**3. Methodology**

This research begins by investigating the impact of the employment portfolio in a county on the survival rates of new business establishments in that county. Growth in employment in the county is measured through the average annual growth in wage and salary employment. Risk in employment in the county represents the standard deviation in wage and salary employment during the same period.

Before it can be established that risk–return trade-off in a county affects business survival rates, it is imperative to establish the existence of a risk–return relationship. Investigation into risk–return trade-off has shown a U-shaped relationship for states, metro areas, and commuting zones [2–4]. Plotting the risk and growth variables for all counties for the 1996–2005 timeframe suggests that a U-shaped relationship does exist (Figure 2).

**Figure 2.** County WSE Risk and Return, 1996–2005.

The relationship between risk and return appears to be nonlinear. As returns increase, the risk declines. However, beyond a certain level of growth, the risk starts rising again. This indicates that the growth in returns (or job growth) has a dual effect on the risk,

hence quadratic variation in the growth variable, growth-squared, is also included as an additional parameter in the model.

Visual observation suggests that the relationship between risk and returns is nonlinear. To confirm this inference, this relationship is tested econometrically. A widely used technique for this purpose is stochastic frontier estimation [1,4]. This technique may help in identifying the shape of the frontier and the parameters that define this shape. A nonlinear estimator, the maximum likelihood estimator (MLE), is used to estimate the model. The proposed model to be estimated is as follows:

$$
\sigma\_{\dot{l}} = \alpha\_{\dot{l}} + \beta\_{\dot{l}} \mathbf{G}\_{\dot{l}} + \beta\_{2} \mathbf{G}^{2}{}\_{\dot{l}} + \varepsilon\_{\dot{l}} \tag{1}
$$

where

*σ<sup>i</sup>* = *the standard deviation of WSE for region i G<sup>i</sup>* = *the annual rate of growth of WSE for region i β*<sup>1</sup> = *parameter 1 to be estimated β*<sup>2</sup> = *parameter 2 to be estimated*

The results displayed in Table 1 confirm that the risk–return trade-off is indeed Ushaped. The risk–return profile can now be used to estimate whether the employment portfolio in a county influences the survival rate of new businesses in that county.

**Table 1.** Test for U-shaped risk–return trade-off in counties.


\*\*\* *p* < 0.01.

We test the hypothesized relationship using the model developed by [21]. We use the following reduced form equation to identify the labor market dynamics, manifested through the portfolio, in the context of new business survival (*S<sup>i</sup>* ) in the selected regional unit. Broadly, new business survival depends on the regional labor market portfolio (*L<sup>i</sup>* ), amenity score (*A<sup>i</sup>* ), demand shock (*D<sup>i</sup>* ), local workforce education measures (*EE<sup>i</sup>* ), bank deposits (*B<sup>i</sup>* ), regional housing market variables (*H<sup>i</sup>* ), regional income variables (*I<sup>i</sup>* ), market access (*M<sup>i</sup>* ), and regional employment variables (*E<sup>i</sup>* ).

$$S\_{\rm i} = f(L\_{\rm i}, A\_{\rm i}, D\_{\rm i}, EE\_{\rm i}, B\_{\rm i}, H\_{\rm i}, I\_{\rm i}, M\_{\rm i}, E\_{\rm i}) \tag{2}$$

(3)

The above reduced -form model evolves into the following empirical model:

$$\text{Survival Rate}\_{i} = \beta\_{0} + \beta\_{1} \\ \text{Local Employment Portfolio}\_{i} + \beta\_{2} \\ \text{Median Home Value}\_{i} \\ \text{2000}\_{i}$$

+*β*3*Owner Occupied Houses*, 2000*<sup>i</sup>* + *β*4*BartikShock<sup>i</sup>*

+*β*5*CountyIncome per capita*, 2000*<sup>i</sup>* + *β*6*Demand Shocks<sup>i</sup>* + *β*7*Distance to Metro<sup>i</sup>*

+*β*8*Density<sup>i</sup>* + *β*9*Amenities<sup>i</sup>* + *β*10*County Employment*

+*β*11*CountyIncome per capita growth rate*, 2000 − 07*<sup>i</sup>*

+*β*<sup>12</sup> *Share o f pop living in Rural*, 2000*<sup>i</sup>*

+*β*<sup>13</sup> *County Employment growth rate*, 2000 − 07*<sup>i</sup>* + *β*<sup>14</sup> *Sel f Employment rate<sup>i</sup>*

+*β*<sup>15</sup> *Population growth<sup>i</sup>* + *β*<sup>16</sup> *Share o f Population with HighSchool*, 2000*<sup>i</sup>*

+*β*<sup>17</sup> *Share o f Population with BA*+, 2000*<sup>i</sup>* + *β*<sup>18</sup> *Bank Deposits per capita*, 2005*<sup>i</sup>*
