Likelihood Inference in an Autoregression With Fixed Effects

Dhaene, Geert; Jochmans, Koen

doi:10.1017/s0266466615000146

Cited by 36 publications

(49 citation statements)

References 39 publications

(50 reference statements)

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…The TML and RML estimators in this study are also related to the adjusted profile likelihood of Dhaene and Jochmans () in the sense that the estimators provide a bias‐correction to the standard FE OLS estimator, which is inconsistent for small T (Nickell, ). The estimating equation of this bias‐corrected FE estimator is of the following form:

\frac{1}{N {\overset{σ}{true}}^{2} false(italicϕ false)} \sum_{i = 1}^{N} \sum_{t = 1}^{T} {\overset{y}{true}}_{i, t - 1} false({\overset{false~}{y}}_{i, t} - italicϕ {\overset{false~}{y}}_{i, t - 1} false) + \frac{1}{T} ξ false(italicϕ, T false) = 0,

where, as in section ‘Asymptotic results for T > 2 and TML’,

ξ false(italicϕ, T false) = \sum_{t = 0}^{T - 2} false(T - t - 1 false) {italicϕ}^{t}

.…”

Section: Multiple Solutions and Bounded Estimationmentioning

confidence: 99%

See 1 more Smart Citation

On Maximum Likelihood Estimation of Dynamic Panel Data Models

2017

View full text Add to dashboard Cite

We analyse the finite sample properties of maximum likelihood estimators for dynamic panel data models. In particular, we consider transformed maximum likelihood (TML) and random effects maximum likelihood (RML) estimation. We show that TML and RML estimators are solutions to a cubic first‐order condition in the autoregressive parameter. Furthermore, in finite samples both likelihood estimators might lead to a negative estimate of the variance of the individual‐specific effects. We consider different approaches taking into account the non‐negativity restriction for the variance. We show that these approaches may lead to a solution different from the unique global unconstrained maximum. In an extensive Monte Carlo study we find that this issue is non‐negligible for small values of T and that different approaches might lead to different finite sample properties. Furthermore, we find that the Likelihood Ratio statistic provides size control in small samples, albeit with low power due to the flatness of the log‐likelihood function. We illustrate these issues modelling US state level unemployment dynamics.

show abstract

\frac{1}{N {\overset{σ}{true}}^{2} false(italicϕ false)} \sum_{i = 1}^{N} \sum_{t = 1}^{T} {\overset{y}{true}}_{i, t - 1} false({\overset{false~}{y}}_{i, t} - italicϕ {\overset{false~}{y}}_{i, t - 1} false) + \frac{1}{T} ξ false(italicϕ, T false) = 0,

where, as in section ‘Asymptotic results for T > 2 and TML’,

ξ false(italicϕ, T false) = \sum_{t = 0}^{T - 2} false(T - t - 1 false) {italicϕ}^{t}

.…”

Section: Multiple Solutions and Bounded Estimationmentioning

confidence: 99%

“… Dhaene and Jochmans () extend the setup of Lancaster () and show that the adjusted profile likelihood can also be viewed as a penalized log‐likelihood proposed by Bester and Hansen (), or as a bias‐corrected estimator of Bun and Carree (). …”

mentioning

confidence: 99%

On Maximum Likelihood Estimation of Dynamic Panel Data Models

2017

View full text Add to dashboard Cite

show abstract

“…For example: the simulation results in Arellano and Bover [3], Hahn and Kuersteiner [4], Alvarez and Arellano [5], Hahn et al [6], Kiviet [7], Kruiniger [8], Okui [9], Roodman [10], Hayakawa [11] and Han and Phillips [12] just concern the panel AR(1) model under homoskedasticity. Although an extra regressor is included in the simulation studies in Arellano and Bond [1], Kiviet [13], Bowsher [14], Hsiao et al [15], Bond and Windmeijer [16], Bun and Carree [17,18], Bun and Kiviet [19], Gouriéroux et al [20], Hayakawa [21], Dhaene and Jochmans [22], Flannery and Hankins [23], Everaert [24] and Kripfganz and Schwarz [25], this regressor is (weakly-)exogenous and most experiments just concern homoskedastic disturbances and stationarity regarding the impact of individual effects. Blundell et al [26] and Bun and Sarafidis [27] include an endogenous regressor, but their design does not allow us to control the degree of simultaneity; moreover, they stick to homoskedasticity.…”

Section: Introductionmentioning

confidence: 99%

Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models

Kiviet

Pleus²,

Poldermans

2017

Econometrics

View full text Add to dashboard Cite

Studies employing Arellano-Bond and Blundell-Bond generalized method of moments (GMM) estimation for linear dynamic panel data models are growing exponentially in number. However, for researchers it is hard to make a reasoned choice between many different possible implementations of these estimators and associated tests. By simulation, the effects are examined in terms of many options regarding: (i) reducing, extending or modifying the set of instruments; (ii) specifying the weighting matrix in relation to the type of heteroskedasticity; (iii) using (robustified) 1-step or (corrected) 2-step variance estimators; (iv) employing 1-step or 2-step residuals in Sargan-Hansen overall or incremental overidentification restrictions tests. This is all done for models in which some regressors may be either strictly exogenous, predetermined or endogenous. Surprisingly, particular asymptotically optimal and relatively robust weighting matrices are found to be superior in finite samples to ostensibly more appropriate versions. Most of the variants of tests for overidentification and coefficient restrictions show serious deficiencies. The variance of the individual effects is shown to be a major determinant of the poor quality of most asymptotic approximations; therefore, the accurate estimation of this nuisance parameter is investigated. A modification of GMM is found to have some potential when the cross-sectional heteroskedasticity is pronounced and the time-series dimension of the sample is not too small. Finally, all techniques are employed to actual data and lead to insights which differ considerably from those published earlier.

show abstract

“…Dhaene and Jochmans (2016) prove that this assumption is violated, i.e. I L T (θ * ) is singular, when T = 2 or ρ * = 1.…”

Section: Lancaster's Estimatormentioning

confidence: 88%

“…2 ) as in standard maximum likelihood theory (see Dhaene and Jochmans (2016)). Nonetheless, Theorem 3, proved by Lancaster (2002), shows that the posterior (6) can be used to consistently estimate the structural parameters.…”

Section: Lancaster's Estimatormentioning

confidence: 99%

Likelihood inference and the role of initial conditions for the dynamic panel data model

Barbosa

Moreira

2017

View full text Add to dashboard Cite

Lancaster (2002) proposes an estimator for the dynamic panel data model with homoskedastic errors and zero initial conditions. In this paper, we show this estimator is invariant to orthogonal transformations, but is inefficient because it ignores additional information available in the data. The zero initial condition is trivially satisfied by subtracting initial observations from the data. We show that differencing out the data further erodes efficiency compared to drawing inference conditional on the first observations. Finally, we compare the conditional method with standard random effects approaches for unobserved data. Standard approaches implicitly rely on normal approximations, which may not be reliable when unobserved data is very skewed with some mass at zero values. For example, panel data on firms naturally depend on the first period in which the firm enters on a new state. It seems unreasonable then to assume that the process determining unobserved data is known or stationary. We can instead make inference on structural parameters by conditioning on the initial observations.

show abstract

Likelihood Inference in an Autoregression With Fixed Effects

Cited by 36 publications

References 39 publications

On Maximum Likelihood Estimation of Dynamic Panel Data Models

On Maximum Likelihood Estimation of Dynamic Panel Data Models

Accuracy and Efficiency of Various GMM Inference Techniques in Dynamic Micro Panel Data Models

Likelihood inference and the role of initial conditions for the dynamic panel data model

Contact Info

Product

Resources

About