Alan, S. (2006). âEntry costs and stock market participation over the life cycleâ, Review of Economic Dynamics, 9(4), pp. 588-611. https://doi.org/10.1016/j.red.2006.06.003 Alan, S. (2012). âDo disaster expectations explain household portfolios?â, Quantitative Economics, 3(1), pp. 1-28. https://doi.org/10.3982/QE128 Arellano, M. (2003). Panel data econometrics, Oxford University Press. https://doi. org/10.1093/0199245282.001.0001 Arellano, M., R. Blundell, and S. Bonhomme (2017). âEarnings and consumption dynamics: A non-linear panel data frameworkâ, Econometrica, 85(3), pp. 693-734. https://doi.
- All Stockholders Non-stockholders Persistent Transitory Persistent Transitory Persistent Transitory Canonical 0.29 0.99 0.34 0.99 0.31 0.99 Non-linear 0.41 0.99 0.44 0.99 0.38 0.99 Table 11: Consumption insurance parameters, implied Blundell et al. (2008) coefficients. We finally compute the average derivative effects for non-stockholders and stockholders, in the case of the economy with the nonlinear earnings process. The results that we obtain are in Figure 15. The top left panel illustrates that the derivative effects with respect to consumption for non-stockholders is higher than that of stockholders.
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- All Stockholders Non-stockholders Persistent Transitory Persistent Transitory Persistent Transitory Canonical 0.29 0.99 0.34 0.99 0.31 0.99 Non-linear 0.41 0.99 0.44 0.99 0.38 0.99 Table 11: Consumption insurance parameters, implied Blundell et al. (2008) coefficients. We finally compute the average derivative effects for non-stockholders and stockholders, in the case of the economy with the nonlinear earnings process. The results that we obtain are in Figure 15. The top left panel illustrates that the derivative effects with respect to consumption for non-stockholders is higher than that of stockholders.
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- BANCO DE ESPAÃA 42 DOCUMENTO DE TRABAJO N. 2241 (ε) shocks are age-dependent, as well as the persistence of the persistent component (Ït). Identification of the parameters of the income process can be obtained via covariance restriction-type arguments, and are outlined in Karahan and Ozkan (2013). We estimate the parameters of this income process via a minimum distance estimator.
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- BANCO DE ESPAÃA 49 DOCUMENTO DE TRABAJO N. 2241 French and Jones (2010)): V = (1 + Ï)(D WD)â1 D WSWD(D WD)â1 (23) where Ï is the ratio between the number of simulated households in the model and the number of households in the data. Our results do not change if we consider that S has zeros outside of the main diagonal.
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- Data from the PSID, 1999 to 2017. All measures are biennial.
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- Following Arellano et al. (2017), we approximate the consumption function with the following specification: cit = K k=1 akfk(ηit, εit, ait, ageit) + a0(Ï), (26) where ak are piecewise polynomial interpolating splines, and fkâs are dictionaries of functions, which are assumed to be Hermite polynomials. We estimate this model on BANCO DE ESPAÃA 54 DOCUMENTO DE TRABAJO N. 2241 with the nonlinear earnings process, and the economy with the canonical earnings process. To be consistent with Arellano et al. (2017), we use the same approximating polynomials as their paper.13 As this is a nonlinear regression model, we estimate the parameter estimates via OLS. Given that we can observe the otherwise latent earnings components, we do not have to resort to a simulation-based estimation algorithm.
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- For simplicity, we assume that the borrowing constraint on mortgages is always binding mt+1 = âλhphht+1 (as in Vestman (2019)). Finally, we define xt = (1 + rs t+1)st + (1 + r)at + (1 + rm )mt (33) as the amount of cash-on-hand that an individual has at the beginning of period t. Householdsâ problem Households thus solve the following problem: Vt(xt, yt, It, ht) = max ct,at+1,st+1,ht+1
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- For the purposes of this study, we focus on the biennial waves that started in 1999. This is because starting from this wave, the PSID has continuous information on household earnings, assets, and consumption.
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- Given that the SCF oversamples the wealthy, we use weights in the calculation of the auxiliary statistics. To have a comparable sample period as with the PSID, we work with the 1998-2016 waves. A.3 Some summary statistics We now compare some summary statistics that we obtain with the PSID and the SCF. In particular, we show statistics with respect to income, wealth, the conditional risky 36 share and stock ownership, which we show in Table 8. As the table illustrates, the resulting distributions and summary statistics are similar in both datasets.
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- Guiso, L., P. Sapienza, and L. Zingales (2008). âTrusting the stock marketâ, The Journal of Finance, 63(6), pp. 2557-2600. https://doi.org/10.1111/j.1540-6261.2008.01408.x Guvenen, F., F. Karahan, S. Ozkan, and J. Song (2016). What do data on millions of U.S. workers reveal about life-cycle earnings risk?, Working paper, University of Minnesota. https://doi. org/10.21034/wp.719 Guvenen, F., F. Karahan, S. Ozkan, and J. Song (2021). âWhat do data on millions of U.S. workers reveal about life-cycle earnings dynamics?â, Econometrica, 89(5), pp. 2303-2339.
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- However, a significant amount of household wealth is held in the form of housing, raising the total wealth-to-income ratio in the United States to close to 5. As a result, in our baseline results the discount rates are remarkably low (in the region of 0.70, similarly to Fagereng et al. (2017), who also target only financial wealth). In Section 5.4 we showed that our main implications are also present in a model in which housing is considered explicitly. Here, we perform an additional experiment that is also frequently considered in the literature: we estimate the model to the total amount of wealth in the economy, counterfactually assuming that it is all financial wealth. This also implies changing the wealth component in our OLS regression to reflect total, rather than financial, wealth.
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- In order to calculate the statistics that we use for comparison with the PSID, we use similar criteria as in Blundell et al. (2016). We also remove households with incomplete information on education, age, and other demographic information. We also remove households that have zero labor income, and who have less than $100 in financial assets, following Fagereng et al. (2017). This criteria gives us a sample of 54,321 households.
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- In order to compute the standard errors for our parameter estimates, we compute a variance covariance matrix V determined by (following the notation in De Nardi, 48 French and Jones (2010)): V = (1 + Ï)(D WD)â1 D WSWD(D WD)â1 (23) where Ï is the ratio between the number of simulated households in the model and the number of households in the data. Our results do not change if we consider that S has zeros outside of the main diagonal. C.3 Life-cycle profiles In Figure 11, we compare the resulting life-cycle profiles from the structural models that we have estimated with the life-cycle profiles from the data.12 We find that both versions of the model are able to fit well the life-cycle profiles.
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- Nicodano, G., F.-C. Bagliano, and C. Fugazza (2021). Life-cycle risk-taking with personal disaster risk, Technical report, University of Torino.
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- org/10.3982/ECTA13795 Blundell, R., L. Pistaferri, and I. Preston (2008). âConsumption inequality and partial insuranceâ, The American Economic Review, 98(5), pp. 1887-1921. https://doi.org/10.1257/ aer.98.5.1887 Blundell, R., L. Pistaferri, and I. Saporta-Eksten (2016). âConsumption inequality and family labor supplyâ, The American Economic Review, 106(2), pp. 387-435. https://doi. org/10.1257/aer.20121549 Bonaparte, Y., G. Korniotis, and A. Kumar (2020). Income risk, ownership dynamics, and portfolio decisions, DP 15370, CEPR.
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003).
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003). 38 eters of the quantile models via ordinary quantile regression. However, as these are latent variables, we proceed with a simulation-based algorithm. Starting with an initial guess of the parameter coefficients, we iterate sequentially between draws from the posterior distribution of the latent earnings components and quantile regression estimation until convergence of the sequence of parameter estimates. Standard errors are computed via nonparametric bootstrap, with 500 replications.
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003). 38 eters of the quantile models via ordinary quantile regression. However, as these are latent variables, we proceed with a simulation-based algorithm. Starting with an initial guess of the parameter coefficients, we iterate sequentially between draws from the posterior distribution of the latent earnings components and quantile regression estimation until convergence of the sequence of parameter estimates. Standard errors are computed via nonparametric bootstrap, with 500 replications.
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003). 38 latent variables, we proceed with a simulation-based algorithm. Starting with an initial guess of the parameter coefficients, we iterate sequentially between draws from the posterior distribution of the latent earnings components and quantile regression estimation until convergence of the sequence of parameter estimates. Standard errors are computed via nonparametric bootstrap, with 500 replications.
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003). 38 latent variables, we proceed with a simulation-based algorithm. Starting with an initial guess of the parameter coefficients, we iterate sequentially between draws from the posterior distribution of the latent earnings components and quantile regression estimation until convergence of the sequence of parameter estimates. Standard errors are computed via nonparametric bootstrap, with 500 replications.
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- The assumptions on the earnings process imply the following moments: νit = Ïtâ1 ηi0 + t j=2 Ïtâj uij + εit (16) 11 Identification of the canonical earnings process follows standard covariance arguments outlined in Arellano (2003). 38 latent variables, we proceed with a simulation-based algorithm. Starting with an initial guess of the parameter coefficients, we iterate sequentially between draws from the posterior distribution of the latent earnings components and quantile regression estimation until convergence of the sequence of parameter estimates. Standard errors are computed via nonparametric bootstrap, with 500 replications.
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- The top right panel presents the conditional skewness of earnings simulated from the nonlinear model. The bottom panel presents the conditional skewness of the persistent component η. The graphs were computed via a non-parametric bootstrap with 500 replications. 46 C Model and model implications C.1 Moments for the structural estimation The targeted moments that we choose for the structural estimation follow the literature that aims to estimate the structure of stock market participation costs (see, e.g., Alan (2006), Alan (2012), and Bonaparte et al. (2020)). We choose nine moments to fit four parameters, which we obtain from the more recent waves of the PSID.
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- These results imply that stockholders are able to effectively insure their consumption with respect to shocks to persistent income. The MPCâs with respect to wealth are 13 This is (2,1,2,1), where the order is (persistent,transitory,wealth,age). 55 a simulated panel of households from 25 to 60 years old coming from the economy with the nonlinear earnings process, and the economy with the canonical earnings process. To be consistent with Arellano et al. (2017), we use the same approximating polynomials as their paper.13 As this is a nonlinear regression model, we estimate the parameter estimates via OLS. Given that we can observe the otherwise latent earnings components, we do not have to resort to a simulation-based estimation algorithm.
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- To construct the statistics that we use for estimation, we follow the sample selection criterion in Blundell, Pistaferri and Saporta-Eksten (2016). In particular, we consider households with heads aged 25 to 60 years old, who are continuously married, and who have continuously participated in the labor force. This leaves us with 10,655 household-year observations. We exclude individuals who are part of the SEO to obtain a representative sample.
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- We are particularly interested that our model under both earnings processes closely replicates stock market participation, conditional risky shares, and median financial wealth to income ratios. Thus, we choose to increase the weight of these moments in our estimation procedure. Thus, our weighting matrix W is diagonal and is formed of the inverse of the standard deviations of the data moments (for the OLS parameters), 10 (for the wealth to income ratio), and 1000 (participation ratio and risky share).
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- We report estimates of the average derivative effect Ït(a), as a function of age and assets, for both economies. The results show that, on average, the estimated parameter Ït(a) lies between 0.25 to 0.75, close to the Arellano et al. (2017) result. The equivalent parameter estimates for the economy with the canonical earnings process is around 0.45 to 0.95. Both surfaces indicate that the marginal propensity to consume out of persistent income is positive, but decreasing in assets and age, consistent with theory. The implied Blundell et al. (2008) coefficients, which are in Table 14, show that compared to the benchmark BPP estimate, consumption insurance is higher in the non-linear economy than in the canonical economy.
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- We report estimates of the average derivative effect Ït(a), as a function of age and assets, for both economies. The results show that, on average, the estimated parameter Ït(a) lies between 0.25 to 0.75, close to the Arellano et al. (2017) result. The equivalent parameter estimates for the economy with the canonical earnings process is around 0.45 to 0.95. Both surfaces indicate that the marginal propensity to consume out of persistent income is positive, but decreasing in assets and age, consistent with theory. The implied Blundell et al. (2008) coefficients, which are in Table 14, show that compared to the benchmark BPP estimate, consumption insurance is higher in the non-linear economy than in the canonical economy.
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