Endogenous Financial Constraints and Innovation

We investigate which indicators of a firm’s innovation activities are associated with financial constraints and analyse the nature and direction of causal links between innovation and financial constraints. By estimating simultaneous bivariate probit models on data from the UK Innovation Surveys, we show that among innovation inputs, R&amp;D activity increases the likelihood that firms face financial constraints while innovation outputs in the form of new-to-market products seem to generate financial constraints. Reverse effects on innovation appear limited to external R&amp;D.


Introduction
Innovation is widely recognised as a fundamental driver of economic growth, but the pathways to innovation are complex and often hindered by the fundamentally uncertain nature of research and development processes and their market outcomes (Rosenberg, 1994). Access to capital can be a significant barrier to innovation because it reduces investments in its core inputs (e.g., R&D) which in turn may result in fewer new products and lower growth rates relative to the optimal case of frictionless capital markets (Hall and Lerner, 2010). By inducing risk and informational asymmetries into the relation between firms and investors, innovation can restrict the availability of finance when internal funds are not sufficient to sponsor R&D projects (Cosh et al., 2009). This problem acquired special relevance in the aftermath of the 2008 financial crisis, during which the more innovative firms (and young and small firms in particular) might have been hit especially hard by reduced availability or rising external cost of capital (OECD, 2009), a likely consequence of higher product market uncertainty and the stronger information asymmetries associated with it.
However, Kahle and Stulz's (2013) study of a large sample of public U.S. firms during the post-Lehman period casts doubt on the link between a shock in the supply of credit and firms' capital expenditures.
Despite a number of studies on the cash flow sensitivity of R&D investments (see, for example, Hall, 1992;Himmelberg and Petersen, 1994;Harhoff, 1998;Mulkay et al., 2000;Bond et al., 2005), the extent to and the way in which innovation activities of firms may exacerbate financial constraints are not sufficiently understood (Hall, 2010). The literature on financial constraints discusses the identification and nature of financial constraints (Fazzari et al., 1988(Fazzari et al., , 2000Kaplan andZingales, 1997, 2000;Carpenter et al., 1998;Cleary, 1999;Cleary et al., 2007;Hadlock and Pierce, 2010;Farre-Mensa and Ljungqvist, 2016) but tends to neglect the study of their determinants, particularly in the innovation domain: financial constraints are typically difficult to observe, and this often prevents their use as an outcome variable. Increasing recognition of the multidimensional nature of innovation calls for analytical approaches that focus not only on the role Electronic copy available at: https://ssrn.com/abstract=3316197 of innovation inputs (e.g., R&D) but also on the relationship between innovation outputs (e.g., new products or new production processes) and financial constraints. Some of these innovation outcomes have recently been related to financial constraints in cross-sectional studies (Hottenrott and Peters, 2012;Audretsch et al., 2014;Mancusi and Vezzulli, 2014;Lee et al., 2015). However, a comprehensive study of their relative importance of innovation inputs and outputs in determining and being determined by financial constraints is missing.
More importantly, the potential feedback loop between financial constraints and innovation must be taken into account. On the one hand, financial constraints can limit firms' engagement in risky R&D activities (Hall and Lerner, 2010); on the other hand, innovation can generate financial constraints through associated asymmetric information caused by the high costs and uncertainties generated in lengthy processes of R&D, testing, distribution and marketing (Scherer, 1999;. The existing literature either assumes exogeneity of financial constraints or employs indirect procedures, such as Heckman-type corrections or regression discontinuity designs, to estimate the treatment effect of financial constraints on innovation (Acharya and Xu, 2016).
However, a modelling approach that directly addresses the fundamental endogeneity problem in the relationship between firm financing and innovation is preferable, as endogeneity can have serious implications for the validity of empirical findings and consequently for the lessons that can be drawn from this body of evidence to inform policy.
In this paper, we investigate the link between financial constraints and innovation through multivariate longitudinal analyses of direct measures of a firm's financial constraints and innovation characteristics. We model firms' innovation-financing behaviours comprehensively and simultaneously along different dimensions of innovation, including inputs, processes and outputs, and not simply R&D. Our strategy is to treat financial constraints and innovation as a simultaneous dynamic system while accounting for unobserved firm-specific effects. We develop a set of simultaneous equations models, suited to the treatment of endogeneity, and apply them to UK Innovation Survey panel data available through the UK Office of National Statistics (ONS). These Electronic copy available at: https://ssrn.com/abstract=3316197 data contain a wealth of information on firm innovation activities that have not been used to date to address the problem of firm financing in a simultaneous setting. We also consider in our analysis small and non-listed firms. These are usually missing from studies of cash-flow sensitivities of investment, even though small and medium-size firms (SMEs) play a fundamental role in the dynamics of Schumpeterian creative destruction that characterise modern competitive processes (Schumpeter, 1942;Acs and Audretsch, 1990;Breschi et al., 2000;Aghion et al., 2013).
Our results suggest that innovating firms are more likely to experience financial constraints.
By considering a broad range of innovation indicators, we show that only some innovation inputs and outputs increase the likelihood that firms experience financial constraints. We further show that innovation outputs in the form of products that are new to the market cause financial constraints. In line with theory, effects of innovation on financial constraints are strongest where informationally opaque activities and uncertain market outcomes create a potential for severe agency conflicts. The reverse effect of financial constraints on the likelihood of innovation appears limited to external R&D activity that is not captured by formal R&D spending. While the literature has traditionally emphasised that financial constraints may prevent firms from innovating, we stress that the resource requirements of firms increase when they innovate. This implies that from a policy viewpoint attention should be paid not only to the costs of technological search, but also to the capital outlays required by the exploitation of innovation, which are often underestimated.
First, we investigate the relative importance of a broad range of indicators of a firm's innovation Electronic copy available at: https://ssrn.com/abstract=3316197 profile as determinants of financial constraints, including measures of R&D and the firm's innovation outcomes. Secondly, we employ a structural model to account for endogeneity in the relationship between financial constraints and innovation and are thus able to study the bivariate and dynamic interaction of both variables and to resolve previous conflicting evidence. Thirdly, we contribute to the literature on the identification of financial constraints based on survey data.
The paper is organised as follows. The next section reviews the relevant literature and frames our research design. Section 3 presents our data, models and estimation approach. Section 4 presents the results of our main analyses. Section 5 extends the results by showing alternative model configurations and estimation methods. It further discusses and tests the validity of our measure of financial constraints. In section 6 we draw the study to a close by reflecting on its contribution to the literature and by commenting on its policy implications.

Financial constraints and investments in innovation
We begin the literature review by discussing the problems of identification and evaluation of the drivers of financial constraints. We then reflect on the specific role of innovation and focus on the bidirectional relationship between innovation and financial constraints.

Measurement and determinants of financial constraints
Empirical studies of firms' financing behaviours reflect the existence of constraints on raising external finance (e.g., Fazzari et al., 1988Fazzari et al., , 2000Whited, 1992;Bond and Meghir, 1994;Carpenter et al., 1998;Bond et al., 2003;Mulier et al., 2016). Authors typically measure the degree of financial constraint by screening a firm's financial reports for evidence of firms identifying themselves as financially constrained or by comparing the cash flow sensitivity of investment between subsamples constructed from a measure that proxies for constraints. Among the first of these studies, Kaplan and Zingales (1997) (KZ) examine the management's discussion of the firm's liquidity (i.e., future needs for funds and sources of liquidity, as well as demand for funds) and classify the firm into five categories according to the degree of financial constraint, using quantitative information to augment the qualitative data (e.g., information on dividends and share  (Whited and Wu, 2006;Hadlock and Pierce, 2010). Hoberg and Maksimovic (2015) find that constraints are more severe for R&D-intensive firms, supporting earlier findings by Brown, Fazzari and Petersen (2009).
If dynamic investment models of the firm (Bond and Meghir, 1994)  The analytical framework of regressing investment on cash flow and average Q (approximating marginal Q) -including the very identification of financial constraint and financial distress -has, however, been challenged in subsequent studies on methodological and theoretical grounds (Schiantarelli, 1996;Kaplan andZingales, 1997, 2000;Cleary, 1999;Cleary et al., 2007;Chen and Chen, 2012). The use of conventional regressions of investment on cash flow has been criticised for neglecting the potential endogeneity of cash flow and for not controlling for external financing ). Hu and Schiantarelli (1998) (2010) and Whited and Wu (2006)) are equally or better able to adjust their leverage in response to changes in the local tax regime.
In addition to these theoretical and methodological difficulties, the scope of potential determinants of financial frictions has largely been limited to readily available accounting information. However, a firm's financial statements do not always accurately capture its business activities to a degree that can easily be related to its ability to raise finance. For example, a firm's supply schedule of capital varies with its projects and is likely to depend on availability of collateral and information asymmetries caused by R&D activities (Farre-Mensa and Ljungqvist, 2016).
Proponents of the "wedge" model of financial constraints, which assumes a higher cost of capital for external than for internal finance, maintain that such a wedge can be due to the opaqueness of a firm's projects and private information that cannot easily be communicated to external parties (Myers and Majluf, 1984;Krasker, 1986;Brown et al., , 2012. It can be argued that a firm's efforts to innovate, a main cause of financing constraints, has received relatively little attention, partly as a result of limited data availability, although there are hardly any activities within firms that create a greater potential for moral hazard and similar agency problems related to asymmetric information.

Endogeneity and the multifaceted nature of innovation
Another reason for the lack of conclusive evidence on firms' innovation characteristics in relation to their financing behaviour is the bidirectional causality between the two constructs. While innovation is likely to affect a firm's ability to raise finance, the availability of funding can also constrain its ability to carry out research and innovation projects. Existing studies address this fundamental methodological problem in various ways. A number of studies concerned with technical change exploit the deregulation of intrastate and interstate branch banking in the U.S. in the 1970s until the mid-1990s as a natural experiment that relaxes financing constraints. While increased competition among banks as a result of interstate banking deregulation in the 1980s increases the number and quality of patents (Amore et al., 2013;Chava et al., 2013), increased market power of banks due to intrastate deregulation seems to reduce patenting (Chava et al., 2013).
Banking deregulation mainly benefits private firms, which previously had limited access to credit Electronic copy available at: https://ssrn.com/abstract=3316197 from local banks (Cornaggia et al., 2015). Within the cash flow sensitivity framework, there also is some evidence of binding financial constraints for R&D investment, which nonetheless appear to vary considerably across time periods and countries (Hall, 1992;Himmelberg and Petersen, 1994;Harhoff, 1998;Mulkay et al., 2000;Bond et al., 2005;Cincera and Ravet, 2010;Brown et al., 2012), often not unlike physical investment (Carpenter et al., 1998).
In addition to the problem of endogeneity of financial constraints as a determinant of innovation, this stream of contributions has a narrow focus on traditional indicators of innovation (predominantly audited R&D expenditures and to a lesser extent patents). Following Schumpeter (1934), several authors have instead highlighted that innovation processes are multi-dimensional (see, for example, Kline and Rosenberg, 1986;Dosi, 1988;Crépon et al., 1998;Jaffe and Trajtenberg, 2002). Innovation inputs (e.g., R&D, associated with the highest level of investment risk and information asymmetries) can be distinguished from intermediate outputs (e.g., inventions measured by patents) as well as from final outputs (innovated products, processes and services, which may be new to the firm or new the market). Moreover, each of these dimensions can be significantly affected by a range of practices and strategic choices about the sourcing of external knowledge, the acquisition of technologies and access to other complementary assets (Stoneman, 2001;Teece, 1992;2010). The use of a broader and more precise range of innovation indicators has great potential to refine our understanding of firms' financing behaviours (Canepa and Stoneman, 2007).
We expect innovation characteristics of a firm that are related to intangible assets and uncertain market prospects to affect its perceived financing constraints to a greater extent than investment in externally observable and examinable new products and services with a well-known market. Expenses for research and development and advertising, which can be seen as proxies for asset intangibility, shape a firm's capital structure and are associated with smaller degrees of leverage (Bah and Dumontier, 2001;Carpenter and Petersen, 2002;Kayo and Kimura, 2011). The large information asymmetries and agency costs associated with new product development -Electronic copy available at: https://ssrn.com/abstract=3316197 especially in the high-tech industry -require complex and thus costly financing solutions, which often involve equity in the form of venture capital (Gompers, 1995). Czarnitzki and Hottenrott (2011) report evidence that cutting-edge R&D projects may cause credit constraints more often than routine R&D investments. Lee et al. (2015) find that new-to-the-market innovations make it more difficult to access external capital. We thus expect that innovation activities and investment in early product development and opaque internal R&D projects will more likely generate financing difficulties than innovation outcomes such as new products in established markets or new business processes.

The introduction and continued implementation of Community Innovation Surveys (CIS) in
Europe has enabled the measurement of different stages and dimensions of innovations on a large scale. The CIS also contains two specific questions on firms' perceived financial constraints (namely the extent to which 'access to finance' and 'cost of finance' constitute barriers to innovation). Systematic research into the links between environmental constraints and the inputs, processes and outputs of innovation has only begun relatively recently (Canepa and Stoneman, 2007;Savignac, 2008;Mohnen et al., 2008;Müller and Zimmermann, 2009;D'Este et al., 2012;Hottenrott and Peters, 2012;Audretsch et al., 2014;Acharya and Xu, 2016). 2 Despite the quality of these contributions, there are considerable margins for progress on theoretical, methodological and empirical grounds. For example, the predominantly cross-sectional nature of the innovation output data used in the literature does not capture dynamic effects and state dependence in innovation activities. It also makes it difficult to identify the potential reverse causality between financial constraints and innovation. Prior art on this topic typically models either constraints or innovation as exogenous or introduces simultaneity by adding contemporaneous error correlation without allowing for two-way causality. One rare exception is a study of French firms by Hajivassiliou and Savignac (2016), who use bivariate probit modelling with state dependency in both financial constraints and innovation variables. This analysis is limited by the use of only two CIS waves, but the findings suggest the possibility that innovation outcomes increase financial constraints, while financial constraints may reduce the likelihood of innovation. Hottenrott and Peters (2012) instead exploit a speculative question only contained in one wave of the Mannheim Innovation Panel to explore the determinants of financial constraints. Results obtained from crosssectional estimations suggest that financial constraints do not depend solely on the availability of internal finance but can be driven by the increased financial needs of innovating firms. Even though external investors might be able to observe the successful outcome of firms' R&D investments, the effect of greater resources requirements or of market uncertainty appear to outweigh the reduction of information asymmetries. These insights deserve further investigation in a broader longitudinal setting that fully accounts for dynamic effects and reverse causality.

Data
The Community Innovation Surveys (CIS) provide a rich direct source of information on firms' innovation activities and the economic environment in which these take place. In the UK, the data employees, a census was used. Small and medium sized enterprises were sampled at random within each stratum.
We use four CIS-UK waves (CIS4 to CIS7, covering the periods 2002-2004, 2004-2006, 2006-2008 and 2008-2010)  and 559 three-period panels, which yields 6,995 firm-year observations in total for our bivariate models. Because lagged dependent variables consume on observation per firm, dependent variables in our bivariate models have up to 6,995 + 3,218 = 10,213 observations. Single-variable models have slightly more observations because observations for which the second dependent variable in our bivariate model would be missing remain in the sample. We match the CIS dataset with the Business Structure Database 4 (BSD) to obtain additional variables on firm age and legal form, as well as for our analysis of firm death.
One feature of the data that needs special attention is a one-year overlap between consecutive surveys: each survey asks firms every two years about their activities over the previous three years.
The potential serial correlation induced in the variables that are affected by this overlap has at least three implications for our modelling strategy. First, we use a dynamic model structure with lagged dependent variables to formally capture autocorrelation. Second, we choose lagged independent variables to construct economically meaningful models. are overrepresented compared to the UK population of firms with more than 9 employees (32.7% vs 19.3%) at the expense of other sectors, most notably hotels and restaurants (5.5% vs 12.5%), trade (17.7% vs 23.0%) and construction (7.6% vs 11.2%).

Variables
Because we aim to simultaneously predict the presence of innovation activities and financial constraints in firms, all our dependent variables are binary indicator variables based on firms' selfreported measures of financial constraints and innovation. This choice of variables is further motivated by the observation that many firms report no R&D expenditures but say they engage in 5 The respondents' tendency to answer survey questions with the most recent year in mind (Tversky and Kahneman, 1973) is likely to help mitigate correlations across time periods. The availability heuristic will favour data that are more readily available in the respondent's memory and will underweight earlier years, thus attenuating possible autocorrelation effects that are not due to underlying economic processes but to survey design.
Electronic copy available at: https://ssrn.com/abstract=3316197 R&D activities. There is evidence that firms do not report R&D expenses in their financial statements but still file patents (Koh and Reeb, 2015) or achieve product innovations (Santamaría et al., 2009). The reporting of R&D activities, if not the decision processes within firms, may follow a two-step process, in which firms first decide whether to engage in R&D (i.e., a binary decision) and then decide whether and how much audited R&D expenditures to report. For all our dependent variables on financial constraints and innovation, we either use survey items directly or construct binary variables from them.
Our six binary measures for R&D activities are based on two survey questions. First, the questionnaire asks firms, "During the 3 year period [survey period, e.g. [2006][2007][2008], did this business invest in any of the following, for the purposes of current or future innovation?" with answers "Internal Research and Development" and "Acquisition of external Research and Development," which translate into our dependent variables "R&D internal (activity)" and "R&D external (activity)." The binary variable "R&D any (activity)" equals one whenever any of these two variables is answered positively by the firm. The second question is, "for each of the main significantly improved services?" and "did this business introduce any new or significantly improved processes for producing or supplying goods or services?" Additionally, we distinguish new goods and services that are new to the market from those that have been introduced by a competitor and are merely new to the firm. Finally, the variable "Innovation (any)" measures whether the firm introduced any type of innovation -good, service, or process.
To assess financial constraints, firms answer the question, "how important were the following factors in constraining innovation activities: […] availability of finance." "Cost of finance" was another possible constraint in this block of items. We focus on the availability of finance, however, to stay close to the meaning of financial constraints as an unobserved differential between internal and external cost of finance that limits the availability of external finance. One important advantage of using a self-response measure over cash-flow sensitivities is that we can directly observe changes over time. In other words, instead of searching for latent financial constraints in different groups of firms, we can directly investigate their determinants and impact on innovation. Whenever firms answer this item with "high" or "medium," we code this answer as "experiencing financial constraints" and treat the firm as unconstrained if the answer is "low" or "not experienced." About one quarter of the sample's firms report financial constraints, a proportion that is largely driven by the two CIS waves in 2008 and 2010, as one might expect from the general economic climate at the time. An econometric advantage of the UK Innovation Survey relative to the innovation surveys of other European countries is that all sample firms were asked whether they experienced financial constraints rather than only those that report innovation activities. We find a substantial proportion of firms in all innovation and constraint regimes, including financially constrained non-innovating firms. Potential selection biases within our sample are therefore greatly reduced.
Independent variables in our analyses relate to a firms' innovative capacity and the likelihood of financial constraints. The range of variables is limited by their availability in official -and linkable -ONS datasets. We measure a firm's size as the natural logarithm of its turnover in the last year of each survey period. Firm age is calculated as (2010 -birth year), where birth year is obtained from the BSD dataset and thus does not vary over time. Since age changes in much the same way for all firms over time, the likelihood of detecting a time series effect in addition to the cross-sectional one is quite small given the short panel. However, treating age as firm-year specific would introduce four additional parameters (Wooldridge terms, see Wooldridge, 2005), which remain insignificant in our tests. Whether a firm is a member of a group, is a subsidiary of a foreign Electronic copy available at: https://ssrn.com/abstract=3316197 firm and whether it has the legal status "company" can proxy for the availability of external finance and the availability of information about the firm to investors. Similarly, the market scope of a firm can be related to information production, but also to competitiveness in the market and the constant need to be ahead of the competition by innovating. Human capital is expected to have a positive impact not only on the likelihood to innovate, but also on the likelihood of financial constraints due to information asymmetries in firms with substantial intangible assets.
We augment this set of explanatory variables by adding the firm's market share to the R&D and innovation equations and the gross profit margin as a regressor for financial constraints, such that each variable appears in only one of the two equations of our model. Market share has long been hypothesised to affect firm innovation activities (Scherer, 1967;Blundell, Griffith and Van Reenen, 1999;Aghion et al., 2005;Cohen, 2010). A firm's gross operating margin is correlated with cash flow and hence with financial constraints (as discussed in section 0) but not directly

Model specification and estimation
We model the interaction between financing constraints and innovation as two simultaneous dynamic equations with concurrent error correlation between equations. This design formally captures the mutual endogeneity of financial constraints and innovation in a structural model that does not prioritise one or the other variable. It also makes it possible to cleanly accommodate two endogenous binary dependent variables in a regression framework.
The UK Innovation Survey's structure enables us to specify a dynamic panel structure, combining several past waves to form a proper panel (T>2). 7 Linking four survey waves allows us, in addition to incorporating first-order dynamics, to use Wooldridge's (2005) approach to address the initial conditions problem in dynamic panels. This modelling approach, in combination with the panel dataset, has the advantage that we can directly address the effects of unobserved firm characteristics. As a result, we can model the entire population of firms regardless of their ex-ante innovation characteristics, such as being a potential innovator, rather than having to exclude noninnovators from the sample that may otherwise induce a spurious positive correlation between innovation and financial constraints that can be observed in cross-sectional studies (Pellegrino and Savona, 2017;Mancusi and Vezzulli, 2014;Savignac, 2008).

The system of equations for observed innovation activities ( )
A it y and financial constraints Prior studies often lose observations in their attempts to incorporate lagged dependent variables by merging several cross-sections and therefore have to restrict the scope of their analysis to cross-sections (Silva and Carreira, 2012; Hajivassiliou and Savignac, 2016).
Electronic copy available at: https://ssrn.com/abstract=3316197 error variances need to be normalised to unity as in univariate probit models. Analogous to Wooldridge's (2005) panel probit estimator, we add random effects conditional on exogenous variables and initial values of both dependent variables.
These random effects can be written as Since the likelihood function for both equations is analytically intractable, we use a maximum simulated likelihood (MSL) method to estimate this system of equations. 8 The error terms in all estimations are derived from 100 random draws. We tested smaller and larger sets of random errors and found that the added precision in larger samples is tiny compared to the increased computational costs of estimation, which are of the order of several hours per estimation. Standard errors shown in our results are based on the outer product of the gradient (OPG) method.

Results
If we want to identify the dynamic effect of financial constraints on innovation and the reverse effect, we need to observe firms that switch from being constrained to unconstrained and from innovation-active to inactive or in the opposite direction. Table 2 shows the pattern of state transitions we observe in the data. A large number of firms remain inactive and unconstrained ("no/no" in the upper left corner in both panels). A plausible island of stability can also be identified for financially unconstrained R&D performers and innovators (i.e., the "Yes/No" cell). As expected, the most unusual state transitions are firms that are financially constrained but start performing R&D in the next period (1.4% + 1.2% = 2.6%). However, there are also relatively few firms that perform R&D in one period and who are constrained and stop their R&D efforts in the [ Table 2 about here]

R&D models
Results from the estimation of simultaneous equation models with R&D and financial constraints (Table 3) reveal high persistence in both indicators over time. Financial constraints do not affect R&D with the sole exception of a negative effect in our model for external R&D activities. The coefficient for external R&D expenditures has the next largest magnitude among R&D models but is insignificant. This finding suggests that external R&D is more sensitive to changes in the availability of finance than internal R&D. It is also plausible from the firm's point of view to reduce risky external procurement of R&D when resources become scarce in favour of more informationally transparent and vital internal R&D. Firms have been found to smooth their R&D expenditures by varying their cash holdings (Brown and Petersen, 2011), which explains the limited effect of financial constraints on R&D in our sample. Because internal R&D investments have large adjustment costs (Himmelberg and Petersen, 1994;Hall, 2002), as they tend to involve long-term investment in human capital or specialised equipment that cannot easily be sold, external R&D contracts may be easier to terminate in the event of a liquidity shock. The long-term nature and cost-smoothing of most R&D projects also explains the seeming disparity between firms' positive answer to the survey question on financial constraints (i.e., they admit that financial constraints are important in constraining their innovation activities) and our finding that there is no relationship with most R&D variables: firms feel constrained in their activities, but they do not stop them altogether. They may, however, curtail expenses for non-vital projects, which tend to be external research projects more often than internal ones.
[ Table 3 about here] In line with earlier cross-sectional findings of increased financial constraints in technology firms with high R&D expenditures (Westhead and Storey, 1997), R&D increases financial constraints, but only in models using indicators of R&D activity (Models 2 and 6), as opposed to R&D expenditures (Models 1, 3 and 5). This suggests that firms engaging in informal R&D activities have greater difficulties in attracting external finance relative to firms that engage in formal R&D that is recorded in financial accounts and thus more readily observable by investors than unreported activities. From a theoretical viewpoint, this result supports the interpretation on innovation variables as measuring the potential for asymmetric information in a firm's innovation activities because informal R&D activities may be even harder for external investors to evaluate than those reported in audited financial statements.
There are no regular and systematically strong effects across R&D indicators for other timevarying variables. In two instances (Models 2 and 6), turnover seems to exert a negative effect on the likelihood of a subsequent internal R&D activity -a possible sign that growing firms slow down R&D in the following survey period. Interestingly, time effects in the R&D equations reflect external macroeconomic conditions. Firms report R&D activities more frequently for CIS6 are a more appropriate explanation of these effects relative to the financial environment because we already control for the firms' financing conditions. Foreign ownership is negatively associated with R&D in four (Models 1, 2, 5, 6) out of six models, which implies that R&D investments may be overall closer to the firms' overseas headquarters. 9 Finally, time-varying market share is only positive and weakly significant in one model, which mirrors the diverse theoretical predictions on 9 It is important to note that the presence of xi in equation (3) prevents us from identifying time-constant variables, because we cannot separate the effect of these variables on both outcome variables from their correlation with the random effects in equation (3). For example, firms owned by a foreign parent seem to perform less internal R&D.
Because the indicator for UK subsidiaries of foreign firms would also enter the conditional distribution of the random effects, including this variable in Xit would cause perfect collinearity with the one in xi. Hence, instead of foreign ownership directly causing less R&D, it might be related to some unobserved quality which in turn is associated with less R&D without any implication of causality. It might even be the case that less research-intensive businesses are acquired by foreign firms more often.
Electronic copy available at: https://ssrn.com/abstract=3316197 the effect of market structure on innovation (Cohen, 2010), although we note that market share as a Wooldridge term positively predicts R&D in most models, as well as in single-variable regressions (see section 5.1).
Among the determinants of firm financial constraints, besides the role of R&D, results show negative and significant effects for human capital, operating margin and age -that is, these firm characteristics mitigate financial constraints. The effect of firm age is to be expected because information about older firms is more readily available than for younger firms, thus reducing information asymmetries and consequently the cost of external relative to internal capital. 10 Firms with higher operating margins tend to have more free cash flow, while belonging to a group may enable firms to access an internal capital market, both of which reduces their dependency on external finance. The apparent negative effect of human capital is instead more difficult to interpret: intangible assets, such as human capital, should in theory aggravate information asymmetries in the market for external capital, and prior cross-sectional evidence points toward an increased likelihood of financial constraints for firms with a high level of human capital (Hottenrott and Peters, 2012).
On the one hand, variations in human capital over time seem unable to explain the likelihood of observing R&D. On the other hand, human capital is positively related to R&D through unobserved firm effects (Wooldridge terms in the R&D equation), which explains why we do not find a positive effect for time-varying human capital. Turning to the relationship between human capital and financial constraints, we find that firms with a larger share of employees with a degree are more likely to face financial constraints, but only through unobservable firm characteristics related to human capital. Over time, instead, human capital mitigates financial constraints. A negative effect can be explained if we assume that increasing human capital can lead to higher productivity, which in turn -ceteris paribus -should be associated with growth and therefore more favourable financial prospects. It is also possible that after controlling for the adverse effect of R&D on constraints, human capital, as measured by the ratio of staff with a degree, exerts a residual beneficial effect by helping to overcome information gaps between the firm and potential investors.

Innovation models
The results generated by models with innovation measures (Table 4)  [ Table 4 about here] 11 An alternative explanation is that firms had to introduce new products to adapt to changes in demand.
While financial constraints do not affect innovation, inspection of the results for the financial constraints equation in Table 4 reveals that some types of innovation aggravate financial constraints. We find positive coefficients for new-to-market innovation (

Unobserved heterogeneity in R&D and innovation
The inclusion of cross-sectional variables in our specifications of random effects provides some estimation benefits and offers insights into unobserved firm characteristics. Controlling for initial conditions through Wooldridge (2005) terms in both equations contributes to the identification of sensible and stable coefficients but reduces many significant coefficients found in univariate models (see Tables 6 and 7 in section 5.1). Our modelling strategy thus reduces the likelihood of spurious results that are due to unobserved heterogeneity. For example, initial conditions of R&D, innovation and financial constraints (i.e., in CIS4, corresponding to the first two lines under Wooldridge terms in Tables 3 and 4), which enter the conditional distribution of random effects in equation (3), turn out to be highly significant and positive in the R&D and financial constraints equations. This finding also suggests that future research might benefit from investigating the unobservables that link a firm's financial environment and its innovation capabilities.
The inclusion of initial states for both outcomes in both equations, while retaining first-order dynamics, offers further insights into unobservable firm characteristics. Consider the positive coefficients for initial R&D conditions ("R&D in CIS4") in the financial constraints equation in Table 3. Initial R&D activities are positively correlated with unobservables related to financial constraints, whereas time-varying R&D itself ("R&D (lag)") is significant but only in two models.
This suggests that being R&D active -interpreted as a firm effect -could lead to financial constraints, whereas observed year-on-year changes in R&D status are less important for financial constraints. Nothing may have changed in the underlying characteristics of the firm, although it temporarily does not show any R&D activities. Capital market participants may thus be able to distinguish R&D performers, including those in a latent R&D-performing state without visible activities, from non-performers.
Similarly, success at innovating as a firm effect does not affect financial constraints ("Innovation in CIS4" in the financial constraints equation in Table 4), as would be expected under standard agency theory, because innovation in itself does not cause information asymmetries.
Another interpretation is that there is no such thing as a latent innovation state, that is, there is no firm effect for innovation that adds to the overall firm random effect in the financial constraints equation. Innovations might be entirely random conditional on our observed variables. These interpretations are available under the normal interpretation of the financial constraints variable, that is to say a differential between external and internal financing costs and therefore a shortage of external funds. New-to-market innovations increase financial constraints, because these are more fundamental innovations that carry a greater risk of information asymmetries. In addition to this conventional explanation, we can interpret the survey question on constraints in more general terms as a signal of the demand for finance that usually follows successful innovations. Firms introducing novel products may find it necessary to approach external capital markets for expansion financing (ramping up production and marketing). This increase in the demand for finance, if unmet, produces a higher likelihood of financial constraints as detected in the Innovation Survey data.
Overall, innovation success in the previous period is more important for future innovation success than past R&D is for future R&D when compared to the importance of initial conditions. In other words, coefficients for lagged innovation are about as large as coefficients for initial innovation conditions ("Innovation at CIS4"), while initial R&D conditions have a much stronger effect on future R&D activities than lagged R&D. This again suggests that there are unobserved firm characteristics that predispose firms to constantly perform R&D. Innovation, on the other hand, depends less on constant firm characteristics, but rather on past success in innovating. In general, the link between innovation outcomes and financial constraints appears weaker than the one between R&D and financial constraints. Although both indicators for inputs or outputs in the innovation process explain financial constraints, the relationship through cross-equation correlation and random effects is considerably weaker. Initial conditions of innovation and financial constraints in one equation are not significant in the other in Table 4. 12 Hence, unobserved firm heterogeneity in one variable seems to be unrelated to the other. The substantial correlation in unobserved firm effects nevertheless suggests the presence of unobserved firm characteristics that explain both innovation and financial constraints.

Financial constraints and firm exit
Our classification of firms into financially constrained and unconstrained is based on firms' answers to a question in the Community Innovation Survey about whether "availability of finance" constitutes a barrier to innovation. Because of the nature of the survey, this variable is self-reported and may be seen as subjective. The design of our financial constraints measure reflects the qualitative approach of Hoberg and Maksimovic (2015) Results of these probit models shown in Table 5 suggest a strong effect of self-reported financial constraints on firm death, despite the loss of demographic events in the matching process.
Turnover and firm age are negatively related to firm death, which is expected if informational asymmetries or financial distress indeed drive survey responses to the question about the availability of finance. When we include measures of R&D and innovation in models 2 to 4, results reveal a positive effect of R&D activities, R&D expenditures and innovation on firm survival.
Interestingly, informal R&D activities predict firm death better than innovation outcomes.
Correlation among R&D and innovation variables prevents them from becoming significant if all measures are included simultaneously, but a top-down approach starting with a full model and removing insignificant measures of R&D and innovation one by one (results not reported here) suggests that informal internal R&D activities contribute most to firm survival.

Additional estimations and robustness checks
In order to validate our results, we run a series of complementary and additional estimations. First, we compare the results obtained from simultaneous panel models with results generated by simpler models that do not control for reverse causality. We then perform robustness checks on the estimation technique by replacing the Wooldridge (2005) specification of the random effects' means by time averages of these terms as suggested by Mundlak (1978). Finally, we explore and contrast continuous and binary measures of R&D.

Simultaneous vs independent equations
Tables 6 and 7 show the results of independent estimations of the effects of financial constraints on R&D (Table 6, Models 1-6) and of R&D on financial constraints (Table 6, Model 7); and financial constraints on innovation (Table 7, Models 1-6) and of innovation on financial constraints (Table 7, Model 7). To demonstrate how different these results are, let us consider as an illustrative example the results presented in Table 6. Some of these show positive effects of financial constraints on R&D, a counter-intuitive result which can be explained by observing the structure of error correlations. Correlation coefficients for firm-year errors between both equations are substantial and significant in almost all our specifications, supporting our modelling strategy. This suggests that the curious positive effect of financial constraints on R&D and innovation seen in these regressions is caused by unobserved heterogeneity that is correlated between equations.
[Tables 6 and 7 about here]

Time-average random effects
We aim to employ an estimation methodology that models random effects with as many degrees of freedom as possible. The Wooldridge (2005) specification of random effects, however, can lead to a proliferation of nuisance parameters, as each time-varying variable requires as many additional parameters as there are time periods in the data. These additional parameters may be close to redundant and may cause the model to fit the error terms rather than underlying economic relationships. To counter this potential problem, we estimate simpler models using time averages of panel variables (Mundlak, 1978).
Replacing Wooldridge (2005) terms with Mundlak (1978) terms in these alternative models produces results that are almost identical to our main results. Tables 8 and 9 show these robustness tests. All relationships between R&D and financial constraints in our main results in Table 3 carry over to the robustness tests presented in Table 8. The negative effect of time-varying turnover on R&D activities in Table 3 becomes slightly more significant, which is to be expected if degrees of freedom are removed from the model. Foreign ownership, turnover, market scope and human capital remain significant cross-sectional predictors of R&D. The only difference for the R&D equation we find is a reduced effect of a firm's market share on external R&D. Results for control variables in the financial constraints equation in Tables 3 and 8 are similarly robust to the alternative specification of random effects. A difference can only be observed in the effect of market scope, which is now insignificant where the more comprehensive model in Table 3 was able to distinguish time-varying effects from cross-sectional ones.
[ Tables 8 and 9 about here] When testing our innovation models from Table 4 for robustness to an alternative random effect specification in Table 9, we find similarly stable results. All relationships between innovation indicators and financial constraints within and across equations remain the same, with the sole exception of process innovation, which loses its slightly significant effect on financial constraints.
The substantial impact of new-to-the-market innovation, however, remains in place. Time-varying market scope loses some of its significance in favour of its cross-sectional effect on innovation, in line with our findings in robustness tests for R&D. Market scope also loses its effect on financial constraints, while all other control variables retain their effects. In sum, our findings are robust to a simpler specification using Mundlak (1978) random effects.

Continuous vs binary measures of R&D
Our estimation design is driven by the observation that firms often do not perform any R&D (Audretsch et al., 2014), while the intensity of R&D may be a secondary decision once a firm engages in R&D. In principle, a continuous measure of R&D expenditures is available from the CIS data and would enable a more precise estimation of bi-directional effects in models with financial constraints. However, data restrictions do not allow us to estimate feasible models of R&D that incorporate the endogeneity of financial constraints while at the same time taking account of a twostage decision process for whether or not to engage in R&D and its volume.
However, we try a number of possible specifications to estimate the effect of financial constraints on continuous R&D expenditures. First, we estimate a cross-sectional OLS model of the natural logarithm of R&D expenditures using the R&D equation from our main models above.
Coefficients of financial constraints in this regression are similar to the results we obtain from binary single-equation models. Second, instrumenting financial constraints with gross operating profits yields an insignificant effect of financial constraints on R&D. Third, to incorporate dynamics into the relationship between R&D expenditures and financial constraints, we estimate the model for R&D expenditures by system GMM (using all available lags of the dependent variables as GMM-style instruments and the firm's operating margin as IV-style instrument) but find no significant effect of financial constraints. All dynamic models of R&D expenditures suffer from a lack of observations because observations where R&D is zero drop out of the sample. This causes many holes in the panels (T=4 for few firms, mostly T=3). Treating non-existent R&D as £1 when taking logs to retain these observations in the sample does not result in any model improvement.
In summary, running models for continuous R&D variables does not seem to be feasible with a sample of firms that sometimes start and stop spending on R&D. A full treatment of this twostage process with a binary R&D indicator and continuous expenditures would need a third equation and a larger sample, even though the UK already runs a larger survey than most other European countries for which Community Innovation Surveys are available. Adding future CIS waves would certainly be desirable given that we are trying to estimate models with first order dynamics. This would not only increase the precision of coefficients for lagged variables, but also help us disentangle the direct effect of exogenous variables from their correlation with unobserved firm heterogeneity (in Wooldridge coefficients). 13 Adding a third equation to the system would require 13 An ONS decision to increase sample size seems unlikely at least in the short term, but new models could perhaps use the information contained in the ordinal measure for financial constraints to estimate panel version of ordered response models.
Electronic copy available at: https://ssrn.com/abstract=3316197 the further development of custom estimation algorithms that can incorporate both binary and continuous dependent variables, as well as greater computing power than is currently available at the ONS's secure data service. However, because the first decision that firms need to make is whether or not to perform R&D activities, and then decide on the depth of R&D engagement, we believe our modelling strategy uncovers important and interesting dynamics and constitutes a novel point of departure for further studies with a potential focus on the intensity of R&D investment as well as the volume of innovation outputs.

Conclusion
This paper analyses the nature and direction of the relationship between financial constraints and innovation and provides new evidence for a range of innovation inputs and outputs. To the best of our knowledge, this is the first study that compares a broad range of innovation characteristics and models their relationship with financial constraints as a dynamic bivariate process capable of addressing the initial conditions problem through Wooldridge's (2005) method in a panel setting.
This allows us for the first time to test theoretical predictions on the effects of a set of innovation activities on firms' capital market access while taking account of reverse causality and dynamic effects. The CIS data cover small and non-listed firms, which are not included in existing studies on the cash-flow sensitivity of investment (e.g., Carpenter and Petersen, 2002), and they provide direct information on the perception of financial constraints combined with detailed information on the innovative profile of firms, covering R&D expenditures and informal R&D activities in its internal and external forms as well as several innovation outputs. Hence, our results highlight new aspects of the UK innovation-finance landscape that cannot be easily observed through a traditional cashflow sensitivity approach, which is usually tested on samples of listed large firms. Our validation test of the financial constraints measure also shows that this measure is able to capture consequences of reduced access to external capital.
Our results contain few indications that past financial constraints affect R&D programs or innovation output. While businesses might be affected by difficulties in raising finance in the short term as reflected in their response to the survey question about financial constraints, financing problems do not induce firms to stop their innovative activities altogether. Our results still allow for the possibility that firms reduce the number or intensity of their R&D projects without completely abandoning their R&D or innovation programs. The reverse effect of R&D on financial constraints, which is expected from theory, can be clearly identified in our results.
More surprisingly, there is evidence that innovation, and in particular new-to-market and product innovation, cause financial constraints. This finding has especially important implications for policy: it highlights the fact that the financing challenges of innovation do not stop when firms introduce a new product or service, but continue -and may in fact intensify -in the early stages of technology diffusion. This fact is systematically underestimated or -even more often -completely neglected in the literature. While support for the generation of new products may be vital in many sectors of the economy, support for early firm growth may be at least as important, in particular for SMEs, to build capacity and enable the full exploitation of their innovation activities. Similarly, our results suggest that while specific measures can be useful to alleviate the financial constraints of younger firms, public support may be targeted not primarily at formal R&D activities (typically covered by R&D tax credit schemes), but also at informal R&D activities that do not result in reported R&D expenditures.
In relation to the broader macroeconomic framework in which this study is set, time effects reflect the impact of the recent financial crisis. Firms were significantly more often financially constrained during 2007/8 than in the preceding period. Financial pressure fell slightly after 2008, but remains high compared with pre-crisis years. While an effect of the crisis can be found in concurrent time effects on financial constraints, investment in research and development lags the macroeconomic climate. Expenditures in R&D kept increasing until 2008 and only dropped below pre-crisis levels towards the end of the sample period. This finding lends support to the theory that R&D investment becomes pro-cyclical when firms face tightening credit constraints (Aghion et al., 2012).
Electronic copy available at: https://ssrn.com/abstract=3316197 The significant dynamic effects we find are of course only a part of the whole picture. R&D activities can explain financial constraints, but other firm characteristics correlated with innovation might offer richer insights into the causes of constraints. Unobserved heterogeneity as well as firm- year errors appear to be correlated, which explains implausibly positive effects of financial constraints on innovation generated by simpler models. Future research could aim to address these hidden firm characteristics by collecting and merging additional information about firms' innovative capabilities and financial outlooks. Further methodological developments may also address the problem of integrating information on the volume of R&D expenditures into a trivariate dynamic model.  The firm states positive internal or external R&D expenditures.

R&D internal (activity)
The firm engaged in creative work on an occasional or regular basis to increase the stock of knowledge or used it to devise new and improved goods, services and processes. Dummy variable. R&D external (activity) The firm engaged in external R&D activities; same as internal R&D, but purchased by the firm and performed by other companies (including other businesses within its group) or by public or private research organisations. Dummy variable. R&D any (activity) The firm engaged in internal or external R&D activities. Innovation (any) The firm introduced any kind of innovation as defined below. Innovation new to market The firm introduced a new good or service onto the market before its competitors. Dummy variable.

Innovation new to firm
The firm introduced a new good or service that was essentially the same as a product already available from its competitors. Dummy variable. Innovation (good) The firm introduced new or significantly improved goods. Innovation (process) The firm introduced any new or significantly improved processes for producing or supplying products. Innovation (service) The firm introduced new or significantly improved services. Fin. constraint The firm faced constraints in the availability of finance. This dummy variable is derived from the corresponding survey question "How important were the following factors as constraints on innovation activities in influencing a decision not to innovate?" Firms answering "not experienced" or "low" are treated as not being financially constrained, while those answering "medium" or "high" are defined as financially constrained. Turnover (log) The firm's turnover in GBP (thousands, natural logarithm) for the last year of the survey period. This variable is lagged by one period. For a small number of firm, turnover was missing, but could be recovered from the corresponding entries in the Business Structure Database (BSD). Reading example: There are 2159 observation in the interval [0,7.5].

Market scope
The largest geographic market in which a firm sells goods or services. Possible answers are 1="Local/regional within the UK", 2="UK", 3="Other Europe" and 4="All other countries".

Human Capital
The proportion of a firm's employees in the last year of the survey period that were educated to degree level or above. The maximum value is 2, since this variable adds the survey items "science or engineering subjects" and "other subjects". This variable is lagged by one period.

Operating margin
Operating margin, defined as gross value added at factor cost minus total labour cost, divided by turnover. A firm's operating margin is calculated for the first year of the relevant CIS wave. For example, the operating margin used to predict dependent variables in CIS7 (2008−2010) is from 2008. About 59% of all observations for this variable have been imputed using regression imputation. Market share Market share of the firm, defined as the firm's turnover divided by concurrent total market turnover. A market is defined based on five-digit SIC2007 codes, using the full sample and sampling weights of the Annual Respondents Database (ARD). About 2% of all observations for this variable have been imputed using regression imputation. Age (log) Firm age (natural logarithm) calculated as (2010 minus birth year). Firm birth is censored at 1973 in the Business Structure Database. In order to avoid potential biases due to censored right-hand variables, we impute censored values using predicted values from a tobit regression of birth year on all other independent variables. This places many observations in the interval (3.8,4.1].

Group member
The firm is part of an enterprise group in the first period (CIS4). Dummy variable.

Company
The firm has status "company" as opposed to sole proprietorship etc. in the Business Structure Database. Dummy variable.

Foreign ownership
The firm is under foreign ownership (ultimately) in CIS5 (2004CIS5 ( -2006 25, 23, 26, 27, 28, 36, 37, 20, 21, 22, 15, 16, 17, 18,  Notes: This table shows summary statistics and definitions for the variables used in our analyses. Exact minimum, maximum and median values cannot be shown due to rules regulating statistical disclosure at the Secure Data Service/ONS. Instead, we provide frequency statistics for intervals containing the minimum and maximum under the "Min" and "Max" headings for continuous variables. The number of observations is the maximum number of observations for all time periods for panel variables (p), crosssectional variables (i) and time variables (t). Due to missing variables in dependent variables, individual analyses may have slightly fewer observations. For independent variables, there are 2659 two-period panels and 559 three-period panels, which yields 3218 panels with a maximum of 6995 observations in total for independent variables in bivariate panel analysis. Dependent variables have more observations, since the first observation for each firm is used up for lagged dependent variables.               Notes: This table presents results for bivariate panel probit models with six R&D measures and a financial constraints measure as dependent variables. All models are estimated using maximum simulated likelihood with 100 random draws and standard errors (in parentheses) based on the outer product of the matrix of contributions to the gradient. Intercepts and industry effects are not shown. All specifications in this table use Mundlak (1978) time averages rather than Wooldridge terms for the random effect's conditional mean. Significance levels: *** p<0.01, ** p<0.05, * p<0.1.  Notes: This table presents results for bivariate panel probit models with six innovation measures and a financial constraints measure as dependent variables. All models are estimated using maximum simulated likelihood with 100 random draws and standard errors (in parentheses) based on the outer product of the matrix of contributions to the gradient. Intercepts and industry effects are not shown. All specifications in this table use Mundlak (1978) time averages rather than Wooldridge terms for the random effect's conditional mean. Significance levels: *** p<0.01, ** p<0.05, * p<0.1.