Incorporating Piecewise-Linear Variables into an Empirical Model of
Non-Current Asset Impairment Timeliness*
KEISHI FUJIYAMA†

Research Institute for Economics and Business Administration,
KOBE UNIVERSITY

ABSTRACT
While prior research employs linear stock returns as a proxy for economic losses, thisstudy uses piecewise-linear stock returns to separate positive and negative stock returns.
It also examines the relationships between non-current asset impairments and changes
in sales and cash flows from operations, which can be viewed as short-term indicators of
economic impairments. Consistent with prior research, I find a negative relationshipbetween non-current asset impairments and negative stock returns in five years before
their recognition. Contrary to prior research, I also find such a relationship in therecognition years. The results indicate that th e relationships are stronger one or two years
before their recognition than in the recognition years and three years before theirrecognition. These results suggest that the non-current asset impairment losses reported
by Japanese firms are consistent with the Japanese accounting standard, although suchlosses are not necessarily reported in a timely manner. In addition, I find evidence
suggesting that changes in sales and cash flows from operations in recognition years areshort-term indicators of non-current asset impairments. Overall, incorporating
piecewise-linear variables improves the empirical model of non-current asset impairment
timeliness.
JEL Classification: M41
Keywords: Non-Current Asset Impairment; Timeliness; Piecewise-Linear Regression* I thank Masahiro Enomoto (editor), Tomoaki Yamashita, and two anonymous reviewers for their helpful suggestions.
I acknowledge financial support from Research Institute for Economics and Business Administration, Kobe University.
†
Address: Research Institute for Economics and Business Administration, Kobe University, Rokkodai 2-1, Nada, Kobe,
657-8501 Japan. Phone: +81-78-803-7270; Email: fujiyama@rieb.kobe-u.ac.jp
Received December 2, 2020; accepted December 2, 2021; available online April 27, 2022 (Advance publication by J-Stage)
DOI: 10.11640/tjar.12.2022.01
Copyright©2022 Research Institute for Economics and Business Administration – Kobe University.

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1. Introduction
This study investigates whether incorporating piecewise-linear stock returns and short-term
indicators improves the empirical model of non-current asset impairment timeliness. Prior researchsuggests that a non-current asset impairment is subject to management discretion and reflects
management incentives such as “big bath,” income smoothing, and management turnovers in Japan(e.g., Enomoto 2008; Obinata and Okada 2008; Hu and Kurumado 2012; Fujiyama 2014a, 2014c;
Kimura 2015). Consistently, using data on Japanese firms, Fujiyama (2014b) finds that non-current
asset impairments are not correlated with linear returns in the years of their recognition, but thatsuch relationships exist in the period from one year to four (or five) years before their recognition,suggesting that Japanese firms can record non-current asset impairments in a less timely mannerthan expected by accounting standards.1 Moreover, the timeliness of non-current asset impairment
is particularly controversial in Japan. In general, the degree of loss recognition timeliness, orconditional conservatism, is lower in Japan than in common law countries such as the U.S. and the
U.K. (Ball et al. 2000). Non-current asset impairment losses are a major component of accounting
conservatism (Beaver and Ryan 2005). Therefore, non-current asset impairment timeliness is ofgreat concern to practitioners and researchers and it is important to improve the empirical models
used in prior research, such as Fujiyama (2014b), and construct a better model.
While Fujiyama (2014b) employs linear stock returns as a proxy for economic losses toinvestigate non-current asset impairment timeliness in Japan, Banker et al. (2017) recommend
piecewise-linear stock returns and short-term indicators.2 Non-current asset impairment losses
reflect only economic losses or bad news, as accounting standards prohibit recording upward
valuation profits. Thus, separating positive (good news) from negative stock returns (bad news) is
expected to better reflect the asymmetric timeliness of profit and loss accounting. Accordingly, priorresearch on accounting conservatism captures the asymmetric timeliness of gains and losses using
piecewise-linear stock returns (e.g. Basu, 1997). However, studies on asset impairments employ
linear stock returns to capture economic losses (e.g., Riedl 2004; Lapointe-Antunes et al. 2009;
Fujiyama 2014b; Albersmann and Quick 2020), which may result in estimation bias. An exception
is Iatridis et al. (2021), who employ piecewise-linear stock returns only for year t but not for theyears before impairment recognition. Moreover, Banker et al. (2017) suggest that different
indicators, such as stock returns and changes in sales and cash flows from operations, predict cash
flows over varying time horizons and have different impacts on asset classes. Stock returns capturechanges in cash flows over the long-term, and changes in sales and operating cash flows capturesuch changes over the short-term. Thus, changes in sales and operating cash flows are expected toindicate non-current asset impairments incremental to stock returns. As tangible assets have a finite
useful life and goodwill has an indefinite future life, goodwill impairments are more strongly

1

Prior research investigates the timeliness of asset impairments using other models and provides mixed evidence
regarding the timeliness of the impairment losses of assets, such as non-current assets and goodwill (Chen et al. 2008;
Choi 2008; Li and Sloan 2017). The timeliness of goodwill impairment losses is affected by narrative disclosure quality(Iatridis et al. 2021), CEO overconfidence (Chung and Hribar 2021), and audit quality (Albersmann and Quick 2020).
André et al. (2016) show that goodwill impairment practices differ in the U.S. and European countries from theviewpoint of timeliness. Glaum et al. (2018) find that country-level enforcement determines goodwill impairment
timeliness.
2
Note that some argue that a piece-wise linear regression of earnings on stock returns provides an estimation bias in thepresence of the skewness of stock returns ( Jarva and Lof 2021; Obinata 2021).

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness3

correlated with stock returns than are tangible asset impairments. Note that stock returns are amore important impairment indicator even for tangible assets than operating cash flows and sales
changes (Banker et al. 2017). Consistently, Banker et al. (2017) show that Riedl’s (2004) resultschange when the empirical model incorporates piecewise-linear stock returns and piecewise-linear
short-term indicators of asset impairments. Therefore, it is important to investigate whether the
new empirical model alters Fujiyama’s (2014b) results.
In this study, I re-examine the timeliness of non-current asset impairments based on Fujiyama(2014b) and using piecewise-linear stock returns, as suggested by Banker et al. (2017). In addition,
I examine the relationships between non-current asset impairments and changes in sales and cash
flows from operations (CFO), which Banker et al. (2017) suggest can be viewed as short-term
indicators of economic loss. Using data on Japanese firms during 2007–2019, I find a negative
relationship between non-current asset impairments (positive values) in year t and negative stock
returns in year t–5, consistent with Fujiyama (2014b). Second, non-current asset impairments arenegatively correlated with negative stock returns in year t, which is inconsistent with Fujiyama(2014b), who does not observe any correlation between impairments and linear stock returns inyear t. Third, the relationships between non-current asset impairments and negative stock returns
are strongest in years t–1 and t–2. These results suggest that consistent with the “probability
criterion” of the impairment recognition employed by the Japanese standard, contrary to the“economic criterion” employed by International Financial Reporting Standards, the relationshipbetween impairments and negative stock returns is stronger in years t–1 and t–2 than in year t.3
Meanwhile, the negative relationships from years t–5 to t–3 indicate that Japanese firms do notnecessarily recognize non-current asset impairments in a timely manner. Fourth, I find statisticallysignificant correlations between non-current asset impairments and negative changes in sales and
CFO, suggesting that changes in sales and CFO are short-term indicators of economic losses.
Finally, additional analyses reveal that using non-zero thresholds for non-current asset impairment
triggers provides a minor improvement in the explanatory power of the empirical model of noncurrent asset impairment timeliness.
This study contributes to the literature in two ways. First, it improves the findings of Fujiyama(2014b). While the finding of a negative relationship between non-current asset impairments andstock returns in year t–5 is consistent with Fujiyama (2014b), here I present a statistically significant
relationship between impairments and negative stock returns in year t. Moreover, the adjusted Rsquared is higher for the models employed in this study. My findings suggest that piecewise-linear
stock returns better reflect the asymmetric timeliness of non-current asset impairments and that3

For the recognition of non-current asset impairments, the Japanese standard and the U.S. GAAP employ “probability
criterion,” which requires a firm to recognize an impairment loss “only if it is considered probable that the carrying
amount of an asset cannot be fully recovered” (IAS 36, APPENDIX B, B81); IFRS employs “economic criterion,”
which requires a firm to recognize an impairment loss “whenever the recoverable amount of an asset is below its
carrying amount” (IAS 36, APPENDIX, B88). Further, see Gordon and Hsu (2018) for the difference in therecognition criteria for asset impairments. The Japanese standard requires a firm to test the impairment of an asset
when the signs of a non-current asset impairment, including operating losses or cash flows in two consecutive years or
more, are observed and compare the undiscounted future cash flows with the carrying amount of an asset. IAS 36
provides several examples of asset impairment indications, including a significant decline in an asset’s market value, theratio of the carrying amount of a firm’s net asset over its market capitalization, and unfavorable internal reporting. It
requires a firm to compare value in use, such as discounted future cash flows, with the carrying amount of an asset
when some indicators are observed.

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piecewise-linear changes in sales and CFO capture the existence of non-current asset impairments.
In addition, my findings suggest using statistical tests that the largest economic losses occur one or
two years prior to their accounting recognition.
Second, this study contributes to the research on the determinants of non-current asset
impairments. Prior research on the determinants of non-current asset impairments often employs
the model developed by Riedl (2004) (e.g., Enomoto 2008; Hu and Kurumado 2012; Fujiyama
2014c). Although this study does not replicate Riedl’s (2004) model with piecewise-linear
indicators such as stock returns, sales, and CFO, as implemented by Banker et al. (2017), my
findings indicate that non-current asset impairments have non-linear relationships with thoseindicators, suggesting that piecewise-linear variables better control for the economic determinantsof non-current asset impairments. Moreover, the findings suggest that research on accounting
conservatism and the timeliness of earnings can better reflect differences in the time horizons ofcash flows among accounting items by incorporating piecewise changes in sales and cash flows fromoperations.

2. Timeliness Models for Non-Current Asset Impairments in Prior ResearchPrior research has investigated the timeliness of non-current asset impairment losses, especially
goodwill impairments, using several empirical models. In this section, I review the empirical models
used in prior research. The most frequently used model employs the amount or recognition of
impairment losses as the explained variable and stock returns as the explanatory variable (LapointeAntunes et al. 2009; Glaum et al. 2018; Albersmann and Quick 2020; Iatridis et al. 2021).
Lapointe-Antunes et al. (2009) estimate the following OLS regression:
GoodwillImpairmenti,t = α0 + α1Reti,t + α2Reti,t-1 + α3Reti,t-2 + εi,t(1),where GoodwillImpairmenti,t is the reported goodwill and Reti,t is firm i’s annual stock return in year
t.4 Glaum et al. (2018) employ a recognition dummy as the explained variable, include only linear
stock returns in years t and t–1, and compare the magnitude of these two coefficients; Albersmann
and Quick (2020) employ a recognition dummy as the explained variable and examine its
relationships with linear stock returns in years t, t–1, and t–2; Iatridis et al. (2021) investigate only
the relationship between the reported goodwill impairments and stock returns in year t but
incorporate piecewise-linear stock returns. In line with this stream of research, Fujiyama (2014b)
incorporates linear stock returns from years t to t–6. Similarly, Chen et al. (2008) use earnings
before extraordinary items but after impairment charges as the explained variable, and incorporate
an interaction term between linear stock returns and impairment recognition as an explanatory
variable. Another timeliness model employs stock returns as the explained variable and impairment
losses as an explanatory variable, controlling for reported earnings (Choi 2008; Chen et al. 2008).
The following two studies identify signs of economic goodwill impairment. André et al. (2016)
define impairment indicators as [market value of equity – book value of equity] < book goodwill,
market-to-book ratio less than one, or EBITDA less than zero. Further, they compare therecognition of goodwill impairments by the EU and U.S. firms when observing each indicator. Li

4

As the purpose of this section is to explain the overview of the empirical models used in prior research, I do not discuss
the details of the definitions of the variables employed.

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness5

and Sloan (2017) consider the following two indicators. One is a book-to-market ratio of morethan one in year t–1. The other takes the value of one if [book goodwill / total assets] is more than
10% and the return on assets (ROA) is less than zero, the negative value of one if [book goodwill /total assets] is less than 5% and ROA is more than 5%, and zero otherwise in year t–1. A negativevalue of one indicates that firms are unlikely to experience economic impairment in book goodwill.
Then, they regress the goodwill impairment dummy in year t on these two indicators in year t–1.
They interpret goodwill impairments as less timely if these indicators in year t–1 predict them inyear t.
Chung and Hribar (2021) employ the Cox proportional hazards model to investigate therelationship between non-impairment duration and CEO overconfidence.
Overall, prior research has investigated the timeliness of non-current asset impairments,
especially goodwill impairments, by (1) using stock returns as an explanatory variable, (2) using
stock returns as the explained variable, (3) identifying impairment indicators, and (4) employing a
hazard model. As my focus is on non-current assets and not only on goodwill, the use of (3)impairment indicators and (4) a hazard model has some limitations. Specifically, a frequently usedindicator of goodwill impairment, the book-to-market ratio, is not suitable for non-current assets
such as fixed assets (e.g., property, plant, and equipment). For example, if a firm without bookgoodwill experiences a more than one BTM ratio, there lies a possibility that its inventories are
economically impaired; they are not subject to accounting for non-current asset impairments inJapan. A hazard model may not be suitable for non-current asset impairments. As the U.S.
Generally Accepted Accounting Principles (GAAP) and International Financial ReportingStandards require a non-amortization method for goodwill, book goodwill is expensed only for
goodwill impairment. This allows for a study to identify the timing of expensing book goodwill.
However, a proportion of non-current assets are subject to periodic depreciation and amortization,
which complicates identifying the duration between the economic existence and recognition timingof non-current asset impairments. Moreover, the use of stock returns as the explained variablemakes it difficult to control for the economic losses that occur in other fiscal years. Therefore, using
stock returns as an explanatory variable is a better model for investigating the timeliness of noncurrent asset impairments. This study aims to improve the model that uses stock returns as an
explanatory variable by introducing piecewise-linear stock returns and considering the years before
impairment recognition in a setting of non-current asset impairments.

3. Empirical Models
Following Lapointe-Antunes et al. (2009), Fujiyama (2014b) estimates the following OLS
regression:
Impi,t = a0 + a1Ri,t + a2Ri,t-1 + a3Ri,t-2 + a4Ri,t-3 + a5Ri,t-4 + a6Ri,t-5 + a7Ri,t-6+ ΣYear + εi,t(2),where Impi,t is the positive value of the reported non-current asset impairment losses in year t,
deflated by market capitalization at the end of year t–1, and Ri,k is firm i’s buy-and-hold annual
stock return. k denotes the observed year (i.e., year t, year t–1…year t–6). Fujiyama (2014b) assumes
a linear relationship between non-current asset impairments and stock returns.

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However, Banker et al. (2017) point to different relationships between non-current asset
impairments and positive and negative stock returns. Thus, they propose incorporating a dummy
variable, Deci,k, which takes the value of one if firm i’s stock return is negative and zero otherwise,
and its interaction with Ri,k. Accordingly, I estimate the following OLS regression model
incorporating these variables:
Impi,t = b0 + b1Ri,t + b2Ri,t-1 + b3Ri,t-2 + b4Ri,t-3 + b5Ri,t-4 + b6Ri,t-5 + b7Ri,t-6+ b8Ri,t × Deci,t + b9Ri,t-1 × Deci,t-1 + b10Ri,t-2 × Deci,t-2 + b11Ri,t-3 × Deci,t-3+ b12Ri,t-4 × Deci,t-4 + b13Ri,t-5 × Deci,t-5 + b14Ri,t-6 × Deci,t-6 + b15Deci,t+ b16Deci,t-1 + b17Deci,t-2 + b18Deci,t-3 + b19Deci,t-4 + b20Deci,t-5+ b21Deci,t-6 + ΣYear + ΣIndustry +εi,t(3).

Note that in this study, I compute Ri,k by adjusting dividends and stock splits and Impi,t by adjusting
the stock splits.5 Equation (3) also controls for industry-fixed effects in addition to year-fixed
effects.
In addition, following Ball and Shivakumar (2006) and Banker et al. (2017), I estimate thefollowing OLS regression model incorporating short-term indicators:
Impi,t = c0 + c1Ri,t + c2Ri,t-1 + c3Ri,t-2 + c4Ri,t-3 + c5Ri,t-4 + c6Ri,t-5 + c7Ri,t-6+ c8Ri,t × Deci,t + c9Ri,t-1 × Deci,t-1 + c10Ri,t-2 × Deci,t-2 + c11Ri,t-3 × Deci,t-3+ c12Ri,t-4 × Deci,t-4 + c13Ri,t-5 × Deci,t-5 + c14Ri,t-6 × Deci,t-6 + c15ΔSalesi,t+ c16ΔSalesi,t × DecSalesi,t + c17DecSalesi,t + c18ΔCFOi,t+ c19ΔCFOi,t × DecCFOi,t + c20DecCFOi,t + c21Deci,t + c22Deci,t-1+ c23Deci,t-2 + c24Deci,t-3 + c25Deci,t-4 + c26Deci,t-5 + c27Deci,t-6+ΣYear +ΣIndustry + εi,t(4),where ΔSalesi,t is the adjusted per-share change in sales in year t and ΔCFOi,t is the adjusted pershare change in CFO in year t. Both ΔSalesi,t and ΔCFOi,t are deflated by a dividend and share-split
adjusted stock price. DecSalesi,t and DecCFOi,t take the value of one if ΔSalesi,t and ΔCFOi,t are
negative, respectively. I also estimate models incorporating ΔSalesi,k and ΔCFOi,k from year t to t–6
to confirm that they are short-term indicators of economic impairment.
As stock returns capture long-term changes in cash flows, they can be assumed to overlap withshort-term changes in future cash flows, which are captured by changes in operating cash flows andsales. Nevertheless, the incorporation of these short-term indicators is important in two respects.
First, short-term indicators are likely to capture management and auditor decision processes.
Operating cash flow forecasts are a major basis for impairment tests for non-current assets, andsales forecasts are a major input for operating cash flow forecasts. Referring to Chase (2013), Banker
et al. (2017) argue that because a sales forecast is based on the projection of a recent sales trend, acurrent sales change is an important determinant of a cash flow forecast by accountants. Thus, the5

I use the cumulative adjustment coefficients B and A from NEEDS-FinancialQuest 2.0 for Ri,k and Impi,t, respectively.
Cumulative adjustment coefficients A and B adjust share splits, share consolidation, and so on, excluding and including
dividends, respectively.

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness7

incorporation of short-term indicators partly controls for managers’ and auditors’ impairment
testing processes, which are expected to affect the timeliness of non-current asset impairments.
Second, research on non-current asset impairment determinants generally does not control for
lagged stock returns. The use of piecewise short-term indicators can improve empirical models of
non-current asset impairment determinants to the extent that lagged stock returns can capture apart of the economic losses captured by short-term indicators.

4. Data
Financial and price data are obtained from the NEEDS-FinancialQUEST 2.0. I obtain dataon firms with fiscal year ends in March for the period 2007–2019. I exclude the firms whose
accounting period is not 12 months, whose accounting standards are not Japanese GAAP, thatbelong to financial industries, and whose necessary data are not available.6 As a result of this sample
selection, the final sample size is 25,860 firm-year observations. Each continuous variable is
winsorized at the upper and bottom 1st percentile by year. Impi,t is winsorized at the upper 1st
percentile value by year.

5. Empirical Results
5.1. Descriptive Statistics and Correlation Matrix
Table 1 presents the descriptive statistics. The mean value of Impi,t is 0.0068 and its medianvalue is 0.0000, indicating that most firms do not record impairment losses. The second row ofTable 1 presents the descriptive statistics of Impi,t for only impairment firms. The mean and medianvalues are 0.0147 and 0.0037, respectively, whereas the 75th percentile value is 0.0121. Thus, a small
proportion of impairment firms record large impairment losses.
Table 2 reports the correlation matrix. Stock returns are not highly correlated each year. ΔSalest
is not highly correlated with ΔCFOi,t. However, ΔCFOi,t is relatively highly correlated with ΔCFOi,t1, (coefficient = –0.3627; untabulated). ΔCFOi,t is not highly correlated with ΔCFOi,t-2 (coefficient= –0.0231; untabulated).

5.2. Timeliness of Non-Current Asset Impairment Losses
Table 3 presents the results of the timeliness test of non-current asset impairments. Panel A in
Table 3 reports the regression results. Column (1) reports the results for Fujiyama (2014b). Column(2) presents the results of Fujiyama’s (2014b) replication. These results are similar, suggesting thatthe sample used in this study is similar to that of Fujiyama (2014b).
Columns (3) to (5) present the results obtained after using dividend- and share-split-adjusted
returns but not employing the piecewise regression method. These results are similar to those of
Fujiyama (2014b), except for the results of Ri,t in Columns (3) and (4). In Column (5), thecoefficient of Ri,t is negative but not statistically significant (coefficient = –0.0022; t = –1.29). The
difference between Columns (4) and (5) is the standard error adjustment. As Fujiyama (2014c)
shows that non-current asset impairment losses are correlated with the changes in gross domestic
product in Japan, macroeconomic conditions, such as years, are factors affecting firms’ non-current
asset impairments. Moreover, stock returns are also affected by the macroeconomic conditions.
6This study does not exclude observations with multiple impairment losses recorded in year t and other years (from year
t–1 to year t–6), assuming that impairment losses in years t–1 to t–6 are not correlated to those in year t.

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TABLE 1. DESCRIPTIVE STATISTICS (n =25,860)
Impt
Impt (only Impt > 0)
Rt
Rt-1
Rt-2
Rt-3
Rt-4
Rt-5
Rt-6
ΔSalestΔSalest-1
ΔSalest-2
ΔSalest-3
ΔSalest-4
ΔSalest-5
ΔSalest-6
ΔCFOt
ΔCFOt-1
ΔCFOt-2
ΔCFOt-3
ΔCFOt-4
ΔCFOt-5
ΔCFOt-6

Mean
0.00680.01470.06790.1076
0.10930.14910.14550.1197
0.0974-0.0231-0.0285-0.0164-0.0067-0.0197
0.01170.06030.00680.00650.00580.00800.00980.01030.0119SD
0.02280.03190.38570.4096
0.41640.48430.49390.51030.51800.60881.0326
1.9183
2.10412.22403.43373.04360.18630.21180.2236
0.24530.26450.27470.262825P
0.00000.0010-0.1663-0.1398-0.1406-0.1373-0.1450-0.1719-0.1917-0.0762-0.0793-0.0837-0.0857-0.0941-0.1153-0.1187-0.0460-0.0485-0.0508-0.0541-0.0565-0.0593-0.0609

Median0.00000.00370.02180.05330.05240.06400.06140.03380.01120.02330.02510.02600.02960.02950.02360.02160.00220.00280.00290.00270.00350.00300.002075P
0.00300.01210.22520.27150.27330.31970.31810.28430.25990.12300.13010.13570.14710.15210.14760.14440.0546
0.05750.05930.06250.06720.06890.0685

Notes: Impi,t is non-current asset impairment losses per share in year t, deflated by the adjusted
stock price at the end of fiscal year t–1. Ri,k is the adjusted stock return in year k. ΔSalesi,k is thechange in sales in year k, deflated by the adjusted stock price at the end of fiscal year k–1. ΔCFOi,kis the change in cash flows from operations in year k, deflated by the adjusted stock price at theend of fiscal year k–1. The number of firm-year observations with impairment losses is 11,868(row 2).

Thus, it may be better to adjust standard errors by clustering by year instead of using White’s (1980)
method in addition to year-fixed effects.
The results in Columns (6) and (7) are my main interests and are obtained by estimating
piecewise-linear regression models. Ri,k × Deci,k is statistically significant from year t–4 to year t,
indicating the asymmetric relationship of non-current asset impairments with positive and negative
stock returns. In addition, the use of the piecewise-linear regression model improves the
explanatory power of the estimation model; that is, the adjusted R2 in Column (5) is 3.42% andthat in Columns (6) and (7) is 7.23% and 8.52%, improving 3.81% and 5.10% of the explanatory

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness

9

TABLE 2. PEARSON CORRELATION MATRIX (n =25,860)(1) Impt(2) Rt(3) Rt-1(4) Rt-2(5) Rt-3(6) Rt-4(7) Rt-5(8) Rt-6(9) ΔSalest(10) ΔCFOt(1)
1.0000-0.0111-0.1225-0.1011-0.0500-0.02360.01430.0247-0.1206
0.0019

(2)

(3)

(4)

(5)

(6)

(7)

(8)

(9)

1.0000-0.0381-0.1182-0.1120-0.0757-0.0884
0.06750.0581
0.09761.00000.0022-0.0008-0.1540-0.0922-0.09930.1658-0.05641.00000.01990.0011-0.1749-0.1100
0.0963-0.0196

1.0000-0.0255-0.0502-0.19450.03840.01221.0000-0.0029-0.0269-0.04210.01241.0000-0.0026-0.0711-0.0053

1.0000-0.12850.01911.00000.0527

Notes: Impi,t is non-current asset impairment losses per share in year t, deflated by the adjusted
stock price at the end of fiscal year t–1. Ri,k is the adjusted stock return in year k. ΔSalesi,t is thechange in sales in year t, deflated by the adjusted stock price at the end of fiscal year t–1. ΔCFOi,tis the change in cash flows from operations in year t, deflated by the adjusted stock price at theend of fiscal year t–1. Bold letters indicate statistical significance at the 5% level.

power, respectively. The coefficients of Ri,k are negative and statistically significant for years t-1 tot–6, suggesting that impairment firms experience a smaller increase in their stock prices even whenthese prices increase before their impairment recognition.
Panel B of Table 3 presents the coefficients of stock returns for observations with negative
stock returns (i.e., Ri,k + Ri,k × Deci,k) and compares these coefficients. The coefficients forobservations with negative stock returns are statistically significant at least at the 5% level from year
t–5 to year t in Columns (6) and (7) and at the 10% level in year t–6 in Column (6). This suggeststhat non-current asset impairments occur gradually approximately five years before theirrecognition. Contrary to Fujiyama (2014b), I find a statistically significant association between
non-current asset impairments and stock returns for observations with negative stock returns inyear t (coefficient = –0.0179 and –0.0186; t = –4.49 and –4.67 in Columns 6 and 7, respectively).
These results suggest that economic impairments occur gradually for several years before
recognition.
Comparing the coefficients for observations with negative stock returns, the difference
between those for years t and t–1 is 0.0116 and statistically significant at the 1% level (t = 3.13 and3.26 in Columns 6 and 7, respectively), indicating that the coefficients for year t–1 are smaller thanthose for year t. While the difference between those for years t–1 and t–2 is insignificant, thedifferences between those for years t–2 and t–3 are –0.0091 and –0.0092, respectively, andstatistically significant at the 10% level in Columns (6) and (7), respectively. In addition, thedifference between years t–1 and t–3 is statistically significant at the 1% level (untabulated). These
results suggest that the economic impairments of non-current assets occur to a greater extent inyears t–1 and t–2, consistent with the accounting standard that employs the “probability criterion”
instead of the “economic criterion.” An example of the signs of non-current asset impairments
under the Japanese GAAP is to record negative CFO or operating losses for a cash-generating unitRobust14,0940.0195# of observations
adj-R2Yes
No

SE adjustment

Year
Industry

13,9980.0242

RobustYesNo

13,9980.0365

RobustYesNo

25,8600.0342

Robust

Yes
No

19.66
-3.52
-16.35-13.86
-9.73
-6.31
-4.44
-0.99

t-value

Coef.
6.07
-1.29
-3.93
-3.69
-3.12
-3.13
-3.43
-0.98

t-value

25,8600.0342Year-clusteredYes
No

0.0098***-0.0022-0.0067***-0.0054***-0.0033***-0.0024***-0.0018***-0.0005

Coef.
t-value

25,8600.0723

Yes
Yes

-0.30
-1.78
-1.58
0.11
0.50
-0.39
-0.18

-5.07
-6.66
-3.80
-3.61
-1.92
-1.37
-0.56

3.95
1.30
-4.73
-8.81
-3.31
-4.27
-4.58
-1.97

t-value

25,8600.0852Year-clustered-0.0002-0.0012-0.0008
0.00000.0002-0.0002-0.0001-0.0191***-0.0260***-0.0174***-0.0089***-0.0045*-0.0023-0.00100.0051***0.0006-0.0042***-0.0045***-0.0038***-0.0032***-0.0031***-0.0014*

Coef.

(7) Full sample period(continued on next page)

Year-clustered

Yes
No

-0.25
-1.79
-1.64
0.24
0.59
-0.42
-0.24

Coef.
0.0098***-0.0022***-0.0067***-0.0054***-0.0033***-0.0024***-0.0018***-0.0005-0.0002-0.0011*-0.00070.00010.0002-0.0002-0.0001

16.56
-2.93
-12.46-11.23
-7.33
-6.10
-3.54
-0.51

t-value

Dect
Dect-1Dect-2Dect-3Dect-4Dect-5Dect-6

Coef.
0.0115***-0.0033***-0.0097***-0.0075***-0.0036***-0.0036***-0.0023***-0.0003(6) Full sample period

-4.87
-6.78
-3.51
-3.00
-1.90
-1.48
-1.03

13.76
-0.89
-9.74
-9.26
-4.01
-2.99
-1.71
0.60

(5) Full sample period-0.0185***-0.0253***-0.0168***-0.0084**-0.0044*-0.0024-0.0016

Constant
Rt
Rt-1
Rt-2
Rt-3
Rt-4
Rt-5
Rt-6

0.0127***-0.0012-0.0094***-0.0076***-0.0026***-0.0023***-0.0014*0.0005(4) Full sample period

Rt × Dect
Rt-1 × Dect-1
Rt-2 × Dect-2
Rt-3 × Dect-3
Rt-4 × Dect-4
Rt-5 × Dect-5
Rt-6 × Dect-6

12.74
0.44
-8.47
-7.56
-4.28
-3.12
-2.10
0.52

(3) Sample period sameas Fujiyama (2014b)

5.28
1.29
-4.88
-9.19
-3.36
-4.29
-4.31
-1.87

t-value

Coef.

0.0134***0.0008-0.0098***-0.0075***-0.0003***-0.0025***-0.0019**0.0005(2) Sample period andresearch design of
Fujiyama (2014b)
Coef.
t-value
0.0042***0.0006-0.0042***-0.0044***-0.0038***-0.0032***-0.0030***-0.0013*

Dep. = Impt(1) Fujiyama(2014b)Panel A: OLS Regression Results

TABLE 3. TEST OF TIMELINESS OF NON-CURRENT ASSET IMPAIRMENT LOSSES

10The Japanese Accounting Review, 12 (2022), 1-21

-4.36
-4.74
-3.49
-3.13
-2.16
3.13
-1.66
-1.90

-0.0213***-0.0122******-0.0076-0.0054**-0.0028*0.0116***-0.0082-0.0091*-0.0046-0.0022-0.0026[3] Rt-2 + Rt-2 × Dect-2[4] Rt-3 + Rt-3 × Dect-3[5] Rt-4 + Rt-4 × Dect-4[6] Rt-5 + Rt-5 × Dect-5[7] Rt-6 + Rt-6 × Dect-6[1] - [2][2] - [3][3] - [4][4] - [5][5] - [6][6] - [7]-0.0030-0.0023-0.0050-0.0092*-0.0083

0.0116***-0.0024-0.0054**-0.0077***-0.0127***-0.0219***-0.0302***

-1.20

-0.88

-1.30

-2.05

-1.76

3.26

-1.58

-2.97

-3.47

-5.58

-4.64

-7.53

-4.67

Notes: Panel A presents the OLS regression results of the timeliness test of non-current asset impairments. Panel B reports the coefficientsof stock returns for observations with negative stock returns and their comparisons between years k and k–1. Impi,t is non-current asset
impairment losses per share in year t, deflated by the adjusted stock price at the end of fiscal year t–1. Ri,k is the adjusted stock return inyear k. Deci,k takes the value of one if Rk is negative. Column (1) shows the results of Fujiyama (2014b) using market capitalization tocompute stock returns. Column (2) employs the same regression model as Fujiyama (2014b) and estimates it using my sample. Columns(3)-(7) use dividend- and share-split-adjusted stock prices to compute stock returns. In Columns (1) to (4), standard errors are adjusted
based on White (1980) as in Fujiyama (2014b). In Columns (5) to (7), standard errors are clustered by year. ***, **, and * indicate statisticalsignificance at the 1%, 5%, and 10% levels, respectively.

-1.13

-0.87

-1.16

-7.69

-0.0295***

t-value[2] Rt-1 + Rt-1 × Dect-1-0.0186***-4.49-0.0179***at-value[1] Rt + Rt × Dect

(7) Full sample period
Coef./Diff.

(6) Full sample period
Coef./Diff.

Panel B: Coefficients for Observations with Negative Stock Returns and Their Comparisons

TABLE 3. (continued)

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness 11

12

The Japanese Accounting Review, 12 (2022), 1-21

for two consecutive years.
Overall, the use of piecewise-linear regression is likely to improve the tests of non-current asset
impairment timeliness. In addition, the results suggest that the reported impairment losses aretimelier than Fujiyama (2014b) finds; however, such losses are not necessarily recorded in a timely
manner as they gradually occurred five years before their recognition.

5.3. Test of the Short-Term Indicators of Non-Current Asset Impairments
Table 4 reports the results incorporating changes in sales and CFO as the short-term indicatorsof non-current asset impairments. In Panel A, only results for the observations with negative stock
returns and/or changes in sales and/or CFO are presented. Only changes in sales and CFO in year
t are incorporated in Column (1) while those for years t to t–6 are incorporated in Columns (2) to(6). In Column (1), the coefficients of ΔSalesi,t × DecSalesi,t and ΔCFOi,t × DecCFOi,t are negativeand statistically significant at the 1% level (coefficient = –0.0081 and –0.0218; t = –4.28 and –5.74
for ΔSalesi,t × DecSalesi,t and ΔCFOi,t × DecCFOi,t, respectively). The negative coefficients of ΔSalesi,t× DecSalesi,t and ΔCFOi,t × DecCFOi,t are consistently presented in Columns (2) to (6). These
coefficients for year t–1 are negative but insignificant in Columns (2) to (6). The coefficients of
ΔSalesi,k × DecSalesi,k and ΔCFOi,k × DecCFOi,k before year t–1 are insignificant, while the coefficientof ΔCFOi,t-6 × DecCFOi,t-6 is negative and statistically significant at the 10% level in Column (5),but not in Columns (4) and (6). Thus, positive and negative changes in sales and CFO, which are
expected to be short-term indicators of non-current asset impairments, have asymmetrical
relationships with reported non-current asset impairment losses only in year t.
Panel B of Table 4 presents the coefficients of stock returns and changes in sales and cash flows
from operations for observations with negative returns or changes in sales or CFO. Columns (1),(2), (3), and (6) show that the combined coefficients of ΔSalesi,t and ΔSalesi,t × DecSalesi,t areconsistently negative and statistically significant at the 1% level. In Columns (1), (4), (5), and (6),the combined coefficients of ΔCFOi,t and ΔCFOi,t × DecCFOi,t are consistently negative andstatistically significant at the 1% level. The combined coefficients of both ΔSalesi,k and ΔSalesi,k ×
DecSalesi,k, and ΔCFOi,k and ΔCFOi,k × DecCFOi,k are insignificant for years t–6 to t–1. The
combined coefficients of ΔCFOi,t-4 and ΔCFOi,t-4 × DecCFOi,t-4 are positive and statisticallysignificant. However, the sign is opposite to that of the prediction and is not interpretable.
The results for negative stock returns are consistent with those in Table 3. The difference inthe combined coefficients of Ri,k and Ri,k × Deci,k between years t and t–1 is consistently andstatistically significant at the 5% level, even when controlling for changes in sales and CFO. The
difference between years t–2 and t–3 is statistically significant at the 10% level in Column (1) but
not in Columns (3), (5), and (6). Note that the difference between years t–1 and t–3 is consistently
statistically significant at the 1% level in all the columns (untabulated). Assuming that changes inoperating cash flows and sales partly control for the non-current asset-impairment testing processesof managers and auditors because they are major impairment test inputs, the effectiveness of thetimeliness model holds even after undertaking such management and auditor decision processes.
Interestingly, the combined coefficients of Ri,k and Ri,k × Deci,k in Column (1) of Panel B of
Table 4 are slightly different from those in Column (7) of Panel B of Table 3. Specifically, thosein Tables 3 and 4 are –0.0186 and –0.0169 for year t, –0.0302 and –0.0241 for year t–1, –0.0219
and –0.0180 for year t–2, –0.0127 and –0.0100 for year t–3, –0.0077 and –0.0064 for year t–4, and–0.0054 and –0.0042 for year t–5, respectively. The differences are 0.0017 for year t, 0.0061 foryear t–1, 0.0039 for year t–2, 0.0027 for year t–3, 0.0013 for year t–4, and 0.0012 for year t–5. The

-5.02
-7.31
-3.33
-3.01
-1.84
-1.00
-0.03

-0.0081***-0.0218***

Rt × Dect
Rt-1 × Dect-1
Rt-2 × Dect-2
Rt-3 × Dect-3
Rt-4 × Dect-4
Rt-5 × Dect-5
Rt-6 × Dect-6

ΔSalest × DecSalest
ΔSalest-1 × DecSalest-1
ΔSalest-2 × DecSalest-2
ΔSalest-3 × DecSalest-3
ΔSalest-4 × DecSalest-4
ΔSalest-5 × DecSalest-5
ΔSalest-6 × DecSalest-6

ΔCFOt × DecCFOt
ΔCFOt-1 × DecCFOt-1
ΔCFOt-2 × DecCFOt-2
ΔCFOt-3 × DecCFOt-3
ΔCFOt-4 × DecCFOt-4
ΔCFOt-5 × DecCFOt-5
ΔCFOt-6 × DecCFOt-6

Yes
Yes

Yes

Year-clustered

25,8600.0997Year
Industry

Other variables

SE adjustment# of observations
adj-R2

-5.74

-4.28

t-value

Coef.

-0.0162***-0.0203***-0.0141***-0.0067***-0.0036*-0.0014-0.0001

Dep. = Impt

(1) Changes in sales and
CFO in year t

Panel A: OLS Regression Results

-8.02
1.21
0.68
0.62
0.41
-0.98
0.79

t-value

25,8600.0674Year-clustered

Yes

Yes
Yes

-0.0153***0.00190.00070.00040.0002-0.0004
0.0004Coef.

(2) Only changes in
sales

-8.57
1.29
0.44
0.30
-0.47
-1.18
0.49

-4.83
-7.25
-3.19
-3.14
-2.06
-1.03
0.34

t-value

25,8600.0979Year-clustered

Yes

Yes
Yes

-0.0116***0.00160.00040.0002-0.0002-0.0005
0.0003-0.0162***-0.0208***-0.0139***-0.0069***-0.0040*-0.00150.0006Coef.

(3) Stock returns andchanges in sales

-9.04
-1.80
-0.24
0.20
2.79
0.02
-0.70

t-value

25,8600.0538Year-clustered

Yes

Yes
Yes

-0.0447***-0.0070-0.0006
0.00030.0032**0.0000-0.0013

Coef.

(4) Only changes inCFO

25,8600.0947

-5.56
0.02
-0.24
-0.11
3.09
-1.00
-0.90

-7.28
1.15
0.35
0.37
-0.77
-0.79
0.92

-4.75
-7.19
-2.88
-2.85
-1.84
-0.99
0.17

t-value

25,8600.1020Year-clustered

Yes

Yes
Yes

-0.0202***0.0001-0.0007-0.00020.0035***-0.0018-0.0027-0.0094***0.00160.00040.0003-0.0003-0.00030.0006-0.0159***-0.0196***-0.0133**-0.0064**-0.0037*-0.00150.0003Coef.

(6) Stock returns andchanges in sales and CFO(continued on next page)

-7.37
-0.82
-0.23
-0.33
2.11
-1.27
-2.01

-4.99
-6.61
-3.16
-3.04
-1.66
-1.09
-0.45

t-valueYear-clustered

Yes

Yes
Yes

-0.0274***-0.0030-0.0005-0.0006
0.0022*-0.0020-0.0039*-0.0179***-0.0230***-0.0150***-0.0073***-0.0036-0.0017-0.0007

Coef.

(5) Stock returns andchanges in CFO

TABLE 4. SHORT-TERM INDICATORS OF NON-CURRENT ASSET IMPAIRMENT LOSSES

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness 13

-4.91
-8.58
-4.18
-4.95
-3.37
-2.88
-1.15
2.84
-1.42
-1.86
-1.10
-0.98
-1.21

-0.0169***-0.0241***-0.0180***-0.0100***-0.0064***-0.0042**-0.00160.0072**-0.0061-0.0080*-0.0036-0.0023-0.0026[1] Rt + Rt × Dect[2] Rt-1 + Rt-1 × Dect-1[3] Rt-2 + Rt-2 × Dect-2[4] Rt-3 + Rt-3 × Dect-3[5] Rt-4 + Rt-4 × Dect-4[6] Rt-5 + Rt-5 × Dect-5[7] Rt-6 + Rt-6 × Dect-6[1] - [2][2] - [3][3] - [4][4] - [5][5] - [6][6] - [7]-0.0072***-0.0015-0.0004
0.00000.0001-0.0004
0.0001
-4.87
-1.50
-0.63
-0.08
0.31
-1.11
0.37

(2) Only changes
in salesCoef.
t-value

0.0079***-0.0067-0.0075-0.0034-0.0026-0.0034-0.0165***-0.0244***-0.0177***-0.0102***-0.0068***-0.0042**-0.0008-0.0049***-0.0005
0.00010.00040.0002-0.0004
0.0001

3.09
-1.57
-1.69
-1.02
-1.14
-1.61

-4.65
-8.19
-3.98
-4.93
-3.66
-2.73
-0.60

-4.72
-0.54
0.21
0.98
0.89
-1.05
0.18

(3) Stock returns andchanges in sales
Coef.
t-value-0.0246***-0.0048*-0.0014-0.0009
0.0012*-0.0001-0.0016
-7.23
-1.93
-0.73
-0.72
2.03
-0.09
-1.23

(4) Only changes in
CFO
Coef.
t-value0.0088**-0.0077-0.0083-0.0042-0.0019-0.0025-0.0180***-0.0268***-0.0191***-0.0108***-0.0066***-0.0048**-0.0022-0.0163***-0.0027-0.0007-0.0006
0.0016**-0.0002-0.0024*

2.82
-1.51
-1.75
-1.12
-0.75
-1.13

-4.71
-7.62
-3.91
-4.83
-3.16
-2.78
-1.62

-5.63
-1.27
-0.37
-0.50
2.27
-0.16
-1.79

(5) Stock returns andchanges in CFO
Coef.
t-value

0.0064**-0.0059-0.0073-0.0032-0.0021-0.0031-0.0164***-0.0228***-0.0169***-0.0096***-0.0064***-0.0043**-0.0012-0.0121***-0.0014-0.0009-0.0005
0.0022**-0.0002-0.0017-0.0042***-0.00020.00020.00040.0001-0.00030.0004

2.57
-1.25
-1.54
-0.91
-0.89
-1.45

-4.60
-8.18
-3.56
-4.50
-3.26
-2.58
-0.87

-4.54
-0.97
-0.38
-0.35
2.56
-0.14
-0.87

-4.30
-0.23
0.25
1.05
0.62
-0.68
0.85

(6) Stock returns andchanges in sales and CFO
Coef.
t-value

Notes: Panel A presents the OLS regression results of the timeliness test of non-current asset impairments incorporating changes in sales
and cash flows from operations. Panel B reports the coefficients of stock returns and changes in sales and CFO for observations withnegative stock returns or changes in sales or CFO and their comparisons between years k and k–1. Impi,t is non-current asset impairment
losses per share in year t, deflated by the adjusted stock price at the end of fiscal year t–1. Ri,k is the adjusted stock return in year k. Deci,ktakes the value of one if Ri,k is negative. ΔSalesi,k is the change in sales in year k, deflated by the adjusted stock price at the end of fiscal
year k–1. DecSalesi,k takes the value of one if ΔSalesi,k is negative. ΔCFOi,k is the change in cash flows from operations in year k, deflatedby the adjusted stock price at the end of fiscal year k–1. DecCFOi,k takes the value of one if ΔCFOi,k is negative. Standard errors are
clustered by year. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

-5.31-0.0121***

ΔCFOt + ΔCFOt × DecCFOt
ΔCFOt-1 + ΔCFOt-1 × DecCFOt-1
ΔCFOt-2 + ΔCFOt-2 × DecCFOt-2
ΔCFOt-3 + ΔCFOt-3 × DecCFOt-3
ΔCFOt-4 + ΔCFOt-4 × DecCFOt-4
ΔCFOt-5 + ΔCFOt-5 × DecCFOt-5
ΔCFOt-6 + ΔCFOt-6 × DecCFOt-6-2.44-0.0033**

ΔSalest + ΔSalest × DecSalest
ΔSalest-1 + ΔSalest-1 × DecSalest-1
ΔSalest-2 + ΔSalest-2 × DecSalest-2
ΔSalest-3 + ΔSalest-3 × DecSalest-3
ΔSalest-4 + ΔSalest-4 × DecSalest-4
ΔSalest-5 + ΔSalest-5 × DecSalest-5
ΔSalest-6 + ΔSalest-6 × DecSalest-6(1) Changes in sales
and CFO in year t
Coef.
t-value

Panel B: Coefficients for Observations with Negative Stock Returns or Changes in Sales or CFO and Their Comparisons

TABLE 4. (continued)

14
The Japanese Accounting Review, 12 (2022), 1-21

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness 15

difference in the combined coefficients in Tables 3 and 4 is largest in year t–1 and decreases
afterwards. This result is consistent with the view that lagged stock returns capture long-term cash
flow changes, which are partly captured by short-term indicators. It is useful to recognize the tradeoff between the control for impairment testing processes and the overlap between short-term
indicators and lagged stock returns when future research on non-current asset impairment
timeliness employs the full model, that is, Equation (4).
Overall, the results suggest that changes in sales and CFO are short-term indicators of noncurrent asset impairments. To the extent that changes in sales and CFO are short-term indicatorsof non-current asset impairments, a model incorporating sales and CFO variables only for year t
can better reflect short-term changes in firms’ economic conditions.

6. Additional Analysis
As Banker et al. (2017) suggest that an impairment trigger is different from the value of zerofor all the three indicators, that is, stock return, sales change and operating cash flow change, I
analyze the timeliness of non-current asset impairments by using different impairment trigger
thresholds. Although Banker et al. (2017) employ a censored regression model, I employ an OLS
regression model because the purpose of this study is to improve Fujiyama’s (2014b) impairmenttimeliness model. Moreover, while they use grid search, I use certain thresholds of Deci,k, DecSalesi,t,and DecCFOi,t: 0.1, 0.05, –0.05, –0.1, –0.15, –0.2, –0.25, and –0.3, because the optimal value changes
as the sample changes.
Table 5 presents the results for different stock return thresholds. The adjusted R2 is the highest
for the threshold of –0.1, improving the adjusted R2 by 0.12% compared with the zero threshold(Panel A). Panel B reports the results of the coefficients of stock returns for observations withnegative stock returns (i.e., Ri,k + Ri,k × Deci,k) and compares the coefficients. For all thresholds, thecoefficients for observations below the thresholds are the largest in year t–1, which is consistent
with the main result. Although there are some differences for Deck < –0.25 and Deck < –0.3, theresults are qualitatively similar to those of Deck < 0 in the case of other thresholds.
Panels A and B of Table 6 present the results of the different thresholds for changes in sales
and CFO, respectively. In Panel A, the coefficients of sales changes for all thresholds are similar to
those of the main analysis except for those of DecSalesi,t < –0.25 and –0.3. In Panel B, the coefficientsof CFO changes for all the thresholds are similar to those of the main analysis. Moreover, theadjusted R2 for changes in sales and CFO are the highest for the thresholds of –0.1 and –0.05,
respectively. However, minor improvements in explanatory power are observed (0.05% and 0.01%
for changes in sales and CFO, respectively).
Overall, although a non-zero threshold would improve the model of non-current asset
impairment timeliness, the improvement appears to be minor for both the long- and short-term
indicators. Therefore, if one sets a non-zero threshold, it is better to justify the threshold bycomparing it with other thresholds.

7. Conclusions
This study re-examines the timeliness of non-current asset impairment losses, which Fujiyama(2014b) investigates, by using the piecewise-linear regression model proposed by Banker et al.
(2017). Similar to Fujiyama (2014b), I find a negative relationship between non-current asset
impairments (positive values) and negative stock returns in year t–5. However, contrary to Fujiyama

-5.47
-5.79
-3.98
-3.42
-1.85
-1.86
-0.68

2.81
2.28
1.61
0.30
2.05
0.01
-0.12

-0.0175***-0.0219***-0.0146***-0.0084***-0.0041*-0.0023*-0.00110.0012**0.0008**0.00060.00010.0005*0.00000.0000Rt × Dect
Rt-1 × Dect-1
Rt-2 × Dect-2
Rt-3 × Dect-3
Rt-4 × Dect-4
Rt-5 × Dect-5
Rt-6 × Dect-6

Dect
Dect-1Dect-2Dect-3Dect-4Dect-5Dect-6Year-clustered

25,8600.0834

SE adjustment# of observations
adj-R2

Yes
Yes

2.74
2.90
-4.01
-6.89
-3.35
-4.06
-5.27
-1.85

0.0034**0.0014**-0.0036***-0.0041***-0.0038***-0.0030***-0.0029***-0.0013*

Constant
Rt
Rt-1
Rt-2
Rt-3
Rt-4
Rt-5
Rt-6

Year
Industry

t-value

Deck < 0.1

Coef.

Dep. = Impt

Panel A: Regression Results

1.16
0.06
-0.52
-0.20
0.01
1.07
0.94

-5.28
-6.01
-3.90
-3.58
-2.21
-1.04
-0.40

3.06
2.06
-4.30
-7.64
-3.34
-4.09
-4.48
-1.71

t-value

25,8600.0845Year-clustered

Yes
Yes

0.00060.0000-0.0002-0.0001
0.00000.00050.0003-0.0182***-0.0236***-0.0160***-0.0089***-0.0048**-0.0016-0.00070.0041***0.0010*-0.0039***-0.0044***-0.0039***-0.0032***-0.0028***-0.0013

Coef.

Deck < 0.05

-0.30
-1.78
-1.58
0.11
0.50
-0.39
-0.18

-5.07
-6.66
-3.80
-3.61
-1.92
-1.37
-0.56

3.95
1.30
-4.73
-8.81
-3.31
-4.27
-4.58
-1.97

t-value

25,8600.0852Year-clustered

Yes
Yes

-0.0002-0.0012-0.0008
0.00000.0002-0.0002-0.0001-0.0191***-0.0260***-0.0174***-0.0089***-0.0045*-0.0023-0.00100.0051***0.0006-0.0042***-0.0045***-0.0038***-0.0032***-0.0031***-0.0014*

Coef.

Deck < 0

-1.12
-2.88
-1.68
-0.23
0.37
-0.98
-0.15

-4.84
-7.38
-3.61
-3.73
-1.78
-1.51
-0.51

4.88
0.30
-5.03
-9.13
-3.35
-4.37
-4.87
-1.97

t-value

25,8600.0860Year-clustered

Yes
Yes

-0.0011-0.0027**-0.0012-0.0001
0.0002-0.0005-0.0001-0.0202***-0.0289***-0.0184***-0.0092***-0.0045-0.0029-0.00100.0057***0.0001-0.0045***-0.0045***-0.0038***-0.0033***-0.0032***-0.0014*

Coef.

Deck < -0.05

-2.07
-3.36
-1.53
-0.10
0.12
-0.11
0.74

-4.82
-7.79
-3.36
-3.19
-1.69
-1.06
-0.11

5.29
-0.69
-5.46
-8.92
-3.52
-4.70
-4.33
-1.79

t-value

25,8600.0865Year-clustered

Yes
Yes

-0.0022*-0.0042***-0.0016-0.0001
0.0001-0.0001
0.0004-0.0218***-0.0320***-0.0191***-0.0089***-0.0046-0.0025-0.0003

0.0061***-0.0003-0.0046***-0.0045***-0.0038***-0.0034***-0.0031***-0.0014*

Coef.

Deck < -0.1

-1.92
-4.30
-1.49
-1.31
-0.47
-1.41
0.37

-4.58
-8.68
-3.06
-3.43
-1.85
-1.80
-0.24

5.80
-1.16
-5.79
-8.18
-3.48
-4.75
-4.67
-1.81

t-value

25,8600.0863Year-clustered

Yes
Yes

-0.0027*-0.0061***-0.0028-0.0009-0.0004-0.0009
0.0003-0.0226***-0.0358***-0.0209***-0.0102***-0.0054*-0.0041*-0.0006

0.0068***-0.0005-0.0049***-0.0047***-0.0040***-0.0034***-0.0032***-0.0014*

Coef.

Deck < -0.15

-2.30
-3.28
-1.00
-0.90
0.81
-1.11
0.82

-4.44
-7.39
-2.82
-5.09
-0.89
-1.64
0.17

5.97
-1.87
-6.11
-8.47
-3.51
-4.68
-4.49
-1.77

t-value

25,8600.0864Year-clustered

Yes
Yes

-0.0036**-0.0073***-0.0023-0.0008
0.0008-0.00130.0009-0.0236***-0.0382***-0.0196**-0.0098***-0.0031-0.00490.00050.0071***-0.0008*-0.0049***-0.0047***-0.0040***-0.0034***-0.0032***-0.0014

Coef.

Deck < -0.2

TABLE 5. IMPAIRMENT TRIGGER THRESHOLDS FOR STOCK RETURNS

-2.45
-6.49
-0.21
-0.10
0.76
-0.49
0.89

-4.29
-9.50
-2.30
-5.01
-0.81
-1.07
0.28

6.19
-2.53
-6.21
-8.34
-3.53
-4.78
-4.20
-1.80

-2.42
-8.45
-0.70
0.48
0.95
-0.07
-0.80

-4.37
-12.87
-2.36
-1.59
-0.18
-0.75
-0.80

6.09
-2.93
-6.83
-7.37
-3.60
-4.74
-4.42
-2.21

25,8600.0844Year-clustered

Yes
Yes

-0.0041**-0.0141***-0.00200.00110.0021-0.0001-0.0010-0.0228***-0.0503***-0.0174**-0.0058-0.0009-0.0035-0.0027

0.0076***-0.0014**-0.0053***-0.0050***-0.0039***-0.0033***-0.0031***-0.0015**

t-value

Deck < -0.3
Coef.

(continued on next page)

25,8600.086

Year-clustered

Yes
Yes

-0.0041**-0.0124***-0.0006-0.0001
0.0010-0.00080.0012-0.0236***-0.0472***-0.0161**-0.0083***-0.0030-0.00430.00100.0073***-0.0012**-0.0053***-0.0046***-0.0040***-0.0034***-0.0032***-0.0014*t-value

Deck < -0.25
Coef.

16
The Japanese Accounting Review, 12 (2022), 1-21

-5.48

-3.35

2.97

-1.99

-0.0072-0.0053*** -4.04

-1.74

***

-0.00240.0093***-0.0067-0.0065-0.0051-0.0019-0.0029[4] Rt-3 + Rt-3 × Dect-3[5] Rt-4 + Rt-4 × Dect-4[6] Rt-5 + Rt-5 × Dect-5[7] Rt-6 + Rt-6 × Dect-6[1] - [2][2] - [3][3] - [4][4] - [5][5] - [6][6] - [7]

-1.49

-0.92

-1.38

-3.88

-5.70

-0.0025-0.0036
-1.09

-1.53

-1.31

-1.83

-0.0047-0.0076

-1.73

*

2.91

-1.29

-0.00700.0102**-0.0020-0.0045** -2.83-0.0080***-0.0128

***

-3.47

-5.58

-4.64

-1.58

-0.0030-0.0023-0.0050-0.0092*-0.0083

-1.20

-0.88

-1.30

-2.05

-1.76

0.0116*** 3.26

-0.0024-0.0054** -2.97-0.0077***-0.0127***-0.0219***-0.0302*** -7.53

Deck < 0
Coef. t-value-0.0186*** -4.67

-3.16

-5.62

-4.44

-1.30

-0.0037-0.0017-0.0052-0.0099*-0.0105

*

-1.29

-0.52

-1.30

-2.13

-2.07

0.0134*** 3.52

-0.0024-0.0061** -2.98-0.0078***-0.0130***-0.0229***-0.0334*** -8.17

Deck < -0.05
Coef. t-value-0.0201*** -4.56

-3.03

-4.97

-4.14

-0.71

-0.0040-0.0024-0.0047-0.0109*-0.0130

*

-1.08

-0.62

-1.13

-2.00

-2.34

0.0145*** 3.88

-0.0016-0.0056** -2.29-0.0080**-0.0127***-0.0237***-0.0367*** -8.47

Deck < -0.10
Coef. t-value-0.0221*** -4.65

-3.09

-5.05

-3.71

-0.81

-0.0053-0.0015-0.0053-0.0115-0.0151

*

-1.45

-0.36

-1.29

-1.77

-2.16

0.0175*** 4.50

-0.0020-0.0073** -3.14-0.0088**-0.0141***-0.0256***-0.0407*** -9.31

-1.89

-7.89

-3.50

-0.26

-1.47

-2.37

-0.00730.0016

-1.49

0.32

-0.0073* -1.94-0.0106-0.0188**0.0187*** 4.85

-0.0008-0.0081** -2.75-0.0065*-0.0138***-0.0243***-0.0431*** -8.03

-1.76

-7.39

-2.99

-0.10

-1.04

-3.97

-0.00710.0011

-1.29

0.17

-0.0060* -1.80-0.0084-0.0318***

0.0278*** 6.70

-0.0004-0.0074* -1.86-0.0063-0.0123***-0.0207**-0.0525*** -10.04

-1.23

-1.39

-0.83

-0.00240.0024-0.0055-0.0126

-0.45

0.27

-1.28

-1.36

-0.0333*** -4.77

0.0314*** 5.97

-0.0043-0.0066-0.0043-0.0097** -2.75-0.0223*** -3.07-0.0556*** -13.62

Deck < -0.15
Deck < -0.2
Deck < -0.25
Deck < -0.3
Coef. t-value
Coef. t-value
Coef. t-value
Coef. t-value-0.0231*** -4.51 -0.0244*** -4.45 -0.0247*** -4.38 -0.0242*** -4.52

Notes: Impi,t is non-current asset impairment losses per share in year t, deflated by the adjusted stock price at the end of fiscal year t–1.
Ri,k is the adjusted stock return in year k. Deci,k takes the value of one if Ri,k is below a threshold. Standard errors are clustered by year. ***, **,and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

-0.0122

-1.64

-4.72

***

[3] Rt-2 + Rt-2 × Dect-2

-4.71

***

***

[2] Rt-1 + Rt-1 × Dect-1-0.0204-0.0274*** -6.81-0.0254*** -6.58[1] Rt + Rt × Dect-0.0187

Deck < 0.05
Coef. t-value-0.0172*** -4.71

Deck < 0.1
Coef. t-value-0.0161*** -4.85

Panel B: Coefficients for Bad News Observations

TABLE 5. (continued)

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness 17

-1.17-10.96-0.69-0.0007-0.0167-0.0003

0.0049**-0.0084**0.0011***0.0098***-0.0221***0.0001Rt
Rt × Dect
Dect

ΔSalestΔSalest × DecSalest
DecSalest

ΔCFOt
ΔCFOt × DecCFOt
DecCFOt

-5.10
-2.66
-5.23

25,8600.0993# of observations
adj-R2-0.0173***-0.0035**-0.0123***

Year-clusteredSE adjustment

Rt + Rt × Dect
ΔSalest + ΔSalest × DecSalest
ΔCFOt + ΔCFOt × DecCFOt

Yes
Yes
Yes

Other variables
Year
Industry

7.37-10.400.44

7.42-11.142.80

t-value

DecSalest < 0.1

Coef.

Dep. = Impt

5.18
-5.63
0.54

3.94
-4.40
2.98

-1.44
-5.14
-0.52

t-value-0.0172***-0.0034**-0.0123***

25,8600.0994
-5.03
-2.57
-5.23

Year-clustered

Yes
Yes
Yes

0.0098***-0.0221***0.0001***0.0049***-0.0084***0.0013**-0.0006-0.0166***-0.0003

Coef.

DecSalest < 0.05

Panel A: Results for Sales Changes

5.24
-5.74
0.44

4.18
-4.28
3.96

-1.50
-5.02
-0.52

t-value-0.0169***-0.0033**-0.0121***25,8600.0997
-4.91
-2.44
-5.31

Year-clustered

Yes
Yes
Yes

0.0097***-0.0218***0.00010.0048***-0.0081***0.0016***-0.0006-0.0162***-0.0003

Coef.

DecSalest < 0

5.39
-5.92
0.56

4.54
-4.18
4.21

-1.53
-5.14
-0.49

t-value-0.0167***-0.0030**-0.0118***

25,8600.1002
-5.02
-2.24
-5.38

Year-clustered

Yes
Yes
Yes

0.0095***-0.0213***0.00010.0048***-0.0078***0.0023***-0.0007-0.0161***-0.0003

Coef.

DecSalest < -0.05

5.44
-6.05
0.63

4.36
-3.95
4.40

-1.58
-5.35
-0.47

t-value-0.0168***-0.0028*-0.0117***

25,8600.1003
-5.22
-2.09
-5.49

Year-clustered

Yes
Yes
Yes

0.0095***-0.0213***0.00010.0046***-0.0073***
0.0027***-0.0007-0.0161***-0.0003

Coef.

DecSalest < -0.1

5.57
-6.19
0.77

4.05
-3.74
4.26

-1.58
-5.39
-0.44

t-value-0.0169***-0.0027*-0.0118***

25,8600.1000
-5.28
-2.00
-5.58

Year-clustered

Yes
Yes
Yes

0.0096***-0.0215***0.00020.0042***-0.0068***
0.0028***-0.0007-0.0162***-0.0003

Coef.

DecSalest < -0.15

5.63
-6.34
0.85

4.16
-3.59
3.81

-1.57
-5.50
-0.42

t-value-0.0170***-0.0024*-0.0119***

25,8600.0999
-5.37
-1.85
-5.75

Year-clustered

Yes
Yes
Yes

0.0097***-0.0216***0.00020.0039***-0.0063***
0.0031***-0.0007-0.0163***-0.0002

Coef.

DecSalest < -0.2

5.86
-6.63
0.85

4.12
-3.54
2.07

-1.56
-5.43
-0.41

t-value

-5.30
-1.76
-6.02

5.97
-6.82
0.81

3.64
-3.31
2.17

-1.54
-5.44
-0.39

t-value-0.0173***-0.0023-0.0125***

25,8600.0989
-5.32
-1.63
-6.20

Year-clustered

Yes
Yes
Yes

0.0101***-0.0226***0.0002**0.0031***-0.0054**0.0029***-0.0006-0.0166-0.0002

Coef.

DecSalest < -0.3

(continued on next page)-0.0172***-0.0024-0.0124***

25,8600.0989Year-clustered

Yes
Yes
Yes

0.0101***-0.0225***0.00020.0033***-0.0057***
0.0026*-0.0007-0.0166***-0.0002

Coef.

DecSalest < -0.25

TABLE 6. IMPAIRMENT TRIGGER THRESHOLDS FOR CHANGES IN SALES AND OPERATING CASH FLOWS

18
The Japanese Accounting Review, 12 (2022), 1-21

-1.33-5.00-0.53-0.0006-0.0163-0.0003

0.0050***-0.0084***0.0016***0.0099***-0.0199***0.0008Rt
Rt × Dect
Dect

ΔSalestΔSalest × DecSalest
DecSalest

ΔCFOt
ΔCFOt × DecCFOt
DecCFOt
5.08
-5.50
0.07

4.19
-4.31
3.98

-1.47
-5.01
-0.55

t-value-0.0169***-0.0033**-0.0116***

25,8600.0996
-4.89
-2.46
-5.33

Year-clustered

Yes
Yes
Yes

0.0091***-0.0208***
0.00000.0049***-0.0082***0.0016***-0.0006-0.0162-0.0003

Coef.

DecCFOt < 0.05

5.24
-5.74
0.44

4.18
-4.28
3.96

-1.50
-5.02
-0.52

t-value-0.0169***-0.0033**-0.0121***25,8600.0997
-4.91
-2.44
-5.31

Year-clustered

Yes
Yes
Yes

0.0097***-0.0218***0.00010.0048***-0.0081***0.0016***-0.0006-0.0162***-0.0003

Coef.

DecCFOt < 0

5.39
-6.17
1.02

4.17
-4.31
3.90

-1.49
-5.08
-0.50

t-value-0.0169***-0.0033**-0.0109***25,8600.0998
-4.98
-2.45
-4.74

Year-clustered

Yes
Yes
Yes

0.0093***-0.0202***0.00050.0048***-0.0082***0.0016***-0.0006-0.0162***-0.0003

Coef.

DecCFOt < -0.05

6.70
-5.58
-0.51

4.38
-4.45
4.04

-1.45
-5.02
-0.45

t-value-0.0170***-0.0034**-0.0116***

25,8600.0992
-4.91
-2.45
-4.20

Year-clustered

Yes
Yes
Yes

0.0075***-0.0190***-0.0003

0.0050***-0.0084***0.0017***-0.0006-0.0164***-0.0003

Coef.

DecCFOt < -0.1

6.54
-5.09
-1.12

4.59
-4.56
4.17

-1.42
-5.01
-0.45

t-value-0.0171***-0.0034**-0.0121***25,8600.0988
-4.90
-2.46
-4.18

Year-clustered

Yes
Yes
Yes

0.0061***-0.0182***-0.00100.0052***-0.0086***0.0018***-0.0006-0.0165***-0.0003

Coef.

DecCFOt < -0.15

6.19
-4.48
-0.56

4.73
-4.64
4.22

-1.38
-5.01
-0.45

t-value-0.0171***-0.0034**-0.0114***25,8600.0986
-4.89
-2.47
-3.70

Year-clustered

Yes
Yes
Yes

0.0054***-0.0168***-0.00070.0053***-0.0088***0.0018***-0.0006-0.0165***-0.0003

Coef.

DecCFOt < -0.2

4.30
-5.58
-1.43

9.49
-13.105.53-0.97-10.86-0.60

t-value-0.0171***-0.0035**-0.0128***

25,8600.0981
-4.87
-2.48
-3.15

Year-clustered

Yes
Yes
Yes

0.0043***-0.0171***-0.00200.0055***-0.0090***0.0019***-0.0005-0.0166***-0.0003

Coef.

DecCFOt < -0.25

3.98
-3.16
-0.38

5.00
-4.76
4.23

-1.20
-5.01
-0.41

t-value-0.0171***-0.0035**-0.0112***25,8600.0981
-4.86
-2.48
-2.48

Year-clustered

Yes
Yes
Yes

0.0040***-0.0152***-0.00100.0056***-0.0091***0.0019***-0.0005-0.0166-0.0002

Coef.

DecCFOt < -0.3

Notes: Impi,t is non-current asset impairment losses per share in year t, deflated by the adjusted stock price at the end of fiscal year t–1.
Ri,k is the adjusted stock return in year k. Deci,k takes the value of one if Ri,k is negative. ΔSalesi,t is the change in sales in year t, deflated by
the adjusted stock price at the end of fiscal year t–1. DecSalesi,t takes the value of one if ΔSalesi,t is below a threshold for Panel A andnegative for Panel B. ΔCFOi,t is the change in cash flows from operations in year t, deflated by the adjusted stock price at the end of fiscal
year t–1. DecCFOi,t takes the value of one if ΔCFOi,t is negative for Panel A and below a threshold for Panel B. Standard errors are
clustered by year. ***, **, and * indicate statistical significance at the 1%, 5%, and 10% levels, respectively.

-4.87
-2.47
-5.06

25,8600.0993# of observations
adj-R2-0.0168***-0.0034**-0.0100***

Year-clusteredSE adjustment

Rt + Rt × Dect
ΔSalest + ΔSalest × DecSalest
ΔCFOt + ΔCFOt × DecCFOt

Yes
Yes
Yes

Other variables
Year
Industry

4.92
-5.38
1.34

4.44
-4.47
3.99

t-value

DecCFOt < 0.1

Coef.

Dep. = Impt

Panel B: Results for CFO Changes

TABLE 6. (continued)

Fujiyama: Incorporating Piecewise-Linear Variables into an Empirical Model of Non-Current Asset Impairment Timeliness 19

20

The Japanese Accounting Review, 12 (2022), 1-21

(2014b), I find a negative relationship between non-current asset impairments and negative stock
returns in year t. The negative relationship is stronger in years t–1 and t–2 than it is in years t and
t–3. These results suggest that while the reported non-current asset impairments are not necessarily
timely, the recognition of impairment losses is consistent with the “probability criterion” employedby the accounting standard for non-current asset impairment in Japan. In addition, I find arelationship between non-current asset impairments and changes in sales and cash flows fromoperations (CFO) in year t, suggesting that changes in sales and CFO can be short-term indicatorsof non-current asset impairments. Therefore, future research on non-current asset impairments andpossibly accounting conservatism can better observe the timeliness of losses and control for the
economic factors of losses by employing the piecewise-linear regression model recommended byBanker et al. (2017). Moreover, it can control for economic factors using piecewise-linear variablesof changes in sales and CFO.
This study has at least two limitations. First, the model becomes complicated when a study
focuses on two factors. Because the model uses a piecewise interaction term, one needs toincorporate a four-variable interaction term when adding two factors. In this case, the model thatuses stock returns as the explained variable may be the better, introducing a three-variableinteraction term, that is, an interaction term among an impairment variable, factor 1, and factor 2.
Or, it may be better to use linear stock returns as an explanatory variable and introduce aninteraction term between factor 1 and factor 2. Second, the piecewise interaction term may not besuitable for non-linear regression models, as questioned by Ai and Norton (2003) in the context ofprobit and logistic regression models. For example, Riedl (2004) and Glaum et al. (2018) employ
the Tobit and logistic regression models, respectively, while Ramanna and Watts (2012) employ the
OLS regression model. Thus, one needs to pay attention to model specification when using apiecewise-linear stock return.

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