Although recent experience with the sulfur dioxide trading program
in the United States has changed many perceptions, there are still
questions about how well tradable permit systems for environmental
pollution, greenhouse gases, agricultural production, and natural
resources can work in practice. Such skepticism is in part warranted by
the limited number of ex post assessments on the performance of created
markets. Because building the necessary institutions can require
significant political and economic costs, it is imperative to develop an
empirical record of the performance of created markets in practice.
One area where market-based systems are subject to a significant
degree of skepticism is in the management of ocean fisheries. One such
system is individual fishing quotas, in which the total catch is capped
and shares of the catch are allocated. An individual transferable quota
(ITQ) system results when transfer of the shares is permitted. Over
time, the least efficient fishermen should find it more profitable to
sell their quota rather than fish it, both reducing excess capacity and
increasing the efficiency of vessels operating in the fishery.
For ITQs to address the common pool problem in practice, it is
important that quota markets are competitive and convey appropriate
price signals. Price signals sent through the quota market are an
essential source of information on the expected profitability of fishing
and an important criterion for decisions to enter, exit, expand, or
contract individual fishing activity. Quota prices also send signals to
policymakers about the economic and biological health of a fishery.
Arnason (1990) showed that under the assumption of competitive markets,
monitoring the effect of changing the total allowable catch (TAC) on
quota prices could be used to determine the optimal TAC.
In a previous study, Newell, Sanchirico, and Kerr (2005) (hereafter
NSK) investigate the performance of ITQ markets using the most
comprehensive dataset gathered to date for the largest system of its
kind in the world. The panel dataset from New Zealand covers 15 years of
transactions across the 33 species that were in the program as of 1998
and includes price and quantity data on transactions in more than 150
fishing quota markets. Markets exist in New Zealand both for selling the
perpetual right to a share of a stock's TAC, as well as for leases
of that right to catch a given tonnage in a particular year. NSK found
that market activity appears sufficiently high to support a reasonably
competitive market for most of the major quota species and that price
dispersion has decreased over time. Investigating the asset and lease
markets separately, they find evidence of economically rational behavior
in each of the quota markets and their results show an increase in quota
asset prices, consistent with increased profitability.
We extend the analysis of NSK by econometrically examining the
relationship between the annual lease and sale prices in the perpetual
quota asset markets. A notable exception to the virtually nonexistent
literature examining quota prices in fisheries is the paper by Batstone
and Sharp (2003), which investigates the relationship between fishing
quota sale and lease prices and changes in the total allowable catch for
the New Zealand red snapper fishery (region 1). Batstone and Sharp
(2003) find support for the relationship proposed by Arnason (1990).
Other related research in fisheries includes Karpoff (1984a, 1984b,
1995) and Huppert, Ellis, and Noble (1996), who look at the relationship
between license prices and fishery rents in Alaska salmon fisheries.
With competitive markets, rational asset pricing theory suggests
that the price of an income-producing asset in period t, [p.sub.t],
should be determined by the real per-period profits from the asset,
[[pi].sub.t], and the real discount rate, [r.sub.t]:
(1) [p.sub.t] = [[infinity].summation over (j=0)]
[E.sub.t([[pi].sub.t] + j)]/ [[PI].sup.j.sub.k=0] (1 +
[E.sub.t]([r.sub.t] + k)])
where E(*) is the expectations operator. In our setting, equation
(1) states that the current quota asset price should be equal to the
present discounted value of all future expected earnings, where the
lease prices represent the annual flow of profits from holding quota.
The price of the quota asset, therefore, will vary across fish stocks
and over time based on changes in expected future lease prices or
changes in the expected discount rate over time.
Under the simplifying assumption that expected lease prices and
discount rates remain constant in the future, the price of the asset
would simply equal the lease price divided by the discount rate, or
[p.sub.t] = [[pi].sub.t]/[r.sub.t]. The expected rate of return from
holding fishing quota (or dividend-price ratio) would be equal to
[[pi].sub.t]/[p.sub.t]. Figure 1 supports the basic structure of such a
relationship in New Zealand fishing quota, with the dividend-price ratio
tracking both the level and the trend in New Zealand short-term interest
rates over the sample period. For example, at the same time the
dividend-price ratio fell by about half from 13% to 7%, the interest
rate as measured by New Zealand Treasury bills fell from 10% to about 4%
in real terms. Overall, the quota dividend-price ratio is about 2%-3%
higher than the risk-free rate on average. Figure 2 likewise suggests a
close, relatively linear association between asset and lease prices (in
logs). The level of the average asset price is also approximately 10
times the lease price over the sample period, roughly equal to the
present value of a perpetuity discounted at 10%.
[FIGURES 1-2 OMITTED]
Figure 1 also shows that there is considerable cross-sectional
variation in the dividend-price ratio across fish stocks markets, where
the upper and lower plus signs represent the 25th and 75th percentiles.
Why might such variation exist? One reason could be that if fishers are
risk averse they will prefer fish stocks with lower variance, other
things equal. This effect is consistent with a higher discount rate, or
higher required rate of return for riskier stocks. Such volatility could
be associated with natural variation in stock abundance and economic
variability in costs and fish prices. Another explanation could be
differences in the expected growth rate of profits over time (Melichar
1979), possibly due to differences in output price growth, changes in
fish populations, or other factors affecting costs such as cost
rationalization due to quota trading.
Using panel data econometric techniques on an updated NSK dataset,
we estimate models that relate the asset price of quota to their annual
lease (or rental) price and observed determinants of the growth rate and
volatility of rents. Within this framework, we explore the relationship
between asset and lease prices, as well as whether differences in asset
prices are due to differential risks associated with holding quota
across fish stocks and/or different expected growth rates in fishery
rents in those stocks. These data are uniquely qualified to address
these questions, because of the relatively long time series, breadth of
markets, and cross-sectional heterogeneity, as the market
characteristics are diverse across both economic and ecological
dimensions (see table 1 for a list of species included). For example, in
2000 the export value of these species ranges from about NZ$700 per ton
for jack mackerel to about NZ$40,000 per ton for rock lobster. (1)
Consistent with asset pricing theory, we find a statistically (and
economically) significant relationship between asset prices and
contemporaneous lease prices. Stocks with a higher degree of biological
volatility tend to have lower asset prices, and stocks that have rising
returns or falling costs from fishing are found to have higher asset
prices, ceteris paribus. Taken together, these results suggest that the
price signals generated by the ITQ system are a good indication of the
future profitability of individual fishing quota stocks. (2) The
magnitude of some interrelationships is muted relative to what the
theory suggests, possibly due to measurement error.
Our analysis also contributes to the extensive literature
investigating asset prices by utilizing micro-level trading data across
multiple (related) markets to measure the relationships embedded in
equation (1), and the relative importance of the different factors
behind the heterogeneity in figure 1. Nonfishery studies relevant to
ours that investigate agricultural land prices and farming rents (e.g.,
Melichar 1979; Alston 1986; Falk 1991; Clark, Fulton, and Scott 1993;
Just and Mirinowski 1993) or agricultural production quota (e.g.,
Barichello 1996; Wilson and Sumner 2004) typically focus on aggregate
data and/or concentrate on a single market. For example, Falk (1991)
models farmland prices in Iowa using aggregate price and rent data, and
Wilson and Summer (2004) analyze the market for diary quota in
California. The same holds for Batstone and Sharp (2003), who
investigate a single quota market. Clark, Fulton, and Scott (1993) argue
that a cross-sectional comparison of land markets can help illuminate
the factors important in understanding the empirical relationship in
equation (1).
In the next section, we provide a selected review of the literature
modeling asset prices and dividends. This is followed by a description
of the design of the ITQ system in New Zealand, paying particular
attention to market characteristics. We then develop an empirical model
that is appropriate to a multiple-asset setting like the New Zealand
fishing quota market. We discuss the empirical specification, data
sources, time-series properties of the data, estimation approach, and
results, before we conclude by summarizing our findings.
Modeling Asset Prices and Dividends
The literature exploring the relationship between asset prices,
dividends, and other relevant factors (e.g., firm size) is extensive. A
thorough literature review is therefore beyond the scope of this
article, and interested readers should consult Cochrane (2001) and
Campbell, Lo, and MacKinley (1997) or the review articles by LeRoy
(1989), Fama (1991, 1998), and Campbell (2000). (3)
Simplifying equation (1) under the assumption that the expected
discount rate follows a martingale process yields (4)
(2) [p.sub.t] = [[infinity].summation over s=0]
[E.sub.t]([[pi].sub.t+s])/ [(1 + [r.sub.t].sup.s+1].
Equation (2) illustrates how the asset price is dependent on the
expected future stream of earnings, so that information available at
time t along with type of expectation process is important in modeling
the relationship between asset prices and dividends. For example, if one
assumes that expected future earnings are constant, then
[E.sub.t]([[pi].sub.t+s]) = [E.sub.t]([pi]). Huppert, Ellis, and Noble
(1996) model and find support for an adaptive expectations process where
[E.sub.t]([pi]) = [beta][[pi].sub.t-1] + (1 - [beta]) [E.sub.t-1]([pi])
with [beta] [member of [0, 1], and Karpoff (1984b) models a myopic
process where [beta] = 1. Wilson and Sumner (2004) find support for a
second-order adaptive expectation process in California dairy quota
prices. Just and Miranowski (1993) test myopic, adaptive, and rational
expectation regimes and find that farmland price data support myopic
expectations. Falk (1991) finds a similar result. Orazem and Miranowski
(1986) provide an empirical strategy for testing competing hypotheses of
expectations regimes when direct measures of expectations are
unavailable. Applied to farm acreage allocation decisions as a function
of expected commodity prices, it yielded little evidence for favoring
any of the three regimes.
If future profits (lease prices) grow at a constant rate g, then
[[pi].sub.t] = (1 + g) [[pi].sub.t-1] + [[epsilon].sub.t], where
[[epsilon].sub.t] is a white noise error term. Taking expectations and
solving equation (2) forward in time with g < r, the asset price
follows
(3) [p.sub.t] = [[pi].sub.t]/[r.sub.t] - g.
Equation (3) is the dynamic "Gordon growth model"
(Campbell, Lo, and MacKinley 1997) that forms the basis of the majority
of studies on the relationship between asset prices and dividends.
Due to a divergence between simple present-value relationships and
empirical observations on agricultural land prices and rents during the
1970s and 1980s, a number of authors have extended this basic structure
to include other factors, such as taxes (e.g., Robison, Lins, and
VenKataraman 1985; Alston 1986), changes in risks (Barry 1980), and
credit market constraints (Shalit and Schmitz 1982). Instead of
investigating these many factors separately, Just and Miranowski (1993)
develop a detailed structural model of the determinants of asset prices,
which is a function of inflation, taxes, credit market imperfections,
transaction costs, and risk aversion.
Others have focused on estimating a reduced form that is consistent
with equation (2). For example, Burt (1986) argues that movements in
asset prices may occur because of continued adjustment to past changes
in returns, implying that the price does not adjust instantaneously to
changes in expected future returns. In addition, expectations of future
rents may be based on past, as well as current, values of [[pi].sub.t].
He approximated the effect of both sources of dynamic behavior by using
a multiplicative distributed lag specification for [[pi].sub.t], with a
restriction that the lag coefficients sum to unity.
Background on NZ ITQ System
We include a brief review of the New Zealand ITQ system with
special attention to the elements that are most relevant for our
analysis. For further history and institutional detail, see Batstone and
Sharp (1999), Yandle (2001), NSK, and the references cited therein.
The New Zealand government passed the Fisheries Amendment Act in
1986, creating a national ITQ system. The system initially covered
seventeen inshore species and nine offshore species, which together
expanded to a total of forty-five species by 2000. Under the system, the
New Zealand Exclusive Economic Zone (EEZ) is geographically delineated
into quota management regions for each species based on the location of
major fish populations. Rights for catching fish are defined in terms of
fish stocks that correspond to a specific species taken from a
particular quota management region. In 2000, the total number of
fishing-quota markets stood at 275, ranging from 1 for the species hoki
to 11 for abalone. As of the mid-1990s, the species managed under the
ITQ system accounted for more than 85% of the total commercial catch
taken from New Zealand's EEZ and from our calculations had an
estimated market capitalization of about NZ$3 billion.
The New Zealand Ministry of Fisheries sets a TAC for each fish
stock based on an intertemporal biological assessment (including the
prior year's catch level) and other relevant environmental, social,
and economic factors. The TACs are legislated to maintain the fish
population at a level (or move it to a level) that will support the
largest possible annual catch (i.e., maximum sustainable yield), after
an allowance for recreational and other noncommercial fishing. Not all
species have their TACs adjusted for noncommercial uses, especially
those in the offshore sector where there is little if any recreational
fishing (see table 1).5 Most TACs remain constant from year to year and
for many fish stocks (especially those of low value) there are no formal
stock assessments (Annala 1996). When a TAC needs to be adjusted there
is no automatic process, and the appropriate level of the adjustment is
discussed with the quota owners (Sanchirico et al. 2006).
Individual quota were initially allocated to fishermen free of
charge as fixed annual tonnages in perpetuity based on their average
catch level over two of the years spanning 1982-1984. Beginning with the
1990 fishing year, however, the government switched from quota rights
based on fixed tonnages to quota denominated as a share of the TAC.
Compliance and enforcement is undertaken through a detailed set of
reporting procedures that track the flow of fish from a vessel to a
licensed fish receiver (on land) to export records, along with an at-sea
surveillance program including onboard observers.
Given the uncertainty around the quantity and composition of catch,
a fisherman's quota holdings represent a mix of ex ante and ex post
leases, as well as asset purchases and sales to cover actual catch.
Although there are no official statistics, the general belief is that
brokers handle a majority of the transactions between small and
medium-sized quota (with a fee between 1% and 3% of the total value of
the trade paid by the seller) and larger companies typically have quota
managers on staff and engage in bilateral trades with other large
companies. Whether ex ante or ex post transactions, fishing quota are
generally tradable only within the same fish stock, and not across
regions or species or years, although there have been some minor
exceptions. (6) The quota rights can be broken up and sold in smaller
quantities and any amount may be leased or subleased any number of
times. Virtually all leases are for one year or less. There are also
legislative limits on aggregation for particular stocks and regions, and
limitations on foreign quota holdings.
NSK find that the quota markets are active, with about 140,000
leases and 23,000 quota asset sales occurring between economically
distinct private entities between 1986 and 2000--an annual average of
about 9,300 leases and 1,500 asset sales. Market participation has also
increased over time with around 70% of quota owners taking part in a
market transaction in 2000. Although some individual quota markets are
thin, these tend to be of low economic importance in the size and value
of the catch. The annual number of leases has risen ten-fold between
1986 and 2000, and the median percentage of total quota that are leased
in these markets has risen consistently, from 9% in 1987 to 44% in 2000.
At the same time, the total number of quota asset sales declined from a
high of about 3,200 sales in 1986 (when initial quota allocations for
most species took place), leveling off to around 1,000 sales in the late
1990s. The median shows a similar decline, with the percentage of total
outstanding quota sold per year being as high as 23% at the start of the
program, gradually decreasing in subsequent years to around 5% in the
late 1990s. This pattern of asset sales is consistent with a period of
rationalization and reallocation proximate to the initial allocation of
quota, with sales activity decreasing after the less profitable
producers have exited.
Empirical Analysis of Fishing Quota Asset Prices
Empirical Model
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.
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 n