# Unemployment Insurance Generosity and Self-Employment

Alexandre Gaillard, Sumudu Kankanamge

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Alexandre Gaillard, Sumudu Kankanamge. Unemployment Insurance Generosity and Self-Employment. 2025. hal-05398346

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# Unemployment Insurance Generosity and Self-Employment*

Alexandre Gaillard†

Brown University

Sumudu Kankanamge‡

Le Mans University (GAINS-TEPP, IRA), France

April 2025

## Abstract

We show that more generous unemployment insurance (UI) reduces self-employment, with an elasticity twice as negative as the job search disincentive. This results in a sizable decline in aggregate self-employment. Using a structural model of the U.S. labor market, we trace this negative response to two features of UI policy: the exclusion of the self-employed from UI coverage and job search monitoring for UI recipients. The model predicts that neutralizing monitoring requirements and allowing the self-employed to gain UI coverage over time dampen the negative impact of increased UI generosity on self-employment, but also reduce the employment rate.

**Keywords:** Self-employment, Unemployment Insurance, Labor Market Mobility, Monitoring.

<footnote>*This paper supersedes an earlier working paper titled "Gross Labor Market Flows, Self-Employment, and Unemployment Insurance". We are especially grateful to Christian Hellwig for his many helpful comments. We thank in no specific order Anmol Bhandari, Fabrice Collard, Patrick Fève, Eugenia Gonzalez-Aguado, and Tim Lee for their useful comments and discussions. The authors are solely responsible for any remaining errors or omissions.</footnote>

<footnote>†Email: alexandre_gaillard@brown.edu.</footnote>

<footnote>‡Email: sumudu.kankanamge@univ-lemans.fr.</footnote>
# 1 Introduction

In the US and many other countries, self-employed agents neither contribute to nor are covered by UI instruments. Still, if higher UI generosity disincentivizes job search, could it also discourage efforts by insured unemployed individuals to start a business, especially since UI regulations do not consider such efforts as qualifying to keep receiving UI benefits?<fnref n="1" /> In other words, how does an increase in UI generosity affect the incentives to become self-employed and what are the corresponding responses of labor market flows in and out of this activity? Consequently, what are the aggregate effects on the self-employment pool, and how do they influence overall employment and unemployment? In this paper, we evaluate the unintended effects of a higher UI generosity on self-employment. We show that changes in UI generosity strongly impact self-employment leading to, at the micro-level, disincentivizing the efforts to establish a business more than those to search for a job, and, at the macro level, to significant reallocation effects between the self-employment, unemployment, and employment pools. Our contribution is primarily structural: our model-based quantitative approach uncovers the main determinants of the above disincentive and reallocation effects and evaluates policy adjustments that mitigate the adverse impact on self-employment.

We start by empirically assessing the magnitude of the self-employment response to changes in UI generosity, which disciplines the structural analysis that follows. To that end, we measure the empirical elasticities of exiting insured unemployment to either employment or self-employment following an increase in UI generosity. We primarily use Current Population Survey (CPS) data to track occupational flows between unemployment, self-employment, and employment. We then combine this dataset with over time and across US states variations in, on the one hand, regular UI changes (i.e. excluding recession periods) and, on the other hand, extended duration programs activated during various economic downturns. We find a strong negative effect of a higher UI generosity on exits from unemployment to self-employment: a standard deviation increase in regular (resp. extended) UI benefits, representing a 30% average increase in generosity, leads to an 11% (resp. 6%) decrease in the proportion of recently laid-off individuals

<footnote n="1">¹Contributions on the job search disincentive channel include Moffitt (1985); Meyer (1990); Browning and Crossley (2001); Chetty (2008) among others.</footnote>
transitioning to self-employment. In fact, we find a substantial elasticity gap between the negative response of flows from unemployment to self-employment and that of flows from unemployment to employment: the detrimental effect on exits to self-employment is at least two times larger. We refer to this elasticity gap as the *UI elasticity gap from unemployment*. At the aggregate level, we empirically quantify the effects of these responses on the employment, unemployment, and self-employment rates. We find that a higher UI generosity is significantly correlated with a decrease in the self-employment rate and an increase in the unemployment rate. In terms of magnitude, transitioning from a less generous (25th percentile) to a more generous (75th percentile) US state could lead to an increase in the unemployment rate by 0.42 percentage points (a 7.5% increase) and a decrease in the self-employment rate by 0.65 percentage points (a 5% decrease). Conversely, its effect on the employment rate, while positive, is not statistically significant.

Our quantitative model uses an incomplete markets general equilibrium setting with job and business search frictions across three occupations: unemployment, employment, and self-employment. Individuals have heterogeneous abilities at work and in running their businesses. They also differ in wealth, a key factor that explains the search incentives of wealth-poor individuals. The economy has a representative corporate production sector alongside a self-employment sector. The latter runs a flexible CES entrepreneurial production technology. This feature lets us realistically capture the substantial number of self-employed individuals operating businesses below the US median wealth level, sometimes without any business capital. Importantly, the model incorporates key features of the US UI system, such as (i) UI coverage for laid-off workers but not for formerly self-employed new unemployed individuals; (ii) a detailed representation of UI generosity, including benefits durations, amount, and cap; and (iii) a monitoring system of program applicants, checking active job search efforts. Finally, laid-off workers can endogenously take up UI benefits, such that, consistent with the data, only a subset of this population benefit from UI coverage.

We calibrate the model to match aggregate labor market flows and occupational rates, the relative income and wealth across occupations, and the relative importance of the self-employment sector in aggregate production. Importantly, the model-based responsiveness of gross labor market flows and occupational rates to changes in UI generosity
are consistent with the signs and magnitudes of our empirical elasticities. Notably, and although not specifically targeted, the model effectively captures the *UI elasticity gap from unemployment*. This gap persists across the entire income and wealth distribution.

We use our calibrated model to show that design elements of current UI systems significantly contribute to the responsiveness of gross labor market flows and aggregate occupational rates. A first key element is the inherent asymmetry in the insurance coverage between the employment and self-employment activities. Indeed, employed agents have access to UI in case of a layoff. No similar insurance covers the loss of a self-employed activity, for instance, due to business failure. An increase in UI generosity reinforces this insurance coverage effect and disincentivizes the efforts to start a business. This inherent insurance asymmetry is evident in the bidirectional elasticities of transitions between employment and self-employment. An increase in UI generosity results in a significant negative elasticity of the gross flow from employment to self-employment while the reverse flow shows a significant positive elasticity. To better evaluate the impact of this insurance asymmetry, we conduct a thought experiment in which self-employed agents gain access to UI coverage over time. In this experiment, upon business failure, eligible individuals become insured unemployed agents and receive benefits scaled to individual entrepreneurial abilities, mirroring the UI mechanism for employed agents. Therefore, an increase in UI generosity results in mitigating the risks associated with self-employment, thereby reducing the insurance coverage asymmetry between self-employment and employment. Our results indicate that this mechanism reduces the *UI elasticity gap from unemployment* by about 33% compared to our baseline. Moreover, the bidirectional elasticities of transitions between employment and self-employment now have opposite signs: following an increase in UI generosity, the flow from employment to self-employment becomes significantly positive, and the reverse flow significantly negative.

A second key element is the monitoring of UI program applicants: UI agencies mandate insured unemployed agents to provide ongoing proof of job search efforts. However, efforts to establish a business do not validate this condition. Therefore, an increase in UI generosity, by amplifying the potential loss associated with shirking job search, has unintended consequences on the self-employed activity. To measure the effect of monitoring UI applicants, we neutralize this mechanism in the model. The implications are substantial
tial across different gross flows. Notably, the negative elasticity of the transition from un-employment to employment doubles, reflecting that, without monitoring, the incentives to search for a job fall. Perhaps more surprisingly, the negative elasticity of a transition from unemployment to self-employment is also reinforced, albeit moderately: without monitoring, insured individuals do not expect to lose their benefits before the end of the regulatory UI period, leading to lower incentives to search for a job and to start a business. Overall, the first effect largely dominates, reducing the *UI elasticity gap from unemployment* by about 43% compared to our baseline. Thus, monitoring UI recipients is crucial in promoting job search but has unintended consequences on self-employment. Finally, combining self-employment insurance with the absence of monitoring almost eliminates the *UI elasticity gap from unemployment*, reducing it by 88%.

How do the micro-level elasticities translate into the aggregate economy? Our baseline model shows that, consistent with empirical findings, increasing UI generosity raises the unemployment rate and lowers the self-employment rate. The employment rate is at minimum non-responsive and otherwise positively responsive, depending on who bears the cost of a change in UI generosity. But, importantly, self-employment is a key margin in producing this latter result: without this margin, the employment response is largely negative. This is because micro-level behaviors following a change in UI generosity result in an aggregate reallocation of individuals from self-employment to employment.

Finally, we address the aggregate implications of the design elements of current UI systems. A key result of our self-employment insurance experiment is that the employment response is reversed relative to the baseline. In fact, while the employment elasticity becomes negative, the negative impact on the self-employment rate is reduced by more than half. Under this experiment, while higher UI benefits reduce the incentives for self-employed individuals to leave their businesses for jobs, it also encourages non-self-employed individuals to pursue self-employment. Neutralizing the job search monitoring of UI program applicants also has a detrimental effect on the employment response. However, it only leads to reducing the baseline positive effect by half. Interestingly, the negative self-employment response is larger than in the baseline. Indeed, absent monitoring, the insured unemployed situation is more beneficial to currently unemployed individuals and to future laid-off workers. This virtually widens the effects of the asymmetry
in insurance coverage between self-employment and employment. Finally, all cases lead
to an understandably higher unemployment rate relative to our baseline.

**Related literature** Our paper first relates to the literature exploring the effects of UI gen-
erosity beyond its impact on job search efforts (Rothstein (2011); Farber et al. (2015); Hsu
et al. (2018); Agrawal and Matsa (2013), among many others). We find that UI generosity
substantially influences the decision to become self-employed, leading to significant real-
location effects at the aggregate level between unemployment and self-employment, with
little impact on the employment margin. Consistent with this idea, Chodorow-Reich et al.
(2019) and Boone et al. (2021) find limited effects of UI on the aggregate employment rate.

Our quantitative framework combines a search model in the spirit of Mortensen and Pissarides (1994) and occupational choice models with self-employment in the spirit of Quadrini (2000), Cagetti and De Nardi (2006), and in line with Herreño and Ocampo (2023). On the one hand, we incorporate the influence of income heterogeneity and wealth on labor market flows as highlighted by Browning and Crossley (2001), Chetty (2008), Krusell et al. (2010), Nakajima (2012), Krusell et al. (2017), Landais et al. (2018), Birinci and See (2023), Kekre (2023), among others. On the other hand, we extend standard entrepreneurial models by introducing a self-employment margin that allows for production without physical capital, closely aligning with observed data and making our setting quantitatively relevant and tractable.

Our results align with a key strand of literature demonstrating that income prospects
and risk are crucial factors in occupational decisions (Fuchs-Schündeln and Schündeln,
2005), particularly for self-employment (Caliendo and Künn (2011); Dillon and Stanton
(2017); Humphries (2017); Poschke (2019); Hamilton et al. (2019); Rubinstein and Levine
(2020); Hombert et al. (2020); da Fonseca (2021), among others). Also consistent with
our findings, Røed and Skogstrøm (2014) demonstrates that large-scale insurance pro-
visions significantly influence the entry and exit decisions of self-employed individuals.
Similarly, albeit to a lesser extent, Hombert et al. (2020) and Gaillard and Kankanamge
(forthcoming) show that specific reforms allowing unemployed individuals to retain UI
benefits when starting a business have a notable impact on self-employment margins. In
contrast, this paper demonstrates both empirically and quantitatively, that higher UI gen-
erosity strongly and significantly impacts the decision to pursue self-employment under
existing UI regulations. This is primarily because (i) self-employed individuals are ineligible for UI benefits, and (ii) insured unemployed agents looking to start a business risk losing their UI benefits. On the role of monitoring, Abbring et al. (2005), McVicar (2008), and Walsh (2023) highlight its significant impact, alongside sanctions, on individual re-employment rates—a factor that we also demonstrate affects the decision to transition from unemployment to self-employment.

**Outline** Section 2 discusses our empirical findings. Section 3 introduces our model, its parameterization, and validates its ability to generate the responsiveness of gross labor market flows and masses relative to UI generosity changes. Section 4 evaluates the role of the design of the UI system in driving these responses and discusses their aggregate implications. Section 5 concludes.

# 2 Empirical Elasticities

In this section, we measure the impact of higher unemployment insurance (UI) generosity on the micro-level flows between labor market occupations using US data. We then measure the resulting impact on the aggregate employment, unemployment, and self-employment rates.

## 2.1 Data and Definitions

Our analysis mainly uses the Current Population Survey (CPS) from 1994:I to 2015:IV, for all respondents aged 20 to 65. The workforce is sorted into three groups. Workers in paid employment (W) are individuals currently working in a paid job or declaring being temporarily absent from a paid job. Unemployed individuals (U) are those who declare being unemployed while still actively searching for a job. Self-employed individuals (S) are those declaring being self-employed as their main occupation.<fnref n="2" />

<footnote n="2">²To ensure consistency, our CPS sample begins in 1994 as that year introduced a pivotal change in the definition of self-employment. We extend the sample through 2015 to align with analyses and model valuations based on the Survey of Income and Program Participation (SIPP). Notably, due to a major redesign in 2014, we exclude the 2014 SIPP panel, a common practice in related research (see Carr et al. (2020)). CPS results over a 1994 to 2019 sample remain similar. Refer to the Online Appendix Table A8 for details, including commentary on the COVID pandemic, during which job-seeking and business creation conditions differed significantly.</footnote>
In the US, each state sets its own UI benefit schedule. Individuals receive a weekly benefit amount (WBA) that typically replaces 35-50% of their previous wage but is subject to a cap that sets a maximum benefit level. Each state also sets the duration of UI as a maximum number of weeks during which UI benefits can be claimed. In regular times i.e. excluding recession periods, the typical UI duration has been 26 weeks. As a result, much of the variation in UI benefits in regular times is due to changes in the maximum WBA. All regular UI duration and WBA data at the state level are sourced from the U.S. Department of Labor's biannual reports. We follow the lead of the literature by defining UI generosity based on the maximum UI generosity available in a given state (e.g. Agrawal and Matsa (2013) and Hsu et al. (2018)). Such a measure of generosity might not necessarily reflect the actual amount received by unemployed individuals. However, as shown by Hsu et al. (2018) and confirmed in sample in the Online Appendix Table A7, the log - log correlation between Max Regular UI to total actual compensation payments at the state level is large and significant. Moreover, comparing the pass-through of maximum WBA onto the actual change in household benefits, they find that 60% of UI claimants are capped, so that Max WBA captures changes in UI benefits well for the vast majority of unemployed. Specifically, the regular UI generosity in state s at time t is the product between the maximum WBA and the regular number of weeks of benefits claim: $Max Regular UI_{st} = Max WBA_{st} \times Max Regular Weeks_{st}$.

In recession times, US states have provided extended benefits to individuals exhausting their regular benefits in the form of additional weeks. The Extended Benefits (EB) and the Emergency Unemployment Compensation (EUC) programs (also called EUC91, TEUC, and EUC08) are examples of such regulations. Notably, during the Great Recession, these programs implemented diverse emergency extensions (via EB and EUC08), granting extended durations of UI benefits for up to 99 weeks in some states. Extending the data from Farber et al. (2015) on successive per US state activations of these extensions, we define the total UI generosity, including extensions, as $Max Extended UI_{st} = Max Regular UI_{st} + Max WBA_{st} \times Max EB EUC Weeks_{st}$.

<footnote n="3">³As shown in Figure A1 in Online Appendix A.1, variations in both the generosity of regular benefits and extended benefits are large, not only in the cross-section but also over time within states.</footnote>
## 2.2 Labor Market and Aggregate Effects of UI Generosity

### 2.2.1 Transitions out of unemployment

We start with flows out of unemployment, as they are likely the most significantly affected by an increase in UI generosity. Specifically, we use respondents' employment history from the preceding two months to create a variable called *Layoff*. It indicates whether an unemployed individual has recently been on layoff and unemployed for a period within the state's maximum UI coverage duration. Following, for instance, Gruber (1994), Hsu et al. (2018), our analysis uses *Layoff* as a proxy for UI eligibility rather than UI receipts on the basis that individuals accurately self-report employment history while underreporting received benefits.<fnref n="4" /> The underlying assumption is that variations in UI should primarily affect recently laid-off individuals, as they are more likely to qualify for benefits. As a result, and anticipating our findings, our estimate of the propensity to exit insured unemployment (a subset of eligible unemployed) due to higher UI generosity can be interpreted as a lower bound.

Our empirical strategy uses a standard two-way fixed effects approach, comparing the impact of within-state changes in UI benefits between *Layoff* and non-*Layoff* unemployed individuals by estimating the following linear probability model:

$$ U to Occ_{ist} = \beta UIgenerosity_{st} + \gamma Layoff_{it} + \delta (UIgenerosity_{st} \times Layoff_{it}) + \zeta X_{it} + \eta Z_{st} + \lambda_s + \mu_t + \epsilon_{ist}. \quad (1) $$

The indicator $U to Occ_{ist}$ captures whether an unemployed individual $i$ in state $s$ transitions to a specific occupation ($Occ.$), either self-employment ($S$) or paid employment ($W$), over a period of two months from month $t$.<fnref n="5" /> The variable $UIgenerosity_{st}$ is either regular UI generosity ($\log(Max Regular UI_{st})$) or extended UI generosity ($\log(Max Extended UI_{st})$), depending on the analysis considered. $X_{it}$ is a vector of individual characteristics that includes household income brackets, educational attainment,

<footnote n="4">⁴For instance, Bowler (2006) finds that self-reported employment data closely matches business records whereas Meyer et al. (2009) document that self-reported UI payment data is 30-40% lower than administrative records.</footnote>

<footnote n="5">⁵Throughout the paper, we adopt a bimonthly frequency to maximize the number of observed transitions, thereby reducing noise, especially in the context of transitions in and out of self-employment.</footnote>
ethnicity, sex, age, age squared, marital status, unemployment duration, and an indicator
of whether the spouse is currently employed. The vector $\lambda_s$ and $\mu_t$ are states and year-
month fixed effects that aim to capture specific state policies invariant across time, and
specific business cycles features that affect all US states. Finally, $\epsilon_{ist}$ is an error term.

Our identification rests on the assumption that fluctuations in UI generosity are not
correlated with changes in time-varying, unobserved state-level factors that could influ-
ence the exit decisions of unemployed individuals. As shown in Hsu et al. (2018) and in
section A.4.1 of the Online Appendix, regular UI changes do not seem correlated with
economic conditions or state-level transfers, excluding UI payments. Still, we include
time-varying U.S. state characteristics $Z_{st}$ to control for potential confounding from omit-
ted variables. The vector includes the state unemployment rate, the average wage, the
log real GDP per capita, a log home price index, the insured unemployment rate, union
coverage, the UI trust fund reserve ratio, and an indicator for a negative UI trust fund
balance. Finally, when using $\log(\text{Max Extended UI}_{st})$, we must control for the endogenous
EUC and EB activations. We follow Rothstein (2011) and Hsu et al. (2018) and account
for this by flexibly controlling for smooth cubic polynomial functions of the state's unem-
ployment rate and insured unemployment rate in the initial period of the transition.

Table 1 report our results.<fnref n="6" /> Column (1) (resp. column (2)) displays $\delta$, the effect of the generosity of regular UI benefits (resp. extended UI benefits) on the propensity to switch to self-employment among the recently laid-off workers relative to other unemployed individuals. It is significant and negative. To get a sense of the magnitude of the effect, a standard deviation increase in regular (resp. extended) UI benefits, i.e. a 30% increase in average generosity, would lead to an 11% (resp. 6%) decline in the fraction of recently laid-off unemployed individuals becoming self-employed. This magnitude would correspond to an increase of about 8,000$ in total UI generosity. This could broadly be illustrated as the difference in total regular UI generosity between the states of Pennsylvania and Michigan. We also find that, among those who were not recently laid off and therefore do not receive UI benefits, this propensity, albeit negative, is not statistically significant. Concerning transitions to paid employment, the point estimate for regular

<footnote n="6">⁶In the reported results, the U to $\text{Occ}_{ist}$ variable is divided by the average transition rate from unemployment to the specific occupation over the sample, such that our estimates will reflect the percentage point change relative to the average probability of switching.</footnote>
<table><caption>**Table 1.** UI generosity and exit probability out of unemployment.</caption><thead><tr><th></th><th colspan="2">U to S</th><th colspan="2">U to W</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>Layoff</td><td>1.30<sup>***</sup><br>(0.27)</td><td>0.63<sup>***</sup><br>(0.22)</td><td>0.50<sup>***</sup><br>(0.15)</td><td>0.51<sup>***</sup><br>(0.06)</td></tr><tr><td>log(Max Regular UI)</td><td>-0.02<br>(0.16)</td><td></td><td>0.07<br>(0.06)</td><td></td></tr><tr><td>Layoff x log(Max Regular UI)</td><td>-0.38<sup>***</sup><br>(0.08)</td><td></td><td>-0.04<br>(0.05)</td><td></td></tr><tr><td>log(Max Extended UI)</td><td></td><td>-0.08<br>(0.16)</td><td></td><td>0.08<sup>*</sup><br>(0.04)</td></tr><tr><td>Layoff x log(Max Extended UI)</td><td></td><td>-0.20<sup>***</sup><br>(0.06)</td><td></td><td>-0.09<sup>***</sup><br>(0.01)</td></tr><tr><td>Observations</td><td colspan="4">348,025</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Individual &amp; state controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses. See the text for the list of controls. OLS estimates are normalized by the mean transition rate of the flow and can be interpreted as an elasticity relative to that mean transition rate. S refers to self-employment, U denotes unemployment, and W represents employed workers.

UI generosity (Columns (3)) is negative but not statistically significant. For extended UI generosity (Columns (4)), the point estimate for transitions to employment is negative and significant and, remarkably, half the size of that of transitions to self-employment. We refer to the mean difference in elasticity between transitions from insured unemployment to self-employment and from insured unemployment to paid employment as the *UI elasticity gap from unemployment*.<fnref n="7" />

### 2.2.2 Transitions between self-employment and paid employment

Because self-employed business failures are by nature not covered by the UI system, ad-

<footnote n="7">⁷As detailed in Online Appendix Table A8, results are robust to a different notion of self-employment based on incorporation, and when we separate part-time and full-time work. Similar conclusions are also obtained from multinomial logit specifications, when using UI duration (weeks) and UI benefits separately, or when we use the *level* of UI generosity. The effects are stronger when UI variation stems from regular benefit amounts rather than duration extensions. This is particularly true for the 1994–2007 period, when UI changes were mostly driven by benefit levels. The results also hold for 2008–2015, when changes were largely due to extended durations. Unobservable factors do not appear to explain our results: adding state–year–month fixed effects that absorb the effect of UI generosity does not alter the point estimates concerning the interaction term between UI generosity and eligibility. Finally, despite its longitudinal focus and smaller sample size, using the SIPP waves covering the 1996–2014 period produces similar results and magnitudes for both the flows toward employment and self-employment.</footnote>
justing UI coverage may affect occupational decisions beyond the direct effects on the pool of unemployed individuals. In particular, we are attentive to unintended effects of increases in UI generosity, thereby increasing the overall insurance level of the paid employment occupation, on transitions between paid employment and self-employment in both directions. To investigate this, we use changes in regular UI generosity between 1994 and 2010, focusing on variations that are more likely to affect career choices among the concerned groups and excluding short-term UI duration adjustments due to the Great Recession. Similar to specification (1), we estimate $Occ. to Occ.'_{ist} = \beta UI generosity_{st} + \xi X_{it} + \eta Z_{st} + \lambda_s + \mu_t + \epsilon_{ist}$, where $Occ., Occ.' \in \{W, S\}$ and $Occ. \neq Occ.'$. The results (Table 2) show that the effects of UI generosity on the W to S flow and S to W flows have signs going in the expected direction: a reduction in the paid employment to self-employment flow and an increase in the reverse flow. However, the estimates are not statistically significant at the 10% confidence level. As such, if UI does affect these decisions, the CPS does not allow us to be more conclusive because of small point estimates and possibly noisy flow rates.

<table><caption>**Table 2.** UI generosity and transitions in and out of employment and self-employment.</caption><thead><tr><th></th><th>S to W</th><th>W to S</th></tr></thead><tbody><tr><td>log(Max Regular UI)</td><td>0.13<br>(0.08)</td><td>-0.08<br>(0.10)</td></tr><tr><td>Observations</td><td>623,132</td><td>4,563,038</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td></tr><tr><td>Individual &amp; state controls</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses. S refers to self-employment and W represents employed workers.

### 2.2.3 Aggregate occupational rates

Finally, we examine the relation between UI generosity and aggregate unemployment, employment, and self-employment rates, again exploiting variations in the UI system among US states and over time. Specifically, we run the following linear model: $Occ. rate_{st} = \alpha + \beta \log(Max Regular UI_{st}) + \eta Z_{st} + \lambda_s + \mu_t + \epsilon_{st}$. with state ($\lambda_s$) and year ($\mu_s$) fixed effects, and control for a housing index and per capita income ($Z_{st}$). We focus on the effect on a given occupational rate of the amount of regular UI benefits (Max Regular UI$_{st}$) as UI
duration extensions are correlated with the unemployment rate by construction. Results are reported in Table 3.

To put things into perspective, our findings indicate that moving from a less generous US state (25th percentile) to a more generous one (75th percentile) would result in a statistically significant increase in the unemployment rate by 0.42pp (a 7.5% increase). Conversely, the self-employment rate would decrease by a statistically significant 0.65pp (a 5% decrease). In contrast, the employment rate is the least responsive, with a positive but non-statistically significant adjustment. This low (or even positive) employment response aligns with recent estimates by Boone et al. (2021), who find a small or non-significant positive effect of UI generosity on aggregate employment by comparing adjacent counties in neighboring states with different levels of UI generosity. Similarly, by exploiting measurement errors in the process of UI extension activation, Chodorow-Reich et al. (2019) estimate a minimal impact of increased UI generosity on the unemployment rate.

<table><caption>**Table 3.** Effect of regular UI generosity on occupational masses in the CPS <sup>a,b</sup>.</caption><thead><tr><th></th><th>U rate</th><th>W rate</th><th>S rate</th></tr></thead><tbody><tr><td>log(Max Regular UI)</td><td>0.70**<br>(0.33)</td><td>0.46<br>(0.67)</td><td>-1.15**<br>(0.49)</td></tr><tr><td>Observations</td><td>1,122</td><td>1,122</td><td>1,122</td></tr><tr><td>State and Year FE + controls</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses.

<sup>a</sup> These results are robust to excluding the Great Recession period, calculating rates by including individuals not in the labor force, or considering higher panel frequencies (monthly or quarterly).

<sup>b</sup> The numbers describe adjustments in terms of semi-elasticities, constructed as shown in regression equation (2.2.3). The row numbers sum to zero, allowing them to be understood in terms of the percentage point changes in occupational rates. S refers to self-employment, U denotes unemployment, and W represents employed workers.

Overall, our empirical investigations demonstrate that variations in the generosity of UI significantly impact labor market dynamics, influencing the formation of the unemployment, employment, and self-employment rates. A key takeaway is that the effects of changing UI generosity are large on the self-employment occupation. On the one hand, these effects translate into significantly fewer entries into self-employment and a drop in the aggregate self-employment rate. On the other hand, these effects are significantly larger than the ones impacting the employment margin. In the rest of the paper, we develop a model to evaluate how the design of the current UI system contributes to these
observed responsiveness patterns and assess their aggregate implications.

# 3 The Model

This section introduces a general equilibrium model characterizing gross labor market flows across the employment, unemployment, and self-employment occupations. It provides a detailed specification of the current US unemployment insurance system while accounting for the relative income and wealth across occupations.

## 3.1 Environment

The economy is populated by a unit mass of households indexed by $i$. Every period, each agent falls in one of three occupations $o_{it} \in \mathcal{O} \equiv \{S, W, U\}$ corresponding to self-employment ($S$), paid-employment worker ($W$), or unemployment ($U$). Self-employed agents run small and middle-sized businesses and, together with a representative corporate firms sector, provide the production of the economy.

A household's flow utility derives from consumption $c_t$ and disutility from search such that:

$$u(c_{it}, e_{w,it}, e_{s,it}) = \frac{c_{it}^{1-\sigma} - 1}{1-\sigma} - e_{w,it}^2 - e_{s,it}^2, \quad (2)$$

where $e_{w,it}$ and $e_{s,it}$ are search efforts exerted respectively to find a new job and start a business. Labor is supplied inelastically. Agent's savings are noted $a_{it} \in \mathcal{A}$. $r_t$ and $w_t$ are respectively the interest rate on savings and the wage rate in the economy. In the following, we drop the individual and time indexes $i$ and $t$ unless necessary.

All individuals have an ability component $\vartheta \in \Theta$. The labor income of a working household, the replacement income of an unemployed individual, and the business income of a self-employed household all depend on this ability $\vartheta$. This component follows a Markov process with transition probability $\pi_{\vartheta}(\vartheta'|\vartheta)$.<fnref n="8" /> Moreover, two occupation-specific shocks affect the decision to be self-employed or employed. First, workers are subject to an additional persistent idiosyncratic shock $y$ on their labor income, starting and ending with a specific job, and that we call *match-quality*. It follows a Markov process with

<footnote n="8">⁸Ability can change over time in order to generate additional saving motives as our model abstracts from life-cycle aspects, human capital, or health risks which can explain a large productivity dispersion in the data.</footnote>
transition probability $\pi_y(y'|y)$. A new worker draws this shock from the invariant distribution $\Pi_y$. Second, self-employed agents face a persistent idiosyncratic business shock $z$ attached to the firm they run. It follows a Markov process with transition probability $\pi_z(z'|z)$. A new self-employed agent draws her initial business shock from the invariant distribution $\Pi_z$. Finally, individuals retire and exit the model with probability $\zeta$ and discount the future at rate $\beta$. Upon retirement, they are replaced by new agents entering the labor market with no asset holdings and skills $\theta$ drawn from the invariant distribution $\Pi_\theta$ given by the markov chain $\pi_\theta(\theta'|\theta)$. We assume that retiring agents' assets are fully taxed, with proceeds allocated to government expenditures that do not affect households.<fnref n="9" />

On the unemployment side, the number of periods during which an individual can claim UI benefits, a key component, is tracked by the state variable $j \in \{0, ..., J\}$, where $J$ depends on the regulatory maximum UI duration. Uninsured individuals are identified by $j = 0$. Consistent with the current U.S. unemployment insurance scheme, involuntarily laid-off workers are eligible for UI with the maximum insurance duration (i.e., $j = J$) and are subject to a *take-up* mechanism. In the benchmark economy, non-laid-off separated workers and the self-employed are uninsured (i.e., $j = 0$).

The state vectors of workers, unemployed and self-employed individuals are respectively $\mathbf{x}_W \equiv (a, \theta, y)$, $\mathbf{x}_U \equiv (a, \theta)$, and $\mathbf{x}_S \equiv (a, \theta, z)$. We denote the full state vector as $\mathbf{x} \equiv (a, \theta, z, y)$. The associated value functions are $W(\mathbf{x}_W)$, $U_j(\mathbf{x}_U) \equiv U(\mathbf{x}_U, j)$, and $S_j(\mathbf{x}_S) \equiv S(\mathbf{x}_S, j)$. Note that, although self-employment insurance is not available in the benchmark case, we still index $S_j(\mathbf{x}_S)$ with $j$, anticipating this extension later on.

### 3.1.1 Workers

Workers earn after-tax labor income $(1 - \tau_w)h(\theta)yw$, where $\tau_w$ is a flat labor income tax. The function $h: \theta \mapsto \mathbb{R}$ maps their individual ability $\theta$ into a working ability.

Each worker has a probability $\eta(\theta)$ of being exogenously laid off from their current job

<footnote n="9">⁹We do not adjust the discount factor for the retirement probability because we assume agents continue to receive the same flow utility after exiting the labor market. Our results remain entirely unchanged if we recalibrate the model with a discount factor of $\beta(1 - \zeta)$, which corresponds to the alternative assumption of no utility upon retirement. Moreover, a version with a retirement phase and intergenerational asset transmission does not change our conclusions or focus on labor market dynamics but complicates the model. In fact, this simplifying assumption goes in the direction of the data, as young labor market entrants are generally poorer and face higher unemployment.</footnote>
through no fault of their own, qualifying them for maximum unemployment insurance rights ($j = J$). However, in the US, a significant fraction of eligible unemployed individuals do not collect their UI benefits. To mirror this fact, we introduce a take-up mechanism where the eligible job looser pays a search cost $e_l$ upfront, corresponding to unemployment benefits collection efforts. The corresponding benefits take-up probability is then $\pi(e_l)$. The value of take-up, noted $\mathcal{J}(\mathbf{x}_U)$, appears as a continuation value between the last decision of the worker and the first decision of the unemployed. This value takes the form:

$$ \mathcal{J}(\mathbf{x}_U) = \max_{e_l} \left\{ -e_l^2 + \pi_l(e_l) U_J(\mathbf{x}_U) + (1 - \pi_l(e_l)) U_0(\mathbf{x}_U) \right\}, \quad (3) $$

where $U_J(\mathbf{x}_U)$ and $U_0(\mathbf{x}_U)$ correspond, respectively, to the value of an insured unemployed agent with $J$ remaining periods of UI and an uninsured unemployed agent, as detailed below.

In addition, following mostly a bad shock on their match-quality $y$, workers can compare the value of their paid-employment situation with unemployment and decide to voluntarily quit their job (which could be rationalized as moving, family, or health issues among others). In this case, the newly unemployed individual is not eligible for UI rights.

By providing effort $e_s$, workers can search for business ideas on-the-job and start a business in the next period with probability $\pi_s(e_s)$. This effort encompasses market research on the feasibility of an idea, competition assessment, business education, agency costs, or the time needed to fill administrative forms, validate product norms, etc. Workers then voluntarily change their occupation, lose their UI rights and can expect a continuation value $S_0(\mathbf{x}_S)$ corresponding to a self-employed individual without unemployment insurance rights.

To simplify notations, we denote $\eta \equiv \eta(\theta)$, $\pi_s \equiv \pi_s(e_s)$, and $\pi_w \equiv \pi_w(e_w)$. The worker's recursive program is given by:

$$ W(\mathbf{x}_W) = \max_{c,a' \ge 0, e_s} \left\{ u(c, 0, e_s) + \beta \mathbb{E}_{\theta', y', z'} \left[ (1-\eta) \left[ \begin{aligned} & (1-\pi_s) \max \{ W(\mathbf{x}'_W), U_0(\mathbf{x}'_U) \} \\ & + \pi_s \max \{ S_0(\mathbf{x}'_S), W(\mathbf{x}'_W), U_0(\mathbf{x}'_U) \} \end{aligned} \right] \right. \right. \\ \left. \left. + \eta \left[ (1-\pi_s) \mathcal{J}(\mathbf{x}'_U) + \pi_s \max \{ S_0(\mathbf{x}'_S), \mathcal{J}(\mathbf{x}'_U) \} \right] \right\} \quad (4) $$

$$ \text{s.t.} \quad c + a' = (1 - \tau_w)h(\theta)wy + (1 + r)a. $$
### 3.1.2 Unemployed individuals

Unemployed agents search for both a business idea and a job opportunity with respective efforts $e_s$ and $e_w$ and corresponding success probabilities $\pi_s(e_s)$ and $\pi_w(e_w)$. Upon finding a job, they can become workers with continuation value $W(x'_W)$. Similarly, upon having a business idea, they can become self-employed with continuation value $S_0(x'_S)$.

We use a tractable UI specification that captures key features of the U.S. system. We denote the path of UI benefits as $b(\theta, j)_{j=J}^{j=0}$, where $J \ge 1$ is the integer number of model periods that immediately exceeds the regulatory maximum UI duration, $\bar{J} \ge 0$. The benefits level of an insured individual, $b(\theta, j)$, is contingent on her past employed earnings $h(\theta)w$ in proportion to the replacement rate $\mu$ and subject to a cap defined by the maximum benefit amount $\bar{b}$. Thus, UI benefits in the current period are:

$$b(\theta, j) = \min \left\{ w\mu h(\theta), \bar{b} \right\} \cdot \left[ 1_{\{j \in [2J]\}} + 1_{\{j=1\}} \cdot (1 - (J - \bar{J})) + 1_{\{j=0\}} \cdot 0 \right], \quad (5)$$

Following the above scheme, insured unemployed individuals ($j > 0$) receive benefits $b(\theta, j)$. By claiming UI in the current period, insured unemployed agents shift from $j$ periods of remaining UI rights to $j - 1$.<fnref n="10" /> However, this is only allowed if individuals actively searched for a job and provided enough effort to meet the applicable UI regulations. We denote $\pi_m(e_w)$ the probability of meeting this requirement. This can be viewed as imperfect monitoring of program applicants due to, for instance, asymmetric information. Thus, $e_w$ influences both the probability of finding a job and the risk of sanctions that may lead to losing UI rights due to insufficient job search. Non-eligible individuals and those who have exhausted (or lost) their rights ($j = 0$) receive no benefits. Finally, independently of UI, all unemployed individuals receive a fixed safety-net transfer $b$.

To simplify notations, we denote $\pi_m \equiv \pi_m(e_w)$. The recursive program of an unemployed individual reads:

$$U(\mathbf{x}_{UI}, j) = \max_{\substack{c>0, \\ a', e_w, e_s \ge 0}} u(c, e_w, e_s) + \beta \mathbb{E}_{\theta', y', z'} \left\{ \pi_w \left[ (1 - \pi_s) \mathbf{U}(\mathbf{x}', j) + \pi_s \mathbf{U}(\mathbf{x}', j) \right] \right. \\ \left. + (1 - \pi_w) \left[ (1 - \pi_s) \mathbf{U}(\mathbf{x}', j) + \pi_s \mathbf{U}(\mathbf{x}', j) \right] \right\} \quad (6)$$

<footnote n="10">¹⁰In the last period of benefits, as shown in (5), we use a simple linear rule to account for exact regulatory UI duration $\bar{J}$. See Online Appendix B.1 for details and an example.</footnote>
s.t.

$$c + a' = \underline{b} + b(\vartheta, j)(1 - \tau_w) + (1+r)a,$$

$$\underset{UU}{U}(\mathbf{x}', j) = \pi_m \max\{W(\mathbf{x}'_W), U_{\max\{0,j-1\}}(\mathbf{x}'_U)\} + (1 - \pi_m)\max\{W(\mathbf{x}'_W), U_0(\mathbf{x}'_U)\},$$

$$\underset{WS}{U}(\mathbf{x}', j) = \pi_m \max\{W(\mathbf{x}'_W), S_0(\mathbf{x}'_S), U_{\max\{0,j-1\}}(\mathbf{x}'_U)\} + (1 - \pi_m) \max\{W(\mathbf{x}'_W), S_0(\mathbf{x}'_S), U_0(\mathbf{x}'_U)\},$$

$$\underset{UU}{U}(\mathbf{x}', j) = \pi_m U_{\max\{0,j-1\}}(\mathbf{x}'_U) + (1 - \pi_m) U_0(\mathbf{x}'_U),$$

$$\underset{SU}{U}(\mathbf{x}', j) = \pi_m \max\{S_0(\mathbf{x}'_S), U_{\max\{0,j-1\}}(\mathbf{x}'_U)\} + (1 - \pi_m) \max\{S_0(\mathbf{x}'_S), U_0(\mathbf{x}'_U)\}.$$

### 3.1.3 Self-employed agents

Self-employed agents produce using capital $k$ and their own labor $l$ using the following technology:

$$\mathcal{Y}(k, \vartheta, z) = zg(\vartheta) (\omega k^p + (1 - \omega) \underline{l}^p)^{\nu/p} \quad (7)$$

with $\nu \in (0, 1)$ the degree of homogeneity which characterizes returns to scale, $p > 0$ the degree of substitutability, and $\omega \in [0, 1]$ the share of each production factor. Equation (7) departs from the entrepreneurial technology specification found, for instance, in Quadrini (2000), Cagetti and De Nardi (2006), or Kitao (2008) among others.<fnref n="11" /> This specification lets us generate self-employment income even without any business capital $k$. This assumption is empirically relevant given our definition of self-employment: in the Survey of Consumer Finances (SCF), about 35-40% of the self-employed individuals are using less than 1000$ of business capital. This specification also lets us better capture the gross flows in and out of self-employment estimated from the Survey of Income and Program Participation (SIPP). The function $g: \vartheta \mapsto \mathbb{R}$ maps individual ability into entrepreneurial ability. However, due to the presence of the entrepreneurial business shock $z$ and the transitory match-quality shock $y$, there is an imperfect correlation between employment and self-employed incomes.

To invest an amount $k$ in their business, self-employed individuals can use their own wealth and borrow funds from a financial intermediary. However, their borrowing capac-

<footnote n="11">¹¹Unlike Cagetti and De Nardi (2009), we abstract from entrepreneurial labor demand. However, we believe our setup is sufficient to replicate the dynamics of the data. Indeed, with a static entrepreneurial labor demand, workers are hired in proportion to entrepreneurial capital and productivity and the wage rate. Mechanically, a higher number of self-employed agents leads to a higher labor demand and thus a higher equilibrium wage. In our setting, as the number of self-employed reduces the labor force in the corporate sector, its labor supply is lower, and therefore equilibrium wages increase.</footnote>
ity is limited to a fixed fraction ($\lambda$) of their total assets (a). Agents are borrowing if $k > a$ and saving if $k < a$. The entrepreneurial profit $\Pi(k, \vartheta, z)$ is defined as the entrepreneurial production net of capital depreciation, any interest repayments, and a fixed cost $F$. The latter accounts for all additional functioning costs of a self-employed business.

By providing effort $e_w$, self-employed agents can search for a job opportunity on-the-business and change occupation in the next period with probability $\pi_w(e_w)$ and value $W(\mathbf{x}'_W)$. Otherwise, they can endogenously quit and join the uninsured unemployment pool with value $U_0(\mathbf{x}'_U)$.

The self-employed agents' recursive program in the benchmark economy is:

$$ 
\begin{aligned}
S_0(\mathbf{x}_S) &= \max_{c,a' \ge 0, k, e_w} u(c, e_w, 0) + \beta \mathbb{E}_{\vartheta', y', z'} \left\{ \pi_w \max \left\{ S_0(\mathbf{x}'_S), W(\mathbf{x}'_W), U_0(\mathbf{x}'_U) \right\} \right. \\
&\qquad \left. + (1 - \pi_w) \max \left\{ S_0(\mathbf{x}'_S), U_0(\mathbf{x}'_U) \right\} \right\} \\
\text{s.t.} \quad & c + a' = (1 - \tau_s) \Pi(k, \vartheta, z) + a + r(a-k) \mathbb{1}_{\{k \le a\}}, \\
& \Pi(k, \vartheta, z) = \mathcal{Y}(k, \vartheta, z) - \delta k - r(k-a) \mathbb{1}_{\{k \ge a\}} - F, \\
& k \le \lambda a,
\end{aligned}
\quad (8) $$

where $\delta$ is the depreciation rate and $\tau_s$ a tax rate on self-employment income.

### 3.1.4 Corporate sector

A representative corporate firm produces $\mathcal{Y}_t^C$ using a Cobb-Douglas technology, with total factor productivity $A$, capital level $K_t^C$ and labor $L_t^C$, such that: $\mathcal{Y}_t^C = F(K_t^C, L_t^C) = A(K_t^C)^\alpha (L_t^C)^{1-\alpha}$, where $\alpha \in (0,1)$ is the capital share. Profit maximization produces the competitive interest rate $r_t = A\alpha \left(\frac{L_t^C}{K_t^C}\right)^{1-\alpha} - \delta$ and wage rate $w_t = A(1-\alpha) \left(\frac{K_t^C}{L_t^C}\right)^\alpha$.

### 3.1.5 Government

The government runs a UI system which covers laid-off unemployed individuals and finances it using labor income and self-employment income taxes. Total government revenues ($T$) are:

$$ T = \int \tau_w h(\vartheta) wy \, d\Gamma_W(\mathbf{x}_W) + \int \tau_w b(\vartheta, j) \, d\Gamma_U(\mathbf{x}_U, j) + \int \tau_s \Pi(k, \vartheta, z) \, d\Gamma_S(\mathbf{x}_S, j), \quad (9) $$
with $\Gamma_W(\mathbf{x}_W)$, $\Gamma_S(\mathbf{x}_S, j)$, $\Gamma_U(\mathbf{x}_U, j)$ the measure over workers, unemployed individuals, and self-employed individuals. Government expenditures $G$ are equal to the allocated UI benefits and safety-net programs: $G = \int (b(\vartheta, j) + \underline{b}) d\Gamma_U(\mathbf{x}_U, j)$. We assume that the costs of the UI and safety-net programs are shared between self-employed individuals and workers such that $\tau_s = d \cdot \tau_w$, where $d \ge 0$ is a parameter governing this split, and $\tau_w$ balances the government budget. A value of $d = 1$ indicates an equal split, while $d = 0$ means that only workers bear the costs.

## 3.2 Equilibrium

A stationary recursive equilibrium in this economy consists of a set of value functions $W(\mathbf{x}_W)$, $U_j(\mathbf{x}_U)$, $S_j(\mathbf{x}_S)$, policy rules over savings $a'(\mathbf{x}_o, j)$, consumption $c(\mathbf{x}_o, j)$, job search effort $e_w(\mathbf{x}_o, j)$, business search effort $e_s(\mathbf{x}_o, j)$, business investment $k(\mathbf{x}_S, j)$, occupational choices, prices $(r, w) \in \mathbb{R}^+$, tax rate $\tau_w$, $\tau_s \in \mathbb{R}^+$ and a stationary measure over individuals $\Gamma(\mathbf{x}, j)$ and the respective measures $\Gamma_W(\mathbf{x}_W)$, $\Gamma_S(\mathbf{x}_S, j)$, $\Gamma_U(\mathbf{x}_U, j)$, such that:

(i) The policy rules and value functions solve household individual programs;

(ii) The wage $w$ and the interest rate $r$ are equal to the marginal products of the respective production factor in the corporate sector;

(iii) Goods and factor markets clear: (a) capital: $\int a'(\mathbf{x}, j)d\Gamma(\mathbf{x}, j) = K^C + K^S$, with aggregate entrepreneurial capital $K^S = \int k(\mathbf{x}_S, j)d\Gamma_S(\mathbf{x}_S, j)$, (b) the measure of corporate workers $d\Gamma_W(\mathbf{x}_W)$ is equal to corporate labor demand $L^C$;

(iv) Given $d$, $\tau_w$ balance the government budget ($T = G$).

Finally, we define total output $Y$ as the sum of corporate sector output and entrepreneurial sector output such that $Y = Y^C + Y^S = Y^C + \int \mathcal{Y}(k(\mathbf{x}_S), \vartheta, z)d\Gamma_S(\mathbf{x}_S, j)^{12}$

## 3.3 Parameterization

We parameterize the model to fit key features of the US self-employment sector and gross labor market flows between employment, unemployment, and self-employment. Most

<footnote n="12">¹²The model has no closed-form solution and must be solved numerically. The Online Appendix B details our numerical algorithm and the behavior of the resulting search policy functions.</footnote>
labor market moments are calculated from the March CPS data from 1994:I to 2015:IV.
Other data counterparts are taken from the 2004 Survey of Consumer Finances (SCF) and
the Survey of Income and Program Participation (SIPP). As for the data, a model period
is set to two months.

3.3.1 Exogenously set parameters

We first describe parameters assigned using standard values or estimates in the literature.
The coefficient of relative risk aversion is set to $\sigma = 1.5$. The corporate TFP $A$ is set to
normalize aggregate annual output to 1. The depreciation rate $\delta$ is 6.1% annually or 1%
every two months. The capital share in the corporate sector $\alpha$ and the self-employment
sector $\omega$ are set to 0.33. Consistent with the CPS, the retirement probability is set to $\zeta =$
0.6%.

As in Kitao (2008), we set the borrowing parameter $\lambda$ to 1.5. The entrepreneurial labor
supply $l$ is set to 1. Consistent with estimates in Castro et al. (2015) and values used
in Clementi and Palazzo (2016), the idiosyncratic business process $z$ follows an AR(1)
process in logs: $log(z) = \rho_z log(z_{-1}) + \epsilon_z$, where $\epsilon_z \sim N(0, \sigma_z)$, with $\rho_z = 0.91$ and $\sigma_z$
calibrated endogenously.

We normalize the persistent individual working ability to $h(\vartheta) = \vartheta$ and assume that
it follows an AR(1) process in logs: $log(\vartheta) = \rho_\vartheta log(\vartheta_{-1}) + \epsilon_\vartheta$, where $\epsilon_\vartheta \sim N(0, \sigma_\vartheta)$,
with $\rho_\vartheta = 0.985$. The variance $\sigma_\vartheta^2 = 0.013$ is pinned down to generate an earnings Gini
coefficient of 0.38. The less persistent match-quality process follows an AR(1) process in
logs: $log(y) = \rho_y log(y_{-1}) + \epsilon_y$, where $\epsilon_y \sim N(0, \sigma_y)$, with $\rho_y = 0.85$ and $\sigma_y^2 = 0.02$.
Those values fall in the range of the transitory and permanent components of earnings
estimated in the literature (e.g. Storesletten et al. (2004) using the PSID).

In addition to the *match-quality* process *y* described above, we assume that an absorbing state $y_0 = 0$ occurs with probability $p_{y_0}$, aimed at capturing job changes not related to economic reasons (for example, migration decisions, preferences, etc.). We calibrate $p_{y_0}$ to generate a sufficient separation rate in addition to involuntary exits due to layoffs. Similarly, self-employed agents can be compelled to quit upon reaching an absorbing state $z_0 = 0$ with probability $p_{z_0}$, translating the fact that they might be forced exit indepen-
dently of their ability to self-insure against bad business shocks.<fnref n="13" /> In the data, 20-30% of long-established business owners declare ceasing their activity due to reasons not related to economic conditions in the Survey of Business Owners (2007) and the Annual Survey of Entrepreneurs (2014:2016). Therefore, we set the probability to draw the absorbing state $z_0$ to 20% of the total self-employment exit probability, yielding $p_{z_0} = 0.011$.

The relationship between the transition from employment to involuntary unemployment (due to layoff) with respect to earnings terciles is decreasing in the CPS. By aligning the earnings terciles within the model, the layoff rates, $\eta(\theta)$, are adjusted to match the same transition rate as observed in the CPS. For our three-states discretization of $\theta$, we obtain $\eta(\theta) = \{0.0096, 0.0042, 0.003\}$.

Our baseline calibration is designed to replicate the average UI system in the US. The UI replacement rate $\mu$ is set to 0.45, close to the average replacement rate across the US in recent decades and the UI duration is set to $\bar{J} = 3$, which corresponds to 26 weeks of regular benefits. The UI cap $\bar{b}$ is set to represent 50% of the average wage, which corresponds approximately to the average applied across US states. The safety-net transfers $b$ are set to represent 0.5% of total GDP, following values reported in the U.S. government budget for non-taxable transfers including supplemental nutrition and family assistance programs. In the benchmark model, we assume taxes have minimal distortive effects on the choice between becoming a worker or a self-employed agent. Specifically, we set $d = 1$, ensuring $\tau_s = \tau_w$, meaning that the burden of UI contributions is equally split. This approach allows us to focus on core dynamics without delving into tax-induced distortions, as analyzing tax effects is not the primary focus of this paper. Moreover, in reality, it is not entirely clear who bears the cost of regular UI benefits: while employers (including some self-employed individuals who act as employers) are nominally responsible for financing UI through state and federal taxes, much of this cost is passed on to workers through lower earnings, as argued by Anderson and Meyer (2000). Our model also considers the impact of extended UI benefits, which are largely funded by the federal government and ultimately borne by all taxpayers or financed through federal debt. Thus, assuming an equal tax split serves as a reasonable benchmark for our analysis. Nevertheless, in sec-

<footnote n="13">¹³For clarity, we augment both Markov process $z$ and $y$ in a similar way. For instance, in the case of $z$, we define an additional state $z_0 = 0$ and redefine the transition matrix with $\tilde{\pi}_z(z'|z) = \pi_z(z'|z)(1-p_{z_0})$ for $z, z' \in \{z_1, \dots, z_Z\}$, $\tilde{\pi}_z(z_0|z \in \{z_1, \dots, z_Z\}) = p_{z_0}$ and $\tilde{\pi}_z(z' \in \{z_1, \dots, z_Z\}|z_0) = 0$, $\tilde{\pi}_z(z_0|z_0) = 1$, with $\pi_z(z'|z)$ the discretized transition matrix of the AR(1) process.</footnote>
tion 3.4.3, we explore variations to this benchmark, including the case where $d = 0$, and show that this does not change our main conclusions. If anything, setting $d = 0$ would produce counterfactual responsiveness in labor market flows, reinforcing the robustness of our chosen calibration.

### 3.3.2 Endogenously calibrated parameters and target moments

We now describe parameters picked endogenously to match targets in the data. Although a given parameter does not affect only one particular moment due to the non-linearity of the model, specific parameters can be somewhat tied to particular moments. Table 4 presents a summary of endogenous parameters and related moments.

<table><caption>**Table 4.** Calibrated parameters and fit.</caption><thead><tr><th>Symbol</th><th>Value</th><th>Moment</th><th>Target</th><th>Model</th></tr></thead><tbody><tr><td>β</td><td>0.989</td><td>K/Y (annual)</td><td>2.7</td><td>2.7</td></tr><tr><td>ν</td><td>0.740</td><td>Share of total income, self-employed (%)</td><td>23.0</td><td>23.1</td></tr><tr><td>F</td><td>0.036</td><td>Exit rate from self-employment (%)</td><td>5.6</td><td>5.9</td></tr><tr><td>p<sub>y0</sub></td><td>0.012</td><td>W to U flow (%)</td><td>1.7</td><td>1.7</td></tr><tr><td>g(θ)</td><td>See text</td><td>W to S by quantile/avg rate (%)</td><td>see text</td><td>see text</td></tr><tr><td>p</td><td>0.750</td><td>Ratio of median wealth (worker/self-employed)</td><td>5.5</td><td>5.8</td></tr><tr><td>σ<sup>2</sup><sub>z</sub></td><td>0.064</td><td>Gini coefficient of business income</td><td>0.44</td><td>0.44</td></tr><tr><td>κ<sub>s</sub></td><td>0.180</td><td>Share of self-employment (%)</td><td>11.0</td><td>11.1</td></tr><tr><td>κ<sub>w</sub></td><td>0.455</td><td>U → W transition (%)</td><td>37.4</td><td>37.9</td></tr><tr><td>κ<sub>l</sub></td><td>3.295</td><td>Insured unemployment rate (%)</td><td>2.3</td><td>2.3</td></tr><tr><td>κ<sub>m</sub></td><td>5.000</td><td>Share of sanctioned insured unemployed (%)</td><td>1.0</td><td>1.0</td></tr></tbody></table>

The respective probabilities of getting a business idea, a job opportunity, claiming UI benefits, and meeting the active job search requirement arrive at a Poisson rate such that:

$$ \pi_x(e_x) = 1 - \exp(-\kappa_x e_x) \text{ for } x \in \{w, s, \iota\}, \text{ and } \pi_m(e_w) = 1 - \exp(-\kappa_m e_w), \quad (10) $$

with {$κ_s, κ_w, κ_l, κ_m$} parameters targeting specific flows or occupational masses. $κ_w$ is set to capture the about 40% of unemployed individuals who move to employment, as observed in the CPS. Relative to various definitions of self-employment in the literature, all self-employed agents are relevant for our analysis. This population accounts for 10% to 12.5% of the workforce in the CPS and the SCF. We use a self-employment rate of 11% with $κ_s$ set to match this target. Concerning the UI system in the US, insufficient job search
activities are disqualified from receiving their total UI benefits. According to the Department of Labor Statistics, approximately 8% of claimants are sanctioned each quarter for failing to conduct a sufficiently active job search, resulting in either denial of UI benefits or reductions in overall UI recipiency. Among those who meet the necessary filing requirements, around 1% are still disqualified for not being available for work or for refusing a suitable job.<fnref n="14" /> The usual sanction is a complete or temporary (one to several weeks) loss of benefits. We set $\kappa_m$ such that 1% of the insured unemployed individuals in the model are sanctioned each quarter following detection by the UI agency. We view this choice as conservative since the model-implied permanent benefit loss following detection is likely stronger than in reality. Finally, the parameter $\kappa_t$ targets the insured unemployment rate (IUR), defined as the ratio of UI claimants to workers (excluding self-employed individuals). This rate is set at 2.3%, consistent with estimates by the U.S. Department of Labor over our sample period. This parameter implies that around 80% of laid-off unemployed individuals in our model take up UI benefits, resulting in a fraction of insured unemployed (among all unemployed individuals) of 34%, consistent with available empirical evidence and estimates in Auray et al. (2019).

The estimation of $g(\theta)$ is challenging since the contribution of the skills of a self-employed agent to the performances of a business is generally unobservable. We indirectly infer the mapping between worker and self-employed individual productivities using the observed relationship in the $W \rightarrow S$ transition by earnings quantiles. We divide the labor income distribution into 3 quantiles and compute in each the ratio of workers starting a business over the average ratio of workers starting a business in the economy. In our CPS sample, workers in the first earnings quantile are 16% more likely to start a business than the average worker. In the middle quantile, they are about 16% less likely. In the third quantile, they are as likely as the average worker. We use those relative flows to pin down the following values: $g(\theta) = \{0.101, 0.150, 0.216\}$.

To evaluate the substitutability between labor and capital in self-employment, we compare the ratio of the median wealth of self-employed individuals to that of workers in

<footnote n="14">¹⁴These statistics are collected in the ETA 9128 — Reemployment and Eligibility Assessment Workload data of the Department of Labor Statistics. We use the number of claimants disqualified for failing to meet reporting requirements, failing to report availability for work, or refusing a suitable job offer, relative to the total number of claimants. These statistics are in line with what is reported by (Grubb, 2001) using historical labor market data.</footnote>
the model and the data. Under the assumption of a Cobb-Douglas production function, individuals with limited wealth (and thus capital) would not choose self-employment due to borrowing limits, leading to a high median net worth ratio among the self-employed. However, by increasing the parameter *p*, we enable individuals with lower wealth to engage in self-employment by utilizing their own labor. A substitutability parameter of *p* = 0.75 generates a median wealth ratio close to 5.5, as observed in the SCF.

The remaining parameters are chosen as follows. The discount factor $\beta$ helps to generate a realistic annual capital (excluding public capital) to output ratio of 2.7. The returns to scale parameter in the self-employment sector $v$ lets us fit the 23% of total income received by the self-employed agents in the SCF. By adjusting the probability $p_{y0}$ of the absorbing match-quality state $y_0 = 0$, we can control the remaining exits from paid employment to unemployment so that they coincide with the CPS data. Accordingly, we obtain $p_{y0} = 0.0119$. The variance $\sigma_z^2$ is set to generate a Gini coefficient for business income of 0.44, consistent with the SCF. Finally, the fixed production cost $F$ captures the 5.6% of self-employed who exit each period in the CPS.

## 3.4 Model Responsiveness to UI Generosity

In this section, we validate the model by evaluating how it responds to changes in UI generosity. Therefore, we analyze how our baseline parameterization reproduces the elasticity of flows and occupational rates established in section 2, notably the high responsiveness of flows from insured unemployment to self-employment relative to employment, and the responsiveness of aggregate occupational rates following a change in UI generosity. While not the primary focus of this section, the model also validates key labor market properties, including aggregate gross flows between occupations, wealth-based flow patterns, and relative income and wealth across occupations. These are discussed in detail in Appendix A.

### 3.4.1 Counterfactual Framework

Our analysis of the model's responsiveness to changes in UI generosity builds on counterfactual economies, indexed $i$, under alternative UI designs with varying levels of UI generosity. In model generated data, we define UI generosity as the product of: (i) a
maximum duration $\bar{J}$ (that we will express in weeks equivalents hereafter), (ii) and the maximum benefit amount, constructed in the model from the replacement rate $\mu$ and the benefit cap $\bar{b}$, such that:

$$ \text{UI max}_i = \min \left\{ wh(\bar{\theta})\mu_i, \bar{b}_i \right\} \times \bar{J}_i, \quad (11) $$

where we define $\bar{\theta} = \int \theta d\Gamma(\mathbf{x}, j)$ to be the average ability level in the economy.

We run a large number of counterfactual deviations in which the parameters $\bar{J}$, $\mu$, and $\bar{b}$ are uniformly drawn, such that the model variations fall in the range of those observed in US states and over time, including UI extensions. The replacement rate varies from 30% to 50%, the duration varies from 16 to 99 weeks, and the maximum UI benefit amount varies from 25% to 60% of the mean wage.

To measure the impact of UI generosity on labor market transitions in the model, we estimate elasticities based on our counterfactual deviations, such that:

$$ \log(f_{X \to Y})_i = \beta_{X \to Y} \log(\text{UI max}_i) + \text{err}_i, \quad (12) $$

with X any occupation out of which the flow $f_{X \to Y}$ is originating and Y the destination occupation. The elasticity of the flow from occupation X to occupation Y with respect to UI generosity, $\beta_{X \to Y}$, is the percentage change in the likelihood of a transition from occupation X to occupation Y when UI generosity changes by 1%.

As in section 2, because UI eligibility is not observable, we divide individuals into observable groups: the *Layoff* ($U_e$) and non-Layoff ($U_n$) unemployed individuals, workers ($W$), and self-employed individuals ($S$). To ensure that our analysis accurately reflects the impact of UI generosity on individual occupational choices ruling out any compositional effects, we estimate equation (12) using the stationary distribution of the economy under our baseline UI parameters. Concretely, agents in this stationary equilibrium face an unanticipated UI shock corresponding to the specific counterfactual $\{\bar{J}, \mu, \bar{b}\}$ set. We then capture the change in the average flow from a given pool of individuals, i.e. $f_{X \to Y}$, arising from variations in search intensities and decisions to switch while holding the population, prices, and taxes unchanged.<fnref n="15" />

<footnote n="15">¹⁵If the distribution of wealth and abilities among agents vary, it can bias the estimate, as individuals</footnote>
### 3.4.2 Elasticities Out of Unemployment

We begin by assessing the responsiveness of laid-off unemployed workers who are directly affected by the policy change. The baseline model results are reported in Table 5 alongside a summary of the CPS results for convenience. Overall, model elasticities align remarkably well with the responsiveness evaluated in the data, despite the fact that they were not targeted in our calibration. For instance, a 30% increase of the baseline UI generosity (a standard deviation increase) would lead to a 6.6% reduction in the fraction of insured unemployed individuals moving to self-employment, against 6% to 11% in the data depending on whether UI extensions are taken into account or not. Comparing these elasticities with those from laid-off unemployment to paid employment, we find the latter to be two to three times lower. As such, the model is able to capture the *UI elasticity gap from unemployment* observed in the data, i.e. the difference in elasticities between the response to UI generosity of transitions from insured unemployment to self-employment relative to that from insured unemployment to paid employment. Finally, also consistent with the data, the pool of non-Layoff unemployed individuals does not react to the policy change in the model while this effect is not significantly different from zero in the data.

<table><caption>**Table 5.** Elasticity of unemployment flows to UI generosity: model and data.</caption><thead><tr><th rowspan="3"></th><th colspan="4">Data<sup>a</sup></th><th colspan="2">Model</th></tr><tr><th colspan="2">Regular UI</th><th colspan="2">Extended UI</th><th rowspan="2">U→S</th><th rowspan="2">U→W</th></tr><tr><th>U→S</th><th>U→W</th><th>U→S</th><th>U→W</th></tr></thead><tbody><tr><td>Layoff</td><td>-0.38<sup>***</sup><br>(0.08)</td><td>-0.04<br>(0.05)</td><td>-0.20<sup>***</sup><br>(0.06)</td><td>-0.09<sup>***</sup><br>(0.01)</td><td>-0.25<sup>***</sup><br>(0.01)</td><td>-0.09<sup>***</sup><br>(0.00)</td></tr><tr><td>Non-Layoff</td><td>-0.02<br>(0.16)</td><td>0.07<br>(0.06)</td><td>-0.08<br>(0.16)</td><td>0.08<sup>*</sup><br>(0.04)</td><td>-0.01<sup>***</sup><br>(0.00)</td><td>0.00<sup>***</sup><br>(0.00)</td></tr></tbody></table>

*Notes:* \*p<0.1; \*\*p<0.05; \*\*\*p<0.01. Standard errors are reported in parentheses.

We also find that the model implied $\beta_{U_e→S}$ elasticity when adjusting only the UI benefits amount (as opposed to both the amount and the duration) is -0.4. This magnitude is comparable to the point estimate in the CPS (-0.38) in regular times, for which the variations are predominantly driven by changes in the weekly benefit amount. This is also

<footnote>with different levels of wealth and ability may be more or less sensitive to UI variations. Maintaining the same distribution of agents across counterfactuals ensures that the impact we measure is comparable to the data. Results are similar using new stationary distributions, but we retain this specification for consistency.</footnote>
consistent with the argument that because a change in the amount of UI benefits has a contemporaneous effect, we should expect that variations in that dimension should have stronger effects on the responsiveness relative to change in UI duration.

In Appendix A.3, we further decompose these elasticities by wealth and income in both the model and the data, showing that the gaps persist across the wealth and income distributions.

### 3.4.3 Labor Market and Occupational Masses

We now examine how the gross flow responses impact the aggregate occupational rates in the model, mirroring our empirical findings of section 2. Specifically, once all transitional adjustments have been completed and new equilibrium prices have been reached for each counterfactual experiment, we gather the implied occupational rates and run a specification similar to equation (2.2.3).

The impact is a priori ambiguous and difficult to predict using only information on gross flows, as the relative number of individuals in each occupation varies and UI likely affects more than just insured unemployed individuals. For example, while unemployed individuals may have a significant response to changes in UI, they only make up for a small percentage (5%-6%) of the workforce. In contrast, workers and self-employed individuals account for the majority of the population but tend to have a much weaker response to UI changes.

Table 6 shows the estimated effects of UI generosity on occupational rates in the model under various assumptions and compares them to our previous CPS results. In the data, we have shown that a higher UI generosity is associated with a modest (non-significant) increase in the employment rate, while simultaneously leading to a significant rise in the unemployment rate and a significant decline in self-employment. In the baseline model, and to put the tabulated results in perspective, doubling the generosity of UI results in a 0.35pp increase in the unemployment rate, a 0.52pp increase in the employment rate, and a 0.84pp decrease in the self-employment rate. Therefore, compared to the empirical evidence, the baseline model slightly overestimates adjustments along the employment margin. Overall, the model adjustments capture the direction and most of the magnitude of the empirical responses, indicating that a key effect of UI generosity is to reallocate
workers from self-employment to paid employment, alongside an increase in the unemployment rate.

<table><caption>**Table 6.** Effect of UI generosity on occupational masses: Data and Model.</caption><thead><tr><th></th><th>U rate</th><th>W rate</th><th>S rate</th></tr></thead><tbody><tr><td><em>A. CPS data</em></td><td></td><td></td><td></td></tr><tr><td>Estimate of log(Max Regular UI)</td><td>0.70<sup>**</sup> (0.33)</td><td>0.46 (0.67)</td><td>-1.15<sup>**</sup> (0.49)</td></tr><tr><td><em>B. Model estimates</em></td><td></td><td></td><td></td></tr><tr><td>Baseline</td><td>0.51<sup>***</sup> (0.07)</td><td>0.71<sup>***</sup> (0.03)</td><td>-1.21<sup>***</sup> (0.09)</td></tr><tr><td>No self-employment</td><td>0.52<sup>***</sup> (0.07)</td><td>-0.52<sup>***</sup> (0.07)</td><td>-</td></tr><tr><td>Baseline with alternative taxes</td><td>0.48<sup>***</sup> (0.06)</td><td>0.08<sup>*</sup> (0.03)</td><td>-0.56<sup>***</sup> (0.05)</td></tr></tbody></table>

*Notes*: \*p<0.1; \*\*p<0.05; \*\*\*p<0.01, standard errors in parenthesis. We use variations in regular benefits as UI weeks extensions depend on the state-level unemployment rate. The results (ranking, sign, and magnitude of the elasticities) are robust to using a sample excluding the Great Recession. State controls include a housing index and per capita income. The numbers describe adjustments in terms of semi-elasticities, constructed as shown in regression equation (2.2.3). The row numbers sum to zero, allowing them to be understood in terms of the percentage point changes in occupational rates.

The next-to-last row of Table 6 demonstrates that the inclusion of self-employment is crucial for understanding the impact of UI generosity on the employment rate. Indeed, absent the self-employment margin in the model, the sign of the response of the employment rate is reversed from positive to negative. This is related to important existing results in the literature. At the micro level, increasing UI generosity generally induces strongly negative and significant effects on occupational flows out of insured unemployment, consistent with moral hazard and liquidity effects (Meyer (1990); Chetty (2008); Farber et al. (2015)). However, at the macro level, Chodorow-Reich et al. (2019) and Boone et al. (2021) find a small and non-significant effect of UI generosity on aggregate employment. In Boone et al. (2021), where self-employed individuals are not accounted for, no statistically significant impact of increasing UI generosity on aggregate employment is found during the Great Recession. Moreover, Chodorow-Reich et al. (2019) find that an increase in the duration of benefits during the Great Recession on the unemployment rate is small, at most 0.3pp.

This apparent disconnect between micro-level transitions out of unemployment and adjustments in the aggregate employment is difficult to reconcile absent self-employment. When accounting for self-employment, the micro-level adjustments between unemployment and employment may not necessarily align with the macro effects on occupational
masses. Indeed, the employment rate may increase with UI generosity due to a real-
location between self-employment and employment consistent with both a drop in the
individuals entering self-employment and an increase in those exiting it.

Finally, using an alternative tax scenario (last row of Table 6), we show that the em-
ployment elasticity is at minimum positive but barely responsive, and, thus, closer to the
empirical results in Chodorow-Reich et al. (2019) and Boone et al. (2021). The baseline
model posits that the tax burden from increased UI generosity is equally distributed be-
tween employed and self-employed individuals. This assumption serves two purposes:
(i) it prevents a direct connection between occupational choices and UI through taxation,
and (ii) it is consistent with the ambiguity surrounding who ultimately bears the cost of
UI as a portion of the tax may effectively be passed on to workers. In the alternative tax
assumption, workers bear the entire cost of UI, i.e. d = 0, such that τp = 0 and τw > 0.
This leads to the muted response of the employment rate to UI generosity, with the self-
employment rate experiencing a decline. In essence, this tends to show that there is a tax
channel associated with the above responsiveness and that the self-employment margin
again plays a role in this channel depending on whether self-employed agents bear some
of the tax burden as employers in the economy. In the next section, we delve deeper into
the mechanisms explaining this self-employment margin.

4 UI Design and the Self-employment Margin

This section utilizes our model to evaluate how the design of the UI system contributes to
the responsiveness of both occupational flows and masses to UI generosity. We especially
highlight the role of two common but key features in UI systems: (i) the asymmetry in UI
coverage between self-employment and paid employment as self-employed individuals
are typically not eligible to UI, and (ii) the monitoring of UI program applicants and
what is accepted as valid search efforts. We also discuss the impact of these features on
key macroeconomic variables such as production, unemployment take-up, firm size, and
economic costs.
## 4.1 Asymmetric Insurance Coverage

Typically, UI provides insurance in case of job loss but does not provide any direct benefit to self-employed agents who would, for instance, face adverse business shocks.<fnref n="16" /> Consequently, an increase in UI generosity diminishes the relative risk associated with being in paid employment compared to being self-employed. Therefore, we should expect a reallocation between those two occupations with increased generosity. In this section, we evaluate the role of this asymmetric insurance effect.

First, this effect is directly evident in the elasticity of the bidirectional transitions between paid employment and self-employment, which respond noticeably to an increase in UI generosity. While we do not detect statistically significant effects in the CPS, as shown in Table 2, the point estimates tend to align with the expected signs. Our baseline model corroborates the existence of this effect, albeit with a small magnitude. As reported in Table 7, we find that $\beta_{W \to S} = -0.033^{***}$: there is a significant and negative elasticity of the flow from employment to self-employment in response to an increase in UI generosity. The reverse flow also corroborates this asymmetry, with a significant and positive elasticity of the transition from self-employment to employment in response to an increase in UI generosity, with $\beta_{S \to W} = 0.014^{***}$.

Second, to evaluate the importance of the above asymmetric insurance coverage on the overall responses of flows and occupational rates, we use a thought experiment. We introduce a fictitious mechanism to mitigate the above asymmetry by directly providing insurance to established self-employed individuals. The specification follows this logic: when an individual transitions to self-employment, she initially has no rights on any insurance claims. But, over time, there is a probability $\chi$ that she will gain full UI rights while self-employed. Once these rights are acquired, it will be possible to become an insured unemployed individual in the event of an adverse business shock. For the sake of simplicity, we assume that the insurance benefits are scaled to the entrepreneurial ability, similarly to how they were scaled to previous earnings for workers. We elaborate on the technical details in Appendix B.

<footnote n="16">¹⁶Exceptions exist in the form of pilot programs like the Self Employment Assistance Program (SEAP), implemented in only a few US states and constrained by quotas. As highlighted by Gaillard and Kankanamge (forthcoming), this program extends insurance to previously unemployed workers when they initiate their business activities, yet it does not grant UI benefits directly to the self-employed.</footnote>
Below, we focus on the following application: we set the probability of self-employment insurance such that 50% of new entrepreneurs are insured after 6 months of establishment, 75% after 1 year, and 94% after 2 years. We view this as a conservative time horizon, avoiding the hazard effects of accessing insurance through this occupation without spending enough time on it.

Row (2) of Table 7 (top panel) summarizes the effects of the self-employment UI mechanism on the dynamics of the labor market. It shows that expanding UI to cover self-employment significantly reduces the transition from self-employment to paid employment and increases the one from employment to self-employment relative to the baseline. In fact, in both cases, the sign of the effect is reversed as compared to the baseline. This occurs because the self-employed UI evens out some of the asymmetric UI coverage with respect to paid employment. Moreover, the response from the laid-off unemployment to self-employment flow is largely weakened, from an elasticity of -0.248 to -0.197. The latter change corresponds to a decrease by 33% of the baseline economy *UI elasticity gap from unemployment* between $\beta_{U_e \to S}$ and $\beta_{U_e \to W}$.

Concerning the impact on the occupational rates (bottom panel of Table 7, row (2)), the above transition responses imply that the relationship between the unemployment rate and UI generosity is stronger, while the negative relationship with the self-employment rate is weakened. This larger response of the unemployment rate is primarily due to the increased proportion of insured unemployed individuals in the economy, as some previously self-employed individuals are now insured. Since this group is initially more responsive to UI generosity, it mechanically translates into a bigger increase in the unemployment rate. We also find that while the employment rate is positively correlated with higher UI generosity in the baseline, it becomes negatively correlated in the presence of the self-employment UI mechanism. Thus, our model predicts that the insurance coverage asymmetry between employment and self-employment is a key determinant of the positive elasticity response of employment to UI generosity.

## 4.2 Monitoring incentives

A second factor driving the significant impact of UI generosity on self-employment, as opposed to paid employment, comes from the monitoring of UI program applicants. UI
<table><caption>**Table 7.** Elasticity of unemployment flows to UI generosity under self-employment insurance</caption><thead><tr><th rowspan="2"></th><th colspan="4">Elasticity of flows (β<sub>X→Y</sub>)</th><th rowspan="2">Elasticity gap reduction (in %)<sup>a</sup></th></tr><tr><th>U<sub>e</sub>→S</th><th>U<sub>e</sub>→W</th><th>W→S</th><th>S→W</th></tr></thead><tbody><tr><td>(1) Baseline model</td><td>-0.248***</td><td>-0.092***</td><td>-0.033***</td><td>0.014***</td><td>-</td></tr><tr><td>(2) Self-employment UI</td><td>-0.197***</td><td>-0.093***</td><td>0.020***</td><td>-0.036***</td><td>33</td></tr><tr><td>(3) No monitoring</td><td>-0.267***</td><td>-0.178***</td><td>-0.041***</td><td>0.020***</td><td>43</td></tr><tr><td>(2)+(3)</td><td>-0.199***</td><td>-0.181***</td><td>0.029***</td><td>-0.050***</td><td>88</td></tr><tr><td>CPS Data</td><td>-0.20***</td><td>-0.09***</td><td>-0.08</td><td>0.13</td><td>-</td></tr></tbody><thead><tr><th rowspan="2"></th><th colspan="3">Effects on occupational rates<sup>b</sup></th></tr><tr><th>U</th><th>W</th><th>S</th></tr></thead><tbody><tr><td>(1) Baseline model</td><td>0.51***</td><td>0.71***</td><td>-1.21***</td></tr><tr><td>(2) Self-employment UI</td><td>1.08***</td><td>-0.51***</td><td>-0.57***</td></tr><tr><td>(3) No monitoring</td><td>1.05***</td><td>0.35***</td><td>-1.40***</td></tr><tr><td>(2)+(3)</td><td>2.02***</td><td>-1.40***</td><td>-0.62***</td></tr><tr><td>CPS Data</td><td>0.70**</td><td>0.46</td><td>-1.15**</td></tr></tbody></table>

<sup>a</sup> This is the elasticity gap $\Delta(\beta_{U_e \to S} - \beta_{U_e \to W})$ reduction, comparing the out of unemployment elasticity to self-employment versus employment, relative to the baseline. For instance, for the self-employment UI alone, we measure it as $1 - (0.197 - 0.093)/(0.248 - 0.092) = 33\%$.

<sup>b</sup> The numbers describe adjustments in terms of semi-elasticities, constructed as shown in regression equation (2.2.3). The row numbers sum to zero, allowing them to be understood in terms of the percentage point changes in occupational rates.

agencies typically mandate insured unemployed agents to provide ongoing proof of job search efforts as a key condition for maintaining UI benefits eligibility. But, at the same time, efforts to establish a business are excluded from those eligibility conditions.<sup>17</sup>

To evaluate the importance of this requirement, we neutralize monitoring in the model by setting the Poisson rate $\kappa_m$ at which individuals are detected by the UI agency to a large value.<sup>18</sup> The implications of this adjustment are reported in row (3) of Table 7 (top panel). We find that the monitoring system plays a crucial role in promoting job search efforts out of unemployment by markedly diminishing how job search responsiveness is affected by changes in UI generosity. Notably, there is a doubling of the $\beta_{U_e \to W}$ elasticity of a transition from unemployment to paid employment. The self-employment response is quite

<footnote n="17"><sup>17</sup>For instance, section 402(h) of Pennsylvania Unemployment Compensation Law states: "A claimant is ineligible for any week in which he/she is engaged in self-employment. When a claimant is starting a new business, the claimant becomes self-employed with the first positive step toward starting the business."</footnote>

<footnote n="18"><sup>18</sup>Interestingly, this is similar to implemented real-world experiments and studied by Abbring et al. (2005), McVicar (2008), and more recently Walsh (2023). All these papers find a strong and significant impact of monitoring and sanctioning on individual re-employment rates.</footnote>
interesting: the corresponding $\beta_{U_e \to S}$ elasticity is even more negative than in the baseline, albeit moderately, which is at first puzzling. This is explained by a combination of effects. First, without monitoring, no insured unemployment agent expects to lose their UI before the end of the regulatory duration. As a result, global incentives to search are lower, including the efforts to establish a business. Second, when the monitoring system is in place, UI recipients below the required job search effort level lose their UI benefits, becoming effectively uninsured unemployed. These agents have to increase their search efforts across all activities, including some that will then transition to self-employment. Absent monitoring, there are fewer uninsured unemployed agents, lowering global incentives to search. Overall, the effects on $\beta_{U_e \to W}$ and $\beta_{U_e \to S}$ combine, leading to a decrease by 43% of the baseline economy *UI elasticity gap from unemployment*.

Concerning occupational rates (bottom panel, row (3)), we observe that the responsiveness to UI generosity of the employment rate decreases by half compared to the baseline while the unemployment rate response shows a slightly bigger increase. Interestingly, the negative effect on the self-employment rate is larger than in the baseline. This effect originates from the flows between employment and self-employment in both directions. Indeed, no monitoring implicitly implies that the insured unemployed situation is more beneficial both to currently unemployed individuals and to future laid-off workers, which virtually widens the effects of the asymmetry in insurance coverage between self-employment and employment.

Finally, the row marked (2)+(3) in Table 7 combines the effects of the self-employment UI experiment with the absence of job search effort monitoring for program applicants. Here, while the experiment to extend UI to self-employment tends to decrease the $\beta_{U_e \to S}$ elasticity, the lack of monitoring programs increases the $\beta_{U_e \to W}$ elasticity. As a result, combining these two factors nearly neutralizes the *UI elasticity gap from unemployment* (a decrease by 88% of the baseline elasticity gap). On occupational rates, this results in a significant responsiveness of unemployment to UI generosity, primarily driven by adjustments in the employment margin.
rate. Here, a doubling of UI generosity would reduce the self-employment output by approximately 2.6%, which mitigates by half the baseline case decrease. Furthermore, the insured unemployment rate is higher because some of the previously self-employed individuals are now able to claim UI in case of adverse shocks. We also note that there is no significant change in the take-up rate, as the self-employment insurance does not substantially alter the cost of taking the insurance versus not taking it—it simply expands the number of potential beneficiaries. Finally, we find that while an increase in UI generosity tends to lower the welfare in the economy, the decrease is less pronounced when self-employed individuals have access to UI.<fnref n="20" />

When we remove the monitoring of program applicants (row (3)), the effect on self-employment production becomes significantly more pronounced compared to the baseline economy. Additionally, the smaller increase in the employment rate implies a smaller corporate production elasticity. The insured unemployment rate also increases mechanically due to the much weaker incentive to exit insured unemployment and the tax rate is significantly higher. The take-up rate increases because the value of being insured while unemployed rises in the absence of monitoring. Additionally, neutralizing job search monitoring significantly reduces welfare because aggregate output is reduced and taxes are higher.

Lastly, we find that the above effects compound when we both extend UI to the self-employed and remove the monitoring of program applicants (row (2)+(3)). Specifically, tax rates are much higher and both the corporate and self-employment sector outputs decrease. This is because, as shown in section 7, there is a significant increase in unemployment and a drastic reduction in the employment rate.

Overall, our experiments show that the current design of UI systems, while incentivizing job search and providing better insurance for the employment activity, has unintended adverse effects on self-employment that drive the high responsiveness of the self-employment margin to changes in UI generosity and can explain a small but positive employment rate response. Moreover, we show that the two features generating a large responsiveness of the occupational rates, namely the insurance asymmetry across occup-

<footnote n="20">²⁰Our welfare measure is based on a consumption equivalent variation (CEV). Its exact computation is detailed in Appendix B.1)</footnote>
pations and the monitoring of UI program applicants, have significant macroeconomic consequences. The key takeaways are that providing more insurance to self-employed agents has effects, in magnitude, comparable to those of removing all monitoring of UI program applicants. Furthermore, reducing the insurance asymmetry can substantially mitigate reallocation effects caused by the current design of the UI system and significantly reduce the impact on production, albeit at a higher cost.

# 5 Conclusion

This paper demonstrates, both empirically and quantitatively, that increasing the generosity of unemployment insurance has a significant and adverse effect on the self-employment margin. A detailed analysis of labor market flows reveals that higher UI generosity substantially hampers the transition from laid-off unemployment to self-employment as well as the bi-directional transitions from employment to self-employment. These responses, in turn, drive large reallocations from self-employment to employment. Notably, these shifts result in an increased employment rate but a marked decrease in self-employment as UI generosity increases. Through a general equilibrium model of the US labor market, we establish that the observed responsiveness of flows and occupational rates is largely due to the UI system's design, particularly the asymmetry in insurance coverage and the monitoring of program applicants. An intriguing avenue for future research lies in examining how incorporating the self-employment margin affects the optimal design of UI, including the exploration of instruments like an optimal self-employment UI extension.

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# Appendix

## A Validation: Gross Flows and Micro Level Behaviors

In this section, we assess the ability of our benchmark economy to generate key labor market properties and other notable features such as the relative income and wealth across occupations.

### A.1 Resulting gross flows

Table 9 reports bimonthly aggregate gross flows between employment, unemployment, and self-employment in the CPS and the model. With one occupational mass and two transitions calibrated in the model, we are left with three degrees of freedom as targeting masses indirectly impact flows (up to the exogenous entry $\zeta$). The remaining discrepancies can be attributed to transitions out of the labor force, deaths, and relocations in the data that are not captured by the model.

Two important sets of facts deserve further attention. First, unemployed individuals are much more likely than workers to start a business. Second, the model replicates the large transition from self-employment to employment ($S \to W$) of 4.3%, while generating the low transition from self-employment to unemployment ($S \to U$) of 1.3%. The combination of those flows leads to a share of new self-employed out-of-unemployment of 21.7% in the model against 20.5% in the CPS. According to the Kauffman Indicators of Entrepreneurship, this fraction is higher for individuals with less than a high school degree (27%) and lower for college graduates (17%). In the model, the corresponding shares are consistent: 31% and 21% for low and high ability.

Beyond the required match of aggregate occupational flows, recent research has stressed the importance of consistent labor market micro-level behaviors (Krusell et al., 2017). We now discuss the model's ability to fit gross flows along the wealth distribution, a dimension that plays an important role in occupational decisions regarding self-employment (see Quadrini (2000) or Cagetti and De Nardi (2006)) and for the unemployed (see Chetty (2008)). For example, wealth drives incentives to quickly exit unemployment due to borrowing constraints or to enter self-employment as personal wealth scales the expected
<table><caption>**Table 9.** Bimonthly gross flow between occupations in the data and the model.</caption><thead><tr><th rowspan="2">From</th><th colspan="3">Data<sup>a</sup></th><th colspan="3">Model</th></tr><tr><th colspan="3">To</th><th colspan="3">To</th></tr><tr><th></th><th>W</th><th>S</th><th>U</th><th>W</th><th>S</th><th>U</th></tr></thead><tbody><tr><th>W</th><td>97.8</td><td>0.5</td><td>1.7</td><td>97.6</td><td>0.7</td><td>1.7</td></tr><tr><th>S</th><td>4.3</td><td>94.4</td><td>1.3</td><td>4.5</td><td>94.1</td><td>1.4</td></tr><tr><th>U</th><td>37.4</td><td>3.3</td><td>59.2</td><td>37.9</td><td>3.0</td><td>59.1</td></tr></tbody></table>

profits of a potential business due to the entrepreneurial collateral constraint.

Because the CPS does not report individual wealth, we rely on the 1996-2008 panels of the SIPP, which covers the December 1995 to November 2013 period with gaps. Households are interviewed three times a year about their labor market status over the previous four months in each panel. Every two to four years, they also report their asset holdings (savings and checking accounts, mutual funds, retirement accounts, real estate, business assets, and other equity). Although the definitions of occupations in the SIPP and the CPS differ, we create close enough counterparts. <sup>21</sup> Table 10 presents the transition data for occupational choice by wealth quantiles in the SIPP and the model. Results are similar for total or liquid wealth (checking accounts and savings), we only present the former.

<table><caption>**Table 10.** Decomposition of occupational flow rates by wealth terciles.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Data</th><th colspan="3">Model</th></tr><tr><th>T1</th><th>T2</th><th>T3</th><th>T1</th><th>T2</th><th>T3</th></tr></thead><tbody><tr><th>W → S</th><td>0.78</td><td>0.89</td><td>1.33</td><td>0.18</td><td>0.68</td><td>2.13</td></tr><tr><th>W → U</th><td>1.47</td><td>0.85</td><td>0.68</td><td>1.32</td><td>0.89</td><td>0.78</td></tr><tr><th>S → W</th><td>1.35</td><td>0.97</td><td>0.69</td><td>1.75</td><td>0.77</td><td>0.46</td></tr><tr><th>S → U</th><td>1.79</td><td>0.81</td><td>0.40</td><td>1.62</td><td>0.93</td><td>0.44</td></tr><tr><th>U → S</th><td>0.75</td><td>0.94</td><td>1.31</td><td>0.49</td><td>1.00</td><td>1.52</td></tr><tr><th>U → W</th><td>1.02</td><td>0.98</td><td>0.99</td><td>1.32</td><td>0.95</td><td>0.72</td></tr></tbody></table>

*Notes:* Authors' computations using the SIPP (1996-2008) panels.

We find that the W to U transition by wealth terciles is decreasing. This is due to the selection of high-ability types with lower firing rates at higher levels of wealth. The U to W transition is nearly flat in the data but decreasing in the model. Similar to Krusell

<footnote><sup>a</sup> Data sources: authors' computations using CPS data.</footnote>

<footnote n="21"><sup>21</sup> In section A.3 of the Online Appendix, we show the SIPP aggregate occupational transition matrix. The latter is quite similar to its CPS analog above but not identical as the SIPP is a longitudinal survey.</footnote>
et al. (2017), this discrepancy can be explained by the fact that, in the model, wealth-poor individuals have a higher incentive to search for a job opportunity and face the same labor market frictions ($\kappa_w$) as wealthier households. More specific to this model, the $S$ to $W$ and $S$ to $U$ transitions are decreasing both in the data and the model. Intuitively, the wealthy can self-insure against the risk of an adverse business shock using their own wealth and are thus less likely to exit. This is also a result of the effect of wealth on the incentive to exit self-employment, as business income is scaled to personal wealth due to the collateral constraint. Related to these arguments, the $U$ to $S$ and $W$ to $S$ transitions are increasing, consistent with the data, but the model somewhat overshoots the wealthiest agent T3 tercile of the $W$ to $S$ transition.<fnref n="22" /> Despite the few drawbacks, we believe that the model produces a reasonably good fit of gross labor market flows, especially in and out of unemployment.

## A.2 Cross-sectional validation

The model also has cross-sectional implications regarding income and wealth distributions. The median ratio of self-employment (resp. worker's) income (including capital gains) to net worth (i.e. total assets minus debt) is 0.16 (resp. 0.70) in the model, while it is 0.19 (resp. 0.73) in the data. In the model, the median ratio of self-employment income over workers' income is 1.6 against 1.4 in the SCF. Self-employed agents in the model own roughly 33% of total capital, in line with the 33% found by Cagetti and De Nardi (2006). The fraction of zero (or negative) net worth is roughly 8% in the SCF, whereas it is 7% in the model. The model underestimates the wealth Gini: we find 0.66 compared to 0.8 in the SCF.<fnref n="23" />

<footnote n="22">²²Interestingly, when falling back to the Cobb-Douglas case (by setting $p \to 0$) and self-employed agents cannot produce without capital as in most of the literature, those transitions are not reproducible. In such an environment, none of the individuals in the first wealth tercile among the unemployed and employed individuals is willing to become self-employed, which is at odds with the SIPP evidence. In contrast, a higher $p$ allows relatively wealth-poor agents to start their businesses. This result is available upon request.</footnote>

<footnote n="23">²³An alternative version of the model including a superstar state of business shock $z$ can match the wealth distribution and produces similar results otherwise.</footnote>
## A.3 Responsiveness to UI generosity by wealth and income

### A.3.1 The role of wealth

As shown in Table 10, the model generates flows that are consistent across wealth terciles. This is an important consideration, given that two well-known effects influence the decision to exit unemployment following an increase in UI generosity: a traditional moral hazard effect, and a Chetty (2008) type liquidity effect. The former effect captures the fact that, following an increase in UI generosity, the expected relative outcome of taking a job reduces, disincentivizing job search, regardless of any wealth considerations. In contrast, the latter effect is very much tied to wealth considerations: in a world where agents can be borrowing constrained, the closer an unemployed agent is to her borrowing constraint, the more difficult it is for her to smooth consumption and the stronger her incentive to search for a job. An increase in UI generosity relaxes this constraint by moving the agent away from her borrowing constraint and, therefore, reducing incentives to search. Table 11 reports the decompositions of the elasticities $\beta_{U_e \to S}$ and $\beta_{U_e \to W}$ by wealth. Consistent with the liquidity effect, wealth-poor individuals (below the median) display a stronger response than wealthier ones. We further notice that the responsiveness gap in transitions from laid-off unemployment to self-employment relative to transitions from laid-off unemployment to paid employment remains substantial.

<table><caption>**Table 11.** Elasticity of unemployment flows to UI generosity depending on wealth.</caption><thead><tr><th rowspan="2"></th><th colspan="2">Net worth</th></tr><tr><th>a &lt; median</th><th>a ≥ median</th></tr></thead><tbody><tr><th>β<sub>U<sub>e</sub>→S</sub></th><td>-0.43</td><td>-0.14</td></tr><tr><th>β<sub>U<sub>e</sub>→W</sub></th><td>-0.08</td><td>-0.01</td></tr></tbody></table>

To test the implications of wealth in the data, we use our SIPP sample. Our strategy is to interact the level of total wealth with the interaction between *Layoff* and UI generosity. We report the results in Table 12. We find a weakly statistically significant positive effect of wealth on the responsiveness of laid-off individuals to regular UI generosity. In contrast, the effect is not significant when using extended UI benefits. This low significance can be attributed to the fact that reported wealth does not necessarily align with the timing of the decision – as wealth is reported only at an annual frequency and only a few times for
a specific wave. However, the point estimates suggest that wealth has a consistent effect with our findings above.

<table><caption>**Table 12.** UI generosity, exit probability out of unemployment, and wealth (SIPP data)</caption><thead><tr><th></th><th colspan="2">U to S</th><th colspan="2">U to W</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>log(Max Regular UI) × Layoff</td><td>-0.38***<br>(0.13)</td><td></td><td>-0.05<br>(0.05)</td><td></td></tr><tr><td>log(Max Regular UI) × Layoff × Wealth</td><td>0.11*<br>(0.06)</td><td></td><td>0.009<br>(0.01)</td><td></td></tr><tr><td>log(Max Extended UI) × Layoff</td><td></td><td>-0.20**<br>(0.09)</td><td></td><td>-0.02<br>(0.03)</td></tr><tr><td>log(Max Extended UI) × Layoff × Wealth</td><td></td><td>0.08<br>(0.05)</td><td></td><td>0.007<br>(0.009)</td></tr><tr><td>Observations</td><td>358,252</td><td>358,252</td><td>358,252</td><td>358,252</td></tr><tr><td>State-year-month FE</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Individual controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses.

### A.3.2 The role of income and education

Table 13 decomposes the elasticities of the flows to examine the influence of income, with ability $\vartheta$ as a proxy. We find that the responsiveness is less pronounced among high-income individuals. This finding can be primarily attributed to a selection effect: individuals with a higher $\vartheta$-ability typically possess greater wealth, thus mitigating the pressure of the liquidity constraint. Once again, there is an appreciable gap in responsiveness between transitions to self-employment and those to employment.

<table><caption>**Table 13.** Elasticity of unemployment flows to UI generosity by ability.</caption><thead><tr><th></th><th colspan="3">Ability</th></tr><tr><th></th><th>θ<sub>1</sub></th><th>θ<sub>2</sub></th><th>θ<sub>3</sub></th></tr></thead><tbody><tr><td>β<sub>U<sub>e</sub>→S</sub></td><td>-0.31</td><td>-0.27</td><td>-0.17</td></tr><tr><td>β<sub>U<sub>e</sub>→W</sub></td><td>-0.10</td><td>-0.07</td><td>-0.05</td></tr></tbody></table>

We align these findings with empirical data from the CPS by using an individual's educational degree as a proxy for ability. Specifically, we construct a *College* degree dummy indicating whether the individual has attended college. We then interact this dummy
with the interaction of UI generosity and the *Layoff* dummy from the main empirical specification in equation (1). Table 14 reports the results. We find a statistically significant contrast in the $\beta_{U_e \to S}$ elasticity between non-college graduates (-0.46) and college graduates (-0.07 = -0.46 + 0.39) regarding regular UI generosity. This contrast, however, is less pronounced for UI extensions. Additionally, when considering variations in extended benefits, we find a negative and significant effect on the $\beta_{U_e \to W}$ elasticity, with an elasticity of -0.10 for the non-college graduates against -0.05 = -0.10 + 0.05 for college graduates. Overall, consistent with the model, the point estimates confirm that *College* does seem to be an important contributing factor, especially for the selection into self-employment.

<table><caption>**Table 14.** UI generosity, exit probability out of unemployment, and College degree (CPS data).</caption><thead><tr><th></th><th colspan="2">U to S</th><th colspan="2">U to W</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>log(Max Regular UI) × Layoff</td><td>-0.46<sup>***</sup><br>(0.07)</td><td></td><td>-0.02<br>(0.05)</td><td></td></tr><tr><td>College × log(Max Regular UI) × Layoff</td><td>0.39<sup>**</sup><br>(0.15)</td><td></td><td>-0.08<br>(0.05)</td><td></td></tr><tr><td>log(Max Extended UI) × Layoff</td><td></td><td>-0.19<sup>***</sup><br>(0.06)</td><td></td><td>-0.10<sup>***</sup><br>(0.01)</td></tr><tr><td>College × log(Max Extended UI) × Layoff</td><td></td><td>0.02<br>(0.07)</td><td></td><td>0.05<sup>***</sup><br>(0.02)</td></tr><tr><td>Observations</td><td>348,025</td><td>348,025</td><td>348,025</td><td>348,025</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Ind. &amp; state controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p*<0.1; **p*<0.05; ***p*<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses.
# B Self-Employment Insurance: Model

Let $\pi_w(e_w) \equiv \pi_w$, with the possibility to access unemployment insurance, the program of the self-employed individual now reads:

$$ S_0(\mathbf{x}_S) = \max_{\substack{c>0, \\ a', k, e_w \ge 0}} u(c, e_w, 0) + \beta \mathbb{E}_{\theta', y', z'} \left\{ \begin{aligned} & \chi \left( \pi_w \max\{S_J(\mathbf{x}'_S), W(\mathbf{x}'_W), \mathcal{J}(\mathbf{x}'_U)\} \right) \\ & + (1 - \pi_w) \max\{S_J(\mathbf{x}'_S), \mathcal{J}(\mathbf{x}'_U)\} \right\} + (1 - \chi) \left( \pi_w \max\{S_0(\mathbf{x}'_S), W(\mathbf{x}'_W), U_0(\mathbf{x}'_U)\} \right) \\ & + (1 - \pi_w) \max\{S_0(\mathbf{x}'_S), U_0(\mathbf{x}'_U)\} \end{aligned} \right\}, $$

$$ S_J(\mathbf{x}_S) = \max_{\substack{c>0, \\ a', k, e_w \ge 0}} u(c, e_w, 0) + \beta \mathbb{E}_{\theta', y', z'} \left\{ \begin{aligned} & \pi_w \max\{S_J(\mathbf{x}'_S), W(\mathbf{x}'_W), \mathcal{J}(\mathbf{x}'_U)\} \\ & + (1 - \pi_w) \max\{S_J(\mathbf{x}'_S), \mathcal{J}(\mathbf{x}'_U)\} \end{aligned} \right\}, $$

$$ \begin{array}{l} \text{s.t.} \quad c + a' = (1 - \tau_s) \Pi(k, \vartheta, z) + a + r(a - k) \mathbb{1}_{\{k \le a\}}, \\ \Pi(k, \vartheta, z) = \mathcal{Y}(k, \vartheta, z) - \delta k - r(k - a) \mathbb{1}_{\{k \ge a\}} - F, \\ k \le \lambda a, \end{array} $$

where the only difference relative to the benchmark model is that now self-employment individuals can claim UI rights in case of bad business shock z, and reach the take-up continuation value $\mathcal{J}(\mathbf{x}'_U)$. $\chi$ is the probability of gaining full rights to self-employed UI.

## B.1 Welfare Definitions

$\Delta^{CEV}$ is the consumption percentage change needed to make a randomly selected new-born indifferent between the initial and new steady states of per-period consumption while holding all other factors constant. In our economy, it is given by:

$$ W_{\text{benchmark}}^* = \int_{\mathbf{x}} \mathbb{E}_0 \left[ \sum_{t=0}^{\infty} \beta^t \frac{(c_t^* [1 + \Delta^{CEV}])^{1-\sigma}}{1-\sigma} - (e_{w,t}^*)^2 - (e_{s,t}^*)^2 - (e_{i,t}^*)^2 \right] d\Gamma^*(\mathbf{x}) = \\ \int_{\mathbf{x}} \mathbb{E}_0 \left[ \sum_{t=0}^{\infty} \beta^t \frac{\tilde{c}_t^{1-\sigma}}{1-\sigma} - \tilde{e}_{w,t}^2 - \tilde{e}_{s,t}^2 - \tilde{e}_{i,t}^2 \right] d\tilde{\Gamma}(\mathbf{x}) = \tilde{W}_{\text{reformed}} $$
where * refers to the baseline allocations and distributions, while ~ refers to the new ones under the reformed economy. The $\Delta^{CEV}$ can be simply expressed as:

$$ \Delta^{CEV} = \left[ \left( \tilde{W}_{\text{reformed}} - W_{\text{benchmark}}^* \right) / \left( \sum_{t=0}^{\infty} \beta^t \frac{c_t^{1-\sigma}}{1-\sigma} \right) + 1 \right]^{1/(1-\sigma)} - 1 \quad (13) $$

A positive CEV indicates that average welfare is higher in the new steady state. Households would only choose to stay in the initial steady state if they receive higher consumption as compensation.
# Supplemental Appendix to:
Unemployment Insurance Generosity and Self-Employment

For Online Publication

Alexandre Gaillard*
Brown University

Sumudu Kankanamge†
Le Mans University (GAINS-TEPP, IRA), France

## Contents

<table><tr><td><b>A</b></td><td><b>Empirical Appendix</b></td><td><b>2</b></td></tr><tr><td>A.1</td><td>UI generosity in the Data</td><td>2</td></tr><tr><td>A.2</td><td>Additional Details on the CPS</td><td>2</td></tr><tr><td>A.2.1</td><td>Summary Statistics</td><td>3</td></tr><tr><td>A.2.2</td><td>Characteristics of newly self-employed from unemployment and employment</td><td>3</td></tr><tr><td>A.3</td><td>Additional Details on the SIPP</td><td>5</td></tr><tr><td>A.4</td><td>UI Generosity</td><td>5</td></tr><tr><td>A.4.1</td><td>Regular UI benefit changes and economic conditions</td><td>5</td></tr><tr><td>A.5</td><td>Empirical Results: Robustness and Additional Details</td><td>6</td></tr><tr><td>A.5.1</td><td>Sensitivity Analysis</td><td>6</td></tr><tr><td>A.5.2</td><td>Estimates of UI on flows toward Not In the Labor Force (NILF)</td><td>8</td></tr><tr><td>A.5.3</td><td>Regression in the SIPP</td><td>10</td></tr><tr><td><b>B</b></td><td><b>Additional Model Specifications and Quantitative Results</b></td><td><b>12</b></td></tr><tr><td>B.1</td><td>Additional Model Specifications</td><td>12</td></tr></table>

<footnote>*Email: alexandre_gaillard@brown.edu.</footnote>

<footnote>†Email: sumudu.kankanamge@univ-lemans.fr.</footnote>
<table><tr><td>B.2 Algorithm</td><td>12</td></tr><tr><td>B.3 Search Policy Functions</td><td>13</td></tr><tr><td>B.3.1 Optimal Search Efforts</td><td>13</td></tr></table>

# A Empirical Appendix

## A.1 UI generosity in the Data

<figure><img src="image_2.png" /><figcaption>Figure A1. Maximum UI benefits duration and amount: US average and selected states.</figcaption></figure>

Left panel: maximum duration (Max Regular Weeks<sub>st</sub> + Max EB EUC Weeks<sub>st</sub>). Middle panel: maximum weekly benefit (Max WBA<sub>st</sub>), CPI adjusted. Right panel: total claimable benefits (Max Extended UI<sub>st</sub>), CPI adjusted. The black line is the US average. Grey areas report NBER recessions.

Sources: US Department of Labor, significant provisions of state unemployment insurance laws biannual reports.

## A.2 Additional Details on the CPS

**Sample construction** When building the CPS panel of the main paper, we construct a specific individual identifier that checks for age, sex, ethnicity, and US state. We identify and exclude erroneous matches by detecting instances where the person's age exhibits a bimonthly change greater than 1 (this removes around 100,000 false matches (<1%)). We use the first-month respondent weight WTFINL throughout the empirical analysis.

**Occupation definition** We classify as a worker an individual who currently works in a paid job or who declares being temporarily absent from a paid job (EMPSTAT = 1, 10, 12, and CLASSWKR = 20 : 28).
Individuals are classified as unemployed if they did not work for pay or profit and did not have a job from which they were briefly absent. The variable EMPSTAT = 20 : 22 identifies unemployed individuals. We distinguish layoff unemployed persons when WHYUNEMP = 1,2 which records job loser/ on layoff and other job losers. All other unemployed individuals are considered non-eligible for unemployment insurance. We further condition the *layoff* category with DURUNEMP, which allows us to further select groups of eligible UI claimants with respect to their unemployment duration. When studying the effect of regular UI benefits, we define laid-off individuals eligible for UI as those with less than 30 weeks of unemployment duration, which is the maximum regular US state duration. When considering UI extensions, we define laid-off unemployed agents as unemployed individuals with less than 99 weeks of unemployment. In a robustness check, we further restrict a *laid-off* unemployed to those who declare having worked in the last twelve months (WNFTLOOK to be either 0 or 11). Results remain similar over these alternatives.

We define a self-employed as a self-employed worker (CLASSWKR = 10, 13, 14), who currently works (EMPSTAT = 1, 10, 12). We perform an additional robustness check for self-employed individuals who own their business (HHBUS = 1).<fnref n="1" />

### A.2.1 Summary Statistics

Table A1 presents the summary statistics for the sample of unemployed individuals and the main variables used throughout the empirical part.

### A.2.2 Characteristics of newly self-employed from unemployment and employment

**Demographics** Table A2 displays the demographic characteristics of unemployed and employed individuals. First, individuals who switch to self-employment out of unemployment and employment are more likely to be male. Second, they are more likely to be older, suggesting that accumulating either sufficient experience and/or wealth is important before switching to such an occupation. Third, they are also more likely to be married, which suggests that, in the case where the new business is not successful, a part-

<footnote n="1">¹We check for business ownership by creating a specific variable that indicates whether the individual owned her firm from 1994 to 2015, letting us control for measurement errors arising in the survey. Without this additional variable, the flow from self-employment to employment during a quarter jumps to 16%, which is inconsistent with yearly flows. One limitation is that we are not able to finely track changes in ownership status over the period with this approach.</footnote>
<table><caption>**Table A1.** Descriptive statistics.</caption><thead><tr><th>Statistic</th><th>Mean</th><th>St. Dev.</th><th>Min</th><th>Max</th></tr></thead><tbody><tr><td>Age</td><td>38.6</td><td>12.4</td><td>20</td><td>65</td></tr><tr><td>Partner has a job</td><td>0.4</td><td>0.5</td><td>0</td><td>1</td></tr><tr><td>Went to college</td><td>0.2</td><td>0.4</td><td>0</td><td>1</td></tr><tr><td>Duration unemployment (weeks)</td><td>24.0</td><td>29.6</td><td>0</td><td>124</td></tr><tr><td>Eligible</td><td>0.5</td><td>0.5</td><td>0</td><td>1</td></tr><tr><td>Max UI duration (extension)</td><td>45.9</td><td>26.5</td><td>14.0</td><td>99.0</td></tr><tr><td>Max UI duration (regular)</td><td>25.9</td><td>1.4</td><td>12</td><td>30</td></tr><tr><td>Max Weekly Benefit Amount (CPI adjusted)</td><td>423.9</td><td>113.0</td><td>212.8</td><td>963.4</td></tr><tr><td>Unemployment rate</td><td>6.5</td><td>2.2</td><td>2.1</td><td>14.6</td></tr><tr><td>log real GDP</td><td>10.8</td><td>0.2</td><td>10.3</td><td>12.1</td></tr><tr><td>log per capita income</td><td>10.5</td><td>0.3</td><td>9.7</td><td>11.2</td></tr><tr><td>Average state-level wage</td><td>784.2</td><td>205.1</td><td>352.5</td><td>1,608.4</td></tr></tbody></table>

ner with a job may be a source of self-insurance within the household. Finally, individuals transitioning to self-employment are more likely to be graduates.

<table><caption>**Table A2.** Demographics of unemployed and employed individuals.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Unemployed</th><th colspan="2">Employed</th></tr><tr><th>All</th><th>U → S</th><th>U → W</th><th>All</th><th>W → S</th></tr></thead><tbody><tr><td>Female (in %)</td><td>46</td><td>30</td><td>45</td><td>48</td><td>39</td></tr><tr><td>Age</td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>20-34 (in %)</td><td>45</td><td>31</td><td>49</td><td>34</td><td>29</td></tr><tr><td>35-49 (in %)</td><td>33</td><td>41</td><td>33</td><td>40</td><td>41</td></tr><tr><td>50-65 (in %)</td><td>22</td><td>28</td><td>18</td><td>26</td><td>30</td></tr><tr><td>Single (versus married) (in %)</td><td>57</td><td>44</td><td>55</td><td>39</td><td>33</td></tr><tr><td>College degree (in %)</td><td>18</td><td>25</td><td>19</td><td>32</td><td>34</td></tr></tbody></table>

**By sector** Table A3 displays the industry in which employed and unemployed individuals are reported to work/have worked when switching to self-employment. Overall, we do not see big differences in the sectors in which individuals who switch to self-employment are operating. However, we notice that newly self-employed individuals are more likely to be in the construction sector and in sectors related to professional, scientific, and technical services. The latter suggests a prevalence for self-employed individuals to work as freelancers for other companies.
<table><caption>**Table A3.** Sectors of unemployed and employed individuals.</caption><thead><tr><th rowspan="2"></th><th colspan="3">Unemployed</th><th colspan="2">Employed</th></tr><tr><th>All</th><th>U→S</th><th>U→W</th><th>All</th><th>W→S</th></tr></thead><tbody><tr><td>Agriculture, forestry, fisheries, mining</td><td>4</td><td>4</td><td>4</td><td>2</td><td>3</td></tr><tr><td>Arts, Entertainment, Recreation, Accommodation and Food Services</td><td>9</td><td>8</td><td>8</td><td>5</td><td>6</td></tr><tr><td>Construction</td><td>13</td><td>24</td><td>14</td><td>6</td><td>13</td></tr><tr><td>Educational Services, and Health Care and Social Assistance</td><td>11</td><td>8</td><td>11</td><td>16</td><td>13</td></tr><tr><td>Finance, Insurance, Real Estate and Rental and Leasing</td><td>5</td><td>5</td><td>4</td><td>7</td><td>7</td></tr><tr><td>Information</td><td>2</td><td>2</td><td>2</td><td>3</td><td>2</td></tr><tr><td>Manufacturing</td><td>14</td><td>8</td><td>13</td><td>14</td><td>9</td></tr><tr><td>Other Services, Public Administration, Active Duty Military</td><td>11</td><td>11</td><td>10</td><td>11</td><td>13</td></tr><tr><td>Professional, Scientific, and Technical Services</td><td>11</td><td>14</td><td>12</td><td>16</td><td>15</td></tr><tr><td>Retail trade</td><td>14</td><td>9</td><td>14</td><td>12</td><td>11</td></tr><tr><td>Transportation, Warehousing, Utilities</td><td>4</td><td>4</td><td>4</td><td>5</td><td>6</td></tr><tr><td>Wholesale trade</td><td>3</td><td>2</td><td>3</td><td>3</td><td>3</td></tr></tbody></table>

## A.3 Additional Details on the SIPP

We utilize the 1996-2008 waves of the SIPP dataset. The definitions of self-employment, wage employment, and unemployment closely align with those used in our CPS sample. However, regarding the self-employment margin, there is no explicit question inquiring about self-reported self-employment status. In the SIPP, we define a self-employed individual as someone who is currently working and derives their main source of income from a business (by comparing variables TBMSUM and TPMSUM), and who either declares owning a business (EBUSCNTR), working in a business (EBIZNOW), or earning a salary or non-salary income from a business (EOINCB and ESLRYB).

**Gross flow rates** We describe in Table A4 the corresponding bimonthly flows between occupations. Because of the longitudinal nature of the SIPP, there are well-known discrepancies between SIPP and CPS gross flow levels. Nevertheless, the magnitudes are close to the ones we report for the CPS sample, both for the occupational rates and the gross labor market flows.

## A.4 UI Generosity

### A.4.1 Regular UI benefit changes and economic conditions

We examine the correlation between variations in regular UI benefits and economic conditions at the state level. Table A5 and Table A6 evaluate the determinants of state UI
<table><caption>**Table A4.** Bimonthly gross flows rate in the SIPP.</caption><thead><tr><th rowspan="2">From</th><th colspan="3">Gross flow (%) to</th><th rowspan="2">Masses (%)</th></tr><tr><th>W</th><th>S</th><th>U</th></tr></thead><tbody><tr><td>W</td><td>98.1</td><td>0.4</td><td>1.6</td><td>83.8</td></tr><tr><td>S</td><td>2.8</td><td>96.5</td><td>0.7</td><td>10.2</td></tr><tr><td>U</td><td>27.0</td><td>1.7</td><td>71.3</td><td>6.0</td></tr></tbody></table>

*Note:* 1996:2008 SIPP panel (1995–2013 period).

benefits with various state contemporaneous (averaged over six months) and lagged (averaged over the previous 6 months) macroeconomic variables and union coverage, conditional on state and year fixed effects. Our set of determinants is similar to that in Hsu et al. (2018) and we find no evidence of a relation over the 1994-2007 period. The estimated correlations are small and not statistically significant for the state unemployment rate, union coverage, housing HPI index, log real GDP per capita, average wage, log per capita income, and the UI trust fund reserves. The only variable that seems to be maybe slightly correlated is the lagged log per capita income.

In addition to assessing the impact on economic conditions, it is important to examine the correlation between UI generosity and aggregate UI payments. Table A7 confirms this correlation. Furthermore, there does not seem to be a correlation between UI generosity and other public expenditures.

## A.5 Empirical Results: Robustness and Additional Details

### A.5.1 Sensitivity Analysis

Table A8 provides robustness regarding the responsiveness of flows out of unemployment with respect to UI variations in the CPS. Alternative measures using incorporated and unincorporated self-employment (1st and 2nd rows) indicate that all groups react to UI extensions with especially high elasticities. The distinction between part-time and full-time transitions reveals that the later flow is more sensitive to changes in UI generosity. When distinguishing between variations in the number of UI weeks (duration) and variations in the weekly benefit amount (WBA), we observe that the effect is stronger with the latter.

Our results remain consistent whether we consider only or exclude the Great Recession.
<table><caption>**Table A5.** Regular UI benefits and aggregate economic variables.</caption><thead><tr><th>Dependent Variable:</th><th colspan="9">log(Total Max Regular Benefits)</th></tr><tr><th>Model:</th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th></tr></thead><tbody><tr><td><em>Variables</em></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td></td></tr><tr><td>Unemployment rate (%)</td><td>0.01<br>(0.01)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.01<br>(0.01)</td></tr><tr><td>Log(housing HPI)</td><td></td><td>0.03<br>(0.11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.13<br>(0.11)</td></tr><tr><td>Log real GDP per capita</td><td></td><td></td><td>0.24<br>(0.20)</td><td></td><td></td><td></td><td></td><td></td><td>0.26<br>(0.21)</td></tr><tr><td>Log per capita income</td><td></td><td></td><td></td><td>2.8<br>(2.3)</td><td></td><td></td><td></td><td></td><td>3.5<br>(3.5)</td></tr><tr><td>Average wage</td><td></td><td></td><td></td><td></td><td>-0.0002<br>(0.0003)</td><td></td><td></td><td></td><td>-0.0005<br>(0.0003)</td></tr><tr><td>Union coverage (%)</td><td></td><td></td><td></td><td></td><td></td><td>0.01<br>(0.56)</td><td></td><td></td><td>-0.06<br>(0.45)</td></tr><tr><td>UI trust fund reserves</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.02<br>(0.02)</td><td></td><td>-0.01<br>(0.02)</td></tr><tr><td>IUR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.03<br>(0.02)</td><td>0.03<br>(0.03)</td></tr><tr><td>state</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>year</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>R<sup>2</sup></td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.95</td></tr><tr><td>Observations</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard deviation clustered by state in parentheses. The measure of Total Max Regular<sub>benefit</sub> is in thousands of dollars.

sion from the analysis. Interestingly, the flow from unemployment to wage employment appears to be particularly responsive when considering the Great Recession, as most of the variation in UI generosity stems from differences in the UI duration rather than regular WBA.

The results obtained from multinomial logit regression align with those reported using the linear probability model. In the multinomial logit regression, the probabilities are displayed relative to the alternative state 'remain unemployed'. The flow from unemployment to self-employment is especially reactive to UI generosity, observed over the entire sample, during the Great Recession, and when excluding the Great Recession, with and without considering UI extensions.

Incorporating state-by-year-by-month fixed effects, which help account for unobserved heterogeneity at the state level and over time, does not change the conclusions or the significance of our findings. In fact, it changes only marginally the point estimates, assuring that the main specification of the paper captures most of the unobserved heterogeneity.
<table><caption>**Table A6.** Regular UI benefits and lagged aggregate economic variables.</caption><thead><tr><th>Dependent Variable:<br>Model:</th><th colspan="9">log(Total Max Regular Benefits)</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th><th>(6)</th><th>(7)</th><th>(8)</th><th>(9)</th></tr></thead><tbody><tr><td colspan="10"><em>lagged Variables</em></td></tr><tr><td>Unemployment rate (%)</td><td>0.007<br>(0.010)</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.009<br>(0.01)</td></tr><tr><td>Log(housing HPI)</td><td></td><td>0.07<br>(0.11)</td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.14<br>(0.12)</td></tr><tr><td>Log real GDP per capita</td><td></td><td></td><td>0.34<br>(0.21)</td><td></td><td></td><td></td><td></td><td></td><td>0.30<br>(0.22)</td></tr><tr><td>Log per capita income</td><td></td><td></td><td></td><td>4.5*<br>(2.4)</td><td></td><td></td><td></td><td></td><td>4.2<br>(3.7)</td></tr><tr><td>Average wage</td><td></td><td></td><td></td><td></td><td>-6.1 × 10<sup>-5</sup><br>(0.0004)</td><td></td><td></td><td></td><td>-0.0005<br>(0.0004)</td></tr><tr><td>Union coverage (%)</td><td></td><td></td><td></td><td></td><td></td><td>0.03<br>(0.53)</td><td></td><td></td><td>-0.03<br>(0.43)</td></tr><tr><td>UI trust fund reserves</td><td></td><td></td><td></td><td></td><td></td><td></td><td>-0.01<br>(0.02)</td><td></td><td>-0.005<br>(0.01)</td></tr><tr><td>IUR</td><td></td><td></td><td></td><td></td><td></td><td></td><td></td><td>0.02<br>(0.02)</td><td>0.03<br>(0.03)</td></tr><tr><td>state</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>year</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>R<sup>2</sup></td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.95</td></tr><tr><td>Observations</td><td>663</td><td>663</td><td>663</td><td>663</td><td>663</td><td>663</td><td>663</td><td>663</td><td>663</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard deviation clustered by state in parentheses. The measure of Total Max Regular<sub>benefit</sub> is in thousands of dollars.

Extending the panel analysis to 2019 confirms the paper's main findings. We then examine the COVID period, characterized by rapid labor market shifts, lockdown restrictions, and significant changes in employment dynamics. To account for these unique conditions, we incorporate state-by-year-by-month fixed effects, capturing all specific events and variations occurring during this turbulent period. This approach allows us to focus solely on the interaction between the layoff indicator and UI generosity, with other influences absorbed by the fixed effects. Our analysis indicates that the effects of UI generosity are not significant during this period, reflecting a notably different labor market behavior throughout the COVID era.

### A.5.2 Estimates of UI on flows toward Not In the Labor Force (NILF)

Table A9 shows the result of the main regression of the core paper including OLS results concerning the flows toward the Not in the Labor Force (NILF) pool and those that remain unemployed. We find that UI generosity has no significant effect on the flows to
<table><caption>**Table A7.** Regular UI benefits and lagged aggregate economic variables.</caption><thead><tr><th>Dependent Variable:<br>Model:</th><th colspan="5">log(Total Max Regular Benefits)</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th><th>(5)</th></tr></thead><tbody><tr><td>log(Ui payments)</td><td>0.17***<br>(0.04)</td><td></td><td></td><td></td><td>0.19***<br>(0.04)</td></tr><tr><td>log(Income maintenance benefits)</td><td></td><td>0.21<br>(1.2)</td><td></td><td></td><td>-1.7<br>(1.3)</td></tr><tr><td>log(Medical benefits)</td><td></td><td></td><td>0.32<br>(1.9)</td><td></td><td>0.58<br>(2.0)</td></tr><tr><td>log(Veteran benefits)</td><td></td><td></td><td></td><td>-0.01<br>(0.97)</td><td>0.84<br>(1.1)</td></tr><tr><td>state + year fixed effects</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>R<sup>2</sup></td><td>0.95</td><td>0.94</td><td>0.94</td><td>0.94</td><td>0.95</td></tr><tr><td>Observations</td><td>714</td><td>714</td><td>714</td><td>714</td><td>714</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard deviation clustered by state in parentheses.

<table><caption>**Table A8.** Sensitivity analysis: main regression.</caption><thead><tr><th></th><th>ext. UI</th><th>U → S</th><th>U → W</th><th>Fixed effects</th><th>Sample</th></tr></thead><tbody><tr><td>S Uncorporated</td><td>No</td><td>-0.32***</td><td>-</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>S Incorporated</td><td>No</td><td>-0.89***</td><td>-</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>Part-time</td><td>No</td><td>-0.28**</td><td>-</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>Full-time</td><td>No</td><td>-0.46***</td><td>-</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>log(Ui weeks)</td><td>Yes</td><td>-0.16***</td><td>-0.11***</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>log(Ui WBA)</td><td>No</td><td>-0.38***</td><td>-0.03</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>Including only the GR</td><td>Yes</td><td>-0.23***</td><td>-0.11***</td><td>State + year_month</td><td>2008-2015, CPS</td></tr><tr><td>Excluding the GR</td><td>No</td><td>-0.25**</td><td>-0.04</td><td>State + year_month</td><td>1994-2007, CPS</td></tr><tr><td>Multinomial Logit<sup>b</sup></td><td>No</td><td>-0.17***</td><td>-0.15***</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>Multinomial Logit<sup>b</sup></td><td>Yes</td><td>-0.14***</td><td>-0.11***</td><td>State + year_month</td><td>1994-2015, CPS</td></tr><tr><td>Multinomial Logit<sup>b</sup></td><td>No</td><td>-0.17***</td><td>-0.01***</td><td>State + year_month</td><td>1994-2007, CPS</td></tr><tr><td>Multinomial Logit<sup>b</sup></td><td>Yes</td><td>-0.29***</td><td>-0.11***</td><td>State + year_month</td><td>2008-2015, CPS</td></tr><tr><td>State + year + month FE</td><td>No</td><td>-0.38***</td><td>-0.03</td><td>State_year_month</td><td>1994-2015, CPS</td></tr><tr><td>State + year + month FE</td><td>Yes</td><td>-0.19***</td><td>-0.09***</td><td>State_year_month</td><td>1994-2015, CPS</td></tr><tr><td>Extended CPS sample</td><td>No</td><td>-0.33***</td><td>-0.06</td><td>State + year_month</td><td>1994-2019, CPS</td></tr><tr><td>Extended CPS sample</td><td>Yes</td><td>-0.19***</td><td>-0.10***</td><td>State + year_month</td><td>1994-2019, CPS</td></tr><tr><td>COVID-period</td><td>No</td><td>-0.17</td><td>0.03</td><td>State_year_month</td><td>2020-2021, CPS</td></tr><tr><td>COVID-period</td><td>Yes</td><td>-0.21</td><td>-0.02</td><td>State_year_month</td><td>2020-2021, CPS</td></tr></tbody></table>

NILF. The estimate is both statistically insignificant and economically small. In contrast, higher UI generosity is associated with a higher fraction of unemployed individuals who remain unemployed, as shown by the results concerning U → U flows. Overall, our re-

<footnote><sup>a</sup> Notes: *p<0.1; **p<0.05; ***p<0.01. In parenthesis: std. deviations. SE clustered by US states. FE stands for fixed effects and YM stands for Year-Month and S for state. Experiments using no UI extensions use a definition of laid-off unemployed individuals with less than 26 weeks of unemployment. The estimation methods are OLS. Results are robust using mLogit.</footnote>

<footnote><sup>b</sup> Results concerning the multinomial Logit use "stay unemployed" as a reference state.</footnote>
results confirm the effects of UI generosity on the exit from unemployment documented in the literature. Those results are consistent with results obtained with multinominal logits.

<table><caption>**Table A9.** UI generosity and exit probability out of unemployment.</caption><thead><tr><th></th><th colspan="2">U → U</th><th colspan="2">U → NILF</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>D<sup>eligible</sup></td><td>-0.19**<br>(0.09)</td><td>-0.09***<br>(0.03)</td><td>-0.42***<br>(0.08)</td><td>-0.56***<br>(0.04)</td></tr><tr><td>log(Max Regular UI)</td><td>-0.05<br>(0.04)</td><td></td><td>0.02<br>(0.04)</td><td></td></tr><tr><td>D<sup>eligible</sup> × log(Max Regular UI)</td><td>0.06**<br>(0.03)</td><td></td><td>-0.03<br>(0.03)</td><td></td></tr><tr><td>log(Max Extended UI)</td><td></td><td>-0.04<br>(0.03)</td><td></td><td>-0.01<br>(0.03)</td></tr><tr><td>D<sup>eligible</sup> × log(Max Extended UI)</td><td></td><td>0.06***<br>(0.008)</td><td></td><td>0.02<br>(0.01)</td></tr><tr><td>Observations</td><td colspan="4">348,025</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Ind. &amp; state controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses. See the text for the list of controls. OLS estimates are normalized by the mean transition rate of the flow and can be interpreted as an elasticity relative to that mean transition rate.

### A.5.3 Regression in the SIPP

As an additional robustness check, we replicated the core paper's specification using our SIPP sample. As mentioned earlier, one key distinction from the CPS sample is that the definition of self-employed individuals is less clear in the SIPP. The SIPP counterpart of eligibility flagged as 1 corresponds to individuals reporting their employment status as "on layoff" and when they have the variable "no job all month, on layoff or looking for work" (RMESR) equal to 6 or 7, along with the variable (ERSNOWRK) equal to 9.

Table A10 shows that the main effect of UI generosity on the unemployed pool for transition toward self-employment and employment remains valid in the SIPP, both in magnitude and statistical significance. Regular and extended UI benefits are associated with a strong negative selection into self-employment.

Table A11 shows that the effects of UI generosity for the transition toward self-employment out of employment and employment out of self-employment are not statistically sig-
<table><caption>**Table A10.** UI generosity and exit probability out of unemployment in the SIPP.</caption><thead><tr><th></th><th colspan="2">U → S</th><th colspan="2">U → W</th></tr><tr><th></th><th>(1)</th><th>(2)</th><th>(3)</th><th>(4)</th></tr></thead><tbody><tr><td>D<sup>eligible</sup></td><td>0.82<br>(0.53)</td><td>0.13<br>(0.32)</td><td>-1.0<sup>***</sup><br>(0.18)</td><td>-1.1<sup>***</sup><br>(0.10)</td></tr><tr><td>log(Max Regular UI)</td><td>-0.05<br>(0.33)</td><td></td><td>-0.07<br>(0.08)</td><td></td></tr><tr><td>D<sup>eligible</sup> × log(Max Regular UI)</td><td>-0.34<sup>**</sup><br>(0.13)</td><td></td><td>-0.02<br>(0.05)</td><td></td></tr><tr><td>log(Max Extended UI)</td><td></td><td>-0.03<br>(0.26)</td><td></td><td>-0.005<br>(0.05)</td></tr><tr><td>D<sup>eligible</sup> × log(Max Extended UI)</td><td></td><td>-0.17<sup>**</sup><br>(0.08)</td><td></td><td>0.009<br>(0.04)</td></tr><tr><td>Observations</td><td colspan="4">358,252</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr><tr><td>Ind. &amp; state controls</td><td>Yes</td><td>Yes</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses. See the text for the list of controls. OLS estimates are normalized by the mean transition rate of the flow and can be interpreted as an elasticity relative to that mean transition rate.

nificant. However, the signs of the effects are consistent with a reallocation from self-employment toward employment.

<table><caption>**Table A11.** UI and transitions in and out of employment and self-employment in the SIPP.</caption><thead><tr><th></th><th>S to W</th><th>W to S</th></tr></thead><tbody><tr><td>log(Max Regular UI)</td><td>0.09<br>(0.18)</td><td>-0.14<br>(0.15)</td></tr><tr><td>Observations</td><td>630,382</td><td>4,384,422</td></tr><tr><td>State, year-month FE</td><td>Yes</td><td>Yes</td></tr><tr><td>Ind. &amp; state controls</td><td>Yes</td><td>Yes</td></tr></tbody></table>

Notes: *p<0.1; **p<0.05; ***p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses.
# B Additional Model Specifications and Quantitative Results

## B.1 Additional Model Specifications

**Exact regulatory maximum UI duration** In the model the path of UI benefits is:

$$b(\theta, j) = \min \{w\mu h(\theta), \bar{b}\} \cdot [1_{\{j \in [2J]\}} + 1_{\{j=1\}} \cdot (1 - (J - \bar{J})) + 1_{\{j=0\}} \cdot 0],$$

Here, we use a linear rule in the last remaining period of UI receipt to account for the exact regulatory maximum UI duration $\bar{J}$. For example, this approach allows us to handle cases where the regulatory maximum UI duration is $\bar{J} = 3.5$. In such a scenario, we set $J = 4$. If an unemployed worker remains insured, they receive full benefits for $j \in \{4, 3, 2\}$, with $b(\theta, 4) = b(\theta, 3) = b(\theta, 2)$. For the final remaining UI period, $j = 1$, they receive partial benefits equal to $b(\theta, 4) \cdot 0.5$. Once benefits are exhausted, there is no UI coverage ($j = 0$).

## B.2 Algorithm

We organize the algorithm as follows.

1. Initialize a full dimension grid space composed of all different possible asset values (a), productivity level (y), innate ability (θ), and entrepreneurial state (z). The maximum asset level is chosen sufficiently large to get the ergodicity of the policy functions.

2. Guess initial tax rate $\tau_w$ and prices $\{w, r\}$.

3. Given prices, we solve the consumption-saving-search (CSS) problem using the En-dogenous Grid Method (EGM). The value functions are sufficiently smooth, ensuring the solution is unique. Given the value functions, we solve for search efforts using a Newton algorithm.

4. Construct the transition matrix $M$ generated by $\Pi_y$, $\Pi_z$ and $\Pi_\theta$, $a'(x)$, $e_w(x)$, $e_s(x)$, $e_l(x)$. Compute the associated stationary measure of individuals $\Gamma(x)$, by first guess-
ing an initial mass of one of households with zero assets and then by iterating on
$\Gamma'(\mathbf{x}) = \mathbf{M}\Gamma(\mathbf{x})$ until $|\Gamma'(\mathbf{x}) - \Gamma(\mathbf{x})| < \mu$, with $\mu$ very small.

5. Compute the resulting total asset level, total labor supplied, and total investment in the entrepreneurial sector. Total capital invested in the corporate sector is given as the difference between total savings and total capital invested in the entrepreneurial sector. The total labor used in the corporate sector is given by the total labor supplied by workers.

6. Update prices {$r, w$} using the marginal productivities in the corporate sector and tax rate $\tau_w$ to close the government budget using a relaxation scheme. Back to step 2 until the convergence of labor income tax rate and prices.

## B.3 Search Policy Functions

### B.3.1 Optimal Search Efforts

Figure A2 (top panels) reports how ability and wealth interact with optimal job and business search efforts.

The model job search effort $e_w$ is decreasing with wealth, consistent with established results (Lentz and Tranaes, 2005). Wealth provides a means to smooth consumption that conditions the ability to wait for a job and in turn the search effort. Moreover, high-ability individuals have a higher job search effort due to the high wages they can earn in employment.

The novel aspects are displayed in the bottom panels, where the optimal business search efforts $e_s$ exhibit a hump-shaped pattern with respect to wealth. This is influenced by two opposing effects. Firstly, wealth-poor individuals, who are more likely to face credit constraints, exhibit lower search efforts due to limited interest in running very small firms. This effect is partly mitigated, particularly for unemployed individuals, by the CES entrepreneurial production structure. As wealth increases, individuals can invest more capital and increase their search efforts. Secondly, beyond a certain wealth threshold, the incentives to start a business decline as the returns from financial wealth become large compared to the additional income from business capital.

These results are consistent with what we observe in the SIPP data, as discussed in the Appendix of the core paper. In the SIPP dataset, we find that the transition from unem-
<figure><img src="image_3.png" /><figcaption>**Figure A2.** Implied optimal probability to find a job for unemployed individuals (top left) and self-employed (top right). Implied optimal probability to find a business idea for unemployed individuals (bottom left) and workers (bottom right).</figcaption></figure>

*Note:* the worker's match component *y* and the self-employed's business shock *z* are set to their average values. Policy functions out of unemployment are for *j* = *J*.

ployment to self-employment is concave and increasing in wealth, up to a certain threshold. Conversely, the transition from unemployment to wage employment exhibits a convex pattern and decreases as wealth increases. Similar patterns are also observed when analyzing the exit from self-employment to wage employment, which shows a decreasing relationship with wealth. Likewise, the exit from wage employment to self-employment displays an increasing and concave relationship with wealth.

<table><caption>**Table A12.** Exit probability out of unemployment and wealth.</caption><thead><tr><th></th><th>U → S</th><th>U → W</th></tr></thead><tbody><tr><td>Total wealth</td><td>7.9 × 10<sup>-7</sup>***<br>(1.1 × 10<sup>-7</sup>)</td><td>-5 × 10<sup>-8</sup>**<br>(2.4 × 10<sup>-8</sup>)</td></tr><tr><td>Total wealth square</td><td>-7.8 × 10<sup>-15</sup>***<br>(1.1 × 10<sup>-15</sup>)</td><td>3.9 × 10<sup>-16</sup>*<br>(2.3 × 10<sup>-16</sup>)</td></tr><tr><td>Observations</td><td>358,252</td><td>358,252</td></tr><tr><td>State-year-month FE</td><td>Yes</td><td>Yes</td></tr><tr><td>Individual controls</td><td>Yes</td><td>Yes</td></tr></tbody></table>

*Notes:* \*p<0.1; \*\*p<0.05; \*\*\*p<0.01. Standard errors, adjusted for clustering at the state level, are reported in parentheses.
References

Hsu, J.W., Matsa, D.A., Melzer, B.T., 2018. Unemployment insurance as a housing market stabilizer. American Economic Review 108, 49–81.

Lentz, R., Tranaes, T., 2005. Job search and savings: Wealth effects and duration dependence. Journal of labor Economics 23, 467–489.