Asset pricing in created markets.

Our empirical assessment of the relationship between quota asset prices and expected future profits from fishing quota is based directly on the dynamic Gordon growth model (equation (3)). Within this framework, we explore possible explanations for the heterogeneity in quota asset prices across the different fishing quota markets, as illustrated in figure 1. Potential reasons for the heterogeneity include different growth rates of profits due to expected changes in revenues or costs, or because fish stocks are associated with different risk premia.

It is straightforward to allow for different asset prices, profits, and expected growth rates of profits across fish stocks, i. To investigate different risk premia, we follow the methods employed in Alston (1986) and Cochrane (1992) by decomposing the discount rate into a real market interest rate, [[??].sub.t], and an asset-specific risk premium, [[theta].sub.i]. Formally, this leads to

(4) [p.sub.i,t] = [[pi].sub.i,t]/[[??].sub.t] + [[theta].sub.i] - [g.sub.i].

In fishing quota markets, a major difference in risks stems from ecological volatility, whereby some fish stocks have more variable populations from one year to the next. Because search costs depend on the stock size and location, greater fluctuations in population abundance could lead to greater harvest and cost uncertainty.

In our setting, another important issue arises when considering the application of equation (4), which, for simplicity, assumes continuous growth into the indefinite future. In particular, fishing quota markets are created to address the "tragedy of the commons," and our analysis includes a period over which there was a market-based transition away from regulated open access conditions. Typically, when quota markets are created, fishing capital and labor inputs are distorted and fish populations are depleted due to years of operating under regulated open access conditions. An implication of this is that there will likely be a divergence between the current lease-asset ratio and the longer-term equilibrium, at least early on in the market, because at that time the contemporaneous lease price is not a good indicator of future profitability. This means that the asset price of a stock anticipating rationalization would initially be relatively high compared to its lease price. This divergence would decline over time as the stock achieved its anticipated profit increases and higher lease prices. Figure 1 suggests support for this hypothesis, as the difference between the 25th and 75th percentiles follows a downward trend.

Why might the divergence decrease over time? Initially, trades of the perpetual right to fish will occur as high-cost fishers find it more profitable to sell their quota rather than fish it. The gains from trade and elimination of excess fishing capital should result in cost savings. In addition, in many fisheries the cost function is likely to be stock-dependent, so that costs increase as the fish stock size falls and it becomes harder to find the fish (i.e., searching costs increase). As a result, if the TACs are set to allow stock recovery, then the gains due to stock rebuilding will also be incorporated in the expectation of future costs. The ability to time fishing trips to higher product prices rather than being forced to operate in short seasons, along with the shift from maximizing quantity to maximizing quality, will also feature in near-term expectations of future revenue growth. (7) These effects will likely dissipate over time as the potential gains are realized, where the rate of dissipation is an empirical question.

We modify equation (4) to account for these transitory effects by including a multiplicatively separable function, [psi](*), representing the transition associated with ITQs:

(5) [p.sub.i,t] = [[pi].sub.i,t]/[[??].sub.t] + [[theta].sub.i] - [g.sub.i] [psi](*).

We expect [psi](*) to be greater than one, because asset prices in ITQ markets will initially be above the levels predicted by the long-run relationships due to short-run expected profitability gains. Furthermore, we expect it to be larger for stocks with greater short-term gains, but to be decreasing over time, as asset prices should converge to the long-run relationship after some interval of time, holding everything else equal. The arguments of [psi](*) can include, for example, time since the market was created, and variables that represent gains from trade and fish stock recovery.

Empirical Specification and Data

After adding and subtracting 1 in the denominator of equation (5) (see footnote 12), we take a logarithmic approximation. We also approximate ln[psi](*) by [[beta].sub.5][s.sub.ijy] + [[beta].sub.6][a.sub.ij] +[[beta].sub.7][a.sub.ij[t.sub.y], where s is a measure of expected future cost declines due to reallocation of fishing effort through trading, a indicates the effect of expected future cost reductions on increases in fish stock abundance, and t is an annual time index. (8) Specifically, the relationship we bring to the quota asset price data is

(6) [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]

where p is the quarterly average quota asset price, [pi] is the contemporaneous quota lease price (as a measure of the annual profits from fishing), [??] is the real interest rate, ln[theta] is proxied by each species natural mortality rate (a measure of risk), and g is proxied by a measure of expected future growth in the output price of fish species i. (9) We also include a dummy variable (d) for shellfish stocks (i.e., abalone, rock lobster, and scallops), a set of quarterly fixed effects ([[alpha].sub.q]), a set of yearly fixed effects ([[alpha].sub.y]), a fish-stock-specific effect ([v.sub.ij]), whose specification varies depending on the estimation approach (e.g., fixed or random effects), and an independent and identically distributed error term ([epsilon]). Species are denoted by the subscript i and regions by j, so that each ij combination indexes a different fishing quota market. Time is indexed by quarter q of year y.

The model and accompanying discussion above imply the following hypotheses for the model: [[beta].sub.1] > 0, [[beta].sub.2] < 0, [[beta].sub.3] < 0, [[beta].sub.4] > 0, [[beta].sub.5] > 0, [[beta].sub.6 > 0, and [[beta].sub.7] < 0. Strict interpretation of the logarithmic approximation given by equation (6) further implies the following hypotheses about the specific magnitudes of certain coefficients: [[beta].sub.1] = 1, [[beta].sub.1] [approximately equal to] -(1 + r)/(r + [theta] - g), [[beta].sub.3] [approximately equal to] -[theta]/(r + [theta] - g), and [[beta].sub.4] [approximately equal to] (1 + g)/(r + [theta] -g), where each of the variables in these formulae is taken to be its mean value (the point of approximation). We do not impose these as restrictions, but rather consider them when interpreting the findings below.

We estimate equation (6) using the comprehensive panel dataset described in detail in NSK, which was constructed using information from New Zealand government agencies and other sources. We include 152 fish stocks representing 32 different species that had entered the New Zealand ITQ system by 1998. The data cover 14 years from the 1987-1988 fishing year until the end of the 2000-2001 fishing year. All monetary figures were adjusted for inflation to year 2000 New Zealand dollars, using the producer price index (PPI) from Statistics New Zealand. Table 2 gives descriptive statistics for the 4,120 observations that comprise the estimation sample; the included variables exhibit a large degree of variation.

As described above, the quota asset and lease prices are quarterly averages for each species-region specific fish stock quota market, based on more than 140,000 underlying lease transactions and more than 23,000 asset transactions. (10) The real market interest rate, [??], is the 90-day New Zealand Treasury bill rate, adjusted for inflation using the New Zealand CPI. As a measure of variation in the risk premium across species, ln[theta], we use each species' natural mortality rate. Species with higher mortality rates have population sizes that are typically more variable due to fewer age classes, which we argue leads to increasingly greater uncertainty in the amount of fish likely to be caught with a given level of effort. As a consequence, there is greater uncertainty in the profits from fishing high-mortality species, and we would therefore expect higher mortality rates to have a negative effect on quota asset prices. (11) We base g on the historic growth rate in output prices, where output prices are based on the export price per greenweight ton using data from Statistics New Zealand over the period 1986-2001, deflated using the NZ PPI (see NSK). (12)

Empirically, the components of the approximation to the [psi](*) function are as follows. To represent expected future profit increases due to reallocation of fishing effort through trading, s, we use the annual percentage of quota assets sold for each fish stock, normalized by dividing by each stock's average percentage sold. The hypothesis is that reallocation of quota assets is an indication of expected future profits from that trade, most likely through cost reductions.