We first prove that assumption al implies th at E is never forced to retire. We substi tute (3.6) in (4.6) obtaining the following:
kt+i + x% -j- < Wt + (6.20)
the left hand side of (6.20) is constrained downwards by constraints (3.1), (4.3) and (4.4). Therefore, if we substitute u>t using (4.6), and x%, kt+i and lt+i from constraints (3.1), (4.3) and (4.4) holding with equality in (6.20), we get the following condition:
y t + ^ ( l - h ) h > b t
(6.21)
condition (6.21) is symmetric to (4.5) and is necessary to ensure th at E is not forced to violate (4.3) to repay the debt. We determine Z^in, the constant level of variable capital supplied by E , as the level of lE such that (6.21) is always satisfied for all the possible levels of state variables Wt, kt and 0*. The left hand side of (6.21) is monotonously decreasing in
6t and It, therefore the worst possible situation is the one in which It —> 0 and 9t = 9l-
We substitute these two limit values in (6.21), and we substitute yt using (4.1). We also define k as the maximum feasible level of kt compatible with 9t = 9l. Solving (6.21) in terms of lE yields the following:
lE >
BA = Imin (6-22)
Where 9 = Et(9t+\ | 9t = 0l)« We then prove that assumption a2 implies th a t E
never voluntary retires. Since E is risk neutral, in order to prove th at continuation is always optimal it is sufficient to prove th a t expected return from the investment in the firm is always greater than R. If irreversibility is not binding, E is always able to choose
a combination of kt+i and lt+i such th at this condition is satisfied. We consider instead the case when irreversibility is binding. The case in which continuation is less likely to be optimal is the one in which E is most constrained. At the limit: Wt = w™in, rrjf = 0 and
lt+1 = 0, because all the resources are used to repay bt , and there is no money to invest
in variable capital. E compares two choices: i) if she continues, she borrows up to the maximum. By substituting the limit values x% = 0, lt+i = 0 and bt+i = Tf-h+i in (4.6) we get the following:
<*+! = « * / ( 1 - ^ ) (6.23)
therefore E invests kt+i, and receives expected total revenues, net of debt repayment, equal to:
Et (7Tt+i | Dt = 1) = (1 + 77) Et (#t+i) kt+ilE + (1 — 6k — Tfc) kt+ 1 (6.24)
ii) if E retires, she is indifferent between consuming and investing wt in the risk free asset. Therefore substituting Wt from (6.23), her expected return is:
E t (TTt+1 I Dt = 0) = Rwt = R ( 1 - fcm (6.25)
therefore E always prefers to continue if Et (7r*+i | Dt = 1) > Et (nt+i \ Dt = 0) for t > 0,
which is exactly the condition imposed by a2. ■
Proof of proposition 5.
We start by noting th at from (6.15) it follows that, for j = 0 ,1 ,..., 0 0 and for s > j:
^ \wt+j<wMAX<® (6.26)
from (4.10) and (6.26) it follows th at 4>t decreases if the expected rate of growth of financial wealth increases. Therefore in order to prove proposition 5 it is sufficient to prove th a t the expected rate of accumulation of financial wealth is lower when irreversibility is binding. In order to prove it, let’s consider (6.3) evaluated at x* = 0 :
by taking expectations:
E t (Awt+i) = rwt + E t (^ t+ i) (6-28) Now recall that by definition a binding irreversibility constraint implies th at fixed capital is inefficiently high: (1 — 6k)kt = kt+\ > k°+1. k°+1 is the optimal level of capital when fixed capital is reversible. Also proposition 3 implies th a t k°+l > A£+1, which is the level of capital th at maximises Et • Therefore, since the concavity of the production function implies that Et monotonously decreases in the level of capital for kt+i >
A£+1, it follows that:
E t (Awf+i | (1 - 6k)kt = kt+1 > kf+1) < E t (Awt+i \ k$+1) (6.29)
proposition 5 is proved by generalising (6.29) for any future Et (Aw t + j ) with j = 1,2, ...oo.B
Proof of proposition 6.
Proposition 6 follow directly from (6.16), (6.17) and (6.18), and from the fact that, when wt is smaller than wt, the concavity of the production function implies th a t A^ monotonously decreases in w ^ M
Appendix 2: description of the data
The empirical analysis illustrated in chapters 2 and 5 of this thesis is based on two datasets of Italian manufacturing firms:
I) A panel of balance sheet data for 5289 Italian manufacturing firms. This is a subset of the Centrale dei Bilanci dataset (64.463 firms at 1992 according to the Cerved database) which includes only firms with complete balance sheet d ata from 1982 to 19922. The advantage of this dataset is the amount of quantitative information available on the firms: the panel data includes assets and liabilities, profit and losses, and detailed information on the financial flows. The disadvantage is the absence of entry and exit during the sample period and the fact th at the sample is not representative of the population of Italian manufacturing firms, because it is mainly composed of small and medium firms below 500 employees.
II) The three Mediocredito Centrale surveys on small and medium Italian manufac turing firms. The research department of Mediocredito Centrale, the Italian largest in vestment bank, compiled the three surveys in 1992, 1995 and 1998. Each survey includes a large questionnaire on firms activity, ranging from the form of ownership, to the invest ment and financial policy, to other organisational aspects. Each questionnaire covers the three years before its compilation (1989-91, 1992-94 and 1995-97 respectively) and includes balance sheet data for the same three years for around 4000 firms. The unique advantage of this dataset is the direct information about firms financial policy. In particular in this thesis we use the information about the financing problems the entrepreneurs faced in funding new investment projects and the information about the financing sources mostly used to fund them. The other advantage is th at the surveyed firms are representative of the Italian population: in each survey the sample is randomly stratified (it reflects the sector’s geographical and dimensional distribution of Italian firms) for firms below 500 employees, while it is by census for firms with more than 500 employees. The main dis advantage of this dataset is the fact that the sample composition changes across surveys,
2 Actually the sample ranges from 1992 to 1994, but we do not use in the thesis the information from
1993 and 1994 balance sheets, except than in figures 6-2 and 6-3, because there are inconsistencies in some assets and liabilities tim e series between 1992 and 1993, probably due to the fact that the accounting rules changed in 1993 as a result of the E.C. armonisation of accounting procedures.
and as a consequence only 347 firms have both qualitative and quantitative d ata from all the three surveys.
The most interesting aspect of these datasets is th at they have a fairly large number of firms in common. In particular in section 2.2 and in chapter 5 we consider the 891 firms present in both the Centrale dei Bilanci dataset and in the first Mediocredito Cen trale survey. Such firms have both complete balance sheet data, from 1982 to 1992, and the detailed qualitative information from the first Mediocredito Survey, which refers to the 1989-1991 period. In particular the survey asked if the firms had one of the follow ing problems in financing new investment projects in the 1989-1991 period: i) ’’lack of medium-long term loans” ; ii) ’’too high cost of debt” or iii) ’’lack of collateral”3. Also the second and third Mediocredito surveys asked direct questions about financing prob lems. Unfortunately each survey asked substantially different questions to reveal financing constraints, and hence it is not possible to pool such information across surveys.
Such pooling is instead very useful when we describe the more general link between financial policy and growth in section 2.3. This is because all the three surveys asked identical questions regarding the composition of the new investment financing.