Procesamiento de Datos

2.6.1

A comparison with a macroprudential loan-to-value (LTV)

ratio

Most of the works analysing the interaction between monetary and macroprudential policy focus on the implementation of a macroprudential policy for the loan-to-value (LTV) ratio, rather than

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The fact that the best-performing policy leads to the best stabilization of household debt can be also found in Angelini et al. (2012)[1], Lambertini et al. (2013)[49]. Likewise, in these works the improvement in stabilization of private debt comes at the cost of bearing more variability in output and inflation.

the cap on debt-to-income ratio28. This way the macroprudential authority may target more directly the real estate sector, where the over-valuation of real estate values takes place. By this virtue, an increase in household debt is tackled with a reduction of the loan-to-value ratio. Our framework allows to compare the performance of the LTV policy with the policy on the cap on DTI and, ultimately, to combine the two so as to design a joint macroprudential policy. To this end, we introduce in the our model a countercyclical rule for the LTV which is specular to the one adopted for the cap on DTI:

mt=m bb_t bb −mb (2.41)

with mb ≥0. We therefore optimize the parameter mb over the range [0,3].

INSERT TABLE 2.8

Results displayed in Table 2.8 clearly uncover that a LTV policy grants a welfare-gain with respect to the estimated model. Interestingly enough, with the LTV policy the stabilization of household debt is greatly attained. However, the macroprudential cap on DTI seems to perform unambiguously better than the LTV policy. Thus, we find the the macroprudential DTI is a more efficient policy than the standard LTV policy.

Finally, we explore the case when these two macroprudential policies are jointly used to achieve a better performance in terms of financial stability. It turns out that a combined use of the two policies improves on the performance of the LTV although, surprisingly enough, macroprudential DTI alone represents the best policy outcome.

2.6.2

Coordination vs. Non Coordination

In the previous section we found the optimal combination of the social-welfare maximizing pa- rameters of the monetary policy rule and the macroprudential policy. In this regard, we assumed that the two authorities were maximizing jointly, under perfect coordination. Nonetheless, no- body would guarantee that perfect coordination allows to obtain the best policy outcome. In fact, in the literature there is no unanimous consensus on whether the two policies should be adopted in coordinated or non-coordinated way. As an example, Bean et al. (2010) [3] and Angelini et al. (2012)[1] argue for a coordination between the two policies, whereas Svensson

28_{The rule for the loan-to-value ratio as a macroprudential policy has been extensively studied in the literature}

(see, among the others, Lambertini et al. (2013)[49], Carrasco-Galego and Rubio (2014)[14]). Furthermore, empirical studies show that this instrument has been widely used in the aftermath of the crisis, also in combination with a macroprudential cap on DTI. An active countercyclical policy for the loan-to-value (LTV) has been first applied in Asia since the housing boom of mid-2000s. Refer to Lim et al (2011)[50] for a comprehensive focus on the application of the countercyclical LTV rule.

(2012) [74] and Carrasco-Galego and Rubio [14] find that non-coordinated policies are associated to a better policy outcome.

INSERT TABLE 2.9

In Table 2.9 we compare the case in which the two authorities coordinate with the case of non-coordination, namely when one authority acts as ”leader” and therefore optimizes first, followed by the other authority, which instead behaves as ”follower”. Interestingly enough, it emerges that the case of coordination is Pareto-improving, delivering higher social welfare (- 124.7088) than when central bank optimizes first (-124.7110) and when instead the leader is the macroprudential authority (-124.7095).

2.6.3

Social welfare function

Results drawn so far are based on a social welfare criterion, according to which welfare measures specific to both type of agents are aggregated. Fundamental is the way through which these measures enter the social welfare function (2.35). Thus far we have assumed that these two are equally weighted, so that µ = 0.5. We now investigate to what degree the welfare analysis changes as long as the different weights are assigned to agents’ welfare measure. Table 10 reports the cases in which savers’ welfare is assumed to have a larger (µ= 0.75) and a smaller (µ= 0.25) weight. Importantly, the latter case reflects the case considered by Lambertini et al. (2013)[49] and Carrasco-Gallego and Rubio (2014)[14], where borrowers’ welfare is given a more sizeable weight in social welfare function29.

INSERT TABLE 2.10

It clearly arises that when savers’ welfare matters more in social welfare function, namely when µ = 0.75, the optimal macroprudential policy implies that the financial amplification mechanism that works through the collateral is fully cushioned, as household debt is only related to borrowers’ labor income (γ? = 0). As a result, the countercyclical DTI has now the largest impact on the economy. By contrast, when borrowers’ welfare matters to a larger extent (µ = 0.25), credit supply decision would be entirely driven by real estate values (γ? = 0), and thus a countercyclical rule for the cap on DTI would play no role. Obviously, in this scenario financial

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In particular, these works assume that weights to savers and borrowers’ welfare are assigned in a way that the planner equalizes utility across savers and borrowers in case of an equal constant consumption stream. Thus, social welfare function is written as: V ≡ (1−βs)Vs+(1−βb)Vb. In our framework, adopting this formulation

for social welfare would imply that borrowers’ welfare is given a weight which is approximately equal to (1-µ) = 0.92.

stability would become problematic, as shocks in the housing market fully impact on household debt.