The Macrodynamics of Employment Under Uncertainty

See, e.g., [16, 26], and for the Portuguese case [23, 30, 38].

See, e.g., [7, 8, 12, 15, 21].

See [4, 11].

See [17].

We follow [8].

We are assuming that all firms face a common demand schedule (\(P_{j,t} = P_{t}\)) and that the wage rate and the real cost of capital is constant over time, but not necessarily across firms.

On the hiring side, examples of adjustment costs are the costs of advertising, recruiting and training the new workers, including the costs resulting from disruption in production when the new workers are hired. On the firing side, adjustment costs include mandatory advance notice requirements, severance pay and other procedural inconveniences to dismissal caused by employment protection legislation. A significant part of these adjustment costs are related to personnel and legal departments to deal with hires and fires and thus fixed, i.e., independent of the number of workers that are hired or dismissed (see, e.g., [27, 32]). A firm also incurs in irreversible cost to buy physical assets like firm specific equipment or intangible assets such as reputation, acquired by investments in marketing and advertising, or technical knowledge (see, e.g., [24, 35, 36]). Other non-firm specific investments like office equipment, cars, trucks and computers can have a resale value well below their purchase cost due to the “lemons” problem [36,, p. 1111].

In this setting, the decision to enter is akin to the hiring decision, and the decision to exit is akin to the firing decision. This simplification does not change the conclusions of the model as we can consider a firm divided into single production units, with every unit represented individually [8].

See [25] for a complete description of the model.

The value function for a firm that enters the market is \(V _{j,t} = \frac{P_{t}-w_{t}-r_{j}k_{j}} {1-\delta } - H_{j}\), while the value function for remaining outside the market is 0. Therefore, the entry condition is \(\frac{P_{t}-w_{t}-r_{j}k_{j}} {1-\delta } - H_{j}> 0.\)

The value function for a firm to remain active is \(V _{j,t} = \frac{P_{t}-w_{t}-r_{j}k_{j}} {1-\delta }\), while the value function for exiting the market is − F _j . Therefore, the exit condition is \(\frac{P_{t}-w_{t}-r_{j}k_{j}} {1-\delta } <-F_{j}.\)

Although, we consider only revenue uncertainty, there could be also uncertainty in input costs (like in the interest rates), exchange rate uncertainty, and tax and regulatory policies uncertainty (see [22, p. 14]).

See [7, 10] for more detail.

See [7] for more detail.

Belke [6] extends this argument to the effect of fiscal stimulus package to deal with the recent crisis.

Preisach-type models of hysteresis have been used as a vehicle to describe the macrodynamics of economic systems—see [2, 3, 18] for an early application to economic problems.

In fact, the market price can be influenced by the internal market dynamics as in [37], but this is not essential here.

The determinantes the unemployment rate are complex. Unemployment can be caused by: (1) the time people take to move between jobs (frictional unemployment); (2) a mismatch of skills in the labour market due to a lack of occupational and geographical mobility, and by technological change (structural unemployment); (3) a lack of aggregate demand (cyclical unemployment). Here we emphasise the third cause. We consider the firms as potential units of labour, with the set of all potential units of labour representing all the jobs that can potentially be created in the economy [28], and unemployment occurs when the economy is bellow full capacity. Moreover, cyclical unemployment may be transformed into structural unemployment by hysteresis mechanisms blurring the distinction between these two types of unemployment.

See [22, p. 15].

There is a certain lack of consensus in literature concerning the best way to construct a proxy for uncertainty. Nonetheless, typically uncertainty is captured by moving variances of the relevant variables like output, inflation, real wages, interest rates, exchanges rates, etc. (see [17], for a survey).

We apply the Trace Test performed with four lags in the VAR representation and with an intercept and time trend in the cointegration equation. We report the results of testing the null hypothesis of no cointegration (r = 0) against the existence of at least one cointegrated vector (r).

By applying Johansen cointegrating test to the three samples, we do not reject the hypothesis of a single cointegrating vector relating the variables. The trace test statistic, 52.405, 58.81, and 48.166 for the whole sample, for the subsample of small firms and for the subsample of large firms respectively, is greater than the 5 % critical value (42.91).

We also report the estimation results for the case of a constant splitting factor (play) in the employment equation.

As the estimated play width is greater for the sub sample of the small firms, the linear play algorithm originates a transformed series, which us smoother than in the case of the large firms.

\(F\left (\delta = 0\right ) = \frac{\left (R_{unrestricted}^{2}-R_{restricted}^{2}\right )/m} {\left (1-R_{unrestricted}^{2}\right )/\left (N-K\right )}.\)

We are relying on 2008 data from Statistics Portugal.