A. Colin Cameron (University
of California - Davis)
ANALYSIS OF ECONOMICS
DATA: AN INTRODUCTION TO ECONOMETRICS
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THESE ARE FOR THE INITIAL VERSION
manuscript dated December 2021
and released January 5 2022
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A FULLY CORRECTED VERSION 1.1 manuscript
dated February 2022 was released February 24 2022.
IMPORTANT ERRATA (Minor typos not listed)
Chapter 1
p.4 Chapter 1.3 "a higher price is associated with a higher price"
should be "a larger house size is associated with a higher price"
Chapter 2
p.14 Chapter 2.1.6 "below the mid-point of $93,000" should be "below
the mid-range of $85,475"
p.29 Chapter 2.8 Question 4 "x_32=6 and x_33=7" should be "x_31=6
and x_32=7"
p.32 Chapter 2.8 Question 23 Use data from January 1957 to November
2012
Chapter 2 Exercise Solutions
p.475 Question 5. xbar=2, s=sqrt(8/3)=1.633,
skew=0/(8/32)^1.5=0, kurt=(32/4)/(8/4)^2=2.
p.476 Question 21(a). skewness=1.01 and kurtosis=4.54>3.
Chapter 3
p.37 Chapter 3.1.4 Text before Definition 2 should say variance is
denoted sigma^2.
p.38 Chapter 3.1.5 First displayed equation should be E[X] =
3*(1/4) + 4*(3/8) + 5*(3/8) = 4 and 1/8.
p.40 Chapter 3.3.2 Curve in second panel of Figure 3.1 is actually
that of N(0.499, 0.086^2).
p.46 Chapter 3.5.3 Curve in second panel of Figure 3.3 is actually
that of N(23.78, 3.76^2).
p.57 Chapter 3.10 Question 18(c) "z=(xbar-200)/50" should be
"z=(xbar-200)/10"
Chapter 3 Exercise Solutions
p.476 Question 9. Var[Xbar] one-quarter as large, standard
deviation of Xbar one-half as large.
p.476 Question 12(a). s = 0.037151 approximately equals
sqrt((5/36)/100).
Chapter 4
p.63 Chapter 4.2.3 The Figure 1 title should be "Student's t
distribution: T(4) and T(30) compared to the standard normal"
p.66 Chapter 4.3.1 Definition 1 "with probability alpha" should be
"with probability 0.025"
p.68 Chapter 4.3.5 In the third paragraph in fact 91 of the 100
samples had 95% confidence intervals that include mu.
And for the coin toss example 388 of the 400 95% confidence
intervals (or 97%) included 0.5.
p.75 Chapter 4.5.3 At the bottom the alternative hypothesis is mu
not equal to 2.0.
p.76 Chapter 4.5.3 Should be p = Pr[|T_240|]>|-0.68|] = 0.946.
p.78 Chapter 4.6.2 Last paragraph of section change "... we do not
reject at significance level 0.05 the hypothesis ..."
to "... we do not reject at significance level 0.05 the null
hypothesis ..."
p.90 Chapter 4.10 Question 27(a) test whether or not mu = 0.
Chapter 4 Exercise Solutions
p.477 Question 5(d). The 1,000 t's have mean 0.00415 and
variance 2.197.
p.477 Question 15. The answers to parts (c) and (d) are
reversed.
p.477 Question 25(c). t_108,.025 = 1.982.
p.478 Question 31(c). t=(25-15)/4=2.5.
Chapter 5
p.120 Chapter 5.14 Question 11 Repeat exercise 7 ....
p.120 Chapter 5.14 Question 12(d) Should be ... equals that from
regression of y2 on x2, y3 on x3, and y4 on x4.
Chapter 5 Exercise Solutions
p.478 Question 9. The answers to 9a) and (b) are reversed.
p.478 Question 15(d) In formula for s_e^2 should be 1/(3-2) and not
1/(3-1). Final answer of 2.450 isl correct.
p.478 Question 15(g) Should be b_2 = -6/24 = 0.25 which does not
equal (1/-3).
p.479 Question 21(d) Should be A one unit increase ... and not A one
standard deviation increase ...
Chapter 6
p.141 Chapter 6.6 Question 2. The population model is y = -1 + 3x +
u.
p.142 Chapter 6.6 Question 12. Change ".. b2 is inconsistent ..." to
".. b2 is unbiased ..."
Chapter 6 Exercise Solutions
p.479 Question 1(d) Should be e_2 = 0.68 (no minus sign).
Chapter 7
p.148 Chapter 7.3.1 Remark 51 "... with probability alpha ..."
should be " ... with probability alpha/2 ..."
p.152 Chapter 7.4.4 The displayed equation should divide by square
root of 1 - r_xy^2 (i.e. square r_xy)
p.159 Chapter 7.7.1 In the formula for se_bet(b2) use e_i^2
(i.e. square e_i)
p.161 Chapter 7.9 Question 1(e) Should be "Verify your answer in (c)
...."
Chapter 7 Exercise Solutions
p.480 Question 3(d) R^2 = 0.04777 = 0.2184^2.
Chapter 8
p.171 Chapter 8.3.3 Data go to October 2012 (and not October 2013 or
September 2013).
p.171 Chapter 8.3.3 Second paragraph should be 100*(1.0055^12 - 1) =
6.8%.
p.177 Chapter 8.5 Question 5(b) and 5(c) should be per capita health
expenditures.
Chapter 8 Exercise Solutions
Chapter 9
p.180 Chapter 9.1.1 Near bottom of page change to "Manipulating
leads to delta lnx = deltax / x."
p.184 Chapter 9.3.4 In the first paragraph delete all but the first
sentence.
p.192 Chapter 9.8 Question 6(a) Should be earns = -18000 + 17*hours
p.192 Chapter 9.8 Question 15(a) Should be data to November 2012
p.192 Chapter 9.8 Question 16(a),(b) Should be data to November 2012
p.192 Chapter 9.8 Question 19(f) Drop
Chapter 9 Exercise Solutions
p.481 Question 15(b) Latter part of the 2.000's (June 2007 to
February 2009)
p.481 Question 17(c) Should be dlnx/dtime = 0.40/20 = 0.02 or
2% per year.
Chapter 10
p.198 Chapter 10.1 Table 10.2 Third last entry should be price =
213,000
p.213 Chapter 10.10 Question 3(e) should be "... adding a bathroom
..."
p.213 Chapter 10.10 Question 5 should be " .... sales in units ..."
p.214 Chapter 10.10 Question 6(a) Should be "Sales are now measured
in thousands of units rather than number of units".
p.214 Chapter 10.10 Question 6(b_ Should be "TV and radio
advertising ..."
p.214 Chapter 10.10 Question 6(c) Should be ".... using dependent
variable sales divided by 1,000."
p.214 Chapter 10.10 Question 13 Should be "... with exactly three
bedrooms.
Chapter 10 Exercise Solutions
p.481 Question 1(c) Should be "After controlling for math SAT
score, an increase in the verbal SAT score .... "
p.482 Question 13 Should be "... the value of bedrooms (3) equals
three times the intercept (1)."
Chapter 11
p.226 Chapter 11.4.5 Third paragraph should be se(b2-b3) =
sqrt(se(b2)^2-c23+se(b3)^2).
p.228 Chapter 11.5.1 Figure 1 Title and text below should be F(3,30)
and F(10,30).
p.229 Chapter 11.5.4 Definition 27 should be ... Ha: At least one of
the q parameter restrictions implied by the restricted model is
incorrect.
p.235 Chapter 11.7 There are may errors in the standard error, t
statistic, p-values and confidence intervals for the intercept and
Size. Table 11.4 has the correct values.
p.238 Chapter 11.9 Question 5(b) Change to Will the OLS estimator of
beta_3 be unbiased? Explain.
p.239 Chapter 11.9 Question 11 Change to k = 7
p.239 Chapter 11.9 Question 13 Answer questions assuming default
standard errors are used.
Chapter 11 Exercise Solutions
p.482 Question 1(a) Final answer is 17 and 1(b) final answer is
17.8-17=0.8.
p.482 Question 7(a) correlation = 0.2184 and 7(f) Rbar-squared
increases from 0.0466 to 0.0658.
p.482 Question 11(a) Reject as p=0.0154 11(b)
F_6,43,.05=2.318.
p.483 Question 17 (a) Statistically significant as |t|>3.
Chapter 12
p.224 Chapter 12.1.3 Table 12.2 YEar built should be Age and Age
should be Month sold.
p.255 Chapter 12.2.5 The ordering of variables differs from that
eslewhere.
Reorder to a 2000 square foot house with 4 bedrooms, 2 bathrooms,
medium lot size, 40 years old, sold in June.
Then yhat = b1 + 2000b2 + 4b3 + 2b4 + 2b5 + 40b6 + 6b7 = 257691.
p.270 Chapter 12.11 Question 10 The variables are inflgdp and
inflgdp1yr
p.270 Chapter 12.11 Question 11(f) should be ... plotted against
month.
p.271 Chapter 12.11 Question 15(e) should be ... confidence interval
for the forecast price.
Chapter 12 Exercise Solutions
p.483 Question 3 Reverse the order of the last two coefficients and
standard errors.
Chapter 13
p.309 Chapter 13.10 Question 3. The data are for the years
2021-2014.
p.309 Chapter 13.10 Question 4. Repeat the previous exercise using
data for 2012.
p.309 Chapter 13.10 Question 8. .. use curbwt rather than hp ...
p.309 Chapter 13.10 Question 13(d). Regress margin on an intercept
and win.
Chapter 13 Exercise Solutions
p.484 Question 1(a) API score increases by 54.29 points.
p.484 Question 3(d) F = 4.46 with p=0.0400 so reject H0.
p.484 Question 7(e) 6.77%. 7(f) 4.4 times larger (=
.0440/.0100) 7(g) 4.67%.
p.484 Question 9(a) $1,436, $879, $1,030, $650, $1,024, $637.
Chapter 14
p.317 Chapter 14.2.2 The standard errors of the intercept and slope
coefficients are 2776 and 3217.
Then t=-16396/3217=-5.10, so p = Pr[|T_870|>5.10] = 0.000 and the
95% confidence interval is (-227111, -10081).
p.321 Chapter 14.3.3 near bottom should be ... while a similar
separate OLS regression for the female-only (d=1) sample yields
coefficients that are equal to the sum of the coefficients
of the original and interacted variables in the final column. For
example .... 4191 = 6314 + (-2123).
p.321 Chapter 14.4.1 0.117+0.747+0.136=1 should be ...
0.091+0.760+0.149=1.
p.329 Chapter 14.6 Question 2 Change to ... Repeat the
previous exercise where in part (a) ybar=30 for d=1 and y=50 for
d=0, and in part (b) y=5-3d.
Chapter 14 Exercise Solutions
p.485 Question 7(b) yhat = 6 + 7d - 4x - 2dx.
Chapter 15
p.336 Chapter 15.2.2 Before Remark 124 should be MER equals ME at x
= x*.
p.349 Chapter 15.9 Question 3(e). Change to Give the marginal effect
of a change in d.
p.350 Chapter 15.9 Question 7(f). Change to Given your plot in part
9e) do you think it is correct ....
Chapter 15 Exercise Solutions
p.486 Question 3(e) Should be ME = 4+7x.
p.486 Question 5(b) Should be t = -6.63. 5(c) should be F =
22.70.
p.486 Question 7 Gave results for different variables. Answer should
be as follows.
7(a) lnhlthpc=-5.0096+1.256*lngdppc. (b) A 1% increase in gdp pc is
associated with a 1.256% increase in health spending pc.
(c) ME=1.256×3255/33054=0.124. (d) 0.00124 is similar to 0.089 from
levels OLS.
(g) Averages for hlthpc and predictions in parts (e) and (f) are
3255, 3232 and 3297.
(In this example the usually preferred corrected prediction
overpredicts by more than the naive prediction underpredicts.)
Chapter 16
p.370 Chapter 16.8.4 At bottom should be ... |DFITS| >
2*sqrt(7/131) ...
p.373 Chapter 16.10 Question 3(b) highgradeXage = highgrade * age
p.375 Chapter 16.10 Question 11(e) Generate y_t = 2 +0.8y_t-1 +
4x_t + u_t
p.375 Chapter 16.10 Question 13 Should be gender = 1 (not female =
1).
p.375 Chapter 16.10 Question 14 Should be gender = 0 (not female =
0).
Chapter 16 Exercise Solutions
p.487 Question 11(a) Should be yes. The coefficient of x is 3.91,
close to 4.
p.487 Question 139a) Answer should just be Yes.
p.487 Question 13 (e) Should be |dfits| > 2 * sqrt(4/384) =
0.206.
Chapter 17
p.382 Chapter 17.2.4 The mean-differenced model should have
subscript i on the averages. So
y_it - ybar_i = β₂(x_2i - xbar_2i) + ⋯ + β_k(x_kit -
xbar_ki) + (ε_it - ε_i),
where, for example, ybar_i = (1/T) Sum_t y_it is the averge over
time for individual i.
p.383 Chapter 17.2.5 Similarly for the ransom effects estimator the
averages should have subscript i (not t).
p.415 Chapter 17.8.11 In last paragraph should be ... the null
hypothesis of no autocorrelation ..
p.419 Chapter 17.11 Question 12(a) OLS regress outpat on ....
p.420 Chapter 17.11 Question 13 Should be ... u_i = 0.8v_i +
0.6w_i.
p.420 Chapter 17.11 Question 14 Should be ... u_i = 0.6v_i + 0.8w_i.
p.420 Chapter 17.11 Question 15(g) Should be ... Could col4 be a
weak instrument?
p.421 Chapter 17.11 Question 16(c) Should be ... Is the IV estimate
of grade76 statistically significant at 5%.
p.423 Chapter 17.11 Question 27(a) and 27(b) should be 13,363
observations.
p.426 Chapter 17.11 Question 39(a), 39(b) and 39(c) change to ...
appear to be serially correlated?
p.426 Chapter 17.11 Question 41(b) and 43(d) change to ... appear to
be serially correlated?
p.427 Chapter 17.11 Question 43(b) and 43(c) and 43(e) change to ...
appear to be serially correlated?
p.427 Chapter 17.11 Question 45(b) change to ... appear to be
serially correlated?
Chapter 17 Exercise Solutions
p.488 Question 1(b) Should be 0.1366/0.0331 = 4.13 times the
default.
p.488 Question 3(b) Should be 0.0183/0.080 = 2.29 times the default.
p.489 Question 17(b) Should be ME = 0.052
p.489 Question 21(c) Should be 0.202*0.798*0.374 = 0.0603.
p.490 Question 43(b) Should be No, |rho_hat_l| < 0.10 for
all j<=12.
p.490 Question 45(b) Should be No, |rho_hat_l| < 0.10 for
all j<=12.
Appendix A
p.454 Appendix B.1.1 Should be Pr[a <= X < b] =
Pr[X=a] + .... + Pr[X=b] = Pr[X <= b] - Pr[x < a].
A. Colin Cameron / University of California - Davis / cameron.econ.ucdavis.edu