Esman M. Nyamongo Central Bank of Kenya Panel data analysis Econometrics Course organized by the COMESA Monetary Institute (CMI) on 9-13 February 2015, Kampala, Uganda Esman M. Nyamongo Central Bank of Kenya

Dynamic panel estimation

Dynamics…. …. Economic issues are dynamic in nature and use the panel data structure to understand adjustment Demand (present demand depends on past demand) Dynamic wage equation Employment models Investment of firms

Dynamic panel estimation A dynamic panel model contains at least a lagged variable. Consider the following: with: if i=j and s=t Here the choice between FE and RE formulation has implications for estimations that are of a different nature than those associated with the static panels.

If the lagged dependent variable also appear as explanatory variable then strict exogeneity of the regressors no longer holds. The lagged variable introduces endogeneity problem The LSDV is no longer consistent when N tends to infinity and T is fixed.

The problem with LSDV in DP The LSDV estimator is consistent for the static model whether the effects are fixed or random. therefore need to show that the LSDV is inconsistent for a dynamic panel data with individual effects, whether the effects are fixed or random The bias of the LSDV estimator in a dynamic model is generally known as dynamic bias or Nickell’s bias (1981) Nickell, S. 1981’ Biases in Dynamic Models with Fixed Effects, Econometrica, 49, 1399-1416. Proof needed if possible

In this case, both estimators and are biased. What is the way out? The LSDV for dynamic individual-effects model remains biased with the introduction of exogenous variables if T is small; In this case, both estimators and are biased. What is the way out? ML or FIML Feasible GLS LSDV bias corrected (Kiviet, 1995) IV approach (Anderson and Hsiao, 1982) GMM approach (Arellano and Bond, 1985)

A dynamic panel model contains at least a lagged variable. with: if i=j and s=t The dynamic relationship is characterised by the presence of lagged dependent variable (Yit-1) among the regressors Including the lagged var. introduces endogeneity problem Recall in FE, Y is a function of individual effects therefore it lag is also a function of these effects

To overcome this problem we use GMM. Therefore Yit-1 is correlated with the error term => OLS cannot solve our problems. FE cannot manage cos Yit-1 is correlated with individual effects To overcome this problem we use GMM. Arellano and Bond estimator Arellano and Bover estimator

Arellano and bond estimator To get consistent estimates in GMM for a dynamic panel model, Arellano and Bond appeals to orthogonality condition that exists between Yit-1 and vit to choose the instruments Consider the following simple AR(1) model: To get a consistent estimate of as N-> infinity with fixed T, we need to difference this equation to eliminate individual effects.

Consider t=3 [first year with data] In this case yi1 is a valid instrument of (Yi2- yi1), since it is highly correlated with (yi2-yi1) and not correlated with (vi3-vi2) Consider t=4 What are the instruments? What about when t=5, ………..T?

For period T, set of instrument (w) will be: The combination of the instruments could be defined as: Because the instruments are not correlated with the remaining error term, then our moment condition is stated as:

Pre-multiplying our difference equation by wi yields: Estimating this equation by GLS yields the preliminary Arellano and Bond one-step consistent estimator In case there are other regressors then:

Practical session