RDP 202111: Smells Like Animal Spirits: The Effect of Corporate Sentiment on Investment 5. Robustness Tests and Extensions
November 2021
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Several robustness tests and extensions are outlined below.^{[6]} These tests are generally designed to inspect the mechanism(s) behind the link between sentiment and investment at the company level.
5.1 Why does corporate sentiment matter to investment?
5.1.1 Private knowledge of company managers
I first explore whether the positive association between sentiment and investment is due to company managers being better informed than investors about the fundamentals of the company. If this ‘private knowledge hypothesis’ is true, we should expect that the correlation between sentiment and investment is stronger at companies that are more difficult for investors to value. To test this, indicators are constructed for whether a firm is more difficult to value ex ante based on three metrics: 1) size, 2) age and 3) share turnover (the total number of shares traded during the year divided by the average number of shares outstanding). Separate dummy variables (D_{i}) are constructed to indicate whether the company is small (with total assets valued at less than $10 million), young (less than four years of age) and/or low in turnover (in the bottom quartile of the stock turnover distribution). The dummy variable for hardtovalue companies is interacted with each of the indicators for sentiment, uncertainty and Tobin's Q in separate regressions that augment the baseline model:
If the private knowledge hypothesis is true, there should be a stronger positive correlation between sentiment and investment for these hardtovalue companies $\left({\beta}_{2}>0\right)$.
Based on these indicators there is little evidence that the positive effect of sentiment on investment is stronger for hardtovalue companies (Table 3). The sentiment effect is slightly stronger at smaller companies, but the effect is not statistically significant. The age effects point in the opposite direction, with the sensitivity of investment to sentiment being weaker at young companies, though also not statistically significant. These tests provide limited support for the idea that the sensitivity of investment to sentiment is explained by the private knowledge of corporate managers.^{[7]}
Based on size  Based on age  Based on share turnover  

Sentiment  0.03** (4.89) 
0.03*** (4.79) 
0.03*** (4.52) 
Sentiment × Hardtovalue indicator  0.01 (0.54) 
−0.02 (−1.57) 
−0.00 (−0.48) 
Tobin's Q  0.04*** (3.57) 
0.02*** (2.87) 
0.02*** (3.25) 
Tobin's Q × Hardtovalue indicator  −0.04*** (−2.85) 
0.04*** (2.22) 
−0.01 (−0.57) 
Uncertainty  −0.01 (−1.18) 
−0.04*** (−4.26) 
−0.03*** (−3.79) 
Uncertainty × Hardtovalue indicator  −0.06*** (−3.45) 
0.02 (0.98) 
−0.01 (−0.50) 
Company fixed effects  Y  Y  Y 
Year fixed effects  Y  Y  Y 
R squared  34.2%  33.4%  33.2% 
Companies  998  998  998 
Observations  7,208  7,208  7,208 
Notes: *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively, with tstatistics in parentheses; standard errors are twoway clustered by firm and year; coefficient estimates for the control variables (return on assets, sales growth, lagged sales and lagged capital stock), constant, firm dummies and year dummies are omitted Sources: Author's calculations; Connect 4; Morningstar; Refinitiv Eikon 
An alternative identification strategy to test whether the sensitivity of investment to sentiment is due to private knowledge is to explore the dynamics of the relationship between sentiment and company value, rather than investment. If the sentiment indicator is a proxy for managerial private knowledge about company fundamentals, then changes in sentiment should predict future company profits. I test this idea by estimating the same local projections as before, but the dependent variable is changed from investment to company profits (as measured by the return on assets). I then explore how profits react to (past) changes in sentiment and Tobin's Q.
The LP estimates reveal that the return on assets increases by about 4 percentage points in the year following a one standard deviation increase in the sentiment indicator, but the effect fades quickly (Figure 8). The effect of a change in Tobin's Q is slightly weaker (at about 2 percentage points at the peak) but more persistent, lasting a few years. Overall, these results suggest that the sentiment indicator may provide some shortterm news about the company, but given the effect is very transitory, the sensitivity of investment to sentiment does not appear to be fully explained by managers having private information about company prospects.
5.1.2 Positive versus negative sentiment
To further unpack the mechanism, the sentiment indicator can be decomposed into positive and negative sentiment, so that we can explore which matters more to investment. For this, the net balance measure is split into two indicators – the share of positive words (‘positive sentiment’) and the share of negative words (‘negative sentiment’) that are expressed in corporate disclosures. The model is then reestimated using these two separate indicators simultaneously.
The results indicate that both positive and negative sentiment matter to investment, though the effect is stronger for ‘negativity’ expressed in corporate disclosures (Table 4). This may be because negative words provide a stronger indicator of how a company is faring. Companies presumably avoid using negative words if they can, so when they do use them it is more informative than the use of positive words. This may indicate the sensitivity of investment to sentiment is at least partly due to managers having some private knowledge about the company's future (bad) prospects. However, it could also be that the text analysis is better able to capture negative language than positive language, because positive language may be more nuanced. This would suggest that there is more measurement error in the positive sentiment indicator.
OLS with no controls  Fixed effects with controls  

Positive sentiment  −0.01* (−3.24) 
0.02* (2.18) 
Negative sentiment  −0.03*** (−10.89) 
−0.03*** (−6.68) 
Tobin's Q  0.01 (0.88) 

Uncertainty  −0.03*** (−2.72) 

Return on assets  0.09*** (3.26) 

Sales growth  0.17*** (9.02) 

Lagged sales level  0.16*** (8.34) 

Lagged capital stock level  −0.26*** (−17.46) 

Company fixed effects  N  Y 
Year fixed effects  N  Y 
R squared  1.0%  32.2% 
Companies  1,964  964 
Observations  11,200  6,931 
Notes: *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively, with tstatistics in parentheses; standard errors are twoway clustered by firm and year; coefficient estimates for constant, firm dummies and year dummies are omitted Sources: Author's calculations; Connect 4; Morningstar; Refinitiv Eikon 
5.2 The measurement of corporate fundamentals
5.2.1 Measurement error in corporate fundamentals and sentiment
A key challenge to establishing a causal link between sentiment and investment is potential measurement error in the explanatory variables. Even if the sentiment indicator is measured perfectly, the estimated correlation between sentiment and investment will be affected by poor measurement of other explanatory variables, such as Tobin's Q. It has long been recognised that Tobin's Q can be a poor proxy for unobserved investment opportunities, and various fixes have been proposed (Erickson and Whited 2012).
In a bivariate regression of investment on a single explanatory variable that is measured with error, the estimated coefficient will be biased towards zero due to ‘attenuation bias’. But, in a multivariate setting, it is more complicated and difficult to sign the effect of the bias on any one explanatory variable due to mismeasurement of other explanatory variables (Pishcke 2007).
But, in some special cases, it is possible to sign the estimation bias. For instance, assume that, in the absence of error, sentiment and marginal q are positively correlated, say, because an increase in productivity increases the value of the company and makes company managers more optimistic about the future. In this case, classical error in measuring q will cause investment to be too sensitive to changes in sentiment but not sensitive enough to changes in Tobin's Q (Pishcke 2007).
To identify the role of measurement error, I follow an ‘errorinvariables’ approach and estimate the effect of sentiment on investment using the Erickson and Whited (2012) (EW) estimator. This is a minimum distance technique that relies on higherorder moments to strip out the effect of measurement error. This technique assumes that marginal q and sentiment follow nonnormal distributions, which seems reasonable in practice given how skewed the observable data are.
The benchmark OLS regression estimates are shown in column 1, Table 5. The results of using the EW estimator are shown separately for the case where marginal q is assumed to be the only variable measured with error (column 2) and also where both marginal q and sentiment are assumed to be measured with error (column 3).
Baseline  Mismeasured Tobin's Q  Mismeasured Tobin's Q and sentiment  

Sentiment  0.01*** (3.80) 
0.02*** (4.40) 
0.23 (1.16) 
Tobin's Q  0.02*** (4.04) 
0.02 (1.09) 
0.03 (1.19) 
Company fixed effects  N  N  N 
Year fixed effects  N  N  N 
R squared  8.1%  17.3%  21.2% 
Companies  999  999  999 
Observations  7,215  7,215  7,215 
Notes: *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively, with tstatistics in parentheses; coefficient estimates for some of the control variables (return on assets, sales growth, lagged sales and lagged capital stock) and constant are omitted Sources: Author's calculations; Connect4; Morningstar; Refinitiv Eikon 
Under the assumption that Tobin's Q is the only variable that is mismeasured, the sensitivity of investment to sentiment is stronger, and the effect of Tobin's Q is basically unchanged (comparing columns 1 and 2). Under the assumption that both Tobin's Q and sentiment are poorly measured, the sensitivity to sentiment becomes nearly ten times stronger, albeit not statistically significant (comparing columns 2 and 3). Overall, these results suggest that measurement error could be an issue, and that the effects of sentiment and Tobin's Q would be even stronger in the absence of such measurement issues. However, the results appear to be sensitive to model specification (including the order of moments to use in estimation).
5.2.2 Alternative measures of corporate fundamentals
We can also gauge the importance of sentiment and uncertainty for investment based on alternative measures of corporate fundamentals, such as companyspecific expected profits. For this exercise, the Tobin's Q measure of fundamentals is replaced with equity analyst forecasts for earnings per share in the year ahead, and the baseline regression is reestimated.
As discussed earlier, the timing of corporate disclosures may also give an information advantage to managers over the market in that they know more about the fundamentals at the time of writing the annual report. To address this, I consider an alternative version of the baseline model in which the sentiment indicator is lagged by one year and Tobin's Q is measured based on the share price and number of outstanding shares at the end of the financial year (after the release of the relevant financial report). So, for a hypothetical company that reports investment in 2019/20, sentiment is measured in 2018/19 and Tobin's Q is measured at the end of June 2020.
The effect of sentiment on investment is unchanged, measured both in terms of economic magnitude and statistical significance, despite the inclusion of the expected profit indicator in column 1 (Table 6). Perhaps more remarkably, the sensitivity of investment to sentiment persists, despite the sample size being drastically reduced by the inclusion of this expected profit measure (as it is reported for only a select group of companies). The expected profit measure is also positively correlated with investment, as expected. Notably, the inclusion clearly affects the statistical significance of almost all the other variables in the model, but not sentiment and expected profits.
Similarly, investment remains sensitive to sentiment even when investors potentially have an information advantage over the managers because the market value of the company is measured at the end of the financial year (column 2 of Table 6). This is remarkable given that at least some investors are presumably using a similar text analysis approach to identify relevant information about future company prospects based on the language used in the annual disclosures. The net balance of positive and negative words can be easily measured by anyone with knowledge of machine learning techniques (or even straight dictionarybased analysis as used here) and access to the publicly available company reports. This should mean that any information gleaned from the language in the reports is already embedded in the share price and hence captured in Tobin's Q measured at the end of the financial year. And yet sentiment, as captured in corporate disclosures, still matters to investment.
Expected profits (based on equity analyst forecasts)  Lagged sentiment and endperiod Tobin's Q  

Sentiment  0.02** (4.46) 
0.03*** (5.36) 

Expected profits  0.04* (1.77) 

Tobin's Q (end period)  0.02* (2.03) 

Uncertainty  −0.01 (−0.84) 
−0.04*** (−3.54) 

Return on assets  −0.03 (−0.11) 
0.14*** (4.96) 

Sales growth  0.12 (1.58) 
0.13*** (6.56) 

Lagged sales level  0.03 (0.56) 
0.13*** (5.78) 

Lagged capital stock level  −0.27*** (−6.77) 
−0.25*** (−12.13) 

Company fixed effects  Y  Y  
Year fixed effects  Y  Y  
R squared  49.5%  33.5%  
Companies  274  805  
Observations  1,620  5,597  
Notes: *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively, with tstatistics in parentheses; standard errors are twoway clustered by firm and year; coefficient estimates for constant, firm dummies and year dummies are omitted Sources: Author's calculations; Connect 4; Morningstar; Refinitiv Eikon 
5.3 Corporate sentiment and business surveys
To further explore the mechanism linking sentiment to investment, I test whether the sentiment indicator is correlated with traditional surveybased measures of business sentiment. If there is a correlation with the surveybased measures, this should give us more comfort that corporate sentiment is capturing variation in beliefs amongst managers. For this exercise, I compare the (unweighted) average level of corporate sentiment in each financial year to an annualised measure of current business conditions as reported in the National Australia Bank's (NAB's) monthly business survey. Given the sentiment indicator is estimated on annual data, this exercise is restricted to a small sample size of 18 years (from 2002/03 to 2019/20).
To explore the correlations, I estimate an OLS regression of the average sentiment indicator on the NAB measure of business conditions, as well as controls for aggregate real GDP growth (to capture the business cycle) and a dummy for the GFC period which is equal to one if the financial year is 2008/09 or 2009/10 and is zero otherwise (to capture the drop in economic activity at this time).
Despite the limited time series variation, the average level of sentiment is positively correlated with current business conditions as reported in the NAB survey (Table 7). This holds true even when controlling for aggregate GDP growth and the large swings in economic activity during the GFC. This provides further evidence that the sentiment indicator is capturing the beliefs of company managers, rather than other confounding factors associated with the business cycle.
OLS with no controls  OLS with controls  

Business conditions  0.05* (1.77) 
0.05** (3.32) 
GDP growth  −19.89 (−0.90) 

GFC dummy  −1.32*** (−5.78) 

Company fixed effects  N  N 
Year fixed effects  N  N 
R squared  17.3%  34.7% 
Observations  18  18 
Notes: *, ** and *** denote statistical significance at the 10, 5 and 1 per cent levels, respectively, with tstatistics in parentheses; standard errors are robust; coefficient estimate for constant is omitted Sources: ABS; Author's calculations; Connect 4; Morningstar; NAB; Refinitiv Eikon 
5.4 Explaining the postGFC weakness in investment
Next, I quantify how much of the postGFC weakness in investment can be explained by changes in sentiment, uncertainty and other demandside factors, such as profits and growth. For this empirical exercise, I consider a version of the baseline model:
where the regression is as before, but, for simplicity, the year fixed effects have been replaced by two dummy variables – one for the GFC period (GFC_{t}) which is assumed to cover the financial years from 2009 to 2010, and one for the postGFC period (POST_{t}) which is assumed to cover the financial years since 2011. These dummies capture the mean change in the investment rate from the period prior to the GFC.
I consider three versions of this regression. First, an unrestricted version that is estimated as above. Second, a slightly restricted version in which investment depends on sentiment and uncertainty but none of the other timevarying explanatory variables $\left(\gamma =\delta =0\right).$ Third, a fully restricted version in which there are no explanatory variables other than the company fixed effects and period dummies $\left(\beta =\gamma =\pi =\delta =0\right).$
The comparison of the unrestricted and fully restricted models indicates that the demandside factors can explain about 80 per cent of the decline in corporate investment during the GFC (Figure 9). Demandside factors also account for more than half the decline in investment in the period since the GFC. A comparison of the unrestricted and somewhat restricted models shows that these measures of sentiment and uncertainty explain about a quarter of the decline in investment during the GFC, but account for very little of the postGFC weakness.
Overall, this empirical exercise suggests that weak demandside factors are important for understanding the persistent weakness in corporate investment in the postGFC period. And while low sentiment and heightened uncertainty were important contributing factors during the GFC, they have not obviously weighed on investment since that time.
Footnotes
The key results are similar if investment is measured as the ratio of capital spending to revenue rather than the change in the net capital stock. I also find that the effect of sentiment on investment varies somewhat by industry, with the effect of sentiment being stronger in the mining sector. The effect of sentiment on investment is not any weaker or stronger during economic downturns such as the GFC and the COVID19 pandemic. [6]
It might be the case that firm size and age proxy for financial constraints, as well as information frictions, and that the investment behaviour of such financially constrained firms may be less sensitive to sentiment shocks simply because the firms are unable to respond to such changes in expected activity. Some of the control variables will capture financial constraints, such as the return on assets and sales growth, but they are likely to be imperfect controls. [7]