B-03.08
Review the unadjusted trial balance below and prepare adjusting journal entries to record the various described items
below. Record in the space provided at the bottom of this spreadsheet. After completing journal entries, complete the
adjusted tr
There are two problems this week. Click on the tab at the bottom of the spreadsheet to see problem 2.
Compute the ending inventory using the FIFO and the weighted average method below. These are the same transactions used in week 3 homework:
1-Jan
14-Jan
PROBLEM 1
There are two homework problems this week. The first is below and the second one is on the second tab at the
bottom left of the screen
Below you will see an unadjusted trial balance run at year end followed by information needed to make adjustin
Week 6
There are 3 problems this week. Click on the tabs at the bottom of the spreadsheet to view each problem.
Problem 1
Prepare the journal entries for the eight following transactions. Use dates but descriptions are not required.
On 10/1/15, Equipment
probability, and call . Since the t-ratio is asymptotically pivotal, the asymptotic
coverage probability isinterval for independent of the parameter It is useful
to contrast the confidence interval (7.45) with (5.12) for the normal regression
model. They
notation we have introduced may be somewhat confusing so it is helpful to write
it down in one place. The exact variance of b (under the assumptions of the linear
regression model) and the asymptotic variance of b (under the more
general assumptions of th
integer N(0and b setting increases, the sampling distribution
becomes highly skewed 4, 6 and 8. As = 1 for = 100 1) asymptotic
approximationand non-normal. The lesson from Figures 7.2 and 7.3 is that the
N(0 is never guaranteed to be accurate. CHAPTER 7.
proof, see Exercise 8.9. Theorem 8.5.2 shows that the minimum distance estimator
is asymptotically normal for all positive definite weight matrices. The asymptotic
variance depends on W. The theorem includes the CLS estimator as a special
case by setting
special case where and V Error when x0cov(x 2 (7.14) = 0 Condition
(7.14) holds in the homoskedastic linear regression model, but is somewhat
broader. Under (7.14) the asymptotic variance formulae simplify as = E x0 x
E 2 2 (7.15)= Q = Q1V Q1 = Q1 2 V 0
range of values in the confidence interval are too wide based on the point
estimate alone. then do not jump to a conclusion about to learn about For
illustration, consider the three examples presented in Section 7.11 based on the
log wage regression for m
interval, we need to estimate the conditional distribution of which is a much
more difficult task. Perhaps due to this difficulty, many applied+1 = xgiven x
forecasters use the simple approximate interval h x0 b(x)b 2 i despite the lack
of a convincing ju
estimating the model by least-squares, starting with the first 5 observations, and
continuing until the full sample is used, the sequence of estimates are displayed in
Figure 7.1. You can see how the least-squares estimate changes with the sample
size, bu
described in the previous section, a natural estimator for Q1 is Qb 1 defined
in , where Qb (7.1). CHAPTER 7. ASYMPTOTIC THEORY FOR LEAST SQUARES
179 The moment estimator for is b = 1 X =1 x0x b2 (7.25) leading to
the plug-in covariance matrix estimator V
contradictory constraints). The constraint 2 = 0 discussed above is a special case
of the constraint (8.1) with R = 0 I (8.2) a selector matrix, and c = 0. 2 =
11+Another common restriction is that a set of coefficients sum to a known
constant, i.e. This
we find that the asymptotic distribution equals emd ) + W1R V
N (0 R0 W1R1 (W) (8.42)V =N( where = W1R R0 W1R1
The asymptotic distribution (8.42) is an approximation of the sampling distribution
of the restricted estimator under misspecification. The di
b (8.17) () is small if is close to b, This is a (squared) weighted
Euclidean distance between b and and is minimized at zero only if = b. A
minimum distance estimator emd for minimizes () subject to the constraint
(8.1), that is, emd = argmin 0 = (8.18)
Theorem 7.16.1, a good choice for a confidence region is the ellipse 1()
b = cfw_ : 2 quantile of the the 1 1with ) It can be computed)=1
1( distribution. (Thus ,q)in MATLAB.by, for example, chi2inv(1Theorem 7.16.1 implies Pr b Pr 2 1 = 1 b has
asympto
R0 (X01 X) 0 and is hence invertible.1 R (See Section A.9.) Substituting this
expression into (8.6) and solving for ecls we find the solution to the constrained
minimization problem (8.3) ecls = b X0 X1 R h R0 X0 X1 R i1 R0 b
c (8.9) (See Exercise 8.4 to
such as V 7.11 Asymptotic Standard Errors As described in Section 4.13, a
standard error is an estimate of the standard deviation of the is an estimate of
the covariance matrix of b, then standarddistribution of an estimator. Thus if
Vb errors are the squ
Solution
Salary
Interest credit on capital balance (5% of capital
balance)1
Total allocation before remainder divided
Less pre-allocation net income
Remainder2
Total allocation
1
5% x $150,000; $120,000; $258,000
2
$47,400 / 3 = $15,800
John
Alice
Dan
$ 9
Problem 1
For each of the bonds listed below, record the three requested journal entries.
Dates and descriptions are not required.
Invested $100,000 in 5-year bonds. The bonds were purchased at par and bear interest at a rate of 8% per annum,
payable semi
Problem 1
GENERAL JOURNAL
DATE
ACCOUNT
1/2/2016 Cash
Capital Stock
Issued stock to Amanda Smith for cash
1/4/2016 Equipment
Accounts Payable
Purchased equipment on account
DEBIT
20,000
20,000
15,000
15,000
1/12/2016 Cash
Revenue
Provided services for cash
0 R0 R + R0V W R (R0 W R) 1 R0 R (R0V W R) 1 R0 W R Thus C0
(W) V V C = C0 (W)C C0V V C = 0 0 0 R0 W R (R0 W R) 1 R0
R (R0V W R) 1 R0 W R 0 (W) V Since C is invertible it follows that V
0 which is (8.28). Proof of Theorem 8.10.1. We show the result for
that under random sampling with finite variances and large samples, no individual
observation should have a large leverage value. Consequently individual
observations should not be influential, unless one of these conditions is violated.
CHAPTER 7. ASYMPT
b1 1 V 11) N (0 That is, subsets of b are approximately normal
with variances given by the comformable subcomponents of V . Then 6= for
= To illustrate the case of a nonlinear transformation, take the example
R = r() = )1 ( . . . ) ( . . . )
( . . . ) (
E x0x 2 = E k2kx 2 E k4kx 21 E 4 21 This is a
more compact argument (often described as more elegant) but it such
manipulations should not be done without understanding the notation and the
applicability of each step of the argument. Regardless, the fini
Triangle Inequality b 1 X =1 x0x b2 )(1 1
1 1 X =1 k2kx b2 ! (1 ) 1 1 (1) under Assumption
7.1.2 by the same argumentThe sum in parenthesis can be shown to be as in in
the proof of Theorem 7.7.1. (In fact, it can be shown to converge in probability to
CH
H0 is truean asymptotic distribution under H0 (9.5) . This is not a
substantive restriction, for some continuously-distributed random variable
as ) denote the distribution ) = Pr (as most conventional econometric
tests satisfy (9.5). Let ) the asymptotic
explain each step in brief and then in greater detail. First, observe that the OLS
estimator b = 1 X =1 x0x !1 1 X =1 x ! = Qb 1 Qb =
1is a function of the sample moments Qb P x0=1 x = 1 and Qb P
=1 x Second, by an application of the WLLN these sample mom
to (7.52) we obtain max 1 | max b| 1 kkx b
)2+11(= We have shown the following. kTheorem 7.21.1 Under
Assumption 7.1.2 and E(kx , then uniformly) in 1
(7.53)2+11( + = b so the rate 4 Assumption 7.1.2 requires
The rate of convergence in (7.53) depends on
efficient, such as note that we can write 2 = E x0 2 = E 2
2E x0 + 0 E x0x Q1 Q= Q b2 equals Similarly
the estimator and Q Qwhich is a smooth function of the moments b2
= 1 X =1 b2 Qb 1 Qb b= Qb 2Since the variables x0
x0 and x the conditions of L4() a
to write that the regression finds that female union membership has no effect on
wages. This is an incorrect and most unfortunate interpretation. The test has
failed to reject the hypothesis that the coefficient is zero, but that does not mean
that the co