On the role of the rank condition in CCE estimation of factor-augmented panel regressions

Karabiyik, Hande; Reese, Simon; Westerlund, Joakim

doi:10.1016/j.jeconom.2016.10.006

Cited by 47 publications

(42 citation statements)

References 10 publications

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“…We also see that the mean of the asymptotic distribution is generally not zero, but rather

- \sqrt{τ} {boldΣ}_{boldv}^{−1} false({boldm}_{1} + {boldm}_{2} false)

. This result is very interesting in that it shows how the results reported in Theorem 3 of Karabiyik et al ( ) under the assumption of stationary factors continue to hold also under Assumption , which is much more general. If F is known, it is easy to show that

\sqrt{N T} false(\overset{b}{true} - bold-italicβ false) \vec{true} N false({bold0}_{k \times 1}, {boldΣ}_{boldv}^{−1} boldS {boldΣ}_{boldv}^{−1} false)

N, T \to \infty

regardless of the relative expansion rate of N and T .…”

Section: Asymptotic Resultssupporting

confidence: 54%

“…According to Theorem 3.1, √ NT ( b − β) converges to a normal distribution with covariance matrix −1 v S −1 v , which is identically the asymptotic distribution of the pooled CCE estimator based on knowing F. We also see that the mean of the asymptotic distribution is generally not zero, but rather − √ τ −1 v (m 1 + m 2 ). This result is very interesting in that it shows how the results reported in Theorem 3 of Karabiyik et al (2017) under the assumption of stationary factors continue to hold also under Assumption F, which is much more general. If F is known, it is easy to show that…”

Section: Asymptotic Distributionmentioning

confidence: 59%

“… Karabiyik et al ( ) and Westerlund and Urbain ( ) both recognize the presence of bias, but fail to provide a correction approach that is asymptotically valid when

m < k + 1

. …”

mentioning

confidence: 99%

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CCE in panels with general unknown factors

Westerlund

2018

The Econometrics Journal

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A popular approach to factor-augmented panel regressions is the common correlated effects (CCE) estimator of Pesaran (Estimation and inference in large heterogeneous panels with a multifactor error structure. Econometrica 74, 2006). In fact, the approach is so popular that it has given rise to a separate CCE literature. A common assumption in this literature is that the common factors are stationary, which would seem to rule out many empirically relevant cases. Moreover, deterministic factors are typically treated as known, which raises the issue of model misspecification. In the current paper, we show how the conditions placed on the factors in CCE can be made much more general than was previously thought possible. In fact, save for some mild regulatory moment conditions, the factors are essentially unrestricted. One implication of this result is that there is no need to discriminate between deterministic and stochastic factors, but that one can instead treat them all as unknown. This is very convenient for practitioners, because it means that under certain conditions they are spared of the problem of having to decide on which deterministic terms to include in the model.

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“…We also see that the mean of the asymptotic distribution is generally not zero, but rather

- \sqrt{τ} {boldΣ}_{boldv}^{−1} false({boldm}_{1} + {boldm}_{2} false)

\sqrt{N T} false(\overset{b}{true} - bold-italicβ false) \vec{true} N false({bold0}_{k \times 1}, {boldΣ}_{boldv}^{−1} boldS {boldΣ}_{boldv}^{−1} false)

N, T \to \infty

regardless of the relative expansion rate of N and T .…”

Section: Asymptotic Resultssupporting

confidence: 54%

Section: Asymptotic Distributionmentioning

confidence: 59%

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CCE in panels with general unknown factors

Westerlund

2018

The Econometrics Journal

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“…To put this result into context, we compare to the existing large‐ T literature. One of the results of this literature is that, while consistent, the asymptotic distribution of the CCEP estimator is biased when T / N → τ > 0 as N , T → ∞ jointly, which obviously poses a problem for inference (see Karabiyik, Reese, & Westerlund, ; Westerlund, ). It is possible to perform an analytic correction, but only in the empirically irrelevant case when m = k + 1.…”

Section: Resultsmentioning

confidence: 99%

CCE in fixed‐T panels

Westerlund

Petrova

Norkutė

2019

J of Applied Econometrics

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Summary The presence of unobserved heterogeneity and its likely detrimental effect on inference has recently motivated the use of factor‐augmented panel regression models. The workhorse of this literature is based on first estimating the unknown factors using the cross‐section averages of the observables, and then applying ordinary least squares conditional on the first‐step factor estimates. This is the common correlated effects (CCE) approach, the existing asymptotic theory for which is based on the requirement that both the number of time series observations, T, and the number of cross‐section units, N, tend to infinity. The obvious implication of this theory for empirical work is that both N and T should be large, which means that CCE is impossible for the typical micro panel where only N is large. In the current paper, we put the existing CCE theory and its implications to a test. This is done by developing a new theory that enables T to be fixed. The results show that many of the previously derived large‐T results hold even if T is fixed. In particular, the pooled CCE estimator is still consistent and asymptotically normal, which means that CCE is more applicable than previously thought. In fact, not only do we allow T to be fixed, but the conditions placed on the time series properties of the factors and idiosyncratic errors are also much more general than those considered previously.

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“…Following Pesaran (2006) and Karabiyik, Reese, and Westerlund (2017), we make the following assumptions:…”

Section: The Model and The Simple Factmentioning

confidence: 99%

Testing for Correlated Factor Loadings in Cross Sectionally Dependent Panels

Kapetanios

Serlenga

Shin³

2019

SSRN Journal

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A large strand of the literature on panel data models has focused on explicitly modelling the cross-section dependence between panel units. Factor augmented approaches have been proposed to deal with this issue. Under a mild restriction on the correlation of the factor loadings, we show that factor augmented panel data models can be encompassed by a standard two-way fixed e §ect model. This highlights the importance of verifying whether the factor loadings are correlated, which, we argue, is an important hypothesis to be tested, in practice. As a main contribution, we propose a Hausman-type test that determines the presence of correlated factor loadings in panels with interactive e §ects. Furthermore, we develop two nonparametric variance estimators that are robust to the presence of heteroscedasticity, autocorrelation as well as slope heterogeneity. Via Monte Carlo simulations, we demonstrate desirable size and power performance of the proposed test, even in small samples. Finally, we provide extensive empirical evidence in favour of uncorrelated factor loadings in panels with interactive e §ects.

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On the role of the rank condition in CCE estimation of factor-augmented panel regressions

Cited by 47 publications

References 10 publications

CCE in panels with general unknown factors

CCE in panels with general unknown factors

CCE in fixed‐T panels

Testing for Correlated Factor Loadings in Cross Sectionally Dependent Panels

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