The Trends and Gaps in the Sensitivity of Investment to Cash Flow: Evidence from China

: The ability of using internally generated funds to ﬁnance investments affects corporate sustainability. We empirically examine trends and gaps in the reliance of company’s investments on internally generated funds. We collect ﬁnancial data of Chinese listed companies from 1998 to 2020, use corporate cash ﬂow as a proxy for internally generated funds, control for corporate investment opportunity Q, and specify a two-way ﬁxed effects model of investment on cash ﬂow. We ﬁnd that investment-cash ﬂow sensitivity exhibits a decreasing trend over time; ﬁrm size, government equity, and the HP and WW indices effectively explain the gaps in the sensitivity of investment to cash ﬂow between two types of ﬁrms with tighter and looser ﬁnancing constraints, but cash dividends do not explain the gaps; and the gaps in the sensitivity of investment to cash ﬂow are narrowing in the long term. These empirical ﬁndings indicate that compared to external funding, internal funding is becoming less important in supporting a ﬁrm’s investment-induced sustainability.


Introduction
Investment decisions have long-term effects on a company's continuous earnings and growth potential and hence investment decisions are arguably a fundamental issue in corporate sustainability. Financial markets are subject to frictions, such as taxes, issuance costs, agency conflicts, bankruptcy costs, and asymmetric information. Therefore, investment decisions are affected by a wedge between the costs of a firm's internal and external funds. The degree of dependence of investments on internal funds is commonly measured by the sensitivity of investment to cash flow.
The sensitivity of investment to cash flow was originally proposed in the seminal study of Fazzari et al. [1]. They find firms facing tighter financing constraints have to depend more on internally generated funds to invest. Their findings have been further corroborated by rich empirical literature [2][3][4]. Another strand of literature diverges from the findings and argues that less financially constrained firms are linked to larger estimates of sensitivity [5,6]. Allayannis and Mozumdar argue the finding that investment is more sensitive to cash flow for the least financially constrained firms can be explained by negative cash flow observations or be driven by a few outlying observations in a small sample [7]. Erickson and Whited argue that the measurement error in Tobin's Q, a proxy for marginal Q, can affect the estimate of investment-cash flow sensitivity and hence most of the stylized facts resulted from regression of investment on cash flow and marginal Q are artifacts of the measurement error [8,9]. The connection between various measures of financial performance and firm value and environmental management have been explored in the context of China [10].
An emerging tranche of literature has started to explore the trend in the sensitivity of investment to cash flow worldwide. Chen and Chen and Larkin et al. find that there is a decline in the sensitivity of investment to cash flow over time and even a complete cash flow identity approach of investment measurement that we propose here under China's accounting standards is instructive for future research on investment of China's companies.
The rest of the paper is organized as follows. Section 2 is a very brief theoretical review with predictions. Section 3 presents empirical designs. In Section 4, we report empirical results. Section 5 discusses asymmetric changes in the sensitivity of investment to cash flow. The final section concludes.

Theoretical Review
To provide a theoretical basis for empirical specification, we start with a very brief theoretical review of the link between investment and cash flow.
The value of a firm is given by the expected present value of its future sustainable profits as follows: where E{· · · } is the expectation operator and β denotes the constant discount factor; i and t represent the firm and the period of time, respectively. The profit function is π(K is , θ is ). The beginning-of-period capital stock is K is and θ is denotes an exogenous stochastic shock. We assume that there are convex costs of adjusting the capital stock K is and C(I is , K is , λ is ) includes three arguments, the capital stock K is , investment I is , and an exogenous stochastic shock λ is , We further assume that exogenous stochastic shocks θ is and λ is follow Markov processes. The objective function (1) is subject to the capital accumulation constraint that evolves through time according to K is = (1 − δ)K is−1 + I is . We assume new capital resulting from investment becomes productive within the current period.
We solve the constrained maximization problem and attain the first-order condition with respect to investment as follows: where C I (· · · ). is partial derivative with respective to investment I. The left-hand term in Equation (2) is the marginal cost resulting from each additional unit of investment and the right-hand term is the corresponding marginal revenue (the expected discounted value of the future profits from each additional unit of investment). The right-hand term E ∑ ∞ s=0 β s t (1 − δ) s [π K (K i,t+s , θ i,t+s ) − C K (K i,t+s , λ i,t+s )] is denoted as Q it and it measures a firm's investment opportunity.
To make Equation (2) concrete for empirical design, we next assume the adjustment cost to be typically quadratic in I it /K it as follows: where α denotes an adjustment-cost parameter. Substituting the specification of the adjustment cost into Equation (2) yields an investment model including marginal Q it . After a series of arrangements and simplifications, we have: Equation (4) is representative of a model under frictionless capital markets. It illustrates that investment should be unrelated to a firm's net worth and depends solely on marginal Q it in a world without financial frictions.
In the real world, financial markets are always full of frictions. The frictions lead to a firm facing a high premium in the cost of external financing relative to internal financing, and shifts in a firm's net worth affect its investment. Accordingly, a firm's net worth should be included as an independent variable to explain a firm's investment behavior. A firm's cash flow is commonly employed to measure a change in net worth. We further assume that λ it is unobservable noise, then we can express the relation between investment and marginal Q it in the real world as follows: (5) where the coefficient b measures the sensitivity of investment to cash flow.

Prediction Development
Based on the theoretical review, we know that in a world without financial frictions, investment cash flow sensitivity should be zero if marginal Q captures the firm's investment opportunities perfectly. The real world has financial frictions. Financial frictions lead to a wedge between external and internal funding costs and the firm's investment cash flow sensitivity should be significantly positive. That is, the coefficient b in Equation (5) is significantly positive. In summary, we make the first prediction that the estimate of the sensitivity of investment to cash flow is significantly positive.
Although the financing constraints faced by firms always exist, the status of the financing constraints changes continuously with social evolution, institutional changes, and technological advances [21,22], e.g., the company has higher value collateral available to creditors, the company strives to improve corporate governance to protect the interests of all stakeholders, the company operates in an environment where contracts are fairly signed and effectively enforced, advances in financial technology reduce information asymmetry, and so on. These forces of social evolution, institutional change, and technological advancement reduce friction in financial markets. The company's investments are more easily financed with external funds and the company further reduces its reliance on internal funding. As a result, the sensitivity of investments to cash flow in the long term has been decreasing. Therefore, we present a second prediction that investment-cash flow sensitivity exhibits a continued downward trend.
The widespread and perpetual existence of firm heterogeneity causes differences in the ease and availability of external financing for firms. Some firms have tighter external financing constraints, while others are relatively loose. As a result, these two types of firms exhibit differences in their reliance on internal funding for investment. On the one hand, social evolution, institutional changes, and technological advances are universal and all companies will thus be less constrained by external financing. The universal effect facilitates the closing of the gaps in sensitivity. On the other hand, the limited rationality of external financiers and their quest for funds safety and profitability may make them reluctant to finance firms with poor operations, lack of cash flow, insufficient valuable collateral, or slow technological advances [23][24][25]. External financing thus becomes more difficult to obtain for these companies. The selection effect of funders can cause the gap in sensitivity to expand. Thus, there are two opposing effects that lead to changes in the investment cash flow sensitivity gap. One is the reduction of the gap due to the universal effect caused by social evolution, institutional change, and technological progress, and the other is the widening of the gap due to the selection effect of external fund providers. For the gap in the sensitivity of investment to cash flow and its trend in the long run, no prediction is given by the existing theory and no evidence is given by the extant empirical studies. We do not know which of these two opposing effects on the change in the gap dominates. It is likely to be an empirical problem. We randomly pick one of the two possibilities as the third prediction that gaps in the sensitivity of investment to cash flow between firms with tighter and looser financing constraints exist. Moreover, the gaps continue to get wider as time goes on. The theoretical review sheds light on why our baseline model is quite parsimonious and only includes proxies for marginal Q and cash flow CF to investigate trends and gaps in the sensitivity of investment to cash flow [26]. Marginal Q is unobservable, and Tobin's Q is commonly employed to be a proxy for the marginal Q. To control for the possible heteroskedasticity due to differences in firms' size, we scale the investment and cash flow using the total assets of the end of last year. Therefore, the baseline model is specified as follows: where I i,t , scaled by its total assets of the end of last year, represents the total investment of a firm i for the current year t; CF i,t is a firm i's cash flow divided by its total assets of the end of last year; Q i,t−1 is a proxy for investment opportunities; and α i and µ t denote firm and industry-year fixed effects, respectively. ε it is error. We first examine overall trends based on nineteen rolling five-year subperiods. Then, the sample is divided by firm size, whether cash dividends are paid, whether government ownership is present, and the WW and the HP indices. Based on the above subsamples, gaps in the sensitivity of investment to cash flow and their trends are examined.

The Definitions of Key Variables
Cash flow CF is commonly calculated as profits plus depreciation [1,15]. The calculation includes a true cash component from operation and a noncash component in the form of working capital accruals. Recent literature suggests that the empirical relation between investment and cash flow is mainly explained by the naturally positive correlation between investment and working capital accruals [14,16]. In order to mitigate the concern that the empirical results are driven by the natural positive correlation, we measure cash flow using data from the statement of cash flows and define cash flow CF as a firm's operating cash flows in the statement of cash flows net of the change in working capital. We treat the change in working capital as a component of investment here.
In addition to capital expenditures, measures of firm investment should include expenditures that affect a firm's earnings and growth potential, such as expenditures for patents and cash for mergers and acquisitions. Recent literature echoes this change in the measure of investment, and they propose to measure firm investment based on the firm's cash flow identity using flow-of-funds data [14,16]. The identity is as follows.
where the sources of funds include the internally generated cash flow CF and external financing EXT that includes net debt issuance and net equity issuance. The uses of funds consist of investment INV, the change in cash holdings CASH, and cash dividends DIVD. We follow these lines of literature on investment measurement to measure investment as accurately as possible. It is worth noting that those literature are based on the U.S. listed firms, while we use data from Chinese listed firms, and we cannot directly apply the firm cash flow identity proposed by those literature in measuring firm investment. Interest expense is one of the most important expenses of a company; it is accounted for as operating cash flow under the U.S. GAAP, but as financing cash flow in Chinese accounting standard. In order to measure corporate investment of listed companies in China as accurately as possible, we modify the cash flow identity (7) to: We employ data from the statement of cash flows to measure cash flow. China's Ministry of Finance issued Accounting Standard for Businesses No. 31-Statement of Cash Flows on 20 March 1998. It requires listed companies in China to produce and publicly disclose a statement of cash flows from 1998 onwards. Therefore, we select the sample since 1998. To make the sample more homogenous, the listed firms in financial industry are dropped. Firm-year observations are also dropped if the value for net fixed assets or sales is less than or equal to zero. Extreme observation values of marginal Q measure exceeding 20 are also eliminated. After that, 2415 publicly traded firms with 19,864 firmyear observations are left. We scale level variables by one-period lag of total assets and then all variables are winsorized annually at their 1st and 99th percentiles to reduce the impact of outliers. Table 1 presents the definitions of key variables and descriptive statistics. Level variables including investment I, cash flow CF, and the change in external financing EXT are scaled by one-period lagged total assets. There is a decrease in number of observations from 19,864 of level variables to 14,577 due to scaling. Firms' size SIZE is the natural logarithm of total assets (in million RMB Yuan) that are GDP deflator-adjusted to base year 1998. The average investment is equal to 8% of total assets of the end of last year and firms' investment varies from a high of 0.56 of total assets of the end of the last year to a low of −0.13. The average cash flow is equal to 3% of total assets of the end of the last year, which is less than the mean of investment. The amount of average external financing is 6% of total assets of the end of the last year, which shows weak evidence that external financing including net debt issuance and net equity issuance is an importance source of investment. The mean of the cash dividend payment dummy variable DIVD is 0.84 and it indicates 84% of firm-year observations pay cash dividends. The mean 0.31 of GOVT indicates 31% of firm-year observations with government equity. The means of the HP index and the WW index are −13.69 and −1.02, respectively. The HP and the WW indices range from a maximum of −11.56 to a minimum of −16.88 and from −0.29 to −1.30, respectively. These indicate that the sample distribution of the HP index is to the left side of the counterpart of the WW index. Figure 1 is comprised of parts (a) and (b) and they show how the mean heterogeneity of investment I and cash flow CF evolve through time, respectively. We scale the investment I and cash flow CF by one-period lagged total assets and hence the year on the horizontal axis starts with 1999. The number of firms in the sample becomes highly volatile across the years. The minimum number of firms is 36 in 1999. It slowly increases to 179 firms in 2007 and subsequently rapidly move up to the maximum 1872 in 2014. After that, it dives to around 500 firms in 2017. The means of investment I and cash flow CF show similar time-series variation and hence seem to be serially correlated. The yearly means become more volatile in the first segment from years 1999 to 2005 than those from 2006 to the end. The widths of the 95% confidence interval for the means of investment I and cash flow CF both get narrow as the firms' numbers increases. The dotted line in Figure 1b represents zero and three negative means of yearly cash flow (1999,2000,2016) occur. The mean of investment starts to slowly rise from 2012 on to the peak in 2016 and then rapidly fall. On the contrary, the mean of cash flow starts to fall from 2012 on to the trough in 2016 and then rapidly increase. That is, the time-series variation of the mean of investment from year 2012 onwards turns out to be the very reverse of the means of cash flow. cash flow CF both get narrow as the firms' numbers increases. The dotted line in Fi 1b represents zero and three negative means of yearly cash flow (1999,2000,2016) oc The mean of investment starts to slowly rise from 2012 on to the peak in 2016 and rapidly fall. On the contrary, the mean of cash flow starts to fall from 2012 on to the tro in 2016 and then rapidly increase. That is, the time-series variation of the mean of inv ment from year 2012 onwards turns out to be the very reverse of the means of cash fl

Simple Linear Regressions
To obtain the most intuitive understanding of how investment relates to cash flow, we conduct simple linear regressions over yearly cross-sectional data. To save space, we report the scatter plots and regression lines only for years 2000, 2010, and 2020. Figure Figure 2 gives us a visual that internal funding is becoming less important in supporting a firm's investment-induced sustainability. Figure 1 is comprised of parts (a) and (b) and they show how the mean heterogenei of investment I and cash flow CF evolve through time, respectively. We scale the inve ment I and cash flow CF by one-period lagged total assets and hence the year on the ho izontal axis starts with 1999. The number of firms in the sample becomes highly volat across the years. The minimum number of firms is 36 in 1999. It slowly increases to 1 firms in 2007 and subsequently rapidly move up to the maximum 1872 in 2014. After th it dives to around 500 firms in 2017. The means of investment I and cash flow CF sho similar time-series variation and hence seem to be serially correlated. The yearly mea become more volatile in the first segment from years 1999 to 2005 than those from 2006 the end. The widths of the 95% confidence interval for the means of investment I an cash flow CF both get narrow as the firms' numbers increases. The dotted line in Figu 1b represents zero and three negative means of yearly cash flow (1999,2000,2016) occu The mean of investment starts to slowly rise from 2012 on to the peak in 2016 and th rapidly fall. On the contrary, the mean of cash flow starts to fall from 2012 on to the troug in 2016 and then rapidly increase. That is, the time-series variation of the mean of inve ment from year 2012 onwards turns out to be the very reverse of the means of cash flow

Simple Linear Regressions
To obtain the most intuitive understanding of how investment relates to cash flo we conduct simple linear regressions over yearly cross-sectional data. To save space, w report the scatter plots and regression lines only for years 2000, 2010, and 2020.    Table 2 is comprised of panels A and B. Panel A reports the regression results of Equation (6) over the full sample. In order to explore time-series variation in the sensitivity of investment to cash flow, we run regressions of Equation (6) over rolling five-year subperiods. Specifically, the first regression is over the subperiod 1998-2002, the second one over the subperiod 1999-2003, and so on. Panel B of Table 2 presents empirical results over the nineteen five-year subperiods. The nineteen subperiods are consecutively denoted by P 1 to P 19 .  Table 2 reports estimates of the sensitivities of investment to cash flow, standard errors, sample sizes (N), R 2 s, and F statistics over the full sample and the rolling five-year subperiods (rolling nineteen five-year subperiods in total and denoted by P 1 through P 19 , respectively). The dependent variables are investment I scaled by one-period lagged total assets K t−1 . The explanatory variables include cash flow CF divided by one-period lagged total assets and one-period lagged Marginal Q t−1 . All variables are defined in Table 1. All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.

The Link between Investment and Cash Flow
As is evident in Panel A of Table 2, a unit of cash flow is associated with an extra 0.0481 of investment at the 1% significance level. A significant positive estimate suggests the existence of frictions in the Chinese financial markets and the first prediction is supported statistically. The estimate of coefficient on Q t−1 is 0.0200 and the coefficient is significant at the 1% level. It shows future investment opportunity has a positive impact on firms' investment. Theoretical review in Section 2 demonstrates internally generated cash flow and future investment opportunity are both the determinants of firms' investment, but future investment opportunity is fundamental to investment. The standardized regression coefficients of cash flow and investment opportunity are 0.0743 and 0.2218, respectively. It suggests that, as expected by theory, investment opportunities play a more important role than internally generated funds in explaining the investment behavior of firms in China. These empirical results further verify previous literature [3,14].
The empirical results from rolling nineteen regressions over five-year subperiods are presented in Panel B of Table 2 The estimate over the first five-year subsample is not significant even at the 10% level. The four estimates over four continuously rolling samples are negative but they are not statistically significant. It indicates that the sensitivity of investment to cash flow is completely disappearing over the four continuously rolling samples. Extant literature also finds some evidence on completely disappearing sensitivity of investment to cash flow. For example, Larkin et al. finds that the completely disappearing sensitivity emerges for some countries excluding the U.S. over the two years prior to 2011 [4]. The negative investment-cash flow sensitivities here for four consecutive subsample periods appears to reflect the opposite trend of investment and cash flow means from 2012 onward in Figure 2. Turning to the estimates of coefficients on marginal Q t−1 , we find that fifteen of the nineteen estimates on Q t−1 are positive and vary from a high of 0.2823 over the subperiod 1999 to 2003 and to a low of 0.0097 over 2009 to 2013. The corresponding coefficients are significant either at the 1% level or 5% level. It is worth pointing out that the estimates over the subperiod 2012 to 2019 are not only positive but also statistically significant at the 1% level. It shows investment is driven mainly by investment opportunity over the period of time. Standardized regression coefficients further indicate that, for the rolling regressions, future investment opportunity is still a more important explanatory variable in explaining firms' investment than internally generated funds. For example, standardized regression coefficients on cash flow CF and marginal Q t−1 are 0.0776 and 0.4170 over the subperiod 2016 to 2020, respectively.

Time-Series Variation of the Sensitivity of Investment to Cash Flow
We employ Figure 3 to clearly view the time-series variation of the sensitivity of investment to cash flow.
regression coefficients further indicate that, for the rolling regressions, future invest opportunity is still a more important explanatory variable in explaining firms' invest than internally generated funds. For example, standardized regression coefficien cash flow CF and marginal Q are 0.0776 and 0.4170 over the subperiod 2016 to respectively.

Time-Series Variation of the Sensitivity of Investment to Cash Flow
We employ Figure 3 to clearly view the time-series variation of the sensitivity vestment to cash flow.  Figure 3 prese plot of the sensitivity of investment to cash flow against the nineteen subperiods. The within mator performs OLS on mean-differenced data. The IV estimator conducts a two-stage least sq estimator using lagged returns as instruments.
Two curves are depicted in Figure 3. One is the steel blue solid curve with solid c and the other is the black dotted curve with circles. The former represents the estim of sensitivity using the within estimator while the latter denotes the estimates from instrument variable (IV) estimator (IV will be discussed in Section 4.2). On the vertica of Figure 3 are the sensitivity coefficients, which are within and IV estimates of the c cient of β s in Equation (6) over the rolling nineteen subperiods. The steel blue solid c with solid circles, which depicts the time-series variation of the sensitivity of invest to cash flow, has three segments. The first segment is comprised of the first four sub ods and the curve is steeply upright-sloping, which indicates that firms have become and more dependent on internally generated cash flow. The second segment covers sequent rolling thirteen subperiods and the sensitivity heads downhill. It demonst that over a long time period, firms have come to rely less and less on cash flow. Th two subperiods are the third segment in which the sensitivity starts going slightly up  Figure 3 presents a plot of the sensitivity of investment to cash flow against the nineteen subperiods. The within estimator performs OLS on mean-differenced data. The IV estimator conducts a two-stage least squares estimator using lagged returns as instruments.
Two curves are depicted in Figure 3. One is the steel blue solid curve with solid circles and the other is the black dotted curve with circles. The former represents the estimates of sensitivity using the within estimator while the latter denotes the estimates from the instrument variable (IV) estimator (IV will be discussed in Section 4.2). On the vertical axis of Figure 3 are the sensitivity coefficients, which are within and IV estimates of the coefficient of β 1 s in Equation (6) over the rolling nineteen subperiods. The steel blue solid curve with solid circles, which depicts the time-series variation of the sensitivity of investment to cash flow, has three segments. The first segment is comprised of the first four subperiods and the curve is steeply upright-sloping, which indicates that firms have become more and more dependent on internally generated cash flow. The second segment covers subsequent rolling thirteen subperiods and the sensitivity heads downhill. It demonstrates that over a long time period, firms have come to rely less and less on cash flow. The last two subperiods are the third segment in which the sensitivity starts going slightly up. We take the three segments as a whole and we have a visual sense that the sensitivity is decreasing during the full sample period. Our findings of a decreasing sensitivity of investment to cash flow over time are consistent with existing literature [4,11,12].
The plot that the sensitivity of investment to cash flow is fading away over time is only visual. The visual view needs to further be statistically supported. For that purpose, we design two recursive statistical tests. The first one is to explore the statistical difference between the high of sensitivity coefficient over the subperiod 2001-2005 and the low of sensitivity over 2014 to 2018. If the test indicates the difference is statistically significant, then we perform the second test to investigate statistical difference between the first subperiod 1998 to 2002 and the last subperiod 2016 to 2020. If the first test shows the difference is not statistically significant, we do not need to further conduct the second one. At this point, we conclude that the declining trend in sensitivity is not statistically significant. We define two dummy variables for the two recursive tests. For the first test, the dummy takes a value of 0 for the subperiod 2001 to 2005 and value of 1 over 2014 to 2018. Likewise, for the second test, the dummy variable takes 0 for the first subperiod 1998 to 2002 and 1 over 2016 to 2020. Table 3 reports the empirical results of the two tests. The first test indicates that the estimate of sensitivity coefficient on cash flow is 0.3924, the standard error is 0.0686, and the coefficient is significant at the 1% level. The coefficient on interaction of the first dummy and cash flow is −0.4323, the interaction standard error is 0.0729, and the coefficient on the interaction is significant at the 1% level. The negative and significant coefficient on the interaction suggests a prerequisite for the second test is satisfied. For the second recursive test, the estimate of the coefficient on cash flow is 0.2284 (a t-value of 4.9799 and significant at the 1% level), and the estimate of coefficient on the interaction is −0.1856 (a t-value of −3.7781 and significant at the 1% level). Most noteworthy for us are again the estimate and significance of the coefficient on the interaction. The negative and significant coefficient on the interaction in the second test demonstrates that the above visual sense of decreasing sensitivity is statistically corroborated. The aforementioned empirical results and the corresponding trend graph of investment-cash flow sensitivity show that the second prediction is supported by the data. The firms' investment has become less and less dependent on internally generated funds as time goes on. That is, internal funding is becoming less important in supporting a firm's investment-induced sustainability.

Measurement Error in Tobin's Q
As is described previously, we use Tobin's Q as a proxy for marginal Q. Tobin's Q might be an imperfect proxy because of measurement error in Tobin's Q. If marginal Q is replaced with the error-laden Tobin's Q, the cash flow effects on investment discussed previously could be explained by investment opportunity.
We next address how to effectively remedy the measurement error in Tobin's Q. The most common remedy is to find additional observables that can serve as instruments. One approach in the earlier literature is to employ lagged market to book ratio as an instrument variable (IV). An IV estimator using lagged market to book ratio as IV is valid only if serial correlation in measurement error is small or short-lived [30]. An alternative approach in the recent literature is high-order moment estimators originally proposed by Erickson and Whited [8]. Although high-order moment estimators perform well in the presence of serial correlation, it can be applied only to samples that are arguably independently and identically distributed [9]. We follow Lewellen and Lewellen [14] and employ lagged returns as instrument variable for Tobin's Q and then leave the high-order moment estimator as a robustness check. The reasons for using lagged earnings as an instrument are as follows. Tobin's Q is calculated following the logic of market-to-book ratio, a simple comparison of market value with book value of a given firm. Hence, the measurement error in Tobin's Q is more likely to come from book value in the denominator, which is based on the balance sheet, than from market value in the numerator. Even if the true value of a firm is measured with error, the fundamental value of the firm is the most primary determinant of market prices in the long run. On the contrary, returns do not depend on the book value and hence seem less likely to be correlated with the error in the regression of Tobin's Q on marginal Q.
The IV regression of investment on cash flow and Tobin's Q can be estimated using a two-stage least squares estimator on unbalanced panel data. Specifically, we perform a first-stage regression of Tobin's Q on cash flow, one-period lagged returns, and two-period lagged returns. We run a second-stage regression of investment on cash flow and the fitted values from the first-stage regression. Therefore, we obtain a consistent estimate of the coefficient on cash flow. Table 4 presents the empirical results of the IV regression.  Table 4 reports IV estimates of the sensitivities, standard errors, sample sizes (N), R 2 s, F statistics at the first stage, and Sargan statistics over the full sample and the rolling five-year subperiods. The dependent variables are investment I t scaled by one-period lagged total assets K t−1 . The explanatory variables include cash flow CF t divided by one-period lagged total assets and one-period lagged Marginal Q t−1 . The instruments are one-period and two-period lags of returns RETN t−1 and RETN t−2 . All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively. Table 4 consists of panels A and B. Panel A reports results over the full sample while Panel B presents results over the rolling subperiods. The results in Panel A shows that after controlling the measurement error in Tobin's Q, firms invest an extra 0.0478 (t-statistics of 7.710) for each additional unit of cash flow, which is the same sign and similar magnitude as that (0.0481) in Table 2. The results mean that measurement error in Tobin's Q does not fully explain the cash flow effects on investment. We observe the diagnostic statistics of the IV estimator to examine the IV validity in our settings. The first-stage F-statistic from the regression of Tobin's Q t−1 on cash flow and RETN t−1 and RETN t−2 is 909.999, which is drastically greater than 10. It indicates the instruments are not weak and could explain much of the variation in Tobin's Q t−1 . The Sargan statistic is 3.1128 and the corresponding p-value is 0.9223. It indicates that we cannot refuse the null hypothesis that RETN t−1 or RETN t−2 , or both are exogenous. We next move on to Panel B. We find F-statistics at the first stage range from a low of 1.5685 to a high of 540.8360, and these F-statistics become larger as the number of sample observations increases. All Sargan statistics show the null hypotheses of exogeneity are not rejected at the conventional significance levels. Almost all signs and magnitudes of IV estimates are very similar as those in Table 2. We add the IV estimates of the sensitivity of investment to cash flow to Figure 3 and find the sensitivity display a very similar trend to OLS estimates. In addition, Machokoto et al. find, during the last global financial crisis when credit constraints were more significant and binding, the sensitivity of investment to cash flow disappears even for constrained firms [13]. In contrast to the findings of Machokoto et al. [13], the results over three continuously rolling  Tables 3 and 5 show the sensitivity does not disappear but still maintains a declining trend during the crisis in China. We argue that it is highly probable that a Four Trillion Stimulus policy, which was launched by China's central government in 2008, has a relaxation effect of financial constraints at the firm level (The discussions on the financial crisis, the Four Trillion Stimulus policy, and its effects in China are beyond our scope. On the crisis, the policy and the effects in China, see Ouyang and Peng [31]). We follow Erickson and Whited [8] and use high-order moment estimators including the third order moment through the seventh moment to further perform a robustness check. The results show very similar trend to those in Tables 3 and 5.   Table 5 reports the empirical results from the regressions of investment I t on cash flow CF t , external financing EXT t , and Q t−1 over the full sample and the rolling nineteen five-year subperiods. Variables I t , CF t , and EXT t are scaled by one-period lagged total assets K t−1 . All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.

An Inference
So far, we have established that the sensitivity of investment to cash flow decreases at the firm level over time. If the decline in the sensitivity is caused by the relaxing financial constraints, it would be highly probable that firms have easier access to external financing over time. The relaxations of financial constraints allow firms to rely more on externally generated funds. We hence make an inference that while the sensitivity of investment to cash flow drops down, the sensitivity of investment to external financing increases over time. If the inference is not statistically supported, there are reasons to doubt the aforementioned empirical designs and results. Of course, while this inference is supported by the data, it is not necessarily caused by a decline in investment-cash flow sensitivity. The validation of the inference plays a role here similar to that of a placebo test. We test the inference using Equation (9) as follows: where EXT represents the change in book equity plus total debts. The remaining variables are defined previously. Table 5 includes the results from Equation (9). As a comparison, we also report the results for cash flow that does not enter Equation (9). We define it as Equation (9.1). The results from Equation (9) show the estimates of the coefficients on CF and EXT are 0.1709 and 0.2657 over the full sample, respectively. The coefficients on CF and EXT are both significant at the 1% level. It shows that the sensitivity of investment to external funds is greater than that of investment to cash flow. The estimate of the coefficient on EXT in Equation (9.1) is 0.2154, the coefficient is significant at the 1% level, and R 2 is 0.2271. In contrast, the estimate of the sensitivity of investment to cash flow of Equation (6) is 0.0481 over the full sample, the coefficient is significant at the 1% level, and the R 2 is 0.0264. The results show that the variation in investment is primarily explained by external funds rather than cash flow. We turn to the results over the rolling nineteen subperiods in Panel B and we find almost all the estimates of the coefficients on CF and EXT are positive, and the coefficients on CF and EXT are significant at the conventional levels. The estimates of the coefficients on EXT are much larger than those on CF except for 0.2692 less than 0.3014 over the subperiod 1999 to 2003. The results over subperiods primarily corroborate those over the full sample.
The inference consists of two recursive propositions. The first proposition is, after controlling for EXT and Tobin's Q, the sensitivity of investment to cash flow fades over time. If the proposition is not rejected, we further test the second one that investment relies more and more on external funds over time. Table 6 reports the results from the two recursive tests. Test 1 is the results from the regression of the estimates of the coefficients on CF in Equation (9) on the time trend. We find that the estimate of the coefficient on the trend is −0.0112, the standard error is 0.0022, and the hypothesis of coefficient equal to zero is significant at the 1% level. The results indicate that we cannot reject the first proposition. We next perform another regression of the estimates of the coefficients on EXT of Equation (9) on the time trend. Test 2 shows the estimate of the coefficient on the time trend is 0.0091, the robust standard error is 0.0023, and the hypothesis of the trend coefficient equal to zero is significant at the 1% level. The results show the proposition that increasing dependence of firms' investment on externally generated funds are statistically supported. In light of the results from the two recursive tests, we draw a conclusion that the inference that the sensitivity of investment to external funds increases over time is statistically supported. Although increasing reliance of investment on external funding is not necessarily caused by a decrease in investment cash flow sensitivity, our confidence in the previous empirical findings is further reinforced by the fact that the inference of increasing reliance of investment on external funding is confirmed by the data. The aforementioned findings suggest that compared to internal funding, external funding is becoming increasingly important in supporting firms' investment-induced sustainability.  Table 6 reports tests for the sensitivity of investment to external financing. The dependent variable in the test 1 is estimates of the coefficient on cash flow and the dependent in the test 2 is estimates of the coefficients on external financing. The intercepts are not reported. Robust standard errors are shown between brackets. *** denote significance at the 1% level.

Asymmetric Changes in the Sensitivity of Investment to Cash Flow
Although investment-cash flow sensitivity decreases over time, firms' financial positions can exhibit heterogeneity. While some firms have looser external financing constraints, others face tighter external financing constraints. Thus, there are gaps in the sensitivity of investment to cash flow between firms with tighter and looser financing constraints. We examine in this section whether the gaps in the sensitivity of investment to cash flow broadens or narrows over time. To that end, we employ five classification schemes. Specifically, we divided the sample by company size, whether a company pays cash dividends, whether a company has government equity, the WW index, and the HP index and then perform regressions of investment to cash flow over the subperiods. Tables 7 and 8 report the empirical results.   Table 7 only presents asymmetric changes in the sensitivity in terms of the single index: size, dividends dummy, and government dummy. Columns ≤ q30 and ≥q70 denote the bottom and top three deciles of the distribution of the natural logarithm of firms' total assets, which are GDP deflator-adjusted to the base year 1998, respectively. DIVD is 1 if a firm pays cash dividends and 0 otherwise in a given year. GOVT is defined as 1 if a firm owns government equity and 0 otherwise in a given year. The two dummy variables are interacted with cash flow. All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.   Table 8 reports asymmetric changes in the sensitivity in terms of the composite index: the WW index and the HP index. The WW index is given by −0.091 × CF/Assets − 0.062 × Dividend Payer Dummy + 0.021 × long-term debt/Assets − 0.044 × log (Assets) + 0.102 × industry median sales growth ratio − 0.035 × sales growth ratio. The HP index is equal to −0.737 × log (Assets) + 0.043 × log (Assets) 2 + 0.04 × firm's age. Columns ≤ q30 and ≥q70 denote the bottom and top three deciles of the distribution of the WW and HP scores in a given year, respectively. All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.

Results from Classification by the Single Index
A firm is classified as tighter (looser) external financing constraints if the natural logarithm of its assets, which are GDP deflator-adjusted to the base year 1998, is the bottom (top) three deciles of the distribution each year. Columns ≤q30 and ≥q70 in Table 7 present the empirical results of the subsamples of the bottom and the top three deciles, respectively.
Panel A of Table 7 shows that, as opposed to 0.0892 of the top three deciles, the estimate of sensitivity coefficient on cash flow is 0.0969 of the bottom three deciles. The two sensitivity coefficients are both statistically significant at the 1% level. The results demonstrate firms that are classified as tighter financing constraints face more financial frictions, have less channels to external funds, and have to rely more on internally generated cash flow. We further move on to the results of rolling subperiods in Panel B and find the findings are further corroborated by fifteen of the nineteen estimates of sensitivity. Our findings are consistent with financial constraint hypothesis [1,32] and are not consistent with agency conflict theory [33,34].
The column of DIVD in Table 7 presents the results from classification by whether a firm pays cash dividend. We define the dummy as 0 if a firm did not pay cash dividend and 1 otherwise in a given year. The empirical results from both the full sample and rolling subperiods consistently suggest the DIVD does not effectively capture whether a firm faces tighter or looser financial constraints in China. The results are not consistent with either the financial constraint hypothesis [14,32] or agency conflict theory [33,34]. We speculate on the reason why cash dividends are not a useful index indicating external financing constraints. We refer back to the relevant regulatory policies on cash dividends for listed companies in China. In May 2006, China Securities Regulatory Commission (CSRC) issued the Measures for the Administration of Securities Issuance by Listed Companies, which stipulate that the cumulative profits distributed in cash by listed companies in the last three years shall not be less than 20% of the average annual distributable profits realized in the last three years. In October 2008, the CSRC also issued the Decision on Amending Regulations on Cash Dividends for Listed Companies, which required listed companies to increase the above-mentioned cash dividend ratio from the original 20% to 30%. It is easy to see that these two policies not only make mandatory dividend distribution requirements for cash dividends of listed companies in China, but also stipulate the dividend distribution ratio. Therefore, the variation of cash dividends paid by China's listed companies would be small, and thus the coefficient on cash dividends would be statistically insignificant. We use a dummy DIVD as a proxy for external financing constraints, and its mean in Table 1 is 0.84. It is a figure that reflects the fact that firms have distributed cash dividends in the vast majority of years as required by regulations.
Existing research shows that firms with government equity face fewer financial constraints and have easier access to external funding than privately owned firms [35,36]. To capture this financing asymmetry, we define a dummy variable GOVT based on whether the firm owns government equity. GOVT is defined as 1 if a firm owns government equity and 0 otherwise each year. The column GOVT in Table 7 reports the empirical results. For the full sample in Panel A, the estimate of the coefficient on GOVT is −0.0327 and the null hypothesis that there is not a difference in external financing access is significant at the 1% level. We move on to the rolling five-year regressions and find that all the nineteen estimates of coefficients on GOVT are negative and fifteen of the nineteen null hypotheses are significant at the conventional significance levels. The results are consistent with those over the full sample. IV-based estimates of the classifications using one-period and twoperiod lagged returns as instruments for Tobin's Q are very similar to those reported in Table 7. To save space, the IV-based estimates of classification regressions by the single and the composite indices are presented in Appendix B. In sum, listed firms with government equity rely less on internal funds than those with private. Whether a firm owns government equity or not is a second factor that results in a gap in the sensitivity of investment to cash flow in China.

Results from Classification by the Composite Index
The WW index is constructed according to Whited and Wu [29]. It uses more dimensions including a firm's size, cash flow, cash dividends payment, liabilities, sales, and industry sales to measure a firm's financial constraints than the HP index by Hadlock and Pierce [28], which relies heavily on firm size and age. By construction, the WW and HP indices are both composite indices. Higher scores of the two indices suggest a firm faces tighter financing constraints. To save space, Table 8 reports the empirical results for the HP and the WW classifications.
We split the full sample into two groups according to the bottom (≤q30) and top (≥q70) three deciles of the distribution each year. Taking into account that the WW index is more composite, we take the WW index for an example. The estimates of sensitivity coefficients over the bottom and top groups are 0.0183 and 0.1308 over the full sample period in Panel A of Table 8, respectively. They are both significant at the 1% level. The results indicate according to the scheme by the WW index, the sensitivity of tighter financing constrained firms is quite a few times larger than that of the looser financing constrained counterparts. We move on to the results in Panel B and find that thirteen of the nineteen sensitivity estimates for the top three-decile subperiods are greater than those of the bottom threedecile subperiods and the corresponding coefficients on cash flow are significant at the conventional levels. Although five of the remaining six estimates are unexpectedly negative, they are not significant at the conventional levels. The empirical results over the rolling five-year subperiods further corroborate the aforementioned findings over the full sample in Panel A. We turn to the HP index and find the results of the HP index remain qualitatively unchanged. The effect of cash flow predicted by the financial constraint explanation is present. The WW and the HP indices are useful to capture a firm's financial constraints and the classifications by the two indices show gaps in the sensitivity of investment to cash flow in China.
We summarize the asymmetric changes in sensitivity coefficients between firms with tighter and looser external financing constraints in a visual way. As is previously defined, gap in sensitivity is the difference in investment-cash flow sensitivity between firms with tighter and looser external financing. The WW gap and the HP gap are the sensitivity differences between the top and bottom three deciles of the distributions of the WW scores and the HP scores, respectively. The size gap is the difference in sensitivity between the bottom and the top three deciles of the distribution of the natural logarithm of total assets GDP deflator-adjusted to the base year 1998. The government equity gap is the difference in sensitivity between firms without and with government equity. The cash dividend gap is the difference in sensitivity between the non-payment of cash dividends and the payment. Figure 4 plots the five sensitivity gaps including size gap, cash dividends gap, government equity gap, the HP gap, and the WW gap against the rolling nineteen subperiods.
Of the five gap lines, the WW gap line and the government equity gap line are both the most salient. The former is marked by the steel blue line with solid circles and is above the zero line. The latter is marked by the steel blue line with solid triangles and is below the line zero. We select both to describe the time-series pattern of the sensitivity gap. Each gap line can be split into two segments; the first segment is over the first seven subperiods and a second segment includes the last twelve subperiods. The two gaps in sensitivity on the first segment are larger than gaps on the second segment and, moreover, they are subject to larger fluctuation than gaps on the second segment. Each gap line as a whole shows a slightly downward trend and the gaps are narrowing to zero over time. The two lines of the size and the HP gaps display similar patterns to those of the WW and government equity gaps. In addition, we use one-period and two-period lagged returns as instruments for Tobin's Q to investigate the asymmetric change in sensitivity of investment to cash flow and find the results are qualitatively unchanged.
in sensitivity between firms without and with government equity. The cash dividend is the difference in sensitivity between the non-payment of cash dividends and the ment. Figure 4 plots the five sensitivity gaps including size gap, cash dividends gap, ernment equity gap, the HP gap, and the WW gap against the rolling nineteen subper  Figure 4 prese plot of five sensitivity gaps against rolling nineteen five-year subperiods. The gap is defined a difference in the sensitivity of investment to cash flow between firms with tight versus loose fi ing constraints. The WW gap denotes the sensitivity difference between the top and bottom deciles of the WW scores' distribution. The HP gap is the sensitivity difference between the top bottom three deciles of the HP scores' distribution. The government equity gap is the sensi difference between classifications without and with government equity. The cash dividend g the difference in sensitivity between the non-payment of cash dividends and the payment of  Figure 4 presents a plot of five sensitivity gaps against rolling nineteen five-year subperiods. The gap is defined as the difference in the sensitivity of investment to cash flow between firms with tight versus loose financing constraints. The WW gap denotes the sensitivity difference between the top and bottom three deciles of the WW scores' distribution. The HP gap is the sensitivity difference between the top and bottom three deciles of the HP scores' distribution. The government equity gap is the sensitivity difference between classifications without and with government equity. The cash dividend gap is the difference in sensitivity between the non-payment of cash dividends and the payment of cash dividends. The size gap is defined as the sensitivity difference between the bottom and top three deciles of the distribution of firms' total assets. Based on the results from asymmetric changes in the sensitivity of investment to cash flow and the corresponding trend graphs, we find that although the gaps in the sensitivity of investment to cash flow between firms with tighter and looser external financing constraints exist, the prediction that gaps in the sensitivity of investment to cash flow broadens over time is not supported by the data. In contrast, the empirical evidence suggests that the gaps in the sensitivity of investment to cash flow between the two types of firms shrinks over time. The law similar to the Matthew effect that the tighter the external financing constraint the harder it is for a company to obtain external financing and the looser the external financing constraints the easier to obtain external financing does not appear. It suggests that the gap-reducing effect caused by the universal social evolution, institutional change, and technological progress is larger than this gap-widening effect brought about by the willingness of external suppliers of funds to finance firms with fewer financing constraints.

Conclusions
The long-term survival and development of enterprises, as one of the most basic social organizations for the allocation of various types of resources, depends on efficient investment and on adequate financing for that investment. That is, access to financing investment affects corporate sustainability.
We examine two issues related to the dependence of companies' investment on internally generated funding. One is whether a declining trend in the sensitivity of investment to cash flow is exhibited in China; the other is to define the gaps in the sensitivity of investment to cash flow based on asymmetric changes in investment-cash flow sensitivity and further explore the trends in the gaps. We collected financial data from Chinese listed companies over the period 1998-2020. After collating the data, we finally obtained a sample including 2415 listed companies with a total of 19,864 firm-year observations. We find that, as in other countries, China's firms exhibit not only a decreasing trend in investment cash flow sensitivity in the long run, but also evidence of a complete disappearance of sensitivity over a time horizon; there are gaps in the sensitivity of investment to cash flow caused by asymmetric changes in the sensitivity; the gaps are effectively explained by firm size, government equity, and the HP and WW indices, but not by cash dividends; and the gaps in the sensitivity of investment to cash flow are narrowing in the long term. Our marginal contribution to the extant literature lies not only in China's evidence of a continuous decline in investment-cash flow sensitivity, but also in the following two points: first, we define gaps in the sensitivity of investment to cash flow based on asymmetric changes in investment-cash flow sensitivity and then explore the trends of these gaps; second, based on China's accounting standards for interest expense in the statement of cash flows, we modify the cash flow identity presented in the U.S. scenario literature. According to the modified identity, we propose the broadest measure of China's firm investment to reflect the recent changes in investment measures.
The decreasing investment-cash flow sensitivity indicates that while internally generated funding has been a significant support for the companies' investment, it is becoming less so in the long term. The long-term trend of the decreasing gaps in the sensitivity of investment to cash flow suggests that the easing of external financing constraints is not only universal for firms, but also does not exhibit a pattern similar to the Matthew effect. In other words, it does not exhibit a pattern in which firms with tighter financing constraints have less access to external financing and firms with looser financing constraints have easier access to external financing. The empirical findings have two implications. First, for corporate finance, the diminishing sensitivity of investment to cash flow suggests that the role of the sensitivity as a proxy for financing constraints is diminishing and that gaps in the sensitivity can be used as a measure of financial market integration. Second, for firm sustainability, compared to external financing, access to internal financing in supporting investment-induced sustainability is decreasing. The findings also provide insight into how to develop corporate sustainability policies for different types of companies based on gaps in the reliance of investment to cash flow and their changing trends.   Table A1 reports estimates of sensitivities, standard errors, sample sizes (N), R 2 s, and F statistics from the GMM7 (using the third up to the seventh moments) (Erick and Whited, 2000) over the full sample and the rolling five-year subperiods. The dependent variables are investment I t scaled by one-period lagged total assets K t−1 . The explanatory variables include cash flow CF t divided by one-period lagged total assets and one-period lagged Marginal Q t−1 . All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.   Table A2 only presents asymmetric changes in the sensitivity using IV estimator in terms of single indices: size, dividends dummy, and government dummy. Columns ≤ q30 and ≥q70 denote the bottom and top three deciles of the distribution of the natural logarithm of firms' total assets, which are GDP deflator-adjusted to the base year 1998, respectively. DIVD is 1 if a firm pays cash dividends and 0 otherwise in a given year. GOVT is defined as 1 if a firm owns government equity and 0 otherwise in a given year. The two dummy variables are interacted with cash flow. All regressions specify firm and industry-year fixed effects. Standard errors are heteroskedasticity consistent and clustered at the firm level and are shown between brackets. ***, **, and * denote significance at the 1%, 5%, and 10% level, respectively.