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«† Andres Zambrano Universidad de los Andes May 12, 2014 Abstract This paper explores the role of effort and human capital as mechanisms to ...»

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Endogenous Employment and Incomplete

Markets∗

Andres Zambrano

Universidad de los Andes

May 12, 2014

Abstract

This paper explores the role of effort and human capital as mechanisms to alleviate the idiosyncratic risk in the presence of incomplete

markets, and its consequences for the wealth distribution. I construct

a DSGE model where effort and human capital determine the probability of being employed the next period. While effort is a flow variable

that has to be exerted every period, human capital is a stock variable chosen when the agent is born. I first show how effort and assets are inverse related, and that only rich enough households invest in education. In a calibrated version of the model to the US economy, it is shown that in the stationary equilibrium individuals diversify between market and non- market mechanisms, and a positively skewed wealth distribution arises. This is a salient feature of the data that has not been obtained before by similar models. The model also approximates the real wealth distribution conditional on education, replicating the observed skewness and dispersion. The results shed light on the potential implication of combining policies of unemployment insurance and subsidies to education to improve the wealth distribution.

Keywords: Employment, Incomplete markets, Heterogeneity, Endogenous Markov chains JEL codes: D91, E21, E24, E25, J22 ∗ This paper is based on the second chapter of my dissertation at UCLA. The author would like to acknowledge the comments of Andy Atkeson, Francisco Buera, Roger Farmer, Christian Hellwig, Gonzalo Llosa, Lee Ohanian, Venky Venkateswaran, and Pierre-Olivier Weill; as well as participants in the Macro Lunch Proseminar at UCLA, LACEA, Universidad de los Andes, the Midwest Macro Conference, the Central Bank of Colombia, the University of Leipzig and The Guanajuato Workshop for Young Economists. The author is also very grateful for the financial support given by the Central Bank of Colombia. The valuable research assistance of Felipe Acero is greatly aknowledged. The usual disclaimer applies.

† E-mail: ja.zambrano@uniandes.edu.co 1 Introduction Education has been related to higher lifetime earnings through both higher wages and less incidence and duration of unemployment.1 Since college education is usually obtained by richer households, education creates a stronger tension towards a more unequal distribution of wealth. On the other hand, recent empirical papers have provided evidence on the negative effect that wealth has on the probability of employment once a set of control variables, including human capital, are used (Algan, Ch´ron, Hairault, and Langot, e 2003; Bloemen, 2002; Bloemen and Stancanelli, 2001; Stancanelli, 1999). On the theoretical side, such association was rationalized by Lentz and Tranæs (2005) in a search model with savings where effort must be exerted over time to increase the chance of being employed. Thus there seems to be a feedback effect of wealth, via effort, towards a more equitable distribution.

The above observations suggest a rather complex relationship between assets and the probability of employment, which seems to be negative in the short-run but positive in the long run. The purpose of this paper is to build a model to explore the joint role of effort and human capital investment as nonmarket mechanisms used by individuals to deal with their idiosyncratic risk.

The analysis provides potential welfare implications for combining public policies related to unemployment insurance and subsidies to education to improve the wealth distribution and the long-run unemployment.

I develop a dynamic stochastic general equilibrium with heterogeneous agents that builds on the framework proposed by Huggett (1993) and Aiyagari (1994) where a riskless asset is used to smooth consumption. However, we depart from the previous models by endogeneizing the transition probabilities between employment and unemployment. In particular we allow the effort and human capital to determine the transition dynamics and thus they According to the Bureau of Labor Statistics, the unemployment rate in 2011 for college graduates was 4.4% versus 9.6% for non-college graduates. On the other hand, the median duration of spells of unemployment was 2.6 months for less than high school graduate, 2.4 for a high school graduate and 1.9 months for individuals with at least some college.

can be used by agents as non-market mechanisms to smooth consumption.

Effort is modeled as a flow variable that has to be chosen every period to maintain a positive probability of being employed, thus following the literature on unemployment insurance (see for example Hopenhayn and Nicolini (1997) and Wang and Williamson (1996)). This can be seen as search effort when the individual is unemployed, or effort on the job when the agent is employed. We assume the level of effort required in the latter case is more effective that the one when the agent is unemployed. This assumption matches with empirical data that has been studied in search models and emphasize the role of the depreciation of human capital during unemployment (Addison and Portugal (1989); Neal (1995)).

On the other hand, human capital is a binary stock variable that can be acquired when the individual is born. It is assumed that it improves the efficiency of effort when looking for a job or maintaining it. Alternatively, a college degree can be interpreted as a variable that generates better shocks.





Although human capital has been usually studied as a mechanism to increase earnings, previous empirical work has also pointed out the effect of human capital on employment transitions. For example, Card and Sullivan (1988) estimate the effect of training on the probability of employment for the 1976 cohort of adult male participants in the Comprehensive Employment and Training Act (CETA). They found that the effect is positive, even for people who is already employed. Gritz (1993) also found that participation of women in private training programs increases both the frequency and duration of employment spells.

The model eliminates any source of heterogeneity in wages by assuming that the endowments obtained by (un)employed individuals are the same and independent of other variables. Although the wages earned by different individuals may differ because there is heterogeneity in initial abilities, increases in human capital due to college attendance, or because more effort on the job leads to more productivity; this is a simplification we made to obtain a cleaner intuition on the forces shaping the wealth distribution. Moreover, this simplification could be interpreted as if variables are normalized by income and therefore the effect of ability and monetary returns to education and effort is removed. Such normalization is the strategy we follow when the model is compared to the observed data.

As it is usual in this literature, asset holdings are restricted to be greater than a lower bound to prevent situations where individuals get indebted forever. This lower bound is used to model a financial friction usually found in reality, and is calibrated accordingly. An upper bound arises naturally from the optimal decisions and the fact that the interest rate is lower than the rate implied by the intertemporal discount factor. This discourages individuals from accumulating forever their asset holdings.

The role of the asset holdings in our model is similar to the one played in previous literature. When the individual is employed she accumulates assets, while she decreases her holdings when unemployed. Therefore, it keeps track of the employment history the individuals have had. However, assets also have a bequest motive in this model. Individuals die with an exogenous probability and newborns inherit the previous wealth. Given the assumptions, we show that only rich enough newborns will invest in education since their marginal value for assets is lower than the one for poor individuals.

This generates pressure towards more inequality.

On the other hand, effort has an inverse relationship with assets. If an individual becomes unemployed and has sufficient savings, she will not exert too much effort to find a job and instead use the savings to smooth consumption. However, the ability of the assets to smooth consumption loses importance when they are close to the debt limit. At that point effort plays a major role by increasing the likelihood of being employed next period.

We calibrate the model to the US economy and compute the unique stationary equilibrium. I find that the stationary wealth distribution is positively skewed, where most of the individuals hold a small negative credit balance, while few of them have positive savings. This means that most of the individuals combine both market and non-market mechanisms to smooth consumption rather than relying in one of them. This result goes in line with the findings of empirical papers studying the wealth distribution. For example, Wolff (2010) shows that only the top deciles have positive savings, while most households hold some degree of debt. We corroborate such result by applying the normalization described earlier to the data collected by the Survey of Consumer Finances (SCF).

To the best of our knowledge, this is the first paper, within this type of parsimonious models, that obtains a distribution with such characteristics.

Papers that focus on market mechanisms to alleviate risk usually generate wealth distributions negatively skewed since precautionary savings are the only channel to smooth consumption. Moreover, our model allows us to compute the wealth distribution conditional on having a college degree or not, and it remarkably replicates the observed data. Therefore, besides explaining how wealth, effort and education interact; the model also sheds light on how policies, like unemployment insurance and subsidies to education, could shape the wealth distribution.

1.1 Related Literature Idiosyncratic shocks and consumption smoothing has been largely studied in the literature. Models of incomplete markets and heterogenous agents have been used to explain the risk premium (Huggett, 1993), the benefits of in˙ surance (Hansen and Imrohoro˘lu, 1992), optimal fiscal policy (Heathcote, g 2005), and the distribution of income (Aiyagari, 1994; Heckman, Lochner, and Taber, 1998; Krusell and Smith, 1998), among others. The common characteristic of these models is that they use mechanisms affecting the budget constraint to smooth consumption. These mechanisms are usually identified with assets holdings (or credit balances), capital, or savings. However, the labor transitions are always specified exogenously.

Besides the theoretical contribution made by Lentz and Tranæs (2005) on endogenous transitions, other calibrated models of search with savings include Acemoglu and Shimer (2000), Rendon (2006) and Gomes, Greenwood, and Rebelo (2001). However, the do not focus on the wealth distribution and do not include human capital as another source to smooth consumption.

Among the papers who have studied the role of human capital on the wealth distribution in the presence of imperfect credit markets we can find Galor and Zeira (1993) and Krebs (2003). However, their main purpose is to explain different growth paths and thus provide an answer to why there exist persistent differences in per capita output across countries. To the best of our knowledge, the relationship between human capital, effort and imperfect credit markets, along with their consequences on the wealth distribution, has not been explored.

The organization of the paper is as follows. The next section describes the model and the third section defines the equilibrium in this scenario. I then describe the performed numerical exercise, while section 5 devotes attention to its computation. In section 6 we show the results and its implications.

The last section concludes.

2 Model Consider an exchange economy with a continuum of agents with total mass equal to one who face idiosyncratic risk. There are two commodities: one perishable consumption good c and asset holdings a. Each agent receives an stochastic endowment st at the beginning of each period. Assume the endowment can take two possible values sL sH, which are usually associated with unemployed/employed status, respectively.

Effort e 0 is made in order to increase the probability of having a good endowment (state) next period. The probability of being employed next period also depends on whether the agent has a college degree or not, hH or hL, respectively. The probability in period t is defined as Pr(st+1 = sH |st, h) = P (et ; st, h), which is an increasing concave function of the effort with P (0; s, h) = 0 and lime→∞ P (e; s, h) = 1. According to the empirical literature, assume that effort to remain employed is more effective than the effort to become employed when previously unemployed, and effort is also more effective when the individual has a college degree. Formally, P (et ; sH, h) P (et ; sL, h) for all h, P (et ; s, hH ) P (et ; s, hL ) for all s. Finally let the probability be supermodular in e, s, and e,h.

Individuals discount future at rate β and survive next period with probability δ. When an individual dies it is replaced by an unemployed newborn.

The newly born agent inherits previous wealth and decides whether to obtain a college degree or not at a cost φ. Agents are altruistic and maximize lifetime utility of the household. Each individual derives instantaneous utility from consumption and effort according to an additive separable utility function u(c) − e that is strictly concave and satisfies Inada conditions. Separability can be obtained assuming the existence of lotteries and simplifies the analysis importantly (Lentz and Tranæs, 2005). The fact that the disutility of effort is linear is just an innocuous normalization.

Each agent is able to smooth her consumption by holding a single riskless asset. This asset entitles the individual to receive one unit of future consumption for each unit of asset whose price is q 0. The amount of claims held must remain above the limit amin, a restriction that represent the financial friction faced by individual in addition to the incompleteness of the markets. Therefore, the budget constraint faced by an individual who holds a claims, has a current endowment s, and chooses consumption c and future claims a, is given by

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