Intergenerational Persistence and Misallocation. Section 5

5 Quantitative Analysis In this section we quantitatively assess the importance of each of the channels operating in our model (ability, preferences and networks transmission) in delivering occupational persistence. First, we need to assign values to the structural parameters of our model. Next, we will use the calibrated model to decompose occupational persistence and to perform welfare analysis and policy experiments. 5.1 Identication Strategy Our strategy involves xing exogenously some of the parameters, and jointly calibrating all the rest to relevant moments of the UK data. First of all, we x the number of occupations in the model corresponds to one month, hence the discount factor λ is xed to O to 0.9966. 4.25 One period The age shock is set to deliver an average worklife of 40 years (20 as young and 20 as old), implying a value of Last, we x the surplus sharing rule parameter function A and η χ to 0.7, ζ 0.00416. and the parameters governing the matching to 0.1 and 0.5 (as in Petrongolo and Pissarides 2001), respectively. We calibrate the rest of the parameters in order to match relevant features of the data. In order to do so, we rst need to choose the grid of possible values of the workerspecic state variables, as well as the functional forms describing their laws of motion. We let h and n take two dierent values, with the lowest one being normalized to 1: h ∈ {1, 1 + ĥ}, n ∈ {1, 1 + n̂}, where ĥ and n̂ represent the premia of human capital and networks that come from tenure. The accumu- lation/depreciation of these occupationspecic variables are subject to a Markov-process characterized by the following parameters: 25 The − + − p+ h , ph , pn , p n , where the + and − superscripts denote accumulation calibration with 9 occupations (resembling the 1digit level aggregation) is work in progress. 50 (when employed) and depreciation (when unemployed) probabilities, respectively. We also assume that each worker has a talent premium y(τ, ho ) τ̂ . τ in one occupation, where he gets a productivity The minimum level of productivity is normalized to 1. The match production function is assumed to be: y(τ, ho ) =     ho    τ̂ ho if o 6= τ if o=τ In the same way, we assume that each worker has a preferred occupation nonpecuniary benet (φ̂) that is higher than elsewhere. baseline level of preferences for a job φ̄ = 0. Both τ and τ and φ where he obtains a At the same time, we also normalize the φ the probability of drawing the same as the father (values of Let φ, are drawn at birth, with ρτ and ρφ being ρ's equal to 1 represent perfect persistence). be the indicators of the occupation in which a worker has the comparative advantage and the preference premium, respectively: τ=     τ F    o 6= τ F φ=     φF    o 6= φF w.p. ρτ w.p. (1−ρτ ) O w.p. ρφ w.p. (1−ρφ ) O ∀ o 6= τ F ∀ o 6= φF Finally, we assume that the idiosyncratic preference shocks are drawn from an Extreme distribution of Type-1, with standard deviation Together with κ and ξ, σ. we have a total of 14 parameters to be calibrated. We search for the parameter 51 conguration that minimizes the following loss function: qP K n=1 L= where T is a K by1 n 2 ( Mn (Θ)−T ) Tn K , vector containing our target statistics and statistics generated by the model (we pick K = 14, M is a K by1 vector containing the that is the model is exactly identied). Table 7 contains the list of all parameters of the model, each of which is associated to the identifying moment in Column 4. The vacancy posting cost is 0.1251. κ is calibrated in order to match the average monthly UE rate, which A lower posting cost induces more entry from the rms side, implying higher tightness and higher nding rates. The exogenous separation rate is 0.0047. The transmission of networks ξ δ is set in order to match the average EU rate, which is set to replicate the jobnding rate premium (of occupational followers w.r.t. movers. A higher value of ξ 0.0546) of means that sons can take advantage of a larger share of their father's network. The transmission of comparative advantage is calibrated to match the intergenerational wage correlation (from Corak (2006)), that is equal to 0.5 in the UK. An increase in ρτ determines an increase in the wage correlation of followers and a decrease in the wage correlation of movers, as well as an increase in the share of followers. Instead, the parameter governing the transmission of preferences ρφ is pinned down by asking the model to replicate the occupational persistence observed in the data (likelihood ratio of 1.72 at the 1digit level). In other words, we are using the transmission of preferences as the residual channel to match entirely the occupational persistence, above and beyond the persistence already generated by the other two channels. Next, the comparative advantage premium log wage variance. τ̂ is calibrated to match the level of withinoccupation The idea behind this is that the more heterogeneous the productivity levels of workers across occupations are, the more dispersed equilibrium wages will be. The networks premium n̂ is calibrated to match the share of jobs found through networks in the UK, which is 0.23 (Pellizzari 52 (2010)). The higher n̂, the more networks will be present in the economy and used for job search. The preference premium φ̂ is chosen to make the model replicate the average wage discount (of 0.0763 log points) of occupational followers . High values of φ̂ imply that preferences are relatively more important than comparative advantages for the occupational choice. This is necessary, in order for the model to be able to induce some workers to become followers for reasons dierent from productivity. The standard deviation of the preference shocks distribution (σ ) is calibrated to the probability of switching occupation after an unemployment spell (0.3567). frequent occupational changes are. The larger the variance of the shocks, the more The value of unemployment b is calibrated to match the average replacement rate in the UK of 0.53 (OECD). Moreover, we calibrate p+ h = 0.0166 which, together with ĥ = 0.26, implies that the average occupa- tional returns after 5 years are equal to 26%, as observed in the data. The probability of losing human capital p− h is calibrated to match the average wage discount after unemployment of 7.6% (Arulampalam (2001)). The probability of losing networks p− n is set to match the slope of the JF rateunemployment duration prole. In particular, we ask the model to replicate the drop in nding rates that occur between the rst and second month of unemployment duration. Finally, we calibrate the probability of accumulating networks p+ n to the conditional correlation of job nding rates with months of past occupational tenure, which is 0.008. 5.2 Calibration Results The model is able to match all targets precisely, both the crosssectional and the intergenerational ones. We can replicate the entire amount of occupational persistence observed in the data, by making preferences quite persistent across generations (0.48), substantially more than the comparative advantages are (0.36). The share of parental networks exploited by ospring is 0.37, which generates the same jobnding rate premium as in the data. Moreover, a large degree of heterogeneity is needed in order to match the data moments. 53 The preference premium is 0.82, while the comparative advantage premium is even higher, 1.03. The networks premium is also very substantial (0.93), whereas the human capital premium is 0.26 (directly taken from the data). The accumulation of both human capital and networks is slow, while their depreciation over unemployment is very fast, especially for human capital. Search frictions are substantial, as posting a vacancy costs 5.37 units of the consumption good. Finally, the exogenous match destruction rate is 0.003, with the rest of the EU ows being accounted for by endogenous separations. 54 55 Description Transmission of Networks Transmission of Comparative Advantage Transmission of Preferences HC premium Networks premium Comparative Advantage premium Baseline preference for jobs Preference premium Prob. of accumulating HC (employed) Prob. of losing HC (unemployed) Prob. of accumulating networks (employed) Prob. of losing networks (unemployed) Standard deviation of preference shocks O κ δ λ ζ b χ A γ Target/Source Normalization Average UE rate (monthly, BHPS) Average EU rate (monthly, BHPS) From literature Average length of worklife: 20 (young) + 20 (old) years Average replacement rate (OECD) Normalization Normalization Normalization Average occupational tenure returns after 5 years (BHPS) Share of jobs found through contacts (Pellizzari 2010) Withinoccupation log wage variance (BHPS) Normalization Wage discount of followers (BHPS) Avg. occupational tenure returns after 5 years (BHPS) Avg. wage discount after unemp. (Arulampalam 2001) Regression of JF rate vs. past occupational tenure (BHPS) JF rateunemployment duration prole (see text, BHPS) Occupational change rate, after U spell (monthly, BHPS) JF premium of followers (BHPS) Interg. Wage correlation (Corak 2006) Interg. Occupational Persistence (Lik. Ratio, BHPS) Calibration Results 4 5.366 0.003 0.9966 0.00416 0.756 0.7 0.1 0.5 0.260 0.932 1.029 0 0.820 0.0166 0.998 0.006 0.206 0.423 0.369 0.360 0.483 Value Table 7. Number of occupations Vacancy posting cost Exogenous separation rate Discount factor Age shock Unemployment benet Surplus sharing rule TFP parameter of matching function Elasticity of matching function w.r.t. unemp. Environment ĥ n̂ τ̂ φ̄ φ̂ p+ h p− h p+ n p− n σ Heterogeneity and Laws of Motions ξ ρτ ρφ Intergenerational Transmission Parameter 0.125 0.005 40 0.530 - 0.230 0.166 0.076 0.260 0.076 0.008 1.066 0.357 0.055 0.500 1.720 Data 0.125 0.005 40 0.530 - 0.230 0.166 0.076 0.260 0.076 0.008 1.075 0.355 0.055 0.498 1.719 Model 5.3 Occupational Persistence Decomposition and Welfare Analysis The model allows us to study what are the factors behind the occupational choice, and how this possibly varies between followers and movers. In Table 8, we calculate how often the occupational choice is aligned with each of the three possible factors (parental networks, comparative advantage, preferences) under the baseline calibration. All Followers Movers Sorting along comparative advantage (fathers) 0.656 - - Sorting along preferences (fathers) 0.594 - - Sorting along parental networks (sons) 0.430 1.000 0.000 Sorting along comparative advantage (sons) 0.726 0.668 0.770 Sorting along preferences (sons) 0.524 0.573 0.486 Average log wage (sons) 0.311 0.268 0.344 Average unemployment rate (sons) 0.061 0.048 0.071 Table 8. Occupational sorting. For fathers, comparative advantages seem to be more important than preferences for the occupational sorting (respectively, about 66% and 59% of them choose the occupation aligned with that specic factor). Among sons, the same holds true: about 73% of them pick the occupation in which they are most productive, whereas about 52% of them pick their preferred occupation; nally, the occupational choice is aligned with parental networks for all followers (by construction), that is in 43% of the cases. Striking dierences in the sorting arises between followers and movers: the former put more weight on preferences in their occupational decision (57% against 49% of movers) and less on their productivity (67% as opposed to 77% of movers). As a consequence of this, followers earn lower wages, as shown in row 4 of Table 8. At the same time, followers have better employment prospects than movers, with an average unemployment rate of 4.8%, against 7.1% of movers. Summing up, the model economy generates a clear sorting of workers in the two regions highemployment/lowwages, lowemployment/highwages. 56 However suggestive, these correlations are not yet informative on the nature of occupational persistence. For this reason, we now perform the exercise of sequentially shutting down each of the 3 channels delivering occupational persistence. In this way, we are able to: i) quantify the contributions of each channel to the overall persistence; ii) evaluate welfare in the dierent scenarios. Table 9 shows the results of the dierent experiments. In column 1 we have our baseline economy, while in columns 2-8 we set ξ = 0, ρτ = 1/O and ρφ = 1/O, along with all possible combinations of these parameter changes. First, all factors seem to matter for occupational persistence. Shutting down parental networks generates a drop in persistence of about 59% (column 2), while comparative advantages and preferences transmission on their own account for about 26% and 23% (columns 3 and 4) of persistence, respectively. Moreover, networks and preferences transmission seem to reinforce each other as a source of persistence, while comparative advantages and preferences transmission are more independent forces, as shutting down these channels in pairs delivers less (more) of a drop than the sum of the eects separately (columns 57 vs 24). Second, the welfare consequences of a reduction in persistence are very dierent across the dierent experiments. When we shut down parental networks (column 2), welfare improves by 0.1%, due to the better allocation of workers to occupations (the sorting along productivity increases from 73% to 77%) and despite a worse sorting along preferences (it drops from 52% to 48%). As a consequence of the increase in the productivity of the workforce, output per worker goes up and wage variance goes down. Also, despite the fact that less eciency units of search are now exerted in the market, unemployment improves, as rms react to the change in average labor productivity by posting more vacancies. On the contrary, when we shut down the transmission of comparative advantages (column 2), welfare decreases by 0.2%, with declining output per worker (sorting along productivity decreases, the one along preferences improves) and rising unemployment (by 1.3%). Last, shutting down preferences transmission (column 3) has a very similar eect to shutting down parental networks: productivity becomes more prominent in individuals' choice, output per worker increases and unemployment decreases. 57 The net eect of these changes, despite a worse sorting along preferences, is an increase in welfare of 0.2%. 58 59 1.564 Equilibrium Tightness (0.051) (0.003) (0.025) (-0.018) (-0.002) (-0.065) 1.027 0.594 0.656 0.477 0.772 (0.001) (2) X 1.294 (-0.590) (-0.022) (0.003) (-0.011) (0.013) (0.001) (0.021) 0.990 0.594 0.656 0.541 0.709 (-0.002) (3) X 1.535 (-0.255) (0.030) (0.004) (0.015) (-0.013) (-0.002) (-0.038) 1.017 0.594 0.656 0.495 0.754 (0.002) (4) X 1.552 (-0.232) (0.051) (0.003) (0.025) (-0.018) (-0.002) (-0.065) 1.027 0.594 0.656 0.477 0.772 (0.001) (5) X X 1.104 (-0.856) (0.051) (0.003) (0.025) (-0.018) (-0.002) (-0.065) 1.027 0.594 0.656 0.477 0.772 (0.001) (6) X X 1.190 (-0.736) Occupational Persistence Decomposition and Welfare Analysis. 0.005 Average EU Rate (rel. change from baseline) Table 9. 0.125 0.166 Log Wage Variance (rel. change from baseline) Average UE Rate (rel. change from baseline) 1.000 Output per worker (=1 in baseline) 0.061 0.594 Sorting along preferences (fathers) Unemployment Rate (rel. change from baseline) 0.656 Sorting along comparative advantage (fathers) 0.190 0.524 Sorting along preferences (sons) Welfare CV (rel. change from baseline) 0.726 - Sorting along comparative advantage (sons) Welfare (rel. change from baseline) Occupational Persistence (rel. change from baseline) No pref. trans. No comp. adv. trans. No parental net. (1) (ξ = 0) (ρτ = 1/O) (ρφ = 1/O) 1.720 - (0.008) (0.008) (0.004) (-0.000) (-0.001) (-0.016) 1.007 0.594 0.656 0.511 0.738 (-0.000) (7) X X 1.349 (-0.514) (0.051) (0.003) (0.025) (-0.018) (-0.002) (-0.065) 1.027 0.594 0.656 0.478 0.772 (0.001) (8) X X X 1.000 (-1.000) 5.4 Other Counterfactual Experiments 5.4.1 The Importance of Multiple Transmission Channels Our model is characterized by three levels of heterogeneity, and intergenerational persistence concerns all levels of heterogeneity considered here. One interesting exercise is to shut down some of these channels and recalibrate the model in order to match the data with fewer degrees of freedom. This allows us to understand whether all model dimensions are really necessary for replicating the data patterns which are the targets of our baseline calibration. We focus on the transmission of productive abilities as the only transmission channel, because this channel embeds in a reduced form way genetic transmission, educational choices and HC transmission in general, which are the channels most commonly emphasized in the intergenerational literature. Therefore, we set ξ=0 and ρφ = 1/O and ask the model to match all data moments in Table 7 except for the JF rate premium and the intergenerational wage correlation. In general, the t of the model has substantially worsened, as we can see from Table 10. The model is not able to fully account for occupational persistence, producing a likelihood ratio of 1.62. The value of ρτ is higher than in the baseline calibration, as this is now the only source of occupational persistence. As a consequence of this, the model largely undershoots log wage variance, which is only 0.022. Importantly, the model completely fails at generating the wage discount between followers and movers. This reects the fact that with only one source of persistence it is impossible to induce dierent sorting behaviors among agents. By construction, the model also cannot replicate the jobnding rate premium of followers (nontargeted), as any networks transmission is shut down. Finally, the intergenerational wage correlation (nontargeted) implied in the model is 0.35, substantially lower than the one observed in the data (0.50). When we perform the exercise of shutting down occupational persistence in the restricted economy (table 11), it turns out that persistence is absolutely neutral in this economy. Shutting down the only source of persistence delivers an identical economy in all dimensions, except for occupational persistence, 60 that vanishes completely. This is because in this economy persistence is not a sign of any distortion in the occupational choice of individuals. Besides, persistence in this economy is generated only by the fact that fatherson couples tend to be more similar than two randomly picked workers. In this sense, occupational persistence is not a reection of the fact that ospring care about the occupational choices of their fathers and are aected by them. In other words, ospring's policy and value functions are now independent of the father's state variables. 61 62 Description Transmission of Networks Transmission of Comparative Advantage Transmission of Preferences HC premium Networks premium Comparative Advantage premium Baseline preference for jobs Preference premium Prob. of accumulating HC (employed) Prob. of losing HC (unemployed) Prob. of accumulating networks (employed) Prob. of losing networks (unemployed) Standard deviation of preference shocks O κ δ λ ζ b χ A γ Table 10. 4 5.520 0.003 0.9966 0.00416 0.553 0.7 0.1 0.5 0.260 1.721 0.331 0 0.230 0.0166 0.828 0.003 0.146 0.220 0∗ 0.429 0.250∗ Value ∗ Calibration Results, Restricted Model ( Number of occupations Vacancy posting cost Exogenous separation rate Discount factor Age shock Unemployment benet Surplus sharing rule TFP parameter of matching function Elasticity of matching function w.r.t. unemp. Environment ĥ n̂ τ̂ φ̄ φ̂ p+ h p− h p+ n p− n σ Heterogeneity and Laws of Motions ξ ρτ ρφ Intergenerational Transmission Parameter = restricted parameters; [] =nontargeted moments). Normalization Average UE rate (monthly, BHPS) Average EU rate (monthly, BHPS) From literature Average length of worklife: 20 (young) + 20 (old) years Average replacement rate (OECD) Normalization Normalization Normalization Average occupational tenure returns after 5 years (BHPS) Share of jobs found through contacts (Pellizzari 2010) Withinoccupation log wage variance (BHPS) Normalization Wage discount of followers (BHPS) Avg. occupational tenure returns after 5 years (BHPS) Avg. wage discount after unemp. (Arulampalam 2001) Regression of JF rate vs. past occupational tenure (BHPS) JF rateunemployment duration prole (see text, BHPS) Occupational change rate, after U spell (monthly, BHPS) JF premium of followers (BHPS) Interg. Wage correlation (Corak 2006) Interg. Occupational Persistence (Lik. Ratio, BHPS) Target/Source 0.125 0.005 40 0.530 - 0.230 0.166 0.076 0.260 0.076 0.008 1.066 0.357 0.055 0.500 1.720 Data 0.092 0.005 40 0.511 - 0.213 0.022 0.001 0.260 0.068 0.008 1.088 0.307 0.000 0.347 1.616 Model No parental net. No comp. adv. trans. No pref. trans. (ξ = 0) (ρτ = 1/O ) (ρφ = 1/O ) 5.4.2 (2) n.a. n.a. - X n.a. n.a. 1.616 1.000 (∆% from baseline) - (-1.000) Welfare (rel. change from baseline) - (-0.000) Sorting along comparative advantage (sons) 0.997 0.997 Sorting along preferences (sons) 0.253 0.253 Sorting along comparative advantage (fathers) 0.781 0.781 Sorting along preferences (fathers) 0.469 0.469 Output per worker (=1 in baseline) 1.000 1.000 Log Wage Variance (rel. change from baseline) 0.022 (0.000) Welfare CV (rel. changefrom baseline) 0.091 (0.000) Unemployment Rate (rel. change from baseline) 0.083 (0.000) Average UE Rate (rel. change from baseline) 0.092 (-0.000) Average EU Rate (rel. change from baseline) 0.005 (0.000) Equilibrium Tightness 0.850 (-0.000) Occupational Persistence Table 11. (1) Occupational Persistence Decomposition and Welfare Analysis (Restricted Model). The Role of Search Frictions We investigate the role of search frictions, imposing on the UK baseline calibration the degree of frictions implied by the monthly nding rates of dierent economies. We focus on two polar cases among OECD countries, US and Spain. We take the average nding rates estimated in Hobijn & “ahin (2009), who report 0.5630 for the US and 0.0389 for Spain. We recalibrate κ in order to match these rates, keeping all other parameters constant; the implied new values of the parameter are 0.83 and 15.61, respectively. We repeat the exercises of column 24 of the previous table for both of the counterfactual economies, with the results shown in Table 12. 63 Two main results stand out. First, the importance of parental networks crucially depends on the size of the frictions. In the lowfrictions economy, removing the eect of parental networks barely aects persistence (it drops by only 1.4%), whereas the drop in the highfrictions economy is much more pronounced (57%). At the same time, the removal of networks is welfare improving in the high frictions economy (as it raises average labor productivity), but it is welfare decreasing in the lowfrictions economy (it crowds out occupational choice along preferences, as networks are basically not generating any occupational choice not based on productivity in the baseline equilibrium). Second, comparing column 1 to column 5, we can see that search frictions can be responsible at the same time for high unemployment and low productivity. This is a reection of the fact that networks are more distortionary in environments with large frictions, where individuals are more willing to tradeo their productive advantage with better employment prospects. We repeat the same counterfactual exercise under the restricted calibration (in columns 9 to 12). The comparison between column 9 and column 11 reveals that the same conclusions hold true: high levels of frictions cause a worse occupational sorting, and as a consequence a lower level of output per worker and a higher level of unemployment. Even though the transmission of contacts is shut down, changes in the level of frictions interact with how easily workers are willing to reallocate across occupations. That is, when a worker nds himself in an occupation in which he does not have the comparative advantage, he would nd it very unattractive to change occupation (a decision which entails an unemployment spell) in order to pursue high wages. As a consequence, sorting along productivity worsens in the highfrictions economy. Notice that the productivity dierential between the two economies is 6.5%, substantially smaller than the dierential between the two economies under the baseline calibration (about 21%). The absence of intergenerational transmission of networks of the restricted calibration economy implies that search frictions can be harmful to the allocation of the labor force to a much lesser extent than in the baseline economy. 64 65 0.257 2.371 0.022 0.190 0.014 0.565 0.012 32.509 Sorting along pref. (fathers) Output per worker Log Wage Variance Welfare CV Unemployment Rate Average UE Rate Average EU Rate Equilibrium Tightness (0.034) (-0.081) (0.019) (0.002) (-0.001) (-0.006) (0.000) 0.257 0.993 0.256 0.993 (-0.008) (2) X 1.429 (-0.014) (0.024) (0.006) (0.013) (-0.019) (-0.000) (0.009) (-0.000) 0.257 0.993 0.256 0.993 (-0.001) (3) X 1.006 (-0.987) (-0.001) (0.002) (-0.000) (0.000) (0.000) (-0.000) (-0.000) 0.257 0.993 0.256 0.993 (0.000) (4) X 1.434 (-0.002) 0.158 0.005 0.040 0.182 0.192 0.167 1.956 (0.029) (0.000) (0.015) (-0.010) (-0.000) (-0.018) (0.015) 0.615 0.635 0.635 0.615 0.579 0.672 (0.002) (6) X 1.310 (-0.568) 0.602 0.648 - (5) 1.719 - (-0.022) (0.004) (-0.011) (0.011) (-0.000) (0.009) (-0.009) 0.615 0.635 0.617 0.633 (-0.002) (7) X 1.584 (-0.187) (κ = 15.61) (0.031) (0.004) (0.016) (-0.011) (-0.003) (-0.022) (0.018) 0.615 0.635 0.573 0.677 (0.002) (8) X 1.488 (-0.321) 22.041 0.007 0.460 0.014 0.087 0.015 1.570 0.251 0.999 0.251 0.998 - (9) n.a. n.a. 1.711 - (-0.000) (-0.000) (-0.000) (0.000) (0.000) (0.000) (-0.000) 0.251 0.999 0.251 0.998 (-0.000) (10) n.a. X n.a. 1.000 (-1.000) 0.098 0.004 0.031 0.212 0.107 0.034 1.473 0.567 0.681 0.491 0.758 - (11) n.a. n.a. 1.285 - (-0.000) (0.000) (-0.000) (0.000) (0.000) (0.000) (-0.000) 0.567 0.681 0.491 0.758 (-0.000) (12) n.a. X n.a. 1.000 (-1.000) Restricted Model (κ = 0.83) (κ = 15.61) US labor market frictions; Columns (5)-(8) are under the calibration of the restricted model and Spain labor market frictions. under the baseline calibration and Spain labor market frictions; Columns (9)-(10) are under the calibration of the restricted model and the Counterfactual Experiments: Columns (1)-(4) are under the baseline calibration and the US labor market frictions; Columns (5)-(8) are Occupational Persistence Decomposition and Welfare Analysis. Numbers in parentheses are relative changes from baseline. 0.993 Sorting along comp. adv. (fathers) Table 12. 0.256 Sorting along pref. (sons) - (1) 1.436 - 0.993 (ξ = 0) (ρτ = 1/O) (ρφ = 1/O) Sorting along comp. adv. (sons) Welfare Occupational Persistence No pref. trans. No comp. adv. trans. No parental net. (κ = 0.83) Baseline Economy 5.4.3 Policy Experiment: Unemployment Benets We now study how changes in unemployment benets aect the equilibrium of our model economy. In order to assess the welfare consequences of such changes, we introduce lumpsum taxation matches (split among workers and rms, where χ τ on existing is the share paid by the workers) and the government BC. The new value functions for employed workers and rms read as follows: o n h  R 0 i R  E 0  (Ω ) + δ E W (Ω ) , W (Ω) . WoE (Ω) = max φPo + φT,E + w(Ω) − χτ + λ̃ (1 − δ) E W o o h  i Jo (Ω) = 1{RoE (Ω) = 0} y(τ, ho ) − w(Ω) − (1 − χ)τ + λ̃ (1 − δ)E [Jo (Ω 0 )] + δVo0 + (60) (61) 1{RoE (Ω) = 1} Vo . The government is balancing the budget at each period. That is, the change in unemployment benets from the baseline equilibrium needs to be nanced with the tax revenues: ∆b u = τ (1 − u), where u (62) is the unemployment rate of the economy. The rest of the model stays the same. Some of the channels commonly emphasized by the literature through which unemployment benets have an eect on the economy, such as the scope for redistribution (in the presence of risk aversion) or the disincentivizing eect on the search eciency units choice, are absent in our framework. At the same time, unemployment benets interact very strongly with the main tradeo at work in our model. An increase (decrease) in the value of unemployment benets decreases (increases) the distance between the value of employment and unemployment. As a consequence, workers are more (less) prone to accept an unemployment spell, and therefore will be better (worse) matched in terms of productivity, on average. 66 Our mechanism has a very similar avor to the one in Acemoglu & Shimer (2000) and Golosov et al. (2013). As we can see from the upper part of Table 13, an increase of worker to increase by about 0.1% (0.4%), whereas decreasing b same time, unemployment goes up when we increase b 10% (25%) in b causes output per causes output per worker to fall. At the (we have both more endogenous separations and smaller nding rates), and goes down otherwise. This directly follows from the fact that unemployment is now a more (less) attractive option. The overall net eect on welfare is negative in the case of increases in b, and positive in the case of decreases. This reects the fact that the tax rate increases more than proportionally with increases in b, given that unemployment goes up. Notice that the change in τ improvement of the quality of the labor force, rms' entry goes down. is such that, in face of the When we repeat the same exercise under the restricted calibration (lower part of Table 13), we nd that eects are much larger. This is because the sorting along productivity is already almost perfect, and increases in negligible improvements in output per worker. b bring about At the same time, the temporary preference shocks become more prevalent in occupational choice, contributing to a large spike in unemployment (it goes up by more than 29%, when we increase b by 25%). As a consequence, the small improvements in output per worker mitigate the drop in welfare due to increased taxation to a much lesser extent than before. For instance, the welfare cost of increasing b by 25% is 0.9%, as opposed to 0.1% in the baseline economy. Hence, it turns out that having multiple sources of persistence is relevant for the assessment of labor market policy in general. 6 Conclusions We have investigated the determinants of occupational persistence across generations. When persistence comes from multiple sources, it is key to assess their relative importance, in order to understand the 67