Home assignment

Analysis of Cross-Sectional Data

Since we know how to deal only with cross-sectional data, we took into consideration only one year, so our result will be well analyzed, but in real terms they could return biased.

4. The data have been downloaded from AIDA, they refer to Italian companies and starting from this we selected the listed ones such as 407 companies, then we filtered for the ones who made an acquisition in 2020. After we added all the explanatory variables described at the beginning of this paper. Hence, our dataset is based on only one year, whereas we should have used at least 5 years. This choice may lead to some limitations in our analysis because we are not considering historical data.

5. At the beginning we dropped plenty of companies due to the fact that they had many missing data. After a cleaning phase we remained with:

• 260 rows
• 20 columns

Missing data:

• Ros19, Ros20: we have 1 missing data for each of those indexes
• DR20: 51 missing values
• DR19: 36 missing values

Here we have a descriptive table with all our variables.

We have 1 string variable, 17 numeric variables and 2 dummy variables.

.9DR20 | 209 36.15895 24.43991 0 95.59

DR19 | 224 26.53701 20.48292 0 96.86

M | 260 .4769231 .5004305 0 1

D | 260 .4846154 .5007271 0 1

Now we could perform a Skewtest so see if the 2020 data are normally distributed.

sktest Roe20 Roi20 ER20 Ros20 IR20 DFF20 IDL20 DR20

Skewness and kurtosis tests for normality ----- Joint test-----

Variable | Obs Pr(skewness) Pr(kurtosis) Adj chi2(2) Prob>chi2

Roe20 | 260 0.0000 0.0000 138.34 0.0000

Roi20 | 260 0.0001 0.0017 21.31 0.0000

ER20 | 260 0.0128 0.0000 31.14 0.0000

Ros20 | 259 0.0000 0.0000 46.71 0.0000

IR20 | 260 0.0000 0.0000 182.22 0.0000

DFF20 | 260 0.0000 0.0000 148.23 0.0000

IDL20 | 260 0.3726 0.0617 4.31 0.1157

DR20 | 209 0.0301 0.0003 15.14 0.0005

As we can see the only one variable who passed the Jaque-Bera test is IDL20, while all the other are not normally distributed so we will consider to use a Logit model instead of a Probit model since it uses a latent variable

distribution.We performed the same test on the 2019 data and here we have not anynormally distributed variables.Skewness and kurtosis tests for normality ----- Joint test----- Variable | Obs Pr(skewness) Pr(kurtosis) Adj chi2(2)Prob>chi2-------------+-----------------------------------------------------------------Roe19 | 260 0.0000 0.0000 149.020.0000 Roi19 | 260 0.0506 0.1183 6.120.0469 ER19 | 260 0.0016 0.0000 33.860.0000 Ros19 | 259 0.0000 0.0000 57.540.0000 IR19 | 260 0.0000 0.0000 213.640.0000 DFF19 | 260 0.0000 0.0000 216.110.0000 IDL19 | 260 0.0001 0.8270 13.970.0009 DR19 | 224 0.0000 0.5859 17.260.0002reg M Roe20 Roi20 ER20 Ros20 IR20 DFF20 IDL20 DR20 DSource | SS df MS Number of obs =209-------------+---------------------------------- F(9, 199) =16.08 Model | 21.934949 9 2.43721656 Prob > F =0.0000Residual | 30.1703142 199 .151609619 R-squared =0.4210-------------+---------------------------------- Adj R-squared =0.3948 Total | 52.1052632 208 .250506073 Root MSE =

  

    
Variable
    
Obs
    
Mean
    
Std. dev.
    
Min
    
Max
  
  

    
fitted
    
209
    
.4736842
    
.3247406
    

    

  

  

    
Variable
    
Coefficient
    
Std. err.
    
t
    
P>|t|
    
[95% conf.interval]
  
  

    
Roe20
    
.0042185
    
.0023168
    
1.82
    
0.070
    
-.0003502 .0087872
  
  

    
Roi20
    
-.0140183
    
.0074158
    
-1.89
    
0.060
    
-.0286419 .0006052
  
  

    
ER20
    
.0106463
    
.0053722
    
1.98
    
0.049
    
.0000526 .02124
  
  

    
Ros20
    
-.0073206
    
.007593
    
-0.96
    
0.336
    
-.0222937 .0076526
  
  

    
IR20
    
.0036319
    
.0095735
    
0.38
    
0.705
    
-.0152466 .0225104
  
  

    
DFF20
    
-.072976
    
.0300222
    
-2.43
    
0.016
    
-.1321785-.0137736
  
  

    
IDL20
    
-.0483297
    
.1853279
    
-0.26
    
0.795
    
-.4137883 .317129
  
  

    
DR20
    
.000319
    
.00136
    
0.23
    
0.815
    
-.0023628 .0030008
  
  

    
D
    
-.672862
    
.0576375
    
-11.67
    
0.000
    
-.7865208-.5592033
  
  

    
_cons
    
.8217176
    
.1007959
    
8.15
    
0.000
    
.62295241.020483
  

By computing a regression, we note that predicted values are included between -.1843037 and 1.148549, however our dependent variable is a dummy hence values can only be 0 or 1

Now we are going to compute the logit model since we saw a non-normal distribution

logit M Roe20 Roi20 ER20 Ros20 IR20 DFF20 IDL20 DR20 D

Iteration 0: log likelihood = -144.57815

Iteration 1: log likelihood = -95.14023

Iteration 2: log likelihood = -94.502128

Iteration 3: log likelihood = -94.500333

Iteration 4: log likelihood = -94.500333

Logistic regression Number of obs = 209

LR chi2(9) = 100.16

Prob > chi2 = 0.0000

Log likelihood = -94.500333

Pseudo R2 =

0.3464
------------------------------------------------------------------------------
M | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
Roe20 | .0267739 .0162373 1.65 0.099 -.0050505 .0585984
Roi20 | -.0867751 .0500846 -1.73 0.083 -.1849392 .011389
ER20 | .073364 .0397563 1.85 0.065 -.0045568 .1512849
Ros20 | -.0579823 .0541187 -1.07 0.284 -.164053 .0480884
IR20 | .0216559 .0637279 0.34 0.734 -.1032485 .1465603
DFF20 | -.4237106 .203156 -2.09 0.037 -.821889 -.0255322
IDL20 | -.3802979 1.232062 -0.31 0.758 -2.795095 2.034499
DR20 | .0031268 .0095513 0.33 0.743 -.0155935 .0218471
D | -3.563182 .4509901 -7.90 0.000 -4.447106 -2.679257
_cons | 1.609232 .6845157 2.35 0.019 .2676055 2.950858
------------------------------------------------------------------------------
This is the full model, before starting with the stepwise we would like to investigate the
correlation among our variables by computing a pwcorr.

This is an exploratory analysis, we will accept as maximum significance level a 10% value

pwcorr Roe20 Roi20 ER20 Ros20 IR20 DFF20 IDL20 DR20, star(0.05)

| Roe20 Roi20 ER20 Ros20 IR20 DFF20 IDL20 DR20

---------------------------------------------------------------

Roe20 | 1.0000

Roi20 | 0.6648* 1.0000

ER20 | 0.3218* 0.5454* 1.0000

Ros20 | 0.4382* 0.7428* 0.8284* 1.0000

IR20 | -0.0220 -0.1578* -0.2130* -0.3128* 1.0000

DFF20 | 0.0678 0.1305* 0.0264 0.0706 -0.1435* 1.0000

IDL20 | 0.0461 -0.2285* 0.0307 -0.1898* 0.4499* -0.2233* 1.0000

DR20 | -0.1025 -0.2856* -0.0458 -0.1308 -0.1123 -0.3275* 0.3993*

| DR20

-------------+---------

DR20 | 1.0000

Since we see ROI is highly correlated with all other variables, now we could try to estimate the logit model without it.

We tried the stepwise process, so we start to drop every time the variable with highest p-value and then we re-estimated the model, by doing this we found that there was not even one significant model.

Hence, we decided to restart the same

process by keeping the Roi20 fixed and in the end, we obtained this kind of output:

logit M Roi20 DFF20 D
Iteration 0: log likelihood = -179.94125
Iteration 1: log likelihood = -115.134
Iteration 2: log likelihood = -114.37502
Iteration 3: log likelihood = -114.37221
Iteration 4: log likelihood = -114.37221

Logistic regression Number of obs = 260
LR chi2(3) = 131.14
Prob > chi2 = 0.0000
Log likelihood = -114.37221
Pseudo R2 = 0.3644
------------------------------------------------------------------------------
M | Coefficient Std. err. z P>|z| [95% conf. interval]
-------------+----------------------------------------------------------------
Roi20 | -.056127 .0217583 -2.58 0.010 -.0987725 -.0134815
DFF20 | -.3322477 .1618238 -2.05 0.040 -.6494165 -.0150789
D | -3.621511 .3896568 -9.29 0.000 -4.385225 -2.857798
_cons | 2.097647 .3477647 6.03 0.000 1.41604 2.779253
------------------------------------------------------------------------------

This is the final result, the most significant variables

are Roi20, DFF20, and D; we also checkedagain the pwcorr and we found out that there are no multicollinearity problems.

The Pseudo R2 equal to 0.3644 means that the model explains the 36,44% of the unexplainedvariance.

linktest

Iteration 0: log likelihood = -179.94125

Iteration 1: log likelihood = -114.61471

Iteration 2: log likelihood = -114.3718

Iteration 3: log likelihood = -114.37016

Iteration 4: log likelihood = -114.37016

Logistic regression Number of obs = 260

LR chi2(2) = 131.14

Prob > chi2 = 0.0000

Log likelihood = -114.37016

Pseudo R2 = 0.3644

------------------------------------------------------------------------------

M | Coefficient Std. err. z P>|z| [95% conf. interval]

-------------+----------------------------------------------------------------

_hat | 1.00172 .1097661 9.13 0.000 .7865822 1.216857

_hatsq | .0072008 .112424 0.06 0.949 -.2131462 .2275479

_cons | -.0178934 .3258329 -0.05 0.956 -.6565142

.6207275

The variable _hat should be a statistically significant predictor since it is the predicted value from the model. This will be the case unless the model is completely misspecified.

We will now investigate marginal effects with mfx compute:

- mfx compute at mean

Marginal effects after logit y = Pr(M) (predict) = .46037663

variable | dy/dx Std. err. z P>|z| [ 95% C.I. ] X