In Chapter 1, we construct a test for hypotheses about the effect of a recent policy change, when a single unit is treated and there are several control units, with time series observations of each available before and after the policy change. The goal is to incorporate information provided by the control units to conduct inference on the policy effect on the treated unit. It is often necessary to do so in order to eliminate unobserved factors present in the time series of the treated unit that would otherwise prevent attributing a change in outcome to the policy. I consider techniques that combine observations of treated and control groups (in a potentially data-dependent way) into a univariate time series. We provide a new test for a treatment effect occurring at the end of this univariate time series, and prove that data-driven combinations yield a valid test for treatment effects in large samples. We also show that it is necessary to strengthen our assumptions on the dependence of observations across time if one wishes to construct a procedure that has correct asymptotic null rejection probability uniformly over the class of distributions in the null hypothesis. In Chapter 2, we show how the test constructed in Chapter 1 can be employed to conduct more powerful tests for treatment effects when the untreated units are combined in a data-dependent way. This provides a motivation for the use of data-dependent techniques, like the increasingly popular Synthetic Control Method, over others, like Difference in Differences, that do not exploit the data. In particular, we show that if certain unobservables satisfy distributional assumptions, the Synthetic Control Method selects the univariate time series that maximizes the (asymptotic) power of our test against a class of alternatives. We also show how size distortions are impacted by estimation choices that are not reflected in the asymptotic theory, and argue that careful consideration of nominal size distortions is necessary. In Chapter 3, we propose two tests for a parametric specification versus a non-parametric alternative when model parameters are (partially) identified through instrumental variables. The goal is to test whether the true structural function could be at least one of the functions in a parametric family specified by the researcher. Our tests are robust to partial identification of the structural function and are therefore applicable when parametric assumptions fail to point identify unknown parameters. Our procedures can be applied to many empirical settings where parametric specifications are assumed for practicality and are not a direct consequence of economic theory. Moreover, parametric assumptions are often combined with assumptions about the data in order to point identify the finite-dimensional parameter. Much attention has been paid to this issue in the context of weak instrumental variables, where it is well known that inference on model parameters assuming strong instruments can be misleading. In model specification tests, over-rejection of a correct functional form can occur when instruments are assumed to provide point identification. On the other hand, our first test controls the asymptotic null rejection probability and is consistent against any alternative model which provides evidence against the parametric specification, irrespective of instrument strength. Our second test controls the null rejection probability exactly under an easy to interpret local identification condition. The asymptotic distributions of the test statistics are non-standard. Therefore, we outline a bootstrap procedure which consistently estimates the quantiles of these distributions to provide critical values for our tests.

Creator

• Hardwick, Joseph William George

DOI

• https://doi.org/10.21985/n2-znnj-nb52

Subject

• Economics

Language

• en

Alternate Identifier

• etdadmin_upload_772906
• http://dissertations.umi.com/northwestern:15343

Date created

• 2020-01-01

Resource type

• Dissertation

Rights statement

• In Copyright