UK credit and discouragement during the GFC

Abstract

The availability of credit to entrepreneurs with good investment opportunities is an important facilitator of economic growth. Under normal economic conditions, most entrepreneurs who requested loans receive them. In a global financial crisis, popular opinion is that banks are severely restricting lending to smaller businesses. This assumes that low levels of investment are caused by supply-side restrictions in the credit market. Little is said about potential changes in the demand for credit and how it is influenced by entrepreneurs’ perceptions about supply-side restrictions. One particularly interesting, and under-researched, group of small businesses is that who have potentially good investment opportunities, but are discouraged from applying for external funding as they fear rejection. In this study, we question whether these entrepreneurs were correct in their assumptions. We find that levels of discouragement are quite low in general at 2.7 % of the total smaller business population. Further analysis implies that 55.6 % of discouraged borrowers would have got loans had they applied.

Appendix: Testing for over- and weak-identifying instruments in the conditional probit models

In order for the Heckman selection model to be properly identified, the selection equation must contain at least one variable (exclusion restriction, or instrument) that is not in the outcome (main) equation. Ideally in instrumental variable (IV) estimations, a valid instrument must be uncorrelated with the regression’s disturbances, i.e. exogenous. Moreover, a good instrument needs to be strongly correlated with the endogenous explanatory variable. If the partial correlations between the instruments and the endogenous variable are weak, the coefficient estimates can be biased and hypothesis tests distorted even with a very large sample size (Murray 2006).

In this study, the model we adopt is in essence a two-stage regression model taking into consideration the conditionality, or endogeneity of credit demand and application (prob(DEMAND) and prob(APPLY) in the conditional credit application/discouragement and credit denial equation, respectively) using exclusion restrictions in the selection equations as instruments. However, testing instrument validity and that they are not weakly identified are not so straightforward. In a linear IV regression, Sargan test of over-identifying restrictions is usually used to assess the validity of instruments (Sargan 1958) and Stock and Yogo (2005) propose a hypothesis test of weak instruments based on the Cragg and Donald (1993) F-statistic. In order to serve our purpose, we follow Grilli and Murtinu (2014) and run the following pseudo-two-stage IV regressions (2SLS) for pre- and within-recession credit application (discouragement in the pre-recession specification):

$$\begin{aligned} {\text{Second stage}}:APPLY \, ({\text{or }}DISCOURAGED) & = \beta_{0}^{A} + \beta_{1}^{A} DEMAND + \beta_{2}^{A} X_{i}^{A} + \varepsilon_{i}^{A} \\ {\text{First stage}}:DEMAND & = \alpha_{0}^{D} + \alpha_{1}^{D} Z_{i}^{D} + \alpha_{i}^{D} X_{i}^{A} + \mu_{i}^{D} \\ \end{aligned}$$

and credit supply (denial), respectively:

$$\begin{aligned} {\text{Second stage}}:DENIED & = \beta_{0}^{S} + \beta_{1}^{S} {\text{APPLY}} + \beta_{3}^{S} X_{i}^{S} + \varepsilon_{i}^{S} \\ {\text{First stage}}:APPLY & = \alpha_{0}^{A} + \alpha_{1}^{A} Z_{i}^{A} + \alpha_{i}^{A} X_{i}^{S} + \mu_{i}^{A} \\ \end{aligned}$$

In the pseudo-2SLS regressions, Z ^D _i and Z ^A _i are vectors of exclusion restrictions used in the selection equations in Model 1 and Model 2, respectively, in Tables 3 and 4. In turn, X ^A _i and X ^S _i are vectors of exogenous variable used in the outcome (main) equations in Model 1 and Model 2, respectively, in Tables 3 and 4. By definition, Z ^D _i and Z ^A _i are the instruments chosen in the pseudo-2SLS regressions.

Table 5 reports the model diagnostics of the pseudo-two-stage IV regressions for APPLY/DISCOURAGED and DEMAND, respectively. For all four models, the Sargan tests of overidentifying restrictions for the null hypothesis that the instruments are valid cannot be rejected. However, if all the instruments share a common rationale so that one invalid instrument would invalidate all the others, the Sargan statistics could be biased and inconsistent (Murray 2006; Bascle 2008). Therefore, we also perform the difference-in-Sargan test for the specifications on the exogeneity of individual instruments, and all the tests are passed.¹ The Cragg–Donald F-statistics show that for all but the within-recession pseudo credit denial model the null hypothesis that all of the instruments are weak is rejected, where the F-statistics exceed the critical value of 10 (Staiger and Stock 1997; Stock and Yogo 2005). Since the weak instrument test for the within-recession pseudo credit denial function is not passed, we undertake further analyses by running an unconditional, multinomial logit model to check the robustness of our main results (Model 3, Table 4).

Table 5 Pseudo-two-stage IV regression model diagnostics

Alternative Specifications with REGION as identifying restrictions for Table 4:

Variables	Prob(DEMAND)	Prob(APPLY|DEMAND)	Prob(APPLY)	Prob(DENIED|APPLY)
	Coeff.	Coeff.	Coeff.	Coeff.
Firm characteristics
FAMOWN	0.134**	−0.153	−0.156	0.101
	(0.058)	(0.117)	(0.178)	(0.124)
CORP	0.024	0.302**	0.561***	0.069
	(0.080)	(0.134)	(0.212)	(0.174)
EMP	0.003***	0.006**	0.009***	−0.002
	(0.001)	(0.002)	(0.003)	(0.001)
AGE_11TO20	0.040	0.190	0.350	−0.087
	(0.101)	(0.171)	(0.261)	(0.205)
AGE_20UP	−0.096	0.226	0.359	−0.357*
	(0.101)	(0.180)	(0.268)	(0.210)
SALE_DECREASE	0.032	−0.112	0.074	−0.165
	(0.064)	(0.146)	(0.222)	(0.132)
SALE_SAME	−0.109	−0.228	−0.242	−0.057
	(0.072)	(0.158)	(0.245)	(0.157)
PROFIT	−0.006	0.371**	0.463**	−0.092
	(0.096)	(0.164)	(0.231)	(0.203)
Metals Manufacturing	−0.218*	0.187	0.196	0.423*
	(0.119)	(0.318)	(0.413)	(0.243)
Other Manufacturing	−0.252**	−0.290	−0.462	0.200
	(0.127)	(0.304)	(0.397)	(0.272)
Construction	−0.225*	−0.238	−0.313	0.487**
	(0.117)	(0.288)	(0.373)	(0.245)
Retail & Wholesale	−0.036	0.085	0.327	0.199
	(0.143)	(0.359)	(0.470)	(0.289)
Transport & Communication	−0.252**	−0.206	−0.284	0.181
	(0.122)	(0.295)	(0.378)	(0.255)
Business Services	−0.383**	−0.320	−0.444	−0.119
	(0.170)	(0.374)	(0.563)	(0.420)
Other Services	−0.219	0.271	−0.005	0.284
	(0.162)	(0.397)	(0.551)	(0.337)
INNOVATION	0.082	−0.140	−0.075	0.038
	(0.066)	(0.141)	(0.193)	(0.129)
East	0.128		0.184
	(0.117)		(0.366)
London	−0.073		−0.746**
	(0.128)		(0.371)
North East	0.167		−0.081
	(0.144)		(0.474)
North West	0.070		0.141
	(0.119)		(0.388)
South East	0.128		−0.217
	(0.117)		(0.343)
South West	0.090		−0.476
	(0.117)		(0.347)
West Midlands	0.009		−0.309
	(0.141)		(0.400)
York & Humber	0.197		−0.263
	(0.132)		(0.410)
Wales	0.069		−0.131
	(0.117)		(0.372)
Scotland	0.041		−0.232
	(0.159)		(0.414)
Owner/Entrepreneur characteristics
WLED	−0.100	0.110	0.022	0.019
	(0.090)	(0.157)	(0.247)	(0.191)
EXP	−0.169	−0.908*	−1.941**	0.284
	(0.200)	(0.498)	(0.788)	(0.436)
UNIVERSITY	0.086	−0.323***	−0.345**	0.044
	(0.055)	(0.124)	(0.170)	(0.113)
AIMGROW	0.248***	−0.038	0.165	−0.095
	(0.061)	(0.128)	(0.188)	(0.133)
Borrower risk indicators
SOUGHTBEFORE	−0.524***	0.004
	(0.053)	(0.108)
IBANKING	0.197	−0.239	−0.242	−0.644*
	(0.157)	(0.465)	(0.607)	(0.366)
RELATIO_1	−0.477***	0.313**	−0.074	−0.383**
	(0.091)	(0.147)	(0.226)	(0.160)
RELATIO_2	−0.617***	0.491***	0.181	−1.084***
	(0.075)	(0.129)	(0.198)	(0.143)
MISS_1	0.590***	0.213	0.546	0.126
	(0.116)	(0.325)	(0.397)	(0.200)
MISS_2	0.502***	−0.364*	0.011	0.126
	(0.108)	(0.198)	(0.275)	(0.180)
MISS_3	0.775***	−0.764***	−0.573**	0.244
	(0.111)	(0.179)	(0.231)	(0.176)
Recessionary time indicators
WAVE2/3/4	−0.294***	1.918***	2.394***	0.290
	(0.104)	(0.392)	(0.551)	(0.227)
WAVE5	−0.088	−0.155	−0.373	0.257
	(0.093)	(0.168)	(0.232)	(0.192)
WAVE6	−0.165	0.054	−0.163	−0.168
	(0.118)	(0.200)	(0.273)	(0.243)
WAVE7	−0.007	1.072**	1.953**	−0.385
	(0.227)	(0.506)	(0.830)	(0.507)
N		3089		803
Censored N		2286		82
Wald χ 2		114.42***		114.91***
Log likelihood		−1740.231		−541.255
χ 2 (ρ = 0)		5.17**		3.15*