In Chapter 1 I characterize sharp bounds on treatment effects under data combination with instrumental variables. Data combination in this paper refers to having multiple samples drawn from the same population in which observations cannot be linked across samples. I allow for subsets of the outcome, treatment, instrument and covariates to be observed across these samples. The parameters I can bound include the average treatment effect and certain policy relevant treatment effects. The sharp identified upper and lower bounds for the parameter of interest can each be expressed as the optimal value of the objective function in a linear programming problem where the coefficients are probabilities identified from the samples, under certain conditions. These conditions include standard instrumental variables assumptions allowing for heterogeneous effects, finite range of random variables, and a condition regulating which combinations of variables can be observed across samples. This identification strategy forms the basis for estimation, although estimation is not as simple as replacing the identified coefficients with sample estimates. In Chapter 2 the estimation procedure developed in Chapter 1 is applied to algorithmic bail reform. I estimate the identified set for the change in incarceration rate for a move from the status quo to a policy of using an algorithm to determine pretrial release. Whether zero is in, above, or below the identified set indicates whether such a policy of pretrial release would increase or decrease the incarceration rate or whether the sign of the change in incarceration rate cannot be determined from the identified distributions. Whether zero is in the estimate of the identified set depends on which shape restrictions are imposed. Under the commonly used monotonicity assumption, the estimate of the identified set is below zero. If this were the case in the true identified set, that would imply that replacing the status quo with algorithmic pretrial release would reduce the incarceration rate. In Chapter 3 I show an asymptotically optimal choice of a weighting matrix used in the synthetic control method. The synthetic control method takes a weighted average of outcomes for untreated units to estimate the outcome under no treatment for a treated unit. This can then be used to estimate a treatment effect for the treated unit. The weights are chosen such that the weighted average of the outcomes in the pretreatment time periods and of covariates approximates that of the treated unit. In practice, these weights are chosen to minimize a distance which depends on a weighting matrix. I show asymptotic optimality of a leave-one-out cross-validation procedure to choose this weighting matrix. This amounts to performing the synthetic control method, in turn, as if each of the untreated units were instead treated and assessing the prediction on the untreated units for a given weighting matrix. This is not straightforward because there is dependence across these synthetic control estimates.

Creator

• Lee, Ryan Alan

DOI

• https://doi.org/10.21985/n2-ybxj-c876

Subject

• Economics

Language

• en

Alternate Identifier

• etdadmin_upload_743663
• http://dissertations.umi.com/northwestern:15115

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright