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We develop a dynamic model with two-sided limited commitment to study how barriers to competition, such as restrictions to business start-up and non-competitive covenants, affect the incentive to accumulate human capital. When contracts are not enforceable, high barriers lower the outside value of ‘skilled workers’ and reduce the incentive to accumulate human capital. In contrast, low barriers can result in over-accumulation of human capital. This can be socially optimal if there are positive spillovers. A calibration exercise shows that this mechanism can account for a sizable portion of cross-country income inequality.

As Bewley reminds us, labor market conditions ‘external’ to the firm play a crucial role in the determination of wages. Since wages determine the return on human capital, external conditions are also crucial for the incentive of workers to accumulate human capital. In this paper we show that ‘external competitive’ conditions are important if contracts are not enforceable for both employers and employees (double-sided limited commitment). It is not difficult to see why in reality contracts are not fully enforceable for both employers and employees. On the one hand, without slavery or serfdom, workers are free to move to obtain the best return on their human capital. Together with the limited observability of workers’ effort, this reduces the enforcement of contracts for workers. On the other hand, employers could renege on the compensation promised to workers for their effort to accumulate human capital. Under these circumstances, workers would be discouraged from accumulating skills unless their human capital can be easily redeployed outside the firm. Since this depends on the competitiveness of the labor market, competition plays a crucial role in affecting the accumulation of human capital. This mechanism, which was already informally described by Adam Smith but until now has not been extensively explored, is the central focus of this paper. We use a dynamic general equilibrium model where contracts are not enforceable, neither for workers nor for firms (employers). We show that the way limited enforcement affects the accumulation of ‘general’ human capital depends on barriers to the mobility of skilled labor. In particular, high barriers discourage the accumulation of human capital while low barriers have a stimulating effect, both in new and incumbent firms. As a result, differences in ‘barriers to competition’ translate into significant differences in incomes and welfare across economies. While this result vindicates the common wisdom that ‘barriers to the external conditions of the firm’ are ‘barriers to riches’, it also shows that this effect can be greatly amplified when contracts are not enforceable for either party. In fact, a key finding of the paper is that the limited enforcement of contracts matters for the accumulation of human capital only when the limited commitment is double-sided, that is, when both sides can renege on the contract. Instead, with the commitment of at least one party, barriers to the mobility of skilled labor have limited effects on the accumulation of human capital and aggregate output. The central mechanism through which barriers to the mobility of skilled labor affect the accu- mulation of ‘general’ human capital is by reducing the outside opportunities of skilled workers, that is, the value of redeploying their skills outside the firm. With a lower outside value, workers do not have a credible mechanism for punishing the firm for reneging on the promised compen- sation. Anticipating this, the worker makes less effort to acquire skills, and therefore, there is a typical time-inconsistency problem. It is important to emphasize that the analysis focuses on the type of human capital that is not specific to an individual firm, and therefore, it can be trans- ferred to other firms. Otherwise, the outside value of the worker would be independent of human capital. Why do we need double-sided limited commitment? If the worker could commit to staying with the firm and providing effort (one-sided commitment from the worker), the contractual friction associated with the limited commitment of the firm could be resolved by paying the worker in advance. However, without the commitment from the worker, advance payments or ex-post payments conditional on the productivity realized are not incentive-compatible. This is because the worker can simply exert less effort and quit. On the other hand, if the investor could commit, the promised payments would not be reneged on ex-post. Thus, it becomes feasible to implement an incentive-compatible wage mechanism to extract the right level of effort and prevent the worker from quitting. For example, in line with existing Contract Theory, one could solve the commitment problem with an output-sharing agreement or by transferring the total or partial ownership of assets to the workers (e.g. [14]). But with a two-sided lack of commitment, such arrangements are still open to unverifiable de facto renegotiations or skimming. The only way to make the contract free from renegotiation is by choosing a level of invest- ment in human capital that makes the ex-ante payment promised by the firm exactly equal to the ex-post outside value of the worker, making renegotiation superfluous. In our economy, the best outside value for the worker is the one received by entering into a contractual arrangement with a new firm. Therefore, a credible investment policy for an incumbent firm is to mimic the investment decision of a new firm. However, when the investment cost of new firms is high (that is, there are high barriers) their investment is low, implying that the investment by incumbent firms is also low. In contrast, with full or one-sided commitment, incumbent firms do not have to mimic the investment decisions of new firms. In summary, in an economy with full or one- sided commitment, barriers to competition affect only the human capital accumulation of new firms. However, in an economy with two-sided limited commitment, barriers affect the invest- ment decisions of all firms. In particular, in economies where in equilibrium there is no exit or entry, changing the degree of competitiveness may have no effect if there is one-sided limited commitment. If there is two-sided limited commitment instead, the effects could be substantial. Our results are first illustrated with a simple two-stage model which is then extended to a dynamic infinite horizon set-up. The parameterization of the infinite horizon model allows us to quantify the ability of one particular barrier— start-up costs —to account for different levels of human capital accumulation, as well as cross-country income differences. The baseline model can account, roughly, for half of the cross-country income gaps with the US. Even though this number should be taken with caution, given the simplicity of the model, it shows that this mech- anism can be quantitatively important, bringing a new perspective on the role of competition as a factor of growth. In our benchmark model, ‘barriers to the external conditions of the firm’ are given by the cost of starting a new firm (which offers the best outside option to the skilled worker). However, there exist many other barriers that could generate similar qualitative results. For example, we show that covenants (preventing a skilled worker from working for a different employer in the same industry for a period of time) or strong enforcement of Intellectual Property Rights can depress human capital accumulation and possibly explain regional and national income differences. The results of this paper can also be interpreted as saying that barriers to competition de- termine cross-country positions relative to the ‘technology possibility frontier’, without empha- sizing a distinction between innovation and technology adoption. This is consistent with the idea that even the implementation of known technologies requires appropriate human capital. In contrast, Acemoglu et al. [4] develop a theory where the ‘distance to the frontier’ determines a country’s comparative advantage in innovation vs. adoption. While in their theory the cost of barriers depends on the position of a country relative to the frontier, in our framework it is the barriers that determine the position of a country in relation to the frontier. The causality effect is reversed and the policy implications are different. They show that a lack of pro-competition poli- cies becomes more costly as countries approach the world technology frontier, while our theoryimplies that a lack of pro-competition policies can determine a country’s position away from the frontier. Amaral and Quintin [5] also show that limited enforcement of contracts can have a large impact on equilibrium output because it reduces the capital directed to the production sector and the employment of efficient technologies. The main mechanism relies on the accumulation of ‘physical’ capital when contracts are not enforceable for entrepreneurs (one-sided limited enforcement). The accumulation of physical capital is also the key mechanism in [9] and [13]. Our paper, instead, focuses on the accumulation of ‘human’ capital when there is double-sided limited enforcement and emphasizes the central role played by ‘competition’ for human capital. In contrast to these papers, we show that more enforcement is not necessarily welfare enhancing when there are externalities in human capital accumulation. This paper relates to multiple strands of literature. In addition to the studies already cited, at least three more should be mentioned. First, it relates to the extensive literature on growth the- ories based on endogenous human capital accumulation (e.g. [18,23]). In these theories, human capital is rewarded through the usual channel of higher competitive wages. We take a closer look at this channel, showing how it can be affected by the interplay between competition and commit- ment in the skilled labor market. Second, our paper relates to the labor literature that studies the accumulation of skills either within the firm (e.g. [2]) or before workers and firms are matched and wages are negotiated. In most of this literature (e.g. [1,3]), higher outside values worsen the hold-up problem leading to lower accumulation of skills. In our framework, stronger competi- tion results in higher outside values. Third, the paper relates to the literature that emphasizes the role of ’barriers to riches’ in explaining income differences [22,24]. We emphasize the im- portance of barriers to labor mobility and how the effects of these barriers depend on contractual commitment features.

We have developed a theory in which barriers to the mobility of skilled workers affect the accumulation of human capital or knowledge, and therefore, the level of income. The theory does not simply say that competition enhances income. First, it emphasizes that some forms of limited enforcement are intrinsic to competitive labor markets, where wages are determined by supply and demand conditions. Second, it shows how different forms of contract enforcement affect the relation between competition, accumulation of human capital and economic develop- ment. In particular, when both investors and workers cannot commit to long-term contracts, the accumulation of human capital is determined by those firms that value human capital the most; in our benchmark model they are start-up firms. In this way our theory captures Bewley’s view that “ Wages rise quickly and sometimes dramat- ically in response to increases in the market demand for certain type of labor, but these increases are a reaction to competition from other firms, not to internal pressure from employees ”, Bewley [6, p. 407]. Our contribution is to show that ‘competition from other firms’ is also important for the accumulation of human capital. In particular, high levels of human capital are associated with low barriers to the mobility of knowledge because lower barriers increase ‘competition from other firms’. Using a semi-endogenous growth model, we have shown that barriers to business start-up have the potential to explain significant cross-country income differences. It may seem that accounting for 50% of the cross-country income gaps with the US overestimates the real contri- bution of our mechanism since the model is silent about many other features that are important for developing economies. Nevertheless, the fact that investment in human capital—even at the school level—is determined by expectations of future income returns, which in turn are affected by competitive and contractual conditions, seems a powerful mechanism.We have also shown that other barriers to knowledge mobility , such as strict enforcement of Covenants or Intellectual Property Rights, can have similar effects. Although we have modeled ‘on-the-job human capital accumulation’ and abstracted from skill-specific jobs, it should be clear that the mechanism described here is also relevant for ‘before-the-job human capital ac- cumulation’. In particular, the returns to education or to acquiring a specific mix of general and specific skills, depend on expected life-time returns. Our model shows that these returns depend crucially on the interplay between competition for skills in the labor market and the degree of commitment and enforcement.