rubin, D., “Matching to Remove Bias in Observational Studies,” Biometrics 29 (March 1973), 159–183. , “Assignment to a Treatment Group on the Basis of a Covariate,” Journal of Educational Statistics 2:1 (Spring 1977), 1–26. , “Using Multivariate Matched Sampling and Regression Adjustment to Control Bias in Observation Studies,” Journal of the American Statistical Association 74:366 (June 1979), 318–328. , “Discussion of Randomization Analysis of Experimental Data: The Fisher Randomization Test, by D. Basu,” Journal of the American Statistical Association 75:371 (September 1980), 591– 593. , “Discussion of Holland (1986),” Journal of the American Statistical Association 81:396 (December 1986), 961–964. Westat, “Continuous Longitudinal Manpower Survey Net Impact Report No. 1: Impact on 1977 Earnings of New FY 1976 CETA Enrollees in Selected Program Activities,” report prepared for U.S. DOL under contract 23-24-75-07 (1981).

APPENDIX: ESTIMATING THE PROPENSITY SCORE The first step in estimating the treatment effect is to estimate the propensity score. Any standard probability model can be used (for example, logit or probit). It is important to remember that the role of the propensity score is only to reduce the dimensions of the conditioning; as such, it has no behavioral assumptions attached to it. For ease of estimation, most applications in the statistics literature have concentrated on the logit model: e␭h共X i兲 Pr共Ti ⫽ 1兩Xi 兲 ⫽ , 1 ⫹ e␭h共X i兲 where T i is the treatment status and h(X i ) is made up of linear and higher-order terms of the covariates on which we condition to obtain an ignorable treatment assignment.13 13 Because we allow for higher-order terms in X, this choice is not very restrictive. By rearranging and taking logs, we obtain ln(Pr(T i ⫽ 1兩X i )/1 ⫺ Pr(T i ⫽ 1兩X i )) ⫽ ␭h(X i ). A Taylor-series expansion allows us an arbitrarily precise approximation. See also Rosenbaum and Rubin (1983).

161

In estimating the propensity score through a probability model, the choice of which interaction or higher-order term to include is determined solely by the need to condition fully on the observable characteristics that make up the assignment mechanism. The following proposition forms the basis of the algorithm we use to estimate the propensity score (Rosenbaum and Rubin, 1983): Proposition A: X 储 T兩p共X兲. Proof: From the definition of p(X) in proposition 2: E共T i 兩X i , p共X i 兲兲 ⫽ E共T i 兩X i 兲 ⫽ p共X i 兲. The algorithm works as follows. Starting with a parsimonious logistic function with linear covariates to estimate the score, rank all observations by the estimated propensity score (from lowest to highest). Divide the observations into strata such that within each stratum the difference in propensity score for treated and comparison observations is insignificant. Proposition A tells us that within each stratum the distribution of the covariates should be approximately the same across the treated and comparison groups, once the propensity score is controlled for. Within each stratum, we can test for statistically significant differences between the distribution of covariates for treated and comparison units; operationally, t-tests on differences in the first moments are often sufficient, but a joint test for the difference in means for all the variables within each stratum could also be performed.14 When the covariates are not balanced within a particular stratum, the stratum may be too coarsely defined; recall that proposition A deals with observations with an identical propensity score. The solution adopted is to divide the stratum into finer strata and test again for no difference in the distribution of the covariates within the finer strata. If, however, some covariates remain unbalanced for many strata, the score may be poorly estimated, which suggests that additional terms (interaction or higher-order terms) of the unbalanced covariates should be added to the logistic specification to control better for these characteristics. This procedure is repeated for each given stratum until the covariates are balanced. The algorithm is summarized next. A Simple Algorithm for Estimating the Propensity Score 1. Start with a parsimonious logit specification to estimate the score. 2. Sort data according to estimated propensity score (ranking from lowest to highest). 3. Stratify all observations such that estimated propensity scores within a stratum for treated and comparison units are close (no significant difference); for example, start by dividing observations into strata of equal score range (0–0.2, . . . , 0.8–1). 4. Statistical test: for all covariates, differences in means across treated and comparison units within each stratum are not significantly different from zero. a. If covariates are balanced between treated and comparison observations for all strata, stop. b. If covariates are not balanced for some stratum, divide the stratum into finer strata and reevaluate. c. If a covariate is not balanced for many strata, modify the logit by adding interaction terms and/or higher-order terms of the covariate and reevaluate. A key property of this procedure is that it uses a well-defined criterion to determine which interaction terms to use in the estimation, namely those terms that balance the covariates. It also makes no use of the outcome variable, and embodies one of the specification tests proposed by LaLonde (1986) and others in the context of evaluating the impact of training on earnings, namely to test for the regression-adjusted difference in the earnings prior to treatment. 14

More generally, one can also consider higher moments or interactions.

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Does Coordination of Welfare Services Delivery Make a Difference for Extremely Disadvantaged Jobseekers? Evidence from the ‘YP 4 ’ Trial. Economic Record 89:287, 469-489. [Crossref] 804. Laura G. Hill, Robert Rosenman, Vidhura Tennekoon, Bidisha Mandal. 2013. Selection Effects and Prevention Program Outcomes. Prevention Science 14:6, 557-569. [Crossref] 805. José M. Cansino, Jaime Lopez-Melendo, María del P. Pablo-Romero, Antonio Sánchez-Braza. 2013. An economic evaluation of public programs for internationalization: The case of the Diagnostic program in Spain. Evaluation and Program Planning 41, 38-46. [Crossref] 806. Cristina Borra, Almudena Sevilla, Jonathan Gershuny. 2013. Calibrating Time-Use Estimates for the British Household Panel Survey. Social Indicators Research 114:3, 1211-1224. [Crossref] 807. Kornelius Kraft, Julia Lang. 2013. Profit Sharing and Training*. Oxford Bulletin of Economics and Statistics 75:6, 940-961. [Crossref] 808. Jasmin Kantarevic, Boris Kralj. 2013. 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Medicaid Home Visitation and Maternal and Infant Healthcare Utilization. American Journal of Preventive Medicine 45:4, 441-447. [Crossref] 836. C. Barnabe, N. X. Thanh, A. Ohinmaa, J. Homik, S. G. Barr, L. Martin, W. P. Maksymowych. 2013. Healthcare service utilisation costs are reduced when rheumatoid arthritis patients achieve sustained remission. Annals of the Rheumatic Diseases 72:10, 1664-1668. [Crossref] 837. Eva Dettmann, Jutta Günther. 2013. Subsidized vocational training: Stepping stone or trap? Assessing empirical effects using matching techniques. Swiss Journal of Economics and Statistics 149:4, 405-443. [Crossref] 838. Mary E. Costantino, Beth Frey, Benjamin Hall, Philip Painter. 2013. The Influence of a Postdischarge Intervention on Reducing Hospital Readmissions in a Medicare Population. Population Health Management 16:5, 310-316. [Crossref] 839. Sriram Thirumalai, Kingshuk K. Sinha. 2013. To Personalize or Not to Personalize Online Purchase Interactions: Implications of Self-Selection by Retailers. Information Systems Research 24:3, 683-708. [Crossref] 840. Sonja Gensler, Peter Leeflang, Bernd Skiera. 2013. Comparing methods to separate treatment from self-selection effects in an online banking setting. Journal of Business Research 66:9, 1272-1278. [Crossref] 841. Al Dobson, Audrey M. El-Gamil, Matthew T. Shimer, Joan E. DaVanzo, Aris Q. Urbanes, Gerald A. Beathard, Terry Foust Litchfield. 2013. Clinical and Economic Value of Performing Dialysis Vascular Access Procedures in a Freestanding Office-Based

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1201. Sinan Gemici, Jay W. Rojewski. 2010. Contributions of Cooperative Education in Preparing At-Risk Students for Post-High School Transition. Journal of Education for Students Placed at Risk (JESPAR) 15:3, 241-258. [Crossref] 1202. Qin Gao, Fuhua Zhai, Irwin Garfinkel. 2010. How Does Public Assistance Affect Family Expenditures? The Case of Urban China. World Development 38:7, 989-1000. [Crossref] 1203. Rebecca J. Hannagan, Jamie P. Pimlott, Levente Littvay. 2010. Does an EMILY's List Endorsement Predict Electoral Success, or Does EMILY Pick the Winners?. PS: Political Science & Politics 43:03, 503-508. [Crossref] 1204. Javier Becerril, Awudu Abdulai. 2010. The Impact of Improved Maize Varieties on Poverty in Mexico: A Propensity ScoreMatching Approach. World Development 38:7, 1024-1035. [Crossref] 1205. Dohoon Lee. 2010. The early socioeconomic effects oftTeenage childbearing. Demographic Research 23, 697-736. [Crossref] 1206. Richard Funderburg, Heather MacDonald. 2010. 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Liliana Herrera, Maria Felisa Muñoz-Doyague, Mariano Nieto. 2010. Mobility of public researchers, scientific knowledge transfer, and the firm's innovation process. Journal of Business Research 63:5, 510-518. [Crossref] 1212. Lingwen Huang, Yang Yao. 2010. Impacts of privatization on employment: evidence from China. Journal of Chinese Economic and Business Studies 8:2, 133-156. [Crossref] 1213. Mark Berends, Ellen Goldring, Marc Stein, Xiu Cravens. 2010. Instructional Conditions in Charter Schools and Students’ Mathematics Achievement Gains. American Journal of Education 116:3, 303-335. [Crossref] 1214. Sandra Garcia, Jennifer Hill. 2010. Impact of conditional cash transfers on children's school achievement: evidence from Colombia. Journal of Development Effectiveness 2:1, 117-137. [Crossref] 1215. Fabio Veras Soares, Rafael Perez Ribas, Guilherme Issamu Hirata. 2010. Impact evaluation of a rural conditional cash transfer programme on outcomes beyond health and education. 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1226. Soo-yong Byun. 2010. Does policy matter in shadow education spending? Revisiting the effects of the high school equalization policy in South Korea. Asia Pacific Education Review 11:1, 83-96. [Crossref] 1227. Matthew W. Epperson, Nabila El-Bassel, Mingway Chang, Louisa Gilbert. 2010. Examining the Temporal Relationship Between Criminal Justice Involvement and Sexual Risk Behaviors among Drug-Involved Men. Journal of Urban Health 87:2, 324-336. [Crossref] 1228. R. Callahan, L. Wilkinson, C. Muller. 2010. Academic Achievement and Course Taking Among Language Minority Youth in U.S. Schools: Effects of ESL Placement. Educational Evaluation and Policy Analysis 32:1, 84-117. [Crossref] 1229. S. R. Ou, A. J. Reynolds. 2010. Grade Retention, Postsecondary Education, and Public Aid Receipt. Educational Evaluation and Policy Analysis 32:1, 118-139. [Crossref] 1230. Richard G. Funderburg, Hilary Nixon, Marlon G. Boarnet, Gavin Ferguson. 2010. New highways and land use change: Results from a quasi-experimental research design. Transportation Research Part A: Policy and Practice 44:2, 76-98. [Crossref] 1231. Akhter Ali, Awudu Abdulai. 2010. The Adoption of Genetically Modified Cotton and Poverty Reduction in Pakistan. Journal of Agricultural Economics 61:1, 175-192. [Crossref] 1232. Gesine Stephan. 2010. Employer wage subsidies and wages in Germany: empirical evidence from individual data. Zeitschrift für ArbeitsmarktForschung 43:1, 53-71. [Crossref] 1233. Steffen Andersen, Glenn W. Harrison, Morten Igel Lau, E. Elisabet Rutström. 2010. Preference heterogeneity in experiments: Comparing the field and laboratory. Journal of Economic Behavior & Organization 73:2, 209-224. [Crossref] 1234. John L. Gore, Hua-Yin Yu, Claude Setodji, Jan M. Hanley, Mark S. Litwin, Christopher S. Saigal. 2010. Urinary diversion and morbidity after radical cystectomy for bladder cancer. Cancer 116:2, 331-339. [Crossref] 1235. C. D. Mayen, J. V. Balagtas, C. E. Alexander. 2010. Technology Adoption and Technical Efficiency: Organic and Conventional Dairy Farms in the United States. American Journal of Agricultural Economics 92:1, 181-195. [Crossref] 1236. Mohamed Hussein, Joshua S. Benner, David Lee, Anne-Marie Sesti, David S. Battleman, Christina Brock-Wood. 2010. Propensity Score Matching in the Evaluation of Drug Therapy Management Programs. Quality Management in Health Care 19:1, 25-33. [Crossref] 1237. Jay W. Rojewski, In Heok Lee, Sinan Gemici. 2010. Using Propensity Score Matching to Determine the Efficacy of Secondary Career Academies in Raising Educational Aspirations. Career and Technical Education Research 35:1, 3-27. [Crossref] 1238. Hangsheng Liu, Rachel M. Burns, Agnes G. Schaefer, Teague Ruder, Christopher Nelson, Amelia M. Haviland, Wayne B. Gray, John Mendeloff. 2010. The Pennsylvania certified safety committee program: An evaluation of participation and effects on work injury rates. American Journal of Industrial Medicine n/a-n/a. [Crossref] 1239. Lucas Joppa, Alexander Pfaff. 2010. Reassessing the forest impacts of protection. Annals of the New York Academy of Sciences 1185:1, 135-149. [Crossref] 1240. Petra E. Todd. Matching Estimators 108-121. [Crossref] 1241. Lester L. Yuan. 2010. Estimating the effects of excess nutrients on stream invertebrates from observational data. Ecological Applications 20:1, 110-125. [Crossref] 1242. William E. Encinosa, Didem Bernard, Avi Dor. Does prescription drug adherence reduce hospitalizations and costs? The case of diabetes 151-173. [Crossref] 1243. Takako Nomi. 2009. The Effects of Within-Class Ability Grouping on Academic Achievement in Early Elementary Years. Journal of Research on Educational Effectiveness 3:1, 56-92. [Crossref] 1244. Assefa Admassie, Degnet Abebaw, Andinet D. Woldemichael. 2009. Impact evaluation of the Ethiopian Health Services Extension Programme. Journal of Development Effectiveness 1:4, 430-449. [Crossref] 1245. Bertha Nhlema Simwaka, Kisukyabo Simwaka, George Bello. 2009. Retrospective analysis of a school-based malaria treatment programme demonstrates a positive impact on health and education outcomes in Mangochi district, Malawi. Journal of Development Effectiveness 1:4, 492-506. [Crossref] 1246. Ali Mehryar Karim, Timothy Williams, Leslie Patykewich, Disha Ali, Charlotte E. Colvin, Jessica Posner, Gideon Rutaremwa. 2009. The Impact of the African Youth Alliance Program on the Sexual Behavior of Young People in Uganda. Studies in Family Planning 40:4, 289-306. [Crossref] 1247. PIERRE AZOULAY, WAVERLY DING, TOBY STUART. 2009. THE IMPACT OF ACADEMIC PATENTING ON THE RATE, QUALITY AND DIRECTION OF (PUBLIC) RESEARCH OUTPUT. The Journal of Industrial Economics 57:4, 637-676. [Crossref] 1248. Rachel Connelly, Jean Kimmel. 2009. Spousal influences on parents’ non-market time choices. Review of Economics of the Household 7:4, 361-394. [Crossref]

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1272. Michael Lechner. 2009. Long-run labour market and health effects of individual sports activities. Journal of Health Economics 28:4, 839-854. [Crossref] 1273. Azeem M. Shaikh, Marianne Simonsen, Edward J. Vytlacil, Nese Yildiz. 2009. A specification test for the propensity score using its distribution conditional on participation. Journal of Econometrics 151:1, 33-46. [Crossref] 1274. Elizabeth A. Stuart, Sue M. Marcus, Marcela V. Horvitz-Lennon, Robert D. Gibbons, Sharon-Lise T. Normand, C. Hendricks Brown. 2009. Using Non-Experimental Data to Estimate Treatment Effects. Psychiatric Annals 39:7, 719-728. [Crossref] 1275. Olivier Bertrand. 2009. Effects of foreign acquisitions on R&D activity: Evidence from firm-level data for France. Research Policy 38:6, 1021-1031. [Crossref] 1276. Svetlana Yampolskaya, Paul E. Greenbaum, Ilene R. Berson. 2009. Profiles of Child Maltreatment Perpetrators and Risk for Fatal Assault: A Latent Class Analysis. 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1297. Brian C. Briggeman, Charles A. Towe, Mitchell J. Morehart. 2009. Credit Constraints: Their Existence, Determinants, and Implications for U.S. Farm and Nonfarm Sole Proprietorships. American Journal of Agricultural Economics 91:1, 275-289. [Crossref] 1298. Benu Bidani, Niels-Hugo Blunch, Chor-Ching Goh, Christopher O’Leary. 2009. Evaluating job training in two Chinese cities. Journal of Chinese Economic and Business Studies 7:1, 77-94. [Crossref] 1299. Melissa A. Clark, Mary Kay Fox. 2009. Nutritional Quality of the Diets of US Public School Children and the Role of the School Meal Programs. Journal of the American Dietetic Association 109:2, S44-S56. [Crossref] 1300. Carmine Ornaghi. 2009. Mergers and innovation in big pharma. International Journal of Industrial Organization 27:1, 70-79. [Crossref] 1301. Luis Centeno, Mário Centeno, Álvaro A. Novo. 2009. Evaluating job-search programs for old and young individuals: Heterogeneous impact on unemployment duration. Labour Economics 16:1, 12-25. [Crossref] 1302. James J. Heckman, Petra E. Todd. 2009. A note on adapting propensity score matching and selection models to choice based samples. Econometrics Journal 12, S230-S234. [Crossref] 1303. Miet Maertens, Johan F.M. Swinnen. 2009. Trade, Standards, and Poverty: Evidence from Senegal. World Development 37:1, 161-178. [Crossref] 1304. Meliyanni Johar. 2009. The impact of the Indonesian health card program: A matching estimator approach. Journal of Health Economics 28:1, 35-53. [Crossref] 1305. Giuseppe Porro, Stefano Maria Iacus. 2009. Random Recursive Partitioning: a matching method for the estimation of the average treatment effect. Journal of Applied Econometrics 24:1, 163-185. [Crossref] 1306. Nathalie Francken, Bart Minten, Johan F.M. Swinnen. 2009. Media, Monitoring, and Capture of Public Funds: Evidence from Madagascar. World Development 37:1, 242-255. [Crossref] 1307. Rosa Minhyo Cho. 2009. Impact of maternal imprisonment on children's probability of grade retention. Journal of Urban Economics 65:1, 11-23. [Crossref] 1308. Adesegun O. Fatusi, Wenjuan Wang, Jennifer Anyanti. 2009. Multi-Media Campaign Exposure and Interpersonal Communication on Sexual Abstinence among Young People in Nigeria: A Propensity-Matched Study. International Quarterly of Community Health Education 28:4, 289-303. [Crossref] 1309. Andrea M. Maechler, Klaus Schaeck, Martin Cihák, Stéphanie Marie Stolz. 2009. Who Disciplines Bank Managers?. IMF Working Papers 09:272, 1. [Crossref] 1310. P. Christopher Zegras, Yang Chen, Jürg M. Grütter. 2009. Behavior-Based Transportation Greenhouse Gas Mitigation under the Clean Development Mechanism. Transportation Research Record: Journal of the Transportation Research Board 2114:1, 38-46. [Crossref] 1311. B. T. Long, M. Kurlaender. 2008. Do Community Colleges Provide a Viable Pathway to a Baccalaureate Degree?. Educational Evaluation and Policy Analysis 31:1, 30-53. [Crossref] 1312. Lijing Ouyang, Xiangming Fang, James Mercy, Ruth Perou, Scott D. Grosse. 2008. Attention-Deficit/Hyperactivity Disorder Symptoms and Child Maltreatment: A Population-Based Study. The Journal of Pediatrics 153:6, 851-856. [Crossref] 1313. Jochen Kluve, Hartmut Lehmann, Christoph M. Schmidt. 2008. Disentangling Treatment Effects of Active Labor Market Policies: The Role of Labor Force Status Sequences. Labour Economics 15:6, 1270-1295. [Crossref] 1314. Joan M. Teno, David Dosa, Therese Rochon, Virginia Casey, Vincent Mor. 2008. Development of a Brief Survey to Measure Nursing Home Residents' Perceptions of Pain Management. Journal of Pain and Symptom Management 36:6, 572-583. [Crossref] 1315. A. Bíró, P. Elek, J. Vincze. 2008. Model-based sensitivity analysis of the Hungarian economy to macroeconomic shocks and uncertainties. Acta Oeconomica 58:4, 367-401. [Crossref] 1316. Marjan Drukker, Myrte Maarschalkerweerd, Maarten Bak, Ger Driessen, Joost à Campo, Arthur de Bie, Giovanni Poddighe, Jim van Os, Philippe Delespaul. 2008. A real-life observational study of the effectiveness of FACT in a Dutch mental health region. BMC Psychiatry 8:1. . [Crossref] 1317. Georgine M. Pion, David S. Cordray. 2008. The Burroughs Wellcome Career Award in the Biomedical Sciences. Evaluation & the Health Professions 31:4, 335-369. [Crossref] 1318. Nadia Garro, Davide Capodanno, Valeria Cammalleri, Corrado Tamburino. 2008. Very late thrombosis in acute myocardial infarction: drug-eluting versus uncoated stents. EuroIntervention 4:3, 324-330. [Crossref] 1319. R. M. Nayga. 2008. Nutrition, obesity and health: policies and economic research challenges. European Review of Agricultural Economics 35:3, 281-302. [Crossref] 1320. Olivier Bertrand, Habib Zitouna. 2008. Domestic versus cross-border acquisitions: which impact on the target firms’ performance?. Applied Economics 40:17, 2221-2238. [Crossref]

1321. Liliana Herrera, Mariano Nieto. 2008. The national innovation policy effect according to firm location. Technovation 28:8, 540-550. [Crossref] 1322. NEIL MALHOTRA. 2008. Disentangling the Relationship between Legislative Professionalism and Government Spending. Legislative Studies Quarterly 33:3, 387-414. [Crossref] 1323. Deborah N Peikes, Lorenzo Moreno, Sean Michael Orzol. 2008. Propensity Score Matching. The American Statistician 62:3, 222-231. [Crossref] 1324. Simon Cheng, Yingmei Xi, Ming-Hui Chen. 2008. A New Mixture Model for Misclassification With Applications for Survey Data. Sociological Methods & Research 37:1, 75-104. [Crossref] 1325. Cindy D. Kam, Carl L. Palmer. 2008. Reconsidering the Effects of Education on Political Participation. The Journal of Politics 70:3, 612-631. [Crossref] 1326. Giorgia Marini, Marisa Miraldo, Rowena Jacobs, Maria Goddard. 2008. Giving greater financial independence to hospitals—does it make a difference? The case of English NHS Trusts. Health Economics 17:6, 751-775. [Crossref] 1327. Lixin Cai, Guyonne Kalb, Yi-Ping Tseng, Ha Vu. 2008. The Effect of Financial Incentives on Labour Supply: Evidence for Lone Parents from Microsimulation and Quasi-Experimental Evaluation. Fiscal Studies 29:2, 285-325. [Crossref] 1328. KATSUSHI IMAI, PER A. EKLUND. 2008. Women's Organizations and Social Capital to Reduce Prevalence of Child Malnutrition in Papua New Guinea. Oxford Development Studies 36:2, 209-233. [Crossref] 1329. Haruko Noguchi, Satoshi Shimizutani, Yuichiro Masuda. 2008. Regional variations in medical expenditure and hospitalization days for heart attack patients in Japan: evidence from the Tokai Acute Myocardial Study (TAMIS). International Journal of Health Care Finance and Economics 8:2, 123-144. [Crossref] 1330. Stephanie Cosner Berzin. 2008. Difficulties in the Transition to Adulthood: Using Propensity Scoring to Understand What Makes Foster Youth Vulnerable. Social Service Review 82:2, 171-196. [Crossref] 1331. Feng Pan, Michael E. Chernew, A. Mark Fendrick. 2008. Impact of Fixed-Dose Combination Drugs on Adherence to Prescription Medications. Journal of General Internal Medicine 23:5, 611-614. [Crossref] 1332. Eric P. Slade, Elizabeth A. Stuart, David S. Salkever, Mustafa Karakus, Kerry M. Green, Nicholas Ialongo. 2008. Impacts of age of onset of substance use disorders on risk of adult incarceration among disadvantaged urban youth: A propensity score matching approach. Drug and Alcohol Dependence 95:1-2, 1-13. [Crossref] 1333. H. Spencer Banzhaf, Randall P Walsh. 2008. Do People Vote with Their Feet? An Empirical Test of Tiebout's Mechanism. American Economic Review 98:3, 843-863. [Crossref] 1334. David H. Greenberg, Philip K. Robins. 2008. Incorporating nonmarket time into benefit–cost analyses of social programs: An application to the self-sufficiency project. Journal of Public Economics 92:3-4, 766-794. [Crossref] 1335. Neal T. Wallace, K. John McConnell, Charles A. Gallia, Jeanene A. Smith. 2008. How Effective Are Copayments in Reducing Expenditures for Low-Income Adult Medicaid Beneficiaries? Experience from the Oregon Health Plan. Health Services Research 43:2, 515-530. [Crossref] 1336. Barış K. Yörük. 2008. The power of asking in volunteering: Evidence from a matched sample. Economics Letters 99:1, 79-84. [Crossref] 1337. Roni Frish, Noam Zussman. 2008. The effect of transfer payments on the labor supply of single mothers. The Journal of SocioEconomics 37:2, 627-643. [Crossref] 1338. Andrea Ichino, Fabrizia Mealli, Tommaso Nannicini. 2008. From temporary help jobs to permanent employment: what can we learn from matching estimators and their sensitivity?. Journal of Applied Econometrics 23:3, 305-327. [Crossref] 1339. Elaine M. Wolf, Douglas A. Wolf. 2008. Mixed Results in a Transitional Planning Program for Alternative School Students. Evaluation Review 32:2, 187-215. [Crossref] 1340. Jef L. Leroy, Armando García-Guerra, Raquel García, Clara Dominguez, Juan Rivera, Lynnette M. Neufeld. 2008. The Oportunidades Program Increases the Linear Growth of Children Enrolled at Young Ages in Urban Mexico. The Journal of Nutrition 138:4, 793-798. [Crossref] 1341. Eliane El Badaoui, Eric Strobl, Frank Walsh. 2008. Is There an Informal Employment Wage Penalty? Evidence from South Africa. Economic Development and Cultural Change 56:3, 683-710. [Crossref] 1342. Maartje Raaijmakers, Hendrik Koffijberg, Jocelyne Posthumus, Ben van Hout, Herman van Engeland, Walter Matthys. 2008. Assessing performance of a randomized versus a non-randomized study design. Contemporary Clinical Trials 29:2, 293-303. [Crossref] 1343. Isabel Busom, Andrea Fernández-Ribas. 2008. The impact of firm participation in R&D programmes on R&D partnerships. Research Policy 37:2, 240-257. [Crossref]

1344. Menale Kassie, John Pender, Mahmud Yesuf, Gunnar Kohlin, Randy Bluffstone, Elias Mulugeta. 2008. Estimating returns to soil conservation adoption in the northern Ethiopian highlands. Agricultural Economics 38:2, 213-232. [Crossref] 1345. Paula Veloso da Veiga, Ronald P. Wilder. 2008. Maternal Smoking During Pregnancy and Birthweight: A Propensity Score Matching Approach. Maternal and Child Health Journal 12:2, 194-203. [Crossref] 1346. Rebecca Callahan, Lindsey Wilkinson, Chandra Muller. 2008. School Context and the Effect of ESL Placement on MexicanOrigin Adolescents' Achievement*. Social Science Quarterly 89:1, 177-198. [Crossref] 1347. Michael Massoglia. 2008. Incarceration as Exposure: The Prison, Infectious Disease, and Other Stress-Related Illnesses. Journal of Health and Social Behavior 49:1, 56-71. [Crossref] 1348. Conny Wunsch, Michael Lechner. 2008. What Did All the Money Do? On the General Ineffectiveness of Recent West German Labour Market Programmes. Kyklos 61:1, 134-174. [Crossref] 1349. Pandej Chintrakarn. 2008. Estimating the Euro Effects on Trade with Propensity Score Matching*. Review of International Economics 16:1, 186-198. [Crossref] 1350. Kathleen Carey, Avi Dor. 2008. Expense preference behavior and management “outsourcing”: a comparison of adopters and nonadopters of contract management in U.S. hospitals. Journal of Productivity Analysis 29:1, 61-75. [Crossref] 1351. Marco Caliendo, Sabine Kopeinig. 2008. SOME PRACTICAL GUIDANCE FOR THE IMPLEMENTATION OF PROPENSITY SCORE MATCHING. Journal of Economic Surveys 22:1, 31-72. [Crossref] 1352. Petra E. Todd. Matching Estimators 1-11. [Crossref] 1353. Marc A. Winokur, Graig A. Crawford, Ralph C. Longobardi, Deborah P. Valentine. 2008. Matched Comparison of Children in Kinship Care and Foster Care on Child Welfare Outcomes. Families in Society: The Journal of Contemporary Social Services 89:3, 338-346. [Crossref] 1354. Christiane Spiel, Dominik Lapka, Petra Gradinger, Eva Maria Zodlhofer, Ralph Reimann, Barbara Schober, Petra Wagner, Alexander von Eye. 2008. A Euclidean Distance-Based Matching Procedure for Nonrandomized Comparison Studies. European Psychologist 13:3, 180-187. [Crossref] 1355. Antonio Bento, Charles Towe, Jacqueline Geoghegan. 2007. The Effects of Moratoria on Residential Development: Evidence from a Matching Approach. American Journal of Agricultural Economics 89:5, 1211-1218. [Crossref] 1356. Toby E. Stuart, Olav Sorenson. 2007. Strategic networks and entrepreneurial ventures. Strategic Entrepreneurship Journal 1:3-4, 211-227. [Crossref] 1357. Indranil Bardhan, Sunil Mithas, Shu Lin. 2007. Performance Impacts of Strategy, Information Technology Applications, and Business Process Outsourcing in U.S. Manufacturing Plants. Production and Operations Management 16:6, 747-762. [Crossref] 1358. Malgosia Madajewicz, Alexander Pfaff, Alexander van Geen, Joseph Graziano, Iftikhar Hussein, Hasina Momotaj, Roksana Sylvi, Habibul Ahsan. 2007. Can information alone change behavior? Response to arsenic contamination of groundwater in Bangladesh. Journal of Development Economics 84:2, 731-754. [Crossref] 1359. Michael Lechner, Ruth Miquel, Conny Wunsch. 2007. The Curse and Blessing of Training the Unemployed in a Changing Economy: The Case of East Germany After Unification. German Economic Review 8:4, 468-509. [Crossref] 1360. Shu Lin, Haichun Ye. 2007. Does inflation targeting really make a difference? Evaluating the treatment effect of inflation targeting in seven industrial countries. Journal of Monetary Economics 54:8, 2521-2533. [Crossref] 1361. Rachid Baz, Cristina Rodriguez, Alex Z. Fu, Rony Abou Jawde, Matt Kalaycio, Anjali Advani, Ronald Sobecks, Mikkael A. Sekeres. 2007. Impact of remission induction chemotherapy on survival in older adults with acute myeloid leukemia. Cancer 110:8, 1752-1759. [Crossref] 1362. Daniela Del Boca, Daniela Vuri. 2007. The mismatch between employment and child care in Italy: the impact of rationing. Journal of Population Economics 20:4, 805-832. [Crossref] 1363. Arnstein Aassve, Maria A. Davia, Maria Iacovou, Stefano Mazzuco. 2007. Does Leaving Home Make You Poor? Evidence from 13 European Countries. European Journal of Population / Revue européenne de Démographie 23:3-4, 315-338. [Crossref] 1364. Karen Robson, David J. Pevalin. 2007. Gender differences in the predictors and socio-economic outcomes of young parenthood in Great Britain. Research in Social Stratification and Mobility 25:3, 205-218. [Crossref] 1365. Stefano M. Iacus, Giuseppe Porro. 2007. Missing data imputation, matching and other applications of random recursive partitioning. Computational Statistics & Data Analysis 52:2, 773-789. [Crossref] 1366. Jonathan Whitaker, Sunil Mithas, M. S. Krishnan. 2007. A Field Study of RFID Deployment and Return Expectations. Production and Operations Management 16:5, 599-612. [Crossref] 1367. Sunil Mithas, Jonathan Whitaker. 2007. Is the World Flat or Spiky? Information Intensity, Skills, and Global Service Disaggregation. Information Systems Research 18:3, 237-259. [Crossref]

1368. Laura R. Peck. 2007. What Are the Effects of Welfare Sanction Policies? Or, Using Propensity Scores as a Subgroup Indicator to Learn More From Social Experiments. American Journal of Evaluation 28:3, 256-274. [Crossref] 1369. Daniel J. Slottje, Daniel L. Millimet, Michael J. Buchanan. 2007. Econometric analysis of copyrights. Journal of Econometrics 139:2, 303-317. [Crossref] 1370. Michelle L. Frisco, Chandra Muller, Kenneth Frank. 2007. Parents? Union Dissolution and Adolescents? School Performance: Comparing Methodological Approaches. Journal of Marriage and Family 69:3, 721-741. [Crossref] 1371. Gill Green, Jennifer Todd, David Pevalin. 2007. Biographical disruption associated with multiple sclerosis: Using propensity scoring to assess the impact. Social Science & Medicine 65:3, 524-535. [Crossref] 1372. Sourafel Girma, Holger Görg, Eric Strobl. 2007. The effects of government grants on plant survival: A micro-econometric analysis. International Journal of Industrial Organization 25:4, 701-720. [Crossref] 1373. Aron A. Gottesman, Gordon S. Roberts. 2007. Loan Rates and Collateral. The Financial Review 42:3, 401-427. [Crossref] 1374. Gregory D. Berg, Sandeep Wadhwa. 2007. Health Services Outcomes for a Diabetes Disease Management Program for the Elderly. Disease Management 10:4, 226-234. [Crossref] 1375. Arnstein Aassve, Gianni Betti, Stefano Mazzuco, Letizia Mencarini. 2007. Marital disruption and economic well-being: a comparative analysis. Journal of the Royal Statistical Society: Series A (Statistics in Society) 170:3, 781-799. [Crossref] 1376. Yundan Gong, Holger Görg, Sara Maioli. 2007. Employment Effects of Privatisation and Foreign Acquisition of Chinese State‐ owned Enterprises. International Journal of the Economics of Business 14:2, 197-214. [Crossref] 1377. Alan Johnson, Gregory D. Berg, John Long, Sandeep Wadhwa. 2007. A Matched-Cohort Study of Utilization Outcomes for an Adult Medicaid Population Enrolled in an Asthma Disease Management Program. Journal of Ambulatory Care Management 30:3, 241-258. [Crossref] 1378. Dale B. Christensen, Mary Roth, Troy Trygstad, John Byrd. 2007. Evaluation of a pilot medication therapy management project within the North Carolina State Health Plan. Journal of the American Pharmacists Association 47:4, 471-483. [Crossref] 1379. Sonja Gensler, Bernd Skiera, Martin Böhm. 2007. Einfluss der Nutzung des Online-Bankings auf das Produktnutzungsverhalten und die Profitabilität von Bankkunden. Journal of Business Economics 77:6, 675-695. [Crossref] 1380. Mariapia Mendola. 2007. Agricultural technology adoption and poverty reduction: A propensity-score matching analysis for rural Bangladesh. Food Policy 32:3, 372-393. [Crossref] 1381. Sourafel Girma, Richard Kneller, Mauro Pisu. 2007. Do exporters have anything to learn from foreign multinationals?. European Economic Review 51:4, 993-1010. [Crossref] 1382. Gönül Çolak, Toni M. Whited. 2007. Spin-offs, Divestitures, and Conglomerate Investment. Review of Financial Studies 20:3, 557-595. [Crossref] 1383. Alex Z. Fu, Jenny Z. Jiang, Jaxk H. Reeves, Jack E. Fincham, Gordon G. Liu, Matthew Perri. 2007. Potentially Inappropriate Medication Use and Healthcare Expenditures in the US Community-Dwelling Elderly. Medical Care 45:5, 472-476. [Crossref] 1384. Sourafel Girma, Holger Görg. 2007. Evaluating the foreign ownership wage premium using a difference-in-differences matching approach. Journal of International Economics 72:1, 97-112. [Crossref] 1385. Ann  M. Meier. 2007. Adolescent First Sex and Subsequent Mental Health. American Journal of Sociology 112:6, 1811-1847. [Crossref] 1386. Alex Z. Fu, William H. Dow, Gordon G. Liu. 2007. Propensity score and difference-in-difference methods: a study of secondgeneration antidepressant use in patients with bipolar disorder. Health Services and Outcomes Research Methodology 7:1-2, 23-38. [Crossref] 1387. Geoff Perry, Tim Maloney. 2007. Evaluating active labour market programmes in New Zealand. International Journal of Manpower 28:1, 7-29. [Crossref] 1388. Boris Augurzky, Jochen Kluve. 2007. Assessing the performance of matching algorithms when selection into treatment is strong. Journal of Applied Econometrics 22:3, 533-557. [Crossref] 1389. SOURAFEL GIRMA, HOLGER GÖRG. 2007. MULTINATIONALS’ PRODUCTIVITY ADVANTAGE: SCALE OR TECHNOLOGY?. Economic Inquiry 45:2, 350-362. [Crossref] 1390. Jennifer C. Lee, Jeremy Staff. 2007. When Work Matters: The Varying Impact of Work Intensity on High School Dropout. Sociology of Education 80:2, 158-178. [Crossref] 1391. Jeff Borland, Yi-Ping Tseng. 2007. Does a Minimum Job Search Requirement Reduce Time on Unemployment Payments? Evidence from the Jobseeker Diary in Australia. ILR Review 60:3, 357-378. [Crossref]

1392. Per G. Fredriksson, Daniel L. Millimet. 2007. Legislative Organization and Pollution Taxation. Public Choice 131:1-2, 217-242. [Crossref] 1393. Sean Richey. 2007. Manufacturing Trust: Community Currencies and the Creation of Social Capital. Political Behavior 29:1, 69-88. [Crossref] 1394. Seoungpil Ahn, Mark D. Walker. 2007. Corporate governance and the spinoff decision. Journal of Corporate Finance 13:1, 76-93. [Crossref] 1395. Alex Z. Fu, Gordon G. Liu, Dale B. Christensen, Richard A. Hansen. 2007. Effect of Second-Generation Antidepressants on Mania- and Depression-Related Visits in Adults with Bipolar Disorder: A Retrospective Study. Value in Health 10:2, 128-136. [Crossref] 1396. Per G. Fredriksson, Jim R. Wollscheid. 2007. Democratic institutions versus autocratic regimes: The case of environmental policy. Public Choice 130:3-4, 381-393. [Crossref] 1397. Peter Young-Jin Park, Frank Fedel Saccomanno. 2007. Reducing Treatment Selection Bias for Estimating Treatment Effects Using Propensity Score Method. Journal of Transportation Engineering 133:2, 112-118. [Crossref] 1398. RYAN D. KING, MICHAEL MASSOGLIA, ROSS MACMILLAN. 2007. THE CONTEXT OF MARRIAGE AND CRIME: GENDER, THE PROPENSITY TO MARRY, AND OFFENDING IN EARLY ADULTHOOD*. Criminology 45:1, 33-65. [Crossref] 1399. A. Nivorozhkin, E. Nivorozhkin. 2007. Do government sponsored vocational training programmes help the unemployed find jobs? Evidence from Russia. Applied Economics Letters 14:1, 5-10. [Crossref] 1400. Grant H Skrepnek, Edward P Armstrong, Katie Brookler, John Roper, Beth E Martin, Laurel Karabatsos, Christy Hunter. 2007. Cost analysis of a disease management programme for adult Medicaid clients with schizophrenia. Journal of Medical Economics 10:4, 411-426. [Crossref] 1401. Elizabeth Ty Wilde, Robinson Hollister. 2007. How close is close enough? Evaluating propensity score matching using data from a class size reduction experiment. Journal of Policy Analysis and Management 26:3, 455-477. [Crossref] 1402. Orlando Jiménez. 2007. Voluntary agreements in environmental policy: an empirical evaluation for the Chilean case. Journal of Cleaner Production 15:7, 620-637. [Crossref] 1403. Tommaso Nannicini. 2007. Simulation-Based Sensitivity Analysis for Matching Estimators. The Stata Journal: Promoting communications on statistics and Stata 7:3, 334-350. [Crossref] 1404. Raj Echambadi, Benjamin Campbell, Rajshree Agarwal. 2006. Encouraging Best Practice in Quantitative Management Research: An Incomplete List of Opportunities. Journal of Management Studies 43:8, 1801-1820. [Crossref] 1405. Luis Ayala, Magdalena Rodríguez. 2006. The latin model of welfare: Do ‘insertion contracts’ reduce long-term dependence?. Labour Economics 13:6, 799-822. [Crossref] 1406. DEBORAH COBB-CLARK, CHRIS RYAN, ROBERT BREUNIG. 2006. A Couples-Based Approach to the Problem of Workless Families. Economic Record 82:259, 428-444. [Crossref] 1407. Susanne Rässler. 2006. Der Einsatz von Missing Data Techniken in der Arbeitsmarktforschung des IAB. Allgemeines Statistisches Archiv 90:4, 527-552. [Crossref] 1408. Sourafel Girma, Steve Thompson, Peter W. Wright. 2006. International Acquisitions, Domestic Competition and Firm Performance. International Journal of the Economics of Business 13:3, 335-349. [Crossref] 1409. Onur Baser. 2006. Too Much Ado about Propensity Score Models? Comparing Methods of Propensity Score Matching. Value in Health 9:6, 377-385. [Crossref] 1410. William Carbonaro. 2006. Public‐Private Differences in Achievement among Kindergarten Students: Differences in Learning Opportunities and Student Outcomes. American Journal of Education 113:1, 31-65. [Crossref] 1411. Sangeeta Pratap, Erwan Quintin. 2006. Are labor markets segmented in developing countries? A semiparametric approach. European Economic Review 50:7, 1817-1841. [Crossref] 1412. Sourafel Girma, David Paton. 2006. Matching estimates of the impact of over-the-counter emergency birth control on teenage pregnancy. Health Economics 15:9, 1021-1032. [Crossref] 1413. Kornelius Kraft, Marija Ugarković. 2006. Profit sharing and the financial performance of firms: Evidence from Germany. Economics Letters 92:3, 333-338. [Crossref] 1414. Jennie E. Brand, Charles N. Halaby. 2006. Regression and matching estimates of the effects of elite college attendance on educational and career achievement. Social Science Research 35:3, 749-770. [Crossref] 1415. Henrik Winterhager, Anja Heinze, Alexander Spermann. 2006. Deregulating job placement in Europe: A microeconometric evaluation of an innovative voucher scheme in Germany. Labour Economics 13:4, 505-517. [Crossref]

1416. Stephen L. Morgan, David J. Harding. 2006. Matching Estimators of Causal Effects. Sociological Methods & Research 35:1, 3-60. [Crossref] 1417. Pathric Hägglund. 2006. Job‐search assistance using the internet: experiences from a Swedish randomised experiment. International Journal of Manpower 27:5, 434-451. [Crossref] 1418. Jennie E. Brand. 2006. The effects of job displacement on job quality: Findings from the Wisconsin Longitudinal Study. Research in Social Stratification and Mobility 24:3, 275-298. [Crossref] 1419. Cheti Nicoletti. 2006. Nonresponse in dynamic panel data models. Journal of Econometrics 132:2, 461-489. [Crossref] 1420. Ruben Atoyan, Patrick Conway. 2006. Evaluating the impact of IMF programs: A comparison of matching and instrumentalvariable estimators. The Review of International Organizations 1:2, 99-124. [Crossref] 1421. Richard Dorsett. 2006. The new deal for young people: effect on the labour market status of young men. Labour Economics 13:3, 405-422. [Crossref] 1422. Jane Arnold Lincove, Gary Painter. 2006. Does the Age That Children Start Kindergarten Matter? Evidence of Long-Term Educational and Social Outcomes. Educational Evaluation and Policy Analysis 28:2, 153-179. [Crossref] 1423. Michael F. Caldwell, Michael Vitacco, Gregory J. Van Rybroek. 2006. Are Violent Delinquents Worth Treating? A Cost–Benefit Analysis. Journal of Research in Crime and Delinquency 43:2, 148-168. [Crossref] 1424. Mai P. Do, D. Lawrence Kincaid. 2006. Impact of an Entertainment-Education Television Drama on Health Knowledge and Behavior in Bangladesh: An Application of Propensity Score Matching. Journal of Health Communication 11:3, 301-325. [Crossref] 1425. Ariel Linden. 2006. Evaluating the Effectiveness of Home Health as a Disease Management Strategy. Home Health Care Management & Practice 18:3, 216-222. [Crossref] 1426. Richard P. Barth, Chung Kwon Lee, Judith Wildfire, Shenyang Guo. 2006. A Comparison of the Governmental Costs of Long‐ Term Foster Care and Adoption. Social Service Review 80:1, 127-158. [Crossref] 1427. Christina M. Gibson‐Davis, E. Michael Foster. 2006. A Cautionary Tale: Using Propensity Scores to Estimate the Effect of Food Stamps on Food Insecurity. Social Service Review 80:1, 93-126. [Crossref] 1428. D. Lawrence Kincaid, Mai Phuong Do. 2006. Multivariate Causal Attribution and Cost-Effectiveness of a National Mass Media Campaign in the Philippines. Journal of Health Communication 11:sup2, 69-90. [Crossref] 1429. Aaron D. Kugelmass, David J. Cohen, Phillip P. Brown, April W. Simon, Edmund R. Becker, Steven D. Culler. 2006. Hospital Resources Consumed in Treating Complications Associated With Percutaneous Coronary Interventions. The American Journal of Cardiology 97:3, 322-327. [Crossref] 1430. Jaan Sidorov. 2006. Computer-assisted technology: Not if, not when, but how. Journal of General Internal Medicine 21:2, 201-202. [Crossref] 1431. Jack Buckley, Mark Schneider. 2006. Are Charter School Parents More Satisfied With Schools? Evidence From Washington, DC. Peabody Journal of Education 81:1, 57-78. [Crossref] 1432. Rolf Becker, Frank Schubert. 2006. Soziale ungleichheit von lesekompetenzen. KZfSS Kölner Zeitschrift für Soziologie und Sozialpsychologie 58:2, 253-284. [Crossref] 1433. Alison Evans Cuellar, Larkin S. McReynolds, Gail A. Wasserman. 2006. A cure for crime: Can mental health treatment diversion reduce crime among youth?. Journal of Policy Analysis and Management 25:1, 197-214. [Crossref] 1434. G. T. Henry, C. S. Gordon, D. K. Rickman. 2006. Early Education Policy Alternatives: Comparing Quality and Outcomes of Head Start and State Prekindergarten. Educational Evaluation and Policy Analysis 28:1, 77-99. [Crossref] 1435. Geeta Gandhi Kingdon. 2006. Empirical Research Methods in Education. Contemporary Education Dialogue 3:2, 171-174. [Crossref] 1436. Jason K. Luellen, William R. Shadish, M. H. Clark. 2005. Propensity Scores. Evaluation Review 29:6, 530-558. [Crossref] 1437. Arnstein Aassve, Stefano Mazzuco, Letizia Mencarini. 2005. Childbearing and well-being: a comparative analysis of European welfare regimes. Journal of European Social Policy 15:4, 283-299. [Crossref] 1438. Alan Johnson, Gregory Berg, Edward Fleegler, Marilyn Sauerbrun. 2005. A Matched-Cohort Study of Selected Clinical and Utilization Outcomes for an Asthma Care Support Program. Disease Management 8:3, 144-154. [Crossref] 1439. Orlando Jiménez. 2005. Innovation-Oriented Environmental Regulations: Direct versus Indirect Regulations; an Empirical Analysis of Small and Medium-Sized Enterprises in Chile. Environment and Planning A 37:4, 723-750. [Crossref] 1440. Rajeev H. Dehejia. 2005. Program evaluation as a decision problem. Journal of Econometrics 125:1-2, 141-173. [Crossref] 1441. Jeffrey A. Smith, Petra E. Todd. 2005. Does matching overcome LaLonde's critique of nonexperimental estimators?. Journal of Econometrics 125:1-2, 305-353. [Crossref]

1442. Rajeev Dehejia. 2005. Practical propensity score matching: a reply to Smith and Todd. Journal of Econometrics 125:1-2, 355-364. [Crossref] 1443. Gregory D. Berg, Edward Fleegler, Catherine J. vanVonno, Eileen Thomas. 2005. A Matched-Cohort Study of Health Services Utilization Outcomes for a Heart Failure Disease Management Program. Disease Management 8:1, 35-41. [Crossref] 1444. Lawrence M. Berger, Jennifer Hill, Jane Waldfogel. 2005. Maternity Leave, Early Maternal Employment and Child Health and Development in the US. The Economic Journal 115:501, F29-F47. [Crossref] 1445. Ariel Linden, John L Adams, Nancy Roberts. 2005. Using Propensity Scores to Construct Comparable Control Groups for Disease Management Program Evaluation. Disease Management & Health Outcomes 13:2, 107-115. [Crossref] 1446. Alan Johnson, Gregory Berg, Edward Fleegler, Jeanne Lehn. 2005. Clinical and Utilization Outcomes for a Heart Failure Care Support Program. Disease Management & Health Outcomes 13:5, 327-335. [Crossref] 1447. Robert T. Greenbaum, George E. Tita. 2004. The Impact of Violence Surges on Neighbourhood Business Activity. Urban Studies 41:13, 2495-2514. [Crossref] 1448. Glenn W Harrison, John A List. 2004. Field Experiments. Journal of Economic Literature 42:4, 1009-1055. [Crossref] 1449. Daniel L. Millimet, John A. List. 2004. The Case of the Missing Pollution Haven Hypothesis. Journal of Regulatory Economics 26:3, 239-262. [Crossref] 1450. Giovanni Valentini, Maria Chiara Di Guardo. 2004. Design Combination Potential and Get it Done: An Analysis of the Drivers of Technological Performance in Mergers and Acquisitions. Management Research: Journal of the Iberoamerican Academy of Management 2:3, 271-281. [Crossref] 1451. Gregory D. Berg, Sandeep Wadhwa, Alan E. Johnson. 2004. A Matched-Cohort Study of Health Services Utilization and Financial Outcomes for a Heart Failure Disease-Management Program in Elderly Patients. Journal of the American Geriatrics Society 52:10, 1655-1661. [Crossref] 1452. John A. List, W.Warren McHone, Daniel L. Millimet. 2004. Effects of environmental regulation on foreign and domestic plant births: is there a home field advantage?. Journal of Urban Economics 56:2, 303-326. [Crossref] 1453. Per G Fredriksson, Daniel L Millimet. 2004. Electoral rules and environmental policy. Economics Letters 84:2, 237-244. [Crossref] 1454. Per G Fredriksson, Daniel L Millimet. 2004. Comparative politics and environmental taxation. Journal of Environmental Economics and Management 48:1, 705-722. [Crossref] 1455. Lawrence C. Marsh. 2004. The econometrics of higher education: editor's view. Journal of Econometrics 121:1-2, 1-18. [Crossref] 1456. Dan A. Black, Jeffrey A. Smith. 2004. How robust is the evidence on the effects of college quality? Evidence from matching. Journal of Econometrics 121:1-2, 99-124. [Crossref] 1457. Michael Greenstone. 2004. Did the Clean Air Act cause the remarkable decline in sulfur dioxide concentrations?. Journal of Environmental Economics and Management 47:3, 585-611. [Crossref] 1458. Alberto Alesina, Reza Baqir, Caroline Hoxby. 2004. Political Jurisdictions in Heterogeneous Communities. Journal of Political Economy 112:2, 348-396. [Crossref] 1459. Michael M. Hutchison, Ilan Noy. 2003. Macroeconomic effects of IMF-sponsored programs in Latin America: output costs, program recidivism and the vicious cycle of failed stabilizations. Journal of International Money and Finance 22:7, 991-1014. [Crossref] 1460. Christina M. Gibson. 2003. Privileging the Participant: The Importance of Sub-Group Analysis in Social Welfare Evaluations. American Journal of Evaluation 24:4, 443-469. [Crossref] 1461. David I. Levine, Gary Painter. 2003. The Schooling Costs of Teenage Out-of-Wedlock Childbearing: Analysis with a WithinSchool Propensity-Score-Matching Estimator. Review of Economics and Statistics 85:4, 884-900. [Abstract] [PDF] [PDF Plus] 1462. John A. List, Daniel L. Millimet, Per G. Fredriksson, W. Warren McHone. 2003. Effects of Environmental Regulations on Manufacturing Plant Births: Evidence from a Propensity Score Matching Estimator. Review of Economics and Statistics 85:4, 944-952. [Abstract] [PDF] [PDF Plus] 1463. Harry J. Holzer, Jens Ludwig. 2003. Measuring Discrimination in Education: Are Methodologies From Labor and Markets Useful?. Teachers College Record 105:6, 1147-1178. [Crossref] 1464. Gregory D Berg, Alan Johnson, Edward Fleegler. 2003. Clinical and Utilization Outcomes for a Pediatric and Adolescent Telephonic Asthma Care Support Program. Disease Management & Health Outcomes 11:11, 737-743. [Crossref] 1465. Sascha O. Becker, Andrea Ichino. 2002. Estimation of Average Treatment Effects Based on Propensity Scores. The Stata Journal: Promoting communications on statistics and Stata 2:4, 358-377. [Crossref]

1466. Hartmut Lehmann, Jonathan Wadsworth. Wage Arrears and Inequality in the Distribution of Pay: Lessons from Russia 125-155. [Crossref] 1467. Julia Adler-Milstein, Ariel Linden. The Use and Evaluations of IT in Chronic Disease Management 1-18. [Crossref] 1468. Barnabas Kiiza, Glenn Pederson, Stephen Lwasa. The Role of Market Information in Adoption of Agricultural Seed Technology in Rural Uganda 72-88. [Crossref]