Silviase/jgov_v1.4_full_ann huggingface dataset:
the stock for the size of the market, we define $ UsedRatio_{it} $ to be the quantity share of used textbooks for title-edition i during semester t. $ ^{16} $ Another key factor that would affect the price of a new textbook is its remaining life. We capture this effect by including a series of four dummy variables that indicate the remaining life of the edition: $ RmnLife1_{it} $ , $ RmnLife2_{it} $ , $ RmnLife3_{it} $ , and $ RmnLife4_{it} $ . For example, $ RmnLife1_{it} $ equals 1 if a new edition of the same title will be introduced at $ t+1 $ and 0 otherwise. Note that the impact of these dummy variables are identified compared to the textbooks whose remaining life are five or more semesters. Homogeneous consumer models, in which consumers capitalize the used market value of the goods market into their demand for a new good, would predict a negative coefficient for these dummies. In contrast, the model with price discrimination and heterogeneous buyers raises the possibility of a rising price of a textbook - particularly in the last periods of the edition. Because we already have textbook title-edition and semester dummies, note that these “remaining life” dummies are identified with the assumption that the coefficients are constant for periods of remaining-life greater than four. We explore the validity of this assumption later. To construct the remaining-life dummies, we obtained additional sales data for 2004 and 2005 for the textbook titles that existed at the end of 2003.

In addition to the explanatory variables suggested by (6), we also include $ Q_{it} $ in the regression, which is the quantity of new textbook sales for title-edition i in semester t and is a natural regressor in a supply relationship. All prices are deflated by the Consumer Price Index (CPI) for “educational books and supplies,” which includes college textbooks, and in 2003 dollars. Standard errors are corrected for clustering at the title level. That is, we allow the error terms for different editions of the
same title to be arbitrary correlated across semesters. In addition to the log-log specification, we also estimate a model with the linear-linear specification with respect to price and quantity.

In addition to the fixed effects model discussed above, we also estimate a model that takes into account the potential endogeneity of $ Q_{it} $ , and $ UsedRatio_{it} $ in Equation (6). $ Q_{it} $ is endogenous because new book price and quantity are jointly determined. $ UsedRatio_{it} $ is also endogenous, because it is a function of new and used textbook quantities for title-edition i at t, both of which are influenced by the new textbook price. We address the endogeneity problem by constructing instrumental variables that utilize the school-level, textbook adoption data. As we are interested in the supply relationship, a natural place to look for instruments is the demand side. In particular, the number of students enrolled in the courses that use title-edition i at semester t, i.e., $ Enrollment_{it} $ , is a good candidate because it shifts the demand for textbook i but does not affect the marginal cost of producing a new textbook. MRI reports the estimated enrollments for the school-sections that adopted a textbook, and we construct $ Enrollment_{it} $ by aggregating school sections up to the title-edition level. $ ^{17} $

The second instrument, PrevUsed $ _{it} $ , also exploits the school level data and computes the proportion of the schools that used title-edition i in both t and t-1 from the schools that used i at t. For example, suppose that four schools used title-edition i at t. If three of these schools used the same title-edition i at t-1, PrevUsed $ _{it} $ becomes 0.75. Typically, college bookshops “buy back” used textbooks from students at the end of a semester if the same textbook will be used in following semester. We naturally
expect that the supply of used textbooks will be higher at t if more schools “buy back” the textbook at the end of t-1. This suggests that PrevUsed, is positively correlated with UsedRatio. Conversely, after UsedRatio and other regressors are controlled for, there is no strong reason to believe that PrevUsed directly affects new textbook prices. $ ^{18} $ This makes PrevUsed another candidate for the instrumental variable.

As shown in Figure 3, PrevUsed substantially varies across title editions and semesters. Additionally, as shown in Table I, the average number for PrevUsed is 0.34, which indicates that the same title edition is used at the same school in the previous year 34% of the time. However, if we focus on “principles” textbooks, this number goes up to 0.46. $ ^{19} $ Such variation helps us identify UsedRatio in regression models.

### I I-C. Empirical Results

## I I-C1 New textbook prices

Figures 4a-c show the relationship between new textbook prices and UsedRatio for the six most popular textbooks. Utilizing MIR’s textbook categories, we divide the sample into three categories: “principles,” “intermediate,” and “applied.” We pick the two most frequently used textbooks within each respective category. $ ^{20} $ In each graph, new textbook prices are indicated by bar charts, while
UsedRatios are represented by dot charts. An arrow in the figure indicates the semester in which a new edition of the textbook was introduced.

These figures consistently show a strong positive relationship between new textbook prices and UsedRatios. In addition, it appears that the new textbook prices often jump up immediately before the introduction of a new edition. For example, on the left-hand side of the “principles” textbooks (Figure 4a), there is a price hike in semesters 3 and 9, both of which precede the introduction of a new edition. On the right-hand side of the same graph, similar price hikes occur in semesters 3 and 9, although the latter is smaller than the other cases. Similar price hikes are also observed in other textbooks. These pricing patterns are consistent with the price discrimination theory developed in the theory section. Please note that new textbook prices are already deflated by CPI for “educational books and supplies,” and thus, the general price trend in this industry alone may not explain the correlation. Nonetheless, the correlation may be spurious; we examine the relationship more carefully in the regression models below.

Table II presents the estimation results for the fixed-effects model without instrumental variables. In all cases, we estimate models using both the log-log and linear-linear specifications in terms of price and quantity. Standard errors are corrected for clustering at the book title level.

In the first two columns, we report the results when we include only remaining-life dummy variables aside from textbook title-edition fixed effects and semester dummy variables. We find that all of the coefficients for the remaining-life dummies are positive and significant and the coefficients become larger as the end of the life of an edition approaches. This indicates that textbook prices go up as the remaining life becomes shorter, which is consistent with our price discrimination model with heterogeneous buyers but not with Swan-type consumers. Estimated coefficients indicate, for example,
that in the last period of an edition, textbook prices increase by about 5%, or $4.7 relative to the base period.

The next two columns check whether the results change if fewer remaining-life dummies are included in the regression. The results do not change substantially; we continue to see an increase in textbook prices toward the end of an edition, and these effects are statistically significant. Columns 5 and 6 add UsedRatio and Q to the models shown in Columns 1 and 2. In these regressions, the remaining-life dummies continue to show the same pattern as in the previous results. The coefficient for UsedRatio is positive and significant, which indicates that UsedRatio and textbook price are positively correlated; the estimated coefficients imply that textbook prices increase by an average of 3.1%, or $2.2, as the share of used books within a title-edition increases from 0 to 1. The coefficient for Q is small and statistically insignificant in both regressions, which suggests that the quantity of new textbooks has relatively little impact on its price.

In Table III, we present the results that take into account the endogeneity of UsedRatio and Q. In the first two columns, we estimate the same model as in Table II, Columns 5 and 6, except that UsedRatio and Q are treated as endogenous. These two columns represent our preferred specifications. First, as before, the coefficients for the remaining-life dummies are all positive and become larger as the end of an edition approaches. Again, this pricing pattern is consistent with the price discrimination model but not with the traditional Swan-type model. However, these coefficients are statistically significant (or weakly significant) only immediately before the introduction of a new edition, which suggests that the price rise is largely a “last period effect” (see section I-B for the distinction). The results also indicate that UsedRatio continues to affect textbook prices positively and significantly, and the estimated coefficients imply that new textbook prices increase by an average of 8.0%, or $8.9, as
the share of used books within a title-edition increases from 0 to 1. The coefficient for the quantity of new textbooks, Q, continues to be very small in magnitude and statistically insignificant. Cragg-Donald Wald F-statistics for the two excluded instruments are 109.9 and 18.6 for the two regressions, suggesting that the instruments have good explanatory power.

As we discussed in section I-B, the remaining-life dummies are identified based on the assumption that the coefficients for the remaining life of greater than four are constant. While we cannot directly test this assumption, the results reported in Columns 7 and 8 indicate that, with the exception of periods immediately before the introduction of a new edition, the remaining-life dummies are not significantly different from those of the base period, which supports the assumption. Columns 9 and 10 further check the robustness of the results by reducing the number of the remaining-life dummies included in the regression. As reported in Columns 9 and 10, the results change little with the elimination of a remaining-life dummy variable.

## I I-C2 Additional Analysis

## Semester-age dummy variables

The results thus far have been based on the assumption that consumers know exactly when a new edition is coming out. Under this assumption, it was appropriate to include the remaining-life dummies in the regression and examine the price path immediately before the introduction of a new edition. This assumption is supported by Chevalier and Goolsbee (2009), who examined the same textbook data and found that students are forward-looking and behave as if they have rational expectations of publishers' revision decisions. However, to check the robustness of the results, we estimate an alternative model in this section in which consumers are assumed to respond to the “age” of the textbook when they
make purchase decisions.

To capture this idea, we include the semester-age dummies (instead of the remaining-life dummies) in the regression. Specifically, we include a series of dummy variables that correspond to the semester(s) between 4 and 6, 7 and 9, 10 and 12, and 13 and above since the introduction of the current edition. $ ^{21} $ All of the remaining variables and the estimation approach are the same as our preferred specification presented in Table III, Columns 7 and 8.

We report the results in Table IV, Columns 11 and 12. The results change little with the use of the semester-age dummy variables; we continue to see that UsedRatio positively affects new textbook prices, and the estimated coefficients are comparable to the previous results. The coefficients for the semester-age dummies are all positive and become larger as the textbook gets older. Consistent with the price discrimination theory, this indicates that textbook prices go up as the textbook becomes older and the revision of the textbook nears. However, except for a few cases corresponding to the semesters between 4 and 6 and between 7 and 9, the coefficients for the age dummies are not statistically significant. This may be because we observe relatively few textbook revisions beyond the ninth semester, as can be seen in Figure 2. The coefficient for Q is still positive and insignificant in these regressions. We have also experimented with various constructions of the semester-age dummies, finding that the results are not sensitive to how semesters are grouped. As an example, Columns 13 and 14 present the results when the first four semesters since the introduction of an edition are considered as the base period. The results are qualitatively the same as before.
Quantity of new and used textbooks

Thus far, our empirical analysis has focused on whether textbook prices change over the life of an edition as our price discrimination model predicts. Additionally, our price discrimination model predicts that the quantity of new (used) textbooks decreases (increases) over the life of an edition. In Appendix II, we check these predictions by estimating simple fixed effects models of textbook quantity on time trends. We find that the quantity of new (and used) textbooks changes as the model predicts, which provides additional support for the price discrimination model.

### I II. Conclusion

This paper attempted to provide a new perspective on durable goods pricing. Since Swan (1970), durable goods literature has primarily analyzed one type of buyer who purchases goods for current use and then resells them in the used market. In this setup, if durable goods producers periodically introduce new models, the prices of new goods will decline over time as the end of the economic life of the product approaches. While the declining price over its life is commonly observed in various durable goods theories, it is not clear whether the price cycle is sustained when there is heterogeneity in buyers' preferences.

In this paper, we developed a model of monopoly pricing of a durable good when there are heterogeneous buyers. If some buyers continue to place value on the old durable good after a new model is introduced, we showed that durable goods prices could increase over the life of the product. Using a panel data set that contains economics textbooks, we tested the prediction of the model. We found that new textbook prices increase over time as the share of used books increases. In contrast, we found no evidence that textbook prices decline as the end of the current edition approaches.
A general lesson of the paper is that price discrimination can lead to a rising price of a durable good over its life cycle. While our analysis is specific to the textbook market, we expect that a similar pricing pattern can emerge when a used market is active and grows over time. In such markets, "writing off" the low valuation buyers can become optimal as used products accumulate. An analysis of such markets will become more complex because an optimal pricing policy should not only reflect buyer heterogeneity, but also the possibility of intertemporal substitution, from which we could abstract away because of the nature of the textbook market.
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introduction of a new edition. Models 7 and 8 include the squared and cubic terms of the age variable and indicate that the relationship is non-linear; used textbook quantity quickly increases in the initial periods after the introduction of a new edition and levels off after several semesters. These results are consistent with the prediction of the price discrimination model, although alternative theoretical models may also lead to similar time trends.
Figure 1: Distribution of New Textbook Prices (n=4708)

Figure 2: Distribution of the age of textbooks when revised $ (n=382) $
Figure 3 : Distribution of PrevUsed (n=4312)
Figure 4a: The relationship between new textbook prices and UsedRatios: "Principles" textbooks

Figure 4b: "Intermediate" textbooks
Figure 4c: "Applied" textbooks
Table I: Summary statistics

Variable	Obs	Mean	Std. Dev.	Min	Max
year	4708	2000	1.99	1997	2003
edition	4708	3.93	2.97	1	17
newp	4708	91.5	22.2	15.8	191.5
usedp	4162	68.9	15.5	29.8	125.6
newp_PK	4708	91.8	22.1	15.8	191.5
usedp_PK	4200	69.0	15.4	30.2	125.6
est_new_units (Q)	4708	1103	2322	1.98	34458
est_used_units	4708	760	1832	0	27834
UsedRatio	4708	0.401	0.283	0	0.995
PrevUsed	4312	0.342	0.283	0	1
RmnLife1	4708	0.081	0.273	0	1
RmnLife2	4708	0.085	0.278	0	1
RmnLife3	4708	0.086	0.280	0	1
RmnLife4	4708	0.084	0.277	0	1
principles	4708	0.360	0.480	0	1
intermediate	4708	0.073	0.260	0	1
applied	4708	0.568	0.495	0	1
enrollment	4613	3045	7148	0	124037
age (in semester)	4708	6.93	6.39	1	59
Table II: Estimation results for new textbook prices without instrumental variables

VARIABLES	(1)	(2)	(3)	(4)	(5)	(6)
Ln(newp)	newp	Ln(newp)	newp	Ln(newp)	newp
no IV	no IV	no IV	no IV	no IV	no IV
UsedRatio	0.0306**	2.1899**
(0.0131)	(0.9032)
In(est_new_units)	0.0023
(0.0028)
est_new_units	-0.0000
(0.0001)
RmnLife1	0.0513***	4.7016***	0.0442***	4.0105***	0.0422***	4.0441***
(0.0104)	(0.8555)	(0.0088)	(0.7327)	(0.0095)	(0.7803)
RmnLife2	0.0417***	3.8127***	0.0348***	3.1495***	0.0327***	3.1562***
(0.0086)	(0.7227)	(0.0069)	(0.5922)	(0.0080)	(0.6675)
RmnLife3	0.0291***	2.6705***	0.0226***	2.0485***	0.0220***	2.1729***
(0.0069)	(0.5722)	(0.0052)	(0.4406)	(0.0066)	(0.5312)
RmnLife4	0.0154**	1.4863***	0.0106*	1.1670**
(0.0062)	(0.5426)	(0.0058)	(0.4967)
Title-edition FE	yes	yes	yes	yes	yes	yes
Sem. dummies	yes	yes	yes	yes	yes	yes
Obs.	4,609	4,609	4,609	4,609	4,609	4,609
R-squared	0.9005	0.9061	0.9003	0.9059	0.9008	0.9064
N of title-edition	775	775	775	775	775	775

Standard errors, corrected for clustering at the title level, are in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Table III: Estimation results for new textbook prices with instrumental variables

VARIABLES	(7)	(8)	(9)	(10)
Ln(newp)	newp	Ln(newp)	newp
IV	IV	IV	IV
UsedRatio	0.0798**	8.8867***	0.0820**	9.1040***
(0.0370)	(3.1444)	(0.0327)	(2.7509)
In(est_new_units)	0.0004	0.0004
(0.0047)	(0.0047)
est_new_units	0.0019	0.0019
(0.0013)	(0.0013)
RmnLife1	0.0286*	3.5758**	0.0266**	3.4185***
(0.0152)	(1.3916)	(0.0111)	(1.1704)
RmnLife2	0.0176	2.3747*	0.0157	2.2180**
(0.0142)	(1.2433)	(0.0099)	(0.9878)
RmnLife3	0.0110	1.2103	0.0093	1.0651*
(0.0112)	(0.9187)	(0.0073)	(0.6205)
RmnLife4	0.0031	0.2624
(0.0083)	(0.7276)
Title-edition FE	yes	yes	yes	yes
Sem. dummies	yes	yes	yes	yes
Obs.	4,214	4,222	4,214	4,222
R-squared	0.9072	0.9061	0.9071	0.9058
N of title-edition	734	734	734	734

Standard errors, corrected for clustering at the title level, are in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Table IV: Estimation results with textbook age dummies

VARIABLES	(11)	(12)	(13)	(14)
Ln(newp)	newp	Ln(newp)	newp
IV	IV	IV	IV
UsedRatio	0.0874**	10.7956***	0.0971***	12.2566***
(0.0377)	(3.7139)	(0.0301)	(3.5462)
In(est_new_units)	0.0009	0.0013
(0.0046)	(0.0047)
est_new_units	0.0026	0.0030
(0.0018)	(0.0020)
4 ≤ age ≤ 6	0.0130	1.7073**
(0.0099)	(0.8617)
7 ≤ age ≤ 9	0.0190	2.4778*
(0.0163)	(1.3675)
10 ≤ age ≤ 12	0.0226	3.0375
(0.0242)	(1.9855)
age ≥ 13	0.0283	3.7704
(0.0337)	(2.7812)
5 ≤ age ≤ 6	0.0112	1.8695**
(0.0076)	(0.7772)
7 ≤ age ≤ 8	0.0127	2.0175*
(0.0130)	(1.1218)
9 ≤ age ≤ 11	0.0192	2.6807
(0.0194)	(1.6346)
age ≥ 12	0.0244	3.3434
(0.0298)	(2.5213)
Title-edition FE	yes	yes	yes	yes
Sem. dummies	yes	yes	yes	yes
Obs.	4,214	4,222	4,214	4,222
R-squared	0.9067	0.9006	0.9063	0.8970
N of title-edition	734	734	734	734

Standard errors, corrected for clustering at the title level, are in parentheses. *** p<0.01, ** p<0.05, * p<0.1
Table V: Estimation results for new and used textbook quantities

(15)	(16)	(17)	(18)	(19)	(20)	(21)	(22)
Ln(New units)	New units	Ln(New units)	New units	Ln(Used units)	Used units	Ln(Used units)	Used units
VARIABLES
age (in semester)	-0.1272***	-53.3451***	-0.1182***	-147.6189***	0.0726***	57.5528***	0.7932***	319.7042***
(0.0083)	(5.1972)	(0.0210)	(17.8246)	(0.0153)	(10.6123)	(0.0457)	(49.3234)
age squared	-0.0018	6.5143***	-0.0560***	-19.7234***
(0.0018)	(1.1925)	(0.0044)	(3.8523)
age cubic	0.0001	-0.0840***	0.0009***	0.3020***
(0.0000)	(0.0221)	(0.0001)	(0.0810)
Constant	6.4765***	1,472.9943***	6.4710***	1,695.2936***	4.8750***	360.5404***	3.1285***	-235.1040
(0.0578)	(36.0319)	(0.0686)	(59.1645)	(0.1068)	(73.5741)	(0.1226)	(145.5916)
Title-edition FE	yes	yes	yes	yes	yes	yes	yes	yes
Sem. dummies	no	no	no	no	no	no	no	no
Obs.	4,708	4,708	4,708	4,708	4,200	4,708	4,200	4,708
R-squared	0.8100	0.8797	0.8106	0.8816	0.6191	0.7688	0.7278	0.7894
N of title-edition	874	874	874	874	804	874	804	874

Standard errors, corrected for clustering at the title level, are in parentheses. *** p<0.01, ** p<0.05, * p<0.1
## 参考资料

1 文部科学省の組織図（平成27年10月1日現在）… 434
2 学習人口の現状 …… 435
3 学校数（年次別）…… 436
4 在学者数（年次別）…… 436
5 教員数（年次別）…… 436
6 入学者数（年次別）…… 438
7 卒業者・修了者数（年次別）…… 438
8 就学率・進学率（年次別）…… 438
9 卒業者に占める就職者の割合（年次別）…… 440
10 学校建物面積 …… 440
11 文教費 …… 440
12 予算 …… 442
13 組織別研究機関数・研究者数 …… 442
14 文教・科学技術施策年表 …… 443
15 統計調査一覧 …… 445
16 刊行物一覧 …… 446
1 文部科学省の組織図 (平成27年10月1日現在)
◆青少年教育施設 …… 2,004万人

◆女性教育施設 …… 1,017万人

◆社会体育施設 …… 4億8,628万人

◆民間体育施設 …… 1億3,642万人

◆生涯学習センター …… 2,648万人

（資料）文部科学省「学校基本調査報告書」（平成27年度），「社会教育調査報告書」（平成23年度），「子どもの学校外での学習活動に関する実態調査報告」（平成19年度）等