Issues in Empirical Finance Research

Henrique C. Martins


The challenge

  • I will discuss some issues in using plain OLS models in Corporate Finance & Governance Research
  • I will avoid the word “endogeneity” as much as I can
  • I will also avoid the word “identification” because identification does not guarantee causality and vice-versa (Kahn and Whited 2017)

The challenge

  • Imagine that you want to investigate the effect of Governance on Q

    • You may have more covariates explaining Q (omitted from slides)

\(𝑸_{i} = α + 𝜷_{i} × Gov + Controls + error\)

All the issues in the next slides will make it not possible to infer that changing Gov will CAUSE a change in Q

That is, cannot infer causality

1) Reverse causation

One source of bias is: reverse causation

  • Perhaps it is Q that causes Gov

  • OLS based methods do not tell the difference between these two betas:

\(𝑄_{i} = α + 𝜷_{i} × Gov + Controls + error\)

\(Gov_{i} = α + 𝜷_{i} × Q + Controls + error\)

  • If one Beta is significant, the other will most likely be significant too

  • You need a sound theory!

2) Omitted variable bias (OVB)

The second source of bias is: OVB

  • Imagine that you do not include an important “true” predictor of Q

  • Let’s say, long is: \(𝑸_{i} = 𝜶_{long} + 𝜷_{long}* gov_{i} + δ * omitted + error\)

  • But you estimate short: \(𝑸_{i} = 𝜶_{short} + 𝜷_{short}* gov_{i} + error\)

  • \(𝜷_{short}\) will be:

    • \(𝜷_{short} = 𝜷_{long}\) + bias

    • \(𝜷_{short} = 𝜷_{long}\) + relationship between omitted (omitted) and included (Gov) * effect of omitted in long (δ)

      • Where: relationship between omitted (omitted) and included (Gov) is: \(Omitted = 𝜶 + ϕ *gov_{i} + u\)
  • Thus, OVB is: \(𝜷_{short} – 𝜷_{long} = ϕ * δ\)

  • See an example in r here

3) Specification error

The third source of bias is: Specification error

  • Even if we could perfectly measure gov and all relevant covariates, we would not know for sure the functional form through which each influences q

    • Functional form: linear? Quadratic? Log-log? Semi-log?
  • Misspecification of x’s is similar to OVB

4) Signaling

The fourth source of bias is: Signaling

  • Perhaps, some individuals are signaling the existence of an X without truly having it:

    • For instance: firms signaling they have good governance without having it
  • This is similar to the OVB because you cannot observe the full story

5) Simultaneity

The fifth source of bias is: Simultaneity

  • Perhaps gov and some other variable x are determined simultaneously

  • Perhaps there is bidirectional causation, with q causing gov and gov also causing q

  • In both cases, OLS regression will provide a biased estimate of the effect

  • Also, the sign might be wrong

6) Heterogeneous effects

The sixth source of bias is: Heterogeneous effects

  • Maybe the causal effect of gov on q depends on observed and unobserved firm characteristics:

    • Let’s assume that firms seek to maximize q
    • Different firms have different optimal gov
    • Firms know their optimal gov
    • If we observed all factors that affect q, each firm would be at its own optimum and OLS regression would give a non-significant coefficient
  • In such case, we may find a positive or negative relationship.

  • Neither is the true causal relationship

7) Construct validity

The seventh source of bias is: Construct validity

  • Some constructs (e.g. Corporate governance) are complex, and sometimes have conflicting mechanisms

  • We usually don’t know for sure what “good” governance is, for instance

  • It is common that we use imperfect proxies

  • They may poorly fit the underlying concept

8) Measurement error

The eighth source of bias is: Measurement error

  • “Classical” random measurement error for the outcome will inflate standard errors but will not lead to biased coefficients.

    • \(y^{*} = y + \sigma_{1}\)
    • If you estimante \(y^{*} = f(x)\), you have \(y + \sigma_{1} = x + \epsilon\)
    • \(y = x + u\)
      • where \(u = \epsilon + \sigma_{1}\)
  • “Classical” random measurement error in x’s will bias coefficient estimates toward zero

    • \(x^{*} = x + \sigma_{2}\)
    • Imagine that \(x^{*}\) is a bunch of noise
    • It would not explain anything
    • Thus, your results are biased toward zero

9) Observation bias

The ninth source of bias is: Observation bias

  • This is analogous to the Hawthorne effect, in which observed subjects behave differently because they are observed

  • Firms which change gov may behave differently because their managers or employees think the change in gov matters, when in fact it has no direct effect

10) Interdependent effects

The tenth source of bias is: Interdependent effects

  • Imagine that a governance reform that will not affect share prices for a single firm might be effective if several firms adopt

  • Conversely, a reform that improves efficiency for a single firm might not improve profitability if adopted widely because the gains will be competed away

  • “One swallow doesn’t make a summer”

11) Selection bias

The eleventh source of bias is: Selection bias

  • If you run a regression with two types of companies

    • High gov (let’s say they are the treated group)
    • Low gov (let’s say they are the control group)
  • Without any matching method, these companies are likely not comparable

  • Thus, the estimated beta will contain selection bias

  • The bias can be either be positive or negative

  • It is similar to OVB

12) Self-Selection

The twelfth source of bias is: Self-Selection

  • Self-selection is a type of selection bias

  • Usually, firms decide which level of governance they adopt

  • There are reasons why firms adopt high governance

    • If observable, you need to control for
    • If unobservable, you have a problem
  • It is like they “self-select” into the treatment

    • Units decide whether they receive the treatment of not
  • Your coefficients will be biased