# Credit Ratings: Heterogeneous Effect on Capital Structure

Helmut Wasserbacher*label=e1] [ Martin Spindlerlabel=e2] [ Helmut Wasserbacher
Novartis International AG
Novartis Campus
4002 Basel
Switzerland
E-mail<EMAIL_ADDRESS>Martin Spindler
University of Hamburg
Hamburg Business School
Moorweidenstr. 18
20148 Hamburg
Germany
E-mail<EMAIL_ADDRESS>
###### Abstract

Why do companies choose particular capital structures? A compelling answer to
this question remains elusive despite extensive research. In this article, we
use double machine learning to examine the heterogeneous causal effect of
credit ratings on leverage. Taking advantage of the flexibility of random
forests within the double machine learning framework, we model the
relationship between variables associated with leverage and credit ratings
without imposing strong assumptions about their functional form. This approach
also allows for data-driven variable selection from a large set of individual
company characteristics, supporting valid causal inference. We report three
findings: First, credit ratings causally affect the leverage ratio. Having a
rating, as opposed to having none, increases leverage by approximately 7 to 9
percentage points, or 30% to 40% relative to the sample mean leverage.
However, this result comes with an important caveat, captured in our second
finding: the effect is highly heterogeneous and varies depending on the
specific rating. For AAA and AA ratings, the effect is negative, reducing
leverage by about 5 percentage points. For A and BBB ratings, the effect is
approximately zero. From BB ratings onwards, the effect becomes positive,
exceeding 10 percentage points. Third, contrary to what the second finding
might imply at first glance, the change from no effect to a positive effect
does not occur abruptly at the boundary between investment and speculative
grade ratings. Rather, it is gradual, taking place across the granular rating
notches (“+/-”) within the BBB and BB categories.

JEL classification: ,

C14,

C21,

D22,

G24,

G32,

double machine learning,

heterogeneous treatment effect,

capital structure,

leverage,

credit rating,

machine learning,

###### keywords:

[class=JEL]

###### keywords:

and T1The views and opinions expressed in this document are those of the first
author and do not necessarily reflect the official policy or position of
Novartis or any of its officers.

##  1 Introduction

The specific mix of debt and equity instruments a company uses to finance its
operations represents its “capital structure”. The ratio of debt to equity
within this structure constitutes the company’s financial “leverage” ratio.
Corporate finance theory suggests that the optimal capital structure is that
which maximizes the company’s market value [27, 107]. Surprisingly, however,
the question of why a company chooses a particular capital structure has
remained the subject of extensive debate [52, 48] ever since Stewart Myers
first highlighted the “Capital Structure Puzzle” in 1984 [92]. Additionally,
there is no clear, unifying model for optimal leverage [110, 15, 14, 75].
Empirical research has extensively examined firm and industry characteristics
to determine which factors can explain observed leverage ratios [52, 75]. In
recent years, machine learning approaches have begun to complement traditional
econometric methods [4], enabling researchers to apply tree-based models,
which are more flexible than conventional linear frameworks. Moreover, by
incorporating regularization (shrinkage) methods that perform automatic, data-
driven variable selection [8], machine learning allows researchers to consider
a larger set of potential explanatory factors. However, the primary focus of
most machine learning methods is to maximize predictive performance, rather
than uncovering causal relationships [8, 111]. Causal machine learning is an
emerging field that attempts to fill this gap. It is specifically concerned
with uncovering causal mechanisms through the use of machine learning
techniques. In this paper, we employ the double/debiased machine learning
framework [33, 34] to investigate the causal effect of credit ratings on
leverage. In applying this very recent methodology, we contribute to the
literature by identifying the heterogeneity of this effect across the
different credit rating levels in a complex, high-dimensional setting.

We structure this paper as follows. Section 2 provides a brief overview of the
predominant capital structure theories. Section 3 consists of an introduction
to credit ratings. Section 4 reviews recent publications on the use of machine
learning models to predict leverage or credit ratings, as well as publications
on the impact of credit ratings on leverage. Section 5 introduces the double
machine learning framework we will employ in Section 6 to determine the causal
effect of credit ratings on leverage ratios for a sample of companies from the
Compustat database. Section 7 summarizes our findings, outlines the
limitations of our work and suggests how these could form the basis for
further research. Lastly, section 8 is the appendix, which contains further
details related to several sections of the main text.

##  2 Capital Structure Theories

The capital structure of a company refers to the specific mix of financial
instruments it uses to finance its operations. Alongside decisions regarding
investments, it constitutes a fundamental question for management [57]: what
is the source of funds for our investments? Capital structure analysis
typically focuses on “leverage”, which is the ratio of the total amount of
debt (as a broad asset class) to total equity in the capital structure.

Different theories have been developed about the optimal capital structure, or
the leverage that maximizes the overall market value of a company [52, 75,
107, 48, 27, 21]. Key theories include Modigliani and Miller’s theory of
irrelevance [89] (page 268, “Proposition I”), the trade-off theory [86, 67,
40, 66, 77], the pecking order theory [92, 106, 107] and the market timing
theory [12, 116]. Over time, many extensions and complementary perspectives
have been proposed (e.g., [46] and [22]). In the context of this article, the
inclusion of credit ratings as a factor affecting a company’s leverage is of
particular interest. [71] labelled this the credit rating - capital structure
hypothesis.

Among the theories concerning the optimal capital structure, there is no
consensus, and the reasons why individual companies choose a particular
capital structure remain largely unknown [110, 15, 14, 75]. Thus, the “Capital
Structure Puzzle” [92] remains unsolved. A second important aspect of most
theories is that they do not explicitly specify the functional form through
which the putative factors influence or determine capital structure. In
particular, they neither postulate nor even imply a linear relationship
between leverage and its determining factors.

At the same time, there is extensive empirical research on the potential
determinants of observed leverage ratios, as witnessed by surveys such as [75,
52] or [31]. The considered explanatory variables are mostly financial in
nature and include elements from the balance sheet, income statement and cash
flow statement. These variables are typically scaled by total assets or total
sales and are accompanied by a rationale of what they measure [52]. However,
the precise economic concepts that these measures are intended to proxy and,
thus, the causal mechanisms involved are not always clear [48].

Empirical studies sometimes also attempt to capture individual company
attributes beyond financial characteristics. This typically involves the use
of dummy variables to represent traits such as company maturity, “uniqueness”
(often linked to sub-industry sectors) or operations in regulated industries
such as utilities or railroads. More generally, dummy variables representing a
company’s industry at the two- to four-digit Standard Industrial
Classification (SIC) code level or relying on the Fama and French industry
classification [42] are commonly included as covariates in empirical analyses.
Examples of such approaches can be found in [48, 4] and [72].

Less frequently employed variables are those that attempt to capture concepts
such as management skills [53, 84], effective corporate governance mechanisms
[32, 120], or the impact of the economic regime in which a company operates,
such as the tax system [47]. [75] refers to this group of explanatory factors
as “cognitive variables” (page 115).

Most studies examining leverage include a subset of the aforementioned
explanatory variables using variants of linear regression [75]. However,
empirical research [52, 4] supports the view that “the relation between
leverage and many of these variables is nonlinear” ([52], page 311) and that
these nonlinearities persist even after excluding particular subgroups of
companies, such as distressed firms. However, as highlighted by [52] (page
337), few empirical analyses have explicitly taken account of these nonlinear
dynamics. Machine learning methods, which are adaptable to complex, non-linear
patterns, appear well-suited to address our research question in this
environment [24].

##  3 Credit Ratings

[79] (page 4) define credit ratings as “opinions about credit risk”, that aim
“to provide investors and market participants with information about the
relative credit risk of issuers and individual debt issues.” Indeed, the main
purpose of credit ratings is to reduce information asymmetries in financial
markets, facilitated by credit agencies’ access to privileged information from
company management.

The credit rating market is dominated by three big agencies: S&P Global
Ratings (formerly known as Standard & Poor’s Ratings Services), Moody’s
Investor Services and Fitch Ratings, with S&P holding approximately 50% of the
market share [84].

Ratings are typically assigned using a hierarchical, letter-based scale. For
instance, the highest S&P rating is denoted as “AAA”, corresponding to
“[e]xtremely strong capacity to meet financial commitments”, while the lowest
rating is denoted as “D”, corresponding to “[p]ayment default on a financial
commitment or breach of an imputed promise; also used when a bankruptcy
petition has been filed or similar action taken” [79] (page 9). Further
elements include “+” or “-” signs added to the rating to indicate the relative
standing (“notch”) within a broad rating category, as well as the distinction
between “investment-grade” (from AAA to BBB-) and “speculative-grade” (BB+ and
below) ratings, “outlooks” for possible rating changes anticipated within six
to 24 months, and “watchlists” for more immediate concerns (usually 90 days).
Industry sources such as [88, 79, 80] and [100] provide further details on the
codification of ratings.

For this article, it is important to stress that the credit rating industry
operates almost entirely under the “issuer-pays model”. In this model, a
company seeking a credit rating approaches a rating agency and pays for the
service [11] (page 1961). This approach contrasts with the “investor-pays
model”, under which rating agencies are financed through fees charged to
investors accessing the ratings; this model is now less common. Alternative
models remain marginal, such as the “public-utility model” in China [61].
Thus, the issuance of a company rating is the result of an explicit decision
by the company’s management. For example, Fitch states that “[t]he rating
process usually begins when an issuer […] contacts a member of Fitch’s
Business and Relationship Management (BRM) group with a request to engage
Fitch to provide a credit rating” [101] (page 2). Similarly, “Ratings request
from issuer” is the first box in S&P’s flowchart explaining “Raising Capital
Through Rated Securities” [79] (page 7). Put differently, companies self-
select into having a rating.111At least theoretically, other situations are,
of course, conceivable. For instance, a company might wish to obtain a rating,
but the rating agency does not or cannot provide one (for whatever reason);
or, after initial discussions about requesting a rating, a company withdraws
its request. We believe, however, that such situations are limited in
practice.

The question of potential determinants of corporate credit ratings has been
examined extensively in the empirical literature, with [84] providing a recent
overview. Similar to the determinants of leverage, financial ratios are widely
employed in empirical research on credit ratings [62, 11]; indeed, as [84]
(page 10) asserts, “Studies that omit these variables are almost always
incomplete by definition”. Additionally, some authors indicate that corporate
governance mechanisms also play a role in determining credit ratings [7, 23].
Meanwhile, findings regarding the influence of macroeconomic variables on
credit ratings have yielded mixed results [45, 11], corresponding with the
assertion of credit rating agencies that they already include “the anticipated
ups and downs of the business cycle” in their assessments [79] (page 10).

A further similarity between leverage and rating studies is the predominant
reliance on linear relationships between dependent and independent variables
[84, 114]. [62] (page 545) observe in their literature review that the key
advantage of these models is that they are “succinct and […] easy to explain.”
However, many authors are aware of likely non-linear effects and try to
accommodate these. For instance, [3] (page 2649) first transform interest
coverage into a piecewise linear function and then create four distinct
variables over four regions. [11] (page 1976) include squared and cubed
versions of all explanatory variables. Again, machine learning methods, which
by design are flexible to adapt to complex, non-linear patterns, appear
particularly appropriate in such scenarios [24].

For further details on ratings, the references in [30, 11, 69, 84, 117, 39,
16] and [96] provide good starting points.

##  4 Literature Review

Our review of the literature focuses on the central topic of this paper, which
is the causal effect of credit ratings on capital structure. Here, we discuss
the relatively few existing publications on this subject. In the appendix, we
provide additional information by highlighting relevant findings from selected
studies that employ machine learning methods to investigate leverage ratios or
credit ratings.

A plausible case can be made that credit ratings influence capital structure
decisions. For instance, companies sometimes mention credit rating objectives
in the context of specific financing decisions. Surveys also consistently
indicate that ratings are among the main factors when managers decide about
leverage for their firms (e.g., [51, 13]). Additionally, as early as 1936,
federal regulations in the United States required banks to invest exclusively
in investment-grade bonds (see [117], section 4, for a historical overview).
It is therefore surprising that research on the determinants of capital
structure took so long to consider the potential causal effect of credit
ratings.

Given the possibility that “in the social sciences often that is treated as
important which happens to be accessible to measurement” [113] (page 3), we
hypothesize that the lack of early research on this topic was due to the
initially limited availability of corporate credit rating data. First, prior
to the late 1960s, credit rating agencies operated under the investor-pays
model (see section 3). Thus, credit ratings were private information purchased
by investors. Only with the switch to the issuer-pays model did this
information begin to be “[distributed] to the general public at no charge”
[117] (page 102). Second, ratings became available in popular databases
substantially later than data such as balance sheet and income statement
information. For instance, whereas
Compustat222https://www.marketplace.spglobal.com/en/datasets/compustat-
financials-(8)#dataset-overview (accessed December 8, 2022) was initiated and
already had significant coverage as early as 1950, 1985 was, as [71] (page
1047) points out, the first year in which the S&P long-term credit rating
became available in Compustat.

Published in 2006, [71] claims to be “the first paper to examine the direct
effect of credit ratings on capital structure decisions” (page 1036). In
particular, the author postulates the “Credit Rating - Capital Structure
Hypothesis” (CR-CS) [71] (page 1037), according to which credit ratings
represent a material factor in capital structure decisions due to the discrete
costs and benefits of different rating levels. Above all, changes in credit
ratings trigger costs or benefits that influence the leverage decisions of
companies according to the CR-CS.

The empirical test of the CR-CS theory [71] relies on a sample of 12’336 firm-
years from Compustat from 1986 to 2001. The sample is restricted to companies
for which a Standard & Poor’s Long-Term Domestic Issuer Credit Rating is
available. The fundamental idea of the test is to examine how managers’
concerns about potential rating changes affect their decision to issue debt
versus equity. Using the presence of a plus or minus rating as a proxy for
managerial concern about an impending rating change, the CR-CS theory predicts
that such companies will issue relatively less debt. Indeed, [71] finds that
companies with a credit rating that includes a plus or minus (i.e., “+” or “-”
notch qualification) issue approximately 0.5% to 1% less debt than companies
with a straight rating (i.e., without a plus or minus qualification).

In a subsequent paper on the relationship between ratings and capital
structure, [72] finds that companies reduce leverage by approximately 1.5% to
2.0% of assets following a rating downgrade, whereas rating upgrades do not
affect subsequent leverage levels. This asymmetry suggests that companies
strive to achieve and maintain minimum rating levels. The hypothesized reason
for this behavior is that certain ratings offer discrete benefits, such as the
ability to issue commercial paper.

[43] also explicitly consider the role of credit ratings in the context of
capital structure decisions. However, their argument focuses on the supply
side of capital, especially a company’s access to the public bond market, as
measured based on whether the company has a credit rating. The underlying
reasoning is that a desired level of leverage might be unattainable for a
company if lenders are rationing capital (see, for instance, [27], pages
108-113). Thus, the authors postulate a link between a company’s source of
capital and its leverage. For their empirical analysis (described on pages
51-54), [43] use Compustat data from 1986 to 2000, resulting in 77’659 firm-
years and a dataset similar to that used in [71] and [72]. [43] find that the
effect of having any credit rating (versus having none at all) increases a
company’s leverage by about 6 to 8 percentage points, corresponding to an
approximate 35% increase relative to the average leverage ratio of 22%.
Because [43] (page 54) use the existence of a debt rating as a proxy for
access to the capital market, the authors conclude that companies with access
to the public bond markets have significantly more leverage.

From an analytical perspective, we observe that while the vast majority of
control variables in the five linear regression specifications of [43] are
statistically significant at the 1% level, the $R^{2}$, even of model V, which
includes 12 company control variables and a year dummy, does not exceed 37.3%.
This suggests that capital structures are difficult to predict with linear
model specifications.

Adopting a different approach, [73] took advantage of several changes made by
the rating agency Moody’s333We note that this is one of the very few papers
identified in our literature search that rely on rating information from
Moody’s rather than S&P Global Ratings (Standard and Poor’s). in 2006 to the
calculation and reporting of leverage ratios in relation to pensions,
operating leases, and hybrid securities. The author argues that because these
changes were exogenous to company fundamentals, they provide a natural
experiment (see for instance [105], page 75) to determine their causal impact
on capital structure and investment decisions. The findings across several
analyses support the view that changes to the rating adjustment methods
affected capital structure decisions. [73] therefore concludes that “credit
ratings have a significant impact on financial and real decisions of firms”
(page 581) and “rating agencies have the power to affect corporate decisions”
(page 567).

The results of the studies discussed so far suggest that credit ratings have a
significant but very general effect on leverage. However, [69] provide a more
nuanced view. The authors investigate the validity of the CR-CS model as
proposed in [71] and [72] by testing four hypotheses about company-level
attributes. The authors argue that for companies with these attributes,
maintaining or achieving a certain rating is especially desirable. Thus, these
attributes “should proxy for management’s inclination to adopt the CR-CS
model” ([69], page 574). For instance, depending on their broad rating
category, companies should behave differently because the relative costs of a
change in ratings vary across categories; notably, companies on the verge of
moving from investment-grade (BBB- on the S&P rating scale) to speculative-
grade (BB+ and below) ratings should be highly sensitive to the CR-CS logic
due to the many negative regulatory implications of non-investment-grade
status.

The sample period in [69] spans from 1986 to 2009, leading to a total of
approximately 16’000 company-years. Results across all four hypotheses do not
support the view that credit ratings significantly affect capital structure
decisions. For instance, estimates of the effect of plus/minus ratings on
leverage are generally not significant when companies are split by broad
rating category or by investment- versus non-investment-grade ratings, with
the sole exception of the minus-category of rating class B. [69] (page 574)
infer that “[[71]’s] original findings appear to be driven by the subsample of
firms with extremely low ratings.” [69] conclude “that the CR-CS model is not
a good descriptor of how firms determine their marginal financing decision”
(page 594) and hypothesize that the “marginal financing behavior [of B- rated
firms] to avoid debt may be more an indication of lack of access to the debt
market than an indication of a conscious attempt to decrease debt financing.”

In summary, while existing studies have estimated the average effect of credit
ratings on leverage, the average effect may mask significant heterogeneity.
Indeed, [69] has already provided preliminary evidence that such heterogeneity
exists. In the present paper, we aim to go one step further and determine the
presence, pattern and extent of this effect heterogeneity. To do so, we employ
double machine learning, a modern machine learning approach. The next section
will provide an introduction to double machine learning.

##  5 Double Machine Learning

We have seen from the previous sections that there is no general consensus
regarding the determinants of leverage and how they interact at the company
level. Nevertheless, it is likely that many factors play a role and the
mechanisms by which they influence capital structure are complex. Given the
lack of a strong theoretical framework, isolating the causal effect of credit
ratings poses a formidable challenge. Additionally, we need to consider that
this effect may be heterogeneous. Double machine learning [33, 34, 17, 18] is
a recently developed methodology that can help solve questions of causal
inference in such settings by harnessing what [54] calls “the unreasonable
effectiveness of data.” Among the key advantages of double machine learning
are the following characteristics. First, there is the ability to handle high
feature dimensionality, i.e., the presence of many potential influencing
factors in addition to the treatment variable of interest, and to provide
valid inference on treatment effects in such high-dimensional, complex data
environments. Second, it employs a data-driven approach to select among these
influencing factors. Third, it facilitates the use of various machine learning
algorithms with flexible function-fitting capabilities. Fourth, there is
double-robustness with respect to nuisance functions.

“Partialling-out”, “Neyman orthogonality” and “cross-fitting” are three
important concepts enabling the “doubly robust” nature of the double machine
learning approach. We will briefly discuss each of these concepts in this
section and refer readers to the appendix of this paper and the literature
referenced in this section for further details.

###  5.1 Partialling-out

Double machine learning builds on the concept of Frisch-Waugh-Lovell (FWL)
“partialling out” [81, 37]. According to the FWL theorem, a parameter of
interest $\theta$ in a linear model such as:

$\displaystyle Y=\theta D+\beta X+\epsilon$ (5.1)

with $\mathbb{E}(\mathcal{\epsilon}|D,X)=0$

can be estimated with linear regression using, for example, ordinary least
squares taking either of two approaches. Under the first approach, $\theta$
can be directly estimated by regressing $Y$ on $D$ and $X$. Under the second
approach, $\theta$ is determined in the last step of a three-step procedure:
first, $Y$ is regressed on $X$, and the corresponding residuals $\epsilon_{Y}$
are determined. Second, $D$ is regressed on $X$ and again, the corresponding
residuals $\epsilon_{D}$ are determined. Third, the residuals $\epsilon_{Y}$
from the first step are regressed on the residuals $\epsilon_{D}$ from the
second step. The regression coefficient obtained from this third step
corresponds to $\theta$, the parameter of interest. This latter approach is
employed for double machine learning with machine learning algorithms and even
ensemble methods combining different machine learning methods being used for
the first and second step. We underline that machine learning methods cannot
be used to “directly” estimate equation 5.1 as per the first approach
described above. Such a “naive approach” [18] (page 36) entails a high risk of
yielding a severely biased estimator for the treatment parameter [17, 18,
115], hence leading to invalid inference.

###  5.2 Neyman orthogonality

Following the general outline of [9], we illustrate the approach using a
“partially linear model” [102, 55], which we will also employ in our empirical
analysis in section 6. The usual form of a partially linear regression model
is:

$\displaystyle Y=\theta_{0}D+g_{0}(X)+\zeta$ (5.2)

with $\mathbb{E}(\mathcal{\zeta}|D,X)=0$

and

$\displaystyle D=m_{0}(X)+\mathcal{V}$ (5.3)

with $\mathbb{E}(\mathcal{V}|X)=0$,

where $Y$ is the outcome variable, $D$ is the treatment (policy) variable of
interest, and $X$ is a (potentially high-dimensional) vector of confounding
covariates. $\mathcal{\zeta}$ and $\mathcal{V}$ are error terms. The
regression coefficient $\theta_{0}$ is the parameter of interest. We can
interpret $\theta_{0}$ as a causal parameter, i.e. the causal effect of
treatment $D$ on outcome $Y$, provided that $D$ is “as good as randomly
assigned” [38] (page 73), conditional on the covariates X, thus rendering D
exogenous conditionally on X.

Applying the partialling-out procedure to equations 5.2 and 5.3 removes the
confounding effect of X. Afterwards, by regressing the residuals on each
other, the regularization bias introduced by machine learning methods with a
penalty or regularization mechanism has no first-order effect on the target
parameter [34].

Technically, a method-of-moment estimator for the parameter of interest
$\theta_{0}$ is employed:

$\displaystyle\mathbb{E}[\mathcal{\psi}(W;\theta_{0},\eta_{0})]=0$ (5.4)

where $\psi$ represents the score function, $W=(Y,D,X)$ is the set (data
triplet) of outcome, treatment, and confounding variables, $\theta_{0}$ is the
parameter of interest as already indicated above, and $\eta_{0}$ are nuisance
functions (for instance, $g_{0}$ and $m_{0}$, which we will employ later in
our empirical application).

For the double machine learning inference procedure, the score function
$\psi(W;\theta_{0},\eta_{0})$ from equation 5.4 (with $\theta_{0}$ as the
unique solution) needs to satisfy the Neyman orthogonality [94, 20] condition:

$\displaystyle\partial_{\eta}\mathbb{E}[\mathcal{\psi}(W;\theta_{0},\eta)]|_{\eta=\eta_{0}}=0,$
(5.5)

where the derivative $\partial_{\eta}$ denotes the pathwise Gateaux derivative
operator. Intuitively, Neyman orthogonality in equation 5.5 ensures that the
moment condition $\psi(W;\theta_{0},\eta_{0})$ from equation 5.4 is
insensitive to small errors in the estimation of the nuisance function $\eta$
(around its “true” full population value $\eta_{0}$). Thus, it removes the
bias arising from using a machine learning-based estimator for $\eta_{0}$.

###  5.3 Cross-fitting

A second point to consider is that machine learning methods usually rely on
sample splitting to avoid bias introduced by overfitting [65, 56]. Under
double machine learning, a similar data splitting methodology applies in the
case of a partially linear model with two nuisance functions as described in
the next section with equations 6.1 and 6.2. Only one subset of the data is
used to estimate the nuisance functions, which are partialled-out, while the
other subset is used to estimate the parameter of interest (i.e., the
treatment effect). Of course, such a limited use of the data implies a loss of
efficiency.

To overcome this efficiency loss from data splitting, double machine learning
employs a technique called “cross-fitting” [34] (page C6). In this procedure,
the roles of the two data subsets are swapped, and two estimates for the
parameter of interest are obtained. Because these two estimators are
approximately independent, they can simply be averaged to make use of the full
data set [34] (Figure 2, page C7). The cross-fitting procedure can be expanded
beyond two data sets into a K-fold version to further increase robustness; [9]
(page 13) reports that four to five folds appear to work well in practice.

###  5.4 Double robustness

“Double machine learning” is so named because it applies machine learning
methods to estimate both equation 5.2 and equation 5.3. However, the estimated
treatment effect is also “doubly robust” thanks to the partialling-out
procedure described previously. This robustness means that potential “mistakes
in either of the two prediction problems” [111] (page 221) (i.e., equations
5.2 or 5.3) do not invalidate the effect estimate as long as at least one
equation is sufficiently well estimated. In other words, while it is necessary
“to do a good job on at least one of these two prediction problems” [111]
(page 221), it does not matter which one is more accurately modeled. Although
this feature should not encourage lax model specifications, it underscores
another attractive property of double machine learning, particularly when
uncertainties remain about the precise model characteristics. As noted by [18]
(page 34), “Because model selection mistakes seem inevitable in realistic
settings, it is important to develop inference procedures that are robust to
such mistakes.”

Finally, double machine learning exhibits a general robustness irrespective of
the particular machine learning (ML) algorithm employed. [34] comment
regarding their empirical results that “the choice of the ML method used in
estimating nuisance functions does not substantively change the conclusions“
(page C45). Of course, the machine learning methods need to be of sufficient
quality for given task. Considering the broad spectrum of available machine
learning models, however, this typically does not present a major hurdle, and
even ensemble models are suitable [34] (pages C22-C23).

##  6 Empirical Methodology and Findings

In this section, we employ the double machine learning framework to estimate
the causal effect of ratings on the leverage ratio. We first describe our
study design and the data we employ. Subsequently, we report and discuss the
results, including those of several robustness checks. Our main finding is the
presence of heterogeneous effects of ratings on leverage.

###  6.1 Empirical Design

To estimate the effect of ratings on the leverage ratio, we employ a partially
linear regression model (see for instance [55]) of the following form:

$\displaystyle LDA_{i,t}=\theta^{\prime}D_{i,t}+g_{0}(X_{i,t})+\zeta_{i,t}$
(6.1)

with $\mathbb{E}(\mathcal{\zeta}_{i,t}|D_{i,t},X_{i,t})=0$

and

$\displaystyle D_{i,t}=m_{0}(X_{i,t})+\mathcal{V}_{i,t},$ (6.2)

with $\mathbb{E}(\mathcal{V}_{i,t}|X_{i,t})=0$

where $LDA_{i,t}$ is the outcome variable representing the leverage ratio for
company $i$ in year $t$, defined as the book value of total debt (short-term
and long-term) divided by the book value of total assets, $X_{i,t}$
corresponds to a vector of covariates for company $i$ at time $t$, which are
assumed to be statistically associated with the outcome and treatment
variables, and $\mathcal{\zeta}$ and $\mathcal{V}$ are stochastic error terms.

$D$ represents the “treatment”, i.e., the policy variable of interest in our
study of rating effects. Specifically, $D_{i,t}$ represents the vector of $p$
binary treatment variables for company $i$ in year $t$. To allow for
heterogeneity, $D$ can contain the rating variable and, for example,
interactions with other potentially relevant variables or a refined rating
category coded as dummy variables (we will use such a strategy later on). In
the initial setting, we consider only one treatment variable: the presence
($D=1$) or absence ($D=0$) of a rating for a given company. Subsequently, we
will expand the scope of analysis to conduct simultaneous inference on
different treatment variables, for example, by considering each distinct
rating category (such as AAA, AA+, A, AA-) as a separate treatment. Equation
6.1 contains the parameter vector of interest, $\theta$, which corresponds to
the $p$ causal effect measure(s) of the $p$ treatment(s) on the outcome
variable - i.e., in our case, the effect of rating on leverage. This causal
interpretation is valid if the treatment D is “as good as randomly assigned”
([38] page 73) conditional on the covariates X, making D exogenous
conditionally on X. In other words, the initially non-random treatment
assignment can be ignored if controlling for the correct set of X [105],
because the selection bias towards different treatment types “disappears”
([6], page 54) in this case. Thus, the selection of the covariates X and the
modeling of their relationship with the outcome and treatment variables are
critical for the validity of the analysis. This is precisely where the machine
learning approach proves invaluable, because it is able to perform data-driven
selection from a large number of candidate covariates and can flexibly model
the form of their influence on the outcome variable [111].

$g_{0}$ and $m_{0}$ are two vector-valued functions that capture the
relationship of the covariates $X$ with the outcome $LDA$ and the treatment
$D$, respectively. These two “learner” functions do not need to be linear; in
fact, we will use random forests [28] for our analyses because of their
general strength in capturing non-linear, complex interactions and
relationships, even in high dimensions and with large datasets [83]. The
appropriateness of random forests specifically for empirical analyses of
capital structures and ratings has been further confirmed by recent
publications, which found random forests to perform better than other machine
learning methods (see for instance [4] and [68] for leverage and [114] for
company credit ratings).

While the learner functions $g_{0}$ and $m_{0}$ do not need to be linear and
can be flexibly adapted by the machine learning algorithm, it is important to
remind ourselves that our specification in equation 6.1 corresponds to a
linear effect of D on the outcome. We refer interested readers to the
literature on non-linear response models (e.g., [44]).

###  6.2 Data

We use Compustat data for North American companies for the years 2005 to
2015.444Financial data were extracted from “Compustat Daily Updates -
Fundamentals Annual” and rating data from “Compustat Daily Updates - Ratings”
on September 13, 2022, via Wharton Research Data Services (WRDS).  Similar to
the extant literature,555See for instance: [43] (page 51, page 54), [72] (page
1329), [71] (page 1047), [69] (page 583), [4] (Table 1, page 8). We do not
exclude utilities (unlike [72], page 1329) or winsorize data (unlike [4],
Table 1, page 8). we exclude companies from the financial and public sectors
(SIC codes 6xxx and 9xxx), observations with negative shareholder equity or
negative total debt, and observations involving sales or assets smaller than
one million US dollars. For unreported balance sheet, income, and cash flow
statement items, missing values are replaced by zero, while non-financial
metrics, such as CEO/CFO SOX certification codes or the company’s auditor, are
explicitly coded as “missing”. Following these criteria, we arrive at a sample
of 57’832 company-year observations.

A common characteristic of the publications examining the impact of credit
ratings on leverage described in our literature review in section 4 is their
reliance on an a priori selection of variables deemed related to the leverage
ratio or credit rating. This selection, such as in [43] (page 57) or [71]
(page 1056), is based on capital structure theories or the results of previous
research. We by no means wish to criticize this approach of relying on
previous research findings, which we follow ourselves (as evidenced by our own
use of random forests as learner functions in equations 6.1 and 6.2). What we
intend to highlight, however, is that our machine-learning approach does not
require rigid a priori decisions about the inclusion or exclusion of specific
variables for predicting leverage and the presence of a rating.

Moreover, the ability of random forests to automatically reflect complex
interactions and nonlinearities implies that we only need a very basic level
of researcher-driven “feature engineering”. In fact, in our model, we only
include three transformations. First, we scale balance sheet, income, and cash
flow statement items by sales and total assets (e.g., PP&E as a percentage of
sales and of total assets). Second, as a measure of company size, we add the
logarithm of sales and the logarithm of total assets to the variable set.
Third, we transform certain data items into dummy variables, such as creating
dummies for three-digit SIC codes and for the adoption of certain accounting
changes.666This corresponds to the field “ACCTCHG” in Compustat. For instance,
the adoption of the FASB accounting standard SFAS 157 effective during 2007 is
coded as “FS157”. SFAS 157 concerns measurement and disclosure principles of
“fair value” in generally accepted accounting principles, mainly in illiquid
markets. See https://www.fasb.org/page/PageContent?pageId=/reference-
library/superseded-standards/summary-of-statement-no-157.html&bcpath=tff
(accessed January 20, 2023).

Given our deliberate use of random forests, a highly flexible method capable
of learning complex interactions, we must prevent the algorithm from “back-
calculating” total debt or equity, which are key determinants of the leverage
ratio. We achieve this by removing all data items from the liabilities side of
the balance sheet and excluding debt-related items from the income and cash
flow statements, such as data items related to interest expenses. This clearly
distinguishes the capital structure decision (liability side) from the
investment decision (asset side) in alignment with the two fundamental
managerial decisions discussed in section 2.

Employing this strategy, we compile a total of 1’840 features that comprise
our set X of covariates. We provide a full list of the covariates in the
appendix.

As already mentioned in subsection 6.1, we define the outcome variable, the
leverage ratio $LDA$, as the ratio of total debt to total assets for company
$i$ in year $t$:

$\displaystyle LDA_{i,t}=(\textit{Long-term Debt}_{i,t}+\textit{Short-term
Debt}_{i,t})/\textit{Total Assets}_{i,t}$ (6.3)

We measure $LDA$ (shorthand for “Leverage Debt to Assets”) in terms of book
values, because these reflect the actions of company managers more directly
than do market values [71]. However, we also verify the main results of our
paper using a market value777Because the market value of debt is approximated
by its book value in this definition, this corresponds to a “quasi-market
value measure” [51] (page 316), a concept employed by most extant research
(see e.g., [4, 72, 71, 43]). definition of leverage ($LDMA$), defined in line
with previous research (e.g., [43, 72]) as:

$\displaystyle\begin{split}LDMA_{i,t}=(\textit{Long-term
Debt}_{i,t}+\textit{Short-term Debt}_{i,t})/\\\ (\textit{Total
Assets}_{i,t}-\textit{Book Value of Equity}_{i,t}+\textit{Market Value of
Equity}_{i,t})\end{split}$ (6.4)

Finally, for the treatment variable D, we use “Standard & Poor’s Long-Term
Domestic Issuer Credit Rating” from Compustat888See footnote 4 for the date of
data extraction. to determine whether a rating is present for a given company-
year and, if so, which rating it is. We acknowledge that a company may not
have an S&P rating but could instead hold ratings from other agencies such as
Moody’s Investor Services or Fitch Ratings. However, considering S&P’s
dominant market share of approximately 50% (see section 3) and the fact that
the majority of companies in the US have ratings from at least two leading
rating agencies [78], we see this as a minor concern for our analyses. Another
concern when measuring the impact of individual rating categories is that
companies may have what is called a “split-rating” [26].999For instance, the
pharmaceutical company Novartis reports a split rating in their presentation
dated January 19, 2023, with AA- from S&P one notch higher than A1 from
Moody’s [95] (page 19). A split-rating describes a situation in which a
company is rated differently by two different agencies. While this affects up
to 50% of rated companies, differences are typically at the “notch level”,
i.e. concerning the most granular plus and minus sub-levels within a given
broader rating category [78]. We address this issue in our analyses by
examining the causal impact of specific ratings at different levels of
granularity. The corresponding results, which we report in the appendix,
support the findings presented in the main paper.

Table LABEL:table_LDA_summary provides an overview of the outcome variable,
leverage (LDA), with a split by broad rating category.

We observe several general facts from table LABEL:table_LDA_summary, which are
broadly in line with the extant literature [11, 71, 43]. First, median and
mean leverage are significantly higher for observations that have any kind of
rating compared to observations that have no rating. Leverage increases as the
rating category decreases, except for the particular rating classes “SD”
(which signifies that selective default on a particular debt instrument has
occurred, but it is believed that the company will honor its other
obligations) and “D” (default).101010Most authors do not include the rating
categories “SD” and “D”. Also, the absence of rating class “C” in our sample
is consistent with its rarity in other empirical analyses; for instance, [11]
(Table 1, page 1966) reports only three instances of “C”-ratings out of a
total of almost 30’000 ratings for their 1985-2009 sample. Overall, roughly a
quarter (26%) of observations have a rating, out of which slightly more than
half (14% of 26%) are investment-grade ratings (better than BB).

Table 1: Summary statistics for the outcome variable, leverage (LDA), by
rating category. LDA values (total debt divided by total assets) are displayed
as %. “1st quart.” and “3rd quart.” correspond to the 25th- and 75th-
percentile, respectively. “Observations” refers to the number of company-years
over the 2005-2015 timespan. “% of total” represents the share of observations
of a particular rating class relative to all company-year observations. Values
in this column are displayed as %. The (single) C-rating category is absent
because no firm-year had such a rating over the sample period.  Summary
statistics for LDA (in %) by rating category
---
Rating | 1st | Median | Mean | 3rd | Obser- | % of
category | quart. |  |  | quart. | vations | total
AAA | 5.0 | 12.1 | 17.8 | 20.0 | 86 | 0.1
AA | 11.9 | 20.4 | 20.5 | 26.7 | 391 | 0.7
A | 18.4 | 26.4 | 26.9 | 34.4 | 2’458 | 4.3
BBB | 20.4 | 28.9 | 28.9 | 36.7 | 5’174 | 8.9
BB | 22.8 | 33.3 | 34.0 | 44.7 | 3’732 | 6.5
B | 33.1 | 45.0 | 44.9 | 56.9 | 2’981 | 5.2
CCC | 35.5 | 46.0 | 45.5 | 60.4 | 148 | 0.3
CC | 30.4 | 51.9 | 48.6 | 67.2 | 15 | 0.0
SD | 26.0 | 35.5 | 32.1 | 41.6 | 4 | 0.0
D | 16.7 | 31.1 | 28.8 | 41.4 | 41 | 0.1
Total ratings | 21.7 | 31.6 | 32.9 | 42.5 | 15’030 | 26.0
No rating | 0.1 | 11.1 | 17.1 | 28.2 | 42’802 | 74.0
Grand total | 1.8 | 18.5 | 21.2 | 34.1 | 57’832 | 100.0

###  6.3 Results

In this section, we describe the key results from our analyses of the causal
effect of credit ratings on leverage. We begin with the most fundamental
question: Does having a credit rating affect the leverage ratio? Subsequently,
we examine the individual effects of the 22 most granular rating categories.
For the sake of conciseness, we delegate the more gradual exploration of our
research question and its results to the appendix, where we first assess the
difference in effect between investment-grade and speculative-grade ratings,
followed by a delineation among the 10 broad rating categories. Additionally,
we support our findings with robustness tests, including a second metric for
leverage, different model specifications within the machine learning
framework, and a different sample period.

####  6.3.1 Effect of having any rating versus having no rating

For our first analysis, we estimate the causal effect on the leverage ratio of
having any rating, regardless of the specific rating category, versus not
having a rating.

As mentioned previously, we use regression trees out of the machine learning
toolbox as learners for the two functions $g_{0}$ and $m_{0}$, which capture
the relationship of the covariates $X$ with the outcome, $LDA$, and the
treatment, $D$, respectively. The literature sometimes refers to $g_{0}$ and
$m_{0}$ as “nuisance functions” and their parameters as “nuisance parameters”
[34, 18] because their estimation is not the primary aim of the causal
analysis (which is the estimation of the causal parameter $\theta$). We
therefore limit the scope of their discussion to a brief description here and
refer to the appendix for technical details. For $g_{0}$, we specify the
random forest so that it has 500 trees, each with a maximum depth of seven
levels, to predict $LDA$. This achieves an out-of-sample prediction accuracy
of approximately 53% for the $R^{2}$. This level of accuracy is in line with
existing literature (see for instance [4], Table 2, page 11 or [68], Table 2,
page 23). For $m_{0}$, we also specify the random forest so that it has 500
trees, but with a slightly lower maximum depth of five levels each. Out-of-
sample, we achieve a correct classification rate of approximately 87%, again
in line with the literature (see for instance [11], Table III, Panel A, page
1972).

With the learners $g_{0}$ and $m_{0}$ defined, we can apply the double machine
learning framework described in section 5 to determine the parameter of
interest $\theta$. We follow the practical recommendation from [9] (page 13)
and use a five-fold split as well as two repetitions to arrive at aggregated
parameter estimates and standard errors. Table LABEL:table_Res_General_Rating
summarizes the results. For an immediate robustness check, we also include
here the results based on the alternative (quasi-market value) leverage
definition (LDMA) from 6.4; however, as motivated previously, the focus of our
paper remains leverage as measured by book values (LDA).

Table 2: Results for the estimated causal effect $\theta$ on LDA (book value leverage) and LDMA (quasi-market value leverage) of having or not having a rating. Parameter estimates and standard errors are aggregated over a five-fold split with two repetitions. Subsections 6.1 and 6.2 describe the analytical approach and the data sample. Rating effect on leverage | LDA | LDMA
---|---|---
$\theta$ (rating yes/no) | 0.0878 | 0.0655
Std. error | 0.0021 | 0.0020
t-value | 41.8 | 32.9
p-value | 0.000 | 0.000
Memo: mean LDA/LDMA | 0.212 | 0.202
Rating effect ($\theta$) vs. mean | 41% | 32%

Our estimate of the general rating effect summarized in table
LABEL:table_Res_General_Rating is both statistically111111A discussion of the
relevance and validity of significance levels, including the controversy of
the “5% p-value” and the general topic of the “replication crisis”, go beyond
the scope of this paper. We refer interested readers to sources such as [5,
85, 64]. However, we underline the general relevance of this topic by
highlighting that [69] (a paper we discussed in section 4) mention that they
are unable to replicate the results from [71]. See [69] (footnote 13, page
584).  and economically significant. On average, having a rating increases LDA
by roughly 9 percentage points (pps). Compared to the sample average leverage
ratio of approximately 21%, this represents an increase of 41%. Using LDMA as
the outcome variable to check the robustness of the results, the effect
estimate is roughly 6.5pps (32% increase versus mean LDMA) and also highly
significant. Thus, our results at this very general yes/no rating level
corroborate the finding in [43] that firms with a credit rating have more
debt. Moreover, the order of magnitude is very comparable: [43] conduct their
analysis for market leverage (LDMA) and, in fact, our own LDMA effect estimate
of 32% versus the mean is very close to the 35% they report (page 1).

It is important to put our rating effect estimate of 9pps into perspective
with purely descriptive statistics. Table LABEL:table_LDA_summary shows that,
before adjusting for any confounding company characteristics via the double
machine learning approach, the average leverage ratio for companies with a
rating is nearly 16pps (32.9%-17.1%) higher than that for companies without a
rating. Thus, this figure would overstate the rating effect by 7pps, i.e., by
close to 80% above the value we estimated.

For a second robustness check, we employed different learner specifications
for $g_{0}$ and $m_{0}$. The effect estimates across the different model
alternatives are very consistent, as can be seen from table
LABEL:table_Res_General_Rating_Robust. A detailed description of the
alternative learner specifications and a discussion of the results are
provided in the appendix. Here, we simply remind readers of the “double
robustness” discussed in subsection 5.4: as long as one of the two nuisance
functions is accurately specified within the double machine learning
framework, the overall outcome for the causal parameter of interest is correct
[111].

Table 3: Results for the estimated causal effect $\theta$ on LDA of having or
not having a rating, according to alternative model (AM) specifications. “MM”
refers to the main model specification used throughout the paper. Please refer
to the appendix for details of the specifications for the different AMs.
Robustness check: alternative model specifications
---
Rating effect | MM | AM1 | AM2 | AM3 | AM4
on LDA | (RF/RF) | (DML2) | (LASSO/RF) | (Ridge/RF) | (Restr.)
$\theta$ (rating yes/no) | 0.0878 | 0.0878 | 0.0925 | 0.0935 | 0.0942
Std. error | 0.0021 | 0.0021 | 0.0023 | 0.0369 | 0.0021
t-value | 41.8 | 41.8 | 40.0 | 2.5 | 45.2
p-value | 0.000 | 0.000 | 0.000 | 0.011 | 0.000
Effect ($\theta$) vs. mean | 41% | 41% | 44% | 44% | 44%

####  6.3.2 Effect of rating by individual, granular rating category

In the above analysis of having a rating versus having no rating, we
implicitly assume that it does not matter which rating a company has: all
rating types represent the same “treatment” for leverage; because ratings are
opinions about credit risk, this implies that the type of opinion does not
matter. However, it is easy to argue that different ratings, i.e. different
opinions, may in reality represent different treatments, and thus, different
versions of the treatment exist. Put differently, our initial analysis may
suffer from incorrectly assuming that there are “no hidden variations of
treatments” [63] (pages 10-13). This is one of the assumptions included in the
“stable unit treatment value assumption” (SUTVA) [108], which provides a
fundamental framework for causal analysis ([59, 109, 97, 90, 99] or [38]).

We therefore sequentially investigate different levels of rating granularity.
The first two of these analyses are reported in the appendix: in the first, we
examine whether the rating effect differs between the two very broad
categories of “investment-grade” and “speculative-grade” (non-investment
grade, “junk bond”). In the second analysis, we look at whether the rating
effect differs by broad rating categories as defined by one to three letters
(such as AAA, AA, A, BBB). In the main body of this paper, we report the
effect estimates for the most granular rating categories, i.e., those that
include plus/minus notch qualifications (such as A+, A, and A-) within the
broad rating categories. To avoid confusion, we label the granular sub-
category ratings without a plus or minus sign as “straight” (e.g.
“AAstraight”) and the broad categories as “broad” (e.g. “AAbroad”). Taking AA
as an example, “AA+”, “AAstraight” and “AA-” ratings exist within the broad
category of AAbroad. At this level of detail, we simultaneously test 22
granular rating categories.

We note that moving from a single binary treatment variable to two or more
treatment variables requires some technical adaptations to ensure valid
statistical inference. The “multiplicity problem” is especially relevant in
our case: the possibility of falsely identifying an effect as “significant”
increases with the number of treatments tested. We therefore report multiplier
bootstrap (MB) standard errors and p-values, as well as, for comparison, the
corresponding Romano-Wolf (RoWo) and Bonferroni (Bonf) p-values to account for
simultaneous inference on multiple parameters. We discuss these different
methods briefly in the appendix.

Table LABEL:table_Res_Granular_Rating_Categories summarizes the effect
estimates for the 22 granular rating categories. For ease of direct comparison
and to assess the robustness of our results, we also include the effect
estimates from a less granular analysis based on the 10 “broad” rating
categories as “memo” in this table. As a reminder, these broad rating
categories are defined by one to three letters (such as AAA, AA, A, BBB)
without considering the plus and minus qualifications. Details from this broad
analysis are included in the appendix (see table
LABEL:table_Res_Broad_Rating_Categories).

We first compare results for the four rating categories without notch
qualifications. For AAA, the effect estimates from the granular versus the
broad analysis differ only at the fourth decimal place. The p-values are very
similar, too, albeit slightly higher for AAAstraight in the granular analysis
versus AAAbroad in the broad analysis. Intuitively, this should be expected
because we are simultaneously testing 22 treatment variables in the granular
versus only 10 in the broad analysis; thus, the risk of falsely identifying a
treatment effect as “non-zero” increases. The same characteristic generally
holds for the p-values of the other three rating categories without notch
qualifications (only the Romano-Wolf p-value for Dbroad is slightly higher
than for Dstraight). For CC, the effect estimates differ by approximately 1pp.
We consider this small difference to be reassuring. We again find very
consistent p-values, supporting in both cases the conclusion of a non-zero
treatment effect. For SD, the effect estimates are also very consistent. They
differ by 1pp and are both close to zero, with all p-values consistently
indicating that the null hypothesis should not be rejected. Finally, the
effect estimates for D differ by 1.5pps; however, both estimates are again
very close to zero and the p-values consistently indicate that the null
hypothesis of no treatment effect should not be rejected. In summary, we
interpret the very consistent results for these four rating categories without
notch qualifications as evidence supporting the robustness of our approach.

Next, we turn to the other six categories with notch qualifications. The
pattern of the estimated rating effect within AA follows the rating scale,
with AA+ displaying the largest (negative) effect. The coefficient estimate is
also consistently negative for all three granular AA-ratings. For AA+ and
AAstraight, the p-values are highly significant. However, AA- has the smallest
(negative) coefficient estimate and high p-values, indicating that the null
hypothesis of no rating effect should not be directly rejected (MB is still
slightly below 0.05, while RoWo at 0.24 and Bonferroni at 0.91 are clearly
above 0.05). This situation is consistent when considering the next rating
category, A+. A+ has a smaller (albeit still negative) effect estimate coupled
with higher p-values compared to AA-. The “disappearing” of a clear rating
effect as one moves from AAstraight to the subsequent rating categories AA-
and A+ thus appears to be gradual. Considering the p-values for A+, the null
hypothesis of no effect should definitely not be rejected for A+.

Similar to the transition from AA- to A+, the results for A- in conjunction
with those for BBB+ are consistent with the view that there is a gradual,
smooth change in effect across these granular rating categories. BBB+ also has
an effect estimate of approximately -1pp with p-values that are very similar
to those for A-. Within the broad BBB rating category, we observe the same
“concave” treatment heterogeneity as in the broad A category: the BBB+ and
BBB- coefficient estimates are negative, while the one for BBBbroad in the
middle of the category is positive, or more precisely, very close to zero with
p-values that suggest non-rejection of the null hypothesis. A possible ad-hoc
interpretation for this phenomenon is that BBB+ companies may try to achieve
at least A- status to benefit from the “better letter”.121212For instance, the
European Banking Authority (EBA) maintains mapping tables that match ratings
to certain rules and requirements, such as regulatory capital rules. In this
context, AAA and AA are within the same “credit quality steps” (1), whereas A
(2), BBB (3), BB (4), and B (5) are each in different step categories. From
CCC downward, no distinction applies, and all categories are summarized in
credit quality step 6. Thus, A and BBB ratings have different implications in
this context, even though both are investment-grade ratings [41]. On the other
side of the spectrum, companies rated BBB- and thus at risk of a downgrade
from BBB to BB may preemptively take actions that also lead to lower leverage.
The distinction between BBB and BB is particularly important because this
represents the dividing line between investment- and speculative-grade ratings
with the corresponding economic implications (see section 3). Nevertheless, we
strongly caution against overinterpreting these findings and qualify our ad-
hoc interpretation as speculative. While it is true that both the A and BBB
categories display concavity, their neighboring categories AA, BB and B do
not. This is in line with the findings from [69] discussed in the literature
review in section 4, which show that the general effects attributed to
plus/minus ratings stem from specific sub-samples of low-rated firms. In
particular, [69] find these effects only in the B category - a category in
which we do not find these effects. Thus, the concept of a general plus/minus
rating effect remains doubtful.

Within the BB and B rating categories, the pattern of the estimated effects
follows the rating scale, with BB+ displaying the smallest (positive) effect
and B- the largest. The coefficient estimates are consistently positive for
all granular ratings within these two categories, and the p-values are
generally highly significant; even for BB+, the multiplier bootstrap p-value
is below 0.01. Here, we highlight two points. First, the granular analysis
refines our understanding of the boundary regarding rating impact. While the
analysis based on 10 broad rating categories (reported in the appendix)
identifies the first inflection point of the treatment effect between BBBbroad
and BBbroad, marking the transition from investment- to speculative-grade
ratings, the granular analysis within the BBbroad-category reveals a more
gradual rise; starting at approximately 1% for BB+, moving to 2% for
BBstraight, and peaking at 6% for BB-. Second, and in contrast to what we have
just described for the BB rating category, the effect estimates within the B
rating category are all consistently above 10%. In particular, the increase
from BB- to B+ is immediate and not gradual. Taking these two observations
together, we hypothesize that companies that are still very close to an
investment-grade rating have lower leverage, potentially in anticipation of
regaining investment-grade status. Those that are much farther away and thus
probably not anticipating an upgrade have markedly higher leverage. The fact
that the differences in rating effects between the categories B and CCC are
small provides additional support for this hypothesis (approximately 13% for
both Bbroad and CCCbroad).

Finally, in the CCC category, the rating effects are similar for all notch
categories, leading to a highly significant overall CCCbroad effect of close
to 13%. Of note, the sample size for company-years in this category is limited
with only 148 observations, of which the majority (107) are concentrated in
CCC+.

Table 4: Estimated causal effects on leverage by granular rating category
(i.e., split by the plus and minus notch qualifications within a broad
category) versus the baseline of having no rating. “Straight” indicates the
categories in between the plus and minus notches; pro memoria (“memo:”) and
for ease of comparison, effect estimates from the broad rating analysis
summarized in table LABEL:table_Res_Broad_Rating_Categories in the appendix
have been added in this table as “broad”. The rating categories “AAA”, “CC”,
“SD” and “‘D” do not have notch qualifications. The rating category C is
absent because no firm-year had such a rating over the sample period. The
empirical design (6.1), data (6.2), and random forest characteristics (6.3.1)
are described in the main text. Standard errors and corresponding p-values are
corrected for simultaneous multiple inference: “MB” refers to the multiplier
bootstrapping method, “RoWo” to the Romano-Wolf procedure, and “Bonf” to the
Bonferroni-correction. “Observations” refers to the number of company-years
from 2005 to 2015. “% of total” represents the share of observations of each
rating category relative to all company-year observations. Values in this
column are displayed as %. Granular rating categories
---
Rating effect | Coef. | MB | MB | RoWo | Bonf | Obser- | % of
(on LDA) | estim. | Std. error | p-val. | p-val. | p-val. | vations | total
$\theta^{AAA\ straight}$ | -0.0588 | 0.0191 | 0.002 | 0.020 | 0.046 | 86 | 0.1
memo: $\theta^{AAA\ broad}$ | -0.0582 | 0.0189 | 0.002 | 0.015 | 0.021 | 86 | 0.1
$\theta^{AA+}$ | -0.0683 | 0.0183 | 0.000 | 0.003 | 0.004 | 26 | 0.0
$\theta^{AA\ straight}$ | -0.0547 | 0.0098 | 0.000 | 0.000 | 0.000 | 151 | 0.3
$\theta^{AA-}$ | -0.0169 | 0.0083 | 0.041 | 0.243 | 0.911 | 214 | 0.4
memo: $\theta^{AA\ broad}$ | -0.0385 | 0.0068 | 0.000 | 0.000 | 0.000 | 391 | 0.7
$\theta^{A+}$ | -0.0060 | 0.0051 | 0.242 | 0.663 | 1.000 | 433 | 0.7
$\theta^{A\ straight}$ | 0.0086 | 0.0041 | 0.035 | 0.244 | 0.761 | 906 | 1.6
$\theta^{A-}$ | -0.0115 | 0.0033 | 0.000 | 0.007 | 0.009 | 1’119 | 1.9
memo: $\theta^{A\ broad}$ | 0.0001 | 0.0027 | 0.956 | 0.950 | 1.000 | 2’458 | 4.3
$\theta^{BBB+}$ | -0.0106 | 0.0028 | 0.000 | 0.002 | 0.003 | 1’589 | 2.7
$\theta^{BBB\ straight}$ | 0.0019 | 0.0026 | 0.463 | 0.759 | 1.000 | 2’105 | 3.6
$\theta^{BBB-}$ | -0.0105 | 0.0031 | 0.001 | 0.010 | 0.016 | 1’480 | 2.6
memo: $\theta^{BBB\ broad}$ | -0.0009 | 0.0021 | 0.677 | 0.942 | 1.000 | 5’174 | 8.9
$\theta^{BB+}$ | 0.0110 | 0.0042 | 0.009 | 0.063 | 0.191 | 946 | 1.6
$\theta^{BB\ straight}$ | 0.0235 | 0.0036 | 0.000 | 0.000 | 0.000 | 1’248 | 2.2
$\theta^{BB-}$ | 0.0568 | 0.0036 | 0.000 | 0.000 | 0.000 | 1’538 | 2.7
memo: $\theta^{BB\ broad}$ | 0.0512 | 0.0024 | 0.000 | 0.000 | 0.000 | 3’732 | 6.5
$\theta^{B+}$ | 0.1010 | 0.0041 | 0.000 | 0.000 | 0.000 | 1’413 | 2.5
$\theta^{B\ straight}$ | 0.1069 | 0.0048 | 0.000 | 0.000 | 0.000 | 1’124 | 1.9
$\theta^{B-}$ | 0.1128 | 0.0079 | 0.000 | 0.000 | 0.000 | 444 | 0.8
memo: $\theta^{B\ broad}$ | 0.1301 | 0.0031 | 0.000 | 0.000 | 0.000 | 2’981 | 5.2
$\theta^{CCC+}$ | 0.1034 | 0.0160 | 0.000 | 0.000 | 0.000 | 107 | 0.2
$\theta^{CCC\ straight}$ | 0.1497 | 0.0345 | 0.000 | 0.000 | 0.000 | 32 | 0.1
$\theta^{CCC-}$ | 0.1108 | 0.0595 | 0.062 | 0.269 | 1.000 | 9 | 0.0
memo: $\theta^{CCC\ broad}$ | 0.1284 | 0.0144 | 0.000 | 0.000 | 0.000 | 148 | 0.3
$\theta^{CC\ straight}$ | 0.1367 | 0.0437 | 0.002 | 0.020 | 0.040 | 15 | 0.0
memo: $\theta^{CC\ broad}$ | 0.1471 | 0.0044 | 0.001 | 0.004 | 0.008 | 15 | 0.0
$\theta^{SD\ straight}$ | 0.0482 | 0.0553 | 0.383 | 0.759 | 1.000 | 4 | 0.0
memo: $\theta^{SD\ broad}$ | 0.0597 | 0.0531 | 0.261 | 0.689 | 1.000 | 4 | 0.0
$\theta^{D\ straight}$ | 0.0291 | 0.0289 | 0.920 | 0.917 | 1.000 | 41 | 0.1
memo: $\theta^{D\ broad}$ | 0.0141 | 0.0294 | 0.632 | 0.942 | 1.000 | 41 | 0.1
Total ratings | - | - | - | - | - | 15’030 | 26.0
No rating | - | - | - | - | - | 42’802 | 74.0
Grand total | - | - | - | - | - | 57’832 | 100.0

Having presented the individual effect estimates for the granular ratings, we
now conclude our analysis by taking a holistic view of the pattern of the
effects across the full spectrum of 22 granular ratings. Figure 1 provides
this visual summary. Initially, for the highest rating categories, the effect
estimates are negative, ranging from -5% to -7%. Values for the middle rating
categories hover around what can be seen as neutral to small effects, from -2%
to +2%. Finally, from BB- onward, the effect estimates become significantly
positive and reach double-digit values throughout the B+ to CC categories.
CCC- stands out somewhat because its effect is smaller than those of
CCCstraight and CCstraight and its MB p-value reaches 0.062. However, there
are only nine company-year observations in this particular class.

Figure 1: Graphical representation of table
LABEL:table_Res_Granular_Rating_Categories illustrating the heterogeneity of
the treatment effect estimates for the 22 granular rating categories (gray
bars). The numbers have been rounded to two decimal places. For instance,
-0.07 for AA+ corresponds to -0.0683 in table
LABEL:table_Res_Granular_Rating_Categories and indicates that the leverage for
the granular rating category AA+ is roughly 7pps lower. The values next to the
black crosses indicate the respective multiplier bootstrap (MB) p-values
(rounded to three decimal places). The position of the black crosses has been
selected to provide an intuition about the magnitude of the p-values. Note
that for ease of reading, we have not added ”straight” to the rating category
labels that do not have a plus/minus notch qualification.

In summary, our analysis of granular rating categories yields three important
insights. First, treatment effects are heterogeneous across the rating
spectrum. Second, they follow a distinct pattern along the rating scale, with
initially negative effects on leverage for the highest rating categories, no
or very limited effects for the middle rating categories and large positive
effects towards the lower end of the rating scale. For the two default
categories at the very end of the rating scale, the effect vanishes. Third,
the transition from no/very limited effects to clearly positive effects does
not precisely coincide with the boundary between investment- and speculative-
grade ratings, as the results from the broad analysis would suggest. Rather,
it occurs gradually over the granular ratings within the two categories BBB
and BB, which represent the boundary between investment- and speculative-grade
ratings.

Before closing the empirical section of our article, we report highly
summarized results from two further robustness checks. The appendix contains
full details for each of these analyses. First, we apply our analytical
approach to a data sample from a different time frame. Second, we partially
loosen the restriction of interest-related expense categories from the income
statement. We had initially excluded these items to prevent the random forest
learners from “back-calculating” the leverage ratio. Because interest coverage
is believed to be a decisive factor for credit ratings ([74], pages 645-650),
we will include this metric as a covariate.

####  6.3.3 Rating effects in a different sample period

For this robustness check, we consider a second data sample from a different
time period. Employing double machine learning with the same analytical
methodology and data sources described in subsections 6.1, 6.2, and 6.3.1, we
use data from the years 2000 to 2004 to arrive at a sample of 32’162 company-
year observations.

Table LABEL:table_Res_General_Rating_11vs5years compares the results of our
main analysis (as per table LABEL:table_Res_General_Rating) in the left column
with the results from the second sample period in the right column. The rating
effect estimate amounts to 9.6pps, which is 0.8pps higher than the parameter
estimate of 8.8pps from the main sample. Compared to the mean leverage of the
sample, this corresponds to an impact of 43% versus 41% from the main sample.
Again, the rating effect is highly significant, both statistically and
economically. We interpret this result as further evidence in support of the
presence of a rating effect.

Similarly, the results from the second sample period support the results from
the main analysis for the broadest down to the most granular rating
categories. Full details are provided in the appendix. We restrict ourselves
here in the main text to plotting the effect estimates from the main analysis
next to those from the second data sample for the granular rating categories
(figure 2). The similarity of the shapes from the main and the second data
sample is compelling.

Table 5: Comparison of results for the estimated causal effect $\theta$ on leverage (LDA) of having or not having a rating for the main data sample from 2005 to 2015 with 57’832 company-year observations compared to a second, different data sample for the years 2000 to 2004 with 32’162 company-year observations. The methodology for the second data sample is the same as for the main one (as described in previous sections), including aggregation of parameter estimates and standard errors over a five-fold split with two repetitions. Rating effect | 2005-2015 | 2000-2004
---|---|---
on leverage (LDA) | n=57’832 | n=32’162
$\theta$ (rating yes/no) | 0.0878 | 0.0962
Std. error | 0.0021 | 0.0029
t-value | 41.8 | 32.9
p-value | 0.000 | 0.000
Memo: mean leverage | 0.212 | 0.224
Rating effect ($\theta$) vs. mean | 41% | 43%
Figure 2: Graphical comparison of the results for the 2005-2015 period from
the main analysis (dark gray bars) in this paper with the results from the
2000-2004 period (light gray bars) used as a robustness check for the “effect
shape” of the 22 granular rating categories. Effect estimates have been
rounded to two decimal places. Values below the x-axis indicate negative
values (e.g., -0.0043 displayed as 0.00 for BBB+ in the 2000-2004 sample). For
ease of reading, the chart does not repeat the respective multiplier bootstrap
(MB) p-values (already displayed in previous charts). Moreover, we have not
added “straight” to the rating category labels that do not have a plus/minus
notch qualification.

####  6.3.4 Rating effects when including interest coverage as a covariate

As described in subsection 6.2, we excluded data items that would allow the
random forest to back-calculate total debt or equity. However, we still want
to verify that the rating effect estimates hold when including selected items
that determine credit ratings (or are at least strongly believed to do so).
[74] (pages 645-650) explain that “credit ratings are primarily related to two
financial indicators” (page 647). One of these is size, which we have already
included via items such as the logarithm of sales, the logarithm of assets or
the number of employees in our set of covariates. The second is coverage,
which measures “a company’s ability to comply with its debt service
obligations” (page 648). We therefore include interest coverage ($IntCov$) as
defined in [74] (Exhibit 33.8, left panel, page 649):

$\displaystyle IntCov_{i,t}=\textit{EBITDA}_{i,t}/\textit{Interest
expenses}_{i,t}$ (6.5)

where $EBITDA$ represents earnings before interest, taxes, depreciation and
amortization and $interest$ $expenses$ represents the expenses for servicing a
company’s total financial debt.131313In Compustat, this is the item with code
“xint” (“Interest and Related Expense - Total”).

We use our empirical sample as described in subsection 6.2 and remove company-
years with interest expenses of less than USD ten thousand in a given year and
arrive at 48’585 company-year observations. We make no change to the double
machine learning model described in subsections 6.1 and 6.3.1. Table
LABEL:table_Res_General_Rating_IntCov compares the results for the estimate of
the general rating effect from our main analysis (as per table
LABEL:table_Res_General_Rating) with those from the approach in this
subsection, which includes interest coverage (“IntCov”) as a feature in the
set of covariates. The effect estimate amounts to approximately 7pps including
IntCov, or 29% versus the sample mean leverage of roughly 25%. This effect
estimate is 1.5pps lower than the one from the main analysis, which translates
into a drop of 10pps in the relative effect magnitude versus the mean leverage
(29% versus 41% in the main analysis). Nevertheless, the rating effect remains
clearly present.

Table 6: Comparison of results for the estimated causal effect $\theta$ on leverage (LDA) of having or not having a rating, depending on whether interest coverage (“IntCov”) as defined in equation 6.5 is excluded or included in the set X of covariates as per equations 6.1 and 6.2. The general methodology for “Incl. IntCov” is the same as for the main model used throughout this paper (“Excl. IntCov”, as described in previous sections), including aggregation of parameter estimates and standard errors over a five-fold split with two repetitions. Rating effect | Excl. IntCov | Incl. IntCov
---|---|---
on leverage (LDA) | n=57’832 | n=48’585
$\theta$ (rating yes/no) | 0.0878 | 0.0731
Std. error | 0.0021 | 0.0021
t-value | 41.8 | 35.3
p-value | 0.000 | 0.000
Memo: mean leverage | 0.212 | 0.249
Rating effect ($\theta$) vs. mean | 41% | 29%

Similarly, the results from the analyses including interest coverage support
the results from the main analysis for the broadest down to the most granular
rating categories. Full details are provided in the appendix. We provide here
in the main section the graphical comparison of results for the granular
rating categories in figure 3; the figure displaying the effect estimates
together with the corresponding multiplier bootstrap p-values is located in
the appendix. As can be seen, the results including interest coverage are very
similar to those from the main analysis without interest coverage, both in
terms of magnitude and overall shape. In particular, we also see the gradual
rise in effect size over the notch-ratings within the BBB and BB rating
classes, which supports our previous finding that there is no abrupt divide in
effect between investment-grade and speculative-grade ratings.

Figure 3: Graphical comparison for the effect estimate of the 22 granular
rating categories on leverage (LDA) including “IntCov” as a covariate feature
(light gray bars) versus the results from the main analyses of this paper, in
which “IntCov” was not included (dark gray bars). Effect estimates have been
rounded to two decimal places. Values below (above) the x-axis indicate a
negative (positive) effect (e.g., for BBB incl. IntCov, the effect estimate is
-0.0002, while it is +0.0019 for BBB excl. IntCov; both are displayed as 0.00
in the figure). Note that for ease of reading, we have not added “broad” to
the rating category labels.

In summary, our robustness checks reinforce our three main conclusions
regarding the effects of credit ratings on leverage: first, ratings affect the
leverage ratio. Second, this effect is heterogeneous and depends on the rating
category. Third, the change in effect size is gradual across the individual,
granular categories within BBB and BB and thus does not occur abruptly at the
boundary between investment- and speculative-grade ratings.

##  7 Conclusion

To date, the literature has not provided a definitive explanation for why
individual companies choose particular capital structures. In the absence of a
consensus model and considering the large number of potential influencing
factors, we employed double machine learning to investigate the causal effect
of credit ratings on leverage. This approach allowed us to use random forests,
which are highly flexible models capable of discerning the relationship
between company characteristics, leverage, and ratings from the data, without
the need for assuming linear relationships, pre-selecting a limited set of
variables, or undertaking extensive feature engineering. We were able to
perform valid inference and to estimate the heterogeneity of the treatment
effect using machine learning methods that, without double machine learning,
would have led to bias in the estimated coefficients. As a result, we were
able to document for our empirical sample three important facts about the
effect of ratings on leverage.

First, ratings have a causal effect on the leverage ratio. Holding all else
equal, having a rating increases the book leverage ratio by approximately 7 to
9 percentage points, or roughly 30% to 40% compared to the mean leverage ratio
of our sample. However, this effect exhibits a significant degree of
heterogeneity, captured in our second finding. To use colorful language,
consider a cocktail bar where drinks have an average alcohol content of 9%;
one could remain completely sober or get completely drunk from just one drink
depending on what one is served. Applying this analogy to our context, the
impact of ratings on leverage varies significantly across different rating
categories. For the two highest categories, AAA and AA, the rating effect is
negative, leading to lower leverage. For the next two categories, A and BBB,
the effect is approximately zero. However, beginning with BB, the effect turns
distinctly positive, leading to higher leverage, and then stays high or
increases even further for the last three non-default categories B, CCC, and
CC. Third, and in contrast to what the second point would seem to suggest at
first glance, the transition in the direction of the effect is gradual over
the individual, granular categories within the broad categories of BBB and BB,
and especially over straight BBB, BBB-, BB+, and straight BB. Thus, the shift
from no effect to a positive effect does not occur abruptly at the boundary
between investment- and speculative-grade ratings.

Several different robustness tests corroborate these findings. Nevertheless,
as with most empirical research, our work has a number of limitations, each of
which we see as a potential area for complementary and future study. First,
our empirical data could be enriched in various ways. Obvious dimensions would
be longer or different time periods and additional covariates, including
metrics related to environmental, social, and governance (ESG) criteria, or
company officer characteristics. Second, an interesting next step would be to
understand the mechanisms underlying the relationship between different
ratings and different capital structures: Why do different ratings lead to
different leverage ratios? Third, expectations about the future often play an
important role in economics. As noted by [87] (page 123): “[I]n business,
there is usually no before, during, or after.” Thus, it is highly likely that
ratings are influenced by expectations about company characteristics,
including the leverage ratio itself. Disentangling the effect of expectations
on the relationship between ratings and leverage represents another formidable
research challenge.

[54] (page 8) advise that we sometimes need to refrain from devising
“extremely elegant theories, and instead embrace complexity and make use of
the best ally we have: the unreasonable effectiveness of data.” We hope that
our paper, with double machine learning and data as our allies, has
illuminated the heterogeneous effects of credit ratings on leverage.

##  8 Appendix

In this appendix, we provide additional information pertaining to the main
part of our paper. We begin with an addition to the literature review from the
main section and discuss leverage and rating studies that used machine
learning methods. We then provide an overview of double machine learning which
is more extended than the one in the main paper. For the empirical part, we
provide the full list of covariates used in our analyses, the specifications
of the learner functions for the main model as well as the specifications for
the alternative models used for robustness checks. The appendix also contains
the analyses of the rating effect on leverage at two levels of granularity not
reported for sake of brevity in the main part of the paper. First, the rating
effect split by investment- and speculative-grade rating and second, the
effect by individual broad rating category. Finally, we present here also the
details of two further robustness checks: results from a different sample
period and results including interest coverage as an additional covariate.

###  8.1 Literature review: machine learning-based leverage and rating studies

As indicated in sections 2 and 3 in the main text, machine learning methods
are very flexible to adapt to complex, non-linear patterns. Additionally, they
can handle data that do not follow well-behaved distributions (such as the
normal or at least symmetrical distributions) and can cope with
multicollinearity between covariates [24].

In the context of forecasting credit ratings, machine learning first appeared
in the computer science literature (e.g., [49] and [76] with neural networks
or [62] with support vector machines) rather than in economic research
publications [84]. We hypothesize that one contributing factor is the fact
that the primary objective of machine learning methods has been to maximize
predictive performance, and not to identify causal patterns [8, 111], while
“[t]he goal of most empirical studies in economics and other social sciences
is to determine whether a change in one variable […] causes a change in
another variable” [118] (page 3). For instance, [70] suggest in their recent
review of machine learning-based corporate default predictions that models
should be able to suggest the cause(s) of default in order to increase their
usefulness.

Still, machine learning models have the advantage that they can easily
incorporate large numbers of financial covariates (predictive variables,
features). For instance, [114] use 27 covariates in their credit rating study
and [50] find that their models perform better when the full set is provided
as input and the various neural networks themselves perform feature selection
in the training process. Indeed, the selection of the relevant covariates, and
thus the resulting model, is data-driven with machine learning algorithms.
“This approach contrasts with economics, where (in principle, though rarely in
reality) the researcher picks a model based on principles and estimates it
once” [8] (page 508). Given the absence of a predominant capital structure
theory and the fact that different theories “lead to such different, an in
some ways diametrically opposed, decisions and outcomes” [14] (page 8), this
feature of machine learning appears especially attractive for analyzing
leverage ratios.

Also, the predictive power of machine learning models is generally strong. For
instance, [114] (Table 2, page 194) find in their comparison of model accuracy
for a large set of S&P 500 company ratings that random forests and support
vector models improve prediction accuracy by two to three percentage points
versus linear discriminant analysis, the best-performing non-machine learning
method. The improvements in prediction accuracy by machine learning versus
benchmark statistical methods (predominantly logistic regression and multiple
discriminant analysis) in the rating studies listed by [62] (Table 1, page
547) are even higher, surpassing ten percentage points in several instances.

[4] is a recent paper comparing non-linear machine learning models with linear
models to predict leverage one year in advance. Out of six different models,
the random forest performs best to predict the leverage and improves out-of-
sample $R^{2}$ by 16 percentage points compared to standard linear models,
with an $R^{2}$ for the random forest of 56% versus 40% for linear approaches
([4], Table 2, page 11). The models rely on 34 covariates as input, of which
eight are dummy variables. [4] (page 2) thus “challenge the conventional
wisdom that the standard set of firm and macroeconomic determinants has
limited ability to explain firms’ leverage choices.”

We highlight that none of the eight dummy variables figures among the key
determinants of leverage in the best performing models (random forest and
gradient boosting). Specifically, the binary “debt rating” dummy separating
very low and unrated companies from the others has one of the lowest measures
of variable importance [4] (Figure 3, page 12). We hypothesize that since both
the z-score as a measure of bankruptcy probability [1, 2] and the rating dummy
attempt to measure the general construct of “the ability to meet debt
obligations” (see section 3), the information contained in both covariates is
highly overlapping and thus, the random forest and the gradient boosting
machine selectively use only the one with the higher predictive power.
However, from this observation, we obviously can “merely make associational
claims” [93] (page 2). We cannot make a causal statement which of these two
factors causes leverage (if at all), as opposed to merely predicting it (for
an example of using machine learning for forecasting (prediction) versus
planning (causation) in the corporate finance function, see for instance
[115]).

Finally, even when [4] augment linear models with common non-linear
transformations of the input variables (e.g., squared or cubed values) as well
as a full set of interaction effects between the covariates, the random forest
(excl. transformed and interaction covariates) continues to predict leverage
significantly better ([4], internet appendix, Table A4, page 8). Additionally,
the authors find in untabulated results that the predictive performance of the
random forest does not improve when interaction terms are included. In
summary, out of the machine learning toolbox, random forests appear to be a
very powerful tool, requiring only limited feature pre-selection or feature
engineering.

###  8.2 Double Machine Learning

We have seen from the sections in the main text that there is no general
consensus regarding the determinants of leverage and how they interact at the
company level. Nevertheless, it is likely that many factors play a role and
the mechanisms by which they influence capital structure are complex. Given
the lack of a strong theoretical framework, isolating the causal effect of
credit ratings poses a formidable challenge. Additionally, we need to consider
that this effect may be heterogeneous. Double machine learning [33, 34, 17,
18] is a recently developed methodology that can help solve questions of
causal inference in such settings by harnessing what [54] calls “the
unreasonable effectiveness of data.” Among the key advantages of double
machine learning are the following characteristics. First, there is the
ability to handle high feature dimensionality, i.e., the presence of many
potential influencing factors in addition to the treatment variable of
interest, and to provide valid inference on treatment effects in such high-
dimensional, complex data environments. Second, it employs a data-driven
approach to select among these influencing factors. Third, it facilitates the
use of various machine learning algorithms with flexible function-fitting
capabilities. Fourth, there is double-robustness with respect to nuisance
functions. “Partialling-out”, “Neyman orthogonality” and “cross-fitting” are
three important concepts enabling the “doubly robust” double machine learning
approach. We will discuss each of these terms in this section.

####  8.2.1 Partialling-out

Double machine learning builds on the concept of Frisch-Waugh-Lovell (FWL)
“partialling out” [81, 37]. According to the FWL theorem, a parameter of
interest $\theta$ in a linear model such as:

$\displaystyle Y=\theta D+\beta X+\epsilon$ (8.1)

with $\mathbb{E}(\mathcal{\epsilon}|D,X)=0$

can be estimated with linear regression, using e.g., ordinary least squares,
in either of two ways. Under the first approach, $\theta$ can be directly
estimated by regressing $Y$ on $D$ and $X$. Under the second approach,
$\theta$ is determined in the last step of a three-step procedure: first, $Y$
is regressed on $X$, and the corresponding residuals $\epsilon_{Y}$ are
determined. Second, $D$ is regressed on $X$ and again, the corresponding
residuals $\epsilon_{D}$ are determined. Third, the residuals $\epsilon_{Y}$
from the first step are regressed on the residuals $\epsilon_{D}$ from the
second step. The regression coefficient from this third step corresponds to
$\theta$, the parameter of interest. Both approaches will yield the same
estimate for $\theta$. Throughout this paper, we will continue to use the term
“partialling-out” for the second approach, which is usually employed in the
economics literature. “Residualization” represents another term for the same
technique [111] (pages 219-220).

It would be convenient if machine learning methods could be used instead of
OLS-based linear regression to determine $\theta$. Machine learning has
traditionally emphasized predictive performance, and principally predictive
performance on the validation (hold-out) data sample, which is intentionally
not used for model estimation. Machine learning thus represents the
“algorithmic modeling culture” described by [28] and comes with several
advantages. These include a high flexibility with respect to the model choice
and design. Many machine learning methods do not impose strong assumptions on
the functional forms, but learn those from the data. This constitutes a
valuable safeguard against incorrect model specifications, which also lead to
biased parameter estimates, even if there are no unmeasured confounding
variables. This quality is particularity useful for the empirical analysis in
this paper, because, as we described in section 2, no consensus about a
unifying model for capital structure exists. Additionally, most machine
learning algorithms allow us to rely on a largely “automatic”, data-driven
variable selection process. Again, this is a welcome feature in the absence of
a consensus model and the presence of many potentially influencing factors.
Finally, with the data-driven variable selection approach, machine learning
methods are able to handle high-dimensional settings, in which the number of
potential predictive variables is large compared to the number of
observations. We refer interested readers to the vast literature in this
context, for instance [56, 65, 111] or [91].

The downside of this focus on predictive performance is that inference on the
model parameters, the core of causal inference, is generally not possible with
machine learning methods. Yet, empirical research in many domains, including
economics, is predominantly concerned with causal questions [118, 8], and
e.g., [98] sees the general inability of machine learning methods to uncover
causal relationships as a fundamental obstacle to further expand their
applications. In particular, machine learning methods generally produce biased
parameter estimates. The bias stems from the fact that machine learning
methods use regularization penalties in their data-driven variable selection
procedure. The intuition behind this regularization bias is that the parameter
estimates for covariates that are highly correlated with the treatment
variable will get severely “shrunk” versus their true value (e.g., in the case
of Ridge regression) or even set to zero (e.g., for LASSO), because the
treatment variable by itself has sufficient predictive power. Correspondingly,
the parameter value of the treatment variable will get inflated, because it
will incorporate the effect of correlated covariates. Of course, the reverse
situation with inflated covariate parameters and a significantly shrunk or
even zero treatment parameter is also possible. This is the reason that
machine learning methods cannot be used to “directly” estimate equation 8.1 as
per the first approach described above. Such a “naive approach” [18] (page 36)
incurs a high risk of yielding a severely biased estimator for the treatment
parameter [17, 18, 115].

However, machine learning methods can be employed following the second
approach, i.e. by partialling-out. This leads to the double machine learning
approach for causal analysis. For this approach, Neyman orthogonality plays an
central role which we will detail in the next subsection.

####  8.2.2 Neyman orthogonality

Following the general outline of [9], we illustrate the approach using a
“partially linear regression” model [102, 55], which we will also employ in
our empirical analysis in section 6. The usual form of a partially linear
regression model is:

$\displaystyle Y=\theta_{0}D+g_{0}(X)+\zeta$ (8.2)

with $\mathbb{E}(\mathcal{\zeta}|D,X)=0$

and

$\displaystyle D=m_{0}(X)+\mathcal{V}$ (8.3)

with $\mathbb{E}(\mathcal{V}|X)=0$,

where $Y$ is the outcome variable, $D$ is the treatment (policy) variable of
interest, and $X$ is a (potentially high-dimensional) vector of confounding
covariates. $\mathcal{\zeta}$ and $\mathcal{V}$ are error terms. The
regression coefficient $\theta_{0}$ is the parameter of interest. We can
interpret $\theta_{0}$ as a causal parameter, i.e. the causal effect of
treatment $D$ on outcome $Y$, if $D$ is “as good as randomly assigned” [38]
(page 73) conditional on the covariates X and thus, D is exogenous
conditionally on X. Of course, the other standard assumptions of causal
inference need to hold as well, for instance consistency, conditional
exchangeability, and positivity [58].

Applying the partialling-out procedure on equations 8.2 and 8.3 removes both
the confounding effect of X and the regularization bias141414More precisely,
the first-order effect of the regularization bias is removed. Removing the
first-order effect is usually enough to produce a high-quality, low-bias
estimator for the parameter of interest [9]. [82] expand this to k-th order
orthogonality but show that for partially linear regressions (as employed in
our empirical analysis in section 6), first-order orthogonality is the limit
of robustness when treatment residuals are normally distributed. introduced by
a machine learning method with a penalty or regularization mechanism [34].
Within the partialling-out procedure, cross-validation remains required for
the determination of the residuals to avoid bias from overfitting.

Technically, a method-of-moment estimator for the parameter of interest
$\theta_{0}$ is employed:

$\displaystyle\mathbb{E}[\mathcal{\psi}(W;\theta_{0},\eta_{0})]=0$ (8.4)

where $\psi$ represents the score function, $W=(Y,D,X)$ is the set (data
triplet) of outcome, treatment, and confounding variables, $\theta_{0}$ is the
parameter of interest as already indicated above and $\eta_{0}$ are nuisance
functions (for instance, $g_{0}$ and $m_{0}$, which we will employ later in
our empirical application).

For the double machine learning inference procedure, the score function
$\psi(W;\theta_{0},\eta_{0})$ from equation 8.4 (with $\theta_{0}$ as the
unique solution) needs to satisfy the Neyman orthogonality [94, 20] condition:

$\displaystyle\partial_{\eta}\mathbb{E}[\mathcal{\psi}(W;\theta_{0},\eta)]|_{\eta=\eta_{0}}=0,$
(8.5)

where the derivative $\partial_{\eta}$ denotes the pathwise Gateaux derivative
operator. Intuitively, Neyman orthogonality in equation 8.5 ensures that the
moment condition $\psi(W;\theta_{0},\eta_{0})$ from equation 8.4 is
insensitive to small errors151515Technically, this concerns the “speed” of the
convergence rates. We refer interested readers to [34]. in the estimation of
the nuisance function $\eta$ (around its “true” full population value
$\eta_{0}$). Thus, it removes the bias arising from using a machine learning
based estimator for $\eta_{0}$. As a further consequence, Neyman orthogonality
ensures “adaptivity” of the estimator for $\theta_{0}$: its approximate
distribution does not depend on the fact that the machine learning based
estimate for $\eta_{0}$ contains errors, if the latter are “mild” (as
described in [34]).

####  8.2.3 Cross-fitting

A second point to consider is that machine learning methods usually rely on
sample splitting in order to avoid bias introduced by overfitting. Overfitting
occurs when models follow the data that they are trained on “too closely”,
thus picking up not only the true underlying pattern, but also the noise
contained in the (sample) data. The more complex and flexible a model, the
higher the risk for this behavior [65, 56]. Thus, as mentioned previously,
machine learning typically divides the data into two distinct sub-sets: one
training data set, used to determine the model, and one validation (hold-out)
data set to evaluate the model (but not used to train the model). A similar
data splitting methodology applies in the case of a partially linear model
with two nuisance functions as described in equations 8.2 and 8.3. Only one
part of the data is used to estimate the nuisance functions which are
partialled-out, while the other part of the data is used to estimate the
parameter of interest (i.e., the treatment effect). Of course, such a limited
use of the data implies a loss of efficiency. To overcome this efficiency loss
due to the necessary data splitting, double machine learning employs a
technique called “cross-fitting” [34] (page C6).

Under cross-fitting, the roles of the two data sets are swapped and two
estimates for the parameter of interest are obtained. Since these two
estimators are approximately independent, they can simply be averaged to make
use of the full data set [34] (Figure 2, page C7). The cross-fitting procedure
can be expanded beyond two data sets into a K-fold version to further increase
robustness; [9] (page 13) reports that four to five folds appear to work well
in practice. Furthermore, the cross-fitting procedure can be repeated to
enhance robustness of the estimator with respect to potential effects of a
particular random split of the data in the K-folds. While the specific sample
partition has no impact on results asymptotically [34] (page C30), it is
recommended in practice to repeat the estimation procedure [9] (page 13).

####  8.2.4 Double robustness

“Double Machine Learning” derives its name from the fact that machine learning
methods are used to estimate both equation 8.2 and equation 8.3. However, the
estimated treatment effect is also “doubly robust” thanks to the partialling-
out procedure described previously. This means that potential “mistakes in
either of the two prediction problems” [111] (page 221) (i.e., equations 8.2
or 8.3) do not invalidate the effect estimate as long as at least one of these
two is sufficiently well estimated. In other words, while it is necessary to
“to do a good job on at least one of these two prediction problems” [111]
(page 221), it does not matter on which one. While we caution practitioners
against interpreting this as an invitation to careless model specifications,
we believe that this represents another attractive property of double machine
learning whenever doubts about the precise model characteristics persist. [18]
(page 34) remarks: “Because model selection mistakes seem inevitable in
realistic settings, it is important to develop inference procedures that are
robust to such mistakes.”

Finally, a general robustness of double machine learning with respect to the
particular machine learning (ML) algorithm that is employed has been observed.
For instance, [34] (page C45) comment on their empirical results that “the
choice of the ML method used in estimating nuisance functions does not
substantively change the conclusions.“ Of course, the machine learning methods
employed need to be of sufficient quality for the problem at hand. Considering
the large choice of machine learning models, this is typically not an
important hurdle, and even ensemble models are suitable [34] (pages C22-C23).

###  8.3 Covariates

Tables LABEL:table_Covariates_Financials_Overview and
LABEL:table_Covariates_Dummies_Overview provide an overview of the 1’840
covariates (features) used throughout the empirical analysis. The vector X in
equations 6.1 and 6.2 is composed of these variables. In addition to the
variables displayed in the two tables, only two variables have been
“engineered” to provide a potentially better measure for size, which can be
useful for purely linear models such as LASSO and Ridge regression. These two
variables are the logarithm of sales (code “sale” in table
LABEL:table_Covariates_Financials_Overview) and the logarithm of total assets
(code “at”).

Table 7: Overview of data items sourced from Compustat (“Compustat Daily
Updates - Fundamentals Annual”) and employed as continuous-valued covariates
throughout the empirical analysis (see section 6). Data items are sorted in
alphabetical order of their code. The code and long text are as per the
Compustat Data Guide, accessible via the Wharton Research Data Service (WRDS).
Please see subsection 6.2 for further details. Data items are used as absolute
values (as sourced from Compustat) and as scaled values, once by total assets
(code “at”) and once by total sales (code “sales”). Scaling was not performed
in selected cases where this appeared to be meaningless, for instance for the
fiscal year (code “fyear”). The long text for the codes “afudci” (“Allowance
for Funds Used During Construction (Investing) (Cash Flow)”), “ibad” (“Income
Before Extraordinary Items - Adjusted for Common Stock Equivalents”), “niadj”
(“Net Income Adjusted for Common/Ordinary Stock (Capital) Equivalents”) and
“uniami” (“Net Income before Extraordinary Items and after Noncontrolling
Interest”) has been shortened in the table to limit the breadth of the second
column. Covariates: financial data (absolute and as % of assets and % of
sales)
---
Code | Long text
acchg | Accounting Changes - Cumulative Effect
accrt | ARO Accretion Expense
acdo | Current Assets of Discontinued Operations
aco | Current Assets - Other - Total
acodo | Other Current Assets Excl Discontinued Operations
acominc | Accumulated Other Comprehensive Income (Loss)
acox | Current Assets - Other - Sundry
acqao | Acquired Assets $>$ Other Long-Term Assets
acqcshi | Shares Issued for Acquisition
acqgdwl | Acquired Assets - Goodwill
acqic | Acquisitions - Current Income Contribution
acqintan | Acquired Assets - Intangibles
acqinvt | Acquired Assets - Inventory
acqppe | Acquired Assets $>$ Property, Plant & Equipment
acqsc | Acquisitions - Current Sales Contribution
act | Current Assets - Total
adjex_c | Cumulative Adjustment Factor by Ex-Date - Calendar
adjex_f | Cumulative Adjustment Factor by Ex-Date - Fiscal
afudcc | Allowance for Funds Used During Construction (Cash Flow)
afudci | Allowance for Funds Used During Construction
ajex | Adjustment Factor (Company) - Cumulative by Ex-Date
ajp | Adjustment Factor (Company) - Cumulative byPay-Date
aldo | Long-term Assets of Discontinued Operations
am | Amortization of Intangibles
amc | Amortization (Cash Flow) - Utility
ano | Assets Netting & Other Adjustments
ao | Assets - Other
aocidergl | Accum Other Comp Inc - Derivatives Unrealized Gain/Loss
aociother | Accum Other Comp Inc - Other Adjustments
aocipen | Accum Other Comp Inc - Min Pension Liab Adj
aocisecgl | Accum Other Comp Inc - Unreal G/L Ret Int in Sec Assets
aodo | Other Assets excluding Discontinued Operations
aol2 | Assets Level2 (Observable)
aoloch | Assets and Liabilities - Other - Net Change
aox | Assets - Other - Sundry
aqa | Acquisition/Merger After-tax
aqc | Acquisitions
aqd | Acquisition/Merger Diluted EPS Effect
aqeps | Acquisition/Merger Basic EPS Effect
aqi | Acquisitions - Income Contribution
aqp | Acquisition/Merger Pretax
aqpl1 | Assets Level1 (Quoted Prices)
aqs | Acquisitions - Sales Contribution
arce | As Reported Core - After-tax
arced | As Reported Core - Diluted EPS Effect
arceeps | As Reported Core - Basic EPS Effect
at | Assets - Total
aul3 | Assets Level3 (Unobservable)
bastr | Average Short-Term Borrowings Rate
billexce | Billings in Excess of Cost & Earnings
capsft | Capitalized Software
capx | Capital Expenditures
capxv | Capital Expend Property, Plant and Equipment Schd V
cb | Compensating Balance
cdvc | Cash Dividends on Common Stock (Cash Flow)
ceiexbill | Cost & Earnings in Excess of Billings
ch | Cash
che | Cash and Short-Term Investments
chech | Cash and Cash Equivalents - Increase/(Decrease)
ci | Comprehensive Income - Total
cibegni | Comp Inc - Beginning Net Income
cicurr | Comp Inc - Currency Trans Adj
cidergl | Comp Inc - Derivative Gains/Losses
cimii | Comprehensive Income - Noncontrolling Interest
ciother | Comp Inc - Other Adj
cipen | Comp Inc - Minimum Pension Adj
cisecgl | Comp Inc - Securities Gains/Losses
citotal | Comprehensive Income - Parent
cogs | Cost of Goods Sold
cshfd | Common Shares Used to Calc Earnings Per Share - Fully Diluted
cshi | Common Shares Issued
csho | Common Shares Outstanding
cshpri | Common Shares Used to Calculate Earnings Per Share - Basic
cshr | Common/Ordinary Shareholders
cshtr_c | Common Shares Traded - Annual - Calendar
cshtr_f | Common Shares Traded - Annual - Fiscal
cstke | Common Stock Equivalents - Dollar Savings
currtr | Currency Translation Rate
curuscn | US Canadian Translation Rate
datadate | Data Date
dc | Deferred Charges
depc | Depreciation and Depletion (Cash Flow)
derac | Derivative Assets - Current
deralt | Derivative Assets Long-Term
derhedgl | Gains/Losses on Derivatives and Hedging
diladj | Dilution Adjustment
dilavx | Dilution Available - Excluding Extraordinary Items
dlcch | Current Debt - Changes
dltis | Long-Term Debt - Issuance
do | Discontinued Operations
donr | Nonrecurring Disc Operations
dp | Depreciation and Amortization
dpacre | Accumulated Depreciation of RE Property
dpact | Depreciation, Depletion and Amortization (Accumulated)
dpc | Depreciation and Amortization (Cash Flow)
dpret | Depr/Amort of Property
dpvieb | Depreciation (Accumulated) - Ending Balance (Schedule VI)
drlt | Deferred Revenue - Long-term
dv | Cash Dividends (Cash Flow)
dvc | Dividends Common/Ordinary
dvintf | Dividends & Interest Receivable (Cash Flow)
dvp | Dividends - Preferred/Preference
dvpsp_c | Dividends per Share - Pay Date - Calendar
dvpsp_f | Dividends per Share - Pay Date - Fiscal
dvpsx_c | Dividends per Share - Ex-Date - Calendar
dvpsx_f | Dividends per Share - Ex-Date - Fiscal
dvt | Dividends - Total
ebit | Earnings Before Interest and Taxes
ebitda | Earnings Before Interest
emp | Employees
epsfi | Earnings Per Share (Diluted) - Including Extraordinary Items
epsfx | Earnings Per Share (Diluted) - Excluding Extraordinary Items
epspi | Earnings Per Share (Basic) - Including Extraordinary Items
epspx | Earnings Per Share (Basic) - Excluding Extraordinary Items
esub | Equity in Earnings - Unconsolidated Subsidiaries
esubc | Equity in Net Loss - Earnings
exre | Exchange Rate Effect
fatb | Property, Plant, and Equipment - Buildings at Cost
fatc | Property, Plant, and Equipment - Construction in Progress at Cost
fate | Property, Plant, and Equipment - Machinery and Equipment at Cost
fatl | Property, Plant, and Equipment - Leases at Cost
fatn | Property, Plant, and Equipment - Natural Resources at Cost
fato | Property, Plant, and Equipment - Other at Cost
fatp | Property, Plant, and Equipment - Land and Improvements at Cost
fca | Foreign Exchange Income (Loss)
ffo | Funds From Operations (REIT)
fiao | Financing Activities - Other
finaco | Finance Division Other Current Assets, Total
finao | Finance Division Other Long-Term Assets, Total
fincf | Financing Activities - Net Cash Flow
finch | Finance Division - Cash
finivst | Finance Division Short-Term Investments
finrecc | Finance Division Current Receivables
finreclt | Finance Division Long-Term Receivables
finrev | Finance Division Revenue
finxopr | Finance Division Operating Expense
fopo | Funds from Operations - Other
fopox | Funds from Operations - Other excluding Option Tax Benefit
fopt | Funds From Operations - Total
fsrco | Sources of Funds - Other
fsrct | Sources of Funds - Total
fuseo | Uses of Funds - Other
fuset | Uses of Funds - Total
fyear | Data Year - Fiscal
gdwl | Goodwill
gdwlam | Goodwill Amortization
gdwlia | Impairments of Goodwill After-tax
gdwlid | Impairments of Goodwill Diluted EPS Effect
gdwlieps | Impairments of Goodwill Basic EPS Effect
gdwlip | Impairments of Goodwill Pretax
gla | Gain/Loss After-tax
glcea | Gain/Loss on Sale (Core Earnings Adjusted) After-tax
glced | Gain/Loss on Sale (Core Earnings Adjusted) Diluted EPS
glceeps | Gain/Loss on Sale (Core Earnings Adjusted) Basic EPS Effect
glcep | Gain/Loss on Sale (Core Earnings Adjusted) Pretax
gld | Gain/Loss Diluted EPS Effect
gleps | Gain/Loss Basic EPS Effect
gliv | Gains/Losses on investments
glp | Gain/Loss Pretax
gp | Gross Profit (Loss)
hedgegl | Gain/Loss on Ineffective Hedges
ib | Income Before Extraordinary Items
ibadj | Income Before Extraordinary Items - Adjusted for Common Stock
ibc | Income Before Extraordinary Items (Cash Flow)
ibcom | Income Before Extraordinary Items - Available for Common
ibmii | Income before Extraordinary Items and Noncontrolling Interests
intan | Intangible Assets - Total
intano | Other Intangibles
intc | Interest Capitalized
invch | Inventory - Decrease (Increase)
invfg | Inventories - Finished Goods
invo | Inventories - Other
invrm | Inventories - Raw Materials
invt | Inventories - Total
invwip | Inventories - Work In Process
irent | Rental Income
itcb | Investment Tax Credit (Balance Sheet)
itcc | Investment Tax Credit - Net (Cash Flow) - Utility
itci | Investment Tax Credit (Income Account)
ivaco | Investing Activities - Other
ivch | Increase in Investments
ivncf | Investing Activities - Net Cash Flow
ivst | Short-Term Investments - Total
ivstch | Short-Term Investments - Change
lifr | LIFO Reserve
lifrp | LIFO Reserve - Prior
lno | Liabilities Netting & Other Adjustments
mib | Noncontrolling Interest (Balance Sheet)
mibn | Noncontrolling Interests - Nonredeemable - Balance Sheet
mibt | Noncontrolling Interests - Total - Balance Sheet
mii | Noncontrolling Interest (Income Account)
mkvalt | Market Value - Total - Fiscal
msa | Marketable Securities Adjustment
ni | Net Income (Loss)
niadj | Net Income Adjusted for Common/Ordinary Stock
nipfc | Pro Forma Net Income - Current
nipfp | Pro Forma Net Income - Prior
nopi | Nonoperating Income (Expense)
nopio | Nonoperating Income (Expense) - Other
nrtxt | Nonrecurring Income Taxes After-tax
nrtxtd | Nonrecurring Income Tax Diluted EPS Effect
nrtxteps | Nonrecurring Income Tax Basic EPS Effect
oancf | Operating Activities - Net Cash Flow
ob | Order Backlog
oiadp | Operating Income After Depreciation
oibdp | Operating Income Before Depreciation
opeps | Earnings Per Share from Operations
oprepsx | Earnings Per Share - Diluted - from Operations
optca | Options - Cancelled (-)
optdr | Dividend Rate - Assumption (%)
optex | Options Exercisable (000)
optexd | Options - Exercised (-)
optgr | Options - Granted
optlife | Life of Options - Assumption (# yrs)
optosby | Options Outstanding - Beg of Year
optosey | Options Outstanding - End of Year
optprcby | Options Outstanding Beg of Year - Price
optprcca | Options Cancelled - Price
optprcex | Options Exercised - Price
optprcey | Options Outstanding End of Year - Price
optprcgr | Options Granted - Price
optprcwa | Options Exercisable - Weighted Avg Price
optrfr | Risk Free Rate - Assumption (%)
optvol | Volatility - Assumption (%)
pddur | Period Duration
pdvc | Cash Dividends on Preferred/Preference Stock (Cash Flow)
pi | Pretax Income
pidom | Pretax Income - Domestic
pifo | Pretax Income - Foreign
pnca | Core Pension Adjustment
pncad | Core Pension Adjustment Diluted EPS Effect
pncaeps | Core Pension Adjustment Basic EPS Effect
pncia | Core Pension Interest Adjustment After-tax
pncid | Core Pension Interest Adjustment Diluted EPS Effect
pncieps | Core Pension Interest Adjustment Basic EPS Effect
pncip | Core Pension Interest Adjustment Pretax
pncwia | Core Pension w/o Interest Adjustment After-tax
pncwid | Core Pension w/o Interest Adjustment Diluted EPS Effect
pncwieps | Core Pension w/o Interest Adjustment Basic EPS Effect
pncwip | Core Pension w/o Interest Adjustment Pretax
pnrsho | Nonred Pfd Shares Outs (000)
ppegt | Property, Plant and Equipment - Total (Gross)
ppenc | Property, Plant, and Equipment - Construction in Progress (Net)
ppent | Property, Plant and Equipment - Total (Net)
ppevbb | Property, Plant and Equipment - Beginning Balance (Schedule V)
ppeveb | Property, Plant, and Equipment - Ending Balance (Schedule V)
prca | Core Post Retirement Adjustment
prcad | Core Post Retirement Adjustment Diluted EPS Effect
prcaeps | Core Post Retirement Adjustment Basic EPS Effect
prcc_c | Price Close - Annual - Calendar
prcc_f | Price Close - Annual - Fiscal
prch_c | Price High - Annual - Calendar
prch_f | Price High - Annual - Fiscal
prcl_c | Price Low - Annual - Calendar
prcl_f | Price Low - Annual - Fiscal
prsho | Redeem Pfd Shares Outs (000)
prstkc | Purchase of Common and Preferred Stock
prstkcc | Purchase of Common Stock (Cash Flow)
prstkpc | Purchase of Preferred/Preference Stock (Cash Flow)
rca | Restructuring Costs After-tax
rcd | Restructuring Costs Diluted EPS Effect
rceps | Restructuring Costs Basic EPS Effect
rcp | Restructuring Costs Pretax
rdip | In Process R&D Expense
rdipa | In Process R&D Expense After-tax
rdipd | In Process R&D Expense Diluted EPS Effect
rdipeps | In Process R&D Expense Basic EPS Effect
recch | Accounts Receivable - Decrease (Increase)
recco | Receivables - Current - Other
recd | Receivables - Estimated Doubtful
rect | Receivables - Total
ret | Total RE Property
revt | Revenue - Total
rra | Reversal - Restructruring/Acquisition Aftertax
rrd | Reversal - Restructuring/Acq Diluted EPS Effect
rreps | Reversal - Restructuring/Acq Basic EPS Effect
rrp | Reversal - Restructruring/Acquisition Pretax
rstche | Restricted Cash & Investments - Current
rstchelt | Long-Term Restricted Cash & Investments
sale | Sales/Turnover (Net)
salepfc | Pro Forma Net Sales - Current Year
salepfp | Pro Forma Net Sales - Prior Year
scstkc | Sale of Common Stock (Cash Flow)
seta | Settlement (Litigation/Insurance) After-tax
setd | Settlement (Litigation/Insurance) Diluted EPS Effect
seteps | Settlement (Litigation/Insurance) Basic EPS Effect
setp | Settlement (Litigation/Insurance) Pretax
siv | Sale of Investments
spce | S&P Core Earnings
spced | S&P Core Earnings EPS Diluted
spceeps | S&P Core Earnings EPS Basic
spi | Special Items
spid | Other Special Items Diluted EPS Effect
spieps | Other Special Items Basic EPS Effect
spioa | Other Special Items After-tax
spiop | Other Special Items Pretax
sppe | Sale of Property
sppiv | Sale of Property, Plant and Equipment and Investments - Gain (Loss)
spstkc | Sale of Preferred/Preference Stock (Cash Flow)
sret | Gain/Loss on Sale of Property
sstk | Sale of Common and Preferred Stock
stkco | Stock Compensation Expense
stkcpa | After-tax stock compensation
tdc | Deferred Income Taxes - Net (Cash Flow)
tfva | Total Fair Value Assets
tfvce | Total Fair Value Changes including Earnings
tfvl | Total Fair Value Liabilities
tlcf | Tax Loss Carry Forward
txach | Income Taxes - Accrued - Increase/(Decrease)
txbco | Excess Tax Benefit Stock Options - Cash Flow Operating
txbcof | Excess Tax Benefit of Stock Options - Cash Flow Financing
txc | Income Taxes - Current
txdb | Deferred Taxes (Balance Sheet)
txdba | Deferred Tax Asset - Long Term
txdbca | Deferred Tax Asset - Current
txdbcl | Deferred Tax Liability - Current
txdc | Deferred Taxes (Cash Flow)
txdfed | Deferred Taxes-Federal
txdfo | Deferred Taxes-Foreign
txdi | Income Taxes - Deferred
txditc | Deferred Taxes and Investment Tax Credit
txds | Deferred Taxes-State
txfed | Income Taxes - Federal
txfo | Income Taxes - Foreign
txndb | Net Deferred Tax Asset (Liab) - Total
txndba | Net Deferred Tax Asset
txndbl | Net Deferred Tax Liability
txndbr | Deferred Tax Residual
txo | Income Taxes - Other
txp | Income Taxes Payable
txpd | Income Taxes Paid
txr | Income Tax Refund
txs | Income Taxes - State
txt | Income Taxes - Total
txtubadjust | Other Unrecog Tax Benefit Adj.
txtubbegin | Unrecog. Tax Benefits - Beg of Year
txtubend | Unrecog. Tax Benefits - End of Year
txtubmax | Chg. In Unrecog. Tax Benefits - Max
txtubmin | Chg. In Unrecog. Tax Benefits - Min
txtubposdec | Decrease- Current Tax Positions
txtubposinc | Increase- Current Tax Positions
txtubpospdec | Decrease- Prior Tax Positions
txtubpospinc | Increase- Prior Tax Positions
txtubsettle | Settlements with Tax Authorities
txtubsoflimit | Lapse of Statute of Limitations
txtubtxtr | Impact on Effective Tax Rate
txtubxintbs | Interest & Penalties Accrued - B/S
txtubxintis | Interest & Penalties Reconized - I/S
txw | Excise Taxes
uaoloch | Other Assets and Liabilities - Net Change (Statement of Cash Flows)
uaox | Other Assets - Utility
uapt | Accounts Payable - Utility
uccons | Contributions in Aid of Construction
ucustad | Customer Advances for Construction
udcopres | Deferred Credits and Operating Reserves - Other
udfcc | Deferred Fuel - Increase (Decrease) (Statement of Cash Flows)
udpfa | Depreciation of Fixed Assets
udvp | Preferred Dividend Requirements
ugi | Gross Income (Income Before Interest Charges)
uinvt | Inventories - Utility
ulcm | Current Liabilities - Miscellaneous
ulco | Current Liabilities - Other - Utility
uniami | Net Income before Extraordinary Items
unopinc | Nonoperating Income (Net) - Other
uois | Other Internal Sources - Net (Cash Flow)
uopi | Operating Income - Total - Utility
uopres | Operating Reserves
updvp | Preference Dividend Requirements*
upstksf | Preferred/Preference Stock Sinking Fund Requirement
urect | Receivables (Net)
urectr | Accounts Receivable - Trade - Utility
urevub | Accrued Unbilled Revenues (Balance Sheet)
uspi | Special Items
usubdvp | Subsidiary Preferred Dividends
utme | Maintenance Expense - Total
utxfed | Current Taxes - Federal (Operating)
wcap | Working Capital (Balance Sheet)
wcapc | Working Capital Change - Other - Increase/(Decrease)
wcapch | Working Capital Change - Total
wda | Writedowns After-tax
wdd | Writedowns Diluted EPS Effect
wdeps | Writedowns Basic EPS Effect
wdp | Writedowns Pretax
xacc | Accrued Expenses
xad | Advertising Expense
xi | Extraordinary Items
xido | Extraordinary Items and Discontinued Operations
xidoc | Extraordinary Items and Discontinued Operations (Cash Flow)
xintopt | Implied Option Expense
xlr | Staff Expense - Total
xopr | Operating Expenses - Total
xoptd | Implied Option EPS Diluted
xopteps | Implied Option EPS Basic
xpp | Prepaid Expenses
xpr | Pension and Retirement Expense
xrd | Research and Development Expense
xrdp | Research & Development - Prior
xrent | Rental Expense
xsga | Selling, General and Administrative Expense

Table 8: Overview of data items sourced from Compustat (“Compustat Daily
Updates - Fundamentals Annual”) and transformed into dummy variables
throughout the empirical analysis (see section 6). Data items are sorted in
alphabetical order of their code. The code and long text are as per the
Compustat Data Guide, accessible via the Wharton Research Data Service (WRDS).
Please see subsection 6.2 for further details. “Count” refers to the number of
dummirized variables into which one particular data item was transformed. For
instance, there are six types for “acctchg” in our empirical data set (i.e.,
whether or not a company has adopted a particular new accounting standard),
which translates into five dummy variables. For data items with “count” = 1
(i.e, one single dummy variable), dummy coding corresponds to presence or
absence of the data item. For instance, a company may have or may not have in
a given year a central index key (CIK number, code “cik”) from the FDA, or a
fax number (code “fax”), displayed in Compustat. For the Standard Industry
Classification (code “sic”), dummies have been created at the first (7),
second (58) and third (241) level for a total count of 306. Covariates: dummy
variables
---
Code | Long text | Count
acctchg | Adoption of Accounting Changes | 5
acctstd | Accounting Standard | 3
acqmeth | Acquisition Method | 6
adrr | ADR Ratio | 54
au | Auditor | 21
auop | Auditor Opinion | 5
auopic | Auditor Opinion - Internal Control | 3
bspr | Balance Sheet Presentation | 2
ceoso | Chief Executive Officer SOX Certification | 3
cfoso | Chief Financial Officer SOX Certification | 3
cik | CIK Number | 1
compst | Comparability Status | 10
costat | Active/Inactive Status Marker | 1
curcd | ISO Currency Code | 1
curncd | Native Currency Code | 33
cusip | CUSIP | 1
dldte | Research Company Deletion Date | 1
dlrsn | Research Co Reason for Deletion | 1
exchg | Stock Exchange Code | 12
fax | Fax Number | 1
fic | Current ISO Country Code - Incorporation | 58
final | Final Indicator Flag | 1
fyr | Fiscal Year-end Month | 11
fyrc | Current Fiscal Year End Month | 11
idbflag | International, Domestic, Both Indicator | 1
incorp | Current State/Province of Incorporation Code | 52
ipodate | Company Initial Public Offering Date | 1
ismod | Income Statement Model Number | 2
loc | Current ISO Country Code - Headquarters | 65
ltcm | Long Term Contract Method | 3
ogm | OIL & GAS METHOD | 2
phone | Phone Number | 1
prican | Current Primary Issue Tag - Canada | 1
prirow | Primary Issue Tag - Rest of World | 1
priusa | Current Primary Issue Tag - US | 1
rank | Rank - Auditor | 1
scf | Cash Flow Format | 3
sic | Standard Industry Classification Code | 306
src | Source Document | 7
stalt | Status Alert | 2
state | State/Province | 61
stko | Stock Ownership Code | 3
tic | Ticker Symbol | 1
udpl | Utility - Liberalized Depreciation Code | 3
upd | Update Code | 1
weburl | Web URL | 1

###  8.4 Learner specifications: technical details

We provide here technical details for the learners (“nuisance functions”, [34,
18]) $g_{0}$ and $m_{0}$ from subsection 6.3.1 which capture the relationship
of the covariates $X$ with the outcome $LDA$ and the treatment $D$,
respectively.

For $g_{0}$, we specify the random forest to consist of 500 trees, each with a
maximum depth of seven levels, to predict $LDA$. This achieves an out-of-
sample prediction accuracy of approximately 53% for the $R^{2}$. Specifically,
we use the “regr.ranger” function in R with the following parameters:
$num.trees=500$, $mtry=50$, $min.node.size=10$, $max.depth=7$; we refer
interested readers to the corresponding R package documentation [119]. We
tuned these parameters based on a 30% training - 70% testing sample split. For
reference, the out-of-bag (OOB) $R^{2}$ in the training data is 49%.

For $m_{0}$, we specify the random forest to consist also of 500 trees, but
with a slightly lower maximum depth of five levels each. Specifically, we used
the “classif.ranger” function in R with the following parameters:
$num.trees=500$, $mtry=50$, $min.node.size=10$, $max.depth=5$; we refer
interested readers to the corresponding R package documentation [119]. We
tuned these parameters based on a 30% training - 70% testing sample split. For
reference, the out-of-bag (OOB) correct classification rate is 87% in the
training data. Out-of-sample, we also achieve a correct classification rate of
approximately 87%.

With these learner specifications and a five-fold split as well as two
repetitions (following the recommendation in [9], page 13) total run time with
this set-up was approx. 35 minutes on a standard personal computer (Intel Core
i7, 8 cores) for the analysis with one binary treatment variable.

###  8.5 Robustness check: alternative model specifications

As mentioned in the main section of this paper, we have employed different
learner specifications for $g_{0}$ and $m_{0}$ as a robustness check. The
effect estimates across the different model alternatives are very consistent
as can be seen from table LABEL:table_Res_General_Rating_Robust reported in