Summarizing Relationships among variables

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Lecture 3-4

• Summarizing Relationships among variables

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Topics covered in this lecture note

• We will cover several topics about ordinary least
  square estimation using panel data.
• Estimating a simple regression using panel Data
• A policy analysis using a panel data.

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1. Panel DataIntroduction

• Panel Data is a data set that contains repeated
  observations over time.
• We will see how to deal with such data using an
  example.

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Panel Data -Example-

• Open Panel Data Exercise. This data set
  contains a production data of several
  construction companies for the period between
  1990 and 1997. Production of each company is
  measured by the total material moved in tones.
  Employment is measured by the number of persons
  employed. Equipment is measured by the sum of
  engine powers for all the equipment used.

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Panel Data -Example-

• Notice that for each company, observation is
  collected for several years You have repeated
  observations for the same company over time. This
  is an example of a panel data.
• Suppose you would like to know how many employees
  you have to hire in order to achieve a certain
  level of production. To answer this question, can
  we simply estimate
• (Production)ß0ß1(Employemnt)ß2(Equipment)?
• Or do we have to modify the model to suit the
  panel data?

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Panel Data -Example-

• When we use panel data, we need to consider the
  year effect.
• Year effect refers to the aggregate effect of
  unobserved factors that affect production of all
  the company equally in a particular year. For
  example, the government may have relaxed the
  requirement for environmental regulation for
  construction industry in a particular year. Then,
  such policy would affect the production of all
  the construction companies equally. Next
  Slide

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Panel Data -Example, Year effect-

• If such a change in governmental regulation is
  not observed by the data analysts and if we (as
  data analysts) do not take such an unobserved
  factor into consideration, we may mistakenly
  attribute such year effects to employment or
  equipment. This may give inflated (or deflated)
  image of the effects of employment or equipment
  on the production level. Next Slide

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Panel Data -Example, Year effect-

• Therefore, when we use panel data, we need to
  take into consideration such year effects.
• Year effect refers to the aggregate effects of
  unobserved factors in a particular year that
  affect the production of all the companies
  equally.

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Panel Data -Incorporating Year Effects in the
model-

• The simplest way to incorporate the year
  effects in the model is to incorporate year
  dummy variables in the model.
• Often year dummy variables are called year
  dummies.
• The following slides show how to construct year
  dummy variables.

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Panel Data -Constructing year dummy variables-

• We take the Panel Data exercise, Data A as an
  example. This panel data covers the period
  between 1990 and 1999. Then for each year except
  the first year in the data, you construct the
  dummy variable in the way described in the box.

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Panel Data -Incorporating year dummy variables
in the model-

• After constructing the year dummies, we can
  incorporate these dummy variables in the model in
  the following way.
• (Production)ß0ß1(Employemnt)ß2(Equipment)ß3Yea
  r91 ß4Year92 ß5Year93 ß6Year94 ß7Year95
  ß8Year96 ß9Year97 ß10Year98 ß11Year99

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Year dummies, exercise

• Use Panel Data Exercise Data A, construct the
  year dummy variables.

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More exercise

• Exercise 1. Use the data you constructed in the
  previous exercise, estimate the effect of
  employment and equipment on the production level
  using the following model. Make sure to
  incorporate year dummy variables in your model.
• (Production)ß0ß1(Employemnt)ß2(Equipment)ß3Ye
  ar91 ß4Year92 ß5Year93 ß6Year94 ß7Year95
  ß8Year96 ß9Year97 ß10Year98 ß11Year99
• Exercise 2. Estimate the effect of employment and
  equipment on the production without incorporating
  the year dummies. Compare the results with the
  result from Exercise 1.

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More exercise

• Exercise 3 Using the results of exercise 1,
  answer the following questions.
• Exercise 3-1 If a firm hires 600 workers and
  use the equipment equal to 4000, what would be
  the expected production of the firm. Assume that
  the year effect is equal to the year effect of
  1998.
• Exercise 3-2 Suppose that the firm is using
  equipment equal to 5000. If the firm would like
  to achieve 7000 tones of production, how many
  workers does it have to hire? Assume that the
  year effect is the same as the year effect of
  1998.

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Notes about year dummy variables

• When you use panel data, construct year dummy
  variables except the first year. (More precisely
  speaking, there must be at least one year for
  which you do not use year dummy)
• If you include year dummy for all the years,
  including the first year, you will have a problem
  called perfect multi-colinearity. If this
  happens, OLS regression procedure will not work
  anymore. (Excel will automatically drop one year
  dummy)

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2.Policy analysis using panel data

• Regression analysis is widely used for policy
  analysis.
• Examples of policy analysis include the analysis
  of
• Effect of governmental subsidies on small-medium
  enterprises on the growth of these enterprises.
• Effect of job training on the wage of workers.
• Effect of changing the package of product on the
  revenue from the product.
• Effect of changing compensation scheme on the
  productivity of firms.

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Example The effect of changing the compensation
scheme on the productivity

• We continue using the Panel Data Exercise data
  set.
• Some of the construction companies in the data
  set began to introduce a new compensation scheme
  called productivity bonus. The productivity
  bonus is tied to the amount of production (i.e.,
  The company pays 0.003 for each tone of material
  moved, etc).
• We would like to see if the productivity bonus
  scheme has increased the productivity of these
  companies, and if so by how much.

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Example The effect of changing the compensation
scheme on the productivity, contd

• The simplest way to evaluate the effect of
  productivity bonus is to incorporate dummy
  variable for productivity bonus. We can construct
  dummy variable for productivity bonus in the
  following way.
• (Productivity bonus Dummy)1 if productivity
  bonus exists.
• 
  0 if productivity bonus does not
• 
  exists.
• Such a dummy variable is often called the
  policy dummy variable since the dummy variable
  shows if a particular policy (or compensation
  scheme) exists or not.

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Example The effect of changing the compensation
scheme on the productivity, contd

• Open the data Panel Data Exercise, Data C. This
  data contains the productivity bonus dummy.
• Notice that from 1993, some of the company began
  to introduce productivity bonus scheme. At the
  end of the sample period (year 1999),
  productivity bonus has become fairly prevalent.
  (6 out of 13 firms are using the productivity
  bonus)

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Example The effect of changing the compensation
scheme on the productivity, Exercise

• Then how should we estimate the effect of
  productivity bonus on the productivity of these
  firms?
• Exercise Consider the following model. How
  would we interpret ß3, the coefficient for the
  productivity bonus dummy? Is there any problem
  with this model?
• (Production)ß0ß1(Employment)ß2(Equipment)
• ß3(Productivity Bonus
  Dummy)

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Exercise Answer

• The model, (Production) ß0 ß1(Employment)ß2(Equ
  ipment) ß3(Productivity Bonus Dummy) if a fine
  model if there were no year effects.
• If there were no year effects, ß3 shows the extra
  production the firm can produce holding
  employment and equipment constant If the number
  of employees and the amount of equipment are the
  same, by introducing productivity bonus, the
  production would increase by ß3. Therefore, ß3
  can be interpreted as the effect of productivity
  bonus on the productivity of these companies.

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Exercise Answer, contd

• The problem of the model is that it is unlikely
  that there is no year effects. In the presence of
  year effects, ß3 shows the confound effect of
  productivity bonus and the year effects.
• Therefore, in order to separate the effect of
  productivity bonus from the year effects, we have
  to include year dummies in the model.

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Example The effect of changing the compensation
scheme on the productivity

• A better way to estimate the effect of
  productivity bonus on the productivity of these
  companies is to estimate the following model.
• (Production)ß0ß1(Employment)ß2(Equipment)
  ß3(Productivity Bonus Dummy) ß4(Year91)
  ß5(Year92) ß6(Year93) ß7(Year94) ß8(Year95)
  ß9(Year96) ß10(Year97) ß11(Year98)
  ß12(Year99)

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Exercise

• Use Panel data exercise, Data C. Estimate the
  effect of productivity bonus on the production of
  the construction companies. Make sure to include
  year dummies. Has productivity bonus increased
  the productivity of these firms. By how much has
  it increased the productivity?
• Estimate the model without year dummies, and
  compare the result with the model with year
  dummies. Do you find differences? If there are
  any differences, explain why the differences
  arise.

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Summary for policy analysis using panel data

• Construct a policy dummy variable (productivity
  bonus dummy for our example)
• Construct year dummies for all years except the
  first year.
• Estimate a model including the policy dummy
  variable and year dummies. The coefficient for
  the policy dummy variable can be interpreted as
  the effect of the policy.

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Topics for the next class

• Introduction to probabilities. Basic notations,
  conditional probabilities, bivariate
  probabilities.