Methodology

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However, that leverage helps explain the cross-section of average stock returns in tests that include size as well as betas. According to this concept, we use the national GDP as a substitute variable to the economy size, since our dependent variable is the entire stock market of a country. On the other hand we know higher GDP growth rate will cause higher GDP as well, and because the higher GDP growth rate will be beneficial to stockholder, GDP could also reveal the wealth accumulation process. It is consistent with the stock market return. Following these two reasons, we use GDP as a control variable to the stock return; we expect that the GDP will be positive to the stock return.

Gross domestic saving rate

The rate of capital formation is a fundamental determinant for long-term economic growth, and a good gross domestic saving will cause a quicker capital formation. Garcia and Liu(1999) find that saving rate is an important predictor of market capitalization, and observe a much developed country with higher economic growth rate in East Asia will have higher saving rate. They compare the stock market in Latin American with stock market in East Asia, and find that stock market in most Latin American countries are smaller than that in East Asian countries and so is the saving rate. Then we expect that a country with higher domestic saving rate will also have higher long-term economic growth and lead to a good stock return for stockholders.

3.4 Methodology

Research design

This paper evaluates the effect of national competitiveness variables on stock market return within the context of the standard return regression specification. We

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advantage of panel data over cross-section and time-series data is that panel data use both interpersonal and intertemporal variations of variables, whereas cross-section and time-series data use only one of them. See Myoung(2002) Consequently, model parameters can be estimated more precisely in panel data. This method is better than simply increasing the sample size in cross section or time series.

Compared with cross-section data, panel data holds a number of advantages.

First, a cross-section data provides only a snapshot at a given time; panel data can show whether the cross-section image is stable or not over time by allowing time-varying parameters. Second, while cross-section data has difficulty controlling unobserved variables, panel data can control them much better either by removing them or by providing more instruments; the ability to remove time-invariant unobservable variables can be the most important advantage of panel data. Third, panel data allows dynamic models with lagged response variables and regressors;

with this, short-run effects and short-run dynamic features can be found, whereas cross-section shows only long-run effects for the most part.

Compared with time-series data, panel data has a number of advantages. First, although an arbitrary form of temporal correlations can be allowed for the error terms;

this task, even if possible, requires more assumption in time-series. Second, economic theories are developed usually at the individual level (an economic agent optimizing some function), not at the aggregate level, and with panel data, we can test the theories, which is difficult to do with aggregate time series data: restrictions at the individual level do not necessarily hold at the aggregate level, and vice versa. Third, it is difficult to allow for time-varying parameters in time series (imagine T-many parameters for T-many observations). Panel can allow for time-varying parameters easily (imagine T-many parameters for TN-many observations), in such that, panel

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will mitigate the degree of freedom reducing problem.

A simple panel data model is as below

(1) yi,t =α+ β’Xi,t + μ

i

+ ξi,t

If μi

is related with components of Xi,t , then we will call the model a

“ related-effect” model; otherwise, it is called an “unrelated-effect” model. And we call the former “fixed effect” and the latter one is called “random effect”.

There are a couple of other cases where the term “fixed effect” might be appropriate:

(a)

μ

i is estimated along with β

(b) a likelihood function conditional on μ_i is used.

(c) The sample is equal to the population, there is no sample error to make μ_i random.

Fixed effect

The general fixed effect regression equation for panel data to be estimated is as follows:

(2) yi,t =α+ β’Xi,t + μ t + ηi + ξi,t

The subscripts i, t represent country and time period, respectively. y is the dependent variable, that is, the country stock return. X is the set of country-varying and time-varying explanatory variables. The proxies are gross fixed formation, real GDP growth, GDP, gross domestic saving, overall productivity, and country overall competitiveness, while α is the scalar, β the vector of coefficient to be estimated.

Ultimately, μ t denotes the unobservable individual specific effect (μ t is time-invariant which accounts for any individual specific effect that is not included in the regression.), and ηi is the unobservable time specific effect. The reminder disturbance ξi,t varies with individual and time, and therefore can be thought of as the usual disturbance in the regression. This paper uses the panel data, which is suitable

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for the fixed effect model (FEM) and random effect model (error component model, ECM). FE explores the relationship between predictor and outcome variables within an entity (country, company, person, etc.). Each entity has its own individual characteristic that may or may not influence the predictor variables. We could do that by the dummy variable technique to estimate the individual characteristic effects, such as least-squares dummy variable (LSDV) model. Therefore we could write :

(3) y

i,t

= α + β

1

X

1

,

it

+…+ β

K

X

k

,

it

+ γ

2

E

2

+…+ γ

n

E

n

+ u

it

Where:

- y is the dependent variables, and i = entity, t = time.

- X_k,it

represent the independent variables

- β is the coefficient of the independent variables.

- γ is the coefficient for entity dummy variables

- En

is the entity n’s dummy variables that represent individual effect.

- u is the error term.

Just as we use the dummy variables to account for individual effect, we can allow for time effect in the sense that the function shifts over time because other variables change over time. Such time effects can be easily accounted for if we introduce the time effect dummy variables, one for each year. In (3) we combine the entity effect model and the time effect model to have the entity and time fixed effect regression model.

(4) y

i,t

= α + β

1

X

1

,

it

+…+ β

K

X

k

,

it

+ γ

2

E

2

+…+ γ

n

E

n

+ δ

2

T

2

+…+ δ

t

T

t

+ u

it

where:

- y is the dependent variables, and i = entity, t = time.

- X_k,it

represent the independent variables

- β is the coefficient of the independent variables.

- γ is the coefficient for entity dummy variables

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- E_n

is the entity n’s dummy variable that represents individual effect.

- δ is the coefficient for time dummy variable - T is the time variable that represents time effect.

- u is the error term.

If the E_n and T are assumed to be fixed parameters to be estimated and the remainder disturbance are stochastic with u ~iid(0,ζ²u), then the (3) represents a two-way fixed effects error component model. The X_k,it are assumed independent of the error term u for all i and t. We could test for joint significance of the dummy variables.

H₀: δ₂=……=δ_t =0 and γ₂ =……=γ_n =0

Next, we could test for the existence of time effects given individual effects, i.e.

H₂: δ₂=……=δ_t =0 given γ≠0 for N=2,…,n

Similarly, we can test for the existence of individual effects given time effects, i.e.

H₃: γ_{2 =……}=γ_n =0 given δ≠0 for T=2,…,t

Random effect

The second model this paper uses is the random effect model, for we use too many dummies in the fixed effect model which, according to Kmenta notes; make us fail to include relevant explanatory variables that do not change over time (and possibly others that do change over time but have the same value for all cross-sectional units), and that the inclusion of dummy variables is a cover up of our ignorance. The loss of degrees of freedom can be avoided if the

δ

i and γ_t

can be

assumed random. In this case δi~iid(0,ζ²δ), γt

~ iid(0,ζ

²γ), u ~iid(0,ζ²u), and the δi, γt

are independent of the u. In addition, the X_k,it are independent of the δ_i, γ_t and u, for all i and t. The random effects model is an appropriate specification if we draw N individuals randomly from a large population. If N is large then a fixed effect model

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not of an infinity of individuals, in general, but of an infinity of decisions” that each individual might make. This view is consistent with a random effects specification.

We could derives the random effects model:

Y _it = α+ βX it + u it + ε i

Where:

- Y is the dependent variables, and i = entity, t = time.

- X_it represent the independent variables

- β is the coefficient of the independent variables.

- u_it

is the combined time series and cross-section error component.

- ε i is the cross-section, or individual-specific, error component the usual assumption made by random effect model are as follows:

εi ~N(0,ζ²ε), u_it

~ N(0,ζ

²_u),

E(ε

iuit)=0 E(εiεj)=0 (i≠j)

E(u_itu_is)= E(u_itu_jt)= E(u_itu_js)=0 (i≠ j;t≠ s).

The following are the differences between fixed effect model and random effect model:

In the fixed effect model each cross-sectional unit has its own intercept value, so we get N intercept values for N cross-section units. In random effect model, on the other hand, the intercept represents the mean value of all the cross- sectional intercepts and the error components represent the deviation of individual intercept from this mean value. And the error component is not directly observable; it is an unobservable or latent variable.The most appropriate method to estimate the random

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effect model is the method of generalized least squares (GLS).

Constrained by the statistical data collected, the number of observation for individual i varies across I; so we use T_i instead of T. Then the panel is called an unbalance panel. An unbalanced panel is often turned into a “rectangular panel” by trimming the data so that T becomes a number between min_iT_i or max _iT_i. On the other hand, the unbalanced panel of cross-section data with a group structure, where i indexes city can be called a group, and there are T_i members in each group; ε _i represents the common unobserved characteristics of group i. One critical difference from imbalanced panel is that, within each group, there is no temporal ordering of the observations. Despite this difference, however, panel data techniques can be applied fruitfully to group structure data.

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Chapter4 Data Description and Empirical Result

在文檔中 Economic growth, national competitiveness, and stock retrun (頁 21-28)