**3. Applying Gibrat's Law**

The literature has discussed the various reasons for why Gibrat's Law may be valid, as well as the factors that contribute to rejecting it. Economy-wide and firm-specific effects can aid in both rejecting and accepting the random walk Gibrat describes, depending on if the effects explain the variance or level of firm size. Later in this paper, we include the exchange rate (economy-wide) and the debt level (firm-specific) as variables that explain the size of campsites.

There are statistical and econometric challenges to testing Gibrat's Law (Novoa 2011). When using dynamic panel data analysis, the first choice is that of the dependent variable. There are essentially two alternatives: firm growth and firm size. By choosing growth, one takes the first difference of size, while using size as the explanatory variable (Oliveira and Fortunato 2008). In this case, Gibrat's Law holds if the parameter for size is insignificant. Alternatively, using size as the dependent and explanatory variable, the following model is applied:

$$\mathbf{y}\_{\rm it} = \alpha + \beta \mathbf{y}\_{\rm i, t-1} + \varepsilon\_{\rm it\prime} \tag{1}$$

where yit is the logarithmic value of size for the actual company in a specific sector at time t. The lagged dependent variable is the only explanatory variable, α is a constant and εit is random disturbance term. In this model, Gibrat's Law holds if it is shown that firms follow a random walk; that is, if β = 1. Deviations from this random walk give insight into the distributional trend of the sector's firms.
