计量经济学(英文PPT)Chapter 16 Panel Data Regression Models

Let the intercept vary for each company but still assume that the
slope coefficients are constant across firm.We write (16.2.1) as :
Yit =β1i +β2X2i +β3X3i +uit This is known as the fixed effects model(FEM).
• 5.Panel data enables us to study more complicated behavioral models. Such as economies of scale and technological change.
• 6.Panel data can minimize the bias. The bias might occur when we combine different types of data (such as the data of different provinces or different years).
• 2.The slope coefficients are constant but the intercept varies over individuals.
• 3.The slope coefficients are constant but the intercept varies over individual and time.
We assume that the X's are nonstochastic and
the error term uit ~ N(0, σ2).
16.3 Estimation of Panel Data Regression Models: The Fixed Effects Approach
• 1.Assume that the intercept and slop coefficients are constant across time and space and the error term capture differences over time and individuals.
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But, None of the indiቤተ መጻሕፍቲ ባይዱidual time dummies were individual statistically significant.
This might suggest that perhaps the investment function has not changed much over time.
• Panel data have space as well as time deme-nsion. There are other name for panel data, such as pooled data, combination of time series and cross-section data, micropanel data, lingitudinal data, event history analysis, cohort analysis and so on.
In relation to (16.3.4),model (16.3.1) is a restricted model. Restriction is:
The number of restrictions is 3. Therefore, we can use the restricted F test .
• 3.Panel data are better suited to study the dynamics of change.
• 4.Panel data can better detect and measure effects that simply cannot be observed in pure cross-section or pure time series data.
The FEM also assume that the slope coefficients of the regressions do not vary across individual or over time. We can allow for the intercept to vary between companies by the dummy variable technique. Therefore, we write (16.3.2) as :
...... DUM 53 X 2i X3i Uit
(16.3.7)
The conclusion is that there is pronounced individual company effect but no time effect.
The coefficients of X 2 , X3 are significant.
1 ; if the observation belongs to WEST D4i 0 ; otherwise
represents the intercept of GE (General Electric)
See the regression results of (16.3.4) on page 643.
• 4.All coefficients (the intercept as well as slope coefficients) vary over individuals.
• 5.the intercept as well as slope coefficients vary over individuals and time.
1. All coefficients constant across time and individuals We just combine all 80 observations and use OLS. P641 (16.3.1)
2.Slope coefficient constant but the intercept varies across individuals: The fixed effects or least-squares dummy variable (LSDV) regress-ion model .
• Estimation of (16.21) depends on the assumption we make about the intercept ,the slope coefficients, and the error term. There are several possibilities:
Chapter 16 Panel Data Regression Models
• Panel data regression model is the model in which the same cross-sectional unit (say a family or a form or a state) is surveyed over time.
3. Slope Coefficients Constant but the Intercept Varies over individuals As Well As Time:
We combine (16.3.4) and (16.3.6),as follows:
Yit DGMi DUSi DWESTi DUM 35
DUM 53
X 2it

X 3it
U it
(16.3.6)
Where Dum35 takes a value of 1 for observation in year 1935 and 0 otherwise, etc.
The year 1954 is the base year, whose intercept value is given by
11 12 13 14
The Time Effect:
Since we have date for 20 years, we can introduce 19 time dummies to account for time effect .
Yit 1DUM 35 DUM 36
Yit 1 2 X 2it 3 X 3it uit
i 1, 2,3, 4
t 1, 2,..., 20
（16.21）
Y = real gross investment，
X2 = real value of the firm X3 = real capital stock。
16.1 Why Panel Data? • The advantages of panel data:
• 1.The techniques of panel data estimation can take such heterogeneity in units.
• 2.Panel data give more informative data, more variability, less collinearity among variables, more degrees of freedom and more efficiency.
These differences in the intercepts may be due to unique features of each company.
The model (16.3.3) is known as the least-squares dummy variable (LSDV) model.