Variable 2: Déficit en comprensión lectora Definición conceptual
3.7 Aspectos éticos
The empirical evidence suggests that a successful model with labor and credit frictions should predict a positive comovement between outstanding household debt and labor market variables. In particular, the data show that the extensive margin of labor supply, is the labor related variable which is most strongly correlated with debt.
We …nd that a model that simply nests the features of standard search and match-ing models with those of conventional models with credit frictions, is unable to account for such comovement.
To circumvent this problem we propose a new way of modelling the agency problem between debtors and creditors, by assuming, consistently with empirical …ndings, that employment status provides access to credit.
We …nd that this feature alone, is able to reproduce the observed comovement between employment, total hours and debt.
We document that the model predictions are robust to alternative assumptions on the labor force participating decision. The only aspect in which the model without endogenous participation seems preferable, concerns the relationship between unem-ployment and vacancies. If on one hand this feature is not speci…c to our model, on the other hand it could be interesting to investigate whether the introduction of a wedge between the search and matching mechanism concerning agents in the labor force and that concerning agents out of the labor force, implying for the latter a lower probability of being matched, could be able to reverse the relationship between vacancies and unemployment.
On the negative side, we …nd that neither our proposed model, nor the one with a conventional borrowing constraint, are able to match the comovement between hours per employee and debt. We suggest that extensions accounting for either the presence of unconstrained workers, or imposing a constraint limiting debt repayments to a fraction of labor income, could be able to improve the model’s performance on this aspect.
We leave these questions for future research.
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Chapter 3
Tables
Parameter Value Description
0.36 Capital share
0.99 Patient’s discount factor
0.95 Impatient’s discount factor
2 Inverse of intertemporal elasticity of substitution b 2 Inverse of interest elasticity of money demand)
0.019 Depreciation rate of capital 0.99 Relative share of consumption 1.01 Steady state value of nominal growth rate
m 0.75 Autocorrelation of money growth process
m 0.09 Standard deviation of innovations to money growth process Table 3.1: Calibrated parameters for complete markets model
Percentage of …nancial wealth held by bottom
20% 40% 50% 80% 90% 99% Gini coe¤. % constr.
Data 0.003 0.065 0.2 2.8 9.5 57 0.78 20.5
Model (neutral transfers) 2.4 7 9.7 34.2 56.5 93 0.61 2.2 Model (lump sum transfers) 2.4 7.1 9.9 34.4 56.7 93 0.60 2.16
Percentage of liquid wealth held by bottom
20% 40% 50% 80% 90% 99% Gini coe¤.
Data 0.03 0.35 0.74 5.9 18 66 0.73
Model (neutral transfers) 12.9 28 35.8 65.8 80.3 97.4 0.21 Model (lump sum transfers) 13.1 28.1 36 65.9 80.3 97.4 0.21
Percentage of non monetary wealth held by bottom
20% 40% 50% 80% 90% 99% Gini coe¤.
Data 0.0008 0.04 0.14 2.6 8.8 56 0.79
Model (neutral transfers) 2.2 6.6 9.2 33.5 56 92.9 0.62 Model (lump sum transfers) 2.3 6.7 9.4 33.8 56.1 92.9 0.62
Table 3.2: Distribution of wealth and of its components: data and models
Y Bb N L N L w V UF
Y 1 1.58 0.67 0.29 1.29 0.36 10.81 7.45
Correlations Y Bb N L N L w V UF
Y 1
Bb 0.51 1
N 0.86 0.64 1
L 0.74 0.17 0.61 1
N L 0.88 0.52 0.96 0.67 1
w 0.12 -0.10 0.02 -0.08 -0.15 1
V 0.88 0.50 0.66 -0.01 0.88 -0.76 1
U
F -0.88 -0.54 -0.95 0.11 -0.88 0.06 -0.85 1 Table 3.3: Standard deviations and correlations:Data
Y Bb N L N L w V UF
Y 1 4.27 0.60 0.13 0.49 0.98 1.67 1.17
Correlations Y Bb N L N L w V UF
Y 1
Bb 0.44 1
N 0.25 0.78 1
L -0.06 -0.90 -0.83 1
N L 0.29 0.70 0.99 -0.74 1
w 0.87 0.1 -0.25 0.31 -0.21 1
V 0.28 0.41 0.25 -0.23 0.24 0.13 1
U
F -0.31 -0.07 -0.16 0.06 -0.17 -0.27 0.79 1 Table 3.4: Standard deviations and correlations for the model with endogenous participation and in which employment status is relevant for obtaining credit.
Y Bb N L N L w V UF
Y 1 3.14 0.47 0.08 0.48 0.97 3.81 2.90
Correlations Y Bb N L N L w V UF
Y 1
Bb 0.10 1
N 0.33 -0.15 1
L 0.02 -0.42 0.03 1
N L 0.33 -0.22 0.99 0.19 1
w 0.87 0.25 -0.15 -0.18 -0.17 1
V 0.04 -0.12 -0.33 0.90 -0.18 0.03 1
U
F -0.21 -0.09 -0.48 0.83 -0.33 -0.15 0.96 1 Table 3.5: Standard deviations and correlations for the model with endogenous participation and in which employment status is irrelevant for obtaining credit.
Y Bb N L N L w V UF
Y 1 3.81 0.46 0.10 0.38 0.94 1.34 1.47
Correlations Y Bb N L N L w V UF
Y 1
Bb 0.50 1
N 0.30 0.78 1
L -0.07 -0.87 -0.77 1
N L 0.34 0.70 0.99 -0.65 1
w 0.91 0.24 -0.10 0.19 -0.06 1
V 0.39 0.65 0.56 -0.43 0.55 0.15 1
U
F -0.30 -0.78 -1 0.77 -0.98 0.10 -0.56 1 Table 3.6: Standard deviations and correlations for the model without endogenous participation and in which employment status is relevant for obtaining credit.
Y Bb N L N L w V UF
Y 1 3.42 0.34 0.09 0.38 0.96 2.28 1.10
Correlations Y Bb N L N L w V UF
Y 1
Bb 0.21 1
N 0.34 -0.05 1
L 0.07 -0.44 0.28 1
N L 0.33 -0.15 0.97 0.49 1
w 0.90 0.32 -0.05 -0.22 -0.10 1 V 0.20 -0.08 -0.08 0.85 0.13 0.07 1
U
F -0.34 0.05 -1 -0.28 -0.97 0.05 0.08 1 Table 3.7: Standard deviations and correlations for the model without endogenous participation and in which employment status is i relevant for obtaining credit
Chapter 4
Figures
0 .9 9 3 0 .9 9 4 0 .9 9 5 0 .9 9 6 0 .9 9 7 0 .9 9 8 0 .9 9 9 1 1 .0 0 1 0
0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3 0 .3 5
¬Π=1 .0 1
c1 m1
¬Π=1 .0 3
¬Π=1 .0 5
0 .9 6 0 .9 7 0 .9 8 0 .9 9 1 1 .0 1 1 .0 2 1 .0 3 1 .0 4
0 .9 6 0 .9 7 0 .9 8 0 .9 9 1 1 .0 1 1 .0 2 1 .0 3 1 .0 4
¬Π=1 .0 1
c1 c2
¬¬Π=1 .0 3Π=1 .0 5
Figure 4 1: Unconstrained agent: intertemporal budget constraint (dashed) and indi¤erence curves (solid). Left Panel: (c1; m1) space;
Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05; b = = 0:5
0 .9 8 0 .9 8 2 0 .9 8 4 0 .9 8 6 0 .9 8 8 0 .9 9 0 .9 9 2
Figure 4 2: Unconstrained agent: intertemporal budget constraint (dashed) and indi¤erence curves (solid). Left Panel: (c1; m1) space;
Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05; b = = 1
Figure 4 3: Unconstrained agent: intertemporal budget constraint (dashed) and indi¤erence curves (solid). Left Panel: (c1; m1) space;
Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05; b = = 2
0 .9 6 5 0 .9 7 0 .9 7 5 0 .9 8 0 .9 8 5
Figure 4 4: Constrained Agent: intertemporal budget constraint ( dashed with positive borrowing) and indi¤erence curves (solid). Left Panel: (c1; m1)space; Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05;
Figure 4 5: Constrained Agent: intertemporal budget constraint (dashed with positive borrowing) and indi¤erence curves (solid). Left Panel: (c1; m1)space; Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05;
b = = 1
0 .8 5 0 .8 5 1 0 .8 5 2 0 .8 5 3 0 .8 5 4 0 .8 5 5 0 .8 5 6 0 .8 5 7 0 .8 5 8 0 .8 5 9
Figure 4 6: Constrained Agent: intertemporal budget constraint (dashed with positive borrowing) and indi¤erence curves (solid). Left Panel: (c1; m1)space; Right Panel: (c1; c2) space. = 1:01; 1:03; 1:05;
Figure 4 7: Unconstrained agent. Upper left panel: c1 function of ; Upper right panel:m1 function of ; Lower left panel: mc1
1 function of
; Lower right panel cc2
1 function of . Solid lines: b = = 0:5, Dashed lines: b = = 1; Dotted lines: b = = 2:
1 1 .0 0 5 1 .0 1 1 .0 1 5 1 .0 2 1 .0 2 5 1 .0 3 1 .0 3 5 1 .0 4 1 .0 4 5 1 .0 5
Figure 4 8: Constrained agent. Upper left panel: c1 function of ; Upper right panel:m1 function of ; Lower left panel: mc1
1 function of
Figure 4 9: Impulse response functions (% deviation from steady state) to a positive shock to the growth rate of nominal money sup-ply for di¤erent values of ! and with (ex post) proportional seigniorage transfers.
0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 6 .4
6 .5 6 .6 6 .7 6 .8 6 .9 7 7 .1 7 .2 7 .3
7 .4 Con te m p o ra n e o u s re s p o n s e o f i nfla ti on
ω
Π_t
Figure 4 10: Contemporaneous response of in‡ation (% deviation from steady state) to a positive shock to the growth rate of nominal money supply for di¤erent values of ! and with (ex post) proportional seigniorage transfers.
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
0 0 .0 5 0 .1 0 .1 5 0 .2 0 .2 5 0 .3
0 .3 5 Res p o ns e o f in fl atio n fro m t+1 o n wa rd s
ω=0.9 9 ω=0.6 5 ω=0.1
Figure 4 11: Response of in‡ation (% deviation from steady state) from t + 1 onwards to a positive shock to the growth rate of nominal money supply for di¤erent values of ! and with (ex post) proportional seigniorage transfers.
0 1 0 2 0 3 0 4 0
Figure 4 12: Impulse response functions (% deviation from steady state) to a positive shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seigniorage transfers.
7.6 Contemporaneous response of inflation
ω
Π_t
Figure 4 13: Contemporaneous response of in‡ation (% deviation from steady state) to a positive shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seigniorage transfers.
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
Figure 4 14: Response of in‡ation (% deviation from steady state) from t + 1 onwards to a positive shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seigniorage transfers.
Figure 4 15: Impulse response functions (% deviation from steady state) to a positive one-time shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seignior-age transfers.
0 .1 0 .2 0 .3 0 .4 0 .5 0 .6 0 .7 0 .8 0 .9 1 0 .9 4 5
0 .9 5 0 .9 5 5 0 .9 6 0 .9 6 5 0 .9 7 0 .9 7 5 0 .9 8 0 .9 8 5 0 .9 9
0 .9 9 5 Con te m p o ra n e o u s re s p o n s e o f i nfla ti on
ω
Π_t
Figure 4 16: Contemporaneous response of in‡ation (% deviation from steady state) to a positive one-time shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seigniorage transfers.
0 5 1 0 1 5 2 0 2 5 3 0 3 5 4 0
-5 0 5 1 0 1 5
2 0x 1 0- 3 Res p o ns e o f in fl atio n fro m t+1 o n wa rd s
ω=0.9 9 ω=0.6 5 ω=0.1
Figure 4 17: Response of in‡ation (% deviation from steady state) from t + 1 onwards to a one-time positive shock to the growth rate of nominal money supply for di¤erent values of ! and with symmetric lump sum seigniorage transfers.
0 5 0 1 00 1 50 2 00 2 50 3 00 3 50
Figure 4 18: Decision rules for m; k; c as function of individual wealth calculated for the case in which K; M are at their average simulated value: top row refer to l, bottom row to h. Transfers are ex-post proportional to beginning of period holdings of real balnces.
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 19: Simulation of aggregate capital conditional on e = el
(top row), e = em (second row),e = eh (third row), when transfers are wealth neutral. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 20: Simulation of aggregate real balances conditional on e = el (top row), e = em (second row),e = eh (third row) with wealth neutral transfers. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 21: Simulation of aggregate consumption conditional on e = el (top row), e = em (second row),e = eh (third row) with wealth neutral transfers. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 22: Simulation of economy-wide time series for capital (top row) and real balances (second row) withwealth neutral transfers. On the last row are plotted the realizations of the money growth process,
.
Figure 4 23: Decision rules for m; k; c as function of individual wealth calculated for the case in which K; M are at their average simulated value: top row refer to l, bottom row to h, transfers are rebated as lump sum.
0 1 2 3 4 5 6 7
Figure 4 24: Ratios m=c and k=m at low wealth levels: top row l, bottom row h:
Figure 4 25: Simulation of aggregate capital conditional on e = el
(top row), e = em (second row),e = eh (third row), when transfers are lump sum. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 26: Simulation of aggregate real balances conditional on e = el (top row), e = em (second row),e = eh (third row) with lump sum transfers. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
Figure 4 27: Simulation of aggregate consumption conditional on e = el (top row), e = em (second row),e = eh (third row) with lump sum transfers. On the fourth row are plotted the realizations for the money growth process, .
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00 2 7.8 1 8
2 7.8 2 2 7.8 2 2 2 7.8 2 4 2 7.8 2 6 2 7.8 2 8 2 7.8 3
2 7.8 3 2 Agg re g a te c a p ita l
t
K
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
1 .0 0 6 1 .0 0 8 1 .0 1 1 .0 1 2 1 .0 1 4 1 .0 1 6 1 .0 1 8
1 .0 2 Agg re g a te m o n e y
t
M
0 2 0 4 0 6 0 8 0 1 00 1 20 1 40 1 60 1 80 2 00
1 .0 0 4 1 .0 0 6 1 .0 0 8 1 .0 1 1 .0 1 2 1 .0 1 4
1 .0 1 6 M o n e y g ro wth
t
θ
Figure 4 28: Simulation of economy-wide time series for capital (top row) and real balances (second row) with lump sum transfers. On the last row are plotted the realizations of the money growth process, .
Figure 4 29: HP …ltered real outstanding mortgage debt and total hours worked. Shaded areas represent NBER recessions dates.
Figure 4 30: Top panel: HP …ltered real outstanding mortgage debt and employment rate. Bottom panel: HP …ltered real outstanding mortgage debt and average hours worked (per worker)..
0 1 0 2 0 3 0 4 0
Figure 4 31: Impulse response functions after a technology shock un-der the baseline calibration (% deviations from steady state). Solid line:
model in which employment status matters for obtaining credit; Dot-ted line: model in which employment status is irrelevant for obtaining credit.
0 1 0 2 0 3 0 4 0
Figure 4 32: Impulse response functions after a demand shock for durable goods under the baseline calibration (% deviations from steady state). Solid line: model in which employment status matters for ob-taining credit; Dotted line: model in which employment status is irrel-evant for obtaining credit.
0 1 0 2 0 3 0 4 0
Figure 4 33: Impulse response functions after a …nancial shock under the baseline calibration (% deviations from steady state). Solid line:
model in which employment status matters for obtaining credit; Dot-ted line: model in which employment status is irrelevant for obtaining credit.
Figure 4 34: Impulse response functions after a technology shock un-der the baseline calibration (% deviations from steady state). Solid line: model with endogenous labor market participation; Dotted line:
model in which labor market participation is residual.
0 1 0 2 0 3 0 4 0
Figure 4 35: Impulse response functions after a demand shock under the baseline calibration (% deviations from steady state). Solid line:
model with endogenous labor market participation; Dotted line: model in which labor market participation is residual.
0 1 0 2 0 3 0 4 0
Figure 4 36: Impulse response functions after a …nancial shock under the baseline calibration (% deviations from steady state). Solid line:
model with endogenous labor market participation; Dotted line: model in which labor market participation is residual.
Appendix A
Non-stochastic steady state for the two agents model
The equilibrium relationships describing the non-stochastic steady state of the model described in section 1.3 under the assumption of lump sum transfer are the following:
= (A.1)
Under the assumption of ex-post proportional transfer the steady state solution
is instead:
= (A.13)
r = 1
+ 1 (A.14)
k = r
Z
1 1 l
! (A.15)
w = (1 ) Z !k
l (A.16)
c = k (r ) + wl (A.17)
c0 = wl (A.18)
m = 1
1 b
c (A.19)
m0 = 1
1 b
c0 (A.20)
0 = c0 b[1 (1 + r )] (A.21)
t = ( t 1) mt 1
t
(A.22)
0t = ( t 1) m0t 1
t
(A.23)
Appendix B
Details on the solution algorithm for the incomplete markets model
This Appendix is meant to complement section 1.4.3, by providing full details on the solution algorithm employed for the incomplete market model. The algorithm consists of an outer loop constructed to achieve convergence on the parameters of the laws of motion, and an inner loop for the solution of the Bellman equation. The two loops are linked by the fact that the solution of the Bellman equation (i.e. the optimal decision rules) is used to simulate the economy and obtain a time-series for aggregate capital and real balances through which the parameter convergence is tested.