Econometrics
Fixed effects model
Keisuke Kawata
Hiroshima University
Regression approach
• Let suppose the following population model
� = 0 + ��� + �
⇒Generally, the error term can be decomposed as � =
�: the entity fixed effect, : the date fixed effect,
� : the other effect.
• Even if � � � = 0, the OLS estimator has an bias due to the correlation between �� and
� + + � .
Fixed effect model without control variables
• To control the entity and date fixed effect, we introduce the entity dummy � and the date dummy into the population model
Called as
Remainder: If there exists perfect linear relationship between variables A and B,
⇒ The effects of variables B can be by introducing variable A into the population model.
• From the definition, � and � ( and ) have
⇒By dummy variables, we can the effect of the entity and date fixed terms!!!.
Problem Heterogeneous time trend
• If there are , the estimator has bias. e.g.) The effect of Road construction plan for a village.
Plan for Road
Construction Expenditure ↑
Fixed effect model with control variables
• To eliminate the bias from heterogeneous time trends, we can use
e.g.) Our interest if the effect of �� .
• A time-variant and non-common variable � have effects on �� and the explained variable ⇒
• If our data includes the information about � , we should estimate the following fixed effect model
⇒If all covariates can be observed, we can obtain unbiased estimator.
Assumptions
The assumption in multiple regression 1. The entities of your date are
2.
3. The conditional independence 4. There is no perfect
• If the following assumptions hold, estimators � are –
– have u der the large sa ple size.
pure ra do l dra s.
� vis = 0
ulti olli earit
Question
• True/False question.
Suppose the pure random sampling and panel data.
1. To estimate the effect of occupation on income, we can eliminate the (linear) effect coming from ge e usi g the fi ed effe t approa h.
2. Even if we use the fixed effect approach, the estimators may have bias. 3. To estimate the effect of (physical) distance between countries on trade-
volume, we should use the fixed effect model.
4. Even if we use the fixed effect model, to estimate the effect of occupation on i o e, e should i orporate or pla e as o trol aria les.
Datta (12, JDE)
Purpose: Estimating the effects of road- o stru tio o fir ’s eha ior i I dia. Data: World Bank Enterprise Surveys for India in 2005 and 2008, Unit: Firm
Treatments: New high-way constructing program (Golden Quadrilateral Project )
⇒Upgrade four national highways directly linking four largest metropolitan cities.
• They use two types of treatments.
1. laying in cities that lay along the upgraded highways (treatment firms) or laying other cities (control firms).
2. driving distance of the city that a firm is located in from the nearest city where upgrading high-way.
Treatments
Outcomes
• By reducing the transportation costs, quantity of input inventory can be decreased ⇒can save the stock expense.
⇒outcome 1: Days of inventory of main input
• By reducing the transportation costs, fir s a ha ge supplier to etter o e.
⇒outcome 2: Years in business with main input supplier
Outcome 1
Outcome 1
Outcome 2
Outcome 2
Conclusion
• Using the fixed effect model, we can eliminate the effect of entity fixed and date fixed terms in general cases.
• To use such approach, your explanation variable must have time-series and cross sectional variations.
• If you cannot use such data, you should use other approach ⇒ for instance, instrumental variables approach.
