Cyclicality of labor wedge and informal sector

doi:10.1016/j.econlet.2015.09.024

Economics Letters

Volume 136, November 2015, Pages 141-146

https://doi.org/10.1016/j.econlet.2015.09.024 Get rights and content

Highlights

•
The ‘labor wedge’ is defined as the gap between the household’s marginal rate of substitution and the firm’s marginal product of labor.
•
Empirical evidence suggests that the labor wedge is quite volatile and countercyclical.
•
We argue that the presence of an ‘informal sector’ can provide a key for understanding the observed labor wedge dynamics.

Abstract

Empirical evidence suggests that the labor wedge, defined as the gap between the firm’s marginal product of labor and the household’s marginal rate of substitution, is quite volatile and countercyclical. This article argues that the presence of an ‘informal sector’ can provide a key for understanding the observed countercyclical behavior of the labor wedge.

Introduction

The business cycle literature defines the ‘labor wedge’ as the gap between the marginal rate of substitution of consumption with leisure (MRS) and the marginal product of labor (MPL). In particular, the literature measures the labor wedge as the residual that ensures that the intra-temporal condition of a one-sector model holds with equality when evaluated using data. Based on this, empirical evidence suggests that the US labor wedge–measured using time series data on consumption, hours worked and output–is countercyclical and slightly more volatile than US GDP (see Fig. 1).²

The labor wedge typically captures labor market distortions. Accordingly, a factor that has not been studied in the literature is the distortions arising due to the presence of an ‘informal sector’. In this paper, we argue that, in an economy with informal sector, the theory can capture the observed counter-cyclical behavior of the labor wedge. Specifically, we build a two-sector general equilibrium model calibrated to the US economy and show that the labor wedge is counter-cyclical and volatile in an economy with informal sector. More in details, when the formal sector experiences a negative productivity shock, the demand for formal labor falls, which leads to an increase in informal sector employment. We argue that (i) this counter-cyclical behavior of informal sector, and (ii) the fact that the informal activity cannot be identified from data are the two key features for understanding the observed labor wedge dynamics.

The intuition is as follows. In the presence of informal sector, production is subject to a serious measurement problem: the informal activity in the US economy cannot be identified from data. Accordingly, the total labor input measurements for the US economy does include only the formal sector labor. Therefore, the actual MRS measured from data do not take into account the labor supplied to informal sector. However, our ‘model implied’ MRS takes into account the labor supplied to informal sector when calculating the total labor supply. Therefore, to be consistent with the US data measurements, if we (i) simulate our model as usual to generate series on formal and informal sector, (ii) treat data generated by the model as data for the US, but (iii) ignore the informal sector—construct the labor wedge as if data on informal sector is not available (do not consider informal labor as a part of total labor), then the labor wedge in our model is countercyclical! Moreover, since the informal sector exhibits countercyclical behavior, the measured labor wedge exhibits countercyclical behavior as well. Based on these findings, we argue that the presence of informal sector affects the measured cyclicality of labor wedge, both in the data and in our model.

To sum up, the lesson from this exercise is as follows: When measuring the labor wedge using a one-sector model, we abstract from the informal sector. Accordingly, we show that in the presence of an informal sector, the neoclassical framework can capture the observed countercyclical behavior of labor wedge and our benchmark model can account for 68% of the observed volatility in the US labor wedge.

The literature on the cyclicality of labor wedge is rich, albeit still far from being complete. Chari et al. (2007), Shimer (2009), Shimer (2010), Gourio and Rudanko (2014) and Karabarbounis (2014) provide a non-exhaustive list of papers looking at this issue. Accordingly, multiple factors, such as distortionary taxes, presence of rigidities, intangible capital, social safety nets, home production and search frictions have been highlighted behind the cyclical behavior of the labor wedge.

Even though the literature lacks comprehensive empirical studies using high-frequency datasets with large time series dimension, few existing studies show that the size of the informal sector is counter-cyclical. While Busato and Chiarini (2004), Conesa et al. (2001) and Elgin (2012) indicate that the informal sector exhibits a counter-cyclical behavior in the US economy, Loayza and Rigolini (2006) documents this fact for selected developed and developing economies. Accordingly, the informal sector employment, being counter-cyclical, offers insurance against poor formal labor market conditions in recessions.

The rest of the paper is organized as follows. Section 2 presents the model and characterize the competitive equilibrium. Section 3 discusses the calibration. Section 4 presents the quantitative implications of the model. Section 5 summarizes and concludes.

Section snippets

The model

Time is discrete and indexed by $t = 0, 1, 2 \dots$ . The model economy is populated with a continuum of households with the following preferences: $E_{0} \sum_{t = 0}^{\infty} β^{t} U (c_{t}, n_{f t}, n_{i t}) = E_{0} \sum_{t = 0}^{\infty} β^{t} (ln (c_{t}) - m \frac{ξ}{1 + ξ} {(n_{f t} + n_{i t})}^{\frac{1 + ξ}{ξ}}),$ where $β \in (0, 1)$ is the subjective discount factor, $c_{t}$ denotes consumption, $n_{f t}$ denotes the labor supplied to the formal sector, $n_{i t}$ denotes the labor supplied to the informal sector, $m > 0$ measures the disutility from working and the term $E_{0}$ represents the expectations of households conditional on

Calibration

The model is calibrated on a quarterly basis for the US economy. Table 1 summarizes the parameters used in the benchmark case. We set $β = 0.99$ so that the real interest rate is 4.1% annually. The income share of labor in the formal sector is set to $1 - α = 0.64$ to match its empirical counterpart over the post-war period. Following Conesa et al. (2001), we set $α_{L}^{i} = 0.65$ . While we do not have a direct estimate for the income share of capital in the informal sector, we use the span-of-control estimates

Quantitative analysis

We start by constructing the actual time series of labor wedge for the US economy by using Eq. (10) and time series data on consumption, labor input and output. Fig. 1 displays the cyclical components of the labor wedge, GDP and hours worked in the United States between 1964 and 2010. Two patterns stand out: the labor wedge is volatile and strongly counter-cyclical to GDP and hours worked. We find that the detrended labor wedge is slightly more volatile than the detrended GDP, with a relative

Conclusion

In this paper, we show that in the presence of an ‘informal sector’, the neoclassical framework can capture the observed countercyclical behavior of labor wedge. We find that our model simulations are successful in matching several business cycle moments in the data, improve upon the simulations by a standard one-sector RBC model, as well as account for the observed counter-cyclicality of the labor wedge and its moments.

Acknowledgments

We would like to thank Alexis Anagnostopoulos, Eva Carceles-Poveda and Mehmet Yigit Gurdal for their comments and suggestions.

References (15)

A. Fernandez et al.
Informal employment and business cycles in emerging economies: The case of Mexico
Rev. Econ. Dynam.
(2015)
L. Karabarbounis
The labor wedge: MRS vs. MPN
Rev. Econ. Dynam.
(2014)
J.V. Rios-Rull et al.
Redistributive shocks and productivity shocks
J. Monetary Econ.
(2010)
F. Busato et al.
Market and underground activities in a two-sector dynamic equilibrium model
Econom. Theory
(2004)
V.V. Chari et al.
Business cycle accounting
Econometrica
(2007)
J.C. Conesa et al.
Underground economy and aggregate fluctuations
Spanish Econ. Rev.
(2001)
C. Elgin
Cyclicality of Shadow Economy
Econ. Pap. Econ. Soc. Aust.
(2012)

There are more references available in the full text version of this article.

Cited by (3)

Is the labor wedge due to rigid wages? Evidence from the self-employed
2018, Journal of Macroeconomics
Citation Excerpt :
Constructively, any friction that hits the self-employed in the same way as wage and salary workers is a more likely candidate to explain their comovements, given this papers results. This elevates models that study common shocks, such as implicit marginal taxes (Mulligan, 2012), final good price rigidities (Christiano et al., 2016; Bils et al., 2015), or household production (Atesagaoglu and Elgin, 2015), while casting doubt on matching frictions or labor contracting rigidities as the sole mechanism. The rest of this paper is organized as follows: Section 2 describes the model I use to measure the labor wedges.
A central goal of labor economics is explaining cyclical variation in hours worked. Procyclical hours can always be explained in a market clearing model with a residual tax wedge, the “labor wedge.” Convincing progress has been made in reducing the cyclical volatility in the labor wedge and therefore explaining movements in hours worked by amplifying technology shocks with endogenously rigid wages [Hall, R. E., 2005. Employment Fluctuations with Equilibrium Wage Stickiness. American Economic Review 95 (1), 50–65.],[Shimer, R., 2010. Labor Markets and Business Cycles. Number 9217 in Economics Books, Princeton University Press.], and rigid wages in general. This paper demonstrates that the cyclical component of labor hours for the self-employed, who are not vulnerable to such frictions, is of comparable cyclicality and volatility as the cyclical component of labor hours for wage and salary workers, even conditioning on wages, consumption, and occupation-industry composition. This finding suggests that explaining the labor hours of the self-employed presents a new test for amplification mechanisms.
Informal economies around the world: measures, determinants and consequences
2019, Eurasian Economic Review
Determinants of informality in a group of microenterprises from Guayas-Ecuador
2018, International Journal of Value Chain Management

¹: Address: Bogazici University, Natuk Birkan, Kat 2, Bebek, Istanbul, 34342, Turkey. Tel.: +90 212 3597653.

View full text

Cyclicality of labor wedge and informal sector

Highlights

Abstract

Introduction

Section snippets

The model

Calibration

Quantitative analysis

Conclusion

Acknowledgments

Rev. Econ. Dynam.

Rev. Econ. Dynam.

J. Monetary Econ.

Market and underground activities in a two-sector dynamic equilibrium model

Econom. Theory

Business cycle accounting

Econometrica

Underground economy and aggregate fluctuations

Spanish Econ. Rev.

Cyclicality of Shadow Economy

Econ. Pap. Econ. Soc. Aust.