1. Fixed Effects Model (FEM)
Presented by
Neals M. Frage
April 26, 2006

2. Outline An illustrative example of the Fixed Effects Model (FEM).
Cautions on the use of FEM.
Application of FEM.

3. An illustrative example
Consider the following pooling estimation model:
Y =Gross Investment
X2 = Value of the firm
X3 = Real capital stock

4. Assumptions of a pooling estimation
The intercept value is the same across units or entities (in this case, companies).
The slope coefficient is constant across units or entities (companies).

5. Limitations of a Pooled Regression
Assumptions of constant intercept and slope coefficients are highly restricted and far-fetched.
May distort the “true” relationship between the dependent and independent variables across entities (companies).

6. Account for the “individuality”of each entity.
FIXED EFFECTS APPROACH
A. Slope coefficients constant but the intercept varies across entities.
B. Slope coefficients are constant but the intercept varies over individuals and time.
C. Slope coefficients and the intercept vary across entities.
D. The intercept as well as slope coefficients vary over individuals and time.

7. To see this, consider the following model (16.3.2):
A. Slope coefficients constant but the intercept varies across entities.
To see this, consider the following model (16.3.2):
The subscript i on the intercept suggests that the intercepts of the four firms may be different.

8. Fixed Effects Model (FEM)
Model (16.3.2) is an example of the fixed effects (regression) model.
The term fixed effects is due to the fact that, although the intercept may differ across individual (in this case firms), each individual’s intercept does not vary over time.

9. How to account for the “individual” intercept?
Differential intercept dummies.
The differential intercepts tell us by how much the intercepts of GM, US, and West differ from the intercept of GE.
D2 = GM
D3 = US
D4 = West

10. The Time Effect
Just as we used the dummy variables to account for individual (firm) effect, we can allow for time effect (the function shifts over time) by introducing time dummies.

11. The Time Effect (continued)
Where Dum35 takes a value of 1 for observation in year 1935 or 0 otherwise, etc. (1954 is the base year).
Time effect was found to be insignificant (using the restricted F test).

12. B. Slope coefficients are constant but the intercept varies over individuals and time.
Combine models and to find individual (firm) effect as well as time effect.
Here again, time effect was insignificant (while company effect was significant).

13. C. Slope coefficients and the intercept vary across entities.
To account for differences in the intercepts and slope coefficients, the individual (firm) dummies are introduced in an additive manner (like model ) and in an interactive manner (multiply the dummy by each of the X variables).

14. Differential intercepts and slope coefficients.
Model (16.3.8)

15. Cautions on the use of FEM
Lost of degrees of freedom.
Multicollinearity.
Unable to identify the impact of certain time-invariant variables (e.g. sex, ethnicity, and color).
The error term follows the classical assumptions (which may have to be modified).

16. Application of FEM
Many studies have been done on whether FDI and exports are substitutes or complements. There has been no consensus (results have varied). (Archaic).
“New trade theory” brings an industrial organization approach to international trade.

17. Motivation for Research
I want to investigate the relationship between FDI (foreign direct investment) and exports given the degree of concentration in an industry.
Research Question: How does market structure impact the link between FDI and exports?

18. Data One home country (the UK) and one host country (the US).
1997 US manufacturing industries.
Using NAICS five-digit level data.

19. Empirical Specification
FDI = f (Exports, Ownership-Location-Internalization factors).
FDI = FDI of the UK in the US manufacturing industries.
Exports = Exports from the UK in the US manufacturing industries.
OLI = Factors in the US manufacturing industries that impact and/or determine FDI.

20. OLI factors Ownership (O) = CR4 Location (L) = Sales
Internalization (I) = Advertising cost

21. Using FEM
To find out the differences in the relationship between FDI and exports across market structures, I introduce dummy and interactive dummy variables.
The dummy variables will capture the differential intercepts and the interactive dummies, the differential slope coefficients.

22. Using FEM (continued)
I am interested in the three main types of market structure: Perfect competition, Monopoly, and Oligopoly. Hence, I create two dummy variables.
MD = Monopoly Dummy
OD = Oligopoly Dummy
Base Category = Perfect competition

23. Using FEM (continued)
The creation of the dummy variables is based on the HHI (Herfindahl-Herschman Index) level. The HHI ranges from 0 to 10,000.
HHI < 1000 implies competition
1000 <=HHI<1800 implies Oligopoly
HHI >=1800 implies Monopoly

24. Using FEM (continued) OD=1 if 1000<=HHI<1800 0 Otherwise
MD=1 if HHI >=1800

25. Using FEM (continued)
Since the goal is to capture the differences in the link between FDI and exports across market structures, the dummy variables (MD and OD) are interacted with the independent variable Exports. The interactive terms are ExportsMD and ExportsOD.

26. Simultaneity?
Bi-directional link between Exports and FDI (e.g. Graham, 1997).
Simultaneity problems can result from the bi-directional link .
To deal with the simultaneity problems, I change the specification of the model. Instead of estimating a linear model, I estimate a log-linear model.

27. Estimating FEM
The estimated model is the following:

28. Empirical Results
The coefficients of CR4 and Sales are as expected and significant. The coefficient of advertising cost is negative (as expected) but insignificant.
The relationship between FDI and exports vary across market structures, but never significant.

29. Empirical Results (continued)
Consider the differential intercepts and slope coefficients for the three types of market structure.
Competition: Log(FDI) = – 0.02 Log(Exports)
Oligopoly: Log(FDI) = Log(Exports)
Monopoly: Log(FDI) = Log(Exports)
Insignificant results aside, while the relationship between FDI and exports is negative (substitutes) when the market structure is competitive, it is positive (complements) when the market structure is either oligopoly or monopoly. Thus, the link between FDI and exports in imperfect markets is different than in perfect market.

30. Heteroscedasticity?
Heteroscedasticy is likely when dealing with a cross-sectional dataset and when having qualitative variables.
Both the graphical test and the Breusch-Pagan-Godfrey (BPG) test suggest that heteroscedasticity is present in the fixed-effects estimation.
Weighted least squares (WLS) is used to correct for heteroscedasticity.

31. WLS Results
The WLS results are similar to the previous results except that the coefficient of advertising cost becomes significant.
Consider the differential intercepts and slope coefficients of the WLS for the three types of market structure.
Competition: Log(FD)I = – 0.002Log(Exports)
Oligopoly: Log(FDI) = Log(Exports)
Monopoly: Log(FDI) = Log(Exports)

32. Conclusion
FEM can be cautiously used to account for “individuality” or differences across units.
The link between FDI and exports is positive in imperfect markets and negative in a perfect market (although the results are insignificant).