Human capital misallocation, redistributive policies, and TFP

Abstract

We analyse the impact of human capital misallocation and redistribution on GDP, welfare, and TFP, in economies with financial market imperfections. We present an overlapping generations model in which the innate abilities of children are drawn from a probability distribution and where parents are unable to insure against these shocks or borrow against their child’s future incomes. The government has access to a redistributive tax and transfer system that can partially mitigate the effects of these missing markets. The steady state equilibrium of the model features closed form analytical solutions for the distributions of human capital, physical capital, and income, along with aggregate measures of TFP and welfare. We calibrate the model to the US economy and find that the misallocation, and its adverse effects on TFP and GDP, can be significant. However redistributive policies, aimed at mitigating the misallocation from these missing markets, have only small positive effects on TFP but large negative effects on GDP.

Introduction

The importance of total factor productivity (TFP) for variations in per capita income has been recognized in macroeconomics and development economics ever since the seminal paper of (Solow, 1957). In the context of the standard neoclassical growth model, while factor inputs can play a role in these variations in the short run, TFP is the only source in the long run. Understanding the determinants of TFP in a consistent way requires a theory of TFP – something (Prescott, 1998) famously called for.

A considerable body of work, following Restuccia and Rogerson (2008) and Hsieh and Klenow (2009), has examined the role that the misallocation of resources, due to market distortions of some kind, play in determining TFP differences. Hsieh and Klenow (2009), for example, estimated that, if market distortions were somehow reduced down to US levels, TFP would increase in China by 30–50% and in India by 40–60%. Moreover, in their baseline, if market distortions were eliminated entirely in the US economy, this would increase TFP in that country by 42.9%. These large numbers have attracted considerable attention, and subsequent work has focussed attention on particular markets that may be responsible for these figures.¹

A particular emphasis has been placed on the role that imperfections in financial markets play in misallocation and TFP differences. Buera et al. (2011), for example, estimate that financial frictions can reduce TFP by up to 36%. Midrigan and Xu (2014) found that, while financial frictions do affect misallocation, relative to their effects upon firm entry and technological adoption, these effects are, quantitatively, quite small (reducing TFP by approximately 5% in developing countries). Subsequently, using a (Lucas, 1978) span-of-control model, based on Buera et al. (2011) and Bhattacharya and Ventura (2013), Yoon (2016) found that, by encouraging substitution from physical capital into managerial capital, credit market imperfections can actually increase TFP. David et al. (2016) provide a theoretical link and quantitative estimate of the effects of informational frictions, arising from imperfect information regarding firm-specific demand conditions, indicated by the stock market data and the aggregate inefficiency in the economy, causing a positive variance of marginal products.

Some recent work has focused on the losses to TFP due to the misallocation of human capital. For example Hsieh et al. (2018) offer evidence to demonstrate how barriers to participation based on non-pecuniary factors, such as race and gender, which deter equalization of marginal products, cause loss of TFP and output by discouraging people with talent to pursue occupations in which they have a comparative advantage. Wang et al. (2018) report that a significant reduction in TFP could result from the mismatch between skill and technology reflecting the lack of assimilation of factor inputs in the economy in a way to equalize their marginal products.

In this paper we examine the implications of financial market imperfections upon the distribution of human capital – and their consequent effects on misallocation and TFP. Intuitively, human capital cannot be used as collateral. Consequently, in the presence of idiosyncratic innate talent dispersion among children, there exists no credit market through which rich parents can invest in the education of more talented children born into poorer families than their own. Similarly, current decision makers in families have no way of insuring against the risk that future family members will be born with disappointing innate abilities. Facing these financial frictions, parental investment in the education of children with different abilities can generate a misallocation of human capital (and a reduction in TFP) since, once again, marginal products will be not equated. Given these missing markets, and that the misallocation issue is driven largely by income inequalities across households, it is also natural to ask to what extent they can be mitigated by redistributional policies.

To study this issue, we consider a variant of Benabou’s (2002) model of the joint determination of the distribution of human capital and output, in equilibrium, in an environment with financial market imperfections. Following Benabou, we analyse a dynastical overlapping generations economy in which agents are restricted from passing debts to their descendents and face uninsurable idiosyncratic risks concerning the innate abilities of their offspring. A non-degenerate distribution of income persists in the long-run equilibrium of this model. This income distribution is influenced by, among other things, a redistributive tax-and-transfer scheme operated by the government, with the key policy parameter being the income-weighted average marginal tax and transfer rate, τ. As the government increases the value of τ it redistributes from richer households to poorer ones.

In this setting, facing the financial constraints, poorer households are restricted when financing the education of their young. With diminishing marginal returns to education, this, alone, generates inefficiencies due to misallocation. The misallocation problem is worsened, though, when children are born with different abilities; particularly when poor parents of high-ability children are not able to afford the appropriate level of education for them. Thus an increase in τ can, in principle, mitigate this problem by diminishing the effect of the credit constraint. However, as Benabou points out, this type of redistribution also distorts saving and labor supply decisions. Higher values of τ therefore not only reduce misallocation (a positive effect) but also reduce savings and labor supply (a negative effect). Under reasonable parameter values, steady-state TFP, GDP, and welfare (using a utilitarian social welfare function), are hump-shaped in τ and, in principle, one can find values of τ that maximize each of these variables in equilibrium.²

For tractability, Benabou’s (2002) original model has only one accumulable factor: human capital. His model is effectively one of a small open economy, where physical capital is rented in a large world market with fixed real interest rates. While this is a sensible approach for the issues that Benabou focuses on in his paper, here, we are focusing on determining TFP – and, consequently, physical capital should be treated more explicitly as an accumulable factor. In this paper, following Tang (2008), we introduce physical capital in a way that preserves many of the convenient mathematical properties of Benabou’s model. In particular, analytical solutions are available for all of the key endogenous variables – making both calibration and interpretations relatively easy.³

We calibrate the model to the US, and use it to answer the following quantitative questions. What effects does τ have on TFP, GDP, and welfare? What are the trade-offs between efficiency and equity in the US economy? How far is the current degree of redistribution from the ones that maximize TFP, GDP, and welfare? What are the relative effects of human capital versus physical capital misallocation? To what extent can redistribution eliminate the misallocation induced by the financial constraints?

In the calibrated model we find that steady state TFP, GDP, and welfare are all inverted-U-shaped functions of the policy variable that we focus on: τ. We also find that the values of τ that maximize TFP, GDP, and welfare are quite different from each other: GDP is maximized at ${\tau }^{*}=0.273$ (ie., 27.3%), welfare is maximized at ${\tau }^{**}=0.573,$ and TFP is maximized at ${\tau }^{***}=0.838$. According to the latest estimate, the current value of τ in the US is approximately ${\tau }_0=0.314$ – slightly above the value that maximizes GDP, but significantly below the values that maximize welfare and TFP. In the baseline model an increase in the degree of redistribution, from the current 31.4% up to the welfare-maximizing 57.3%, would lead to a reduction in GDP, but also a reduction in inequality, an increase in welfare, and an increase in TFP. Any increase in τ beyond that rate would reduce GDP and inequality further, but decrease welfare overall, while continuing to increase TFP. If τ is increased beyond 83.8% then GDP, inequality, welfare, and TFP all decrease.

The model also implies that TFP is reduced significantly more by the misallocation of human capital, rather than physical capital. The inclusion of physical capital in this model is quite important, though. In Benabou’s original model without physical capital (corrected), the value of τ that maximizes GDP is significantly higher (34.8%), rather than 27.3% in our model. According to the model without physical capital, the existing value of 31.4% is slightly below the value that maximizes GDP. Allowing the inclusion of physical capital, though, this model implies that the existing value of τ is too high to maximize GDP – but still too low to maximize welfare or TFP.

In the spirit of the (Hsieh and Klenow, 2009) exercise, we also use the model to quantify the overall implications of the misallocation, in equilibrium, upon TFP. We find that the complete elimination of the misallocation problem in this model (by allowing a full set of financial markets) would increase TFP by approximately 15.1% (compared with 42.9% in Hsieh and Klenow (2009)). The effects on TFP through changing the value of τ are considerably smaller. For example, in our baseline model, if the TFP-maximizing tax-and-transfer rate ${\tau }^{***}=0.838$ replaces the existing ${\tau }_0=0.314,$ it increases TFP by only 0.76%. It also decreases GDP by 10.7%.

We conclude, therefore, that human capital misallocation may in fact be an important determinant of TFP. However, using redistributive policy to alleviate this misallocation involves significant trade-offs.

The remainder of the paper is structured as follows. The model is presented in Section 2, its equilibrium dynamics are characterized in Section 3, and its steady state is analysed in Section 4. In Section 5 we present the quantitative analysis, and Section 6 contains some concluding remarks. The appendix in the paper provides proofs for some of the key results, but lengthier proofs are provided in the online appendix.