Asset pricing in created markets.

Improvements in profits through cost reductions can also occur as a result of improvements in fish stock abundance, and associated increases in the catch-per-unit-effort. We represent this feature using a dummy variable, a, that indicates whether each stock faced significant reductions upon implementation of the ITQ program. (13) We expect that fisheries plagued by excess capacity and overfishing prior to the implementation of the ITQ system that also faced significant reductions in allowable catch at the outset of the ITQ program would experience greater increases in profitability through stock rebuilding and cost rationalization than fish stocks without a high degree of overfishing, everything else being equal. Thus, we would expect the coefficient on a to be positive, indicating that for a given lease price, the asset price will be higher for stocks with fish stock rebuilding plans in place.

Over time, however, the gains from such improvements should be realized, implying that future gains will be lower. We capture this effect by interacting a with a time trend, hypothesizing that over time the lease price will rise as stocks improve, and the effect on the asset price of additional future gains will diminish. Under these conditions, we would expect the coefficient on the interaction of a and t to be negative.

Estimation Approach

Time-Series Properties of Data

Before considering estimation of equation (6), it is essential to determine the time series properties of the asset and lease price series. If either one or both of the series are nonstationary, then standard regression techniques will be susceptible to the problem of spurious regression.

While testing for unit roots in panels is a relatively new enterprise, there are several tests available to researchers (see Banjeree [1999] for more information on the tests). We employ three tests, all of which can be thought of as panel data extensions or pooled versions of the Dickey-Fuller test (or Augmented Dickey-Fuller test when lags are included). Full details are given in the supplemental appendix (Newell, Papps, and Sanchirico 2007). In all three cases, we reject the hypothesis of a unit root in both the asset and lease price series at the 1% level. The same result holds when the tests are repeated using species-level (rather than stock-level) data. The agreement in the time series properties of the asset and lease prices satisfies, at least at the panel level, a necessary condition of the present-value model (Falk 1991). (14)

We also test for the possibility of nonstationarity in the quarterly New Zealand real interest rate for thirty-day Treasury bills and the quarterly species-level export price, which is used as an instrument in the econometric analysis for contemporary lease prices. In both cases, we reject the null hypothesis of a unit root. Therefore, the time series variables in the regressions to follow are all stationary, allowing us to draw inferences from the use of standard panel data techniques with variables in levels.

Panel Estimation Techniques

Because lease prices and asset prices are determined simultaneously in the ITQ market each period, it is likely that estimation of equation (6) suffers from simultaneity bias. Statistical tests for endogeneity of the lease price verify this concern. (15) We therefore use instrumental variables estimation throughout, instrumenting for the log lease price using the logged contemporaneous export price of fish and all other regressors, including stock fixed effects. The price of fish is an excellent instrument as it is a significant determinant of profits from fishing, it is highly correlated with quota lease prices ([rho] = 0.77), and it is clearly exogenous. (16) Our estimation approach follows Balestra and Varadharajan-Krishnakumar (1987), employing a two-stage least squares generalization of the standard panel data estimators to correct for endogeneity. See Baltagi (2001) for an introduction to panel data models with endogenous explanatory variables.

Our first specification models the data for all stocks in a pooled fashion. This approach is appropriate if there are no unobserved stock-specific effects. In contrast, our second specification performs the within estimator, which is equivalent to a regression with a full set of stock-specific fixed effects. While the within estimator is consistent, it is not as efficient as other estimators (e.g., random effects) if the unobserved stock-specific effect is uncorrelated with the observed regressors. In addition, with the fixed effects approach it is not possible to recover coefficients on any of the time-invariant regressors, namely the export price growth rate, mortality rate, and recovering stock dummy.

Our third specification performs the between estimator, which is a regression of stock-specific averages over time. As such, this specification cannot identify coefficients on stock-invariant regressors, such as the interest rate. Finally, our fourth specification treats the stock-specific term, [v.sub.ij] as a random effect. This model is more efficient than within estimation when none of the regressors is correlated with the stock-specific effect, however, it is inconsistent when the opposite is true. This assumption of no correlation is typically assessed using a Hausman test. The random effects estimator has the advantage of controlling for stock-specific effects while at the same time allowing for estimation of time-invariant explanatory variables, which are of central interest to this article. Beyond the fixed or random effect, we assume that the remaining error is homoskedastic. This is supported by panel tests of both heteroskedasticity (Pagan and Hall 1983) and autocorrelation (Wooldridge 2002), neither of which rejected a homoskedastic error structure.

Estimation Results

In table 3, we report the results of estimating equation (6) using the fishing quota asset and lease price data described above. Due to some observations having missing values for one or more of the variables, 4,120 observations were available for the four models that are reported. All the four specifications show a high degree of explanatory power, with [R.sup.2] values of 0.77 or above. Overall, the results are consistent with economic predictions about the parameters. The estimated coefficients generally have the expected signs and reasonable magnitudes and are stable across the different specifications.

Regarding the appropriateness of the different specifications, we find that a joint F-test of the fixed effects is highly significant, thereby opening up the standard errors and consistency of the pooled model to misspecification. On the other hand, a Hausman test comparing the fixed effects and random effects estimators clearly indicates that the random effects model is appropriate (i.e., the assumption of no correlation between the regressors and the random effect is not rejected). Hence, the random effects estimates are consistent and more efficient than the fixed effects (or between) estimates. Indeed, the stability of the coefficients across these specifications illustrates the consistency of the parameter estimates in the random effects model.

The four specifications reported in table 3 feature an estimated coefficient on log lease price of between 0.76 and 0.86. We find that the random-effects estimate for the lease price coefficient lies between the within estimate (model ii) and the between estimate (model iii), as one would expect given that the random effects estimator is an efficient weighted average of the within and between estimators (when its assumptions are upheld). These results suggest that changes in lease prices are reflected very closely in changes in the contemporaneous quota asset prices. However, the point estimates are somewhat lower than the expected coefficient of 1 based on the simple present-value model given above, or based on the simple univariate relationship depicted in figure 2. (17)

It is not clear how much this lower-than-expected estimated coefficient casts doubt on the simple present value model represented by equation (6), although it suggests that it may not hold exactly. One possibility is an errors-in-variables problem, with the standard implication that the resulting coefficient is biased toward zero. Another possibility is that the various controls included in the model (e.g., year effects) are simply reducing the amount of variation in lease prices available for estimating that coefficient. This conjecture is supported by a simple random or fixed effects regression of log quota asset prices on (instrumented) log quota lease prices, with no other controls. In these simple models the coefficient on the log lease price is 0.98 in the case of the random effects model and 1.04 in the fixed effects model, with neither of these estimates being statistically different from 1.