The Advantages of Applying Panel Data Analysis to Modelling Data - Assignment Example

? SECTION A a) What are the advantages of applying panel data analysis compared to using pure cross sectional or time series approaches to modelling data? [10 Marks] A panel data is a special type of pooled data in which a cross-sectional unit is surveyed over time (Gujarati 2004, p. 28). Panel data is one of the three types of data generally available for analysis; the other types being timer series and cross section data (Gujarati 2004, p. 636). , Panel data analysis combines the features of time series and cross-section data analysis (Gujarati 2004, p. xxvii). Gujarati (2004, p. 562) pointed out that panel data models combine time series and cross-section observation. Being so, a panel data analysis combines the advantages of both cross sectional and time series approaches (Gujarati 2004, p. xxvii). Panel data analysis is highly feasible because panel data in the social sciences are available (Gujarati 2004, p. xxvii). In the time series data, one observes the values of one or several variables across time (Gujarati 2004, p. 636). In contrast, the values of the variables are collected for one or several sample units or entities at the same point in time (Gujarati 2004, p. 636). The other names for panel data are pooled data, combination of time series and cross-section data, micropanel data, longitudinal data, event history analysis, and cohort analysis (Gujarati 2004, p 636). From panel data, panel data regression models are constructed (Gujarati 2004, p. 634-637). Gujarati (2004, p. 636) reported that Baltagi cited the following advantages of panel data over cross section and timer series analysis: 1. Panel data can consider heterogeneity. 2. Panel data cover more variability, less collinearity, more degrees of freedom and more efficiency. 3. By being able to study cross section observations over time, panel data are better suited to study dynamics of change. 4. Panel data can discover and measure effects that are unobservable using either the pure cross-section or pure time-series analysis: the interrelationship or interaction of variables across time. 5. Panel data can be used to develop or analyze models that more complicated using either of the two pure models (cross-section and timer series). 6. Panel data can minimize that bias that can result from aggregating cases into broad aggregates. Gujarati (2004, p. 638) summarized Baltagi’s six point analysis of the advantages of panel data into this: panel data can improve analysis in ways not possible under cross-section and time series analysis. (b) Explain the intuition behind the fixed effect model (FEM) and describe the least square dummy variable (LSDV) and the time demeaned approaches to estimating a FEM. [30 Marks] According to Brooks (2008, p. 490), there are two kinds of estimation approaches to panel data in financial research: the fixed effects models and the random effects models. The simplest fixed effect allow the intercept in a regression to differ at a given point in time but not across time, while all of the slope estimates are fixed both at a given time moment and across time (Brooks 2008, p. 490). The fixed effect model is considered parsimonious compared to an alternative---the Seemingly Unrelated Regression (SUR) technique---in which each cross-section can have not only different intercepts but also different slopes for a regression (Brooks 2008, p. 490). In illustrating the fixed effect model, Brooks (2008, p. 490) used the equation uit = ui + vit where the disturbance term uit is decomposed into specific disturbance, ui, and “remainder disturbance”, vit, that changes over time and entities thereby supposedly capturing everything unexplained about yit. Based on this, Brooks (2008, p. 491) said that the usual regression function yit = ? + ?xit + uit becomes yit = ? + ?xit + ui + vit where ui represent all the variables that affect yit cross-sectionally or at a given time moment and which does not vary over time. As pointed out by Brooks, some examples of cross-sectional variables that can affect yit include a person’s gender, the country in which the regression applies, or industry in which a firm operates. Thus, given all these, the fundamental intuition behind the fixed effect model is to capture econometrically the effects that are independent of time. Gujarati (2004, p. 642) described the intuition better: in the fixed effect model or FEM, although the intercept may differ across individuals (like companies or nations, for example), each individual intercept does not change over time or is time invariant. Two of the methods for estimating the fixed effects model (FEM) are the least square dummy variable (LSDV) and the time demeaned approaches to estimating the FEM. The LSDV uses dummy variables to estimate a fixed effects model. Suppose there are only three possible companies---Ford, Toyota, and Nissan---the regression equation can be constructed as Yit = ? + ?2D2i + ?3D3i + ?2X2it + ?3X3it + uit where D2i = 1 if the observation belong to Toyota and zero otherwise and D3i = 1 if the observation belongs to Nissan and zero otherwise (Gujarati 2004, p. 642). Based on Gujarati (2004, p. 642), there is no need for a dummy variable for Ford because when D2i = 0 and D3i = 0, it is implied that the observation is for Ford (using a dummy variable for Ford will only result to perfect collinearity that is undesirable for regression equations). Thus, in this example, the dummy variables attempt to capture the fixed effect on Yit of the company or brand. This means that the Yit base differs among the companies covered. Thus, in the LSDV approach, the main tools to identify and capture econometrically the fixed effects, when fixed effects do exist, are dummy variables. Meanwhile, the time demeaned variable approach to estimating the FEM reconstruct the basic model yit = ? + ?xit + uit as departures of each variable from its own time mean or yit - i ?(xit - i ) + ( uit - i) where the values with bars above the variables denote the time mean of the said variable (Brooks 2008, p. 491). An intercept is not required in the regression and the regression is executed based on subtracting each variable value from the time mean of each mean of the each variable or yit - i ?(xit - i ) + ( uit - i) as mentioned earlier. (Brooks 2008, p. 492). (c) Explain the intuition behind the formulation of a random effects model (REM). [15 Marks] Brook (2008, p. 498) pointed out that the random effects model is similar with the fixed model in so far as the random effects proposes different intercept terms for each entity and that each intercepts are constant with time and with the relationship between explanatory and explained variables are held to be constant cross-sectionally and across time as well. The difference between the fixed effects and the random effects model is that the intercept from each crossectional unit are assumed to arise from a common intercept ? plus a random variable ?i that changes cross-sectionally but is constant over time (Brooks 2008, p. 498). The ?i measures the random deviation of each entity’s intercept term from the “global” value of ? (Brooks 2008, p. 498). According to Brooks (2008, p. 498), the random effects model can be represented as yit = ? + ?xit + it where it = ?i + v it . Gujarati (2004, p. 648) clarified that the error term it actually consist of two components: ?i or the cross-section or individual-specific error component or v it which is a combination of a time-series and cross-section error component. Gujarati (2004, p. 647) described the random effects model (REM) as something also known as the error component model (ECM). According to Gujarati (2004, p. 647), the basic idea in the REM or ECM model is that the “constant” term or intercept instead of being fixed is instead conceptualized as a random variable. Thus, intercept ?i = ? + ?i or ?i is a random variable with a mean ? while ?i is a random error term with a mean value of zero. Thus, the fundamental intuition is that while each of the cross-sectional components in the fixed effect model (FEM) has its own intercept, the intercept in the random effects model (REM) is the mean of all cross-sectional intercepts and the error component of the intercept represents the deviation of the individual intercepts from the mean intercept (Gujarati 2004, p. 648). Thus, in the random effects models (REM), regressors have effects on the dependent variables through the slope coefficients but the cross sections have based values represented by the intercepts which deviates from mean intercept through the error component, ?i. (d) An investigator is analysing the impact of government consumption and government investment on the level of GDP and wishes to determine whether to use the fixed effects or random effects model. The investigator has data for the years 1985-2007 for 130 countries. All variables are in constant 1999 prices and are defined as follows: GDP = Gross Domestic Product (billion ?) GCons = Government Consumption (billion ?) GInv = Government Investment (billion ?) C = constant term The Eviews output, given in Tables 1.1 and 1.2, shows the results of the Hausman Specification test. (i) Describe the intuition and specification of the Hausman test. [25 Marks] The specification of the Hausman test is that the null hypothesis of the test is that the fixed effects model (FEM) and the random effects model (REM) do not differ substantially (Gujarati 2004, p. 651). If we are able to reject the null hypothesis in the Hausmann test, implying that the FEM and the REM differ substantially, then the intuition is that REM is not appropriate and that it may be more appropriate to stick to the model that assumes fixed effects (Gujarati 2004, p. 651). (ii) Which of the FEM or REM is better suited for modelling the impact of government spending on GDP? Clearly explain your answer. [10 Marks] Given the Hausman specification test result in Table 1.1, we may reject the null hypothesis at the 0.05 probability level. This means that the fixed effects model (FEM) and the random effects model (REM) differ substantially at the adopted critical probability level. Following Gujarati (2004, p. 651) and Brooks (2008, p. 509), the appropriate view to take is that we may be better off to adopt the fixed effects model or FEM and consider that the random effects model (REM) is not appropriate. In other words, following Brooks (2008, p. 509), what is suggested by the EVIEWS output is that the fixed effects specification “is to be preferred”. At the same time, we must remind ourselves that adopting the viewpoint of Jack Johnston and John DiNardo of 1997, Gujarati (2004, p. 651) echoed the warning of the two men that there are really no simple rules in deciding between fixed and random effects. For example, it may useful to see also the other data on the regression statistics in assessing Table 1.1. Checking on the R-square of the models may be useful but a quick look at Wooldridge 2006 Chapters 13 and 14 does not show that panel data modelling is able to produce good R-squared. More importantly, the relevant or applicable economic theory on an issue should be a fundamental guide on whether fixed effects or random effects modelling should be used because econometrics after all is merely an implementation of the applicable and sound theory on the problem or situation being analyzed. (iii) What do the relative sizes of the FEM and REM coefficients, given in Table 1.2, infer on the results of the Hausman test above. [10 Marks] The cross-section effects test comparisons reflected on Table 1.2 are consistent with the results of Table 1.1. Table 1.2. suggests that the estimates of effects based on the assumption of fixed versus random effects of variable GInv are significantly different from each other at probability level 0.05. The EVIEWS output suggest that we can reject the null hypothesis that the estimate of effects of the variable GInv based on an assumption of fixed effects is equal to the estimate of effects of the variable GInv based on the assumption of random effects. Thus, Table 1.2 suggests that it is preferable to adopt the assumption of fixed effects of the variable GInv on the level of the GDP. The EVIEWS output support the view articulated earlier that we may be better off adopting or preferring the assumption of fixed effects over the assumption of random effects. Similarly, a similar result can be reached on the variable GCons. Like in the earlier discussion, we can reject the null hypothesis that the estimate on the effects of GCons on GDP based on an assumption of fixed effects is equal to the estimate of effects of GCons on GDP based on an assumption of random effects. In sum, like for variable GInv, Table 1.2 suggests that we may be better off adopting or preferring the assumption of fixed effects to the assumption of random effects of GCons on the GDP. In sum, Tables 1.1. and 1.2. provide a strong basis for adopting the fixed effects model or FEM in our analysis of panel data. Firstly, analyzed on a per variable basis, Table 1.2. suggests the adopting the fixed effects model is appropriate. Secondly, analyzed as a whole, Table 1.1. suggests that adopting the fixed effects model is also preferable to the random effects model. EVIEWS OUTPUT Table 1.1 Hausman Specification Test (Random vs. Fixed Effects) Equation: EQ145 Test for correlated cross-section random effects Test Summary Chi-Sq. Statistic Chi-Sq. d.f.   Prob. Cross-Section random 6.2344 119 0.0395 Table 1.2 Cross-section random effects test comparisons: Variable Fixed Random Var(Diff.) Prob. GInv 1.783321 2.890872 1.783321 0.0479 GCons 0.323466 0.889076 0.565s61 0.0294 References Baltagi, B. Econometric Analysis of Panel Data. 4th edition. New York: John Wiley and Sons. Brooks, C., 2008. Introductory econometrics for finance. 2nd edition. Cambridge University Press. Gujarati, D. (2004). Basic Econometrics. 4th edition. New York & London: McGraw Hill Companies. Wooldridge, Jeffrey M. 2003. Introductory econometrics: A modern approach. 2nd edition. Cincinnati: South Western College Publishing. Wooldridge, J., 2006. Introductory econometrics: A modern approach. 3rd edition. Thomson South-Western. Read More