A balancing act : managing financial constraints and agency costs to minimize investment inefficiency in the Chinese market

Using a large panel of Chinese listed firms over the period 1998-2014, we document strong evidence of investment inefficiency, which we explain through a combination of financing constraints and agency problems. Specifically, we argue that firms with cash flow below (above) their optimal level tend to under(over-)invest as a consequence of financial constraints (agency costs). Furthermore, focusing on under-investing firms, we highlight that the sensitivities of abnormal investment to free cash flow rise with traditionally used measures of financing constraints, whilst for over-investing firms, the sensitivities increase with a wide range of firm-specific measures of agency costs.

their marginal revenue equals their marginal cost. However, substantial empirical evidence has documented a significantly positive correlation between cash flow and investment expenditure (Bond and Van Reenen, 2007;Cleary, 1999;Cumming et al., 2006;Fazzari et al., 1988;Hubbard, 1998). The reason for the existence of this positive relation remains, however, controversial.
First, there exists considerable evidence to suggest that the positive correlation between investment and cash flow stems from asymmetric information between corporate insiders and outside creditors (Carpenter and Guariglia, 2008;Fazzari et al., 1988;Myers and Majluf, 1984). This can be explained considering that when external finance such as bank loans, debt and equity are used, the imperfections in capital markets lead to a cost premium. The cost and/or availability of external funds force firms to use internal finance, like retained earnings, in preference to external finance. In these circumstances, financially constrained firms may have to forego good investment projects to avoid the excessively high cost premiums associated with the use of external finance. Thus, when firms face financial constraints, negative cash flow shocks may lead to underinvestment. A high sensitivity of under-investment to free cash flow can therefore be seen as evidence of financial constraints. We refer to this as the financing constraints (FC) hypothesis (H1): H1. Financing Constraints (FC) Hypothesis: Firms which are ex-ante more likely to face financing constraints exhibit higher sensitivities of under-investment to free cash flow.
Second, the positive correlation between investment and cash flow may reflect two types of agency problems: those between controlling shareholder and minority investors, and those between managers and shareholders (Jensen, 1986;Pawlina and Renneboog, 2005;Stulz, 1990). In the Chinese context, given the weak legal system, the high restriction of share trading, and the prevalence of dominant shareholders, the first type of agency problems has been found to be prevalent (Jiang et al., 2010;Liu and Lu, 2007). The risk of controlling shareholders expropriating resources from minority investors (tunneling) is in fact severe. As a result, controlling shareholders are likely to make self-interested and entrenched decisions and prefer to spend the firm's free cash flow on unprofitable projects rather than paying dividends to shareholders, resulting in over-investment. In summary, when firms face agency problems (and in particular are more likely to be subject to tunneling), the more free cash flow they have, the more they prefer to invest, which could lead to over-investment. A positive relationship between overinvestment and free cash flow can hence be interpreted as evidence of the presence of agency problems. We refer to this as the agency costs (AC) hypothesis (H2): H2. Agency Cost (AC) Hypothesis: Firms which are ex-ante more likely to face agency problems exhibit higher sensitivities of over-investment to free cash flow.
Taken together, financial constraints and agency problems can prevent firms from making optimal investment decisions. In other words, both financial constraints and agency problems may increase the sensitivity of investment expenditure to free cash flow and induce investment inefficiency. To discriminate between these two scenarios within the Chinese context, we test hypotheses H1 and H2. Both hypotheses are focused on the sensitivity of abnormal investment to free cash flow, which is defined as the cash flow beyond what is required to maintain assets and finance expected new investments (Richardson, 2006). In the two sections that follow, we outline the methodology that we adopt to test these two hypotheses.  Overinvestment (+) Underinvestment (-) I_main. i,t CFO i,t FCF i,t (+,-) I_main. i,t I e _new i,t Fig. 1. Framework for the construction of (under-or over-) investment and free cash flow. Note: I_total i,t = CAPEX i,t − SalePPE i,t (Capital expendituresale of property, plant, and equipment); I_main .i,t = Depreciation i,t + Amortization i,t ; I_new i,t = I_total i,t − I_main. i,t ; CFO i,t = Net cash flow from operating activities; CF AIP,i,t = Cash flow generated from assets in place; FCF i,t = CF AIP,i,t − I e _new i,t = CFO i,t − I_main. i,t − I e _new i,t .
3. Methodology used to measure abnormal investment and free cash flow

A framework to measure abnormal investment and free cash flow
We measure both under-and over-investment (abnormal investment) and free cash flow (FCF) using Richardson's (2006) accounting-based framework. Fig. 1 outlines our methodology.
Total investment (I_total i,t ) is defined as capital expenditure less receipts from the sale of property, plant, and equipment. 5 I_total i,t can be decomposed into two main parts: new investment expenditure (I_new i,t ), and required investment expenditure to maintain assets in place (I_main. i,t ), which is given by the sum of amortization and depreciation.
New investment expenditure (I_new i,t ) can be further split into two components: expected investment expenditure in new positive net present value (NPV) projects (I e _new i,t ), which is described in the next sub-section, and unexpected investment or abnormal investment (under-or over-investment, I u We then define firms' optimal level of cash flow as the sum of maintenance investment (I_main. i,t ) and expected investment expenditure (I e _new i,t ). Free cash flow (FCF) is computed by subtracting the optimal level of cash flow (I_main. i,t + I e _new i,t ) from net cash flow from operating activities (CFO). 6 Accordingly, FCF can be either positive or negative, depending on whether net cash flow from operating activities (CFO) exceeds the optimal level of cash flow.

Dynamic expectation models of investment expenditure
Following Richardson (2006), a dynamic investment expectation model is used to predict the expected investment expenditure in new positive NPV projects (I e _new i,t ), which can be interpreted as the optimal level of investment expenditure. 7 Specifically, denoting with I_new the firm's new investment expenditure; with Q (Tobin's Q), its market-to-book ratio 8 ; with Cash, its ratio of cash and cash equivalents to total assets; with Size, the natural logarithm of its total assets; with Age, the number of years elapsed since its listing; with ROA, its return on assets 9 ; and with Leverage, the ratio of its short-term and long-term debt to total assets, we estimate the following equation: where the subscript i indexes firms; t indexes years (t = 1998-2014); j, industries; and p, provinces. We use a dynamic model to allow for a partial adjustment mechanism and to control for unobserved factors not included among other regressors. We lag all our independent variables (except Age) to alleviate the simultaneity issue (Duchin et al., 2010;Polk and Sapienza, 2009). The error term in Eq. (1) is made up of five components. v i is a firm-specific effect; v t , a time-specific effect, which we control for by including time dummies capturing business cycle effects; v j , an industry-specific effect, which we take into account by including industry dummies; v p , a province-specific effect capturing uneven developments across different provinces, which we control for by including province dummies; and v j,t takes into account industry-specific business cycles, which we control by including industry dummies interacted with time dummies. Finally, ε i,t is an idiosyncratic component.
Estimates of Eq. (1) obtained using the fixed-effects estimator (Fe) and the system GMM estimator ) are presented and discussed in Appendix A. The fitted values of Eq. (1) can be interpreted as a proxy for optimal investment (I e _new i,t ). 10 The difference between real investment and optimal investment (I u _new i,t ) is then computed and interpreted as unexpected investment. I u _new i,t can be either positive or negative, corresponding to over-investment or under-investment, respectively.
We next test whether there exists a statistically significant relationship between abnormal investment and FCF and, if it does, whether it stems from financing constraints and/or agency costs. 5 It should be noted that Richardson (2006) also includes acquisitions and Research and Development (R&D) expenditure in his proxy for total investment. We chose to use a more parsimonious proxy for two reasons. The first is that capital expenditure is generally used in the finance and economics literatures as a proxy for investment (Hubbard, 1998). The second is that R&D expenditure is not available in our data. Contrary to us, Richardson (2006) also includes R&D expenditure in his proxy for free cash flow. 6 The reason why we deduct expected investment expenditure (I e _new i,t ) rather than actual CAPEX to calculate FCF is that actual CAPEX can be influenced by financial constraints or agency costs. 7 All investment expenditure variables are scaled by total assets. 8 The shares of listed firms in China can be either tradable or non-tradable. Following the literature (Chen et al., 2011;Huang et al., 2011), we calculate Tobin's Q as the sum of the market value of tradable stocks, the book value of non-tradable stocks, and the market value of net debt divided by the book value of total assets. Our results were robust to using the growth of real sales instead of Tobin's Q to proxy for investment opportunities (Konings et al., 2003). This test is motivated by the fact that in the Chinese context, Tobin's Q may be an imperfect measure of investment opportunities. 9 As firms in a less developed market may not make investment decisions based on market valuation (Wang et al., 2009), contrary to Richardson (2006), we use the return on assets (ROA) instead of stock returns in our dynamic investment model. See Appendix A for complete definitions of all variables. 10 All our results were robust to estimating a more parsimonious version of Eq.
(1) only including lagged investment, Q, and the dummies.

Main specification
To analyze the sensitivities of under-or over-investment to free cash flow, we initially estimate the following regression: We partition firm-years into those characterized by over-investment or under-investment on the basis of their I u _new i,t . More specifically, over-investing (under-investing) firms are those who have positive (negative) abnormal investment (I u _new i,t ). We then investigate whether the sensitivity of I u _new i,t to FCF differs for firms facing positive and negative FCF, whereby the former are more likely to be affected by agency problems, while the latter are more likely to suffer from financing constraints. 11 To this end, we interact FCF with the dummy Dum FCF N 0 (Dum FCF b 0 ), which is equal to 1 if the firm has positive (negative) free cash flow, and 0 otherwise. In accordance with the financing constraints hypothesis (H1), we expect a 2 to be positive and precisely determined for under-investing firms, while, in line with the agency costs hypothesis (H2), a 3 should be positive and significant for over-investing firms. 12 We also include the dummy Dum FCF N 0 in the regression, to account for the direct effect that it might have on corporate investment. Finally, we control for business cycle effects. 13 4.2. Are under-or over-investment-free cash flow sensitivities due to financial constraints or agency costs?
To further test for the financial constraints (FC) hypothesis of under-investment and the agency costs (AC) hypothesis of over-investment, we next estimate the following regression: where Dum represents a dummy proxying for the degree of financial constraints or agency costs faced by firms. Specifically, we separate firms into different groups on the basis of their a priori likelihood of facing financial constraints or agency problems measured using different criteria, with the aim of investigating the extent to which different groups of firms have different sensitivities of under-and over-investment to free cash flow. These further tests should enable us to shed more light on whether the financing constraints and agency costs hypotheses can explain investment inefficiency in the Chinese context. We estimate Eqs. (2) and (3) using the fixed effects (Fe) estimator to control for time-invariant firm-specific heterogeneity. 14 5. Main features of the data and descriptive statistics

The dataset
The data used in this paper are drawn from the China Stock Market and Accounting Research (CSMAR) Database and China Center for Economics Research (CCER) Database. They cover Chinese companies that issue A-share stocks on either the Shanghai Stock Exchange (SHSE) or the Shenzhen Stock Exchange (SZSE), during the period 1998-2014. We exclude financial institutions since the operating, investing and financing activities of these firms are distinct from others. We further winsorize observations in the one percent tails for the main regression variables to minimize the potential influence of outliers. Finally, we drop all firms with less than three years of consecutive observations. All variables are deflated using the gross domestic product (GDP) deflator (National Bureau of Statistics of China).
Our final panel consists of 2113 listed firms, which corresponds to 22,373 firm-year observations. The number of firm-year observations of each firm varies from three to seventeen, with number of observations varying from a minimum of 576 in 1998 to a maximum of 2026 in 2012. 15 11 Because free cash flow is defined as operating cash flow net of depreciation and amortization and net of I e _new i,t , positive sensitivities of abnormal investment to free cash flow are unlikely to be caused by free cash flow picking up investment opportunities. Our results were generally robust to estimating a dynamic version of Eqs. (2) and (3). 12 It is important to note that the same firm may face both financial constraints and agency costs at the same time. However, we believe that financing constraints are more pronounced for under-investing firms with negative free cash flow, and that agency costs are more pronounced for over-investing firms with positive free cash flow. See footnotes 21 and 27 for a further discussion of this point. 13 We do not include industry-and province-specific effects in Eqs. (2) and (3) because we estimate these equations using a fixed-effects estimator and these effects would be canceled out through the differencing process. Furthermore, industry-specific business cycle effects do not appear in Eqs. (2) and (3) because some of the dummies take on the value 1 for all observations in a cluster, and 0 otherwise (a singleton indicator). This causes singular outer-product-of-gradients (OPG) variance matrices in computing the robust standard errors, which therefore makes it impossible to compute an F-statistic for the overall fit of the model. 14 The key variables in Eqs. (2) and (3) (unexpected investment and free cash flow) are constructed using the residuals from the estimation of Eq. (1). For this reason, they can be considered as exogenous, which justifies the use of a fixed effects estimator. 15 See Tables A1 and A2 in Appendix A for details on the structure of our sample. Around 18% of firms have the full 17-year observations. Our panel is unbalanced, allowing for both entry and exit. This can be seen as evidence of dynamism and may reduce potential selection and survivor bias.

Initial summary statistics
In order to study the relationship between abnormal (under-or over-) investment and free cash flow, we partition firm-years into 4 sub-groups: Group 1 (under-investing firms with negative FCF), Group 2 (under-investing firms with positive FCF), Group 3 (over-investing firms with positive FCF), and Group 4 (over-investing firms with negative FCF). These groups are illustrated in Fig. 2. Means and medians for the entire sample and four sub-samples based on their abnormal investment and free cash flow are presented in Table 1.
It can be seen that relative to total assets, the average total investment and new investment expenditure in our sample are respectively 5.8% and 2.8%. This suggests that new investment represents a large portion of total investment (around 50%). Moreover, the average free cash flow for all firm-years observations is −0.01. This small value might suggest that listed firms in China are short of free cash flow, which could be due to financial constraints.
Interestingly, the total new investment for Group 2 (under-investing firms with positive FCF) is negative. This happens because the depreciation plus amortization of firms in this group exceeds their total investment. Depreciation and amortization can be  Notes: Firms are classified into four groups according their level of abnormal investment and FCF (free cash flow): G1 (under-investing firms with negative FCF); G2 (under-investing firms with positive FCF); G3 (over-investing firms with positive FCF); G4 (over-investing firms with negative FCF). Total investment (I_total i,t ) is defined as capital expenditure less receipts from the sale of property, plant and equipment. I_new is total investment less investment to maintain existing assets in place. I e _new represents the expected investment expenditure in new positive NPV projects. I u _new represents the abnormal investment (under-or over-investment). FCF is free cash flow which is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). Cash is the ratio of the sum of cash and cash equivalents to total assets. Q is the market-to-book ratio. Size is the natural logarithm of total assets. Age is the number of years elapsed since the firm listed. ROA is the return on assets. Leverage is the ratio of the sum of short-and long-term debt to total assets. All investment expenditure variables are scaled by total assets. All variables except Age are deflated using the GDP deflator. See Appendix A for complete definitions of all variables. Diff is the p-value associated with the t-test and the Wilcoxon rank-sum test for differences in means and equality of medians of corresponding variables between firms in G1 and those in G3. *** indicates significance at the 1% level.
considered as non-cash expenses: if firms are profitable, they might accelerate depreciation and amortization in order to reduce reported profits. Coming to unexpected investment and free cash flow, we observe that firms in Group 1 (under-investing firms with negative FCF) have the highest negative unexpected investment and negative free cash flow, which is in line with the hypothesis according to which, due to financial constraints, firms with negative FCF tend to under-invest. As for firms in Group 3 (over-investing firms with positive FCF), they have the second highest positive unexpected investment and the highest free cash flow, which is in line with the hypothesis according to which firms with positive FCF tend to over-invest due to agency costs.
As for other financial and operating variables, the statistics show that compared to firms in other groups, firms in Group 1 (under-investing firms with negative FCF) are relatively younger, smaller, and have lower ROA and high cash reserves. This could suggest the presence of financial constraints. On the other hand, firms in Group 3 (over-investing firms with positive FCF) are relatively mature, large, and have high Tobin's Q, which might suggest higher agency problems. 16 Finally, it is interesting to note that the number of firm-years in Group 1 (6355 observations) is larger than that in Group 3 (3785 observations), suggesting that there are more firms facing financial constraints than firms susceptible to agency problems. Table 2 presents the key results from the estimation of the relationship between under-and over-investment and negative/ positive free cash flow obtained using the fixed effects estimator (Eq. (2)). Columns 1 and 2 are based on estimates of I u _new i,t obtained by estimating Eq. (1) with system GMM. We observe that the free cash flow coefficients are only significantly positive (at the 1% level) for the under-investing firms with negative free cash flow, which are more likely to suffer from financing constraints (Group 1, column 1); and the over-investing firms with positive free cash flow, which are more likely to suffer from agency problems (Group 3, column 2). These findings support our hypotheses H1 and H2. Similar results are found in columns 3 and 4, which are based on estimates of I u _new i,t obtained from fixed effects estimates of Eq. (1) . 17

Using a quantile estimator
To test the robustness of our results, we estimate Eq. (2) using a quantile estimator with fixed effects. Specifically, we run separate regressions for the 20th, 50th and 80th quantiles of the distribution of I u _new i,t , and differentiate the FCF coefficients across firms with negative and positive FCF. The advantage of using this estimator is that it enables us to examine how free cash flow influences firms' abnormal investment for firms with different levels of abnormal investment. The results, which are reported in columns 1 to 6 of Table 3, are in line with our prior findings: we observe a positive and significant relationship between free cash flow and abnormal investment, stronger for the under-investing firms with negative FCF and the over-investing firms with positive FCF.
More specifically, for under-investing firms, we observe a decreasing trend of the coefficients associated with FCF * Dum FCF b 0 when we move from the smallest quantile of abnormal investment (0.090) to the largest (0.033). This suggests that for firms with free cash flow below their optimal level, more under-investment goes hand in hand with higher FCF sensitivities.
For over-investing firms, we find evidence of an increasing trend for the coefficients associated with FCF * Dum FCF N 0 moving from the smallest quantile of abnormal investment (0.020) to the largest (0.061). This indicates that for firms with free cash flow above their optimal level, more over-investment is accompanied by higher FCF sensitivities. The p-values associated with the test for the equality of the free cash flow coefficients between firms with positive and negative FCF show that these differences are generally significant. This confirms the robustness of our previous results.

Alternative ways of identifying under-/over-investing firms
Bergstresser (2006) notes that the distinction between under-investment and over-investment based on Richardson's (2006) approach might have some flaws as, in a dynamic setting, ex-post abnormal investment may follow ex-ante abnormal investment, causing mean reversion. To take this problem into account, as a further robustness test, predicted abnormal investment is obtained using the fitted values from the model in Eq. (1) estimated in each year using OLS. The results, reported in columns 7 and 8 of Table 3, are consistent with our prior findings: positive and significant coefficients on free cash flow are observed only for underinvesting firms with negative FCF and over-investing firms with positive FCF.
Alternatively, we rank the values of firms' abnormal investment (I u _new i,t ) by magnitude within each industry and year, and classify a firm as under-investing (over-investing) when its abnormal investment lies below (above) the median of the distribution. The results, reported in columns 9 and 10 of Table 3, confirm once again our hypotheses. 16 The p-values associated with the t-test and the Wilcoxon rank-sum test show significant differences in these variables between firms in Group 1 and those in Group 3. 17 With the exception of columns 2 and 4, the p-values associated with the Wald tests show significant differences in the free cash flow coefficients between firms facing negative and positive FCF. Yet, in columns 2 and 4, only the coefficient associated with FCF interacted with the dummy for FCF N 0 is statistically significant.
Finally, we use the approach proposed by Bates (2005) to compute under-and over-investment and free cash flow. Following this approach, we compute the abnormal investment for a given firm in a given year (I u' _new i,t ) as the difference between the firm's new investment expenditure (I_new i,t ) and the industry median level of new investment (I_new j,t ) in that year. This difference (I u′ _new i,t ) can be Notes: All specifications were estimated using the fixed effects estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. The dependent variable is unexpected investment (I u _new i,t ) calculated adopting Richardson's (2006) method, where over-investing (under-investing) firms are characterized by positive (negative) abnormal investment (I u _new i,t ). FCF is free cash flow which is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). Dum_FCF b0 is a dummy variable, which is equal to 1 in year t if a firm's free cash flow in that year is negative (FCF b 0), and 0 otherwise. Dum_FCF N0 is a dummy variable, which is equal to 1 in year t if a firm's free cash flow in that year is positive (FCF N 0), and 0 otherwise. Under_gmm (Over_gmm) and Under_fe (Over_fe) refer to abnormal investment obtained by estimating Eq. (1) using the system GMM and the fixed effects estimator, respectively (see Table A3 in Appendix A). Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients for firms facing positive and negative FCF. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. Notes: The specifications in columns 1 to 6 were estimated using the quantile estimator with fixed effects, and those in columns 7 to 10, using the fixed effects estimator. For the quantile regression, we run separate regressions for the 20th, 50th, 80th quantiles of abnormal investment with bootstrapped standard errors (1000 repetitions). Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. The dependent variable is unexpected investment (I u _new i,t ) calculated using Richardson's (2006) method, where in columns 1 to 6, under-investing (over-investing) firms are characterized by negative (positive) abnormal investment (I u _new i,t ). In columns 7 and 8, under-/over-investment are obtained from the estimation of Eq (1) separately in each year using OLS. In columns 9 and 10, we define under-investment (over-investment) when in a given year, firm i's abnormal investment is below (above) the median value of the distribution of the abnormal investment of all firms belonging to the same industry as firm i in that year. FCF is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). Dum_FCF b0 is a dummy variable, which is equal to 1 in year t if a firm's free cash flow in that year is negative (FCF b 0), and 0 otherwise. Dum_FCF N0 is a dummy variable, which is equal to 1 in year t if a firm's free cash flow in that year is positive (FCF N 0), and 0 otherwise. For the fixed effects regression in columns 7 to 10, ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients for firms facing positive and negative FCF. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. either positive or negative, corresponding respectively to over-investment or under-investment. 18 As for free cash flow (FCF′), we compute it as the difference between cash flow generated from assets in place (CF AIP,i,t ) for a given firm in a given year and the industry median level of cash flow generated from assets in place in that year (CF AIP,j,t ). 19 Accordingly, FCF′ can be either positive or negative.
To examine the relationship between these alternative measures of (under-or over-) investment and free cash flow, we estimate the following dynamic variant of Eq. (1), where Dum FCF' N 0 (Dum FCF' b 0 ) is a dummy equal to 1 if the firm has a positive (negative) FCF' i,t , and 0 otherwise: 18 As the expected investment estimate based on Bates' method (2005) is an out-of-sample estimate in a group of peer companies, this can tackle the concern that the expected investment based on Richardson's (2006) method might be endogenous. If measuring abnormal investment using both methods delivers similar results, we can conclude that our main results based on Richardson's (2006) model are not driven by endogeneity. 19 CF AIP,i,t is calculated as (CFO i,t − I_main .i,t ). Notes: All specifications were estimated using the system GMM estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. Adopting Bates' (2005) method, the dependent variable is I u′ _new i,t , the difference between a firm's new investment expenditure (I_new i,t ) in a given year and that of the median firm in the industry in which the firm operates (I_new j , t ) in that year. Under-investing (over-investing) firms are characterized by negative (positive) abnormal investment (I u′ _new i,t ). FCF′ i,t is calculated as the difference between the firm's cash flow generated from assets in place in a given year (CF AIP,i,t ) and that of the median firm in the industry in which the firm operates in that year (CF AIP,j,t. ). Dum_FCF' b0 is a dummy variable, which is equal to 1 in a given year if a firm's CF AIP,i,t is below its optimal level (proxied by the firm's industry's median CF AIP,j,t ), and 0 otherwise. Dum_FCF' N0 is a dummy variable, which is equal to 1 in a given year if a firm's CF AIP,i,t exceeds its optimal level (i.e. the median of the firm's industry's CF AIP,j,t. ), and 0 otherwise. All variables except Q i,t − 1, Size i,t − 1 and Age i,t are scaled by total assets. We treat I u′ _new , FCF′, Cash , Q, Size , ROA, and Leverage i,t as potentially endogenous variables. Levels of these variables lagged twice or more are used as instruments in the first-differenced equations and first-differences of these same variables lagged once, as additional instruments in the level equations. m2 is a test for second-order serial correlation of the residuals in the differenced equations, asymptotically distributed as N(0,1) under the null of no serial correlation. The Hansen J test of over-identifying restrictions is distributed as Chi-square under the null of instrument validity. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients for firms facing positive and negative FCF′. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. We use the system GMM approach  to estimate Eq. (4), accounting for the possible endogeneity of the regressors, as well as for firm-specific and time-invariant heterogeneity. The results are reported in Table 4. In line with our previous findings, they show that the impact of free cash flow on under-investment is only significantly positive for the firms with negative FCF′ i,t (column 1), while the impact of fee cash flow on over-investment is only significant for firms with positive FCF′ i,t (column 2).
In summary, we have constructed measures of under-and over-investment and free cash flow, and generally found a positive and significant relationship between investment and free cash flow only for Group 1 firms (under-investing firms with negative FCF) and Group 3 firms (over-investing firms with positive FCF). We interpreted these findings as evidence in favor of the financing constraints (FC) and agency costs (AC) hypotheses, respectively. We next dig deeper into these interpretations by analyzing these sensitivities for firms facing higher/lower degrees of financing constraints and agency costs, measured using a variety of different criteria. We now provide further tests of the financing constraints hypothesis of under-investment. To this end, we restrict our sample to under-investing observations, and use two indexes to measure firm-specific levels of the constraints: the Kaplan and Zingales (KZ) index (Lamont et al., 2001) and the Whited and Wu (WW) index (Whited and Wu, 2006).
Focusing on the former, we note that Kaplan and Zingales (1997) classify their sample of US firms into five groups on the basis of their degree of financial constraints based on qualitative information contained in the firms' annual reports, as well as quantitative information regarding management's statements on liquidity. Motivated by Kaplan and Zingales (1997), Lamont et al. (2001) perform an ordered Logit estimation of the categories of constraints on the following five financial ratios, using the original KZ sample: cash flow (CF t , net income + depreciation), dividends (DIV t ), cash and cash equivalents (Cash t ) all deflated by beginning of year capital (K t − 1 ); Tobin's Q (Q t , market value of equity + market value of net debt)/(total assets − net intangible assets)); and debt (Debt t , the sum of the short-term and long-term debt) to total capital (TK t , sum of debt and equity). We use the estimated coefficients that they obtain to construct the Kaplan and Zingales (KZ) index of financial constraints in the following way: A firm with a higher value of the KZ index can be intended to be more financially constrained. We also use an alternative index of constraints (the WW index), constructed by Whited and Wu (2006). This index is a linear function of the following six observable firm characteristics: cash flow [CF t /BA t − 1 , (net income + depreciation)/beginning-ofyear book assets]; a dividend indicator (DIVPOS t, indicating positive dividends); long-term debt (TLTD t /CA t − 1 , long-term debt Notes: KZ and WW represent firm-specific levels of financial constraints: the Kaplan and Zingales (KZ) index (Lamont et al., 2001) and the Whited and Wu (WW) index (Whited and Wu, 2006). Firms are classified into the following four groups: Group 1 (under-investing firms with negative FCF); Group 2 (under-investing firms with positive FCF); Group 3 (over-investing firms with positive FCF); Group 4 (over-investing firms with negative FCF). P25 (50/75) is the 25th (50th/75th) percentile of the respective distribution. Diff is the p-value associated with the t-test and the Wilcoxon rank-sum test for differences in means and equality of medians of the KZ (WW) indexes between groups of under-investing firms (Group 1 and Group 2) or between groups of over-investing firms (Group 3 and Group 4 ). ** and *** indicate significance at the 5% and 1% levels, respectively.
to total current assets); Tobin's Q (Q t ); size (LNTA t , natural log of the book value of assets); firm real sales growth (SGR t ); and industry sales growth (ISG t ). We compute the WW index as follows, using the estimated coefficients from Whited and Wu's (2006) specification: Once again, a higher value of the WW index is representative of a higher level of financial constraints. Table 5 presents summary statistics of the two firm-specific indexes of financing constraints across the four groups of firms based on their abnormal investment and free cash flow. We conduct statistical tests for equality of both sample means (t-test) and sample medians (Wilcoxon rank-sum test) across groups of firms.
According to the financial constraints (FC) hypothesis, firms are more likely to under-invest if they face a higher degree of financing constraints. To test this hypothesis, we compare the two indexes across under-investing firms in Group 1 and Group 2. We find that, regardless of whether we use the mean or the median, the level of financial constraints (measured using both the KZ and WW indexes) for Group 1 (under-investing firms with negative FCF) is larger than that for Group 2 (under-investing firms with positive FCF). As can be seen from the p-values of both tests, the differences in the means and the medians of the indicators between the two groups are generally significant at the 5% level. This suggests that differences in the financial constraints faced by firms are a key factor in distinguishing between the firms in Group 1 and Group 2. Thus, as discussed in the former section, financial constraints may contribute to the higher responsiveness of under-investment to free cash flow for the firms in Group 1.
In order to investigate the extent to which the degree of financial constraints faced by firms affects the sensitivity of underinvestment to free cash flow, Table 6 presents fixed effects estimates of Eq. (3), which tests the effects of free cash flow on under-investment for firms characterized by different degrees of financial constraints, calculated using the KZ index (columns 1 and 2) and the WW index (columns 3 and 4). In columns 1 and 3, following Almeida et al. (2004), we classify firms as facing relatively low (Low_FC = 1), medium (Medium_FC = 1), and high (High_FC = 1) financial constraints in a given year if their KZ or WW index in that year fall respectively in the bottom three, the middle four, and the top three deciles of the distribution Table 6 Under-investment-free cash flow sensitivities: accounting for financial constraints using the KZ and WW indexes. Notes: All specifications were estimated using the fixed effects estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. The dependent variable is unexpected investment (I u _new i,t ) calculated adopting Richardson's (2006) method, where under-investing firms are characterized by negative abnormal investment (I u _new i,t ). FCF i,t is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). High_FC, Medium_FC and Low_FC are dummy variables, equal to 1 in a given year if a firm faces high, medium, or low financial constraints, and 0 otherwise. Specifically, in columns 1 and 3, we consider a firm to be financially constrained (unconstrained) in a given year if its KZ or WW index lies in the top (bottom) three deciles of the distribution of the corresponding variables for all firms belonging to the same industry in that year. The remaining firm-years will be the ones who face a medium level of financial constraints. In columns 2 and 4, a firm is considered to be financially constrained in a given year if its KZ or WW index exceeds the median value of the index calculated in the industry the firm belongs to in that year, and financially unconstrained otherwise. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients across firms characterized by high and low financing constraints. ** and *** indicate significance at the 5% and 1% levels, respectively.
of the indexes of all firms operating in the same industry they belong to. 20 In this way, we allow firms in our sample to transit between categories each year. In columns 2 and 4, we use a 50% threshold. Columns 1 and 3 reveal that for under-investing firms, the higher the KZ index or the WW index, the larger the sensitivities of under-investment to free cash flow. This suggests that sensitivities of abnormal investment to free cash flow tend to increase monotonically with the degree of external financial constraints faced by firms. Similar results are found in columns 2 and 4 when we use a 50% threshold. The p-values of the Wald tests reported at the foot of the Table reject the equality of the coefficients of free cash flow between more and less financially constrained groups. This supports our hypothesis H1: for underinvesting firms, the sensitivities of investment to free cash flow increase with the firm's degree of financial constraints. 21 7.1.2. Further tests: measuring financing constraints using size and age Next, we use different variables based on the a priori likelihood that a firm faces financial constraints to test our Hypothesis 1. If our hypothesis holds, we should expect a stronger relationship between under-investment and free cash flow for firms which are a priori more likely to face financial constraints. Specifically, we focus on firms' size (total real assets) and age, which have been commonly used in the literature to partition firms into a priori more and less likely to face financing constraints. Small and young firms might not have a sufficiently long track record, leading to increased asymmetric information. In addition, small and young firms are typically characterized by high idiosyncratic risk and high bankruptcy costs, which might exclude them from credit markets, or make their access to external finance more costly (Beck et al., 2005;Clementi and Hopenhayn, 2006;Gertler and Gilchrist, 1994;Guariglia, 2008).
The results are reported in Table 7. In columns 1 and 3, we define a firm as facing a high level of financing constraints (High_FC = 1) in a given year if its size (column 1) and age (column 3) fall in the bottom three deciles of the distribution of the assets/age of all firms operating in the same industry as that firm in that year. Similarly, we define as firm-years facing a medium level of financing constraints (Medium_FC = 1) those observations falling in the middle four deciles of the distribution, and as firm-years facing a low level of financing constraints (Low_FC = 1), those observations falling in the top three deciles of the distribution. In columns 2 and 4, we only consider two categories of firm-years: those facing high and low financing constraints, split at the median of real assets (column 2) and age (column 4).
The results in column 1 show a clear increasing trend for the coefficients of free cash flow, moving from large, to mediumsized, to small firms. The Wald test reported at the foot of the table shows that the differences in the FCF coefficients between large and small firm-years are significant at the 1% level. Hence, using firm size as a proxy for financing constraints also supports our Hypothesis 1. Similar results are obtained when firms are split in two size categories (column 2), and when age is used as a partitioning criterion (columns 3 and 4). 22 In summary, the results we obtained using conventional variables as proxies for financial constraints, which suggests that for under-investing firms, the sensitivities of investment to free cash flow increase with the firm's degree of financial constraints faced by firms, are highly consistent with our previous findings and Hypothesis 1.

The agency costs (AC) hypothesis of over-investment
7.2.1. Measuring agency costs using the ratio of other receivables to total assets and the difference between the blockholder's controlling and ownership rights We now move on to testing the agency costs (AC) hypothesis of over-investment. To this end, we focus on over-investing observations. It has been argued that the conflict between controlling shareholders and minority investors (tunneling) is widespread in emerging markets like China since most listed companies tend to have a concentrated ownership structure. 23 In addition, corporate governance mechanisms and the legal system in China offer few options to protect minority shareholders from controlling shareholders (Jiang et al., 2010;Liu and Lu, 2007).
Our initial measures of agency costs emphasize therefore the conflict between controlling shareholders and minority investors. Specifically, following Jiang et al. (2010), we first use the ratio of other receivables to total assets (OREC) to measure how likely controlling shareholders are of expropriating minority investors. 24 A higher value of OREC implies a higher level of expropriation and, hence, a higher level of agency costs. Average other receivables in our sample constitute about 4% of total assets, and the maximum value of the ratio is around 50%, suggesting a high level of agency costs.
Next, inspired by Claessens et al. (2002), Lemmon and Lins (2003), and Jiang et al. (2010), we proxy the likelihood to tunnel using a dummy equal to 1 if the firm exhibits a difference between its largest shareholder's (also known as blockholder) controlling right 20 It is worth mentioning that we do not mean that firms ranked in the top three deciles of the distribution of the KZ and WW indexes are absolutely financially constrained, while firms in the bottom three deciles are absolutely financially unconstrained. Instead, we argue that those firms in the top three deciles are likely to face more severe financing constraints than those in the bottom three deciles. 21 Estimating similar regressions on the sample of over-investing firms delivered similar coefficients across the groups of firms characterized by different degrees of financing constraints. These results, which are not reported for brevity but available on request, confirm that the FC hypothesis is unlikely to hold for over-investing firms. 22 Yet, in column 3, the Wald test shows that the difference in the FCF coefficients between older and younger firm-years is not statistically significant. 23 In China, the ownership of a single dominant shareholder is typically much larger than that of the second shareholder. 24 According to Jiang et al. (2010), "during 1996-2006, tens of billions of RMB were siphoned [through inter-corporate loans] from hundreds of Chinese listed firms by controlling shareholders" (p.2). The authors explain that these inter-corporate loans are typically reported as "other receivables". This variable is also used by Quian and Yeung (2015).
(C) and cash flow ownership right (O), and 0 otherwise. In the presence of a divergence between her/his controlling right and ownership right, the blockholder may control the firm by only holding a relatively low proportion of shares. This is made possible through pyramid structures and cross-holding among firms, which often lead to the expropriation of minority shareholders. Notes: All specifications were estimated using the fixed effects estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. The dependent variable is unexpected investment (I u _new i,t ) calculated adopting Richardson's method (2006), where under-investing firms are characterized by negative abnormal investment (I u _new i,t ). FCF i,t is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). Low_FC, Medium_FC, and High_FC are dummy variables equal to 1 in a given year, respectively, if the firm is likely to face low, medium, and high financial constraints relatively to all firms operating in the same industry it belongs to in that year, and 0 otherwise. Specifically, in columns 1 and 3, we consider a firm facing low (high) financial constraints in a given year if its size (real total assets) and age respectively lie in the top (bottom) three deciles of the distribution of the corresponding variables for all firms belonging to the same industry in that year. The remaining firm-years will be the ones who face a medium level of financial constraints. In columns 2 and 4, we consider a firm facing low (high) financial constraints in a given year if its size and age respectively lie in the bottom (top) half of the distribution of the corresponding variables of all firms belonging to the same industry in that year. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients across firms characterized by high and low financing constraints. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. Notes: OREC (other receivable scaled by total assets) and C/O (dummy equal to 1 if the firm exhibits a divergence between controlling and ownership rights, and 0 otherwise) represent firm-specific levels of agency costs. Firms are classified into the following four groups: Group 1 (under-investing firms with negative FCF); Group 2 (under-investing firms with positive FCF); Group 3 (over-investing firms with positive FCF); Group 4 (over-investing firms with negative FCF). P25 (50/75) is the 25th (50th/75th) percentile of the distribution of the relevant variable. Diff is the p-value associated with the t-test and the Wilcoxon rank-sum test for differences in means and equality of medians of the firm-level agency costs between groups of under-investing firms (Group 1 and Group 2) or between groups of over-investing firms (Group 3 and Group 4). * and *** indicate significance at the 10%, and 1% levels, respectively. Table 8 presents summary statistics of our two firm-specific indicators of agency costs after we categorize firms into the four groups based on their abnormal investments and free cash flow. As in Table 5, we conduct statistical tests for the equality of both sample means (t-test) and sample medians (Wilcoxon rank-sum test) across groups.
Comparing Group 3 (over-investing firms with positive FCF) with Group 4 (over-investing firms with negative FCF), we observe that the mean level of agency costs measured by both OREC and the percentage of firm-year observations exhibiting a difference between the blockholder's controlling and ownership rights (C/O) are higher for the former group. As for the median, it is higher for Group 3 when we focus on OREC, but equal to 0 for both groups of firms when we focus on C/O . 25 These statistics suggest that firms in Group 3 suffer from higher agency costs than those in Group 4. This is not surprising as these firms dispose of a higher FCF, which they can use for tunneling purposes.
To explore this issue further, Table 9 presents the fixed effects estimates of Eq. (3), aimed at testing the effects of changes in free cash flow on over-investment for firms characterized by different levels of agency costs measured using OREC (columns 1 and 2) and C/O (columns 3). Specifically, in column 1, we classify a firm as facing relatively low (Low_AC = 1), medium (Medium_AC = 1), or high (High_AC = 1) agency costs in a given year if its OREC ratio in that year falls respectively in the bottom three, the middle four, or the top three deciles of the corresponding OREC ratios of all firms operating in the same industry the firm belongs to in that year. In column 2, we use a 50% threshold. In both cases, we observe that the sensitivity of investment to free cash flow is positive and significant at the 5% level or higher only for firms with a high degree of agency costs.
In column 3, we define a firm as facing high (low) agency costs in a given year if it exhibits (does not exhibit) a divergence between its blockholder's controlling ownership and cash flow ownership. Only those firms characterized by a divergence exhibit Table 9 Over-investment-free cash flow sensitivities: accounting for agency costs using OREC and C/O. Notes: All specifications were estimated using the fixed effects estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. The dependent variable is unexpected investment (I u _new i,t ) calculated adopting Richardson's method (2006), where over-investing firms are characterized by positive abnormal investment (I u _new i,t ). FCF i,t is computed by subtracting the optimal level of cash flow from operating activities (CFO). High_AC, Medium_AC and Low_AC are dummy variables, equal to 1 in a given year if a firm faces respectively high, medium, and low agency costs compared to all firms belonging to the same industry it belongs to, and 0 otherwise. Specifically, in column 1, we define a firm as facing high (low) agency costs in a given year if its OREC lies in the top (bottom) three deciles of the distribution of the ORECs of all firms operating in its same industry in that year. The remaining firm-years will be the ones who face a medium level of agency costs. As for column 2, a firm is considered as facing high (low) agency costs in a given year if its OREC exceeds (is below) the median value of the distribution of the ORECs of all firms operating in the same industry it belongs to in that year. In column 3, a firm is considered as facing high (low) agency costs in a given year if its blockholder's controlling right exceeds (does not exceed) its cash flow right in a given year. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients across firms characterized by high and low agency costs. *, **, and *** indicate significance at the 10%, 5%, and 1% levels, respectively. a positive and significant sensitivity of over-investment to free cash flow. 26 We can therefore conclude that our results generally provide further support to the agency costs (AC) hypothesis. 27

Further tests: measuring agency costs using blockholder's and CEO shareholding
To better understand the extent to which agency costs matter for the sensitivity of abnormal investment to free cash flow, in this section, we verify whether our results are robust to partitioning firms on the basis of other variables which have been used in the literature to proxy for the presence of agency problems (Ang et al., 2000;Jiang et al., 2010).
Our first alternative measure focuses on the percentage of shares controlled by the largest shareholder (Blockholder i,t ). It has been argued that concentrated ownership is positively associated with firms' agency costs. As mentioned earlier, agency costs arising from the conflict of interest between the controlling shareholder and minority investors, may become apparent when the controlling shareholder extracts private benefits from minority shareholders (tunneling). The ability of the primary owner to expropriate minority investors is expected to increase with his/her ownership. When the interests of the controlling shareholder are not aligned with those of other investors, there is in fact good reason to believe that the former may use his/her power to influence the firm's investment decisions to promote his/her interests at the expense of minority shareholders. Therefore, a high concentration of ownership at the firm level may indicates a strong incentive to tunnel and a high level of agency costs (Liu and Lu, 2007). 26 It should be noted, however, that the Wald tests do not reject the equality of the coefficients of free cash flow between firms with high and low agency costs. 27 Estimating similar regressions on the sample of under-investing firms delivered similar coefficients across the groups of firms characterized by different levels of agency costs. These results, which are not reported for brevity but available on request, confirm that the AC hypothesis is unlikely to hold for under-investing firms. Notes: All specifications were estimated using the fixed effects estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. The dependent variable is unexpected investment (I u _new i,t ) calculated adopting Richardson's (2006) method, where over-investing firms are characterized by positive abnormal investment (I u _new i,t ). FCF i,t is computed by subtracting the optimal level of cash flow from cash flow from operating activities (CFO). Blockhoder is the percentage of shares controlled by the largest shareholder. High_Share (Low_Share) is a dummy variable equal to 1 in a given year if the percentage of shares controlled by the blockholder in a given firm lies in the top (bottom) three deciles of the distribution of the corresponding percentage of all firms operating in the same industry in that year, and 0 otherwise. For the remaining firm-years, the dummy Medium_Share will be equal to 1. In the column labeled Shareholding_CEO, Insider(Outsider) is a dummy variable that takes the value of 1 if the firm's CEO is (is not) holding shares in his/her own company, and 0 otherwise. Diff is the p-value of the Wald statistic for the equality of the free cash flow coefficients across various categories of firms. ** and *** indicate significance at the, 5% and 1% levels, respectively.
However, as discussed in the previous sub-section, primary owners in China, often have rather large power to control the company's operation even by only holding a relatively low stake of shares, through pyramid structures and cross-holding among firms. When the primary owner's controlling right is greater than his/her ownership right, he/she tends to derive more benefits from tunneling activities. Thus, a lower incentive to tunnel, and lower agency costs are expected when the highest percentage of shares is held by the primary owner (Jiang et al., 2010). Additionally, investors with a large ownership stake generally have a strong interest in the firm's profit maximization and have a higher incentive to oversee or monitor the manager. Hence, agency costs intended as the conflict between firm managers and shareholders, tend to decline with the ownership stake of controlling shareholders (Ang et al., 2000;Jensen and Meckling, 1976). The ownership stake of the controlling shareholder is therefore definitely an important determinant of the overall agency costs faced by the firm, but whether it affects these agency costs positively or negatively is ambiguous.
In order to test the extent to which the blockolder's shareholding affects the sensitivity of over-investment to free cash flow, we construct the dummies Low_share i,t , Medium_share i,t , and High_share i,t , which are in turn equal to 1 if the blockolder's shareholding of firm i in year t lies in the bottom three, the middle four, and the top three deciles of the distribution of the corresponding shareholding of all firms operating in the same industry as firm i in year t, and 0 otherwise. We then interact these dummies with free cash flow and examine the coefficients of the interaction terms in our over-investment regressions.
The results are reported in column 1 of Table 10. Interestingly, we observe that the coefficient associated with free cash flow is the largest for the medium shareholding category. This suggests that, the sensitivity of over-investment to FCF initially increases with the shares held by the largest shareholder, then decreases. 28 These differences between categories can be explained considering that, as previously discussed, there are arguments both in favor and against a positive relationship between the percentage of shares controlled by the largest shareholder and agency problems. This finding is in line with Jiang et al. (2010), according to which agency costs indicated by tunneling are highest when the largest shareholder owns a medium percentage (30%) of the firm's shares.
Our next measure of agency costs is motivated by international evidence that agency costs may arise when managerial interests are not in line with those of the firm's shareholders. Managerial ownership tends to relieve principal-agent problems between (outside) shareholders and managers. Thus, agency costs arising from the conflict of interest between managers and shareholders should be lower at firms managed by a shareholder. 29 In order to test whether this is the case, we construct a dummy variable Insider i,t (Outsider i,t ), which is equal to one if a firm is managed by a shareholder (outsider), and 0 otherwise. Specifically, if the top executives, including the CEO, are holding any of their own shares, they will be considered as insiders. We then interact free cash flow with the Insider i,t and Outsider i,t dummies and examine the differences in the coefficients associated with the two interaction terms in our over-investment regressions.
The results appear in column 2 of Table 10. We observe that only the sensitivity of over-investment to free cash flow of firms managed by an outsider is statistically significant. This can be explained considering that outside managers may not have closely aligned interests with the firm's shareholders and suggests that managerial ownership is negatively associated with the firm's principal-agent problems. 30 Thus, for over-investing firms, agency problems between entrenched managers and shareholders can explain the statistically significant sensitivity of over-investment to free cash flow.
In summary, the findings in Table 10 are strongly aligned with our previous results and hypothesis H2: The sensitivity of abnormal investment to free cash flow rises with the degree of agency costs faced by over-investing firms.

Conclusions
In this paper, we provide a portrait of the nature and balance of financial constraints and agency problems in China, giving a picture of the extent to which the economy has suffered from efficiency losses due to both under-and over-investment. Two significant conclusions emerge from our main findings: On the one hand, the limited access to capital markets which characterizes many Chinese firms leads to significant under-investment. On the other hand, the weak corporate governance structures lead managers or controlling shareholders to over-invest their free cash flow in projects with negative NPV.
The identification of financial constraints and agency problems as explanations for under-and over-investment suggests that in order to improve investment efficiency in China, both the financial and the legal system need to be reformed. In particular, since China's financial system is still dominated by under-developed state-owned banks, in order to sustain the rapid growth of the Chinese economy, especially in the private sector, more widespread access to credit markets should be a priority in order to increase firms' investment efficiency. In the long run, the establishment of an effective credit-rating system and the development of equity finance could be a way to achieve this target. 28 It should also be noted that only the interaction between FCF and the dummy equal to 1 for medium shareholding is statistically significant. Yet, the p-values associated with the Wald tests cannot reject the equality of the impact of free cash flow on over-investment between firms characterized by different percentages of shares owned by the largest shareholders. 29 This can be explained considering that inside managers may have interests more closely aligned with the firm's shareholders. Jensen and Meckling (1976) propose a hypothesis of convergence of interests between shareholders and managers, and improvement of corporate performance as managerial ownership increases. Kren and Kerr (1997), Ang et al. (2000), Singh and Davidson III (2003), and McKnight and Weir (2009) also provide support for the argument that managerial ownership reduces agency costs. 30 In our sample, there is often separation between management and ownership. In addition, those few managers who are also shareholders in their company only hold a small percentage of their own shares. Relative low ownership stakes prevent managers from pursuing their own interests at the expense of shareholders, as they are supervised and controlled by the board, as well as by capital markets.
In addition, considering that China's listed firms are still dominated by state shareholders, a further reduction in state ownership may need to be carried out to reduce conflicts of interest between controlling shareholders and minority shareholders, and to increase the intensity of monitoring by other shareholders or independent institutions. This is particularly important at the local level. Imposing constraints or more restrictive regulations to local government bureaucrats to prevent them from making adverse decisions such as expropriation and misappropriation of funds, which ultimately lead to over-investment, should therefore be on the political agenda.
Positive steps in both directions have already been taken. With regards to financing constraints, the recent reforms to the financial system documented in Borst and Lardy (2015) are likely to have played an important role in making finance more accessible, to the extent that Lardy (2014) documents a significant increase in the flow of loans to the previously financially discriminated against private sector in recent years. Focusing on agency costs, Cumming et al. (2012) and Hou et al. (2012) argue that the 2005 split share structure reform, which allowed restricted shares held mainly by state shareholders to become tradable, and permitted equity-based compensation for executives or directors, enhanced the incentives of controlling state shareholders to monitor managers, ensuring they were disciplined against opportunistic behavior and refrained from the expropriation of minority shareholders. 31 Yet, despite these positive steps, more work needs to be done to completely eradicate investment inefficiency from the Chinese economy. To this end, the economic reforms first outlined by the Communist Party Central Committee's Third Plenum in late 2013, and aimed at enhancing the market's role in allocating resources, while making SOEs more efficient, are fundamentally important. These reforms will enable China to smoothly transit from a fast-growing economy, reliant on (often excessive) investment in heavy industry and cheap manufacturing exports, to a "new normal" model of development, characterized by better quality and slower growth (Green and Stern, 2015). This will translate itself into higher efficiency, and a move away from heavyindustrial investment and toward domestic consumption, particularly of services.  190 19,190 Notes: Estimates in column 1 were obtained using the fixed effects estimator. Estimates in column 2 were obtained using the system GMM estimator. Test statistics and standard errors (in parentheses) of all variables in the regressions are asymptotically robust to heteroscedasticity. Adopting Richardson's (2006) method, the dependent variable is I_new i,t , the difference between I total and I main . (see Fig. 1 for definitions of these variables). All variables except Q i,t − 1 , Size i,t − 1 and Age i,t are scaled by total assets. For the fixed effects regression, ρ represents the proportion of the total error variance accounted for by unobserved heterogeneity. For the system GMM regression, m3 is a test for third-order serial correlation of the differenced residuals, asymptotically distributed as N(0,1) under the null of no serial correlation. The Hansen J test of over-identifying restrictions is distributed as Chi-square under the null of instrument validity. We treat I_new i,t − 1 , Cash i,t − 1, Q i,t − 1 , Size i,t − 1, ROA i,t − 1 and Leverage i,t − 1 as potentially endogenous variables. Levels of these variables dated t − 3 and further are used as instruments in the first-differenced equations and first-differences of these same variables lagged twice are used as additional instruments in the level equations. ** and *** indicate significance at the 5% and 1% levels, respectively.