How Does Firm Age Influence Growth When Evaluated at Mean Values?

[mlarson9000]

Homework Statement

Evaluate the partial effect of age of a firm on growth.(evaluated at the means)

Homework Equations

Growth=$$\beta$$0+$$\beta$$1age+$$\beta$$2age^2+$$\beta3$$size*age+$$\beta$$4plant*age

The Attempt at a Solution

We're supposed to do something like this:
Growth=$$\beta$$0+$$\beta$$1age+$$\beta$$2(age-$$\mu$$a)^2+$$\beta$$3(size-$$\mu$$s)*(age-$$\mu$$a)+$$\beta$$4(plant-$$\mu$$p*(age-$$\mu$$a)

or

Growth=$$\beta$$0+$$\beta$$1age+$$\beta$$2age^2+$$\beta$$3(size-$$\mu$$s)*(age-$$\mu$$a)+$$\beta$$4(plant-$$\mu$$p*(age-$$\mu$$a)

=$$\beta$$1+2$$\beta$$2age

=$$\beta$$1+2$$\beta$$2$$\mu$$

 

[mighty2000]

+\beta3(\mu-\mus)+\beta4(\mu-\mup)

where \mu is the mean age of the firms, \mus is the mean size of the firms, and \mup is the mean plant size of the firms.

To evaluate the partial effect of age on growth, we can hold the other variables (size and plant size) at their mean values and vary the age variable. This means that the \beta1 term, representing the base effect of age on growth, will remain the same. However, the \beta2 term, representing the quadratic effect of age on growth, will change as we vary the age variable. This will give us the partial effect of age on growth, evaluated at the means of the other variables.

In summary, the partial effect of age on growth can be calculated by varying the age variable while holding the other variables at their mean values, using the equation Growth=\beta0+\beta1age+\beta2age^2+\beta3(size-\mus)*(age-\mua)+\beta4(plant-\mup*(age-\mua). This will give us the change in growth for a unit change in age, while the other variables are held constant at their mean values.