On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference
Power curves of the Conditional Likelihood Ratio (CLR) and related tests for testing H0:β = β0 in linear models with a single endogenous variable, y = xβ+u, estimated using potentially weak instrumental variables have been presented for two different designs. One design keeps the variance matrix of...
| Main Authors: | , |
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| Format: | Journal article |
| Jezik: | English |
| Izdano: |
Elsevier
2022
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| _version_ | 1826309894122242048 |
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| author | Van de Sijpe, N Windmeijer, F |
| author_facet | Van de Sijpe, N Windmeijer, F |
| author_sort | Van de Sijpe, N |
| collection | OXFORD |
| description | Power curves of the Conditional Likelihood Ratio (CLR) and related tests for testing
H0:β = β0 in linear models with a single endogenous variable, y = xβ+u, estimated
using potentially weak instrumental variables have been presented for two different
designs. One design keeps the variance matrix of the structural and first-stage
errors, Σ, constant, the other instead keeps the variance matrix of the reduced-form
and first-stage errors, Ω, constant. The values of Σ govern the endogeneity features
of the model. The fixed-Ω design changes these endogeneity features with changing
values of β in a way that makes it less suitable for an analysis of the behaviour of
the tests in low to moderate endogeneity settings, or when β and the correlation of
the structural and first-stage errors, ρuv, have the same sign. At larger values of |β|,
the fixed-Ω design implicitly selects values for Σ where the power of the CLR test is
high. We further show that the Likelihood Ratio statistic is identical to the t0(βb
L)
2
statistic as proposed by Mills et al. (2014), where βb
L is the Liml estimator. In fixedΣ design Monte Carlo simulations, we find that Liml- and Fuller-based conditional
Wald tests and the Fuller-based conditional t
2
0
test are more powerful than the CLR
test when the degree of endogeneity is low to moderate. The conditional Wald tests
are further the most powerful of these tests when β and ρuv have the same sign.
We show that in the fixed-Ω design, setting β0 = 0 and the diagonal elements of Ω
equal to 1 is not without loss of generality, unlike in the fixed-Σ design. |
| first_indexed | 2024-03-07T07:42:35Z |
| format | Journal article |
| id | oxford-uuid:7b4c8dd7-699e-42a7-a53a-1c3b657d7893 |
| institution | University of Oxford |
| language | English |
| last_indexed | 2024-03-07T07:42:35Z |
| publishDate | 2022 |
| publisher | Elsevier |
| record_format | dspace |
| spelling | oxford-uuid:7b4c8dd7-699e-42a7-a53a-1c3b657d78932023-05-02T12:47:17ZOn the power of the conditional likelihood ratio and related tests for weak-instrument robust inferenceJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:7b4c8dd7-699e-42a7-a53a-1c3b657d7893EnglishSymplectic ElementsElsevier2022Van de Sijpe, NWindmeijer, FPower curves of the Conditional Likelihood Ratio (CLR) and related tests for testing H0:β = β0 in linear models with a single endogenous variable, y = xβ+u, estimated using potentially weak instrumental variables have been presented for two different designs. One design keeps the variance matrix of the structural and first-stage errors, Σ, constant, the other instead keeps the variance matrix of the reduced-form and first-stage errors, Ω, constant. The values of Σ govern the endogeneity features of the model. The fixed-Ω design changes these endogeneity features with changing values of β in a way that makes it less suitable for an analysis of the behaviour of the tests in low to moderate endogeneity settings, or when β and the correlation of the structural and first-stage errors, ρuv, have the same sign. At larger values of |β|, the fixed-Ω design implicitly selects values for Σ where the power of the CLR test is high. We further show that the Likelihood Ratio statistic is identical to the t0(βb L) 2 statistic as proposed by Mills et al. (2014), where βb L is the Liml estimator. In fixedΣ design Monte Carlo simulations, we find that Liml- and Fuller-based conditional Wald tests and the Fuller-based conditional t 2 0 test are more powerful than the CLR test when the degree of endogeneity is low to moderate. The conditional Wald tests are further the most powerful of these tests when β and ρuv have the same sign. We show that in the fixed-Ω design, setting β0 = 0 and the diagonal elements of Ω equal to 1 is not without loss of generality, unlike in the fixed-Σ design. |
| spellingShingle | Van de Sijpe, N Windmeijer, F On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title | On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title_full | On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title_fullStr | On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title_full_unstemmed | On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title_short | On the power of the conditional likelihood ratio and related tests for weak-instrument robust inference |
| title_sort | on the power of the conditional likelihood ratio and related tests for weak instrument robust inference |
| work_keys_str_mv | AT vandesijpen onthepoweroftheconditionallikelihoodratioandrelatedtestsforweakinstrumentrobustinference AT windmeijerf onthepoweroftheconditionallikelihoodratioandrelatedtestsforweakinstrumentrobustinference |