What does Google say about credit developments in Brazil?

Alberto Ronchi Neto; Osvaldo Candido

doi:10.1515/snde-2019-0122

Abstract

In this paper multivariate State Space (SS) models are used to evaluate and forecast household loans in Brazil, taking into account two Google search terms in order to identify credit demand: financiamento (type of loan used to finance goods) and empréstimo (a more general type of loan). Our framework is coupled with nonlinear features, such as Markov-switching and threshold point. We explore these nonlinearities to build identification strategies to disentangle the supply and demand forces which drive the credit market to equilibrium over time. We also show that the underlying nonlinearities significantly improves the performance of SS models on forecasting the household loans in Brazil, particularly in short-term horizons.

Keywords: credit market; Google trends; household loans; Markov switching; state space models; threshold models

JEL Classification: E50; C32; C53

Corresponding author: Osvaldo Candido, Graduate Program in Economics at the Catholic University of Brasilia (PPGE-UCB), Brasilia, Brazil, E-mail: candido.f@gmail.com

Acknowledgments

The authors gratefully acknowledges financial support from the Brazilian institutions CNPq (National Council for Scientific and Technological Development) and FAPDF (Research Support Foundation of Federal District).

Author contribution: All the authors have accepted responsibility for the entire content of this submitted manuscript and approved submission.
Research funding: None declared.
Conflict of interest statement: The authors declare no conflicts of interest regarding this article.

Appendix A

A.1 Data

Figure 5:

Household loans and interest rate (personal credit).

Source: Central bank of Brazil.

Figure 6:

Google trends indexes – financiamento and empréstimo.

Source: Google.

A.2 Estimated common factors (x_t)

Figure 7:

Common factor – (a) DSSL/DR and (b) DSSL/NDR.

Figure 8:

Common factor – (a) DSSMS/E/DR and (b) DSSMS/E/NDR.

Figure 9:

Common factor – (a) DSSMS/E&F/DR and (b) DSSMS/E&F/NDR.

Figure 10:

Common factor – (a) DSST/E/DR and (b) DSST/E/NDR.

Figure 11:

Common factor – (a) DSST/E&F/DR and (b) DSST/E&F/NDR.

A.3 Linearity tests

In Table 8, we present the results of some linearity tests. The Keenan’s one-degree test for nonlinearity against the null hypothesis that the time series follows some auto-regressive (AR) linear process. The McLeod–Li test checks for the presence of conditional heteroscedascity by computing the Ljung–Box (portmanteau) test with the squared data. Accordingly to Koller and Fischer (2002), the McLeod–Li test is an indirect test and based on the fact that by fitting a linear model to the data, the inherent non-linearity has been swept into the residuals. Tsay’s test evaluates quadratic nonlinearity in a time series. We also carry out the likelihood ratio test for threshold nonlinearity, with the null hypothesis being a normal AR process and the alternative hypothesis being a TAR model with homogeneous, normally distributed errors. The Teraesvirta’s neural network test for neglected nonlinearity, with the null hypotheses of linearity in “mean”. The Lo & Zivot test has three tests available: (i) linear versus 1 threshold TVAR; (ii) linear versus 2 thresholds TVAR; (iii) 1 threshold TVAR versus 2 thresholds TVAR. The tests (i) and (ii) can be seen as linearity tests, whereas the third can be seen as a specification test. In general, the most of the tests rejected linearity. Considering the Lo & Zivot test, we reject linearity in tests (i) and (ii), while the specification test (iii) favors just one regime change (1 threshold TVAR).

Table 8:

Linearity tests.

Tests	p Value
l _t	f _t	e _t
Keenan’s one-degree test for nonlinearity (Keenan 1985)
H0: Time series follows some AR process	0.045	0.643	0.025
McLeod-Li test (Mcleod and Li 1983)
H0: Time series follows some ARIMA process	0.000	0.000	0.000
Tsay’s test for nonlinearity (Tsay 1986)
H0: Time series follows some AR process	0.977	0.029	0.000
Likelihood ratio test for threshold nonlinearity (Chan 1991)
H0: Time series follows AR process/H1: Time series follows TAR process	0.273	0.000	0.028
Teraesvirta’s neural network test^* (Teräsvirta, Lin, and Granger 1993)
H0: Linearity in “mean”	0.000	0.000	0.000
Lo & Zivot multivariate linearity test (Lo and Zivot 2001)
H0: Linear VAR/H1: 1 threshold TVAR		0.001
H0: Linear VAR/H1: 2 thresholds TVAR		0.003
H0: 1 threshold TVAR/H1: 2 thresholds TVAR		0.332

^aCalculated for regression, where l_t = f(f_t, e_t), f_t = f(l_t, e_t) and e_t = f(l_t, f_t).

A.4 Dynamic SS linear models (DSSL)

Among the benchmarks in the in-sample and out-of-sample evaluations, we evaluated the standard linear Gaussian SS model, known as Gaussian SS model, known as Dynamic SS Linear (DSSL) model. In this framework we rule out regime changes on parameters estimation, resulting at the following state-space representation:

(7.1) l t f t e t = β 1 β 2 β 3 x t + 1 0 0 0 1 0 0 0 1 ϵ t , l ϵ t , f ϵ t , e

and

(7.2) R = var ϵ t , l ϵ t , f ϵ t , e = r 11 r 12 r 13 r 21 r 22 r 23 r 31 r 32 r 33

with ϵ t , l ∼ N ( 0 , r 11 ) , ϵ t , f ∼ N ( 0 , r 22 ) and ϵ t , e ∼ N ( 0 , r 33 ) . Also, R is symmetric (r₂₁ = r₁₂, r₃₁ = r₁₃ and r₃₂ = r₂₃) and positive semi-definite.

Once again, the transition equation gives the law of motion for x_t and follows a first order autoregressive process:

(7.3) x t = α 0 + α 1 x t − 1 + ϵ t , x

where the state variance is given by Q^x = var(ϵ_t,x) with a normally distributed noise ( ϵ t , x ∼ N ( 0 , Q x ) ). Adding the assumptions that the noises at transition and measure equations are uncorrelated and the initial state is normally distributed ( x 0 ∼ N ( μ 0 , Σ 0 ) ), we estimate the parameters by Maximum likelihood.

We consider two specifications following this basic structure. The first is a DSSL with diagonal R observation covariance matrix (DSSL/DR). The second one is a DSSL with non-diagonal R observation covariance matrix (DSSL/NDR).

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Supplementary Material

The online version of this article offers supplementary material (https://doi.org/10.1515/snde-2019-0122).

Received: 2019-10-04

Revised: 2021-08-06

Accepted: 2021-08-16

Published Online: 2021-08-30

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Supplementary Material Details

What does Google say about credit developments in Brazil?

Abstract