2/8/2017
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JOB-ORDER AND PROCESS COSTING
LEARNING OBJECTIVE 1
Distinguish between process costing and job-order costing, and identify the production or service processes that
t with each costing method.
In computing the cost of a product or a

The Heteroskedasticity Function Must
Be Estimated: Feasible GLS
In the previous subsection, we saw some examples of where the heteroskedasticity is
known up to a multiplicative form. In most cases, the exact form of heteroskedasticity is
not obvious. In o

Another useful alternative for estimating hi is to replace the independent variables in
regression (8.32) with the OLS fitted values and their squares. In other words, obtain the
g i as the fitted values from the regression of
log(u 2 ) on y , y 2 8.34
an

If the individual-level equation (8.28) satisfies the homoskedasticity assumption,
and the errors within firm i are uncorrelated across employees, then we can show that
the firm-level equation (8.29) has a particular kind of heteroskedasticity. Specifical

What does the finding from part (iii) imply about the proposed form of heteroskedasticity
used in obtaining (8.36)?
(v) Obtain valid standard errors for the WLS estimates that allow the variance function
to be misspecified.
C8.10 Use the data set 401KSUBS

not practically large. For example, if income increases by 10%, cigs is predicted to increase by
(.880/100)(10) _ .088, or less than one-tenth of a cigarette per day. The magnitude of the price
effect
is similar.
Each year of education reduces the average

What If the Assumed Heteroskedasticity
Function Is Wrong?
We just noted that if OLS and WLS produce very different estimates, it is likely that the
conditional mean E(y_x) is misspecified. What are the properties of WLS if the variance
function we use is

big problem in the demand for cigarettes
equation because all the coefficients
maintain the same signs, and the
biggest changes are on variables that
were statistically insignificant when the
equation was estimated by OLS. The
OLS and WLS estimates will a

In the labor force participation example in Section 7.5 [see equation (7.29)], we reported the usual
OLS standard errors. Now, we compute the heteroskedasticity-robust standard errors as well. These
are reported in brackets below the usual standard errors

Now we estimate the _j and _j using WLS estimation of (8.38). That is, after OLS to obtain
the residuals, run the regression in (8.32) to obtain fitted values,
g i _ _ 0 _ _ 1xi1 _ _ _ kxik, 8.41
and then the h i as in (8.33). Using these h i, obtain the

this assumption is false, the standard errors (and any statistics we obtain using those
standard
errors) are not valid. Fortunately, there is an easy fix: just as we can obtain standard
errors for the OLS estimates that are robust to arbitrary heteroskeda

the fitted values y i need not fall in the unit interval. If either y i _ 0 or y i _ 1, equation
(8.47)
shows that h i will be negative. Since WLS proceeds by multiplying observation i by 1/ _
_
h i,
the method will fail if h i is negative (or zero) for a

then the error in the per capita equation has a variance proportional to one over the size
of
the population. Therefore, weighted least squares with weights equal to the population is
appropriate. For example, suppose we have city-level data on per capita

heteroskedasticity in the model.
(v) Use the usual F statistic to test the hypothesis in part (iv). What do you conclude?
(vi) Given the previous analysis, would you say that it is possible to systematically
predict whether the Las Vegas spread will be co

where se(e 0 ) _ cfw_[se(y 0 )]2 _ _ 2 h(x0)1/2.
This interval is exact only if we do not have to estimate the variance function. If we
estimate parameters, as in model (8.30), then we cannot obtain an exact interval. In fact,
accounting for the estimatio

A modern criticism of WLS is that if the variance function is misspecified, it is not
guaranteed to be more efficient than OLS. In fact, that is the case: if Var(y_x) is neither
constant nor equal to _2h(x), where h(x) is the proposed model of heteroskeda

Does part (ii) imply that the new test always delivers a smaller p-value than either
the BP or special case of the White statistic? Explain.
(iv) Suppose someone suggests also adding y i to the newly proposed test. What do you
think of this idea?
8.7 Cons

CONTENTS
5
the Effect of Given Prices Set by Them on Sales;
and in Both Cases the Effect on the Distribution
of the Commodity Among the Competing Buyers . . . . . . . . . . . . . . 218
C. The Effect of Competition in the Supply of a
Good on the Quantity S

8
PRINCIPLES OF ECONOMICS
propensity to truck, barter, and exchange, as suggested by Adam Smith.3 The
exact quantities of goods exchangedtheir prices, in other wordsare determined by the values individuals attach to marginal units of these goods. With a
s

FOREWORD
BY PETER G. KLEIN
There never lived at the same time, wrote Ludwig von Mises, more than
a score of men whose work contributed anything essential to economics.1
One of those men was Carl Menger (18401921), professor of political
economy at the Uni

12 Principles of Economics
known as those of Carl Menger. It is difficult to think of a parallel case
where a work such as the Grundstze has exercised a lasting and persistent influence but has yet, as a result of purely accidental circumstances, had so e

8
PRINCIPLES OF ECONOMICS
propensity to truck, barter, and exchange, as suggested by Adam Smith.3 The
exact quantities of goods exchangedtheir prices, in other wordsare determined by the values individuals attach to marginal units of these goods. With a
s

12 Principles of Economics
known as those of Carl Menger. It is difficult to think of a parallel case
where a work such as the Grundstze has exercised a lasting and persistent influence but has yet, as a result of purely accidental circumstances, had so e

CONTENTS
5
the Effect of Given Prices Set by Them on Sales;
and in Both Cases the Effect on the Distribution
of the Commodity Among the Competing Buyers . . . . . . . . . . . . . . 218
C. The Effect of Competition in the Supply of a
Good on the Quantity S

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linear models do not ensure that predicted values are positive, and our estimated
variances
must be positive in order to perform WLS.
If the parameters _j were known, then we would just apply WLS, as in the previous
subsection. This is not very realistic.

proportional
to income is essentially arbitrary. In fact, in most cases, our choice of weights in
WLS has a degree of arbitrariness. However, there is one case where the weights needed
for WLS arise naturally from an underlying econometric model. This hap