To examine the relationship between external financing and cash flow under financial restrictions, researches have used different methods including ordinary least square, fixed effects, generalized method of moments, and instrumental variable approach. For example, Almeida & Campello (2010) and Gracia & Mira (2014) use ordinary least squares and generalized method of moments to measure the relation between external financing and cash flow. Frank & Goyal (2003) use panel regression approach to examine the external financing ) use generalized method of moments and ordinary least squares to study the empirical determinants of internal funds in the presence of financial constraints. We use fixed effects method to estimate Eq. (1). To take into account the problem of heteroskedasticity, we use robust standard errors.

## We do so to get preliminary insight regarding the relationship between external financing and cash flow for firms included in our analysis

The extended versions of external financing models presented in Eqs. (2) and (3) are dynamic in nature as they include the lagged dependent variable into the specification. The presence of the lagged dependent variable, EXTERNAL_FINANCING_{i, t ? 1}, in the set of explanatory variables may give rise to the problem of autocorrelation in the residuals. Further, the cash flow, the cash holding ratio, and the asset tangibility variables are likely to be endogenous because it is very likely that the causality may run in both directions – from these variables to external financing and vice versa. Thus, these variables may be correlated with the error term. Finally, our panel dataset has a short time dimension (T = 14) and a large firm dimension (N = 450). Because of these aspects, several econometric issues may arise from estimating the extended model of external financing. To over come these problems, we apply the two-step system GMM estimator.

Arellano & Bond (1991), Arellano & Bover (1995), and Blundell & Bond (1998) develop the GMM estimator for a dynamic panel data. As in Rashid & Waqar (2017), the GMM estimator is a suitable estimator for the case when (a) cross-sectional dimension is greater than time-series dimension, (b) the dependent variable is the function of its previous period realizations, (c) explanatory variables are endogenous in nature and likely to be correlated with the error term, (d) there is heteroskedasticity and autocorrelation in the individuals, and (e) researchers want to use different lags of level and first difference of the variables as the instruments. However, one should note that the reliability of the system GMM estimation results is highly conditional to the validity of the instruments. Hence, we apply the J test of Hansen (1982) for testing the validity of the instruments used in the estimation. We also apply the Arellano-Bond AR (2) test to observe the presence of the second-order serial correlation in the residuals.

## Empirical results

As the priine the relationship between external financing and cash flow for financially constrained and unconstrained firms, we classify firm-year observations into financially constrained and unconstrained groups. For this purpose, we utilize three different measures, namely, the KZ index, the debt to asset ratio, and the interest coverage ratio. The classification of firm-year observations is presented in Tables 2 and 3. The debt to asset ratio and KZ index yield almost similar classification of firm-year observations, whereas, the interest rate coverage ratio identifies higher number of firm-year observations as financially constraints https://onedayloan.net/payday-loans-ar/.

We start empirical examination of how external financing decisions of firms relate to cash flow by estimating Eq. (1) for the full sample (combining both financially constrained and unconstrained firms). The estimated coefficients are presented as follows; where the values in parentheses are standard errors. Following the previous studies on this topic, we estimate this model using the fixed effects method with robust standard errors.