Constructing the business and financial cycles

As previously mentioned, there is no clear consensus within the literature regarding

a definitive relationship between banks’ profitability and the cycle. Furthermore,

the potential role of the financial as opposed to the business cycle in predicting

banks’ profitability is largely ignored. Against this background, this current study

constructs estimates for both the business and financial cycles to evaluate their

respective impact on the profitability of banks.

The study takes GDP as the representative variable for the business cycle. I

recognise and acknowledge that a multivariate approach would probably be more

suitable, such as the finance-neutral output gap of Borio et al. (2016) or the finance-

augmented cycle of Montagnoli et al. (2018). However, for simplicity, and conforming

to common practice in this literature, this study will utilise the univariate approach.

Unlike the business cycle, the financial cycle has been far less researched and

defined. Further, there is no agreement on the most reliable econometric method

to analyse its statistical properties, this is usually left to the preference of the re-

searcher. Therefore, this study looks at a number of series to attempt to characterise

it. Studies such as Dell’Ariccia et al. (2012), Jordà et al. (2013) and Taylor (2015)

have used credit to capture the financial cycle, on the grounds that credit captures

the boom-bust of the financial sector. A variable commonly used in policy analysis

is the credit-to-GDP ratio. More often, researchers tend to look at measures of

credit and asset prices, most notably real estate prices (see for example Claessens

et al. (2011) and Claessens et al. (2012)). In Drehmann et al. (2012), credit aggre-

gates (particularly the credit-to-GDP ratio) are used as a proxy for leverage, while

property prices are used as a measure of available collateral. Stremmel (2015) finds

that the key ingredients of the best fitted financial cycle measure for Europe include

credit-to-GDP ratio, credit growth, and house prices to income ratio.

Section 4.3 Chapter 4

This study follows Drehmann et al. (2012), Borio (2014), and Stremmel (2015)

in using three financial variables to approximate the financial cycle.6 These are: (i)

credit to the private, non-financial sector; (ii) credit-to-GDP ratio; and (iii) prop-

erty prices. All the macroeconomic data used to construct the business and financial

cycles span the period 1980–2017. Using such long series allows for capturing var-

ious peaks and troughs, and thus better approximates the cycles. The series used

to approximate the cycles are all in real terms (CPI deflated) and in natural log-

arithmic form. This of course excludes the credit-to-GDP ratio which is expressed

in percentage points. Further, they are all normalised to their respective values in

2010 to maintain comparability.

To construct the cycles, the study uses the recent filter-based method proposed

by Hamilton (2017). The most commonly used technique in literature is the HP-

filter. However, despite its popularity, it comes with several drawbacks that must

be considered when deciding whether to use this approach. For example, Hamilton

(2017) argues that the HP-filter involves several levels of differences, so for a random

walk process, subsequent observed patterns are a mere by-product of having applied

the filter rather than reflecting the underlying data generating process. He further

suggests that the filtered values at the end of the sample vary significantly from

those in the middle, and as such are characterised by spurious dynamics. Hamilton

(2017) finally adds that the HP-filter typically produces values for the smoothing

parameter which are vastly at odds with common practice.

In light of this, Hamilton (2017) suggests an alternative concept of deriving the

cyclical component of a possibly nonstationary series. Specifically, he imposes that

the cyclical component of a possible nonstationary series should address the question

of how different is the value at datet+hfrom the value that would be expected based

6_{In extending this paper, I will adopt a multivariate approach where all three variables will be}

combined in a single measure to construct a proxy of the financial cycle.

Section 4.4 Chapter 4

on its behaviour through date t.7 _{Therefore, he suggests that if an OLS regression}

of yt+h is regressed against some constant and thep= 4 most recent values of y as

of date t,

yt+h =β0+β1yt+β2yt−1+β3yt−2+β4yt−3+vt+h (4.1)

the residuals

b

vt+h =yt+h−βb₀ −βb₁y_t−βb₂y_t−1−βb₃y_t−2−βb₄y_t−3 (4.2)

provide an acceptable approach to gain the transient component for a broad class

of underlying processes.

Hamilton (2017) argues that this proposed procedure holds a few advantages

over the much used HP-filter. First, unlike the cyclical component of the HP-filter,

the value of vbt+h will be difficult to predict from variables that pre-date time t. Second, the value of vbt+h is a model-free and assumption-free summary of the data. Thus, regardless of how the data was generated, as long as (1−L)d_y

t ≤ 4, there

exists a population projection of yt+h on (yt, yt−1, yt−2, yt−3,1)’, which can be used

to consistently estimate a cyclical component from the data. Therefore, borrowing

from Hamilton (2017) approach, this study extracts the cyclical component from real

GDP, property prices, private credit, and credit-to-GDP ratio, in order to provide

proxies for the business and financial cycles.

7_{This concept is related to the definition of the trend component of y}

t as gt =

limh→∞limp→∞E(yt+h|yt, yt−1, ..., yt−p+1) in Beveridge and Nelson (1981). This limit exists and

can be calculated provided that (1−L)yt is a mean-zero stationary process.

Section 4.4 Chapter 4