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GMM estimators are frequently use in autoregressive linear regression models with

small T (time horizon) and large N (units) panels with unobserved firm level

heterogeneity (i.e. fixed effects) . Not considering unobserved heterogeneity faultily

assumes zero correlation between the observed variables and unobserved firm-

specifics. The used of lagged dependent variable as a regressor in a model necessitates

an application of dynamic models because the standard OLS estimators are biased and

inconsistent (i.e. dynamic panel bias). Similarly, LSDV and Within Group estimators

do not eliminate this dynamic panel bias (Nickell 1981). Often in the literature,

standard panel estimators like the fixed effect estimators are employed; however, this

technique is biased in a dynamic setting, where lagged dependent variables are

included in the model26. A dynamic capital structure model with firm-specific effects posed at least two challenges; first, the error term, υit, tends to be correlated with the

lagged dependent variable, M_Leverageit-1.; second, other regressors may be

correlated with firm-specific effect that is time-invariant. A traditional estimator for a

dynamic panel model with firm fixed effects involves first-differencing the model to

26_{Econometrically, an explanatory variable is said to be endogenous if it}

is correlated with the error term of the data generating process.

Endogeneity caused OLS to be biased and inconsistent, thus making estimates of coefficients and inferences invalid.

31 eliminate the firm-specific effect27. Arellano and Bond (1991) also pointed out that a lagged dependent variable in a traditional fixed effect model is correlated with the

error term, and therefore sufficiently endogenous. Taking first-differences will

eliminate the fixed effects but the first difference of lagged dependent variable, Δ

M_Leverageit-1. , is still correlated with the first difference of the error term, Δυit,

through M_Leverageit-1 andυit, thus the fixed model may not necessarily resolve the

endogeneity problem (Wooldridge, 2002).28 A plausible estimation alternative in a dynamic capital structure context with partial adjustment is the dynamic panel

estimators, by utilizing instrumental variables29 estimation technique, through the Generalized Method of Moments (GMM), bias-corrected least squares dummy

variables (LSDVC)30 or fixed effect instrumental variables (FE IV) methods. The justification for instrumentalizing in a dynamic model is not restricted to the concerns

of endogeneity. Instruments are also necessary to address the fact that regressors may

not be strictly exogenous. In other words, outside events that caused a shock to capital

structure may also impact the regressors, and thus may be indirectly correlated with

the present or past error terms. In an attempt to resolve these issues, Arellano/Bond

27_{Anderson and Hsiao (1982), suggest a technique of solving the firm-} specific effect problem, by transforming

the model into first differences to eliminate firm-specific effects, and then use the second lags of the dependent variable, either differenced or in levels, as an instrument for the differenced one-time lagged dependent variable, to eliminate the correlation with the error term.

28_{Fixed effect regression takes out the common time-invariant and firm}

specific effects out of the error term and through first differencing

eliminate completely the fixed effect component of the model. However, in a dynamic panel estimation, where a lagged dependent is necessary, the first differencing is not sufficient to solve the endogeneity problem

(Roberts/Leary 2005, Arellano/Bond 1991, Greene 2003, chap.13).

29_{Instrumental variables have to meet two conditions in a fixed effect}

model. First, they have to be correlated with the lagged dependent variable or independent variables (i.e. if more proxies are included); second, they have to be uncorrelated with the error term.

32 (1991) estimator suggests using instruments for the lagged dependent variables and

endogenous regressors after first-differencing the model. Arellano/Bond (1991)

estimator is a major leap forward, however, with a highly persistent data series such

as leverage, these estimators are sometimes found to be biased when the co-efficient

on lagged dependent variable is close to unity. Arellano and Bover (1995) and

Blundell and Bond (1998) proposed the “system” GMM estimator. The system

estimator transform the model into first differences, and then estimate the model as a “system” by using either the lagged first differences for level equations or lagged

variables for differenced equations as instruments. The combination of these two sets

of moment conditions is therefore the system (SYS) GMM estimator. The key point to

bear in mind regarding the econometrics of capital structure is that there is no perfect

technique. All the various techniques used in the literature have their relative

strengths and weaknesses. Thus, this chapter starts with all four major dynamic

models used in the literature to independently examine adjustment speed for the three

groups (i.e. DC, MNC, and MNC10). I used the traditional fixed effect instrumental

variables estimator (FEIV), which specifically instrumentalized the lagged dependent

variable with its two own lagged, then the Arellano and Bond (1991) one stage and

second staged differenced GMM estimators, and finally, the LSDVC dynamic

estimator is used to estimate the adjustment speed for MNCs and DCs. According to

Bruno (2005), bias corrected least squares dummy (LSDVC) performs better than

other dynamic models, when estimating unbalanced dynamic panel data, however

LSDVC do not generate system standard errors, and are therefore estimated through a

bootstrapping technique. Generally, traditional statistical inference is predicated on

assumptions about the distribution of the population from which the sample is taken

33 normality assumption. In a small sample, improved standard errors may be obtained

by using bootstrap technique. Many prior studies have used bootstrap standard error

estimates for their parameter estimates, and have suggested that inference based on

bootstrap estimates of standard errors may be more accurate in small samples than

inference based on asymptotic standard error estimates (Bruno 2005). Computer

intensive statistical software programs (i.e. Stata) has commands for obtaining

bootstrapped standard errors by evaluating the distribution of a statistic based on

repeated random resampling of the original dataset. Theoretically, the bootstrapping

works as follows: first, random sample with replacement is repeatedly obtained from

the sample dataset; second, desired statistics corresponding to these bootstrap samples are estimated and third, sample standard deviations‟ are calculated of the sampling

distribution of repeated bootstrap samples . There is a lack of specific consensus in

the literature regarding the number of resampling needed for obtaining bootstrapped

standard errors. I suspect the number of iterations in the literature are most likely

influenced by the amount of computing power, time and sample size. Hence

increasing the number of repeated samples cannot increase the amount of information

in the original data. Consequently, I started with 10 iterations, and by successively

increasing the number of iterations, I found no efficiency gain in higher number of

iterations relative to 10 iterations. In other words, the significance level of the

estimated statistics did not change due to increasing iterations. Using Bootstrapped

standard errors has certain specific benefits including the following:

A) When the theoretical distribution of a statistic under investigation is complicated

B) When the sample size is small for traditional statistical inference.

C) Bootstrapped technique only assumes that the sample is representative of the

34 The fixed effect instrumental variables (FEIV) tend to perform well with unbalanced

panel data without generating too many instruments as in the case of GMM

estimators, and it directly generates system standards errors. Thus, the comparative

integrated dynamic partial adjustment model is estimated with the year-controlled,

fixed effect instrumental variables estimator (FEIV).