Transcript Chapter 8

Chapter 8
Dummy Variables and Truncated Variables
What is in this Chapter?
• This chapter relaxes the assumption made
in Chapter 4 that the variables in the
regression are observed as continuous
variables.
– Differences in intercepts and/or slope
coefficients
– The linear probability model and the logit and
probit models.
– Truncated variables, Tobit models
8.1 Introduction
• The variables we will be considering are:
– 1.Dummy variables.
– 2.Truncated variables.
• They can be used to
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1.Allow for differences in intercept terms.
2.Allow for differences in slopes.
3.Estimate equations with cross-equation restrictions.
4.Test for stability of regression coefficients.
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
• Two More Illustrative Examples
• We will discuss two more examples using
dummy variables. They are meant to illustrate
two points worth noting, which are as follows:
– 1. In some studies with a large number of dummy
variables it becomes somewhat difficult to interpret
the signs of the coefficients because they seem to
have the wrong signs. The first example illustrates
this problem
– 2. Sometimes the introduction of dummy variables
produces a drastic change in the slope coefficient.
The second example illustrates this point
8.2 Dummy Variables for Changes
in the Intercept Term
• The first example is a study of the determinants of
automobile prices.
• Griliches regressed the logarithm of new passenger car
prices on various specifications. The results are shown
in Table 8.1
• Since the dependent variable is the logarithm of price,
the regression coefficients can be interpreted as the
estimated percentage change in the price for a unit
change in a particular quality, holding other qualities
constant
• For example, the coefficient of H indicates that an
increase in 10 units of horsepower, ceteris paribus,
results in a 1.2 increase in price
8.2 Dummy Variables for Changes
in the Intercept Term
• However, some of the coefficients have to be interpreted
with caution
• For example, the coefficient of P in the equation for
1960 says that the presence of power steering as
"standard equipment" led to a 22.5 higher price in 1960
• In this case the variable P is obviously not measuring the
effect of power steering alone but is measuring the effect
of "luxuriousness" of the car
• It is also picking up the effects of A and B. This explains
why the coefficient of A is so low in 1960. In fact. A, P,
and B together can perhaps be replaced by a single
dummy that measures "luxuriousness." These variables
appear to be highly intercorrelated
8.2 Dummy Variables for Changes
in the Intercept Term
• Another coefficient, at first sight puzzling, is the
coefficient of V, which, though not significant, is
consistently negative
• Though a V-8 costs more than a six-cylinder engine on a
"comparable" car, what this coefficients says is that,
holding horsepower and other variables constant, a V-8
is cheaper by about 4%
• Since the V-8's have higher horsepower, what this
coefficient is saying is that higher horse power can be
achieved more cheaply if one shifts to V-8 than by using
the six-cylinder engine
8.2 Dummy Variables for Changes
in the Intercept Term
• It measures the decline in price per
horsepower as one shifts to V-8's even
though the total expenditure on
horsepower goes up
• This example illustrates the use of dummy
variables and the interpretation of
seemingly wrong coefficients
8.2 Dummy Variables for Changes
in the Intercept Term
8.2 Dummy Variables for Changes
in the Intercept Term
• As another example consider the estimates of
liquid-asset demand by manufacturing
corporations
• Vogel and Maddala computed regressions of the
form log C =α +ß log S, where C is the cash and
S the sales, on the basis of data from the
Internal Revenue Service, "Statistics of Income,"
for the year 1960-1961.
• The data consisted of 16 industry subgroups
and 14 size classes, size being measured by
total assets. When the regression
8.2 Dummy Variables for Changes
in the Intercept Term
8.3 Dummy Variables for Changes
in Slope Coefficients
8.3 Dummy Variables for Changes
in Slope Coefficients
8.3 Dummy Variables for Changes
in Slope Coefficients
8.3 Dummy Variables for Changes
in Slope Coefficients
8.3 Dummy Variables for Changes
in Slope Coefficients
8.3 Dummy Variables for Changes
in Slope Coefficients
8.4 Dummy Variables for CrossEquation Constraints
8.4 Dummy Variables for CrossEquation Constraints
8.4 Dummy Variables for CrossEquation Constraints
8.4 Dummy Variables for CrossEquation Constraints
8.5 Dummy Variables for Testing
Stability of Regression Coefficients
8.5 Dummy Variables for Testing
Stability of Regression Coefficients
8.5 Dummy Variables for Testing
Stability of Regression Coefficients
8.6 Dummy Variables Under
Heteroskedasticity and Autocorrelation
8.6 Dummy Variables Under
Heteroskedasticity and Autocorrelation
8.6 Dummy Variables Under
Heteroskedasticity and Autocorrelation
8.6 Dummy Variables Under
Heteroskedasticity and Autocorrelation
8.6 Dummy Variables Under
Heteroskedasticity and Autocorrelation
8.7 Dummy Dependent Variables
• Until now we have been considering models where the
explanatory variables are dummy variables.
• We now discuss models where the explained variable is
a dummy variable.
• This dummy variable can take on two or more values but
we consider here the case where it takes on only two
values, zero or 1.
• Considering the other cases is beyond the scope of this
book. Since the dummy variable takes on two values, it
is called a dichotomous variable
• There are numerous examples of dichotomous explained
variables.
8.7 Dummy Dependent Variables
8.8 The Linear Probability Model and
the Linear Discriminant Function
• The Linear Probability Model
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
• The Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.8 The Linear Probability Model and
the Linear Discriminant Function
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.9 The Probit and Logit Models
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model
8.11 Truncated Variables: The Tobit
Model