In-Class Test EF5130 Econometrics
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In-Class Test 2016 EF5130 Econometrics
To test whether and how market conditions may affect investor anxiety that may result in hospitalization, En- gelberg and Parsons (2016) regress measures of hospital addimissions in California on measures of stock market conditions and a set of additional control variables Xt (such as the constant term and day of the week dummy variables). In the following table, each column report estimates of the stock market conditions for a regression but omit estimates for the controls. The outcome variable is ytn, the log of total number of patients admitted to a hospital in California in day t due to non-mental disorders, or ytm, the log number of patients admitted to a hospital in California in day t due to mental disorders. returnt is the return to a stock market index in day t measured in units of the standard deviation of historial returns. Qit is a dummy variable equal to one if returnt is in the i-th quintile of empirical distribution of returns. For example, Q1t = 1 if the market return on day t was in the bottom (worst) 20% of the returns in the sample. The estimates are scaled in units of basis points. For example, the esimate −13.45 in the first column regression means that the number of non-mental disorder patients in California increases by 13.45 basis points (or 0.1345 percent) when the stock market return goes down by one standard deviation, holding constant all other controls Xt (not reported). Heteroskedasticity robust standard errors are in parentheses. The sample size is 7315 in all regressions and covers the period 1983 to 2011.
t returnt −13.45
Adjusted R2 0.80
t+1 t+1 t+1 t+1
yn yn ym ym yn yn ym ym
(a) (10%) The regressions with the quintile dummy variables Qit do not include the dummy variable Q3t for the middle quintile. Explain why this dummy variable is dropped. Carefully interpret the estimated coefficient 24.57 on Q1t in the second column regression.
(b) (10%) From the regression of ym on returnt and Xt (column 7), construct a 95% confidence interval for t+1
the effect of a two standard deviation decrease in stock market return on mental disorder hospital admissions the following day.
(c) (10%) The table reports heteroskedasticity robust standard errors. An alternative would be to use standard errors clustered by, for example, year-month. Explain in what sense clustered standard errors are ‘more’ robust than heteroskedasticity robust standard errors.
(d) (10%) The regressions on returnt restrict the effect of positive and negative returns of the same size to be symmetric. That is, the change in admissions associated with a one standard deviation increase and a one standard deviation decrease are the same in size with different signs. Explain how to test this restriction from the regressions with quintile dummy variables. If there is sufficient information to carry out the test do so. Otherwise, explain what other information you need to carry out the test.
(e) (10%) Suggest an alternative regression specification that you could use to test the symmetry restriction explained in part (d). Explain how you can use your regression to test the symmetry restriction.
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In-Class Test 2016 EF5130 Econometrics
To test whether political corruption can affect firm financial policies, Smith (2016) considers two hypotheses. Under the shielding hypothesis, firms hold less cash and increase leverage (debt) to avoid being expropriated by corrupt regulators. Under the liquidity hypothesis, firms hold more cash and have less leverage to be able to bribe corrupt regulators. Consider panel data regressions of the form
yit = βConvictit +Xitγ +αi +δt +uit
yit is either cash holdings or leverage of firm i in year t both divided by total assets. Convictit is a measure of corruption and is the number of corruption convictions per 100,000 in the judicial district where firm i is headquartered in year t. Xit are other observable characteristics of firm i in year t, αi, δt are the firm and time fixed effects, and uit is the error term.
(a) (10%) Suppose firms tend to choose their headquarters in areas that are known not to be corrupted. Explain how this could affect the statistical properties of the two-way fixed effects estimate of β in the regression above.
(b) (10%) Smith (2016) uses CIndexit, an index of concentration of population around its capitcal city in the area of firm i headquarter in year t. CIndexit ranges from 0 to 1 with 0 indicating that everyone in the area lives as far as possible from the capital. Explain what conditions CIndexit must satisfy to be a valid instrumental variable for Convictit.
(c) (10%) Explain how to test whether the conditions stated in part (b) are satisfied in the sample data.
(d) (10%) Smith (2016) reports that the IV (instrumental variable) estimate of β is −0.02 (0.10) for cash holdings and 0.17 (0.10) for leverage with standard errors clustered by firm and year in parentheses and the sample size is 110,094. Explain whether these results support the two hypotheses stated at the beginning of this question.
(e) (10%) To examine how geographic concentration of a firm’s operation could affect the relation between cor- ruption and leverage, Smith (2016) estimates
Leverageit = 0.02 Convictit − 0.09 HQPercentit + 0.05 Convictit × HQPercentit + Xitγ + αi + δt + eit (0.02) (0.03) (0.02)
HQPercentit is a measure of the percentage of firm operation in the area where the firm i headquarter is located in year t. Clustered standard errors are in parentheses for a sample of size 49,169. Based on this result explain how geographic concentration of a firm’s operation affects the relation between corruption and leverage in this sample.