The idea here is to deliberately vary the predictors IVs to see if they have any causal effects on the outcomes.
The standard solution to this is randomisation: that is, we randomly assign people to different groups, and then give each group a different treatment i. Suppose you wanted to find out if smoking causes lung cancer. And this really matters: for instance, it might be that people who choose to smoke cigarettes also tend to have poor diets, or maybe they tend to work in asbestos mines, or whatever.
The point here is that the groups smokers and non-smokers actually differ on lots of things, not just smoking. So it might be that the higher incidence of lung cancer among smokers is caused by something else, not by smoking per se.
Constants refer to fixed values that the program may not alter and they are called literals. In Algebra, a constant is a number on its own, or sometimes a letter such as a, b or c to stand for a fixed number. A literal is a value that is expressed as itself. A constant is a data type that substitutes a literal. Constants are used when a specific, unchanging value is used various times during the program. A variable can be thought of as a memory location that can hold values of a specific type.
Begin typing your search term above and press enter to search. Press ESC to cancel. Skip to content Home Research Paper What is the main difference between experimental and Nonexperimental research? Research Paper. Ben Davis June 1, What is the main difference between experimental and Nonexperimental research? What is non-experimental design? What is the difference between experimental and Nonexperimental methods of study quizlet? What is the primary difference in experimental and non experimental designs quizlet?
What is the difference between a dependent and independent variable? What variable should be kept constant? How do you know if a variable is constant? However, because it identifies a local average treatment effect, the IV estimator has a lower degree of external validity than an ideal experiment although not necessarily a feasible experiment in the sense defined in Section 2. This is depicted in Figure 1.
Depicts the hypothetical relative ranking of the estimators under consideration based on their internal and external validity as discussed in the text. Regression discontinuity RD methods have gained widespread acceptance in program evaluation in both developed and developing country settings see inter alia Thistlewaite and Campbell ; van der Klaauw , ; Buddlemeyer and Skoufias ; Imbens and Lemieux While we will not review the technical details of RD methods here, it is worthwhile sketching the intuition of this approach.
For example, in Ozier scores on a standardized national exam are used to determine high school admission and the probability of admission rises sharply at the national mean. Assuming that the only discontinuous change at the cutoff is the probability of exposure to the treatment i. In particular, the assumptions are that the distribution of observed and unobserved covariates is continuous at cutoff, that no other treatments are assigned using the same cutoff, and that agents are unable to manipulate their value of the forcing variable.
The essence of the assumption in RD is that the cutoff for assignment to treatment is at least locally arbitrary with respect to other economic variables, i. RD identifies the treatment effect only for those individuals who find themselves just above or just below the cutoff in the forcing variable.
In the terms of the second step the assumptions needed to identify ATEX in the sample , RD requires a little more than a true experiment. Rather than ensuring random assignment through experimental design, in RD we must make key identifying assumptions. While the plausibility of these assumptions will vary depending on the context, one of the virtues of the RD approach is that the these assumptions can be corroborated or tested, at least in part.
The assumption that individuals are not manipulating their value of the forcing variable in order to opt into or out of treatment can be in part tested by looking for evidence of manipulation in the density of the forcing variable.
For example, if a poverty score cutoff is used to determine eligibility for many social assistance programs, then it is likely that individuals will find a way to manipulate their poverty scores and that we will see a bunching up of the poverty distribution just below the poverty threshold.
If instead the mean is sufficiently variable, it would be difficult for students to fine tune their test scores in order to manipulate their chances of admission. The assumption that covariates do not jump discontinuously at the same threshold used to assign the treatment can be tested for observed covariates by looking at the distribution of the covariates in the neighborhood of the threshold.
Of course, for unobserved covariates this assumption cannot be tested and remains just that, an assumption. Figure 1 summarizes the relationship between RD, randomized trials, and IV with respect to internal and external validity. Experiments through design and control in implementation typically offer the highest degree of internal validity. At the same time, in principle an experiment can be conducted on many populations, not just the individuals who happen to be at the cutoff of the forcing variable, and so even feasible experiments potentially offer greater external validity than RD.
RD in turn has greater internal validity than IV, in the sense that many of the key identifying assumptions can be tested or corroborated in the data. Its external validity is more difficult to compare to IV.
The idea behind direct matching methods is closely related to regression discontinuity. Assignment to treatment can depend on unobservables to the extent these are uncorrelated with potential outcomes. The plausibility of the selection on observables assumption depends on the context.
When the process of selection into treatment is well understood and the relevant variables observed, the assumption is plausible and matching has the same internal validity as an experiment. For example Diaz and Handa show that, since PROGRESSA is targeted using community and individual poverty measures, matching on a broad set of community and household poverty and demographic measures replicates the experimentally estimated treatment impact of the program. Instead, in situations in which unobservables i.
Again, Diaz and Handa show that a comparison group drawn from survey similar to the one used in PROGRESSA is better able to replicate the experimentally estimated treatment effect than a comparison group drawn from surveys using a different survey instrument.
In this case, the unobservable factor is the difference in measurement of the relevant variables. In other instances, the unobservable could simply be a key, missing covariate see also the discussion in Heckman et al. The best matching applications use knowledge of the specific context of the application to make the case for selection on observables, and a variety of studies have tried to demonstrate which observables are key determinants of selection into treatment in different contexts.
While the internal validity of matching rests on an assumption, its strength is that the method can be applied to any data set; hence it has a high degree of external validity. As a matter of practice, matching on a single variable is straightforward.
Some standard methods include: one to one matching match a given treated unit to the comparison unit with the closest value of X , with or without replacement ; one to n matching match each treated unit to the n closest comparison units, with or without replacement ; radius matching match each treated unit to the comparison units within a radius defined on X ; and kernel matching match each treated unit to nearby comparison units with weights determined by a kernel.
The greater challenge is when matching is carried out with a multivalued X. The most intuitive method is to use a distance metric to map X into a single Euclidian distance, and then match on that distance.
But as shown by Abadie and Imbens standard matching methods are inconsistent when matching is carried out on more than two continuous covariates. Fortunately, Abadie and Imbens also propose a bias-corrected matching estimator. Since matching can be carried out on large-scale representative and survey data sets, it offers the possibility of a greater degree of external validity than RD, IV, and feasible experiments of course an ideal — but rarely feasible — experiment on a representative population could have the same degree of external validity as matching , but its internal validity is potentially lower since it rests on the assumption of selection on observables, which is both stronger and less amenable to testing than the underlying assumptions of the other three methods.
Propensity score matching is closely related to direct matching on covariates. Indeed, one can think of it as a method for converting direct matching on a vector of covariates into direct matching on a scalar. The key insight, due to Rosenbaum and Rubin , is that rather than conditioning on the entire vector of covariates that determines the probability of assignment to treatment, one can directly condition on the probability of assignment to treatment. For individuals with the same probability of assignment to treatment which individuals are treated and which are not is a matter of random chance.
Two sets of issues arise in implementing propensity score matching. First, how to estimate the propensity score. A variety of methods have been proposed, although the most common are probit or logit functional forms in conjunction with specification tests see Dehejia and Wahba ; Shaikh et al.
Second, how to use the propensity score in an estimator. As suggested above, the intuitive choice is to use the estimated propensity score in one of the univariate matching methods listed in Section 3.
An alternative choice is to use the propensity score as a weight in a linear regression see Dehejia and Wahba ; Wooldridge ; Hirano et al. The advantage of weighting is that it is an efficient estimator and that it shoehorns the propensity score into the easily-implemented framework of regression analysis.
The key advantage of propensity matching with respect to direct matching is that it eschews the bias of direct matching estimators, and hence achieves a greater degree of internal validity. Bias-corrected direct matching offers an alternative to direct matching with many of the virtues of propensity score matching; see Abadie and Imbens This is depicted in Figure 1.
Propensity score matching methods have found wide application within development economics. They argue that it is important to match on both village and individual-level characteristic because selection into piped water occurs at both levels: first a village has to be connected e. See Behrman et al. In this section we discuss methods that are implemented using linear regressions, albeit with different identifying assumptions. Although the methods discussed in the previous section can be reformulated in a regression framework, conceptually their identifying assumptions are more closely related to randomized experiments; indeed, regression discontinuity, instrumental variables, and matching explicitly try to recreate or exploit naturally occurring circumstances that create the advantages of randomized trials.
In this section we instead discuss a set of methods that are more naturally understood directly within the regression framework. The most natural evaluation estimator, at least for economists, is a linear regression of the form:. In this sense, sample selection bias can be reformulated as a selection on unobservables or omitted variables problem. As discussed in Section 3. For example in labor training programs in the US it has been shown that selection on observable factors such as labor market conditions and work history can be more important than unobservables Heckman et al.
Even if we accept the selection on observables assumption, then a second assumption embedded in the regression approach is linearity. While this refers specifically to the linearity of the regression function, in the evaluation context the key question is the extent to which the pretreatment covariates, X , differ between the treatment group and comparison groups. For example, Lalonde finds that linear regressions are unable to control for differences between the treatment and comparison groups in a setting where these groups differ by more than five standard deviations for some covariates.
A lack of overlap in the covariates implies that the treatment effect is being estimated by an extrapolation based on the linear functional form. In contrast, the matching methods discussed in Section 3 make no such assumption on linearity, and equally importantly the process of specification search associated with matching often leads to the discovery of important non-linearities and overlap problems see for example Dehejia and Wahba As a result, in Figure 1 , we denote regression methods as having lower internal validity than matching methods.
At the same time since regressions can be run on the full sample of a data set rather than simply the set of matched treatment and comparison units in matching , we denote it has having potentially greater external validity than matching. There are three responses to the assumption of linearity required for regression methods.
First, one can test for overlap in the covariates between the treatment group and comparison groups; if there is considerable overlap then there is a lesser degree of extrapolation and the estimated treatment impact should be less sensitive to the choice of functional form. Several tests are possible, ranging from a simple comparison of means for each covariate to comparing the estimated propensity score across treatment and comparison groups see Dehejia and Wahba , Second, one can use matching methods, which explicitly do not assume a linear relationship between the covariates and the outcome.
Third, one can use non-parametric regression methods, which we discuss in the next section. In some ways the most natural response to the problem of overlap or non-linearity in the covariates, even if one is willing to assume selection on observables, is to use non-parametric regression estimators, such as the kernel or series estimator. See for example the pioneering work of Deaton e.
The evident advantage of this is that it allows the data to choose the most appropriate non-linear functional form. A classic example of this approach is Subramanian and Deaton While this question can be formulated in the framework of Section 3, this would not be the most natural approach. The data do not offer a natural source of exogenous variation in food prices to use an experimental or experimentally inspired framework.
At the same time, the goal is specifically to understand the relationship between expenditure and calorie consumption for a range of values, not just a local effect at whichever point one might have exogenous variation. Their analysis illustrates the rich rewards of this approach, since the relationship turns out to be non-linear and vary meaningfully at different levels of economic status.
For example, they find that the elasticity of calories declines gradually with increasing economic status, but that substitution between food categories is less important for the poor than the better off. The advantage of this approach is that, setting aside problems of self-selection or endogeneity, the lack of functional form assumptions yields conclusions with a high degree of internal validity. At same time, in settings where endogeneity or selection into treatment are paramount concerns, this method does not in itself offer a solution.
In this sense, the natural comparison is to matching methods. If one is comfortable with the selection on observables assumption, then both methods can yield internally valid estimates of treatment impacts, with two key differences. First, matching methods are naturally set up to estimate treatment impacts, so from binary or more generally discrete treatments, whereas non-parametric regression methods are more useful for continuous treatments or variables of interest.
Second, as with direct matching although unlike propensity score matching , non-parametric methods are subject to the curse of dimensionality; that is these methods are not easy to implement and lack appealing properties when there are a large number of covariates. Hence, in Figure 1 , we depict non-parametric methods as having the same relative merits as direct matching methods.
One of the most widely used regression-based estimators is the difference-in-differences diff-in-diffs estimator see Duflo for an example. The idea behind this method is to use both cross-sectional and time-series variation to relax the assumptions needed for plausible identification of the treatment effect.
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