The effect of cross-listing and cross-delisting to CARs will be studied with ordinary least squares (OLS) regression models. The regression variables of the models will be explained in detail in the next section, 5.2.3. However, before OLS can be run, self-selection of the cross-listers in Sample 1 and self-selection of the cross-decross-listers in Sample 2 has to be taken into account. This is due to the fact that companies that choose to cross-list or cross-delist are not random draws from the population, but they rather choose to list or delist. This complicates the analysis so that one cannot directly estimate an OLS model for CARs with cross-listing or cross-delisting dummies, as the listing and delisting decisions might be related to CARs and, hence, the dummies and error terms would be correlated, possible leading to biased results.
In order to take into account the self selection in Sample 1, I use the Heckman (1979) two-step estimation method, i.e. I first estimate a self selection model, whose results I then use in the final OLS regressions to control for the bias. I follow Torstila and Tolmunen (2005) and employ a probit4 model of cross-listing likelihood as a self selection model. I present here a short summary of the probit model, for a more thorough overview see, e.g., Green (1993). In the probit model there is an unobserved latent variable and observed variable . In studying the company‟s decision to cross-list, the observed dependent variable, receives a value of 0 if the company is not cross-listed at the time of the acquisition, and a value of 1 if the company is cross-listed at the time of the acquisition. The regression relation is defined in terms of the latent variable as:
, (11)
where
if if
Set of variables affecting the likelihood of company to cross-list
error term This relation gives the probability function:
(12)
where F is the cumulative distribution function for the error term, Hence, the functional form of F depends on the assumptions made by the . In probit, it is assumed that the is normally distributed. The likelihood function to be estimated is then:
(13)
As the first stage of Heckman (1979), I estimate the model in Equation 11 and obtain an estimate for . Next, I calculate for each firm the inverse Mills ratio, defined as:
(14)
where refers to the standard normal density distribution and to cumulative distribution function. Then at the second stage of Heckman, I estimate an OLS model employing as an additional explanatory variable for the CARs.
The variables , which I use to estimate the probability of cross-listing are derived from extant literature on cross-listings. The variables, which I employ, relate to both individual firms specific variables and to variables specific for the country of origin of the firm, as suggested by e.g. Doidge, Karolyi, and Stultz (2004).
The probit model of cross-listing likelihood follows the specification in Tolmunen and Torstila (2005). The firm level variables used are logarithm of assets at the last full year balance sheet date prior to an acquisition by a sample company, three-year average sales growth, three-year average P/E ratio, three-year average P/B ratio, and industry dummies based on the major industry class of the SIC code. The country level variables in my model are dummy variables for legal origin, accounting standards, and judicial efficiency as defined
in La Porta, Lopez-de-Silanes, Schleifer, and Vishny (1998). Following Doidge et al. (2004) as well as Tolmunen and Torstila (2005), I further include two additional variables, i.e.
market liquidity, measured as the dollar value of shares traded in a given market divided by the average market capitalization of the market in the year 1997, and the logarithm of the country's per capita GNP in dollars for the same year.
Also cross-delisting is a conscious choice made by the sample companies and, hence, there might be same kind of self-selection issues in Sample 2 as in Sample 1. Thus, I also run OLS regressions separately for a subsample of Sample 2, containing only the acquisitions by companies during cross-listing and after cross-delisting. This allows me to employ the Heckman two-stage procedure to control for the effect of self-selection. I use as the first stage of Heckman a probit model of cross-delisting likelihood. This allows me to also enhance the knowledge on cross-delistings, as the matter has been previously studied by only two authors:
Witmer (2005) and more recently after the change in SEC deregistering requirements Doidge et al. (2008).
The used probit model for cross-delisting is quite similar to the model for cross-listing, but the explanatory variables and the independent variable are different. Namely, in the probit model there is an unobserved latent variable and observed variable . While studying the company‟s decision to cross-delist, the observed dependent variable,
receives a value of 0 if the company is still cross-listed at the time of the acquisition, and a value of 1 if the company has cross-delisted at the time of the acquisition. The regression relation is defined in terms of the latent variable in the same fashion as shown above for cross-listing.
The variables, which I use to estimate the probability of cross-delisting relate to both individual firms specific variables and to variables specific for the country of origin of the firm, as suggested by e.g. Doidge et al. (2008). The firm specific variables in my model are the leverage of the company defined as total debt divided by total assets, logarithm of assets, and three-year average sales growth. In addition to the sales growth, I also use global industry median Tobin‟s q for the year prior to the acquisitions to proxy for the growth opportunities of the company. Tobin‟s q is defined in the usual manner as book value of total assets less book value of equity plus market value of equity, all divided by the book value of total assets.
The industry is defined according to the first two digits of the SIC code. I also include in the
model a measure of the company‟s shares held by insiders of the company. I proxy for this variable by the Worldscope data item closely held shares, which includes, but is not limited to, shares held by officers, directors, and their immediate families, shares held in trust, shares held by other corporations, by pension plans, and by individuals who hold 5% or more of the company‟s outstanding shares. In addition, I also add a dummy variable, which takes a value of 1 if the acquisition is made after the relaxation of deregistering requirements, i.e. post March 21, 2007, when SEC adopted Exchange Act Rule 12h-6, and zero otherwise.
Following Doidge et al. (2008), I obtain my country level variables from La Porta et al.
(1998) and from Djankov, La Porta, Lopez-de-Silanes, and Schleifer (2008). I include a legal index, which is obtained by multiplying the anti-director rights variable from Djankov et al.
by the rule of law index from La Porta et al.. Furthermore, I include stock market capitalization divided by GDP and the logarithm of GDP per capita in $. These two variables are calculated for the year prior to the deal, with the exception that year 2007 figures are used for 2008 as figures for this year were not yet available from the World Bank WDI database.