README.md

In JonasWallin/cams:

cams

R-Package for analysis of firm growth data

To install:

# install.packages("remotes")
remotes::install_github("JonasWallin/cams")

Small tutorial

This is a small tutorial on how to model firm growth using the model proposed in [1]. simulate data, this data is generated so that has similar charateristics as the data used in [1]. Estimate parameters from the simulated data. * Draw inference from the estimate.

[1] N. Ahmed, F. Delmar, J. Wallin Modeling New-Firm Growth and Survival Using Event Magnitude Regression.

simulation

Here we generate ten thousand observations for medium sized companies employees

library(cams)
n <- 10^4
size = "medium"
data <- generate.data(n,size)

the data consists of * $emp - how many people was employeed at current year * $emp_prev - previous number of employees. * $age - age of the company. * $ln_roa - log ROA * $assp_hist - aspiration * $assp_hist_over - $assp_hist * ($assp_hist>0) * $assp_hist_below - $assp_hist * ($assp_hist<0) * $exit - Did the company exit the market

We then create a truncated dummy variable of previous numer of employees:

data <- generate.data(n,size)
data$emp_prev_trunc <- data$emp_prev
data$emp_prev_trunc[data$emp_prev_trunc > trunc_emp_prev] = trunc_emp_prev
data$emp_prev_trunc <- factor(data$emp_prev_trunc)

Estimation

Now we build a cam object where we set the following options: The probability of growth, decline and exit follows a logistic regression model. The growth magnitude follows a geometric distribution (with mean defined by formula Above). * The decline magnitude follows a truncated geometric distribution (with mean defined by formula Below).

We need to spesifiy which are the target variable "emp", which was the previous years target "emp_prev" and the firm exit variable "exit.

cam_obj <- growthObjInit(data, "emp", "emp_prev", exitIndex=  "exit")
formula_list <- list(Above =     " y ~ 1  + ln_roa +  age + assp_hist_over + assp_hist_below +  offset(log(emp_prev))",
                  Below =     " y ~ 1  + ln_roa +  age + assp_hist_over + assp_hist_below +  offset(log(emp_prev))",
                  ProbEqual = " y ~ 1  + ln_roa + assp_hist_over + assp_hist_below + emp_prev_trunc ",
                  ProbAbove = " y ~ 1  + ln_roa + assp_hist_over + assp_hist_below ",
                  ProbExit  = " y ~ 1  + ln_roa + assp_hist_over + assp_hist_below + emp_prev_trunc ")
cam_obj <- growthEstimate(cam_obj, formula = formula_list, dist = list(Above = "geomm", Below = "geommc"))

Inference

We first can explore how well the model fits the data. This is done by diagonstic.geomm that compares the emperical distribution of the data to the fitted model.

diagonstic.geomm(cam_obj$estimate$Above, n.groups=20)

The results looks as follows:

****************************************************** 
Probability         estimated (numerical)
P(Y  =    1 )  =       0.2832  ( 0.2713 )  n =  121 
P(Y  =    2 )  =       0.1960  ( 0.2108 )  n =  94 
P(Y  =    3 )  =       0.1376  ( 0.1592 )  n =  71 
P(Y  =    4 )  =       0.0980  ( 0.0830 )  n =  37 
P(Y  =    5 )  =       0.0706  ( 0.0830 )  n =  37 
P(Y  =    6 )  =       0.0515  ( 0.0448 )  n =  20 
P(Y in (  6 ,  8 ]) =  0.0662  ( 0.0448 )  n =  20 
P(Y in (  8 , 11 ]) =  0.0498  ( 0.0583 )  n =  26 
P(Y in ( 11 , 35 ]) =  0.0465  ( 0.0448 )  n =  20 

All estimated objects are in cam_obj$estimate $ProbExit is a mgcv::gam object for probability of leaving $ProbEqual is a mgcv::gam object for probability of staying at the same number of employees $ProbAbove is a mgcv::gam object for probability of increasing number of employees. $Above is a cams object with effect of magnitude of increasing number of employees. * $Below is a cams object with effect of magnitude of decreasing number of employees.

So for instance:

summary(cam_obj$estimate$ProbExit)

gives:

Family: binomial 
Link function: logit 

Formula:
y ~ 1 + ln_roa + assp_hist_over + assp_hist_below + emp_prev_trunc

Parametric coefficients:
                  Estimate Std. Error z value Pr(>|z|)    
(Intercept)      -2.232507   0.116279 -19.200  < 2e-16 ***
ln_roa           -3.383268   0.375100  -9.020  < 2e-16 ***
assp_hist_over    0.047998   0.008404   5.711 1.12e-08 ***
assp_hist_below   0.026546   0.013627   1.948   0.0514 .  
emp_prev_trunc11 -0.024894   0.152395  -0.163   0.8702    
emp_prev_trunc12  0.147662   0.154145   0.958   0.3381    
emp_prev_trunc13 -0.144305   0.168041  -0.859   0.3905    
emp_prev_trunc14  0.146366   0.164165   0.892   0.3726    
emp_prev_trunc15 -0.094420   0.114590  -0.824   0.4100    
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1


R-sq.(adj) =  0.013   Deviance explained = 2.33%
UBRE = -0.41723  Scale est. = 1         n = 10000

JonasWallin/cams documentation built on April 3, 2022, 2:43 p.m.