financial markets cast doubt on the idea that taxation leads to divestment as outlined in this subsection. How, then, can we justify the deductions granted by lawmakers? The main rationale in this paper is the externality of an heir’s career choice discussed in the next section.
Consult Appendix 1.D for the derivation. In short, the firm is continued with probability F( ¯ω) and sold otherwise. In the latter case, the heir earns the outside wage, taxes are levied on the scrap value of capital, and the sum of the inheritance is deposited and earns interestRd. The idiosyncratic utility costs are not realized. In the former case, the planner uses equity and the after tax value of cash as collateral to expand capital input by factor (1 +Rλl).
Per unit of capital, the planner employsφ−1 workers who produce output Aj but forego the outside optionw. Denote byΩe(kj, xj) the social value of the firm, which is the indirect utility derived from the firm if the planner employs socially optimal quantities.
1.5.2 Career choice
For comparison, I repeat the reservation utility costs of the private career choice,
(x¯ j, kj, Aj) = Ve(xj, kj, Aj)
| {z }
eρ[(1−τs)xj+(1−τe)kj]
−wout−[(1−τs)xj+ (1−τs)skj]Rd. (1.15)
When the heir makes her career choice, she compares the leveraged return on equity to its scrap value at the financial market plus her personal outside option. Her return on equity is a function of the share of production she can reap given her Nash bargaining power (1−η). In contrast, the planner chooses to continue the firm if≤ω(x¯ j, kj, Aj), with
ω(x¯ j, kj, Aj) =Ωe(xj, kj, Aj)−wout−[(1−τs)xj+skj]Rd. (1.16) The social planner compares the complete value of production to the heir’s utility costs and the outside option. The latter includes tax income if the firm is scrapped. The most relevant difference between the social value of the firm and its private counterpart is the worker’s share of production,η.
This is the core externality in the model: in the decentralized solution, heirs do not take into account that high-tenure workers earn a higher wage in the firm and incur earnings losses if the heir makes the “wrong” career choice.
A private solution that internalizes the worker’s losses demands that career choice enters the bargaining between workers and the heir, but career choice
takes place many years before the first bargaining. Now, if the government grants deductions for firm continuation, the company heir internalizes the earnings losses of workers when making her career choice. This rationale is robust to any changes of the tax rateτs. Even if the government levies no inheritance taxes, it is still optimal to subsidize firm continuation.
The planner can decentralize the constrained-efficient solution by impos-ing a tax rate ˜τe which equalizes the private and the planner’s reservation talents,
Ωe(xj, kj, Aj)−Ve(xj, kj, Aj) =τsskjRd.
The planner sets a tax rateeτesuch that the difference between the social and the private value of the firm equals tax revenues of scrapping the firm. The optimal tax reads
˜
τe(kj, xj) =kjτssRd−h
(1−τs)xj+kjih
1 +Rλl φ−1
≡∆w
z }| { η(Aj−w−sφRd)i
kjρ(A]j) ,
which can be simplified to (1.17).
Theorem 1 (Optimal corporate inheritance tax rate) The corporate inheri-tance tax rateτ˜ethat maximizes social welfare and is levied only if the heir chooses to continue the firm is given by
τ˜e(kj, xj) =T −∆wnj|τ
e=0
kjρe , (1.17)
whereT ≡kjτssRd denotes the tax revenue earning the deposit interest rate if the firm is scrapped,nj|τ
e=0 is the employment level absent corporate inheritances taxes,∆w=w(Aj)−wdenotes the earnings losses andkjρeis the gross return on equity.
The optimal inheritance tax on equity can be positive or negative depend-ing on the level of the standard inheritance tax,τs, and the size of the wage losses if the firm is scrapped. If earnings losses are large∆w >>0, a higher firm succession rate is socially efficient. To encourage more heirs to choose the entrepreneurial path, the planner grants a larger tax discount for firm succession,τe<< τs. Turning to the level ofτs: a high non-corporate
inheri-tance tax rate has two implications: first, the higher the tax rate, the larger the tax revenue if the firm is scrapped. The same holds for the opportunity costs of capital, i.e. the deposit interest rate and the reversibility of capital investmentss. The higherτs, the higher the optimal fraction of scrapped firms and the higherτe. Second, a larger tax rateτs creates a heftier penalty on the heir’s outside option. Ifτsis low, firm continuation must be subsidized to let the heir internalize the workers’ earnings losses and the optimalτeeis negative. If tax rateτs is very high, the outside option is costly in terms of tax liabilities and a smaller yet positiveeτecan implement the socially-optimal reservation talent. The private leveraged return on equityρeaffects the size, not the sign, of ˜τe. Suppose it is optimal to subsidize firm continuation, τ˜e<0: a largerρereduces the size of this subsidy because the firm is already more profitable for the heir. Suppose ˜τeis positive: a high return on equity reduces the optimal tax rate, because the private return is also part of the social welfare function.
The assumptions which drive the main result (1.17) are obviously restric-tive. Firms with a small numbers of employees face difficulties trying to find a suitable, yet affordable manager. Asymmetric information and the non-transferability of human capital prevent potential external buyers from buying and managing the firm. However, these assumptions cease to be credible once a company has reached a certain size. As shown in Section 1.3, favourable treatment of business assets is used extensively for very large companies. A large company can be sold at the capital market. Assume that the value of a large firm is not private information (s = 1) and that external buyers will inject the same amount of cash into the firm as the heir would. It follows that the socially-optimal probability of continuing the firm isF(−wout), i.e. the firm should not play any role in the private career choice of the heir, who should instead choose the career which bests matches her personal tastes and talents. In the case of large firms, the planner confiscates the whole excess return of firm heirs:
Corollary 1.1 (Large firm inheritance tax rate) The socially optimal inheri-tance tax rate τ˜e given that the firm can be bought and continued by external
buyers who choose capital inputxj−1(1−τs) +skj−1 is given by
τ˜elarge(kj, xj) =(ρe−Rd)(1−τs)xj+ (ρe−(1−τs)Rds)kj
ρkej , (1.18)
where the numerator summarizes the excess return on capital in the firm compared to the return on scrapped capital at the market.15