2.1 Timing

Timing is as follows. At the beginning of a period, a previously unemployed worker with skill level $h$ draws home productivity $x$ from $F(x)$ and decides whether to participate or to drop out of the labor market. If the worker decides to participate in the labor market, she chooses the level of search effort that determines the probability that she receives a job offer. Specifically, the worker receives a job offer with probability, $f(s) \in (0,1)$ with $f'(s) \gt 0$ . If the worker accepts the job offer, she transitions into employment otherwise, she remains unemployed for one more period.

In each period, employed workers may lose exit the labor market with probability $\delta _{en}$ . They may also lose their jobs with probability $\delta _{eu}$ , which then they may begin collecting UI benefits with probability $\mathcal{E}$ . Finally, in each period, previously non-participating individuals draw a value from $F(x)$ and choose to return to the labor market. Upon return, they can search for a job as UI ineligible unemployed.

In each period, all workers face stochastic accumulation or depreciation of skills depending on their labor market status. Following Ljungqvist and Sargent (Reference Ljungqvist and Sargent1998, Reference Ljungqvist and Sargent2008), I assume that skills can be accumulated during employment and can be depreciated during unemployment and non-participation.Footnote ¹⁰ Specifically, in each period, employed workers with skill h may receive an upgrade of skill to $h'\gt h$ with probability $p_e(h,h')$ . Unemployed workers and non-participating individuals with skill level h may lose skill to $h'\lt h$ with probability $p_u(h,h')$ .

Skill loss creates hysteresis in unemployment and non-participation via changing the return to job search. Specifically, losing skill allows for negative duration dependence of unemployment. In other words, as time passes and unemployed experience a loss in their skill their chances of finding a job decrease. This may imply that workers may spend more time in unemployment. However, it should be emphasized that skill loss, in addition, decreases workers’ tendency to participate in job search and may result in a transition to non-participation. Furthermore, changes in skills have implications for future earnings of workers. In particular, with a skill loss, unemployed would receive a lower earnings upon accepting a job offer. On the other hand, with a skill gain, employed may move up the job ladder over employment spell. I calibrate the skill transition probabilities by targeting relevant labor market transitions and changes in consumption following job loss.

2.2 Recursive problems

Employed. Let $V^e(w,h)$ be the present discounted value of expected utility of an employed worker with wage $w$ and skill level $h$ . This value is given by

(1) \begin{align} V^e(w,h)=u(wh)+\beta (1-\delta _{en}){\bigg \{}&(1-\delta _{eu}) \sum _{h'} p_e(h,h') V^e(w,h')+\delta _{eu} \sum _{h'} p_u(h,h') \bigg [ \nonumber \\ &\mathcal{E}V^u(b,h',j=1) +(1- \mathcal{E})V^u_{ne}(h') \bigg ] {\bigg \}}\nonumber \\ +&\beta \delta _{en} \sum _{h'} p_u(h,h')\int V^n(x',h') dF(x'). \end{align}

In each period, the employed workers receive a flow utility of earning which is the product of their wage and current skill level $wh$ . The wage is assumed to be unchanging over tenure, while employment earnings may increase when workers receive an skill upgrade to $h'\gt h$ .

In addition, in each period, employed workers may exit from the labor market with probability $\delta _{en}$ . They may also face a job separation with probability $\delta _{eu}$ . Following a job separation, a worker may become eligible for UI with probability $\mathcal{E}$ . This implies that with probability $\mathcal{E}$ , a worker would begin collecting UI and her value function would be $V^u(b,h',j=1)$ ; otherwise, she would not receive UI and her value would be $V^u_{ne}(h')$ .

UI eligible unemployed. Let $V^u(b,h,j)$ be the present discounted value of expected utility of an UI-eligible unemployed worker who has received unemployment benefit, $b$ for $j$ periods and has skill level $h$ . This value is represented recursively as follows:

(2) \begin{align} V^u(b,h,j)=&\max _{s\in (0,1]} {\bigg \{}u(b) - c(s)+\beta \sum _{h'}p_u(h,h')\bigg [ \nonumber \\ & f(s)\iint \max \big \{ V^e(w',h'),V^u(b,h',j+1),V^n(x') \big \}dF(x')dG(w')\\&+(1-f(s))\bigg [ \int \max \{V^u(b,h',j+1),V^n(x')\}\;dF(x') \bigg ] \bigg ] {\bigg \}}\nonumber \;\;\; \forall \;j \leq \mathbf{T}. \end{align}

In each period, UI-eligible workers receive a flow value of $u(b)- c(s)$ , where $b$ is the amount of UI benefits that depends on their past earnings and $c(s)$ is the cost of searching for a job. In each period, unemployed workers first decide to participate or to drop out of the labor market. If they choose to participate, they receive a wage offer with probability $f(s)$ which then they decide to accept or to reject. If they reject the job offer, they remain unemployed for another period. With probability $1-f(s)$ , however, workers do not receive a wage offer and stay unemployed for another period. If workers decide to drop out of the labor market, they receive the value of non-participation $V^n(x',h')$ . During unemployment, workers choose the level of search effort $s$ that maximizes their return to job search. This process continues recursively until UI benefits are exhausted.Footnote ¹¹

UI ineligible unemployed. Similarly, let $V^u_{ne}(h)$ be the present discounted value of expected utility of an UI-ineligible unemployed worker with skill level $h$ . This value is represented recursively as follows:

(3) \begin{align} V^u_{ne}(h)=&\max _{s\in (0,1]} \bigg \{ u(\tilde{b})- c(s)+\beta \sum _{h'}p_u(h,h')\bigg [ \nonumber \\ &f(s)\iint \max \big \{ V^e(w',h'),V^u_{ne}(h'),V^n(x') \big \}\;dF(x')dG(w')\\&+(1-f(s))\bigg [ \int \max \{V^u_{ne}(h'),V^n(x') \} \; dF(x') \bigg ] \bigg ] \bigg \}\nonumber. \end{align}

Equation (3) has a similar interpretation to equation (2) with the exception that once the UI benefit expires, the value functions become independent of level and duration of benefit receipt and workers only receive $\tilde{b}$ .Footnote ¹²

Non-participating. Finally, the value of non-participation is

(4) \begin{align} V^n(x,h)= u(xh)+\beta \bigg [&(1-f_{ne}) \sum _{h'}p_u(h,h') \int \max \big \{V^u_{ne}(h')- \psi,V^n(x',h')\big \}\; dF(x') \nonumber \\ +& \;f_{ne} \sum _{h'}p_e(h,h')\int (V^e(w',h') - \psi ) dG(w') \bigg ]. \end{align}

During non-participation, the flow utility of individuals consists of the value of home production/leisure $x$ and skill level $h$ . In each period, non-participating individuals may transition to employment with probability $f_{ne}$ . Otherwise, they may choose to return to unemployment. Non-participation is costly. The utility cost of non-participation is captured by $\psi$ . If the cost is paid, individuals can return to the labor market as either an employed or an UI-ineligible unemployed worker. It should be emphasized that not allowing workers to receive UI benefits upon returning to the labor market reflects a feature of the UI system in the United States specifying that unemployed workers are eligible to receive UI benefits as long as they maintain the job search activity. By assumption, individuals do not search for a job during non-participation. This implies that unemployed workers would lose their UI eligibility when they choose to quit the job search activity.Footnote ¹³

2.3 Decision margins

The optimal decisions associated with equations (1)–(4) can be characterized by a set of decision margins, $\big \{s(b,h,j), s_{ne}(h), \tilde{w}(b,h,j), \tilde{w}_{ne}(h), \tilde{x}(b,h,j), \tilde{x}_{ne}(h) \big \}$ that specifies the optimal search intensity, reservation wage, and reservation participation, depending on workers heterogeneity for UI-eligible and UI-ineligible workers. UI-eligible workers are heterogeneous in the amount of UI benefits, skill level, and duration of receiving the benefits, whereas UI-ineligible workers differ based on their skill level.Footnote ¹⁴

The limited availability of UI influences the expected continuation return to job search and confronts the UI-eligible workers with a decision between receiving $\tilde{b}$ as they exhaust the benefits, accepting a job offer and receiving ( $wh$ ) or dropping out of job search and receiving ( $xh$ ). Since on average $\tilde{b}$ is smaller, in magnitude, than return to employment and non-participation the expected return to remaining unemployed would be decreasing for UI-eligible workers. The decreasing return to job search, in turn, implies that UI-eligible workers would search more intensively, become less selective in accepting the job offer, and become less engaged in labor market participation as $j$ increases. The problem for UI-ineligible workers is similar except that their return to job search does not change with $j$ , and the corresponding decisions are shaped by the level of skill over unemployment.

As discussed above, the decision between choosing employment or non-participation is influenced by the respective expected return over unemployment (level of surplus) and is determined by the heterogeneity of individuals in the model. For instance, higher-skilled individuals may be more prone to dropping out of the labor market for a given draw for $x$ , but they are more likely to remain in non-participation once they have not depleted their skills. On the other hand, a high draw for $x$ may induce the lower-skilled workers to drop out of the labor market. However, with a reversal of $x$ they are more likely to pay the cost (i.e. $\psi$ ) and return to the labor market in the following periods. Therefore, lower skilled are more likely to shape the marginally attached individuals to the job search.

To gain further insight about the implications of the model, in this section, I characterize the decision margins in a simplified version of the model. To fix ideas, I keep the skill level of a workers unchanged and explore the decision margins for a UI-eligible unemployed worker who has received benefits for j periods. I discuss the implications of the full model in Section 4.

In a simplified model, the value function for an unemployed worker who is eligible to receive UI benefits is as follows.

\begin{align*} V^u(j)=\max _{s \in (0,1]} {\bigg \{}u(b) - c(s)+\beta & \bigg [ f(s)\iint \max \big \{ V^e(w'),V^u(j+1),V^n(x') \big \}dF(x')dG(w')\\+&(1-f(s))\bigg [ \int \max \{V^u(j+1),V^n(x')\}\;dF(x') \bigg ] \bigg ] {\bigg \}}\; \forall \;j \leq \mathbf{T}. \end{align*}

The following results hold.Footnote ¹⁵

This result allows us to characterize the decision margins over the duration of unemployment until UI benefits expire.

This result implies that the search effort of workers increases as UI benefits expire, that is, $j=\mathbf{T}$ . This implies that, since workers may enter into unemployment without UI benefits, the UI-ineligible unemployed workers have the highest search effort in the model, conditional on participation.

Following a similar argument, I show that job selectivity of workers declines with increase in j.

This result also implies that as UI benefits expire, workers become less selective in accepting job offers. Therefore, conditional on participation, their exit rate to employment increases until $j=\mathbf{T}$ and it remains unchanged once they lose their UI eligibility.Footnote ¹⁶

Finally, I show that the probability of participating in the job search decreases as UI benefits expire.

Knowing how each decision margin changes with changes in $j$ , it follows that in response to an extension of UI benefits from $\mathbf{T}$ to $\mathbf{T} + \Delta$ , the return to unemployment increases. This implies that search effort declines, but the job selectivity and the labor market participation increase, which in turn drives the transitions of workers between unemployment and non-participation in the model. I analyze this in detail in the next sections.

3.1 Steady-state results

Table 2 reports the steady-state results. In general, the model does well in replicating the targeted moments. As discussed earlier, the focus of the calibration is on targeting the transition of workers across the three labor market states, which is shaped by the decision-making of individuals in the model. In that regard, the model, among the targeted moments, generates a lower UE transition (on average) relative to its target. However, the average transition from unemployment to non-participation and the average transition from non-participation to unemployment are closely targeted by the model.Footnote ²⁶

Table 2. Steady-state results

Overall, the lower UE and UN transition rates together result in a higher unemployment rate in the model (5.86%) compared with the data (4.94%). The model’s implied average duration of unemployment is close to its empirical value. However, the average duration of unemployment among UI-eligible workers in the model is smaller than the data. It should be emphasized that the CPS does not report whether individuals receive UI. I, therefore, estimate the unemployment rate and the average duration of unemployment among UI-eligible workers by focusing on a group of individuals whose primary reason for unemployment is reported as job loss or temporary layoff.Footnote ²⁷

A number of papers estimate the average consumption drop upon job separation. The empirical evidence suggests a range of estimated drop in consumption from 6.8% in Gruber (Reference Gruber1997) to 19% in Aguiar and Hurst (Reference Aguiar and Hurst2005). Using both the Health and Retirement Study (HRS) and Panel Study of Income Dynamics (PSID), Stephens Jr (Reference Stephens2004) estimates that food consumption drops by around 16 and 12 percent, respectively. The model generates a slightly smaller decrease in earnings upon job separation relative to the targeted value. However, the result is consistent with the empirical findings and lies within the plausible range of values.Footnote ²⁸

Among other moments (not explicitly targeted), the model generates a higher fraction of UI receipt across unemployed. This can be explained by the lack of quit or other mechanisms that may result in UI ineligibility directly after job loss. By assumption, following a job separation, every worker is eligible to receive UI; however, only a fraction take up UI. Past research has found that slightly more than half of all unemployed are eligible to collect UI benefits.Footnote ²⁹ Given that not every eligible worker takes up UI, the share of UI receipt among unemployed is larger in the model.

Table 2, in addition, shows that the model slightly underestimates the share of short-term (unemployed less than 3 months) and long-term (unemployed more than 6 months) unemployed relative to data. This implies that the model generates more medium-term (unemployed between 3 and 6 months) unemployment relative to the data. This can also be seen as in Figure 2 (Data-All Unemployed) that displays the distribution of duration of unemployment estimated using CPS and the one generated by the model (blue line).

Consistent with the empirical findings, Figure 2 shows that the model does well in generating the negative duration dependence observed in data. The literature proposes unobserved heterogeneity and true duration dependence (such as skill loss) as the key mechanisms for the negative duration dependence of unemployment observed in data.Footnote ³² A strand of the literature shows that labor market heterogeneity plays a key role in generating negative duration dependence of unemployment.Footnote ³³ In particular, using data from the Survey of Income and Program Participation (SIPP) Fujita and Moscarini (Reference Fujita and Moscarini2017) defines heterogeneity as workers who return to former employer vs workers who find a new employer and shows that the recalls of former employees who separate into unemployment mainly drive the negative duration dependence in data.Footnote ³⁴

The model does not feature recalls. However, the model features both heterogeneity and true duration dependence as mechanisms that explain the negative duration dependence that is discussed in the literature. Specifically, the model incorporates heterogeneity by distinguishing between types of unemployment based on UI entitlement and re-entry to the labor market that in turn implies a different job search. Unemployed also face a stochastic skill loss that generates a decrease in the transition to employment that in turn help to generate the true duration dependence. Together, these features allow the model to generate negative duration dependence.

Finally, as discussed previously, a significant share of re-entrant (i.e. individuals who transition into unemployment from non-participation) report a duration of unemployment that exceeds the number of periods that they have returned to the job search activity. This is displayed in Figure 2 as Data-NU Transition (dark-gray bars). It is shown that (similar to Elsby et al. (Reference Elsby, Hobijn, Şahin and Valletta2011)) around 40% of re-entrants report a duration of unemployment longer than one month (i.e. a fresh start). In addition, Figure 2 displays the role of re-entrants in generating the upticks in the distribution at the longer duration of unemployment. Allowing workers to draw a duration of unemployment from this distribution upon re-entering the labor market facilitates approximating the share of unemployment at the right tail of the distribution, in particular around the upticks.

4.1 Permanent UI extension policy

Table 3 reports changes in the unemployment outcomes in responses to a permanent increase in the maximum duration of UI benefits from 6 months (baseline) to 9 and 10 months. The last column of the table, in addition, reports the effect of a permanent increase in the UI replacement rate, $\tau$ , by 10 percentage points, while keeping the UI benefits duration at $\mathbf{T}=6$ months.

Table 3. Permanent changes in the duration of UI benefits

Past research estimates that the average duration of unemployment increases by around 0.08 and 0.2 weeks in response to one week increase in the UI duration. For instance, following a 13-week extension of UI in New Jersey, Card and Levine (Reference Card and Levine2000) estimate one week increase in the duration of unemployment. Moffitt (Reference Moffitt1985) estimates that a 1-week extension of UI increases the average duration of unemployment among UI recipients by around 0.15 weeks. Katz and Meyer (Reference Katz and Meyer1990) estimate the impact of 0.16–0.2 weeks. More recently, using a sample of workers in Austria, Nekoei and Weber (Reference Nekoei and Weber2017) estimate that a 9-week extension of UI leads to around 0.29 weeks increase in the duration of unemployment. Schmieder et al. (Reference Schmieder, von Wachter and Bender2016) obtain an estimate of 0.15 months in response to a 1-month change in the duration of UI in Germany. Following a 16-week cut in the duration of UI in Missouri, Johnston and Mas (Reference Johnston and Mas2018) estimate that a 1-month reduction in the duration of UI leads to a 0.45 months reduction in the duration of unemployment among the UI recipients and a 0.25 months reduction in the unemployment. Valletta (Reference Valletta2014) obtains an estimate of approximately 1.3 and 1.7 weeks increase in the duration of unemployment for a 100-week extension of UI for the periods of 2007–2011 and 2000–2004, respectively.

In summary, the literature finds a range of 0.03–0.45 months increase in the duration of unemployment in response to one month increase in the duration of UI. I use this range to relate the model’s responses to the empirical findings.

Unemployment, labor market participation, and duration of unemployment. Table 3 shows that a 3 month of additional UI benefit is associated with an increase in the average duration of unemployment among UI-eligible workers by around 0.84 months. This implies that each additional month of UI benefits is associated with an increase in the overall average duration as well as the average duration of unemployment among UI-eligible workers by around 0.13 and 0.28 months, respectively.

The model estimated response of unemployment spells to a change in the duration of UI is in the upper range of the empirical estimates. To understand this finding, it is worth noting that the model findings are associated with only a change in the maximum duration of benefits, hence with an extension of UI workers can freely adjust their decision margins. In reality, however, the extension of benefits and its continuation are typically a policy response to a labor market slack. The extension of benefits may not be perfectly anticipated by workers so that they may not be able to freely adjust their decisions to the policy immediately. Furthermore, in the model, I assume a full UI eligibility upon a job separation. As discussed previously, this assumption in turn causes an overestimation of the share of UI receipt in the model that results in an overestimation (slightly) of the response to a change in the duration of UI. In reality, however, not every worker is eligible to collect UI following a job separation.

Table 3 also reports the response of the long-term unemployment rate and the unemployment rate to a permanent increase in the maximum duration of UI benefits. Relative to the baseline economy, 3 month of extended UI benefits increases the unemployment rate and the long-term unemployment rate by around 0.85 and 5.25 percentage points, respectively.

Furthermore, non-participation in job search activity decreases with the greater availability of UI benefits. Table 3 reports that a 3-month increase in the $\mathbf{T}$ is associated with around 0.9 percentage points decrease in non-participation. This can also be explained by changes in the transition of workers in and out of non-participation as a result of changes in $\mathbf{T}$ .

Past research has found that the average duration of unemployment increases between 0.5 and 1.5 weeks in response to a 10 percentage points increase in the replacement rate of UI.Footnote ³⁵ In the baseline model, the response of the average duration lies at around the lower end of the range of empirical findings. Specifically, the last column in Table 3 reports that for an increase in the replacement rate of the same size, the average duration of unemployment among UI-eligible workers increases by around 0.12 months (around 0.52 weeks).

Labor market transitions. The average transition rate from unemployment to employment decreases with both an extension of UI duration and an increase in the UI replacement rate. It is well known that more generous UI systems discourage workers from search and reduce their transition to employment. The first row in Table 3 reports that with 3 additional months and 10 percentage point higher replacement rate of UI benefits, the average UE transition rate decreases by around 1.49 and 0.9 percentage points, respectively.

The average transition rate from non-participation to unemployment also increases with an increase in the generosity of the UI program. An increase in the generosity of UI, in terms of both larger $\mathbf{T}$ and larger replacement rate, increases the return to job search activity which results in an increase in the transition of non-participating individuals to unemployment.

The second row in Table 3, in addition, reports that an increase in the generosity of UI encourages longer participation of workers in the job search activity that results in a slower transition of unemployed to non-participation. This is consistent with the recent empirical findings in Farber et al. (Reference Farber, Rothstein and Valletta2015), Rothstein (Reference Rothstein2011), and Valletta (Reference Valletta2014). Specifically, I find that the average UN transition rate decreases by around 3.65 percentage points with a 3-month increase in the duration of UI. Table 3 also reveals that an extension of UI results in a larger response of UN transition rate relative to UE transition rate. This result is also consistent with empirical findings that UI extension increases the duration of unemployment primarily through reducing the transition of unemployed to out of the labor force (UN) rather than employment (UE).

4.1.1 Counterfactual mechanisms

Table 3 shows the quantitative implications of an increase in $\mathbf{T}$ in the model. It does not, however, explain to what extent changes in each decision margin contribute to an overall change in the outcomes. In response to an increase in $\mathbf{T}$ , workers may search less intensively for a job. They may also become more selective in accepting a job offer. If benefits are linked to labor market activity, they may remain attached to labor market for a longer period of time.

In this section, I quantify the portion of changes in the outcomes explained by changes in (i) job search intensity, (ii) job selectivity, and (iii) labor market participation decisions. I allow each decision margin to respond to the UI extension policy one at a time, while the other margins remain unresponsive to the policy. The results are reported in Table 4.Footnote ³⁶ The first column reports the overall changes in the outcomes going from an economy with $\mathbf{T}= 6$ months of benefits (baseline) to an economy with $\mathbf{T}= 9$ months of benefits. The second to fourth columns display the contribution of the decision margins to the overall outcomes.Footnote ³⁷

Table 4. Impact of decision margins on the outcomes

Notes: All the numbers except for the average duration of unemployment are reported in percentage points changes.

It should be emphasized that the overall change of each outcome is the result of a change in all of the three margins. This implies that the sum of the counterfactual changes associated with each decision margin may not equal to the total change for each outcome due to the non-linearity captured in the interaction of the decision margins.

Job search. The decline in the search effort, associated with an extension of UI benefits, results in a decline in the UE transition rate. This also results in a decrease in the UN transition rates. Overall, a decrease in the job search effort can increase the unemployment rate by around 0.31 percentage points, which in turn can explain around 36% of the total change.

Job selectivity. Similar to job search, an increase in job selectivity following an extension of UI results in a decrease in the UE and a small decrease in the UN transition rate that, together, explain around 15% of the overall increase in the unemployment rate.

Labor market participation. Finally, an increase in the labor market participation following an extension of UI benefits increases the transition of unemployed to employment by around 0.33 percentage points. The increase in this margin also lowers the UN transition rate and increases the participation rate among the non-participating individuals.Footnote ³⁸ Together, these changes can explain an increase in the unemployment rate by around 0.17 percentage points which translates into around 20% of the total change.

The results of Table 4 point to the decrease in the job search effort as the primary source of the increase in the unemployment rate. However, Table 4 also shows that the response of the participation margin to an extension of UI has a significant bearing on the increase in the unemployment rate. Specifically, it is shown that when an extension of UI benefits increases workers’ tendency to participate longer in the labor market, the resulting increase in the unemployment rate can explain around 20% of the overall increase in the unemployment rate. This finding indicates the importance of labor market participation margin in explaining the impact of UI policy, which has not received much attention in quantitative job search models studying the impact of UI policy on the labor market.

The role of skill heterogeneity. In Section 2.3, I discussed how skill heterogeneity affects workers’ decision margins. It was discussed that skill heterogeneity influences the job finding process and also the attachment of individuals to the labor market by affecting their decision margins. In this section, I examine how skill heterogeneity may drive the response of workers to an extension of UI. In doing so, I begin by examining how much UE, UN, and NU transitions respond to an extension of UI across different levels of skills. This experiment explains how different types of workers contribute to shaping the responses following an extension of UI. I then decompose the portion of the change in each labor market transition explained by changes in job search intensity, job selectivity, and labor market participation decisions for each level of skill.Footnote ³⁹

Table 5 reports the overall responses of UE, UN, and NU transitions as well as the contribution of each decision margin to each outcome following a 3-month extension of UI, for each skill level. As expected, it is shown that with an extension of UI, across different skill levels, the UE transition of high-skilled unemployed workers decreases the most. High-skilled workers, by assumption, receive a higher amount of benefits during unemployment that negatively affects their search intensity and positively affects their job selectivity in the model. An extension of benefits leads to a further decrease in job search and a further increase in job selectivity of high-skilled individuals which together explain the larger decrease in the transition to employment relative to other skill levels. In addition, high-skilled workers are more likely to participate in the job search activity in the model. This explains why the response of the UN among the high-skilled workers is lowest across the skill levels.

Table 5. The role of skill heterogeneity

Notes: All the numbers except for the average duration of unemployment are reported in percentage points changes.

On the other hand, low-skill individuals are more marginally attached to the job search activity. An extension of UI increases the return to job search for low-skill individuals which leads them to participate longer in the labor market. This is shown by the highest (among other skill groups) decrease in the UN transition. Furthermore, an extension of UI results in a higher participation among low- and medium-skill workers. This is also shown by a higher response of the NU transition to an extension of UI among low- and medium-skill individuals.

Similar to Table 4, a decrease in job search following an extension of UI results in a decrease in UE. This is shown across all the skill levels with the largest decrease among the high-skilled workers. An increase in labor market participation due to an extension of UI, in addition, results in a higher NU and a lower UN with the most impact on the low-skilled individuals.

General equilibrium effect. The results presented in this section abstract from two main general equilibrium effects (i) change in the wage offer distribution and (ii) endogenous adjustment in the vacancy creation by firms. Through the first channel, in a general equilibrium setting, firms may offer higher wages to fill a vacancy with more selective workers. This may in turn increase the return to job search and may encourage longer participation in the labor market. The empirical literature, however, has found mixed results on this effect. For instance, while Johnston and Mas (Reference Johnston and Mas2018), Card et al. (Reference Card, Chetty and Weber2007) find statistically insignificant impact of UI on re-employment wages, Nekoei and Weber (Reference Nekoei and Weber2017) obtain a positive impact of extended UI on wages.

Through the second general equilibrium channel, firms may reduce their vacancy creation. This effect would lower the return to job search and may in turn lead to a decrease in job finding and higher unemployment. The empirical literature also shows mixed findings for the vacancy adjustment channel, aka “macro effect.” While some studies such as Hagedorn et al. (Reference Hagedorn, Karahan, Manovskii and Mitman2015) find a large effect of vacancy creation on unemployment, this result has been challenged by some other studies such as Marinescu (Reference Marinescu2017) and Coglianese (Reference Coglianese2015) that find no robust effect of UI extension on vacancy creation.

It should be emphasized that although the model abstracts from the general equilibrium effects, focusing on a partial equilibrium setting, however, allows modeling the decision margins of unemployed workers in a richer, tractable environment with a large state space and a duration-dependent problem in which strategies change over time.

The next experiment addresses the second GE channel and examines (approximately) how accounting for the general equilibrium effect of vacancy creation may affect the unemployment outcomes.

4.1.2 The impact of vacancy creation

Previously, it was discussed that the model abstracts from the response of vacancy creation by firms to UI extension, while in general equilibrium, one may expect that firms reduce their job creation which may result in a slower transition of individuals to employment. To account for this effect, I simulate an economy in which individuals have permanently lower chances of transition to employment, following an extension of UI, from both unemployment and non-participation. I then compare the results with the baseline economy. The difference in the outcomes would highlight the role of slower transition to employment for the labor market outcomes.

To this end, I re-calibrate the two parameters $f_{ne}$ and $\lambda$ that directly affect the transition of individuals to employment.Footnote ⁴⁰ The former controls for the transition of non-participating individuals to employment, while the latter controls for the transition of unemployed workers to employment. It should be emphasized that both parameters affect the return to job search activity. For instance, a lower value for $\lambda$ not only implies a lower UE transition but it may also result in a higher UN and a lower NU transition due to decreasing the return to job search.

In doing so, I decrease $f_{ne} = 0.0581$ reflecting changes in the NE transition in the US economy between 2008 and 2011. I also re-calibrate the job offer meeting rate $\lambda = 0.787$ so that (for a simpler comparison) the response of the unemployment rate to an extension of UI be close to the baseline model.Footnote ⁴¹

The results are reported in Table 6. The first column shows total changes in the model outcome in the baseline economy with higher values for $f_{ne}$ and $\lambda$ . The second column shows total changes in the outcome in this experiment. Similarly, the rest of columns report the counterfactual changes in the outcome associated with the responses of the three decision margins, separately. To have a better understanding of the results, it is worth noting that a decrease in the individual’s chances of finding a job and an extension of UI benefits implies two offsetting effects on the return to job search. On the one hand, an extension of benefits raises the return to job search by subsidizing longer periods of unemployment. On the other hand, the return to job search decreases due to a permanently slower transition to employment. Therefore, changes in the unemployment outcomes are ambiguous and depend on the relative strength of these forces.

Table 6. Impact of decision margins on the outcomes—Low job finding

Notes: All the numbers except for the average duration of unemployment are reported in percentage points changes.

Similar to the results presented in Table 4, in this experiment, I find that the response of participation margin to a change in UI policy can explain a significant response of the unemployment outcomes. For instance, Table 6 reports that a 3-month extension of UI in an economy with low job findings increases the unemployment rate by around 0.85 percentage points. The decomposition experiment reveals that the increase in participation can explain around 25% of the total change, which is around 5 percentage points higher than the baseline. This finding, in addition, highlights the important role of labor market participation for the unemployment rate in times that jobs are harder to find.

4.2 Temporary UI extension policy

In this section, I examine the impact of a temporary extension of UI benefits. I analyze an environment in which the policy reacts to an increase in the unemployment rate by temporarily providing workers with additional periods of benefits. In the previous policy experiment, all workers were entitled to receive the extended benefits once they were separated from their previous job. However, in this experiment, not every worker can receive the extended benefits. More specifically, only workers who are laid-off during the extension period and workers who were still eligible to receive the benefits at the onset of the program could potentially receive the extended benefits. Workers who had exhausted their regular UI before activation of the program do not receive the extended benefits.

In this experiment, starting from the distribution of workers in the baseline economy, I begin with doubling the job separation rate $\delta _{eu}$ in the initial period. The shock is assumed to be unanticipated by workers and reverts to the baseline value in the following periods. I then extend the duration of benefits, $\mathbf{T}$ , by 3 months for a limited period of time and simulate the economy and track workers after the shock.Footnote ⁴² I assume that the extension of benefits is anticipated by workers. In other words, workers treat the policy change as permanent and immediately adjust their decision margins. The extended UI lasts for a limited time period, and once the extension period expires, workers re-adjust their decisions margins back to the pre-shock episode.

I proceed with conducting two scenarios. In the first scenario, I examine how some of the labor market outcomes respond to the shock and the subsequent extension of UI. I compare the results to an economy when government stays unresponsive to the shock. In the next scenario, I examine the contribution of each of the job search decision margins to the overall response of the labor market outcomes.Footnote ⁴³

Figure 3a shows the response of the unemployment rate. Following a job separation shock, both series (No Policy and 3-Month Extension) initially jump up. The two series, however, respond quite differently over the extension period and the entire simulation period. In the No Policy scenario, unemployment gradually declines after the job separation shock. However, since workers anticipate the UI extension and respond to that by reducing their search effort, increasing their job selectivity, and staying longer in the labor market, the unemployment rate in the 3-month extension scenario remains higher over the extension period. Since workers anticipate that the UI is extended temporarily, they adjust their decision margins back to the pre-shock episode. This results in a sharp decrease in the unemployment rate once the extension period expires followed by a gradual decline to the steady-state level.

Figure 3. Impulse responses to a transient, unexpected job separation shock and subsequent UI extension.

The response of the non-participation rate is shown in Figure 3b. It is also shown that the non-participation rate responds quite differently depending on the response of the UI policy to the job separation shock. Specifically, following a job separation shock and an increase in the size of the unemployment pool, the number of workers who transition to non-participation increases. This results in an increase in the non-participation rate initially which is then followed by a gradual decline over time. However, the response of the UI policy results in an increase in the labor market participation among the unemployed workers that in turn offset the impact of the shock and causes a decline in the non-participation rate over the extension period. It is also shown that once the extension period expires and workers adjust their decision margin back to the pre-shock episode, the non-participation gradually increases toward the No Policy scenario.

The bottom panel in Figure 3 shows the responses of the long-term unemployment rate and the average duration of unemployment. Figure 3c shows that, in response to the shock, the long-term unemployment rates initially jump down. The magnitude of decrease depends on the response of the UI policy implying that with UI policy in place, the long-term unemployment rate declines more than the No Policy scenario. Over time, the unemployment rate declines and composition of unemployment pool changes toward workers with longer unemployment spells. This results in an increase in the long-term unemployment rate over the extension period which is followed by a gradual decline toward the No Policy scenario after the end of this period. It is worth noting that the model allows for workers to accumulate skills over employment spell implying that the highest skill would be an absorbing state in the employment. Since the majority of workers who get the separation shock are high-skilled and have higher chances of participation (i.e. a group of workers with similar job search behavior), they enter into long-term unemployment at about the same time. This explains the sharp increase in the long-term unemployment rate during the extension period.

Figure 3d shows that the average duration of unemployment also follows a similar path. Following a job separation shock that results in an increase in the share of short-term unemployed in the unemployment pool, the average duration of unemployment for both scenarios initially jumps down by around 0.4 months. Over the extension period, which is followed by (i) a decline in the job search effort; (ii) an increase in the job selectivity, and (iii) an increase in the labor market participation, workers spend more time in unemployment that results in an increase in the duration of unemployment. It is also shown that once the extension period expires and the duration of UI reverts back to normal times, the average duration of unemployment in the 3-month extension scenario gradually declines toward the No Policy scenario.