Table A1. Variable definitions Variable...

Table A1.

Variable definitions

Variable	Definition and measurement
Dependent variables (Investment efficiency)
Investment variables (Investment efficiency/INVEFFI)
IE	Investment efficiency, the absolute value of the residuals from the Richardson (2006) investment efficiency model multiplied by −1
IED	Investment efficiency dummy, a dummy variable, categorically by residual quartiles. Sort the residuals from the Richardson (2006) investment efficiency model, annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group with a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) with a value of 0
IE_Biddle	Investment efficiency from the Biddle et al.’s (2009) model, the absolute value of the residuals from the Biddle et al.’s (2009) investment efficiency model multiplied by −1
IED_Biddle	Investment efficiency dummy from Biddle et al.’s (2009) model, a dummy variable, categorically by residual quartiles. Sort the residuals from Biddle et al.’s (2009) investment efficiency model, annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group with a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) with a value of 0
IE_Chen	IE from Chen et al.’s (2011a, 2011b) model, the absolute value of the residuals from Chen et al.’s (2011a, 2011b) investment efficiency model multiplied by −1
IED_Chen	Investment efficiency dummy from Chen et al.’s (2011a, 2011b) model, a dummy variable, categorically by residual quartiles. Sort the residuals from Chen et al.’s (2011a, 2011b) investment efficiency model annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group has a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) has a value of 0
Independent variables (Chair-CEO age dissimilarity)
GAPS	Age gap signed, the age difference (in years) between the Chair and the CEO calculated as Chair age minus CEO age
GAPU	Age gap unsigned, the absolute value of the age difference (in years) between the Chair and the CEO
GAP20	Gap20 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 20 years and 0 otherwise This dummy variable measures a generational gap, as reflected by an age difference of at least 20 years, as suggested by Strauss and Howe (1997)
GAP15	Gap15 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 15 years and 0 otherwise
GAP10	Gap10 Chair–CEO, dummy variable set to 1 if the age difference between the Chair and the CEO is at least 10 years, and 0 otherwise. This dummy variable measures a generational gap, as reflected by an age difference of at least 20 years, as suggested by Zhu et al. (2021)
GAP5	Gap5 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 5 years and 0 otherwise
Control variable about characteristics (Chair–CEO)
DIFEDU	Chair–CEO different education, the dummy variable is set to 1 if the Chair and the CEO do not have the same education degree level (bachelor, master, PhD and else), and 0 otherwise
DIFNAT	Chair–CEO different nationalities, dummy variable that is set to 1 if the Chair and the CEO have different nationalities, and 0 otherwise
DIFGEN	Chair–CEO different gender, dummy variable set to 1 if the Chair and the CEO have a different gender, and 0 otherwise
JONTENU	Chair–CEO joint tenure, the number of years the chair and the CEO have been working together in these positions
CHAIRAGE	Chair age, the age of the board’s chair (chair)
CHANGE1	Chair change, dummy variable set to 1 for years when there is a Chair change, and 0 otherwise
TENURE1	Chair tenure, the number of years the chair has been serving as the CEO of the firm
CEOAGE	CEO age, the age of the firm’s chief executive officer (CEO)
CHANGE2	CEO change, dummy variable set to 1 for years when there is a CEO change, and 0 otherwise
TENURE2	CEO tenure, the number of years the CEO has been serving as the CEO of the firm
Control variable about characteristics (firm-level)
BODSIZE	Board size is the total number of members on the board
BKTMK	Book-to-market ratio is the ratio of book value to the market value of firm equity
LEVER	Leverage is measured as the firm’s total liabilities over total assets
FCF	FCF/TA, free cash flow (defined as EBITDA–cap/ex) divided by total assets
FSIZE	Firm size is the natural logarithm of the firm’s total assets
SDSALE	The standard deviation of sales, sales divided by the average total assets from year t − 3 to t
SALEGR	Sales growth, measured by the changes in sales between year t and year t − 1
SOE%	State-owned shares percentage
LOSS	Loss, a dummy variable of value 1 is assigned if the firm reports a negative earning, 0 otherwise
Z-Score	Z-score, a composite score for measuring a firm’s financial risk, is measured following the methodology of Altman (1968). Using the following formula: Z-score = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 + 0.999*X5), where X1 is the working capital/total assets; X2 is retained earnings/total assets; X3 is EBIT/total assets; X4 is market capitalization/total liabilities; X5 is sales/total assets. Using 2.67 and 1.81 as critical values to calculate the range of the sample score. The standard of judgment is that Z-score > 2.67 means a good financial situation with a low possibility of bankruptcy, Z-score < 1.81 means a financial situation with a lurking bankruptcy crisis, and 1.81 < Z-score < 2.67 is the area indicating that the firm’s financial situation is extremely unstable, with a high likelihood of financial distress
TANGI	Tangibility is measured as the ratio of PPE (property, plant and equipment) to total assets
K-Structure	K-structure is a measure of market leverage, measured as the ratio of long-term debt to total available capital (sum of long-term debt and the market value of equity)
MFE	Management fee, measured as managing costs, scaled by total assets
FIRMAGE	Firm age is measured as the logarithm of the number of years since the firm was established
Other variables
GAPD	Age gap dummy, dummy variable set to 1 if there is an age difference between the Chair and CEO, and 0 otherwise
GAPS_mean	GAPS_mean is 1 if GAPS is above the age gap signed mean and 0 otherwise
GAPU_mean	GAPU_mean is 1 if GAPU is above the age gap unsigned mean and 0 otherwise
BLOCKHD 50%	Blockholder 50%, dummy variable that takes the value of 1 if a single shareholder holds at least 50% of the common shares outstanding, and 0 otherwise
SOE	SOE, dummy variable set to 1 if state-owned or state-holding firms and 0 otherwise
HHI_mean	HHI_mean is 1 if the Herfindahl–Hirschman Index (HHI) is above the HHI mean and 0 otherwise. The HHI, calculated by squaring the market share of each competing firm in the same industry and then summing the resulting numbers, weighted by market share in the same industry and in one year, the result is proportional to the average market share (range from 0 to 1). Increases in the HHI generally indicate a decrease in competition and an increase in market power, and vice versa
Intangible	Intangible assets: the firm’s book value of intangible assets is divided by the book value of total assets
CRG	Cultural revolution generation, dummy variable set to 1 if the Chair or the CEO is at least 16 years old during the Cultural Revolution (1966–1976), and 0 otherwise

Variable	Definition and measurement
Dependent variables (Investment efficiency)
Investment variables (Investment efficiency/INVEFFI)
IE	Investment efficiency, the absolute value of the residuals from the Richardson (2006) investment efficiency model multiplied by −1
IED	Investment efficiency dummy, a dummy variable, categorically by residual quartiles. Sort the residuals from the Richardson (2006) investment efficiency model, annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group with a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) with a value of 0
IE_Biddle	Investment efficiency from the Biddle et al.’s (2009) model, the absolute value of the residuals from the Biddle et al.’s (2009) investment efficiency model multiplied by −1
IED_Biddle	Investment efficiency dummy from Biddle et al.’s (2009) model, a dummy variable, categorically by residual quartiles. Sort the residuals from Biddle et al.’s (2009) investment efficiency model, annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group with a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) with a value of 0
IE_Chen	IE from Chen et al.’s (2011a, 2011b) model, the absolute value of the residuals from Chen et al.’s (2011a, 2011b) investment efficiency model multiplied by −1
IED_Chen	Investment efficiency dummy from Chen et al.’s (2011a, 2011b) model, a dummy variable, categorically by residual quartiles. Sort the residuals from Chen et al.’s (2011a, 2011b) investment efficiency model annually into quartiles: the under-investment group for the residuals in the bottom quartile (<25%), the over-investment group for the residuals in the top quartile (>75%), and the benchmark normal investment group for the residuals in the middle two quartiles (between 25% and 75%). The benchmark normal investment group has a value of 1, and the lower investment efficiency group (under-investment group and over-investment group) has a value of 0
Independent variables (Chair-CEO age dissimilarity)
GAPS	Age gap signed, the age difference (in years) between the Chair and the CEO calculated as Chair age minus CEO age
GAPU	Age gap unsigned, the absolute value of the age difference (in years) between the Chair and the CEO
GAP20	Gap20 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 20 years and 0 otherwise This dummy variable measures a generational gap, as reflected by an age difference of at least 20 years, as suggested by Strauss and Howe (1997)
GAP15	Gap15 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 15 years and 0 otherwise
GAP10	Gap10 Chair–CEO, dummy variable set to 1 if the age difference between the Chair and the CEO is at least 10 years, and 0 otherwise. This dummy variable measures a generational gap, as reflected by an age difference of at least 20 years, as suggested by Zhu et al. (2021)
GAP5	Gap5 Chair–CEO is a dummy variable that takes a value of 1 if the age difference between the Chair and the CEO is at least 5 years and 0 otherwise
Control variable about characteristics (Chair–CEO)
DIFEDU	Chair–CEO different education, the dummy variable is set to 1 if the Chair and the CEO do not have the same education degree level (bachelor, master, PhD and else), and 0 otherwise
DIFNAT	Chair–CEO different nationalities, dummy variable that is set to 1 if the Chair and the CEO have different nationalities, and 0 otherwise
DIFGEN	Chair–CEO different gender, dummy variable set to 1 if the Chair and the CEO have a different gender, and 0 otherwise
JONTENU	Chair–CEO joint tenure, the number of years the chair and the CEO have been working together in these positions
CHAIRAGE	Chair age, the age of the board’s chair (chair)
CHANGE1	Chair change, dummy variable set to 1 for years when there is a Chair change, and 0 otherwise
TENURE1	Chair tenure, the number of years the chair has been serving as the CEO of the firm
CEOAGE	CEO age, the age of the firm’s chief executive officer (CEO)
CHANGE2	CEO change, dummy variable set to 1 for years when there is a CEO change, and 0 otherwise
TENURE2	CEO tenure, the number of years the CEO has been serving as the CEO of the firm
Control variable about characteristics (firm-level)
BODSIZE	Board size is the total number of members on the board
BKTMK	Book-to-market ratio is the ratio of book value to the market value of firm equity
LEVER	Leverage is measured as the firm’s total liabilities over total assets
FCF	FCF/TA, free cash flow (defined as EBITDA–cap/ex) divided by total assets
FSIZE	Firm size is the natural logarithm of the firm’s total assets
SDSALE	The standard deviation of sales, sales divided by the average total assets from year t − 3 to t
SALEGR	Sales growth, measured by the changes in sales between year t and year t − 1
SOE%	State-owned shares percentage
LOSS	Loss, a dummy variable of value 1 is assigned if the firm reports a negative earning, 0 otherwise
Z-Score	Z-score, a composite score for measuring a firm’s financial risk, is measured following the methodology of Altman (1968). Using the following formula: Z-score = 0.012X1 + 0.014X2 + 0.033X3 + 0.006X4 + 0.999*X5), where X1 is the working capital/total assets; X2 is retained earnings/total assets; X3 is EBIT/total assets; X4 is market capitalization/total liabilities; X5 is sales/total assets. Using 2.67 and 1.81 as critical values to calculate the range of the sample score. The standard of judgment is that Z-score > 2.67 means a good financial situation with a low possibility of bankruptcy, Z-score < 1.81 means a financial situation with a lurking bankruptcy crisis, and 1.81 < Z-score < 2.67 is the area indicating that the firm’s financial situation is extremely unstable, with a high likelihood of financial distress
TANGI	Tangibility is measured as the ratio of PPE (property, plant and equipment) to total assets
K-Structure	K-structure is a measure of market leverage, measured as the ratio of long-term debt to total available capital (sum of long-term debt and the market value of equity)
MFE	Management fee, measured as managing costs, scaled by total assets
FIRMAGE	Firm age is measured as the logarithm of the number of years since the firm was established
Other variables
GAPD	Age gap dummy, dummy variable set to 1 if there is an age difference between the Chair and CEO, and 0 otherwise
GAPS_mean	GAPS_mean is 1 if GAPS is above the age gap signed mean and 0 otherwise
GAPU_mean	GAPU_mean is 1 if GAPU is above the age gap unsigned mean and 0 otherwise
BLOCKHD 50%	Blockholder 50%, dummy variable that takes the value of 1 if a single shareholder holds at least 50% of the common shares outstanding, and 0 otherwise
SOE	SOE, dummy variable set to 1 if state-owned or state-holding firms and 0 otherwise
HHI_mean	HHI_mean is 1 if the Herfindahl–Hirschman Index (HHI) is above the HHI mean and 0 otherwise. The HHI, calculated by squaring the market share of each competing firm in the same industry and then summing the resulting numbers, weighted by market share in the same industry and in one year, the result is proportional to the average market share (range from 0 to 1). Increases in the HHI generally indicate a decrease in competition and an increase in market power, and vice versa
Intangible	Intangible assets: the firm’s book value of intangible assets is divided by the book value of total assets
CRG	Cultural revolution generation, dummy variable set to 1 if the Chair or the CEO is at least 16 years old during the Cultural Revolution (1966–1976), and 0 otherwise

Source(s): Authors’ calculations

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