Policy Change Anticipation in the Buyback Context

Abstract

To what degree might an anticipated policy change delay the fleet restructuring process initiated by a vessel buyback? This paper addresses the issue by estimating a restricted profit function to analyze an overcapitalized fishing fleet subject to restrictive regulation on the harvest of its primary target species. Fishermen’s expectations and likely responses to the future regulations regarding individual quotas are modeled in the context of a time-limited buyback program. The Polish trawler fleet targeting primarily cod provides an application. Analyzing potential individual quota tradability, we find that considerable shifts in disinvestment are to be found due to anticipated policy change. The mechanisms driving discrepancies include capitalized value of quota, as well as the tradability option capitalized into other inputs with inelastic supply.

Appendices

Appendix A Separability

Homothetic separability between all inputs and all outputs in the short run, conditional upon fixed netputs, implies a transformation of the form:

$$\begin{aligned} f(\mathbf {X_{out};Z_{out}})-g(\mathbf {X_{in};Z_{in}})=0, \end{aligned}$$

(A.1)

where $f(\cdot )$ and $g(\cdot )$ are linearly homogeneous aggregator functions that provide a consistent composite output and input indices respectively. Input–output separability implies no specific interactions between outputs, whether quota-regulated or variable, and inputs, whether variable or quasi-fixed, implying that it is possible to specify one composite output and one composite input. This is of particular interest in the case of fisheries, where it is common to aggregate harvest to a composite output or use total effort as a composite input. Homothetic input–output separability implies that the composition of variable and quota-regulated outputs within a restricted profit function framework is independent of input prices and fixed inputs, and the relationship between the quota-regulated and unregulated species depends upon the functional form of the linearly homogeneous aggregator function for the composite output. This condition can be written as: (1) $\partial \left( \frac{\partial \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/ \partial p_i}{\partial \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/ \partial p_{i'}}\right) /\partial p_{i''}=0$; $i\ne i'$ for every $i,i'\in I_{out}$ and $i''\in I_{in}$, (2) $\partial \left( \frac{\varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/ \partial p_i}{z_j} \right) /\partial p_{i'}=0$ for every $i\in I_{out},j\in J_{out}$ and $i'\in I_{in}$, (3) $\partial \left( \frac{\partial \varPi ({\mathbf {P}}, {\mathbf {W}}; {\mathbf {Z}})/ \partial p_i}{\partial \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/\partial p_{i'}}\right) /\partial z_j=0; i\ne i'$ for every $i,i'\in I_{out}$ and $j\in J_{in}$ and (4) $\partial \left( \frac{\partial \varPi ({\mathbf {P}}, {\mathbf {W}}; {\mathbf {Z}})/\partial p_i}{z_j}\right) / \partial z_{j'}=0$; for every $i\in I_{out}, j\in J_{out}$ and $j'\in J_{in}$.

Appendix B Non-jointness

Input or output non-jointness implies that there are no benefits from combining the production of outputs or using combinations of inputs; the costs of producing outputs or using inputs individually are the same. In this case, the production process can be decomposed into a series of independent processes and the multiproduct or multiinput technology can be expressed as a sum of individual restricted profit functions. In the case of fisheries, a single output profit function implies a separate harvest of each species and there are no economies or diseconomies of scope, whereas a single-input profit function implies the sequential use of different inputs.

The extension of non-jointness of particular interest in this context is almost non-jointness (Livernois and Ryan 1989), in which the production process can be separated into individual processes that depend on the same vector of shared inputs (called public). In this context, elements of ${\mathbf {Z}}$ may be a factor of production that is endogenously selected by the firm in the long run (e.g., the vessel and its equipment in the case of fisheries), a factor of production that is supplied by the government with the properties of a public good or it may incorporate externalities such as crowding in fisheries. In this context, fixed inputs ($\mathbf {Z_{in}}$) are taken as elements of the shared inputs vector and the non-joint in inputs total profit function can be written as:

$$\begin{aligned} \begin{aligned} \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})&= {} \sum _{i\in I_{out}}\pi ^{r(i)}(p_i,\mathbf {P_{in}};\mathbf {Z_{in}})\\&\quad + \sum _{j\in J_{out}}\left( w_j z_j+\pi ^{r(j)}(\mathbf {P_{in}};z_j,\mathbf {Z_{in}})\right) +\sum _{j\in J_{in}}w_j z_j. \end{aligned} \end{aligned}$$

(B.1)

Here $\pi ^{r(i)}(p_i,\mathbf {P_{in}};\mathbf {Z_{in}}),i\in I_{out}$, is a single-output restricted profit function, $w_j z_j+ \pi ^{r(j)}(\mathbf {P_{in}};z_j,\mathbf {Z_{in}})$, $j\in J_{out}$, is a restricted profit from harvesting restricted output that consist of revenue and restricted profit function indicating the cost of quota harvest. The last expression ($\sum _{j\in J_{in}}w_j z_j$) is the cost of fixed inputs added for completeness. $\mathbf {P_{in}}$ indicates the vector of variable input prices and $\mathbf {P_{out}}$ the vector of unrestricted output prices. The requirement for non-jointness in inputs is: $\partial ^2\varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/\partial p_i p_{i'}=0$; $i\ne i'$ for all $i,i'\in I_{out}$ and $\partial ^2 \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})/\partial p_i z_j=0$ for all $i\in I_{out}$ and $j\in J_{out}$. Accepting non-jointness in inputs implies that harvest activities associated with any species, both unrestricted and restricted, are independent with the exception of sharing the fixed inputs. The total non-joint in outputs profit function is specified as:

$$\begin{aligned} \varPi ({\mathbf {P}},{\mathbf {W}};{\mathbf {Z}})=\sum _{i\in I_{in}}\pi ^{r(i)}(p_i,\mathbf {P_{out}};{\mathbf {Z}})+\sum _{j\in J}w_j z_j. \end{aligned}$$

(B.2)

Here $\pi ^{r(i)}(p_i,{{\mathbf {P}}_{out}};{\mathbf {Z}}),i\in I_{in}$, is a single-input restricted profit function. The requirement for non-jointness in outputs is: $\partial ^2\varPi ({\mathbf {P}}, {\mathbf {W}}; {\mathbf {Z}})/ \partial p_i p_{i'} = 0$; $i\ne i'$ for all $i,i'\in I_{in}$. In the case of non-jointness in outputs, there are multiple production functions for each type of variable input, for which the optimal choice depends on fixed factors.

Appendix C Estimation Procedure Details

The model is estimated using a modified micEconSNQP package for R software (Henningsen 2014). The modifications include adding third order terms for non-linear marginal relationships and rewriting the function for the variance-covariance matrix using the wild bootstrap method. The initial run violates the convexity in prices requirement, but convexity can still be imposed, and the model continues to identify elasticities between pairs of netputs. Koebel et al. (2003) describe the procedure. The procedure implies a correction of unrestricted parameters according to: $\widehat{\alpha ^*}=\hat{\alpha }+\widehat{\varOmega _\alpha }\frac{\partial g'(\hat{\alpha })}{\partial \alpha } \left( \frac{\partial g(\hat{\alpha })}{\partial \alpha '}\widehat{\varOmega _\alpha } \frac{\partial g'(\hat{\alpha })}{\partial \alpha }\right) ^{-1} \left( \eta _H^*-\partial g(\hat{\alpha })\right)$, where $\hat{\alpha ^*}$ is corrected for the convexity coefficient, $\hat{\alpha }$ is the original regression coefficient, $\widehat{\varOmega _\alpha }$ is the original regression variance-covariance matrix, $g(\widehat{\alpha })$ is vector of linear independent values of the Hessian matrix for average prices and quantities of fixed factors, and $\eta _H^*-\partial g(\hat{\alpha })$ is difference between the parameters for the convexity restricted and unrestricted Hessians. Because the SNQPF Hessian not only depends on coefficients but also on prices and netput levels, convexity is imposed locally at arithmetic average values or regressors. This procedure is necessary to keep a correct structure for all supply and demand equations, and allow the quota market simulation. Potential reasons include insufficient price variation, multicollinearity and the aggregation method (Squires 1987). In our case, we find aggregation of other species.

Due to optimization involved in the estimation process, the traditional methods for calculating standard errors are not applicable. Instead, the confidence intervals based on empirical distribution are derived applying bootstrap. First, all units are resampled to obtain an intermediate data sample to account for individual unobservable heterogeneity of the unit (Freedman 1981). Then, in order to assure a heteroscedasticity consistent covariance matrix, wild bootstrap (Wu 1986) is applied. The idea of the wild bootstrap is to use the actual residual for each observation, transform it, and multiply it by an IID drawing from a distribution with expectation 0 and variance 1 (Davidson 2007). Here, we use wild efficient residual bootstrap proposed by Davidson and MacKinnon (2007). The transformed residual is derived as: $u_i^*=\sqrt{(N/(N-K)}u_i v_i$, where $u_i$ is original residual, N is number of observations, K is number of coefficients, and $v_i$ is a random variable from Rademacher distribution, according to which: $v_i= \left\{ {\begin{array}{cc} 1\ \textit{with}\ \textit{probability}\ 0.5\\ -1\ \textit{with}\ \textit{probability}\ 0.5 \\ \end{array}}\right.$. The data generation process takes the form: $x_{in}^*=\widehat{x_{i,n}}+u_{in}^*$, where $\widehat{x_{i,n}}$ is the predicted value for netput i from the original input demand or output supply equation, and $u_{in}^*$ is the residual bootstrap. In case of simultaneous equations model, all residuals for a given observation are multiplied by the same value of $v_i$ to preserve the correlation between disturbances (Davidson and MacKinnon 2007). The p values calculated for a one-tailed test indicating probability of rejecting the value of opposite sign or zero follow: p value=$\left\{ {\begin{array}{cc} \frac{1}{R}\sum _{r=1}^R I(\alpha _r\le 0) \ \textit{for}\ \hat{\alpha }>0 \\ \frac{1}{R}\sum _{r=1}^R I(\alpha _r\ge 0)\ for \ \hat{\alpha }>0\end{array}}\right.$, where r is bootstrap sample, R is sum of bootstrap samples calculated, here 999, $\alpha _r$ is coefficient value for r-th bootstrap sample estimated with the same methods as the original model and $\hat{\alpha }$ is the original estimate. Consequently, the p values are based on the empirical distribution and there is no need to make any assumption about the population’s distribution.